ingeniería energ´etica, etsii (escuela t´ecnica superior de ingenieros

Transcription

INGENIERÍA ENERGÉTICA, ETSII (ESCUELA TÉCNICA
SUPERIOR DE INGENIEROS INDUSTRIALES)
HIGH POWER BEAM DUMP PROJECT FOR THE
ACCELERATOR PROTOTYPE LIPAc: COOLING DESIGN
AND ANALYSIS.
AUTOR:
MARCOS PARRO ALBÉNIZ, INGENIERO INDUSTRIAL.
DIRECTORES:
Dña. Beatriz Brañas Lasala, Doctora Ingeniera Industrial.
D. Alberto Abánades Velasco, Doctor Ingeniero Industrial.
Tribunal nombrado por el Magnı́fico y Excelentı́simo Sr. Rector de la Universidad Politécnica de
Madrid el dı́a
de
de 2015.
Presidente: D. José Marı́a Martı́nez-Val Peñalosa.
Vocal: D. Ángel Ibarra Sánchez.
Vocal: D. Javier Sanz Gozalo.
Vocal: D. Fernando Arranz Merino.
Secretario: D. Javier Muñoz Antón.
Realizado el acto de defensa y lectura de la Tesis el dı́a
de
de 2015, en la
E.T.S Ingenieros Industriales.
Calificación:
El presidente:
Vocal:
El secretario:
Vocal:
Vocal:
INGENIERÍA ENERGÉTICA, ETSII (ESCUELA TÉCNICA
SUPERIOR DE INGENIEROS INDUSTRIALES)
HIGH POWER BEAM DUMP PROJECT FOR THE
ACCELERATOR PROTOTYPE LIPAc: COOLING DESIGN
AND ANALYSIS.
AUTOR:
MARCOS PARRO ALBÉNIZ, INGENIERO INDUSTRIAL.
DIRECTORES:
Dña. Beatriz Brañas Lasala, Doctora Ingeniera Industrial.
D. Alberto Abánades Velasco, Doctor Ingeniero Industrial.
Este trabajo ha sido realizado en el Departamento de Fusión del Centro de Investigaciones
Medioambientales, Energéticas y Tecnológicas (CIEMAT), utilizando sus medios técnicos y con la
colaboración de su personal, y ha sido financiado por el MINECO a través de los proyectos
AIC-2010-A-000441 y AIC-A-2011-0654. En particular el circuito hidráulico y el prototipo del
bloque de parada utilizados en los experimentos que se presentan en esta tesis han sido
financiados por el Ministerio a través del Plan Nacional (proyecto ACIONAI ENE2009-11230) y por
CDTI (proyecto Industria de la Ciencia IDC-20101023)
El pueblo ya no sabe nada de todo esto.
La mayorı́a se ha quedado sin apoyo ni guı́a.
No creen en ningún Dios o Dioses,
conoce la Iglesia sólo como partido polı́tico
y la moral como una molesta limitación.
Erwin Schrödinger.
This thesis is dedicated to the loving memory of Panos Karditsas and his family.
Tina thank you very much for your support even in the tough times.
Agradecimientos
Parece ser todo llega a su fin y en este caso el fin empieza por los agradecimientos que no dejan de ser las primeras páginas que se leen. Cuantas vueltas le habré dado a esta parte para acabar
llegando a la conclusión de que no la querı́a escribir, siempre habı́a alguna buena excusa para no
empezar. Y ası́ hasta acabar descubriendo que ha sido de las partes más complicadas de escribir,
puede sonar a risa pero me ha parecido más fácil escribir cualquier otra parte del texto de este documento que estas lı́neas que ahora mismo escribo.
El porqué creo que es sencillo, cómo agradecer seis años en unas lı́neas. Con sólo pensar en la
cantidad de gente con la que has interactuado en este perı́odo parece imposible. Y luego está el
clásico de le estoy agradeciendo a cada una de esas personas en su justa medida. Probablemente
no, y seguro que no se puede ser totalmente justo y al final habrá mucha gente a la que no le puedes
dar las gracias tal y como se lo merece, de antemano un lo siento, mi memoria es limitada y cada dı́a
más.
Y por donde empezar, pues por la primera persona que se preocupo de ubicarme en ese sitio
tan grande que parecı́a el Ciemat de primeras, mi compi de despacho Beatriz. Me acuerdo perfectamente de lo despistado que yo estaba y de ese primer café en la cafeterı́a temporal del Ciemat.
Cuando me vio aparecer debió decir ”que me ponen a un hippie en el despacho!!!”. Pero si hay una
cosa que me gusta de ella, y que para mı́ es lo que más le caracteriza es que le da igual como puedas
ser por fuera, es capaz de ver más allá y respetar las diferencias como muy poca gente hace. Solo
puedo agradecerte, jamás has tenido una mala palabra hacia mı́, todo lo contrario me has defendido
y has dado la cara por mı́ ante cualquiera, mil gracias.
Por cercanı́a tengo que seguir con la cara que más he visto en estos años, mi otro compañero
de despacho, Juan. Básicamente le he visto más la cara porque no habı́a más remedio al tenerle
enfrente jajajaj. Buuuuufff tantas cosas hemos pasado, vivir juntos, compartir frustraciones juntos,
salir hasta morir también juntos, y por supuesto, y fundamentalmente por lo que creo que somos
y seremos amigos para siempre, el enfadarnos como pocas veces el uno con el otro, pero también
juntos. Quiero que sepas que compartir este tiempo contigo ha sido un auténtico honor y un placer.
I
Siguiendo me toca hablar del 20, ni soy fı́sico, ni he participado en los proyectos en los que estaba
la gente del 20, pero siempre he tenido una puerta abierta de todos y cada uno de los despachos.
Álvaro (preocupándose y hasta enfadándose a veces por mi situación en el Ciemat), José, Andrés,
José Manuel, Guille, Fernando, Yupi, Emilio, Fran, Fontdecaba, Pedro y Daniel. Pero especialmente
le tengo que agradecer a Alfonso Ros. El experimento del PHETEN sin su apoyo, colaboración y esfuerzo a lo largo de tardes y tardes no habrı́a llegado a buen puerto y por lo tanto tampoco la Tesis.
Siempre dispuesto a ayudar dejando de hacer sus cosas para estar contigo, dispuesto a enseñarte y
si hace falta aprender dispuesto a que un becario le enseñe. Me quito el sombrero Señor Ros, mil
gracias de corazón.
Y llegamos a mis compañeros de proyectos o por lo menos de división. Sois muchos y hemos
compartido mucho, cumpleaños, quedadas en el doce, desayunos, conferencias perdiendo pósters
por Lieja jajajaj , quedadas por fuera del Ciemat, en fin sin vosotros habrı́a sido todo mucho más
aburrido. Vamos a empezar por la Sinagoga, con Elena, Gerardo, Pablete, Dani ”El coletas”, Jesús y
por supuesto Iván que anda que no ha tenido que aguantarme el pobre, muchas gracias. Y siguiendo
por ese pasillo de cuerdos locos, tenemos a su capitán general Regidor, Kikı́n y nuestros paseos en
bici y encargado principal de conseguir mis bici regalos de cumpleaños, Esther, José Manuel (sı́ beibi
aquı́ estás jejeje), Santi, David Jiménez, Lalia, Cristina, y aunque no estén en ese pasillo no podı́an
faltar Conchi, Iván Podadera, Julio y Marcelo. Espero no olvidarme de nadie.
Mención aparte merecen Iole, Luis Rı́os y Natalia. Mi pequeña italiana feliz anda que no nos han
pasado cosas, muchas gracias por haber estado ahı́ especialmente para todo lo que no tiene que ver
con el Ciemat, sigue ası́. Luis es un placer hablar contigo, no sé porqué pero me transmites paz y
tranquilidad y por supuesto siempre que te he ido a contar mis rollos me has escuchado y aconsejado, mil gracias. Natalia, que te voy a decir, para empezar mi mentora con el CFX que anda que
no ha sido pesadito el niño preguntando, y mira todo un capı́tulo gracias a ti. Y por supuesto antes
que mi compañera de trabajo has sido mi amiga, una gran amiga, un poco loca pero supongo que
acorde a lo que tenı́as delante. Un lujo haberte conocido.
Mis ”locas” favoritas Elisabetta y Begoña, mira que tenı́a que acabar yo antes y al final me habéis
pasado las dos, me alegro mucho, os lo merecéis. Otra persona que ha empleado gran parte de su
tiempo en echarme un cable y sin la cual tampoco estarı́ais leyendo esto, ha sido Juanma . Cada dı́a
le iba con una idea nueva y él siempre dispuesto a sacar un hueco para hacer lo que fuese. Cuando
las cosas iban mal con el experimento casi tenı́a él más fe que yo en que lo solucionarı́amos. Muchas,
muchas gracias por creer en que esto iba a salir y ayudarme en todo, has sido muy importante.
Cristiiiii pensabas que no me iba a acordar de ti, la chica más feliz que me he encontrado y aun
con esas debo ser de los pocos que con mi habilidad habitual te ha conseguido enfadar jejejje. Sin
esas meriendas del 12 cuando el Ciemat ya estaba vacı́o me habrı́a vuelto loco, mil gracias.
Daniel, mi colega metálico, que voy a decir de ti, te has pasado todo el doctorado a mi lado y mira
que últimamente te has ido lejos. Parte de esto es tuyo, eres la persona con la que he trabajado que
II
más pasión le pone y que no para de maravillarme cada dı́a, da igual lo que te pongan delante que
vas a acabar siendo el mejor en eso. Y lo más importante eres un amigo con mayúsculas, y aunque
me vayas a vacilar por esto prefiero dos palabras a seguir escribiendo, te quiero.
Y ya saliendo del Ciemat, como no acordarme de ciertos personajes que tengo por amigos, unos
de un colectivo que espero siga siempre vivo aunque estemos en distintas puntas del mundo. Monteserı́n, Pablo Lorenzo ”El Taper” lo siento pero lo tenı́a que decir, Alvarito y ”El Paez”, han sido unos
años increı́bles chicos, vuestra amistad ha sido lo mejor en este tiempo, sois algo más que amigos.
Mención especial a Israel que se ha marcado una pedazo de portada alternativa, es un placer tener
un Páez en este ”mi libro” como siempre me dices. Juntos desde pequeños y la historia continua.
Y como no mis navarros universales, Oihan y David, mejor no escribo vuestros motes jejeje.
Sois las mejores personas que he conocido, tenéis un corazón enorme. Ese par de añitos que nos
pasamos compartiendo piso y vida fueron de 10, no podrı́a imaginarme mejores compañeros de
piso y amigos. Y ahora a pesar de la distancia seguı́s siempre presentes Maaaaks.
Al Gabi y sus cañitas de Lunes, Nico, Perry, Karles y al Albert que llevan ahı́ desde la Escuela y
no parece que se hayan cansado de mi, sois muy grandes. Albert tú sı́ que has tenido que soportar
un mesecito y medio de Tesis, muchas gracias por acogerme y sacarme a echar unas canastas en
Reading. Por cierto Cris si tenemos al Albert por aquı́ dando vueltas tú no puedes ser menos.
Toda la gente del Erasmus, Daniela, Diego, Javi, Jorge, Andrea, Dariole, Sarinha, Claudio, muchos
ya doctores, llego el último chicos. Y como no, a un hermano italiano que tengo perdido en Francia,
que pase el tiempo que pase siempre va a estar ahı́ como si nos acabásemos de ver el dı́a anterior,
gracias Gelati.
Vitı́n te dejo de los últimos porque eres de los más grandes. Otro que no me libro de él ni
mandándole a China, llamándome desde la otra punta del mundo para ver como estaba, como
sueles decir tú no tengo palabras ”niño”. Desde aquellas mañanas en la ruta del colegio has estado
ahı́ para todo, eres un fiera y te quiero Vait.
Más gente, Blanca, Angeliko, mi camaraden Carla, Javi y nuestros vicios a la play, mi nuevo compi
de piso el Luis, Pirata, Carmen y sus regalos mágicos, Óscar, César, Ana, todo mi equipo de basket, y
aun me olvidaré a alguno.
Y un par de amigos del barrio, Chemi cuantas mañanas con un bombón y unas risas, no te preocupes que ya me toca empezar a producir como me dices siempre. Y como no a Estanis, que está
ahı́ para lo que haga falta, ya sea liarle para desmontar mi bici entera o para hablar de cualquier
frikada, la vida por el barrio sin ti serı́a mucho más aburrida, gracias.
Por supuesto el apoyo más grande ha venido de mi familia, la Tesis se lo dedico a alguien que
fue muy importante para mi en este proceso, Panos Karditsas, pero si hay alguien que también se
III
merece eso es mi abuela, que más que una abuela ha sido una madre. Aunque no entienda muy
bien lo que significa una Tesis a pesar de las mil millones de veces que se lo habré explicado, va
por ella. Soy lo que soy porque la tuve a ella siempre detrás apoyándome en todas mis locuras, que
no han sido pocas, te quiero Yaya. Y por supuesto mi padre, tan importante como mi abuela pero
que me da más caña en todo, quizás por eso siempre quiero llegar a más y llegar siempre por mi
cuenta. Desde pequeño exigiéndome, desde pequeño peleándonos, pero supongo que ası́ somos, si
no fuese ası́ hasta se me harı́a raro Pater. Muchas gracias, esto también es tuyo. Esther a ti también
muchas gracias por soportarnos a los dos y por tratarme como a un hijo más.
Mis tı́os y primos de un lado y otro, sois muchos para poneros a todos pero muchas gracias por
preocuparos por mi y animarme sobre todo estos dos últimos años.
A David Rapisarda, que ha sido una especie de director en la sombra, tengo que agradecerle por
haber estado ahı́ cuando las cosas se torcieron a mitad de doctorado. He aprendido mucho tratando
contigo aunque a veces haya parecido lo contrario David, ya me conoces que soy complicado, pero
muchas gracias de verdad. A Fernando Arranz y Pedro Olmos por haber sacado tiempo de debajo
de las piedras para hacer el experimento.
Por supuesto agradecerle a Beatriz por haberme guiado en todo este proceso. Como con todo
director de Tesis hemos tenido nuestros más y nuestros menos, somos muy diferentes, pero ha sido
un gran apoyo en todo este camino, muchas gracias. A Alberto, mi otro director, por haberme facilitado siempre las cosas y haber estado pendiente de mi.
Y como no también una pequeña corrección sobre los agradecimientos iniciales, aquı́ hay que
corregir todo. Me habı́a olvidado por diferentes motivos de un par muy importantes, de Tara y de
Alba. Tanto pensar en personas que han estado conmigo en todo este camino y me olvidó de quien
ha estado en todo momento, quizás porque no le queda más remedio ya que es un perro, pero no
me podı́a olvidar de mi pequeña la Tara, la que más sonrisas me ha sacado en todo este tiempo. Yo
pensando que era yo quien le sacaba a pasear y muchos dı́as era ella quien me sacaba a mi mientras
yo le daba vueltas a alguna ecuación o parte del código. Y de ti Alba no me habı́a olvidado pero
cuando escribı́ esto quizás no era el momento de decir nada. Has sido mi apoyo y mi compañera en
todo este tiempo, la persona más importante y la que ha estado conmigo en lo bueno que es lo fácil
y en lo malo, que lo malo ha sido muy malo a veces. Gran parte de esto es tuyo, muchas gracias.
IV
List of symbols
Variable
Description
Units
q”
Heat flux
q
Heat
qv
Volumetric heat
[W/m3 ]
q”corr
Corrected heat flux
[W/m2 ]
h
Heat transfer coefficient
[W/m2o C]
hret
Water return heat transfer coefficient
[W/m2o C]
k
Conductivity
[W/m2 ]
[W]
[W/mo C]
n
Perdincular coordinate to the surface
Ts
Wall temperature
[o C, K]
[m]
Tb
Bulk temperature
[o C, K]
Tsb
Inner cone temperature surface-bulk side
[o C, K]
Tret
Water return temperature
[o C, K]
Tsh
Shroud temperature
[o C, K]
l
Characteristic length
[m]
v
Fluid velocity
Nu
Nusselt number
[m/s]
Dimensionless
Re
Reynolds number
Dimensionless
Reε
Roughness Reynolds number
Dimensionless
Do
Outer annular diameter
[m]
Di
Inner annular diameter
[m]
A
Inner cone heat exchange area
[m2 ]
Aret
Shroud heat exchange area
[m2 ]
P
Wetted perimeter
[m]
e
Cooling channel width
[m]
Pr
Prandtl number
µ
dynamic viscosity
[kg/m s]
µs
dynamic viscosity on the surface
[kg/m s]
cp
Constant pressure specific heat
[J/kg K]
ρ
Density
[kg/m3 ]
Dimensionless
V
Variable
Description
Units
hf riction
Friction head loss
[m]
hlinear
Linear head loss
[m]
hlocal
Local head loss
[m]
f
Friction factor
ε
Surface roughness
Dimensionless
[m]
a, b, d, s, r
Auxiliary variables
Dimensionless
g, p, DLA , DCF A
Auxiliary variables
Dimensionless
Rint
Inner cone radius
dA
Differential area
[m2 ]
dT
Differential temperature
[o C]
ṁ
Mass flow
R
Radial distance
[m]
[kg/s]
[m]
P
Fluid pressure
Γ
Stress tensor
[Pa/m]
t
time variable
[s]
v
Velocity vector
fv
Volumetric body force
u
Field variable in Navier-Stokes equation
Dimensionless
Fluctuation over field variable in N-S equation
Dimensionless
Fluctuation mean value over field variable in N-
Dimensionless
0
u
0
u
[Pa, bar]
[m/s]
[N/m3 ]
S equation
u0 2
Fluctuation mean square value over field vari-
Dimensionless
able in N-S equation
[m/s2 ]
g
Gravity acceleration
Dh
Equivalent hidraulic diameter
[m]
o
∆Tsub
Subcooling temperature
[ C, K]
Tmax
Maximum inner cone temperature
[o C, K]
Tsat
Saturation temperature
[o C, K]
Psat
Saturation pressure
[Pa, bar]
CHF
Critical heat flux
[W/m2 ]
CHFAn
Critical heat flux for annular geometry
[W/m2 ]
CHFD=8mm
Critical heat flux for 8 mm pipe diameter
[W/m2 ]
δ
Gap thickness in the CHF calculation
kx
Quality correction factor for CHF
Dimensionless
kδ
Gap size correction factor for CHF
Dimensionless
kp
Pressure correction factor for CHF
Dimensionless
µl
Liquid dynamic viscosity
[kg/m s]
ρl
Liquid density
[kg/m3 ]
ρv
Vapour density
[kg/m3 ]
∆Tsub
Fluid subcooling
ilv
Vaporization latent heat
[mm]
[o C, K]
VI
[J/kg]
Variable
Description
Units
φc
Critical boiling number
Dimensionless
Ec
Eckert number
Dimensionless
Rd
Ratio between liquid and vapour densities
Dimensionless
x
Mass enthalpic quality
Dimensionless
y+
Yplus parameter
Dimensionless
u∗
Friction velocity
[m/s]
ν
Kinematic viscosity
y
Distance from the wall to the first node of the
[m2 /s]
[m]
mesh
[m2 /s]
α
Thermal diffusivity
Fo
Fourier number
Dimensionless
θ
Adimensional temperature parameter
Dimensionless
ζ
Adimensional time and position position
Dimensionless
Bi
Biot number
Dimensionless
erf
Gauss error function
Dimensionless
τ
Adimensional time parameter
Dimensionless
∆P
Pressure difference between saturated and
[Pa, bar]
nominal values
hf riction
Friction head loss
[m]
hpump
Pump head energy
[m]
hturbine
Turbine head energy
cw
i
Copper ion concentration at the wall
[ppm]
cbi
Copper ion concentration at bulk
[ppm]
Kif l
Mass transfer coefficient
Di
Diffusion coefficient
[m2 /s]
v~i
Flow velocity vector
[m/s]
ji
Mass flux
[m/s]
Uch
Flow channel perimeter
Ach
Flowing water cross sectional area
∆h
Newton step
Dimensionless
Sh
Sherwood number
Dimensionless
U
Flow velocity in the TRACT code
ρs
Density of the different isotopes in the fluid
[m]
[m/s]
[m]
[m2 ]
[m/s]
[kg/m3 ]
layer
ρc
Density of the different isotopes in the crud
[kg/m3 ]
layer
ρb
Density of the different isotopes in the bulk
solid layer
VII
[kg/m3 ]
Variable
Description
Units
ρdl
Density of the different isotopes in the deposi-
[kg/m3 ]
tion layer
[kg/m3 ]
ρsol
Local solubility
Def f
Bulk solid diffusion coefficient
Gcr
Source term modelling crud formation
[kg/m3 s]
Gdep
Source term modelling deposition
[kg/m3 s]
Gb
Source term modelling formation of active and
[kg/m3 s]
[m2 /s]
non active elements in the bulk solid
Gdis
Source term modelling dissolution
[kg/m2 s]
Gpre
Source term modelling precipitation
[kg/m2 s]
Gcor
Source term modelling corrosion
[kg/m2 s]
Ger
Source term modelling erosion
[kg/m2 s]
Rir
Irradiation rate
[1/s]
λ
Decay rate
[1/s]
φ
Neutron flux
σ
Total effective flux energy weighted reaction
[n/m2 s]
[m2 ]
cross section
hmtc
Mass transfer coefficient
[m/s]
hef f
Effective mass transfer coefficient
[m/s]
h
Molecular mass transfer
[m/s]
δcl
Corrosion layer thickness
δdl
Deposition layer thickness
[m]
[m]
2
Asp
Specific area
[m /kg]
p
Porosity
hdep
Deposition mass transfer coefficient
wf rac
Mass fraction of the control isotope
Ccoag
Coagulation coefficient
Fer
Fraction of the corrosion layer
Tout
Temperature value of the 2 mm depth thermo-
Dimensionless
[m/s]
Dimensionless
[1/s]
Dimensionless
[o C]
couple
Tmed
[o C]
couple
Tin
[o C]
couple
T1
Temperature value of thermocouple # 1
[o C]
T2
[o C]
T3
[o C]
T4
[o C]
T5
[o C]
VIII
Contents
1 INTRODUCTION
9
1.1 The IFMIF project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.1.1
Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.2
Lithium target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.3
Test cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2 LIPAc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Beam dump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 THEORETICAL BACKGROUND
23
2.1 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.2
Heat transfer coefficient estimation . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.3
Pressure calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Critical heat flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2
Annular geometry CHF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.3
Fusion adapted CHF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2
Corrosion process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.3
Parameters of influence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.3.1
Water Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4.3.2
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.3.3
Radiolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.3.4
Flow Accelerated Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4.3.5
Erosion-Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5 Heat transfer coefficient experimental determination . . . . . . . . . . . . . . . . . . . 42
2.5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.2
HTC measurement on the PHETEN prototype . . . . . . . . . . . . . . . . . . . 45
IX
3 SIMULATION TOOLS
47
3.1 1D analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Computational fluid dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3 1D corrosion analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 TRACT: TRansport and ACTivation code . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.2
Corrosion modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.3
Adaptation to the beam dump corrosion modelling . . . . . . . . . . . . . . . . 57
4 DESIGN AND ANALYSIS OF THE BEAM DUMP COOLING CIRCUIT
59
4.1 Input data and design requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 1D Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.2
Choice of geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.3
Choice of flow and pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.4
Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.5
Results of the 1D beam dump cooling analysis . . . . . . . . . . . . . . . . . . . 67
4.2.6
Final considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.7
Cooling for beam powers lower than nominal . . . . . . . . . . . . . . . . . . . . 72
4.3 Detailed 3D analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.2
Comparison with 1D analysis. Turbulence model influence . . . . . . . . . . . . 74
4.3.3
Detailed analysis of special regions . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.3.1
Tip support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.3.2
180o turn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3.3.3
Length of straight pipe at the beam dump entrance . . . . . . . . . . . 80
4.3.3.4
Effect of manufacturing and mounting tolerances . . . . . . . . . . . . 82
4.3.3.5
Inner cone thickness variation . . . . . . . . . . . . . . . . . . . . . . . 83
4.3.3.6
Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 CORROSION
89
5.1 Introduction. Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 1D transport code results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 TRACT results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.2
Results for pH = 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3.3
Results for pH = 8.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6 EXPERIMENTAL STUDIES
99
6.1 Introduction. Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2 Hydraulic circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 Pressure loss determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
X
6.3.1
Beam dump prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3.2
Pressure loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4 Film transfer coefficient measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4.1
6.4.2
6.4.3
6.4.4
PHETEN prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4.1.1
Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4.1.2
3D simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.4.2.1
Film transfer experimental determination . . . . . . . . . . . . . . . . 111
6.4.2.2
Heating means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.4.2.3
Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Preliminary measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.4.3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.4.3.2
First attempts. Measurement of temperature inside the wall . . . . . . 116
6.4.3.3
Direct measurement of temperature at the water interface . . . . . . . 118
6.4.3.4
Conclusions. Lessons learned
. . . . . . . . . . . . . . . . . . . . . . . 122
Final measurements. Results of HTC measurements . . . . . . . . . . . . . . . . 123
6.4.4.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
CONCLUSIONS AND FUTURE WORK
129
APPENDICES
133
A CALIBRATION
135
B TEMPERATURE MEASUREMENTS INSIDE THE PHETEN WALL
139
B.A Different thermocouple configurations on a stainless steel pipe . . . . . . . . . . . . . 139
B.B Measurements with the bolt thermocouple . . . . . . . . . . . . . . . . . . . . . . . . . 142
C TEMPERATURE MEASUREMENTS AT THE WATER-SURFACE INTERFACE
145
C.A Transient experiments performed on a stainless steel plate . . . . . . . . . . . . . . . . 145
C.B Experiments performed in PHETEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
C.B.1 Thermocouples fixed and covered with Araldit and duct tape . . . . . . . . . . . 148
C.B.2 Thermocouples welded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
D BAND HEATER POWER DENSITY
155
E CHICA CODE
159
XI
XII
List of Figures
1.1
IFMIF layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2
Sketch of the IFMIF accelerators, lithium target and tests modules. . . . . . . . . . . 11
1.3
Lithium target system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4
Test cell design concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5
LIPAc building layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6
LIPAc building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.7
LIPAc accelerator layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.8
Beam dump inner cone and shroud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.9
Beam dump cartridge, together with the water and polyethylene shield. . . . . . . . 16
1.10
Beam dump shield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.11
Flange of the shroud and front end of cylinder . . . . . . . . . . . . . . . . . . . . . . . 18
1.12
Shroud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.13
Tip support. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.14
Beam dump cartridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.15
Beam dump cartridge water flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.16
Beam dump cell and heat exchanging room . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1
Boundary layer scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2
Nukiyama boiling curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3
Mean and fluctuating turbulent variables . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4
Schematic model of the corrosion process . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5
Copper Pourbaix diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6
O2 and CO2 effect on copper corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.7
Copper release rates as function of O2 level and pH . . . . . . . . . . . . . . . . . . . 40
2.8
Literature data and experimental results showing the temperature influence . . . . . 41
2.9
Influence of flow accelerated corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.10
Relationship between τ and θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.11
Relationship between time and dimensionless temperature . . . . . . . . . . . . . . 45
3.1
One dimension analysis scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2
Beam dump return analysis scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
XIII
4.1
Beam dump cartridge water flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2
Beam dump nominal power deposition (average) . . . . . . . . . . . . . . . . . . . . 60
4.3
Transversal sections in x and y planes of the beam at the beam dump entrance . . . 61
4.4
Cu-water (Tsb ) and Cu-beam (Ts ) interface temperatures . . . . . . . . . . . . . . . . 62
4.5
Beam dump cooling design scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.6
Inner and outer radii of the beam dump annular channel . . . . . . . . . . . . . . . . 63
4.7
Beam dump cooling channel thickness . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.8
Inverse beam dump cooling channel cross sectional area . . . . . . . . . . . . . . . . 65
4.9
Minimum margin to saturation along the beam dump for different water flows . . . 66
4.10
Heat transfer coefficient for different roughnesses. . . . . . . . . . . . . . . . . . . . . 67
4.11
Temperature profile at surface bulk interface for different roughnesses. . . . . . . . . 67
4.12
Velocity and film transfer coefficient profiles . . . . . . . . . . . . . . . . . . . . . . . 67
4.13
Coolant temperature profile (Tb ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.14
Cu-water interface temperature (Tsb ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.15
Reynolds number profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.16
Pressure profiles along the beam dump. . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.17
CHF, Nucleate boiling and heat deposition profiles. . . . . . . . . . . . . . . . . . . . 70
4.19
Average shroud temperature profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.18
Velocity and film transfer coefficient profiles for the water return . . . . . . . . . . . 71
4.20
Nominal and boiling heat transfer coefficients. . . . . . . . . . . . . . . . . . . . . . . 71
4.21
Relative heat transfer coefficient margin to nucleate boiling. . . . . . . . . . . . . . . 71
4.22
Film transfer coefficient for the different duty cycles . . . . . . . . . . . . . . . . . . . 73
4.23
Bulk temperature profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.24
Inner cone temperature (Tsb ) profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.25
Temperature profile for the different turbulence models . . . . . . . . . . . . . . . . 75
4.26
HTC for the different turbulence models (CFX output). . . . . . . . . . . . . . . . . . 75
4.27
HTC for the different turbulence models based on temperature calculations. . . . . 75
4.28
Tip support geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.29
Yplus parameter in the tip region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.30
Pressure profile in the tip region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.31
Temperature profile (Tsb ) along the beam dump . . . . . . . . . . . . . . . . . . . . . 78
4.32
180o turn detail in the beam dump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.33
Streamlines in the beam dump water 180o turn passage through the shroud. . . . . . 79
4.34
Temperature profile in the flange.
4.35
Pressure profile through the orifices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.36
Streamlines for the 1.5 m length simulation . . . . . . . . . . . . . . . . . . . . . . . . 80
4.37
Axial velocity profile (v) at the beam dump entrance . . . . . . . . . . . . . . . . . . . 81
4.38
u velocity component profile at the beam dump entrance. . . . . . . . . . . . . . . . 81
4.39
w velocity component profile at the beam dump entrance. . . . . . . . . . . . . . . . 81
4.40
Velocity profile at z = 1.5 m for the 0.65 mm case. . . . . . . . . . . . . . . . . . . . . . 82
4.41
Velocity profile at z = 1.5 m for the 2.5 mm case. . . . . . . . . . . . . . . . . . . . . . 82
4.42
Water velocity at plane z = 1.95 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
XIV
4.43
Water velocity at plane z = 2.01 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.44
Thermocouple installation layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.45
Velocity profile around the thermocouple for the 5 mm case. . . . . . . . . . . . . . . 85
4.46
Velocity profile around the thermocouple for the 1 mm case. . . . . . . . . . . . . . . 86
4.47
Temperature profile on the inner cone for the 1 mm case. . . . . . . . . . . . . . . . . 86
4.48
Temperature profile on the inner cone for the 5 mm case. . . . . . . . . . . . . . . . . 86
5.1
Transient evolution of the copper concentration. . . . . . . . . . . . . . . . . . . . . . 90
5.2
Comparison between the different solution methods. . . . . . . . . . . . . . . . . . . 92
5.3
Solution for a constant velocity of 6.88 m/s. . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4
Cooling system layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.5
Corrosion and deposition layers along the cooling circuit . . . . . . . . . . . . . . . . 93
5.6
Dissolution rate of the corrosion and deposition layers along the beam dump for a
pH of 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.7
Time evolution of the dissolution rate of the corrosion and deposition layers at the
mid point of the beam dump for a pH of 7. . . . . . . . . . . . . . . . . . . . . . . . . 94
5.8
Dissolution rate of the corrosion and deposition layers along the beam dump return
for a pH of 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.9
Corrosion and deposition layers along the cooling circuit . . . . . . . . . . . . . . . . 95
5.10
Dissolution rate of the corrosion and deposition layers along the beam dump for a
pH of 8.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.11
Time evolution of the dissolution rate of the corrosion and deposition layers at the
mid point of the beam dump for a pH of 8.5. . . . . . . . . . . . . . . . . . . . . . . . 96
5.12
Dissolution rate of the corrosion and deposition layers along the beam dump return
for a pH of 8.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.1
Layout of the experimental hydraulic circuit. . . . . . . . . . . . . . . . . . . . . . . . 100
6.2
Hydraulic circuit at Ciemat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3
Detailed layout of the hydraulic circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.4
1:1 beam dump inner cone and tip prototypes. . . . . . . . . . . . . . . . . . . . . . . 103
6.5
1:1 beam dump cartridge prototype. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.6
Flow variation during pressure loss experiment. . . . . . . . . . . . . . . . . . . . . . 104
6.7
Position of the manometers in the hydraulic circuit . . . . . . . . . . . . . . . . . . . 105
6.8
Pressure loss experimental results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.9
PHETEN prototype scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.10
PHETEN prototype flanges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.11
PHETEN prototype partially assembled (left) and mounted in the hydraulic circuit
(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.12
PHETEN entrance flange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.13
Velocity profile in the testing section (zm ) plane . . . . . . . . . . . . . . . . . . . . . 110
6.14
Vector lines at the PHETEN entrance flange . . . . . . . . . . . . . . . . . . . . . . . . 110
6.15
Streamlines downstream the PHETEN outlet flange . . . . . . . . . . . . . . . . . . . 111
6.16
Schematic layout of the PHETEN heat transfer coefficient experiment assembly. . . 112
XV
6.17
Band heater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.18
Type T thermocouple sketch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.19
Standard type T calibration curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.20
Keithley 2000 data acquisition device . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.21
Thermal simulation of the band heater for a water heat transfer coefficient of 25000
W/m2 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.22
Flat plate with thermocouples welded on it. . . . . . . . . . . . . . . . . . . . . . . . . 119
6.23
Cross sectional view of the PHETEN experimental setup . . . . . . . . . . . . . . . . 120
6.24
Thermocouples welded to the PHETEN inner wall (copper tape) . . . . . . . . . . . . 121
6.25
Thermocouples welded to the PHETEN inner wall (Duct tape) . . . . . . . . . . . . . 122
6.26
Heat transfer coefficient experimental setup. . . . . . . . . . . . . . . . . . . . . . . . 124
6.27
T2, T4 and T5 temperature profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.28
Temperature difference between inner surface and water. . . . . . . . . . . . . . . . . 126
6.29
Experimental and theoretical heat transfer coefficients with their associated uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
A.1
Calibration experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
A.2
Calibration thermocouple setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
A.3
Calibration curves of the ten type T thermocouples and the standard response curve. 137
B.1
2, 3 and 4 mm 304L stainless steel sleeves. . . . . . . . . . . . . . . . . . . . . . . . . . 140
B.2
2, 3 and 4 mm 304L stainless steel sleeves. . . . . . . . . . . . . . . . . . . . . . . . . . 142
B.3
4 mm long, 3 mm diameter bolt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.4
Thermocouple response with bolt installed. . . . . . . . . . . . . . . . . . . . . . . . . 143
B.5
Thermocouple response without the bolt installed. . . . . . . . . . . . . . . . . . . . 143
C.1
Temperature evolution with T2 covered with Araldit and T1 and T3 with copper tape. 145
C.2
Temperature evolution with T2 covered with duct tape and T1 and T3 with copper
tape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
C.3
Temperature evolution with bare thermocouples. . . . . . . . . . . . . . . . . . . . . 146
C.4
Temperature evolution with T1 and T2 covered with duct tape and T3 uncovered. . . 147
C.5
Experimental setup scheme for T1 and T2 covered with Araldit and duct tape respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
C.6
Temperature readings of the different thermocouples for the 25 m3 /h water flow. . . 149
C.7
Temperature measured for the 80 m3 /h (left) and 108 m3 /h (right) water flows. . . . 150
C.8
0.2 mm diameter thermocouples fixed with duct tape and Araldit. . . . . . . . . . . . 150
C.9
Temperature difference in the experiment performed with T1 and T2 covered with
Araldit, T3 embedded and T4 covered with duct tape . . . . . . . . . . . . . . . . . . 151
C.10
Temperature difference in the experiment performed with T1 and T2 covered with
Araldit, T3 embedded, T4 covered with duct tape and the presence of the wall thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
C.11
Temperature difference in the experiment with no Araldit and no wall thermocouples.153
XVI
D.1
Different band heater experimental positions . . . . . . . . . . . . . . . . . . . . . . . 155
D.2
Thermocouple response at Position 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
D.3
D.4
D.5
Power density percentage along the band heater. . . . . . . . . . . . . . . . . . . . . . 157
XVII
List of Tables
4.1 Values of T at the water-material interface (Tsb ), saturation pressure (Psat ), pressure
(P) and ∆P = P - Psat at the location of maximum Tsb for different flows . . . . . . . . . 65
4.2 Temperature and stress values for the different duty cycles. . . . . . . . . . . . . . . . . 72
4.3 CFX model parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Parameters of the 0.65 mm, 2.5 mm and 0 mm deviation cases at z = 1.5 m. . . . . . . . 83
6.1 Pressure loss experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 Theoretical and experimental temperature difference values. . . . . . . . . . . . . . . . 125
6.3 Theoretical and experimental HTC values. . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.4 Heat transfer coefficient values and their associated uncertainty. . . . . . . . . . . . . . 128
B.1 Temperature measurement improvement # 1 . . . . . . . . . . . . . . . . . . . . . . . . 139
C.1 Film transfer coefficient results based on T1 and T2 . . . . . . . . . . . . . . . . . . . . 149
C.2 Theoretical and experimental temperature gradient values for the different thermocouples # 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
XVIII
RESUMEN
En el campo de la fusión nuclear y desarrollándose en paralelo a ITER (International Thermonuclear Experimental Reactor), el proyecto IFMIF (International Fusion Material Irradiation Facility)
se enmarca dentro de las actividades complementarias encaminadas a solucionar las barreras tecnológicas que aún plantea la fusión. En concreto IFMIF es una instalación de irradiación cuya
misión es caracterizar materiales resistentes a condiciones extremas como las esperadas en los futuros reactores de fusión como DEMO (DEMOnstration power plant). Consiste en dos aceleradores
de deuterones que proporcionan un haz de 125 mA y 40 MeV cada uno, que al colisionar con un
blanco de litio producen un flujo neutrónico intenso (1018 n/(m2 s)) con un espectro similar al de
los neutrones de fusión [1], [2]. Dicho flujo neutrónico es empleado para irradiar los diferentes
materiales candidatos a ser empleados en reactores de fusión, y las muestras son posteriormente
examinadas en la llamada instalación de post-irradiación.
Como primer paso en tan ambicioso proyecto, una fase de validación y diseño llamada IFMIFEVEDA (Engineering Validation and Engineering Design Activities) se encuentra actualmente en desarrollo. Una de las actividades contempladas en esta fase es la construcción y operación de un
acelarador prototipo llamado LIPAc (Linear IFMIF Prototype Accelerator). Se trata de un acelerador
de deuterones de alta intensidad idéntico a la parte de baja energı́a de los aceleradores de IFMIF.
Los componentes del LIPAc, que será instalado en Japón, son suministrados por diferentes paı́ses
europeos. El acelerador proporcionará un haz continuo de deuterones de 9 MeV con una potencia
de 1.125 MW que tras ser caracterizado deberá pararse de forma segura. Para ello se requiere un
sistema denominado bloque de parada (Beam Dump en inglés) que absorba la energı́a del haz y la
transfiera a un sumidero de calor. España tiene el compromiso de suministrar este componente y
CIEMAT (Centro de Investigaciones Energéticas Medioambientales y Tecnológicas) es responsable
de dicha tarea. La pieza central del bloque de parada, donde se para el haz de iones, es un cono de
cobre con un ángulo de 3.5o , 2.5 m de longitud y 5 mm de espesor. Dicha pieza está refrigerada por
agua que fluye en su superficie externa por el canal que se forma entre el cono de cobre y otra pieza
concéntrica con éste.
Este es el marco en que se desarrolla la presente tesis, cuyo objeto es el diseño del sistema de
refrigeración del bloque de parada del LIPAc. El diseño se ha realizado utilizando un modelo sim1
plificado unidimensional. Se han obtenido los parámetros del agua (presión, caudal, pérdida de
carga) y la geometrı́a requerida en el canal de refrigeración (anchura, rugosidad) para garantizar la
correcta refrigeración del bloque de parada. Se ha comprobado que el diseño permite variaciones
del haz respecto a la situación nominal siendo el flujo crı́tico calorı́fico al menos 2 veces superior al
nominal. Se han realizado asimismo simulaciones fluidodinámicas 3D con ANSYS-CFX en aquellas
zonas del canal de refrigeración que lo requieren.
El bloque de parada se activará como consecuencia de la interacción del haz de partı́culas lo
que impide cualquier cambio o reparación una vez comenzada la operación del acelerador. Por
ello el diseño ha de ser muy robusto y todas las hipótesis utilizadas en la realización de éste deben
ser cuidadosamente comprobadas. Gran parte del esfuerzo de la tesis se centra en la estimación
del coeficiente de transferencia de calor que es determinante en los resultados obtenidos, y que
se emplea además como condición de contorno en los cálculos mecánicos. Para ello por un lado
se han buscado correlaciones cuyo rango de aplicabilidad sea adecuado para las condiciones del
bloque de parada (canal anular, diferencias de temperatura agua-pared de decenas de grados). En
un segundo paso se han comparado los coeficientes de pelı́cula obtenidos a partir de la correlación
seleccionada (Petukhov-Gnielinski) con los que se deducen de simulaciones fluidodinámicas, obteniendo resultados satisfactorios. Por último se ha realizado una validación experimental utilizando
un prototipo y un circuito hidráulico que proporciona un flujo de agua con los parámetros requeridos en el bloque de parada. Tras varios intentos y mejoras en el experimento se han obtenido los
coeficientes de pelı́cula para distintos caudales y potencias de calentamiento. Teniendo en cuenta
la incertidumbre de las medidas, los valores experimentales concuerdan razonablemente bien (en
el rango de un 15%) con los deducidos de las correlaciones.
Por motivos radiológicos es necesario controlar la calidad del agua de refrigeración y minimizar
la corrosión del cobre. Tras un estudio bibliográfico se identificaron los parámetros del agua más
adecuados (conductividad, pH y concentración de oxı́geno disuelto). Como parte de la tesis se ha
realizado asimismo un estudio de la corrosión del circuito de refrigeración del bloque de parada con
el doble fin de determinar si puede poner en riesgo la integridad del componente, y de obtener una
estimación de la velocidad de corrosión para dimensionar el sistema de purificación del agua. Se
ha utilizado el código TRACT (TRansport and ACTivation code) adaptándalo al caso del bloque de
parada, para lo cual se trabajó con el responsable (Panos Karditsas) del código en Culham (UKAEA).
Los resultados confirman que la corrosión del cobre en las condiciones seleccionadas no supone un
problema.
La Tesis se encuentra estructurada de la siguiente manera:
En el primer capı́tulo se realiza una introducción de los proyectos IFMIF y LIPAc dentro de los
cuales se enmarca esta Tesis. Además se describe el bloque de parada, siendo el diseño del sistema
de rerigeración de éste el principal objetivo de la Tesis.
En el segundo y tercer capı́tulo se realiza un resumen de la base teórica ası́ como de las difer2
entes herramientas empleadas en el diseño del sistema de refrigeración.
El capı́tulo cuarto presenta los resultados relativos al sistema de refrigeración. Tanto los obtenidos
del estudio unidimensional, como los obtenidos de las simulaciones fluidodinámicas 3D mediante
el empleo del código ANSYS-CFX. En el quinto capı́tulo se presentan los resultados referentes al
análisis de corrosión del circuito de refrigeración del bloque de parada.
El capı́tulo seis se centra en la descripción del montaje experimental para la obtención de los
valores de pérdida de carga y coeficiente de transferencia del calor. Asimismo se presentan los resultados obtenidos en dichos experimentos.
Finalmente encontramos un capı́tulo de apéndices en el que se describen una serie de experimentos llevados a cabo como pasos intermedios en la obtención del resultado experimental del
coeficiente de pelı́cula. También se presenta el código informático empleado para el análisis unidimensional del sistema de refrigeración del bloque de parada llamado CHICA (Cooling and Heating
Interaction and Corrosion Analysis).
El trabajo desarrollado en esta tesis ha supuesto la publicación de 3 artı́culos en revistas JCR
(”Journal of Nuclear Materials” y ”Fusion Engineering and Design”), ası́ como la presentación en
más de 4 congresos y reuniones de relevancia.
3
4
ABSTRACT
In the nuclear fusion field running in parallel to ITER (International Thermonuclear Experimental Reactor) as one of the complementary activities headed towards solving the technological barriers, IFMIF (International Fusion Material Irradiation Facility) project aims to provide an irradiation
facility to qualify advanced materials resistant to extreme conditions like the ones expected in future fusion reactors like DEMO (DEMOnstration Power Plant). IFMIF consists of two constant wave
deuteron accelerators delivering a 125 mA and 40 MeV beam each, that will collide on a lithium
target producing an intense neutron fluence (1018 n/(m2 s)) with a similar spectra to that of fusion
neutrons [1], [2]. This neutron flux is employed to irradiate the different material candidates to be
employed in the future fusion reactors, and the samples examined after irradiation at the so called
post-irradiative facilities.
As a first step in such an ambitious project, an engineering validation and engineering design
activity phase called IFMIF-EVEDA (Engineering Validation and Engineering Design Activities) is
presently going on. One of the activities consists on the construction and operation of an accelerator prototype named LIPAc (Linear IFMIF Prototype Accelerator). It is a high intensity deuteron
accelerator identical to the low energy part of the IFMIF accelerators. The LIPAc components, which
will be installed in Japan, are delivered by different European countries. The accelerator supplies a
9 MeV constant wave beam of deuterons with a power of 1.125 MW, which after being characterized
by different instruments has to be stopped safely. For such task a beam dump to absorb the beam
energy and take it to a heat sink is needed. Spain has the compromise of delivering such device and
CIEMAT (Centro de Investigaciones Energéticas Medioambientales y Tecnológicas) is responsible
for such task. The central piece of the beam dump, where the ion beam is stopped, is a copper cone
with an angle of 3.5o , 2.5 m long and 5 mm width. This part is cooled by water flowing on its external
surface through the channel formed between the copper cone and a concentric piece with the latter.
The thesis is developed in this realm, and its objective is designing the LIPAc beam dump cooling
system. The design has been performed employing a simplified one dimensional model. The water
parameters (pressure, flow, pressure loss) and the required annular channel geometry (width, rugosity) have been obtained guaranteeing the correct cooling of the beam dump. It has been checked
that the cooling design allows variations of the the beam with respect to the nominal position, being
5
the CHF (Critical Heat Flux) at least twice times higher than the nominal deposited heat flux. 3D
fluid dynamic simulations employing ANSYS-CFX code in the beam dump cooling channel sections
which require a more thorough study have also been performed.
The beam dump will activate as a consequence of the deuteron beam interaction, making impossible any change or maintenance task once the accelerator operation has started. Hence the design
has to be very robust and all the hypotheses employed in the design must be carefully checked. Most
of the work in the thesis is concentrated in estimating the heat transfer coefficient which is decisive
in the obtained results, and is also employed as boundary condition in the mechanical analysis.
For such task, correlations which applicability range is the adequate for the beam dump conditions
(annular channel, water-surface temperature differences of tens of degrees) have been compiled.
In a second step the heat transfer coefficients obtained from the selected correlation (PetukhovGnielinski) have been compared with the ones deduced from the 3D fluid dynamic simulations,
obtaining satisfactory results. Finally an experimental validation has been performed employing a
prototype and a hydraulic circuit that supplies a flow with the requested parameters in the beam
dump. After several tries and improvements in the experiment, the heat transfer coefficients for different flows and heating powers have been obtained. Considering the uncertainty in the measurements, the experimental values agree reasonably well (in the order of 15%) with the ones obtained
from the correlations.
Due to radiological reasons the quality of the cooling water must be controlled, hence minimizing the copper corrosion. After performing a bibliographic study the most adequate water parameters were identified (conductivity, pH and dissolved oxygen concentration). As part of this thesis a
corrosion study of the beam dump cooling circuit has been performed with the double aim of determining if corrosion can pose a risk for the copper beam dump , and obtaining an estimation of the
corrosion velocity to dimension the water purification system. TRACT code (TRansport and ACTivation) has been employed for such study adapting the code for the beam dump case. For such study
a collaboration with the code responsible (Panos Karditsas) at Culham (UKAEA) was established.
In the first chapter an introduction of the IFMIF and LIPAc projects in which the thesis is enshrined. The beam dump, which cooling system design is the objective of the present thesis, is also
described.
In the second and third chapters a summary of the theoretical background employed as well as
of the different employed tools is presented.
The fourth chapter presents the results relative to the beam dump cooling system. The 1D as
well as the 3D ANSYS-CFX fluid dynamic results are shown in this chapter. The results regarding the
corrosion analysis of the beam dump cooling system are presented in the fifth chapter.
The sixth chapter concentrates in the experimental setup description for the pressure loss and
heat transfer coefficient determination. The results of such experiments are also presented.
6
Finally an appendices chapter is found where several experiments carried out as intermediates
steps in the heat transfer coefficient experimental determination are described. The code employed
in the 1D beam dump cooling system design called CHICA (Cooling and Heating Interaction and
Corrosion Analysis) is also shown.
The work developed in this thesis has supposed the publication of three articles in JCR journals
(”Journal of Nuclear Materials” y ”Fusion Engineering and Design”), as well as presentations in more
than four conferences and relevant meetings.
7
8
Chapter
1
INTRODUCTION
In order to understand the context in which the study is enshrined, a general explanation of the
IFMIF and LIPAc projects is needed.
1.1
The IFMIF project
The main objective of the IFMIF (International Fusion Material Irradiation Facility) project is
studying the materials and components behaviour in a fusion like environment, that is exposed to a
neutron flux of about 1018 n/(m2 s) with an energy of 14.1 MeV generated by the deuterium-tritium
nuclear fusion reactions.
The behaviour of the materials under irradiation is a key issue in fusion reactors. A commercial fusion reactor will produce more than 30 dpa (displacements per atom) per year of damage due to the
high energy neutron fluxes generated in the reactor. The plasma facing components must imperatively withstand the severe operating conditions without suffering any significant impact on their
dimensional stability, and on their mechanical and physical properties [3]. The high displacement
per atom can lead to swelling, sputtering and erosion of the materials. ITER (International Thermonuclear Experimental Reactor) the largest tokamak ever to be built, will produce 3 dpa per year,
while in DEMO (DEMOnstration power plant) such value will be multiplied by ten [1]. Therefore
testing is needed in order to achieve success.
The material behaviour is one of the three main challenges regarding fusion technology along
with understanding the physics of a fusion reactor and the development of specific technologies for
fusion applications. Such challenge has been present since the late eighties as it can be seen in the
following references [4], [5], [6], [7], [8] and [9].
Throughout all these years, many data regarding different materials has been collected and a
review of candidates for the ITER project has been prepared [10]. The IFMIF irradiation facility
is needed in order to test candidates for future fusion reactors like ferritic/martensitic (RAFM, Reduced Activation Ferritic Martensitic) steels, martensitic oxide dispersion strengthened (ODS) steels
or non-metallic materials mainly ceramics, with high energy (14 MeV) neutrons [11], [12].
9
IFMIF will generate a neutron flux (1018 n/(m2 /s)) with a broad peak at 14 MeV by Li(d,xn) nuclear reactions to get irradiation conditions comparable to those in the first wall of a fusion reactor
in a volume of 0.5 l that can accommodate around 1000 small specimens. A comparison of IFMIF
with other available neutron sources has been performed showing that the spectrum provided by
IFMIF, reproduces accurately fusion reactors conditions with a narrow flattop in the spectrum at 14
MeV [3].
On figure 1.1 a layout of the project showing the two 125 mA, 40 MeV deuteron linear accelerators
together with the lithium target and the test facility can be observed.
Figure 1.1: IFMIF layout [3].
The main components of the IFMIF project will be briefly described in the following sections.
1.1.1
Accelerator
The requirement for the IFMIF system of 250 mA current of deuterons at 40 MeV is met by
two identical continuous wave 175 MHz linear accelerators running in parallel, each delivering a
deuteron beam of 125 mA at 40 MeV. In this way a total energy of 10 MW is provided to the liquid
lithium target [2].
The accelerator main stages are the following:
• The ion source and LEBT (Low Energy Beam Transport): Generates a 140 mA, 100 keV deuteron
beam that is transferred by the LEBT from the ion source to the RFQ cavity [2].
• RFQ (Radio Frequency Quadrupole) cavity: It bunches and accelerates the 125 mA beam up
to 5 MeV [2].
10
• LINAC(LINear ACcelerator) : A half-wave superconducting LINAC accelerates the beam from
5 MeV up to 40 MeV [2].
• HEBT line (High Energy Beam Transport:) The beam output is transported to the target by
the HEBT line, which includes a series of non-linear optics elements required to tailor the
beam in a flat rectangular shape profile on the flowing lithium target [2].
In figure 1.2 the different parts of the accelerator described above can be observed.
Figure 1.2: Sketch of the IFMIF accelerators, lithium target and tests modules [3].
1.1.2
Lithium target
Figure 1.3: Lithium target system [13].
11
A flowing lithium target is needed to produce the deuteron-lithium stripping reaction generating a high flux neutron field (2 MW/m2 ), in order to provide an irradiation damage up to 50 dpa
per full power year [14]. The lithium target assembly is where the 2 x 5 MW deuteron beams from
the accelerators meet producing the required neutron flux for the irradiation of the test specimens
under conditions similar to the first wall of a fusion reactor. The lithium flows at a nominal velocity
of 15 m/s in a closed loop. The beams impinge in the liquid lithium screen under an angle of ± 9o
in an overlapping manner on the footprint of 200 mm x 50 mm. The requirements of stability and
thickness of the set are quite high since the beams must be safely stopped with the liquid to avoid
damage to the assembly structure [3]. In figure 1.3 a layout of the lithium target system is presented.
1.1.3
Test cell
The test cell is the place where the test samples will be exposed to the neutron flux. It includes
three irradiation zones [15]:
• High flux test module: > 20 dpa/fpy and a volume of 0.5 L.
• Medium flux test module: > 1 dpa/fpy and a volume of 6 L.
• Low flux test module: < 1 dpa/fpy and a volume > 8 L.
In figure 1.4 the reference design of the Target and Test Cell (TTC) is presented [14]. The different
irradiation zones are behind the target assembly starting with the High Flux Test Module (HFTM) positioned in close proximity (2 mm) to the back plate to maximize the neutron flux, and the medium
and low test modules located behind the HFTM. The vessel is covered on the upper part by a concrete module while the surrounding concrete wall is at least 4 meters thick to provide enough shield
(see figure 1.4) [14].
1.2
LIPAc
The IFMIF-EVEDA project, in the framework of the Broader Approach agreement between Europe and Japan was started in June 2007 to complement the ITER program. Its objectives are defined
as [16]:
• Deliver the detailed engineering design file of IFMIF by June 2013 to enable rapid construction.
• Validate the designs for the major sub-systems through designing, manufacturing and testing
prototypes or mock-ups.
The project is divided in three main challenging systems [17]:
â The low energy part of the accelerator (up to 9 MeV), which will be tested at full current (125
mA) in continuous wave at Rokkasho, Japan. This is the LIPAc accelerator.
â The lithium target at a scale 1/3 including all purification (hot and cold traps) and monitoring
systems foreseen for IFMIF and tested at Oarai, Japan.
12
Figure 1.4: Test cell design concept [14].
â The high flux test module main components in particular the 1:1 scale irradiation rigs and
thermo-hydraulic demonstration of the modules tested in Europe.
The accelerator components are designed, manufactured and tested by European institutions
while the building, the auxiliary systems and the supervision of the accelerator control system are
provided by JAEA (Japan Atomic Energy Agency) [18].
At the European level, the Accelerator activities are led by 4 countries: France (CEA-Saclay), Spain
(CIEMAT-Madrid), Italy (INFN-Legnaro) and Belgium (SCK-CEN). JAEA is the agency in charge in
Japan, while Fusion for Energy (F4E) agency coordinates the project.
The accelerator building located in Rokkasho (Japan), consists of an accelerator vault, a nuclear
heating, ventilation and air conditioning (HVAC) area, a heat exchange and cooling water area for
both radiation controlled and non-controlled areas, an access room, a control room and a large hall
for power racks, RF systems (HVPS and RF power chains) and the 4 K refrigerator. The accelerator
vault is surrounded by 1.5 m thick concrete walls and ceiling [3].
In figure 1.5 an scheme of the LIPAc building with all the different described parts can be observed,
while in figure 1.6 the present state of the building is presented.
13
Figure 1.5: LIPAc building layout [3].
The LIPAc accelerator can be divided into the followings parts [17]:
' The injector and its associated Low Energy Beam Transport (LEBT) line; the electron cyclotron
resonance source, associated with a set of five shaping and accelerating electrodes generating
the initial beam of 140 mA, 100 keV.
' The radio frequency quadrupole (RFQ): based on a four vane structure, with a total length of
about 9.8 m and divided in eight main modules and two special ones at each end. The RFQ
will bunch and then accelerate the beam to an energy of 5 MeV.
' The matching section: this section equipped with some diagnostics optimizes the beam before
its acceleration in the Superconducting Radio Frequency LINear ACcelerator (SRF-LINAC).
' SRF-LINAC: Based on Superconducting Half Wave Resonators (HWR). LIPAc SRF-LINAC is
composed of eight HWR cavities.
' The High Energy Beam Transport line (HEBT): The main goal of the HEBT line is the transport
and the transversal matching of the deuteron beam from the SRF to the beam dump.
' The beam dump described in the following paragraph.
' The RF system has been standardized to decrease its cost: two power units based on a standard emitter (105 and 220 kW) are considered. Each one is composed of a pre-driver, a first
amplification stage by means of tetrodes (output power of 11 kW) and the final amplification
stage also based on tetrodes.
14
Figure 1.6: LIPAc building.
In figure 1.7 the different parts of the LIPAc can be observed.
Figure 1.7: LIPAc accelerator layout [3].
1.3
Beam dump
The beam dump will be operative during the accelerator commissioning and during the different
tests carried out in the accelerator to validate the design.
15
The LIPAc beam dump design uses a conical shape for the beam facing surface extracting the deposited heat by means of water flowing at high velocity on the outer side of this surface. The concept
is based on a previous beam dump used at LEDA accelerator (6.7 MeV and 0.1 A proton beam) [19],
although a complete new design was needed due to the higher power of LIPAc and the larger radiation from the deuteron material interaction.
Cono interior
Soporte de la punta
Shroud
Figure 1.8: Beam dump inner cone and shroud.
- Cono interior
Cartucho - Cono exterior
Polietileno
- Cilindro de acero inoxidable
Blindaje de agua (tanques
de Al)
Figure 1.9: Beam dump cartridge, together with the water and polyethylene shield.
Geometry is a key factor when defining the deposited beam power shape. It determines the temperatures and thermal stresses on the inner cone. Different geometries were considered to dissipate
the power deposited by the beam. Finally a conical geometry was chosen because it was the best
16
suited for an axi symmetric beam like the one of the LIPAc facility. It also takes advantage of the
beam divergence by intercepting the densest beam areas after the beam has diverged all along the
beam dump.
Copper was chosen as the beam dump material mainly because of its high thermal conductivity.
Due to the high heat flux deposited on it, up to 2.5 MW/m2 , a high conductivity was essential so that
radial gradients could be lowered and hence the thermal stresses derived from them.
The beam dump consists of the cartridge where the deuteron beam is stopped, and a local shield
to attenuate the resulting radiation (see figures 1.8, 1.9 and 1.10).
Iron shield
Support
Shield trolleys
Figure 1.10: Beam dump shield.
The cartridge is made of three different pieces:
• Inner cone.
• Shroud.
• Cylinder.
The inner cone which receives the deuteron beam in its interior body is made of high purity copper with a length of 2.5 m and an aperture at the cone base of 30 cm, which will have vacuum inside
and a flow of water outside to remove the generated heat. Its thickness is 5 mm except in the last 0.5
m near the aperture where it is increased to 6.5 mm to raise the safety margin against buckling. A
chamfer at the aperture is included to absorb the halo [20].
17
The aperture flange (see figure 1.11) will be made of stainless steel 304L and electro deposited
copper. The stainless steel will allow vacuum leak tight connection with the vacuum tube using a
metallic elastic o-ring. The inner part of the flange will be made of electro deposited copper providing a good thermal conductivity.
The shroud together with the inner cone will provide a channel for the cooling water flow. The
shroud will be fixed to the inner cone at the aperture zone using bolts. Some holes at this zone will
allow the water to leave the cooling channel and slowly flow back towards the tip of the cone in the
space between the shroud and the cylinder (see figure 1.11). The shroud shown in figure 1.12 will
be assembled in the rear flange positioning the shroud concentric with the inner cone. Its exact
variable geometry is given by the beam dump cooling needs, as it will be seen in chapter 4.2.
Figure 1.11: Flange of the shroud (left) and front end of cylinder (right).
Figure 1.12: Shroud.
The tip support will also be made of copper. Its function is positioning concentrically the tip of
the inner cone, allowing the axial displacement due to its thermal expansion during beam operation
(3 to 4 mm), and small rotations of the tip. This is the reason for the spherical shape (see figure
1.13) of the outer part of the tip support. The detailed design of this piece including the three ribs
connecting the inner and outer hubs has been done after performing fluid flow simulations which
18
will be shown in section 4.3.3.1.
Figure 1.13: Tip support.
The cylinder will be made of stainless steel 304L. Cooling water will fill the volume between the
shroud and the cylinder. The inner cone is bolted to the cylinder at the front end (see figure 1.11).
On the outer side the bellow connecting with the vacuum tube is also bolted to the aperture flange
of the inner cone. The flanges of the cylinder have some holes which allow for signal cables to pass
through. The opposite end of the cylinder will receive the rear flange that supports and positions
the inner cone and the shroud. The positioning of the inner cone so that it can be aligned with the
beam is performed using bolts positioned radially around the peripheral surface of the two flanges.
Rear Flange
Cylinder
Tip Support
Inner Cone
Shroud
Figure 1.14: Beam dump cartridge.
Figure 1.14 shows the assembled cartridge. Water enters by the tip support, goes through the
annular cooling channel conformed as explained by the inner cone and the shroud until it reaches
the cone base where the water flows into the space left between the shroud and the cylinder. It then
flows in counter back direction towards the exit of the cartridge (see figure 1.15).
The cartridge will be instrumented with radiation chambers and hydrophones to provide detection of abnormal situations which could lead to failure by detecting incipient boiling. Monitoring
19
Figure 1.15: Beam dump cartridge water flow.
the temperature of the inner cone with thermocouples was considered although finally discarded.
In section 4.3.3.6 an analysis of the thermocouple influence on the flow is presented.
During the beam dump operation deuterons interact with copper giving rise to neutron and
gamma radiation. That is why the cartridge is surrounded by a shield that stops this radiation and is
also employed to shield the residual radiation caused by the activation of the materials that remains
when the accelerator is shut down.
The local shield seen in figures 1.9 and 1.10 consists of high Z and low Z materials:
• Lateral shield: layers of 50 cm of water and 25 cm of iron. The water is contained inside two
aluminium tanks.
• Front and rear shield: layers of 30 cm of polyethylene and 25 cm of iron.
The cartridge is supported on the shield. This fact together with the requisite of avoiding gaps to
obtain a good shield efficiency leads to the need of strict manufacturing tolerances for the required
dimensions.
The beam dump is located at the end of the accelerator line in the beam dump cell as seen in
figure 1.5, while its cooling skid is located in the heat exchanging room (see figure 1.16). The activated beam dump cooling water exists the beam dump cell into the vault, and then towards the
beam dump cooling skid in the heat exchanging room. Water activation once it exists the beam
dump shield is a main concern. Therefore a complete corrosion study to check the amount of material which will dissolve during LIPAc operation has been performed (see chapter 5). This data has
been employed to design the beam dump purification system, part of the beam dump cooling skid
located in the heat exchanging room outside the accelerator vault.
20
Figure 1.16: Beam dump cell and heat exchanging room.
21
Chapter
2
THEORETICAL BACKGROUND
This chapter summarizes the theoretical basis of the models and equations that have been employed for the design and analysis of the beam dump cooling system. It covers the heat transfer
coefficient estimation by experimental and theoretical means, the pressure loss calculation, critical
heat flux estimation employing two different approaches, and an overview of the corrosion phenomenon.
2.1
2.1.1
Heat transfer
Introduction
Systems can exchange energy in different ways. When there is an energy exchange due to a temperature difference the system is transferring energy by means of a heat flux. The heat transfer can
be achieved by three main heat exchanging mechanisms:
• Conduction.
• Convection: either natural or forced.
• Radiation.
The Conduction mechanism is the internal energy transfer between different objects, systems or
parts of them. It is based on the molecules kinetic energy exchange. This energy flux goes from the
particles with higher energy (higher temperature) to the ones with a lower energy and hence lower
temperature. It is a heat transfer mechanism that only takes place within body limits. Most of the
conduction analysis can be tackled analytically [21].
Heat conduction can be modeled by equation 2.1, which is the general cartesian heat transfer
conduction expression, where T stands for temperature, qv is the internal volumetric heat source, k
is the material conductivity and α is the material thermal diffusivity defined in equation 2.2.
∇2 T +
∂2T
∂2T
∂2T
qv
1 ∂T
qv
=
+
+
+
=
2
2
k
∂x
∂y
∂z 2
k
α ∂t
23
(2.1)
24
Chapter2. THEORETICAL BACKGROUND
α=
k
ρcp
(2.2)
Fourier’s law (equation 2.3) establishes that the heat conducted through a given surface is proportional to the temperature gradient taken in a perpendicular direction to such surface.
q = −kA ·
dT
dn
(2.3)
Where:
• q is the transferred heat [W].
• k is the material conductivity [W/m · K].
• T is the temperature of the considered object [K].
• n is the perpendicular coordinate to the surface [m].
• A is the given surface Area [m2 ].
The convection mechanism is described as the heat transfer process taking place in a fluid due
to the conduction and energy transport originated by internal fluid oscillations caused artificially or
by density variations [21].
The convection process strongly depends on the fluid motion. Due to viscosity a flowing fluid
has a zero velocity at the wall. Velocity evolves from the zero value at the wall to a uniform value creating a boundary layer. The boundary layer thickness is defined as the distance from the wall where
99 % of the uniform fluid velocity is reached. Figure 2.1 shows a scheme of the boundary layer for
the different turbulence regimes. When the fluid is in the laminar regime, the fluid layers shift parallel to the wall being most of the heat transferred by conduction. Instead, in the turbulent regime,
flowing layers shift in the transversal direction mixing the fluid and increasing the heat transfer [22].
As well as it exists a velocity boundary layer (also called hydrodynamic), a thermal boundary
layer is present when it happens to be a temperature difference between a wall and the fluid in contact with such wall. The fluid particles in contact with the wall will soon reach thermal equilibrium
with the surface. At the same time these particles exchange energy with the surrounding particles
giving rise to a temperature gradient that conforms the thermal boundary layer. The higher this
temperature gradient the higher the heat extracted.
The relative thickness of velocity and thermal boundary layers depends on the Prandtl number
(see equation 2.4). Where µ is the fluid viscosity, cp the specific heat and k the material conductivity.
If Pr < 1 then the thermal boundary layer is thicker than the velocity one, whereas if Pr > 1 the
velocity boundary layer is thicker than the thermal one. In the beam dump case, Prandtl number is
always higher than one meaning a thicker velocity boundary layer.
Pr =
24
µcp
k
(2.4)
2.1. Heat transfer
25
Figure 2.1: Boundary layer scheme.
The factors influencing the convection heat transfer can be summarized in the heat transfer coefficient (HTC), related to the heat flux by Newton’s law (equation 2.5).
q” = h · (Ts − Tb )
(2.5)
Where h is the heat transfer coefficient, Ts and Tb are the surface and fluid temperatures respectively, and q” [W/m2 ] is the heat flux.
The fluid motion as pointed out previously plays an important role in the convection heat transfer mechanism and hence the Navier-Stokes equations, which are a set of non linear partial differential expressions that describe the fluid motion [23], are linked to convection.
While in the conduction and convection processes a temperature gradient across some kind of
body is needed in the radiation mechanism no matter is needed. All the objects surrounding us are
radiating some energy. This is caused by the oscillations and transitions of the electrons present in
the material. These oscillations are maintained by the internal energy of the material and therefore
the material temperature. The radiated power is proportional to the fourth power of the temperature. Due to the low temperatures obtained in our case (T < 150 o C), radiation is not considered in
the beam dump cooling analysis.
2.1.2
Heat transfer coefficient estimation
A key issue in convection scenarios is determining the heat transfer coefficient. Solving the
Navier Stokes equations for a viscous, incompressible fluid is one of the most difficult tasks in the
field of applied mathematics. There are only solutions for special cases with a simple geometry.
Therefore the way of obtaining useful data is by carrying out experimental campaigns with a high
volume of data so that correlations can be made extensive to other situations within the experimental limits [21], [22].
25
26
Nusselt number is an dimensionless parameter defined as follows:
Nu =
h·l
k
(2.6)
Where l is a characteristic length of the analyzed geometry, k the fluid conductivity and h the heat
transfer coefficient. Nusselt number depends on Reynolds, Prandtl, Eckert and Grashof numbers.
When viscous energy dissipation and vertical gravity force are neglected Nusselt number depends
only on Reynolds and Prandtl numbers (see equation 2.7) [21]. Experimental correlations have been
obtained starting from a defined geometry heating its surface with a known heat flux, and monitoring the fluid and surface temperatures. This procedure is repeated for a wide variety of different
conditions. With these results an algebraic relation between Nusselt, Prandtl and Reynolds number
is deduced. Once Nusselt number is known the HTC is calculated with equation 2.6.
N ux
=
f (Rex , P rx )
n
Nu =
CRe P r
m
(2.7)
(2.8)
In equation 2.9, ρ and µ are the fluid density and dynamic viscosity respectively, v is the fluid
velocity and Dh the hydraulic diameter. As the beam dump cooling channel is annular an equivalent
hydraulic diameter is employed for the fluid calculations. Its expression is presented in equation
2.10, where A and P are the annular cooling channel area and wetted perimeter respectively, and e
is the cooling channel thickness. When dealing with cylindrical or with geometries represented by
the equivalent hydraulic diameter, Nusselt number is represented by N uD .
ρvDh
µ
(2.9)
4A
=2·e
P
(2.10)
Re =
Dh =
By selecting the adequate correlation employing Reynolds and Prandtl numbers as choosing parameters, it is possible to obtain an accurate estimation of the film transfer coefficient.
Different correlations have been considered for the beam dump cooling design. The flow along
the entire cooling channel is highly turbulent and hence laminar correlations like the ones of Hausen
or Colburn are not applicable [21]. Others for turbulent flows like the largely known and employed
Dittus-Boelter correlation (see equation 2.11), is not valid in our case because the temperature difference between the wall and the bulk is higher than 6 o C [21].
N uD = 0.023Re0.8 P rn
(2.11)
Equation 2.12 shows Von Karman correlation [21] which although applicable to our case, it is not
26
2.1. Heat transfer
27
accurate enough. Being f the Moody friction factor.
N uD =
(f /8) ReP r
p
1 + 5 f /8{(P r − 1) + ln[1 +
5
6
(P r − 1)]
(2.12)
Bhatti and Shah correlation [24] for fully rough pipes (equation 2.14) is not applicable to the
beam dump design because the roughness Reynolds number (see equation 2.13, where ε is the surface roughness) in the beam dump oscillates between 39 and 55 whereas it must over 70 so that this
correlation is applicable.
Reε = Re
N uD =
ε p
f /8
Dh
(2.13)
(f /8) ReP r
0.5 − 8.48)
1 + (4.5Re0.2
ε Pr
(2.14)
p
f /8
Petukhov correlation for turbulent regimes is a widely employed correlation due to its accuracy
(see equation 2.15) [25]. In the Dittus-Boelter and Von Karman correlations, ± 20 % errors in the
heat transfer coefficient calculation can be found, while in the Petukhov correlation within the beam
dump application range, errors of ± 6% are foreseen. Reynolds and Prandtl numbers along the beam
dump fall in between the correlation established margins, as well as the ratio between the fluid and
surface kinematic viscosities. Besides it also complies that it is inside the applicability range with
regard to the temperature difference between the bulk and the surface in contact with the bulk [24].
N uD =
(f /8) ReP r
p
1.07 + 12.7 f /8 P r2/3 − 1
(2.15)
Instead of directly using the Petukhov correlation, a correction which accounts for the transitional regime developed by Gnielinski [26], and for the viscosity variation with temperature (µ(T ))
developed by Sieder and Tate is employed [24].
The Petukhov-Gnielinski correlation considering the Sieder-Tate correction presents the following form:
N uD
(f /8) (Re − 1000) P r
p
=
·
1.07 + 12.7 f /8 P r2/3 − 1
µ
µs
n
The following are the conditions under which this correlation is valid:
n = 0.11 for liquids with Ts > Tb
n = 0.25 for liquids with Ts < Tb
n=0
for gases
27
(2.16)
28
0.5 <
Pr
< 200
200 <
Pr
< 2000
with an accuracy of 6%
with an accuracy of 10%
104 < Re < 5 · 106
0<
µ
< 40
µs
It has to be taken into account when applying Petukhov-Gnielinski correlation that the subscript
s stands for surface, the subscript b stands for bulk, and that all the properties are evaluated at Tb
except µs that is evaluated at Ts .
Petukhov and Roizen developed a correlation for annular cooling channels based on the Petukhov
correlation [27]. It is applicable to situations with the internal surface heated, and the outer annulus considered adiabatic. Petukhov-Roizen correlation is shown in equation 2.17, where Do and Di
are the outer and inner annular diameters respectively. This correlation will be compared with the
experimental heat transfer coefficient in section 6.4.4.
N uRoiz
= 0.86
N uP et
2.1.3
Do
Di
0.16
(2.17)
Pressure calculation
Pressure loss is either caused by water flow viscous friction along the hydraulic channel, or by
localized pressure losses originated by obstacles in the water flow. The viscous friction pressure loss
caused by the surface rugosity is calculated employing the Darcy-Weisbach expression (equation
2.18), where hlinear is the friction head loss, f is the Moody friction factor, L is the considered length
and g the gravity.
hlinear = f
L
Dh
v2
2g
(2.18)
The local pressure loss is calculated employing equation 2.19, K is an experimental value that
accounts for the pressure loss of the considered obstacle.
hlocal = K
v2
2g
(2.19)
The total friction head loss is the sum of the linear and local friction losses in the hydraulic circuit
(see equation 2.20).
hf riction = hlinear + hlocal
28
(2.20)
2.1. Heat transfer
29
The Moody friction factor f is estimated using the Colebrook equation (see equation 2.21) [28]. It
is an implicit equation based on experimental studies of turbulent flow in smooth and rough pipes.
It can be solved numerically or approximated by different equations depending on the flow regime,
the geometry of the flowing channel, and the accuracy required.
1
√ = −2 log
f
ε
2.51
√
+
3.7Dh
Re f
(2.21)
The Goudar-Sonnad approximation has been employed to calculate the friction factor along the
copper beam dump surface because it is the most accurate one [29]. Equation 2.22 shows this approximation. All the parameters except for the Reynolds number (Re), the friction factor (f), the
surface roughness (ε) and the hydraulic diameter (Dh ) are auxiliary variables employed in the friction factor calculation.
d
1
√ = a ln
+ DCF A
r
f
a=
d=
(2.22)
2
ln 10
ln 10 · Re
5.2
b=
ε/Dh
3.7
s = b · d + ln(d)
r = ss/(s+1)
m = b · d + ln
p = ln
r
m
DLA = p
DCF A = DLA 1 +
d
r
m
m+1
p/2
(m + 1)2 + (p/3) · (2m − 1)
29
30
2.2
2.2.1
Critical heat flux
Introduction
Boiling is the vaporization of a liquid. It is caused by a heat source capable of raising the surface
temperature above the saturation temperature, the point where the vapor pressure is equal to the
pressure in the surrounding liquid. The heat is transferred from the bulk solid surface to the liquid
forming vapor bubbles that grow and latter are detached from the solid surface [22].
B
D
A
C
Figure 2.2: Nukiyama boiling curve [24].
In 1934 Nukiyama characterized pool boiling. He heated water on an horizontal Nichrome wire
which was employed as heater and thermometer. He found that when water started boiling, as he
increased the power input to the wire, the heat flux rose sharply while the temperature difference
(Twire - Tsat ) increased in a much moderate way. As the input power was increased, it reached a
maximum heat flux (point B in figure 2.2), and then the Nichrome wire suddenly melted (transition from point B to point D in figure 2.2). When the experiment was repeated with a platinum
wire same behaviour was shown, but this time when the power was increased a sudden temperature
boost occurred turning the wire white-hot without melting. He then reduced the power dropping
the temperature in a continuous way until the heat flux was far below the point where the sudden
30
2.2. Critical heat flux
31
temperature change had occurred (point C in figure 2.2). At certain point the temperature dropped
to the original q vs ∆T value.
The critical heat flux (CHF) is the point where nucleate boiling ends leading to transitional and
film boiling (qmax in figure 2.2). It has been a matter of interest since in many industrial fields, cooling devices operate in the boiling regime due to its superior heat extracting capabilities. Much of
the research comes from the fission energy field like the one presented by Cheng and Müller in [30],
where an overview of experimental and theoretical studies on critical heat flux centered in nuclear
engineering applications is presented.
Fusion devices are subjected to high heat fluxes, but the parameters range of interest is different
from that of the fission field, that is higher inlet subcooling, higher velocities and smaller channel
diameter and lengths [31].
Among the many correlations and models developed to predict the critical heat flux value an extensive review can be found in [31] where four correlations, the ones of Levy [32], Tong-Westhinghouse
[33], Tong [34], and Tong-modified [35], and three different mechanistic models are presented, the
ones of Weisman-Ilelamlou [36], Lee-Mudawwar [37] and Katto [38]. These studies either apply to
specific geometrical configurations like vertical fuel rods bundles (Tong-Westhinghouse and Tong)
which is not our case, either are out of our application range like the mechanistic models of LeeMudawwar, Weisman-Ilelamlou, Katto and the Tong-modified correlation or yield errors over 50%
in the CHF prediction like the one of Levy.
In this thesis two different approaches are considered to calculate the CHF. In the first one, Doerfer et al. [39] correction for annular geometry based on Groeneveld et al. [40] look-up tables is
employed. In the second approach the correlation of Boscary et al. [41] developed for the fusion
field is used. They have been chosen by the following reasons:
• Applicable to our case (the parameter applicability lays within the accepted margins).
• Completeness.
• Geometrical compatibility.
• Proved accuracy.
Both of them are calculated and compared to gain confidence on the obtained results. They are
described in the following sections.
2.2.2
Annular geometry CHF
Most of the CHF data is limited to water flowing in vertical pipes typical of fission reactors. Accurate correlations for the prediction of the CHF in annular geometries are scarce. The correction
to the look-up table for critical heat flux by Groeneveld et al. [40], performed by Doerffer et al. [39]
adjusting the CHF for annular geometry is one of the few examples of accurate prediction methods
31
32
for the estimation of the CHF.
The experimental database taken into account to develop the correlation matches in terms of
pressure, mass flow, quality, and geometrical parameters the values considered for the beam dump.
Doerffer et al correlation predicts the CHF value with a r.m.s error of 9.26 %.
CHFAn = CHFD=8mm kx kδ kp
(2.23)
Being CHFAn the annular CHF, CHFD=8mm the experimental value for 8 mm diameter pipes
found in the Groeneveld et al. look-up table, kx , kδ and kp the quality, channel thickness and pressure correction factors respectively (see equation 2.23).
In the beam dump case as the calculated quality is below 0.025 in the whole channel, the quality
correction factor (kx ) is 0.81. The cooling channel has a variable width with the axial position and
therefore the right correlation depending on the beam dump section has to be taken from equations
2.24 and 2.25.
For a channel thickness size: 6.27 mm < δ 6 8.26 mm:
kδ = 0.663 + 64374 exp(−
δ
)
1.242
(2.24)
For δ > 8.26 mm:
kδ = 0.75
(2.25)
kp accounts for the pressure correction factor. As the pressure in the beam dump is much lower
than 3.3 MPa, the considered value is kp = 0.9.
2.2.3
Fusion adapted CHF
As pointed out in [39] and [42], one side heated elements (which is the case of the beam dump)
show a lower CHF than bilaterally heated elements. Boscary has developed a correlation for one side
heated elements but unfortunately the beam dump conditions near the tip are outside the application range of this correlation because the Reynolds number is out the applicability range shown in
equation 2.26 (see figure 4.15 to check the Reynolds number in the beam dump).
7.2 · 104 < Re < 2.8 · 105
(2.26)
Therefore the Boscary correlation [41] developed for bilaterally heated elements as a previous
stage to the one side heated correlation, which is applicable to the beam dump case has been employed.
This correlation is based on five dimensionless numbers:
32
2.2. Critical heat flux
33
1. The critical boiling number (Boc ) shown in equation 2.27 is the only group including the CHF
value, defined by φc , where ρl , ilv and φc represent the liquid density, the vaporization latent
heat and the wall CHF respectively.
φc
ρl ilv
Boc =
(2.27)
2. The Eckert number defined in equation 2.28 characterizes the dissipation of mechanical energy into calorific energy. It is the ratio between the two main dimensional parameters acting
on the CHF calculation, the fluid velocity v and the subcooling ∆Tsub = Tsat - Tsb .
Ec =
v2
cp ∆Tsub
(2.28)
3. Equation 2.29 shows the third dimensionless group considered, the Reynolds number. It characterizes the ratio between the inertial and viscosity forces. It is the only parameter taking into
account the geometry through the hydraulic diameter.
Re =
pl vDh
µl
(2.29)
4. The ratio between the liquid and vapour densities ρl and ρv (see equation 2.30).
Rd =
ρl
ρv
(2.30)
5. The mass enthalpic quality defined in equation 2.31 represents the percentage of mass in a
saturated mixture that is vapour. It is an intensive property to specify the thermodynamic
state of the working fluid.
x=−
cp ∆Tsub
ilv
(2.31)
The proposed correlation for the critical heat flux value is the following:
Boc,unif orm =
1
exp(x2 )[Ec−1/7 Re−1/4 Rd−1/4 (−x)1/10 ]
40
(2.32)
The application range of this correlation is:
8.8 · 10−6 <
Ec
< 4.9 · 10−2
1.2 · 104 <
Re
< 2.3 · 106
20 <
Rd
< 1820
−0.5 <
x
<0
This correlation predicts 70 % of the critical heat flux Celata and Mariani database [43], with an
33
34
accuracy of ± 30% .
2.3
Fluid dynamics
Computational fluid dynamics solve the Navier-Stokes equations [23] giving the velocity and
pressure fields. These equations are the result of applying two of the four basic laws (mass and
momentum), resulting in a set of partial differential equations [44].
The Navier-Stokes equations can be solved in a simplified form while retaining the physics which is
essential to the goals of the simulation, or in more complex forms when such simplification is not
possible. Possible simplified governing equations include the potential flow equations, the Euler
equations or the thin layer Navier-Stokes equations. Depending on the geometry, problem definition and flow conditions, different governing equations can be applied to the problem thus obtaining the most appropriate solution in terms of computational resources and solution accuracy.
The general form of the Navier-Stokes equation is the following:
ρ
∂v
+ v · ∇v
∂t
= −∇P + ∇ · Γ + f v
(2.33)
Where v is the flow velocity, P is the fluid pressure, Γ is the stress tensor and fv the volumetric
body forces. Left side of equation 2.33 is composed of a transient term ρ ∂v
∂t , and a convective term
ρ (v · ∇v). The right side takes into account the stresses in the fluid; these are gradients of body
forces, analogous to stresses in a solid. ∇P is the pressure gradient being the isotropic part of the
stress tensor while ∇ · Γ is the anisotropic part of the stress tensor conventionally describing the
viscous effects. The volumetric body force fv usually describes gravity or electromagnetic forces.
With the Navier-Stokes equations complicated geometries can be modelled. These geometries
have to be meshed so that the computational fluid dynamic solver applies the equations to every
node of the mesh. Obtaining a proper mesh requires a deep knowledge of the modelled geometry and of the flow conditions by means of non dimensional parameters like Reynolds, Prandtl or
Mach numbers. Once the model is adequately meshed boundary conditions are applied. This step
turns to be crucial to obtain the correct solution for the problem, specially in the turbulent regime
(high Reynolds number) [23]. The reason is that turbulent flows are not completely solved by the
full equations of motion, and approximate turbulent models are needed to achieve an appropriate
solution.
Fine meshes are required in order to capture the small scale turbulent eddies. When such a precision is needed Direct Numerical Simulation (DNS) methods are employed. These methods require
an incredible of amount of computational resources.
An alternative to DNS methods is the Large Eddie Simulation (LES) method [45]. It computes
the instantaneous velocity and pressure fields without the high costs of DNS. It captures the transient nature of the flow by spatially averaging and modelling on the sub grid. Hence it solves the
same Navier-Stokes equations as DNS methods but equations are spatially filtered to the size of the
34
2.3. Fluid dynamics
35
grid [46]. Each variable is broken into its large scale (grid scale) and its small scale (sub grid scale),
obtaining spatially or locally averaged values instead of time averaged values like in the Reynolds
Averaged Navier Stokes methods (RANS). As the Reynolds number increases, so does the spectrum
of eddies, requiring a finer mesh to capture all the large scale kinetic energy.
Therefore, LES method directly solves the large scale flow field variables, and models the smallest
scales of solution rather than solving them directly like DNS, employing the Sub grid Scale symmetric tensor (SGS).
We have previously mentioned the Reynolds Averaged Navier-Stokes (RANS) models, named like
this because they are inspired on ideas proposed by Osborne Reynolds over a century ago. In these
models all unsteadiness that is regarded as part of turbulence is averaged. Averaging the non linear
terms of the Navier-Stokes equation gives rise to terms that must be modelled [45]. The variables
are decomposed into time averaged and fluctuating quantities as it is graphically expressed in figure
2.3.
Figure 2.3: Mean and fluctuating turbulent variables [23].
Decomposing the velocity in mean and fluctuating quantities we have:
0
(2.34)
u(x, t) = u(x, t) + u (x, t)
T
1
u =
T
Z
1
u =
T
Z
0
02
(u − u) dt
(2.35)
0
T
0
u 2 dt 6= 0
(2.36)
0
When this notation is applied to the momentum equation, turbulent stresses appear as shown
in equation 2.37, where the momentum equation is presented in cartesian form and applied to the
x axis.
ρ
∂p
∂
du
=−
+ ρg +
dt
∂x
∂x
35
µ
∂u
− ρu0 2
∂x
(2.37)
36
The system of equations is not closed because it contains more variables than equations. The
closure requires the use of some approximations which usually take the form of prescribing the
Reynolds stress tensor ρu0 2 and turbulent scalar fluxes in terms of mean quantities. The equations
needed to make the closure are called turbulence models [45].
3D computational fluid dynamics simulations employing the RANS to model turbulence are performed in order to check the fluid behaviour at certain critical parts of the beam dump design where
1D simulation is not valid. In Section 4.3 the results of the 3D analysis are shown. Details of the employed computational fluid dynamic code (ANSYS CFX) are presented in section 3.2.
2.4
2.4.1
Corrosion
Introduction
Corrosion is a main concern in water operated cooling circuits no matter if stainless steel or copper is employed as contact material. The critical part in the beam dump cooling circuit will be the
cartridge that stops the deuteron beam because it will be subjected to high flow velocities, relatively
high temperatures and radiation. The high temperatures and velocities can enhance the corrosion
process. Due to the radiation environment the water composition must be controlled. Therefore
deionized water will be used in the beam dump cooling circuit. Some studies regarding the copper corrosion on deionized water have pointed out the main concerns when designing a cooling
circuit [47], [48]. In these studies parameters like temperature, water pH or copper solubility are
remarked as elements to keep an eye on when operating the cooling circuit.
Much of the experience and design criteria for fusion cooling circuits comes from the knowledge acquired along several years of power plants operation. These conditions are similar to those
found in fusion first wall cooling circuits. Different tested solutions to suppress corrosion have
been provided derived from its operation since the 1950s up to day [49], [50]. Although empirical
data from power plants has been important, activation codes from fission nuclear operation like
PACTOLE have been adapted to the operating conditions, material compositions and water chemistry of ITER [51], gaining a thorough but still incomplete overview of the corrosion behaviour on
fusion cooling loops.
When operating a cooling circuit in a fusion environment several difficulties arise in comparison
with a standard installation. The appearance of radiolysis and the need to keep a low conductivity
deionized water are probably the main ones [52], [53], [54].
Hence a first review on the cooling water requirements for ITER was made in 1999 as part of
an ITER task [55]. On that document the quality that the cooling water must comply is presented
based on the experience from power plants. In order to be able to predict and correct the effects
derived from radiation on fusion cooling loops, a code called FISPACT that predicts the activation
products when deuterons impinge on the cooled device wall has been developed [56]. In the same
36
2.4. Corrosion
37
trend, TRACT (TRAnsport and ACtivation) simulates the flow and isotope transport inside a network
of 1D channels. This code will be employed to model the beam dump cooling circuit corrosion phenomenon. It is described with more detail in section 3.4.
The corrosion process causes the dissolution and subsequent transport of the dissolved elements
along the cooling circuit. The key issues for the beam dump cooling circuit regarding the corrosion
process are the following:
• The mass removal could lead to reduced cone thickness which could affect its mechanical
performance, and also to changes in the width of the cooling channel and therefore of the heat
transfer coefficient.
• Corrosion of the beam dump leads to a spread of its activation. Dose rates must be kept below
12.5 µSv/h at the heat exchanger room outside the accelerator vault, and also inside the vault
itself when the accelerator is stopped.
2.4.2
Corrosion process
Copper corrosion is unavoidable in contact with water, it is particularly enhanced if deionized
water is employed due to the lack of ions attempting to gain equilibrium by combining with the
surrounding medium [47]. The corrosion of a metal is an electrochemical process by which the
metal is oxidized. The initial corrosion process develops as follows:
1. Small quantities of O2 and CO2 are always present dissolved on water.
2. Oxygen molecules are adsorbed at the copper surface and decay in two atoms, taking electrons
from copper.
3. Simultaneously CO2 partly forms carbonic acid (H2 CO3 ) with water.
From this point, three reactions can take place depending on the conditions:
• Hydrogen ions from dissociated H2 CO3 react with O−2 forming water and Cu+2 goes into solution.
• When higher concentrations of Cu+2 are present, the reaction Cu+2 + O−2 ⇒ CuO takes place.
• When water reaches Cu+2 saturation, copper carbonates form on the metal surface.
In figure 2.4 a summary of the above described reactions is presented. Although there are many
more reactions taking place on a deionized water-copper cooling system, these are the most relevant from the corrosion point of view, without considering side effects such as radiolysis or flow
accelerated corrosion.
Depending on the oxidizing or reducing environment, Cu will react with O2 , H2 O2 , H2 , . . . In low
oxygen and neutral pH systems cuprous oxide (Cu2 O) will be predominant, while in high oxygen alkaline systems the oxide will be mainly cupric oxide (CuO). These oxides create a passive layer over
37
38
Figure 2.4: Schematic model of the corrosion process [47].
the copper surface protecting it from further corrosion. The copper Pourbaix diagram of figure 2.5
shows the stable phases of the system formed by copper and water. It can be seen how copper will
be in oxidizing conditions for acid pH and positive voltage potential (E)1 , and also for high alkaline
pH and positive values of E.
Figure 2.5: Copper Pourbaix diagram [57].
The overall corrosion process in cooling loops is not only limited to the chemical decomposition
of the wall materials. Dissolution, mass transport (precipitation and deposition) and erosion also
play an important role removing or depositing the initial corrosion layer and therefore affecting the
so called corrosion process [58].
1 The potential is evaluated with respect to the standard hydrogen electrode (SHE)
38
2.4. Corrosion
2.4.3
39
Parameters of influence
Different documents [47], [48] and [53] review the parameters and phenomena governing copper
corrosion in aqueous media. These are the following:
• Water chemistry:
1. Water conductivity.
2. pH.
3. Dissolved oxygen.
• Temperature.
• Radiolysis.
• Flow Accelerated Corrosion (FAC).
• Erosion-Corrosion.
Although they are treated independently, all of them except temperature are interrelated with
water chemistry.
2.4.3.1
Water Chemistry
In [54] a good overview on fusion cooling loops water chemistry can be found along with recommendations to keep the corrosion enhancing agents under the allowed limits.
Deionized water is employed in accelerators and fusion installations (electrical conductivity is
neglected), as a method to control impurities relevant from the radio protection point of view and
as a way to avoid Stress Corrosion Cracking (SCC) [59].
The following parameters are usually monitored and controlled [54]:
• Water conductivity.
• pH.
• Dissolved Oxygen.
In order to control the ion content in the water, conductivity is monitored. Single, double or
mixed bed deionizers provided with cation and ion resin beds are used to keep it at the design value.
As O2 is the principal copper corrosion agent, it must be kept below 5 ppb if copper is present in
the cooling loop [54]. In figure 2.6 the effect of O2 and CO2 and its mixed action over copper corrosion rate can be observed.
Water pH also affects corrosion. Recommended values are in the range of 7.5-9.5 as can be observed in figure 2.7 which shows that depending on the oxygen concentration and the pH value,
different corrosion rates are achieved.
39
40
Figure 2.6: O2 and CO2 effect on copper corrosion [47].
Figure 2.7: Copper release rates as function of O2 level and pH [50].
2.4.3.2
Temperature
Different authors agree on the fact [47, 51, 54] that temperature enhances copper corrosion. The
disagreement comes when quantifying this enhancement, probably due to the influence of other
factors like pH or the amount of dissolved oxygen on the corrosion rate. Figure 2.8 shows the increase in copper corrosion rate as temperature increases.
2.4.3.3
Radiolysis
Water radiolysis is the water molecule breakdown into hydrogen peroxide, hydrogen radicals and
assorted oxygen compounds such as ozone due to radiation. In the dissociation and equilibrium
process oxygen is released contributing to copper corrosion.
Radiolysis is affected by the nature of the primary energy, the absorption energy rate (Linear Energy Transfer (LET) and radiation intensity), and the water chemistry [60]. As the only parameter
40
2.4. Corrosion
41
Figure 2.8: Literature data and experimental results showing the temperature influence [51].
that can be controlled is water chemistry, hydrogen addition is recommended.
In the beam dump gammas and neutrons are produced due to the interaction of the beam with
the copper surface. A neutron flux of 4.5 ·1014 n/cm2 s are produced in the beam dump, being the
average neutron flux in the cooling water of 5 ·1010 n/cm2 s. The photon production is similar to the
neutron one (7 ·1010 photons/cm2 s). As a reference comparing these values with the ones obtained
in a PWR (Pressurized Water Reactor), where a neutron flux in the reactor core of 5 ·1013 n/cm2 s and
between 5 ·109 − 1011 n/cm2 s on the reactor wall are found, it is seen that neutron and gamma fluxes
in the beam dump are lower. Hence radiolysis is not considered a corrosion enhancer in the beam
dump cooling circuit.
2.4.3.4
Flow Accelerated Corrosion
Flow accelerated corrosion causes the initial copper oxide layer to be removed and therefore localized corrosion is prone to happen [61]. The hydrodynamic effects controlling flow accelerated
corrosion are shear stress and flow turbulence near the wall [61], [62]. Due to high turbulent flows,
hydrodynamic and diffusion boundary layers are disturbed and therefore steady state condition for
wall shear and mass transfer changes, leading to corrosion in the zones where the boundary layers
are disrupted (figure 2.9) [61].As pointed out in [63], FAC is not only affected by hydrodynamic factors, but also by water chemistry and temperature which can increase FAC corrosion rate.
Some publications [62, 64] suggest the use of CFD in order to identify the potential regions of the
cooling loop prone to suffer flow accelerated corrosion.
41
42
Figure 2.9: Influence of flow accelerated corrosion [61].
Due to the special operating conditions of the beam dump, the water flows at speeds up to 8.5
m/s in order to achieve a high heat transfer coefficient, flow accelerated corrosion is present but in
moderate way because no high shear stresses are foreseen along the cooling channel except in the
tip support and 180o water turn, where FAC is not a concern because these areas are thick enough
to withstand FAC.
2.4.3.5
Erosion-Corrosion
Erosion corrosion is caused by the particles diluted in the cooling water and its effect is enlarged with flow velocity [65]. Some authors consider it exactly the same as flow accelerated corrosion [62], [66], while others study it as a different phenomenon but linked to flow accelerated
corrosion [61], [65], [64].
No matter if it is considered as part of FAC or as an independent issue, erosion-corrosion is controlled by dissolved particles in the flow that affect the metal structure by means of variations in the
hydrodynamic and diffusion boundary layers [61, 64]. As suggested for flow accelerated corrosion,
CFD can be used to identify the regions susceptible of suffering erosion-corrosion.
As one of the design specifications for the beam dump cooling circuit due radio protection reasons is not having a high amount of dissolved particles in the water flow, erosion-corrosion has no
influence in the corrosion process.
2.5
2.5.1
Heat transfer coefficient experimental determination
Introduction
The usual procedure to obtain the heat transfer coefficient experimentally is by provoking a heat
transfer situation in the geometry of study. Such heat transfer can be induced by directly heating
42
2.5. Heat transfer coefficient experimental determination
43
the geometry or by an increase in the temperature of the surrounding fluid. Stationary or transient
methods can be employed to evaluate the induced heat transfer.
Lately examples of stationary setups, where the bulk and water-material temperature are registered
with thermocouples and the heat transfer coefficient obtained solving Newton expression (see equation 2.5), can be found in the field of micro and nanochannels ( [67], [68], [69] and [70]). Liquid crystal thermography based on the change of colour with temperature experienced by thermochromic
liquid crystals (TLCs) became a cheap an easy alternative in the 80s and 90s (see [71] for a complete
review of five different methods of employing TLCs for HTC determination). The progress in image
capturing and data processing has made TLCs a more efficient tool, and nowadays one of the most
popular for heat transfer investigations [72].
Transient methods are based on the simplification of the heat transfer equation for a semi infinite body (see equation 2.38). They require a one dimensional heat transfer situation and a Fourier
number lower than one (see equation 2.39), where T is the body temperature, α is the material thermal diffusivity, t the characteristic time and l the characteristic length).
1 ∂T
∂T 2
=
∂x2
α ∂t
(2.38)
αt
<1
l2
(2.39)
Fo =
Equation 2.38 is solved transforming the partial differential equation with two independent variables into an ordinary one variable differential equation. One of the possible boundary conditions
corresponds to the case in which the semi infinite body is placed in contact with a fluid of constant
temperature (T∞ ) (see equation 2.40).
h (T∞ − T (0, t)) = −k
∂T
∂x
x=0
(2.40)
The solution to equation 2.38 with the mentioned boundary condition has the form of equation
2.41, where θ is a dimensionless temperature, T0 is the constant semi infinite body temperature
away from the surface in contact with the flowing fluid, erf is the Gauss error function, ζ is a dimensionless parameter considering time and position (see equation 2.42), Bi is the Biot number
(equation 2.43), and τ is a time dimensionless parameter (see equation 2.44). A more detailed explanation of the different possible boundary conditions and the step by step solution of the heat
transfer equation can be followed in [24].
θ=
√ T (x, t) − T0
= 1 − erf (ζ) − e(Bi+τ ) 1 − erf ζ + τ
T∞ − T0
r
ζ=
Bi =
43
(2.41)
x2
4αt
(2.42)
hx
k
(2.43)
44
τ=
αt
(k/h)
2
(2.44)
Figure 2.10: Relationship between τ and θ [73].
For small times, right at the beginning of the transient experiment when τ is very small, the so√
lution can be approximated by equation 2.45 (see figure 2.10). Approximating θ/ αt by the tangent
(see figure 2.11), an expression for the heat transfer coefficient is obtained (1equation 2.46).
θ≈2
p
τ /π
√
h
π
≈
tanβ
k
2
(2.45)
(2.46)
TOIRT (Temperature Oscillation InfraRed Thermography) is one of the newest and more precise
methods to determine the heat transfer coefficient. Its main advantage is that it is a non-contact
fluid independent method, therefore simplifying the experimental setup compared with the TLCs
and direct methods. It relies on the measurement of the temperature response on the outside surface of a heat transferring wall to an oscillating heat flux (typically produced by a laser). The temperatures are measured with an IR camera. The heat transfer coefficients are derived from the phase delay of the temperature oscillation using a 3D finite difference thermal model of the wall [74]. In [75]
and [76] some application examples to different geometries and conditions are shown. Further details details can be found in [77].
44
2.5. Heat transfer coefficient experimental determination
45
Figure 2.11: Relationship between time and dimensionless temperature.
2.5.2
HTC measurement on the PHETEN prototype
TOIRT method was initially thought as a good alternative to determine the heat transfer coefficient, but it was discarded because the IR camera available was too slow to determine the temperature oscillation in real time. It was necessary to design a complete and complicated control system
in order to be able to test with these conditions if the method could be useful. Therefore other options were considered.
TLCs experiments although considered were dismissed due to the complicated initial setup. It
implied building a similar device like PHETEN, but with a multilayer structure in order to introduce
a TLCs layer in between the stainless steel material. This complicated the fabrication of such prototype which was to be made at CIEMAT.
The PHETEN device was initially designed to determine the HTC by means of transient methods.
The body could be considered a semi infinite body because its wall thickness was much lower than
its length, and hence heat conduction was one dimensional. The initial plan was to fabricate the
PHETEN with copper but due to its high thermal diffusivity, Fourier number could not be lower than
1 for more than 0.21 s. Performing the experiment in such a reduced period of time was considered
not viable. Hence fabricating the prototype in other material rather than copper was considered.
The chosen one was stainless steel 304 L due to its low diffusivity. The change in the diffusivity allowed for a 65.8 seconds period of time to register the temperatures.
This option was finally discarded due to the difficulties of suddenly changing the flow conditions
(temperature) in a controlled manner so that the transient experiment could be performed.
45
46
Finally direct heating and measuring the temperature difference between the heated surface and
the bulk in a stationary situation using thermocouples was the chosen method for the HTC determination. The reasons were the simplicity of the experimental setup compared with the other options,
and that it was the most suited option for the available means at that time. In section 6.4.2 all the
information related to the experimental setup and HTC results are presented.
46
Chapter
3
SIMULATION TOOLS
One dimensional analysis and computational fluid dynamics (3D) have been employed to define the main parameters of the fluid and the cooling channel geometry. In this chapter the 1D
code called CHICA (Cooling and Heating Interaction and Corrosion Analysis) employed to define
the beam dump cooling channel is described. The main guidelines for the 3D ANSYS CFX analysis
are depicted. The TRACT (TRansport and ACTivation) code used to assess the beam dump corrosion
phenomenon is also outlined.
3.1
1D analysis
A 1D steady state analysis code called CHICA (Cooling and Heating Interaction and Corrosion
Analysis) simulating the heat transfer, fluid dynamics and corrosion phenomenon in the beam dump
has been developed. It serves as a first analysis of the beam dump cooling system and for the definition of its main parameters. A scheme of the LIPAc beam dump cartridge was presented in section
1.3 (see figure 1.15). The LIPAc beam dump cooling analysis can be tackled as a 1D study because of
the following reasons:
7 Axial symmetry.
7 Expected temperature gradients will be mainly radial.
7 Cone thickness (5 mm) is small compared with its radius and length.
7 Heat source from the beam is also axisymmetric.
Temperature dependent properties are considered. Radiation heat transfer is neglected and the
heat transfer through the shroud has been ignored by assuming an adiabatic condition along the
shroud surface. Due to the small beam dump conicity its effect is neglected, considering each discretized beam dump section as a cylinder. Instead of employing cylindrical components for the heat
transfer mechanism, cartesian coordinates are employed, however the heat flux is corrected to ac”
count for the area increase in a cylinder (see equation 3.1, where qcorr
is the corrected heat flux on
the surface in contact with water, q ” is the heat flux deposited by the beam, Rint is the beam side
47
48
Chapter3. SIMULATION TOOLS
inner cone radius and e is the inner cone thickness). Figure 3.1 shows a schematic layout of the one
dimension beam dump cooling analysis.
z
y
Inner cone temperature bulk side
Inner cone temperature beam side
Figure 3.1: One dimension analysis scheme.
”
qcorr
=
q ” · Rint
(Rint + e)
(3.1)
When calculating the heat transfer, it has been considered that it takes place in two almost uncoupled steps:
' The heat transmission from the beam-facing surface through the material, which is governed
by the material conductivity k. The temperature gradient between the beam-facing and coolantfacing surface depends on k and on the material thickness but it is independent of the cooling
system.
' The heat transfer from the material to the coolant, governed by the film transfer coefficient h.
This coefficient and the temperature of the material in contact with the coolant depends on
the coolant flow conditions and on the material properties.
The coolant temperature evolution is obtained from the mass balance equation. The differential
equation that governs its variation along the cooling channel is the following:
ṁcp (T )dT = q”corr (z)dA
48
(3.2)
3.1. 1D analysis
49
Where cp (T) is the specific heat at constant pressure, q”corr (z) the heat flux per unit of area and
ṁ, the coolant mass flow in kg/s.
Considering the differential area (dA) for any cylinder (equation 3.3), equation 3.2 can be solved
and thus the coolant temperature obtained.
dA = 2πRint (z)dz
(3.3)
dT
2π q”corr (z)Rint (z)
=
dz
ṁ
cp (T )
(3.4)
In order to calculate the temperature of the wall in contact with the water Tsb , Newton’s Law is
employed. For such purpose a water film coefficient h(z) must be calculated. Inner wall temperature
is fixed as Tsb and its expression is presented in equation 6.2.
Tsb (z) = Tb (z) +
q”corr (z)
h(z)
(3.5)
Where k(T) and e are respectively the thermal conductivity and thickness of the inner cone. The
conductivity is a temperature dependent variable like the specific heat at constant pressure cp (T ),
the dynamic viscosity µ(T ), Prandtl number Pr(T), and the fluid density ρ(T ).
As pointed out before the shroud is considered an adiabatic surface. However the temperature
difference between the cooling fluid Tb (z) and the return fluid Tret causes a heat being transferred
from the return to the annular cooling channel due to the higher temperature. Figure 3.2 shows a
scheme of the considered variables in the return analysis. This adiabatic assumption will be justified
in the following lines.
Some simplifications have been made:
• An average temperature at each section of the shroud has been assumed (Tsh ) in the calculation (see equation 3.7).
• A constant return temperature of 40 o C is considered, assuming a conservative hypothesis because the water return temperature decreases as it flows back towards the tip support.
• Equal heat flux at both sides of the shroud surface (Aret (z) = A(z)).
In steady state the heat transferred from the water return to the shroud equals that from the
shroud to the beam dump annular cooling channel (equation 3.6). Equation 3.7 shows the shroud
average temperature.
q”ret = hret · (Tret − Tsh ) = h · (Tsh − Tb )
Tsh (z) =
hret (z)Tret + h(z)Tb
hret (z) + h(z)
49
(3.6)
(3.7)
50
Water flow
hret (z)
Tret = 40 ºC
Tb (z)
h (z)
Shroud
Tsh (z)
Water flow
Figure 3.2: Beam dump return analysis scheme.
The heat being transferred from the water return is shown in equation 3.8. The water velocity
in the return is very low, ranging from 0.72 m/s to 0.25 m/s, giving a maximum heat transfer coefficient of 3200 W/m2 K, value much lower than the ones obtained in the beam dump annular cooling
channel. Therefore hret h, and equation 3.8 turns into equation 3.9.
q”ret = hret · h
Tret − Tb
hret + h
q”ret = hret (Tret − Tb )
(3.8)
(3.9)
Knowing that the maximum achievable temperature along the water return Tret is the one at the
end of the annular cooling channel, approximately 40 o C, a maximum heat flux (q”ret ) from the water return towards the annular cooling channel of 30600 W/m2 is obtained. This value is 1.5 % of the
maximum heat deposited on the beam dump. Hence the heat flux coming from the water return
has been neglected in the beam dump design.
Nevertheless the heat flux transferred from the return cooling channel to the annular one has
been calculated with the CHICA code (equation 3.7, but considering the return and annular channel areas), and then added to the heat flux deposited by the beam. A new bulk temperature is calculated and the heat flux is then corrected employing an iterative process until the difference between
the temperature at the end of the annular cooling channel in two consecutive iterative processes is
lower than 1 · 10−10 . The calculation has been conservative because a constant temperature for Tret
has been employed taking into account the worst possible case scenario. It is shown again that the
correction of Tb due to the heat transfer through the shroud is negligible.
50
3.2. Computational fluid dynamics
51
The fluid pressure calculation has been performed employing the steady flow energy equation
(see equation 3.10), which unlike the Bernoulli relation accounts for heat added and the shaft and
viscous work.
P1 (z) v12 (z)
P2 (z) v22 (z)
+
+ y1 (z) =
+
+ y2 (z) + hf riction (z) + hpump (z) + hturbine (z) (3.10)
ρg
2g
ρg
2g
Where P is the fluid pressure, v the fluid velocity, y the radial coordinate, and hf riction , hpump ,
hturbine are the friction head loss, the pump head energy and the turbine head loss respectively. In
the beam dump annular cooling channel only friction head loss is taken into account.
The critical heat flux in the beam dump cooling channel is calculated with the CHICA code implementing the two different approaches mentioned in section 2.2.
The 1D simplified corrosion model implemented in the CHICA code is explained in section 3.3,
while the obtained results are presented in section 5.2.
The CHICA programming task has been performed in Python [78]. Different functions have been
implemented in the code to calculate the heat transfer, fluid dynamic and corrosion main parameters. The results obtained employing this code are presented in sections 4.2 and 5.2. The complete
code is found in appendix E.
3.2
Computational fluid dynamics
Computational fluid dynamics have been employed for the beam dump analysis in order to get
a precise knowledge of the cooling flow. ANSYS CFX code has been used [79]. A complete overview
of the ANSYS CFX technical specifications can be found in [80]. The procedure followed to perform
these simulations is explained in the following.
The analysis starts with the creation of the geometry model. This geometry has been mostly
sketched using the Design Modeler ANSYS tool, except for the manufacturing tolerance model where
CATIA CAD (Computer Aided Design) software was employed. The second step is meshing the geometry model. For such task, the key is obtaining a mesh quality capable of combining an accurate
solution and a reasonable computational cost. In our case after performing a sensitivity study in the
7 mm cooling channel thickness zone, which is the narrower one, it was seen that a 2.3 mm mesh
size element gave the same results as a 2 mm one. Inflation layers that capture the velocity and
temperature gradients perpendicular to the wall are employed as part of the mesh in the vicinity of
solid surfaces, therefore obtaining a more accurate resolution of the boundary layer. An appropriate
first prism height has been chosen for each case so that the inflation layers lay within the boundary
layer. Such situation is later verified when the simulation is finished by means of the yplus parame51
52
ter, which is shown in equation 3.11. Where u∗ is the friction velocity, y is the distance from the wall
to the first node of the mesh, and ν is the kinematic viscosity.
y+ =
u∗ y
ν
(3.11)
An yplus value lower than 10 has been imposed in all the 3D CFX simulations performed in the
thesis (see section 4.3). Once the mesh is generated boundary conditions are applied to the model.
The velocity is employed as boundary condition at the model inlet, while the average static pressure
is taken at the outlet. These values are calculated with the CHICA code. The azimuthally averaged
heat deposition profile shown in figure 4.2 is the one used in these simulations.
Turbulence intensity along the beam dump cooling channel is estimated by means of equation
3.12, obtaining a maximum value of 3%. Therefore a 5% turbulence intensity has been employed in
all the beam dump 3D simulations. Besides, the thermal energy heat transfer model including the
viscous term is employed. The obtained results are shown in section 4.3.
I = 0.16Re−1/8
3.3
(3.12)
1D corrosion analysis
A first attempt to estimate corrosion was made including the diffusion equation into the CHICA
code. This equation was solved by implementing a partial differential equation solver named FiPy
[81]. Based on the corrosion approach made for a liquid metal cooling loop [82], the following equations were solved for the beam dump cooling circuit.
Corrosion phenomenon modelling begins by considering the convective diffusion equation (3.13),
where ci denotes the ion concentration, Di is the diffusion coefficient and v~i is the flow velocity.
∂ci
+ (~
vi ∇) ci = ∇ (Di ∇ci )
∂t
(3.13)
Equation (3.13) is brought into a non-dimensional form showing that it depends on the Reynolds
and Schmidt numbers. Next step is taking profit of the principles of convective mass transfer which
state that under forced convection flow conditions, mass transfer is determined by the Sherwood
number (dimensionless) and therefore advantage between the analogy of heat and mass transfer
can be used [83]. As the convective diffusion equation (3.13) depends on Reynolds and Schmidt
numbers, the Sherwood (Sh) number must also depend on them.
b
The mass flux ji is defined as shown in equation (3.14), where cw
i and ci are the wall and bulk
copper concentrations, and Kif l the mass transfer coefficient (see equation 3.16).
b
ji = Kif l · cw
i − ci
52
(3.14)
3.4. TRACT: TRansport and ACTivation code
53
log(cw ) = 0.98 log(ρ) −
Kif l =
14500
+ 25.5
19.1Tsb + 273.15
(3.15)
Di
Sh
Dh
(3.16)
∂cb (t, z)
Uch,i
∂cbi (t, z)
+ v~i · i
=
· ji (t, z)
∂t
∂z
Ach,i
(3.17)
In equation 3.17 Uch is the flow channel perimeter, Ach is the flowing water cross sectional area,
and Dh the hydraulic diameter.
The main considerations taken into account in the solution of equation (3.17) are the following:
• A 1D approximation is employed.
• No diffusion across radial or azimuthal direction.
• The wall copper concentration is based on test data taken from [84] (see equation 3.15).
• Boundary condition at the entrance: cb (z=0,t=0) = 0. Neumann boundary condition at the exit
(∇cb = 0).
• No extraction is considered.
An improvement of the work presented in [85], is presented in section 5.2.
3.4
TRACT: TRansport and ACTivation code
3.4.1
Introduction
A first approach to the beam dump corrosion phenomenon was performed by modelling the
convective diffusion equation as pointed out in the previous section. Due to the simplicity of this
approach, it was considered necessary to conduct an independent study with a more complete and
validated tool like the TRansport and ACTivation code (TRACT), which has been adapted to the particular case of the LIPAc beam dump cooling channel.
The code TRansport and ACTivation (TRACT) simulates the flow and mass transport of isotopes
inside a network of 1D channels. The code handles liquid or gaseous coolants encountered in fusion devices, and treats an unrestricted number of pipe/channel materials. The model includes the
following [58]:
• Fluid flow simulation calculates pressure drops, flow velocities and pumping power in steady
state.
• Erosion and corrosion calculation of the considered geometry.
53
54
• Mass transfer of corrosion and dissolution rates of the bulk solid cooling channel material
(time and temperature). Solubility in the coolant which dictates precipitation and/or crud
formation and deposition.
• Radioactive decay (activation) of isotopes in irradiation conditions and convection downstream.
• Transmutation of the different isotopes according to the total effective flux energy weighted
reaction cross section.
TRACT has been successfully benchmarked with experimental results from the PICCOLO loop
test section at the FZK which operates with LiPb [86]. Regarding water cooling loops as that of the
LIPAc beam dump, in [87] an ITER water cooling loop calculation is presented and the results compared with previous simulations, showing that the corrosion model is well established. Further information regarding the network definition and calculation can be found in [58] and [60].
3.4.2
Corrosion modelling
The code divides each cooling circuit element in five layers: solid, corroded, fluid, crud and deposition. The solid layer is the initial bulk solid defined in the input. Corroded layer is the result of
corrosion chemical reactions between the material and the coolant. It is placed right above the solid
layer and its thickness follows a power law with time. Experimental corrosion data is introduced in
the form of an input table, and then a polynomial fit is made. Equation 3.22 presents the polynomial fit in the form of a power law with time. Further information regarding the chemistry involved
in TRACT can be found in [88]. The deposition layer is the result of the precipitation from the fluid
and crud layers. Crud particles are the corrosion residual unidentified deposits and they are formed
by a process of successive fusions, termed as coagulation. They do not dissolve, they can only precipitate and crud layer is formed by the formation of such particles. Fluid layer is the flowing fluid
domain.
When the 1D network is initialized, the fluid flow properties are calculated so they can be employed as an input for the unsteady mass transfer model. TRACT simulates model-dependent processes of corrosion, erosion, dissolution, precipitation (crud) and deposition across the five layers
for the whole length of the cooling circuit. The mathematical model employed by TRACT is described by equations 3.18, 3.19, 3.20 and 3.21.
∂ρs
∂ρs
+U
= (Gdiss − Gpre ) ·
∂t
∂x
∂ρc
∂ρc
+U
= Gcr − Gdep ·
∂t
∂x
∂
∂ρb
+
∂t
∂r
∂ρdl
= Gpre ·
∂t
4
Dh
4
Dh
4
Dh
− Gcr − Rir ρs
− Rir ρc
∂ρb
Def f
= Gb − Rir ρb
∂r
+ (Gdep − Gdiss ) ·
54
(3.18)
4
Dh
(3.19)
(3.20)
− Rir ρdl
(3.21)
55
For every isotope in the cooling network (either defined in the material and fluid composition or
produced in the transmutation process if defined), TRACT provides its density evolution by solving
the physical model expressed in equations 3.18, 3.19, 3.20 and 3.21, where:
7 x [m] and r [m] are the length along the flow direction and the radial coordinate (wall thickness)
respectively.
7 U [m/s] and Dh [m] are the flow velocity and hydraulic diameter.
7 ρ [kg/m3 ] are the densities of the different isotopes in the different layers.The different subscripts stand for, s=fluid, c=crud, b=bulk solid and dl=deposit.
7 Def f [m2 /s] is the bulk solid diffusion coefficient.
7 Gcr [kg/m3 s], Gdiss [kg/m2 s], Gpre [kg/m2 s], Gdep [kg/m2 s] and Gb [kg/m3 s] are source terms
modelling crud formation, dissolution, precipitation, deposition and production of active and
non-active isotopes in the bulk solid respectively.
7 Rir = (λ + φσ) [1/s] is the irradiation rate, being φ [n/m2 s] the neutron flux, σ the total effective (flux energy weighted) reaction cross section [m2 ], and λ [1/s] the decay rate.
The different processes involved in the corrosion modelling are the following:
Corrosion of bulk solid metal/alloy is the chemical reaction that occurs between a coolant and
the material surface. The offensive element is usually oxygen, but others like nitrogen, lithium or
chlorine result in the same generic process [58]. Equation 3.22 shows the corrosion process modelling.
Gcorr = Go ta
(3.22)
Dissolution of solid metal is the mass transfer from the bulk solid, corroded and deposited layers
into the coolant. Isotopes dissolve or precipitate following the behaviour of a single control isotope
which is defined as an input depending on the fluid material combination. The local isotope concentration (ρs ) is compared with the local solubility of the control isotope (ρsol ), in order to know
whether it dissolves (ρsol < ρs ) or precipitates (ρs > ρsol ). In the beam dump case the control isotopes are Cu for the EDP copper of the beam dump, and Fe for the stainless steel SS304 L and SS316
considered in the rest of the circuit. The loss rate of mass per unit area for either the corrosion or
deposition layer is given by equation 3.23.
dρ
= hef f (ρs − ρsol ) wf rac
dt
(3.23)
Where wf rac is the mass fraction of the control isotope in either layer. The effective mass transfer
coefficient (hef f ) combines the diffusion times of the control isotope in the corrosion and deposition layers with the mass transfer coefficient (hmtc ). All the other isotopes dissolve as long as the
55
56
control isotope dissolves. The loss rate is the following:
dρ
= hef f (ρs − ρsol ) wf rac isotope
dt
(3.24)
All variables in the right hand side of equation 3.24 are identical to those in expression 3.23, except for the weight fraction which in this case refers to each dissolving isotope.
The dissolution rate Gdiss is evaluated by means of an effective mass transfer coefficient hef f
(m/s) and the density gradient (see equation 3.25).
Gdiss = hef f (ρsol − ρs )
(3.25)
Precipitation to bulk solid, corroded and deposited layers is the soluble elements mass transfer from the coolant to the solid surface. Precipitation rate Gpre can be thought as the reverse of
dissolution and occurs when elements are oversaturated in the coolant, with ρs > ρsol [58].
Gpre = hef f (ρs − ρsol )
(3.26)
As observed in equations 3.26 and 3.25, precipitation and dissolution are mutually exclusive locally.
Crud formation is based on a coagulation coefficient Ccoag (1/s) (equation 3.27).
Gcr = Ccoag (ρsol − ρs )
(3.27)
Deposition from coolant to the deposited layer of the crud particulates formed during the transport calculation is based on the mass transfer coefficient hdep (m/s), which includes coolant and
particulate parameters [58].
Gdep = hdep ρc
(3.28)
Erosion is modelled as the removal of crud particulates from the corroded surface to the coolant.
Erosion rate is based on experimental measurements if they exist. Fer is based on surface conditions
(roughness), material and Reynolds number.
Ger = Fer Gcor
(3.29)
The set of uncoupled equations (3.18, 3.19, 3.20 and 3.21) is discretized in space by the finite
difference method. As the system is non stationary, time is discretized employing the method of
the lines approach, allowing the system of equations to decouple space and time transforming the
system in many one-dimension subproblems [89]. This permits any discretization technique applicable to an initial value problem. The system of differential algebraic equations (DAE) is solved
employing a prediction-corrector method, based on the Leapfrog algorithm in which the predicted
56
57
value is corrected at each time step once the linear system of algebraic equations is solved.
3.4.3
Adaptation to the beam dump corrosion modelling
TRACT has been adapted to the particular case of the LIPAc beam dump cooling channel. The
following changes and additions had to be made:
7 The code could only handle constant channel width while the beam dump has a variable cooling channel geometry (see figure 4.12). Velocity and pressure profiles along the beam dump
modify the overall corrosion and transport processes, therefore the code has been adapted to
accommodate variable cooling channel geometries.
7 A new friction parameter algorithm more adequate to the beam dump case has been implemented. The Darcy-Weisbach friction factor expression (see section 2.1.3 for a detailed explanation) obtained using the approximation of the Colebrook equation performed by Goudar
and Sonnad [29] has been introduced in the code.
7 The TRACT code has been modified to allow each node of the circuit element to have a different temperature value instead of assuming a mean value between the inlet and outlet of each
cooling element. As temperature plays a key role over the solubility values, it is important
being able to consider a variable temperature profile along the beam dump cartridge.
7 The code output has been extended to include:
– Hydraulic and geometric parameters like Reynolds number, variable velocity profiles or
hydraulic diameters.
– Chemical properties such as pH, partial pressures and oxygen concentration
57
Chapter
4
DESIGN AND ANALYSIS OF THE BEAM
DUMP COOLING CIRCUIT
The beam dump cooling system is designed to absorb a total power of 1.125 MW coming from
the 125 mA, 9 MeV deuteron beam. 1D and 3D studies have been performed to define the cooling
geometry and flow parameters. The results shown in this chapter have determined the beam dump
cartridge design and its cooling system. The obtained heat transfer coefficients have been used as a
contour condition for the mechanical analysis. 1
4.1
Input data and design requirements
As a reminder of the beam dump cartridge cooling system, figure 4.1 shows how the water enters
by the tip support, goes through the annular cooling channel conformed as explained by the inner
cone and the shroud until it reaches the cone base where the water flows into the space left between
the shroud and the cylinder. It then flows in counter back direction towards the exit of the cartridge.
The water temperature at the inlet is determined by the secondary cooling circuit. A value of 31
o
C has been assumed given that the secondary circuit guarantees a maximum water temperature at
the heat exchanger inlet of 27 o C.
The main input for the beam dump design is the power deposition profile. This profile depends
on the beam shape at the entrance of the beam dump and therefore on the accelerator design and
operation conditions. The beam profile at the beam dump entrance plane (see figure 4.3) has been
obtained from beam dynamics simulations. It is quasi-symmetric with rms x and y sizes of 39.782
and 39.664 mm respectively, and a maximum size of 123.17 mm in the X axis and 144.67 mm in the
Y axis [20]. Thanks to the low incidence angle, the power deposition density on the beam dump
surface is much lower. Figure 4.2 represents the azimuthally averaged heat deposition profile for the
nominal case, which is the one employed for the 1D and 3D studies presented in this thesis.
1 The 1D and 3D results presented in this chapter take the axial coordinate origin (z=0) at the inner cone tip.
59
60
Chapter4. DESIGN AND ANALYSIS OF THE BEAM DUMP COOLING CIRCUIT
Figure 4.1: Beam dump cartridge water flow.
250
Heat deposition
Pdep [W/cm2]
200
150
100
50
0
0
0.5
1
1.5
2
2.5
z [m]
Figure 4.2: Beam dump nominal power deposition (average).
The shape of the curve in figure 4.2 corresponds to the stopping of the diverging beam by a cone.
Near the tip (z = 0) this shape is affected by particle backscattering. The angle of incidence of the
ions is so low that some of them come out of the wall before being completely stopped. The total
backscattered power is not high but due to the conical geometry of the beam dump, as the tip support is approached, power has to be stopped in a smaller area. Hence a heat density increase in the
vicinity of the tip is observed.
The maximum deposited power density is found in the region between z = 1 m and z = 1.5 m,
60
4.1. Input data and design requirements
61
Figure 4.3: Transversal sections in x and y planes of the beam at the beam dump entrance.
where a peak power deposition of 203 W/cm2 is reached. Note that the maximum local power density will be higher because the power density curve employed is an azimuthal average of the power
densities at each axial coordinate.
The design requirements are the following:
1. The coolant must be liquid water, no two phase flow. Pressure at the inlet must guarantee such
condition.
2. Copper temperature must be lower than 150 o C (figure 4.4). This is a very conservative limit
which assures a moderate corrosion.
3. The inlet pressure must be such that no buckling issues in the long and thin inner cone arise
as a consequence of an excessive pressure value.
4. Avoid high erosion values in the cooling channel. The velocity must be high enough to cool
down the piece without reaching a boiling situation and at the same time not too high to avoid
erosion phenomena.
5. Allow the detection of out range situations by bubble noise monitoring. The cooling system
design has been set to operate in a regime close to coolant boiling but without reaching such
situation. Operating close to the boiling point allows having a closer control of the device.
When the first bubble appears and it is detected by hydrophones immersed in the cartridge
cooling water, a signal will be sent to the accelerator control system to warn of abnormal operation [20].
61
62
6. Manufacturing feasibility. Realistic manufacturing tolerances lead to a cooling channel width
of at least 5 mm.
Tsb
Ts
120
T [oC]
100
80
60
40
0
0.5
1
1.5
2
2.5
z [m]
Figure 4.4: Cu-water (Tsb ) and Cu-beam (Ts ) interface temperatures.
4.2
1D Analysis
4.2.1
Introduction
The geometry and flow parameters of the beam dump cooling circuit have been chosen to fulfil
the design criteria mentioned in section 4.1.
The design process is presented in figure 4.5. Preliminary thermomechanical and radio protection analysis together with manufacturing considerations are taken into account when proposing
an initial beam dump geometry. Pressure at the beam dump entrance is chosen based on buckling
analysis. Then different flow rates are tried obtaining the velocity and heat transfer coefficient values, and hence the inner cone temperature. The margin to boiling depends on the temperature and
on the local pressure values, determined by the inlet pressure and the pressure loss along the cone.
Depending on these values and according to the design criteria (check boiling margin), the flow is
provisionally validated or not. The process is repeated for different flow and pressure values until
the highest margin to boiling is obtained. This is explained in more detail in the following sections.
To perform this analysis the CHICA code described in section 3.1 has been employed.
62
4.2. 1D Analysis
63
Design
Tin
Fabrication
v, h
Geometry
Tsb
Margin boiling
V uniform
P
Pin
Flow
Figure 4.5: Beam dump cooling design scheme.
4.2.2
Choice of geometry
V
IV
III
II
I
Figure 4.6: Inner and outer radii of the beam dump annular channel.
63
64
The coolant channel geometry has been chosen to obtain sufficient velocity avoiding too high
values which can produce vibrations and material erosion, and too low ones which would cause a
poor heat transfer. A high velocity is needed specially at the regions of higher power deposition (from
the cone tip to the middle of the beam dump), where a large heat transfer rate between material and
coolant is required to limit the coolant-material interface temperature (Tsb ) and consequently the
required water pressure. To maintain the velocity along the beam dump it is necessary to reduce the
coolant channel width progressively to compensate the increasing cone radius.
0.024
Cooling channel thickness
0.022
0.02
Thickness [m]
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0
0.5
1
1.5
2
2.5
z[m]
Figure 4.7: Beam dump cooling channel thickness.
Therefore the shroud is divided into five zones (see figure 4.6). The first is an annular section 0.2
m long, sections II, III and IV are formed by the three truncated cones, while section V is caused by
the 1.5 mm thickness increase of the inner cone which takes place in the last 500 mm to increase
buckling resistance (see section 1.3).
Due to fabrication tolerances the cooling channel width in long pieces such as the beam dump
must be larger than 5 mm. A 7 mm minimum gap value was chosen for most of the beam dump
length (figure 4.7).
The channel width evolves from 23 mm at the inlet down to 7 mm at the outlet (see figure 4.7).
Figure 4.8 shows the inverse beam dump cooling channel cross sectional area which determines
together with the mass flow the water velocity. It can be seen that with the chosen channel geometry,
the flow cross sectional area is maintained inside a given range and it is only allowed to increase in
the last 50 - 70 cm of the cone, near its aperture, where the beam power density becomes smaller
(figure 4.2).
64
4.2. 1D Analysis
65
280
1/A
260
1/A [m2]
240
220
200
180
160
140
0
0.5
1
1.5
2
2.5
z[m]
Figure 4.8: Inverse beam dump cooling channel cross sectional area.
4.2.3
Choice of flow and pressure
Flow [kg/s]
25
26
27
28
29
30
31
35
40
Tsb max [o C]
96.75
94.69
92.75
90.91
89.23
87.61
86.11
80.79
75.47
Psat [bar]
1.121
1.004
0.934
0.865
0.803
0.754
0.709
0.563
0.445
P [bar]
3.078
3.045
3.011
2.977
2.940
2.903
2.865
2.699
2.464
∆P [bar]
1.956
2.040
2.066
2.111
2.136
2.148
2.155
2.135
2.018
Table 4.1: Values of T at the water-material interface (Tsb ), saturation pressure (Psat ), pressure (P) and
∆P = P - Psat at the location of maximum Tsb for different flows.
A pressure of 3.5 bar has been found reasonable to obtain a safety margin to buckling around
9.1 [20].The higher the flow, the higher the velocity and the film transfer coefficient and therefore
the lower the surface temperature in contact with the coolant Tsb , and consequently the required
pressure to avoid boiling. However for very high velocities the pressure losses due to friction increase
significantly. Therefore there is an optimum flow rate for which the margin to boiling is maximum
along the cartridge.
65
66
2.16
Minimum P-Psat
2.14
2.12
Min(P-Psat) [bar]
2.1
2.08
2.06
2.04
2.02
2
1.98
1.96
1.94
24
26
28
30
32
34
36
38
40
Q [kg/s]
Figure 4.9: Minimum margin to saturation along the beam dump for different water flows.
In table 4.1 the results obtained with the selected geometry are presented for the different water
flows. Figure 4.9 represents the minimum margin to saturation as a function of the water flow. An
optimum flow rate around 30 kg/s has been found.
Therefore a mass flow rate of 30 kg/s is chosen for the beam dump cooling circuit.
4.2.4
Surface roughness
The influence of surface roughness on the film transfer coefficient value has been studied. The
film transfer coefficient and Tsb variation from a smooth wall situation to a rough pipe with a roughness of 6.5 µm, is presented in figures 4.10 and 4.11. A 4000 W/o C m2 HTC difference between the
smooth case and the 6.5 µm roughness case is observed. The higher the wall surface roughness, the
higher the HTC but also higher pressure losses.
For the 6.5 µm roughness value, the observed increment in the film coefficient produces a decrease in the maximum surface temperature of 9 o C with respect to that corresponding to a smooth
surface (figure 4.11), whereas it will be seen in section 4.2.5 the pressure loss increment with respect
to the smooth channel is small (0.13 bar).
Therefore a 6.5 µm surface roughness has been chosen as a compromise between high HTC values and an acceptable pressure loss. From now on the presented results are calculated assuming a
6.5 µm roughness.
66
4.2. 1D Analysis
67
45000
HTC smooth pipe
HTC 6.5 µm roghness
HTC 1.5 µm roghness
110
Tsb for smooth pipe
Tsb for 6.5 µm roughness
Tsb for 1.5 µm roughness
40000
100
80
30000
70
Tsb [oC]
h [W/m2 oC]
90
35000
60
25000
50
20000
40
30
15000
0
0.5
1
1.5
2
2.5
0
0.5
1
1.5
2
2.5
z [m]
z [m]
Figure 4.10: Heat transfer coefficient for different Figure 4.11: Temperature profile at surface bulk inroughnesses.
terface for different roughnesses.
4.2.5
Results of the 1D beam dump cooling analysis
With a mass flow of 30 kg/s, the water in the beam dump cooling channel reaches speed values
up to 8.2 m/s. There is a wide region from the tip up to z = 1.25 m where the heat deposition is more
significant, reaching speeds around 8-7.5 m/s. Downstream that point the water flow speed diminishes following the trend of the heat deposition curve. This can be clearly observed in figure 4.12.
9.5
Velocity (m/s)
44000
Velocity profile
Film coefficient
42000
9
40000
8.5
38000
8
36000
7.5
34000
7
32000
6.5
30000
6
28000
5.5
26000
5
24000
4.5
22000
4
h [W/m2 oC]
10
20000
0
0.5
1
1.5
2
2.5
z [m]
Figure 4.12: Velocity and film transfer coefficient profiles.
The following figures show the water temperature Tb (figure 4.13), temperature of the cone surface in contact with the coolant Tsb (figure 4.14), Reynolds number (figure 4.15) and water pressure
67
68
P for a 6.5 µm roughness and a smooth pipe (figure 4.16) as a function of the axial coordinate z.
The water temperature experiences a 9.14 o C increment between the entrance and the cone base
(figure 4.13), resulting in an outlet temperature of 40.14 o C. Maximum inner cone temperature at the
copper-water interface (Tsb ) is 87.12 o C at around z=1.5 m. This value is the closest point to boiling
regime and presents as stated in table 4.1 a 2.148 bar margin with respect to the saturation pressure,
ensuring that no boiling occurs along the beam dump under nominal beam conditions. Reynolds
number decreases steadily from the entrance (425000) to the exit of the cooling channel (values
around 100000) as seen in figure 4.15.
41
Bulk temperature profile
Inner cone temperature profile
90
40
39
80
36
60
35
Tsb [oC]
70
37
50
34
33
40
32
31
30
0
0.5
1
1.5
2
2.5 0
0.5
z[m]
450000
1
1.5
2
Figure 4.14: Cu-water interface temperature (Tsb ).
Reynolds number
400000
350000
300000
250000
200000
150000
100000
50000
0
2.5
z[m]
Figure 4.13: Coolant temperature profile (Tb ).
Re
Tb [oC]
38
0.5
1
1.5
z [m]
Figure 4.15: Reynolds number profile.
68
2
2.5
4.2. 1D Analysis
69
Pin
Pout
Figure 4.16: Pressure profiles along the beam dump.
The pressure loss due to friction along the cooling channel, and local pressure drops at the tip
region (klocal = 1.05) 2 , and at the water return (klocal = 2.8) 3 cause a total pressure loss of 0.98 bar.
The klocal values have been obtained from the 3D simulations and the total value has been crosschecked against the experimental cooling loop measurements presented in section 6.3.2. In figure
4.16 the pressure loss profile for a smooth pipe situation is also shown.
The critical heat flux has been estimated in two ways as explained in section 2.2.
• By means of the Boscary correlation (CHFcorr ).
• Employing the Groeneveld database adapted by Doerffer et al. for the annular geometry of the
beam dump (CHFtab ).
In figure 4.17 the critical heat flux values calculated by the two selected methods, together with
the heat deposition profile are plotted. Critical heat flux is at least 3 times higher than the expected
heat deposition, being 2.5 times higher in most of the beam dump cooling channel. It is seen how
the Doerffer equation yields in general lower values than those predicted by the Boscary correlation
with the exception of the 1.5 mm step, where a sudden increase of velocity happens. The heat flux
required to reach the saturation temperature at the material-water interface is also shown in figure
4.17.
It can be observed that the margin is not too big so abnormal operation will be detected well before
2 This value comes from the 3D simulation of the tip support (see section 4.3)
3 This value comes from the 3D simulation of the water return (see section 4.3)
69
70
1000
Nucleate boiling
Heat deposition
Correlated CHF
Tabulated CHF
900
800
Q [W/cm2]
700
600
500
400
300
200
100
0
0
0.5
1
1.5
2
2.5
z[m]
Figure 4.17: CHF, Nucleate boiling and heat deposition profiles.
critical heat flux is reached and therefore well before its catastrophic failure.
Although as pointed out in section 3.1 the water return influence on the beam dump cooling can
de discarded, some calculations have been performed. The water return velocity and film transfer
coefficient are presented in figure 4.18. Although the velocities reached are quite low compared with
the ones obtained in the annular cooling channel (see figure 4.12), the Reynolds number is still turbulent and hence Petukhov-Gnielinski film transfer coefficient correlation has been employed.
41
Shroud average temperature profile
40
39
Tsh (oC)
38
37
36
35
34
33
32
31
0
0.5
1
1.5
2
z [m]
Figure 4.19: Average shroud temperature profile.
70
2.5
4.2. 1D Analysis
71
4500
Velocity
Film coefficient
0.8
4000
0.7
3500
0.6
3000
0.5
2500
0.4
2000
0.3
1500
0.2
h [W/m2 oC]
Velocity (m/s)
0.9
1000
0
0.5
1
1.5
2
2.5
z [m]
Figure 4.18: Velocity and film transfer coefficient profiles for the water return.
In figure 4.19, the average shroud temperature profile (Tsh ) is presented. There is a certain
amount of heat (equal to h · (Tsh - Tret )) being transferred from the water return towards the annular cooling channel. Such heat causes a small increment in the bulk temperature of 0.1 o C at the
cooling channel, hence not affecting the beam dump cooling design.
4.2.6
Final considerations
45000
Boiling film coefficient
Nominal film coefficient
40000
1
Deltah/h
0.9
0.8
30000
25000
0.7
20000
0.6
15000
Deltah/h
h [W/m
2o
C]
35000
0.5
10000
0.4
5000
0
0.3
0
0.5
1
1.5
2
2.5 0
z[m]
0.5
1
1.5
2
2.5
z [m]
Figure 4.20: Nominal and boiling heat transfer coef- Figure 4.21: Relative heat transfer coefficient margin
ficients.
to nucleate boiling.
The film coefficient value determines the temperature of the copper in contact with water. It
is therefore very important to make an accurate estimation of this parameter. The film transfer
71
72
coefficient values which will lead to the onset nucleate boiling have been calculated for every point
of the beam dump cooling channel (figure 4.20). An idea of the maximum uncertainty allowable
in the estimation of the film transfer coefficient can be obtained from the difference between this
value, which represents the minimum HTC needed to avoid boiling, and the nominal one. Figure
4.21 shows that an uncertainty of less than 40 % is required.
4.2.7
Cooling for beam powers lower than nominal
During commissioning the accelerator will operate with pulsed beams. The power during each
pulse will be the maximum (1.125 MW), but average power will be much lower as small duty cycles
will be used. The water flow through the beam dump will decrease accordingly. The objective of this
flow adjustment is two-fold:
1. To obtain material temperatures close to those of nominal operation, so that also in this situation with smaller power the boiling detection can be used as a monitor of off-normal beams.
Even though these off-normal beams at low duty cycle may not pose any risk to the beam
dump, their detection will allow to increase safely the duty cycle up to full power.
2. To avoid unnecessary erosion of the copper cones with the high velocity water flow.
Duty cycle (%)
CW
50
10
1
Flow (kg/s)
30
15
2.2
0.4
Ts (o C)
133
109
96
95
Tsb (o C)
88
86
93
94
Stress (MPa)
64.3
38
16.4
7.99
Table 4.2: Temperature and stress values for the different duty cycles.
Table 4.2 shows the proposed flow values for typical pulsed beams with different duty cycles,
together with the maximum inner cone temperature (beam (Ts ) and coolant (Tsb ) sides) and maximum stress values.
For a 1% duty cycle, the proposed flow rate is 0.4 kg/s. Therefore the flow regime changes from
turbulent to laminar. In the analysis Petukhov-Gnielinski correlation for the turbulent regime, Levenspiel correlation [90] for the transitional regime (2300 < Re < 10000), and Shah correlation [91]
for the laminar regime have been the chosen applied correlations.
The Petukhov-Gnielinski correlation has already been presented in section 2.1.2 (see equation
2.16). The Levenspiel correlation for transitional flow including the viscosity variation with temperature developed by Sieder and Tate has the following form:
0.11
µ
N u = 0.116 Re2/3 − 125 P r1/3
µs
72
(4.1)
4.2. 1D Analysis
73
25000
50 %
10 %
1%
h [W/m2 oC]
20000
15000
10000
5000
0
0
0.5
1
1.5
2
2.5
z [m]
Figure 4.22: Film transfer coefficient for the different duty cycles.
In the Shah correlation depending on the dimensionless parameters one of the two expressions
has to be employed, being D the hydraulic diameter and L the length of the cone:
D
N u0 = 1.953 ReP r
L
1/3
;
D
ReP r
L
≥ 33.3
(4.2)
D
D
N u0 = 4.364 + 0.0722 ReP r
; ReP r
< 33.3
L
L
(4.3)
In figures 4.22, 4.23 and 4.24 the film transfer coefficient, water temperature Tb and copper-water
interface temperature Tsb profiles are plotted. It is observed that maximum temperatures are similar
to those of the 100 % duty cycle case. Therefore adjusting the water flow to 15 kg/s, 2.2 kg/s, and 0.4
kg/s for the 50 %, 10 %, and 1% duty cycles respectively, allows the boiling detection to be employed
as a monitor of off normal beams.
Tb [oC]
42
100
50 %
10 %
1%
50 %
10 %
1%
90
40
80
38
70
36
60
34
50
32
40
30
30
0
0.5
1
1.5
2
2.5
z [m]
0
0.5
1
1.5
2
2.5
z [m]
Figure 4.23: Bulk temperature profiles.
Figure 4.24: Inner cone temperature (Tsb ) profiles.
73
Tsb [oC]
44
74
4.3
Detailed 3D analysis
3D CFD calculations with the ANSYS CFX code have been performed in order to cross-check the
analytical results and analyse local areas in which the 1D approximation is not valid, such as the
beam dump entrance, the 180o turn at the cone aperture and the vicinity of obstacles in the flow like
the cone tip support or the presence of thermocouples across the annular cooling channel [92]. The
obtained results have been used to validate the beam dump detailed design (thickness variation of
the inner cone, 180o turn) and to optimize when needed the design from the cooling point of view
(tip support geometry, straight pipe section at the entrance). The general analysis procedure has
been explained in section 3.2.
4.3.1
Introduction
SST and k-epsilon turbulence models have been employed in the simulations. The enhanced
formulation for the boundary layer should make SST better suited for this analysis [93]. As it will
be explained in the next section (4.3.2), SST turbulence model has been the chosen one for all the
cases presented. The heat deposition profile employed in the simulations is the 1D, axisymmetric,
averaged one used in the former section (figure 4.2).
In table 4.3 a summary of the most relevant model parameters for each case analysed is shown.
The results of the analysis of these six cases are summarized in sections 4.3.3.1 to 4.3.3.6.
Case
Tip support
180o turn
Length of pipe
Manufacturing tol.
Cone thickness
Thermocouples
Mesh size [mm]
2.3
2.3
2.3
1.5
1.5
2
Infl. layers
10
5
5
7
7
8
First prism [mm]
0.01
0.0527
0.1
0.01
0.01
0.01
Exp. factor
1.2
1.0001
1.2
1.2
1.2
1.2
Turb. int.
5%
5%
5%
5%
5%
5%
Table 4.3: CFX model parameters.
4.3.2
Comparison with 1D analysis. Turbulence model influence
Given the strong dependence of the estimated material temperatures and the required coolant
pressure on the correlation employed to calculate the film transfer coefficient (h), it is important
to verify its adequacy. The correlation employed in the beam dump cooling design is the one of
Petukhov-Gnielinski. CFD analysis allows a different estimation of the film transfer coefficient value.
Therefore CFX simulations were launched in order to compare the heat transfer coefficient values
from the correlation with the ones obtained with this method. Several turbulence models (k-epsilon,
SST (Shear Stress Transport) and BSL-RSM (Baseline Reynolds Stress Model)) have been used for the
heat transfer coefficient estimation.
As CFX takes the temperature of the first nodes to calculate the HTC, the accuracy is low. Therefore the temperature profile has been employed to calculate the heat transfer coefficient by means
74
4.3. Detailed 3D analysis
75
of equation 2.5. The obtained coefficient has been designated as alternative heat transfer coefficient
to differentiate it from the one calculated directly by CFX. Figure 4.25 shows the temperature at the
surface in contact with water obtained with different turbulence models These are then employed
to calculate the alternative HTC.
390
Petukhov
BSL-RSM
SST
k-ε
380
370
T [K]
360
350
340
330
320
310
5.0⋅104
1.0⋅105
1.5⋅105
2.0⋅105
2.5⋅105
3.0⋅105
3.5⋅105
4.0⋅105
Re
Figure 4.25: Temperature profile for the different turbulence models.
45000
36000
Petukhov
BSL-RSM
SST
k-ε
40000
Petukhov
BSL-RSM-alt
SST-alt
k-ε-alt
34000
32000
h [W/m2 K]
h [W/m2 K]
30000
35000
30000
28000
26000
24000
22000
25000
20000
20000
5.0⋅104
1.0⋅105
1.5⋅105
2.0⋅105
2.5⋅105
3.0⋅105
3.5⋅105
4.0⋅105
18000
1.0⋅105
1.5⋅105
2.0⋅105
Re
2.5⋅105
3.0⋅105
3.5⋅105
4.0⋅105
Re
Figure 4.26: HTC for the different turbulence models Figure 4.27: HTC for the different turbulence models
(CFX output).
based on temperature calculations.
An inner cone model was selected to test the different turbulence models. The model characteristics are the following:
• A 120◦ section of the inner cone is simulated.
• Boundary condition at the entrance: 7.05 m/s water speed.
• Boundary condition at the exit: 2.2994 bar average static pressure.
• Smooth wall.
75
76
In figures 4.26 and 4.27 the heat transfer coefficient obtained directly from CFX and the alterna-
tive one are compared with the Petukhov-Gnielinski results. Differences of the order of ± 10% are
found, less than the 40% maximum uncertainty that can be allowed (see section 4.2.6), thus with
these simulations confidence is gained on the heat transfer coefficient values used for the beam
dump cartridge and cooling system design.
It is observed that SST turbulence model is the one that best matches the Petukhov-Gnielinski
correlation results, while k- and RSM models overestimate and underestimate respectively the PetukhovGnielinski data. As SST turbulence model gives the closest values to our heat transfer coefficient
reference data with a dispersion in the calculated value of less than 9%, this model has been the
chosen turbulence model for the beam dump CFX simulations. To sum up, SST turbulence model is
the one employed in the following sections because:
• It is in principle more precise [93].
• Gives closer values to the Petukhov-Gnielinski correlation which is our design reference for the
heat transfer coefficient.
• Gives a lower HTC compared with the other models and hence it represents a conservative
assumption.
4.3.3
Detailed analysis of special regions
4.3.3.1
Tip support
As it was explained in section 1.3, the tip of the cone is supported on the shroud through the
tip support piece in such a way that axial displacement is allowed, while azimuthal and radial displacements are restricted. The goal of the CFX simulation is to optimize the design of the tip and its
support from the hydraulic point of view and check the maximum temperature in the material and
the fluid behaviour taking into account the 2D heat transfer expected in this area.
Figure 4.28 shows the geometry of the tip and its support, formed by three blades and a crown immersed into the coolant flow. The simulated region comprises 300 mm prior to the tip support up
to 900 mm downstream of the tip. The boundary conditions imposed are a water flow velocity at the
entrance of 7.05 m/s and an average static pressure at the exit of 3.21 bar. An inlet water temperature
of 304 K is considered.
The mesh characteristics are presented in table 4.3. The Yplus value in the tip region ranging
from 1 to 4 can be observed in figure 4.29.
76
77
Figure 4.28: Tip support geometry.
Figure 4.29: Yplus parameter in the tip region.
Figure 4.30: Pressure profile in the tip region.
The tip design has been optimized trying to avoid too high fluid velocities, low pressure regions
and stagnant flow zones. Different blade geometries varying the front radius r and the length along
the flow L have been tested trying to minimize the perturbation on the flow. A final choice of r =
3mm and L= 45 mm was made. A pressure loss of 0.218 bar is caused by the tip support (figure 4.30).
This value has been used for the total pressure loss estimation in the cartridge (section 4.2.5).
77
78
Figure 4.31: Temperature profile (Tsb ) along the beam dump
No hot points, stagnant flow or low pressure regions are created at the wake caused in the flow
by the cone tip and its support. However higher material temperatures are observed along this wake
(see figure 4.31) although the perturbation is reduced as water flows downstream towards the model
exit.
4.3.3.2
180o turn
The region where the water passes from the cooling channel to the space between the shroud
and the cylinder reversing direction has been simulated. In figure 4.32 a detail of the 180o turn is
shown. The main goals of this study are:
1. Estimate the film transfer coefficient at this region where the 1D approximation is not valid.
This parameter determines the flange cooling and has been used as input for the mechanical
analysis.
2. Verify that the 180o turn in the water flowing direction does not cause any serious disruption
on the flow.
78
79
Stainless steel cylinder
Shroud
Detail A
A
Inner cone
180º turn
Figure 4.32: 180o turn detail in the beam dump.
Figure 4.33: Streamlines in the beam dump water 180o turn passage through the shroud.
The nominal deposited power in the flange is 166.3 W. For the calculations a worst possible case
has been considered in which the beam divergence is 10 % greater than the nominal one producing
a 1313 W deposition at the flange.
A 300 mm long, 90o section of the cone base has been simulated. The boundary conditions considered are a velocity of 5.11 m/s at the inlet and an average static pressure of 2.545 bar at the model
exit. An average bulk temperature at the inlet of 313.6 K is considered. The mesh characteristics are
shown in table 4.3.
79
80
In figure 4.33 the water streamlines can be observed as they flow through the shroud orifices. An
acceptable temperature profile is obtained at the flange (figure 4.34) showing that the film transfer
coefficient (average value of 12390 W/m2 K) guarantees the flange cooling needs.
Figure 4.34: Temperature profile in the flange.
Figure 4.35: Pressure profile through the orifices.
The pressure loss caused by the shroud orifices is approximately 0.35 bar as seen in figure 4.35.
This pressure loss value has been employed to estimate a local pressure loss value (klocal ) for the 1D
simulations (section 4.2.5).
4.3.3.3
Length of straight pipe at the beam dump entrance
Figure 4.36: Streamlines for the 1.5 m length simulation
80
81
This study has been performed to determine the initial straight tube length before the beam
dump entrance so that a stable and well developed flow is obtained. A 3” diameter schedule 10s
(82.8 mm inner diameter) pipe with a 90o bend is modelled. Different pipe lengths between the
bend and the cone tip position have been tested, 600 mm, 800 mm, 1000 mm and 1500 mm. A 300
mm straight pipe length prior to the 90o bend is modelled. An inlet velocity of 5.57 m/s, which corresponds to the 108 m3 /h nominal flow, and an outlet average static pressure of 3.5 bar have been
used as boundary conditions together with a pipe roughness of 6.3 µm.
Figure 4.37: Axial velocity profile (v ) at the beam dump entrance.
Figure 4.38: u velocity component profile at the beam Figure 4.39: w velocity component profile at the
dump entrance.
beam dump entrance.
In figure 4.36 the global velocity is plotted for the 1.5 m straight pipe case. It is seen that the 90o
bend affects the water velocity profile increasing the velocity value up to 7.9 m/s at the inner side of
81
82
the bend.
In figures 4.37, 4.38 and 4.39, the axial (v), y component (u) and z component (w) of the velocity
at the exit of the simulated volume (right at the beam dump entrance) are plotted. It can be seen
that the contribution of the the transversal components (u and w) to the overall velocity is very
small (maximum u is 0.13 m/s and maximum w is 0.24 m/s representing 2.3 % and 4.3 % of the total
velocity respectively). The axial velocity profile shows a zone with a velocity decrease down to 4.5
m/s due to the 90o elbow (see figure 4.36). Therefore, although the water flow still shows a disturbed
pattern, the perturbation is small and the water flow can be considered almost homogeneous.
4.3.3.4
Effect of manufacturing and mounting tolerances
Both the inner cone and the shroud of the beam dump require a great precision in its manufacturing and mounting in order to keep the geometrical tolerances within a close margin. Inaccuracies
in the fabrication process can lead to deviations in the cooling channel and therefore variations in
the cooling design parameters. The most critical part was on z = 2000 mm where nominal cooling
channel thickness is 5.5 mm.
A prototype has been built to test the design. After the prototype delivery deviations were measured. The observed relative deviations between the axes of the two pieces in the region around z =
2 m are close to 0.65 mm. Depending on the mounting procedure a deviation up to 2.5 mm could
be observed. In the first case cooling channel width at z = 2 m changes azimuthally in the range of
7 ± 0.65 mm, whereas in the second case the width varies between 4.5 and 9.5 mm.
Figure 4.40: Velocity profile at z = 1.5 m for the 0.65 Figure 4.41: Velocity profile at z = 1.5 m for the 2.5
mm case.
mm case.
The two cases have been simulated in order to study the effect on the flow of the measured deviations. The model comprises 1.2 m, from z = 1.2 m to z = 2.4 m. In this case the mesh spacing
has been decreased to 1.5 mm so that a good resolution is guaranteed specially where the cooling
channel narrows down to 4.5 mm.
82
83
Initial and boundary conditions on both models are the following:
• Velocity at the inlet: 7.97 m/s.
• Average static pressure at the exit: 2.67 bar.
• Initial temperature: 307.93 K.
• Wall roughness: 6.5 µm.
The velocity profile is affected by the cooling channel width variation and hence the heat transfer
coefficient, the water-material temperature and the pressure profile.
In figures 4.40 and 4.41 the velocity distribution in a perpendicular plane to the water flux, corresponding to z = 1.5 m is presented. For the 0.65 mm deviation the velocity profile suffers slight
changes, while in the 2.5 mm deviation case, velocity varies from 7.83 m/s in the wider part of the
cooling channel down to values close to 6.1 m/s in the narrower part.
Case
2.5 mm shift
0.65 mm shift
0 mm shift
narrow zone
wide zone
narrow zone
wide zone
Symmetric
u (m/s)
6.15
7.83
7.05
7.5
7.5
P (bar)
2.97
3.09
3.04
3.07
2.5
Tsb (K)
359.95
358.95
359.65
358.85
359.15
v (m/s)
-0.501 /
0.501
-0.445 /
0.443
-0.44 / 0.443
w (m/s)
-0.376 /
0.471
-0.422 /
0.449
-0.44 / 0.439
Table 4.4: Parameters of the 0.65 mm, 2.5 mm and 0 mm deviation cases at z = 1.5 m.
From the data of table 4.4 it is seen that the heat transfer coefficient decreases in the narrow section and increases in the wide one with respect to the value for the nominal geometry. The effect is
larger the higher the considered deviation.
However, even in the worst case for the beam dump cooling (narrow region in the 2.5 mm deviation), the heat transfer coefficient reduction is not large (less than 10 %). Therefore no cooling
problems are expected.
It must be pointed out that better manufacturing tolerances than those analysed here can be
achieved with present machinery and manufacturing techniques.
4.3.3.5
Inner cone thickness variation
The thickness change of the inner cone at z = 2 m causes a reduction in the cooling channel
width. It is done increasing the inner cone thickness gradually with a slope of 0.1 (15 mm in the
horizontal). Further details are found in section 1.3.
The same geometry and mesh model as the one employed in the non deviation case of the previous section has been employed to analyse the inner cone thickness variation.
83
84
Figure 4.42: Water velocity at plane z = 1.95 m.
Figure 4.43: Water velocity at plane z = 2.01 m.
An inlet velocity of 7.97 m/s and an outlet average static pressure of 2.67 bar have been considered
together with a water flow inlet temperature of 307.93 K and a wall roughness of 6.5 µm.
The velocity profile at a plane 5 cm prior to the step (z = 1.95 m) and at a plane 1 cm downstream
the step (z = 2.01 m) are shown in figures 4.42 and4.43. The step causes an increase in the velocity
from 5.4 m/s to 6.7 m/s due to the cross section area decrease, but the velocity profiles are homogeneous across the annular channel.
Furthermore the simulation shows that the step does not provoke any flow return or other significant perturbation.
4.3.3.6
Thermocouples
Monitoring the temperature of the copper cone surface in contact with the water Tsb has been
thought as a possibility to check the correct functioning of the beam dump and its cooling system.
Several arrays of four thermocouples each, placed in different axial positions along the beam dump
could be employed so that differences between the thermocouples readouts of the same set could
mean that the beam is not correctly aligned.
The effect of placing thermocouples across the beam dump cooling channel can not be studied
with 1D codes. The thermocouples should be inserted through the shroud, protected with an external case and fixed to the inner cone by means of a micro metric hole on the inner cone surface (see
figure 4.44). To begin with, a 5 mm diameter thermocouple was considered. Even though the results
did not discourage the 5 mm choice, a simulation with a 1 mm thermocouple was also carried out.
The two analysed cases share the same geometry and mesh model except for the thermocouple
diameter so that comparison between both models is straight. A 375 mm, 90o section of the beam
dump has been modelled, corresponding to the axial coordinates between z = 0.4 m and z = 0.775
m. The boundary condition at the model entrance is a velocity of 7.03 m/s, while at the model exit
84
85
Plano de visión
Cono interior
Flujo de agua
Cono exterior
Termopar
Figure 4.44: Thermocouple installation layout.
an average static pressure of 2.842 bar is imposed. An average initial temperature of 304.37 K is
considered in the water.
Figure 4.45: Velocity profile around the thermocouple for the 5 mm case.
85
86
Figure 4.46: Velocity profile around the thermocouple for the 1 mm case.
In figure 4.45 the velocity profile in a plane immediately downstream (see figure 4.44) the 5 mm
thermocouple (z = 0.505 m, 105 mm from the model inlet) is shown. As seen, the thermocouple
disturbs the water flow creating eddies and affecting the velocity profile. Due to these eddies a flow
reversal downstream the thermocouple occurs at the upper and lower parts of the cooling channel.
Figure 4.47: Temperature profile on the inner cone Figure 4.48: Temperature profile on the inner cone
for the 1 mm case.
for the 5 mm case.
When analysing the velocity profile in the 1 mm thermocouple case it is observed that the flow
disruption is much lower. Figure 4.46 shows that no eddies are formed due to the thermocouple.
The velocity components are disturbed but no flow reversal is observed.
86
87
The velocity profile affects the heat transfer coefficient and therefore the temperature distribution. Figures 4.47 and 4.48 represent the temperature profile over the inner cone surface for the two
cases analysed. It is seen that the temperature perturbation caused by the 5 mm thermocouple is
greater than the one caused by the 1 mm thermocouple.
To sum up, the presence of thermocouples disturbs the water flow affecting the velocity profile
and hence the heat transfer coefficient and temperature profiles. The 1 mm diameter thermocouple
perturbation seems to be acceptable for the beam dump cooling. However it has been decided that
no thermocouples will be present in the beam dump annular channel. Other diagnostics that do
not disturb the flow and that are able of detecting in a less localized way abnormal situations which
could give rise to too hot regions will be employed:
• Hydrophones [95].
• Ionization chambers [20].
• Cooling circuit instrumentation.
87
Chapter
5
CORROSION
The corrosion results obtained by means of the simplified 1D transport code (3.3) and by the
TRACT code (3.4) are discussed in this chapter.
5.1
Introduction. Objectives
Corrosion in the beam dump is an issue that deserves attention because as pointed out in section
2.4, mass removal can affect the mechanical and cooling behaviour of the beam dump, and because
activated corrosion products generate radiation all along the beam dump cooling circuit (partially
out of the accelerator shielded vault).
A purification system will remove the corrosion and other products maintaining the necessary
water quality. From the review of the available literature (specially [96] and [53]) presented in section
2.4, the water quality specification for the beam dump cooling has been defined as follows:
• pH in the range of 8 -8.5.
• Dissolved oxygen < 10 ppb.
• Conductivity in the interval 0.5 - 2 µS/cm.
pH will be controlled by ammonia addition, dissolved oxygen (and other gases like CO2 ) will be
eliminated with a deaireator whereas the required conductivity will be maintained using ion exchange resins which will remove ions from the water. All these elements will be located in the heat
exchanger room outside the accelerator vault together with the rest of components of the cooling
system ( pump, heat exchanger, ...).
Although some experimental data on corrosion rates for Cu circuits exist [49] no data for the
conditions of our system (water velocity and temperature) have been found. Therefore an upper
estimate of 50 mg/(m2 · day) based on [49] and on a preliminary study [85], has been employed to
dimension the ion resins and design a lead shield around them to limit the local dose rates due to
89
90
Chapter5. CORROSION
the activated ions accumulation.
A first approach to the beam dump corrosion phenomenon was performed by modelling the
convective diffusion equation [85]. In this work a simplified corrosion model based on copper dissolution was employed. To gain confidence on the estimated corrosion rates, it has been considered convenient to conduct an independent study with a more complete and validated tool like the
TRansport and ACTivation code (TRACT), which simulates processes of corrosion, erosion, dissolution, precipitation (crud) and deposition for the whole length of the cooling circuit.
The main objective pursued with these studies is obtaining an estimate of the beam dump corrosion rate to confirm the upper value used in the design. Considering a trustful value of this parameter is very important because it affects:
• Activation.
• Cooling water.
• Dimensioning of the purification system.
• Beam dump structural integrity and cooling capabilities.
5.2
1D transport code results
As explained in section 3.3, a 1D code has been developed to get a glimpse of the magnitude of
corrosion in the beam dump cooling circuit.
3.5e-06
Cu 5 seconds
Cu 60 seconds
Cu 1 hour
Cu 6 months
Cu concentration [ppm]
3e-06
2.5e-06
2e-06
1.5e-06
1e-06
5e-07
0
0
0.5
1
1.5
2
z [m]
Figure 5.1: Transient evolution of the copper concentration.
90
2.5
5.2. 1D transport code results
91
A finite volume partial differential equation solver based on Python, called FiPy [81], is employed
to obtain the transient solution of equation (3.17).
In figure 5.1 the transient evolution of copper concentration in ppm solved with FiPy is shown. It
is seen that the transport process is close to equilibrium values after 1 hour. When the simulation is
taken up to six months the concentration values along the cooling channel are practically the same.
Validation of the results thus obtained has been done confronting the solution in equilibrium
with two different solutions of the stationary transport equation (equation 5.1):
v~i (x) ·
Uch,i (x)
fi (x)
∂cbi (x)
=
· ji (x) =
∂x
Ach,i (x)
v~i (x)
(5.1)
1. The analytical solution of the stationary transport equation (see equation 5.2):
b
c (x) = exp
Z
Z
Z
−a(x)dx ·
b(x) exp
a(x)dx dx
a(x)
=
b(x)
=
(5.2)
Uch (x)K f l (x)
Ach (x)~v (x)
Uch (x)K f l (x) w
c (x)
Ach (x)~v (x)
Where Uch is the flowing channel perimeter, K f l the mass transfer coefficient, Ach the flowing
water cross sectional area, v is the fluid velocity, cb is the bulk copper concentration, a and b
are auxiliary variables, ji is the mass flux, and fi an auxiliary function.
2. The solution obtained applying the Newton method (see equation 5.3):
cbi+1 (x) = cbi (x) + ∆hfi (x)
(5.3)
Being ∆h the Newton step.
In figure 5.2 a comparison of the three different resolution methods is shown. It can be seen that
FiPy module over predicts the copper concentration from the mid part of the cooling channel until
the end of it, compared with the Newton method and the analytical solutions.
The difference in the copper concentration results obtained by different methods was studied
so that confidence could be gained on the finite difference solver. After monitoring the FiPy solver
results at each step, it was seen that the velocity changes caused by the beam dump geometry was
affecting the solver solution. To verify this, it was decided to simulate a case scenario considering
a constant velocity of 6.88 m/s which is an average value along the cooling channel. The results
show a higher degree of concordance with the analytical solution. Therefore the high concentration
values obtained from FiPy solver are due to the brisk velocity shifts along the beam dump cooling
91
Chapter5. CORROSION
3.5e-06
Analytical solution
Newton method
FIPy solution
3e-06
2.5e-06
Analytical solution
Newton method
FIPy solution for v=6.88 m/s
2e-06
2.5e-06
1.5e-06
2e-06
1.5e-06
1e-06
1e-06
5e-07
92
5e-07
0
0
0
0.5
1
1.5
2
2.5 0
z [m]
0.5
1
1.5
2
2.5
z [m]
Figure 5.2: Comparison between the different solution Figure 5.3: Solution for a constant velocity of 6.88
methods.
m/s.
channel.
The integration of the beam dump released copper yields a total annual corrosion rate of 6.247
g/(m2 · year), diminishing the inner cone thickness a maximum of only 1.12 µm.
5.3
5.3.1
TRACT results
Introduction
In figure 5.4 a layout of the beam dump cooling circuit is presented. The cooling circuit is spread
in three zones, the BD cell, the vault and the heat exchanging room where most of the elements of
the system (pump, heat exchanger, valves, purification system, ...) are located forming the so called
cooling skid. All the elements in contact with the water are made of stainless steel 304 L and 316
except for the beam dump (see figure 1.14), made of copper. The total length of the circuit is around
85 m. The coolant flow is 30 kg/s with an inlet pressure at the beam dump entrance of 3.5 bar and an
inlet temperature of 304 K. Radiation field along the cooling circuit is negligible except on the beam
dump itself.
In the simulation the cooling circuit has been simplified by removing bends, t pipes and certain
valves. A total of 71 isotopes are considered in the calculation including natural isotopes of the cooling circuit materials and the ones produced in the different transmutations. A total period of 90
days is simulated. The initial time step is 1 second so that a good resolution at the beginning of the
simulation when the parameters vary faster is obtained. After 5 days the time step is increased to 5
seconds. As steady state is approached time step is further increased to 20 seconds to speed up the
simulation.
As pH plays a key role in the copper corrosion (see section 2.4), two different simulations have
been performed. In the first one a neutral pH of 7 is considered at the entrance of the beam dump,
92
5.3. TRACT results
93
Figure 5.4: Cooling system layout. The abbreviations stand for the different flow (Q), temperature (T),
pressure (P), and conductivity (C) sensors. The different valves needed to operate the cooling circuit are
also shown.
while the second one is run for a pH of 8.5 which is the value chosen for the beam dump cooling
system design. In the following sections the results obtained from the simulation of the beam dump
cooling circuit with TRACT for the latter mentioned pH values are presented.
5.3.2
Results for pH = 7
The results show that pH values remain almost constant in the whole cooling circuit except in
the beam dump. An inlet pH of 7.196 at the beam dump entrance, an outlet one of 6.785 and a min-
Max
Min
5.24
Corrosion layer (m)
5.238 x 10⁻⁶
1.590 x 10⁻⁶
Deposition layer (m)
1.993 x 10 ⁻¹³
1.839 x 10 ⁻¹⁶
2.0
Dlayer
Clayer
(x 10⁻¹³)
Thickness [m] x (10⁻⁶)
imum value of 6.332 at the middle section of the cone are obtained.
2.62
0.0
0
20
40
Length [m]
60
80
0.0
85
Figure 5.5: Corrosion (green) and deposition (blue) layers along the cooling circuit.
Figure 5.5 shows the thickness of the corrosion and deposition layers along the circuit. The origin
in X axis is placed at the heat exchanger. It can be observed that corrosion mainly takes place in the
93
94
Chapter5. CORROSION
beam dump (x between 35 and 40 m). Dissolution rate of the corrosion layer in the stainless steel
(1.331 · 10−7 g/(m2 · year)) is several orders of magnitude lower than the one of the copper beam
0.99
Max
Min
Dissol rate cl
9.885 x 10⁻¹
1.715 x 10⁻¹
Dissol rate dl
2.846 x 10 ⁻⁹
4.402 x 10 ⁻¹ ⁰
Drate dl
2.85
Drate cl
(x 10⁻⁹)
Rate [g/m²year]
dump.
0.4
0.44
0.17
0
0.5
1.0
Length [m]
1.5
2.0
2.5
Figure 5.6: Dissolution rate of the corrosion (blue) and deposition (green) layers along the beam dump for
a pH of 7.
In figure 5.6 the dissolution rates of the corrosion and deposition layers along the beam dump
annular cooling channel are shown. Their evolution follows that of the fluid velocity. A maximum
corrosion layer dissolution value of 0.9885 g/(m2 · year) is obtained in the middle section of the
beam dump. This point corresponds to the maximum velocity and it is one of the hottest points
along the annular cooling channel. The mass transferred from the corrosion layer to the flowing
fluid depends on the mass transfer coefficient (and hence on velocity), and on the fluid and control
isotope densities (and hence temperature). Therefore the results show their consistency with theory.
The corroded copper is in the form of a corrosion layer or dissolved in the water. As maximum copper concentration in water is below the solubility limit (4.2 · 10−3 g/m3 ), no copper is found as a
deposited layer in the circuit nor in the form of crud particles. Only a small quantity of iron is deposited in the beam dump (see figure 5.5). Figure 5.6 shows that the dissolution rate of such a small
Max
Min
0.93
0.46
Dissol rate cl
9.270 x 10⁻¹
0.000 x 10⁰
Dissol rate dl
3.160 x 10 ⁻⁸
0.000 x 10 ⁰
Drate cl
Drate dl
0.0
0
3.16
50
Step
100
150
(x 10⁻⁸)
Rate [g/m²year]
layer is negligible.
194
0.0
Figure 5.7: Time evolution of the dissolution rate of the corrosion and deposition layers at the mid point
of the beam dump for a pH of 7.
Figure 5.7 shows the time evolution of the dissolution of the corrosion and deposition layers at
the mid point of the beam dump annular cooling channel. The total time of 90 days has been divided in 194 steps. It can be seen that approximately from the 60th simulated day steady state is
94
5.3. TRACT results
95
Dissol rate cl
3.105 x 10⁻¹
2.438 x 10⁻²
Max
Min
0.31
Dissol rate dl
1.622 x 10 ⁻10
6.611 x 10 ⁻¹³
(x 10⁻¹⁰)
Rate [g/m²year]
reached.
Drate cl
0.14
0.02
1.63
Drate dl
0
0.5
1.0
Length [m] 1.5
0.0
2.5
2.0
Figure 5.8: Dissolution rate of the corrosion and deposition layers along the beam dump for a pH of 7.
The beam dump water return has been simulated assuming it is completely built in copper, this
is a conservative assumption because copper is more prone to corrosion than stainless steel 304L. In
figure 5.8 the dissolution rate of corrosion and deposition layers is plotted. A maximum dissolution
rate value of the corrosion layer (0.3105 g/(m2 · year)) is observed right at the start of the water
return, where the temperature and velocity values are maximum. The contribution of the rest of the
path in the water return is negligible.
5.3.3
Results for pH = 8.5
In this simulation an inlet pH at the beam dump entrance of 8.546, an outlet of 8.614, and a
minimum value of 7.286 at the middle section of the beam dump are obtained. As pointed out in
previous sections this is the nominal operational value for the beam dump cooling circuit.
In figure 5.9 the thickness of the corrosion and deposition layers are shown. As for the pH 7
case, corrosion and deposition mainly take place in the beam dump being the thickness values very
Max
Min
5.24
Corrosion layer (m)
5.238 x 10⁻⁶
1.590 x 10⁻⁶
Deposition layer (m)
1.993 x 10 ⁻¹³
1.839 x 10 ⁻¹⁶
2.0
Clayer
Dlayer
(x 10⁻¹³)
Thickness
[m] [m]
x (10⁻⁶)
Thickness
similar to the ones obtained in the previous case (see figure 5.5).
2.62
0.0
0
20
40
Length [m]
60
80
Figure 5.9: Corrosion (green) and deposition (blue) layers along the cooling circuit.
In figure 5.10 dissolution rates of the corrosion and deposition layers are presented. A maximum
corrosion layer dissolution value of 0.01632 g/(m2 · year) is obtained, one order of magnitude lower
than the one obtained for the pH 7 case. This result is in agreement with the literature ( [50] and [49]).
95
0.0
85
Chapter5. CORROSION
Max
Min
Dissol rate cl
1.632 x 10⁻²
3.119 x 10⁻⁴
Dissol rate dl
4.702 x 10 ⁻¹¹
7.978 x 10 ⁻¹ ⁴
1.64
Drate cl
Drate dl
0.47
2.0
0.07
2.5
(x 10⁻¹⁰)
Rate [g/m²year] x (10⁻²)
96
0.79
0.03
0
0.5
1.0
Length [m]
1.5
Figure 5.10: Dissolution rate of the corrosion (green) and deposition (blue) layers along the beam dump
for a pH of 8.5
The dissolution rate profile along the cartridge is influenced by the same parameters as in figure 5.6
and therefore it has a similar shape. The dissolution rate of the deposition layer is negligible but two
1.45
0.73
0.0
Max
Min
Dissol rate cl
1.446 x 10⁻²
0.000 x 10⁰
Dissol rate dl
3.654 x 10 ⁻¹¹
0.000 x 10 ⁰
Drate cl
3.66
Drate dl
(x 10⁻¹¹)
Rate [g/m²year] x (10⁻²)
to three orders of magnitude lower than the obtained for the pH 7 case.
0.0
0
50
Step
100
150
175
Figure 5.11: Time evolution of the dissolution rate of the corrosion and deposition layers at the mid point
of the beam dump for a pH of 8.5.
The evolution of the corrosion and deposition layers dissolution rate is plotted in figure 5.11 for
a point in the middle of the beam dump cooling channel. As for the pH 7 case from the 60th day
steady state is reached.
The stainless steel corrosion layer dissolution rate has a value of 6.075 · 10−11 g/(m2 · year), four
orders of magnitude lower than the one obtained for pH 7.
Regarding the beam dump water return, it can be seen in figure 5.12 that the corrosion and deposition layer dissolution rates are much lower than the ones observed in the beam dump annular
cooling channel. A maximum dissolution rate value of 8.571 · 10−4 g/(m2 · year) for the corrosion
layer is obtained at the return inlet. The maximum value for the deposition layer dissolution rate is
also obtained at the return inlet (4.478 · 10−14 g/(m2 · year)). It is once again negligible compared
with the corrosion layer dissolution rate.
96
Max
Min
8.58
97
Dissol rate cl
8.571 x 10⁻⁴
6.487 x 10⁻⁵
Dissol rate dl
4.478 x 10 ⁻¹ ⁴
1.765 x 10 ⁻¹ ⁵
(x 10⁻¹⁴)
Rate [g/m²year] x (10⁻⁴)
5.3. TRACT results
Drate cl
3.98
0.63
4.48
Drate dl
0.1
0
0.5
1.0
Length [m]
1.5
2.0
2.5
Figure 5.12: Dissolution rate of the corrosion (green) and deposition (blue) layers along the beam dump
return for a pH of 8.5.
5.3.4
Conclusions
• Corrosion rate for a pH of 7 is nearly two orders of magnitude higher than the one obtained for
a pH of 8.5 agreeing with the data presented in [49].
• The obtained dissolution rates assuming the maximum dissolution rate along the whole beam
dump annular cooling channel lead to a lost layer of 117 µ m/ year (0.9885 g/(m2 · year)) for
the 7.5 pH value, and of 1.9 µ m/year (0.016 g/(m2 · year)) for the 8.5 pH value.
• Expected corrosion of the stainless steel components is negligible compared to that of the copper beam dump.
• Therefore:
1. The structural integrity of the beam dump is not compromised by water corrosion.
2. The cooling channel width does not change as the thickness of the deposition and lost
layers are low, hence the cooling variables (velocity and heat transfer coefficient) are not
affected.
3. The chosen water quality pH value of 8.5 is confirmed by the simulations.
4. It is confirmed that the corrosion rate data used to dimension the purification system (50
mg/(m2 · day)) is very conservative.
97
Chapter
6
EXPERIMENTAL STUDIES
In this chapter experiments to validate the beam dump cooling system design are presented. The
obtained results are compared with those derived from the design calculations (chapter 4).
6.1
Introduction. Objectives
Two prototypes have been built:
1. A 1:1 BD cartridge made with the same geometry and material as the LIPAc cartridge. This
prototype has been employed to perform pressure loss experiments, vibration characterization and test boiling detection with hydrophones.
2. A prototype called PHETEN (Prototype for HEat Transfer ExperimeNt) which has been designed exclusively to measure the heat transfer coefficient.
The beam dump cartridge prototype as well as the PHETEN device are installed in a hydraulic
circuit which provides a water flow at the nominal conditions required for the beam dump. The
main objectives of the experimental studies included in this thesis are the following:
N Validate the heat transfer coefficient estimations for the beam dump based on the PetukhovGnielinski correlation.
N Measure the pressure loss along the different parts of the circuit. In particular the pressure loss
in the beam dump cartridge.
The obtained results are detailed in the following sections of this chapter.
Besides the experimental installation has also been employed for other studies (out of the scope
of this thesis):
N Possible vibrations of the prototype since the water is flowing through the cooling channel at
a very high velocity (Flow Induced Vibrations) [97].
99
100
Chapter6. EXPERIMENTAL STUDIES
N Learn about the best way to control the pressure and flow at the beam dump entrance.
N Test hydrophone operation and signals [95].
6.2
Hydraulic circuit
The hydraulic circuit has been designed to provide a flow of water with the conditions required to
the prototypes. This circuit has also been intended as a first check for the initial chosen components
of the hydraulic circuit to be installed in Japan, like the pump, filters and different valves present in
the layout. It has been installed at CIEMAT (building 20).
VA: Relief valve
VR: Throttle valve
P6
P7 T3
H
T2
VM: Butterfly valve
6”
G
PHETEN
VM6
VM: Ball valve
VM5
P5
F2
NR: Check valve
3”
D
C
Pump
VR2
P3
E
6”
Beam Dump
VM3
P4
3”
P
Manometer
F
Flow meter
Thermometer
Flange
T
A
Filter
F
3”
B
VM4
Purging system
Flow-straightener space
Bellows
6”
Expansion tank
P1
P2
F1
T1
VM7
VM2
VM9
VM10 NR
VR1
6”
VM1
Filling
(lowest point)
VM8
Emptying
(lowest point)
Figure 6.1: Layout of the experimental hydraulic circuit.
In figure 6.1 the layout of the hydraulic circuit is presented. It consists of four different lines
which have a common collector:
1. Pump line: where the pump, the necessary valves and the expansion tank are found.
2. The beam dump line containing the cartridge prototype. In the beam dump entrance a safety
valve (set to 4 bar) has been installed to protect it from overpressure.
100
6.2. Hydraulic circuit
101
3. The by-pass line employed for the installation commissioning and flow splitting. In this line a
simple wafer valve acts as flow regulator allowing different regimes of operation. Therefore by
changing the wafer valve position different flow values can be obtained in the testing section.
However the flow can be also regulated by varying the frequency of the pump. This last method
has been the one employed in the heat transfer coefficient measurements.
4. The PHETEN line where the heat transfer experiment is performed.
Figure 6.2: Hydraulic circuit at Ciemat.
The pipes of the second and third lines are 3” diameter while the rest are 6”. All the circuit components are made of stainless steel 304L and 316. In figure 6.2 the assembled and operative hydraulic
circuit is shown.
Pressure transducers have been installed before and after the beam dump and the PHETEN to
measure the pressure loss in both lines. PT-100 temperature transmitters have been installed at the
inlet and outlet of PHETEN.
A couple of bellows (see figure 6.1) are installed at the entrance and exit of the beam dump cartridge to isolate it mechanically from the rest of the circuit avoiding vibration transmission. To avoid
inhomogeneities in the flow at the beam dump entrance, a ball valve (VM3 on figure 6.1) instead of
a wafer valve has been installed.
The pump is a vertical centrifugal multi stage pump manufactured by GRUNDFOS, model CRN120-2 AFA HQQE of 22 kW. It is controlled through a Danfoss frequency variator installed in the general electrical panel which contains digital information from all the circuit sensors. Several alarms
protect the circuit from abnormal situations (overpressure, overheating ...).
101
102
A more complete hydraulic circuit layout is presented in figure 6.3, where all the components
and electrical connections from the different devices to the control panel are detailed.
Figure 6.3: Detailed layout of the hydraulic circuit.
6.3
6.3.1
Pressure loss determination
Beam dump prototype
It consists of a cartridge with the same geometry, dimensions and material as the LIPAc one. The
manufacturing of the inner cone and shroud was done by machining several cone trunks made of
very pure copper (CuETP) and joining them by Electron Beam Welding technique (EBW). In this way
the manufacturing is faster and cheaper than with the electro deposition technique foreseen for the
final cartridge fabrication. The cylinder is made of stainless steel 304 L. Images of the inner cone
and the cartridge are shown in figures 6.4 and 6.5. The geometry of the inner cone and shroud was
measured in a 3D machine.
The prototype cooling channel geometry differs slightly from the theoretical one due to:
• Deviations in the geometry of the manufactured cones.
• Errors in the relative position of both cones produced during the assembly.
102
6.3. Pressure loss determination
103
Figure 6.4: 1:1 beam dump inner cone and tip prototypes.
Figure 6.5: 1:1 beam dump cartridge prototype.
The cooling channel thickness was measured in the assembled cartridge at different azimuthal
and axial positions. These measurements were done through holes drilled on the shroud which were
subsequently closed with little Cu screws fixed with glue.
The position that showed a greatest deviation (0.65 mm) in channel thickness was around z = 2 m.
A CFD simulation of the flow in the annular cooling channel taking into account the observed deviations was performed showing a small influence on the water flow (see section 4.3.3.4).
Although the influence of the observed deviations on cooling seemed to be small, the final beam
dump which will be subjected to high thermal stresses requires stricter tolerances. Tolerances expected in the final cartridge manufactured by electro deposition (EDP) are foreseen to be much
smaller. It could also be manufactured using the EBW technique like the prototype, but it would
require some intermediate steps of machining to reduce the geometrical deviations to acceptable
values.
103
104
6.3.2
Pressure loss
The water pressure loss caused by its passage through the beam dump cartridge has been measured at different flow rates. This experiment employs the AB, EF and CD sections of the hydraulic
circuit (see figure 6.1). Initially the pump is started and gradually reaches the nominal flow of 108
m3 /h. In this start-up phase the water flows through the bypass (section CD) so that correct operation of the hydraulic circuit is verified. Once nominal flow has been reached, section CD is gradually
closed while section EF is opened employing VM3 valve.
The experiment is performed at different flow rates by controlling the aperture of VR2 valve in the
bypass.
140
Beam dump flow(Qbd)
F2 flow measurement (bypass)
F1 flow measurement (pump)
120
Q [m3/h]
100
80
60
40
20
0
10
20
30
40
50
60
70
80
90
100
Qbd percentage compared with nominal flow [%]
Figure 6.6: Flow variation during pressure loss experiment.
Figure 6.6 represents the different flow rates employed. The flow through the beam dump prototype is obtained by subtracting the flow F2 through the bypass from the flow F1 at the pump outlet.
In the experiment pressure loss is measured by means of two manometers (see figure 6.7 where
the red arrows are pointing towards them). The first one is placed 2.07 m upstream the beam
dump entrance, while the second one is placed 0.95 m downstream the entrance. Between the two
manometers the elements that contribute to the overall pressure loss are the following:
• Two 90o elbows.
• One bellow with a lent of 0.17 m.
• 2.85 m of 3” diameter stainless steel straight pipe.
• A safety valve.
104
6.3. Pressure loss determination
105
Figure 6.7: Position of the manometers in the hydraulic circuit.
Hence the measured pressure loss includes not only the beam dump cartridge pressure loss but
also the one introduced by the other elements placed between the two manometers. The beam
dump theoretical pressure loss has been calculated as explained in sections 2.1.3 and 3.1. The pressure loss introduced by the straight pipe section is evaluated by means of the Darcy-Weisbach expression (see equation 2.18). In this case the friction parameter is obtained employing the Haaland
formula [98] (see equation 6.1). The bellow is assumed as part of the 3” stainless steel pipe hence
considering 3.02 m of straight pipe with a rugosity of 0.09 mm. The two 90o elbows and the safety
valve are considered as local pressure losses with local pressure coefficients (K) of 0.165 and 0.75
respectively.
"
1.11 #
1
6.9
ε/D
√ = −1.8 log
+
Re
3.7
f
Qbd [m3 /h]
13.13
26.81
51.33
81.67
107.9
Pin [bar]
3.55
3.57
3.57
3.51
3.56
Pout [bar]
3.55
3.50
3.24
2.65
2.06
Uncertainty [bar]
0.00
0.07
0.06
0.08
0.16
(6.1)
∆P [bar]
0.00
0.07
0.33
0.86
1.5
Table 6.1: Pressure loss experimental data.
Table 6.1 shows the inlet, outlet pressure and manometer uncertainty obtained for the different
105
106
flows. Figure 6.8 compares the experimental values with the calculated ones considering the beam
dump cartridge pressure loss (see section 4.2.5) and the pressure loss of the elements between the
two manometers. Each measurement is accompanied by its experimental uncertainty represented
as an error bar. As the instrumental error was lower than the oscillations observed in the manometers, the latter value was taken for the error propagation analysis. The uncertainty shown in table
6.1 is the sum of the oscillations measured for the inlet and outlet pressure values.
1.8
Theoretical pressure loss
Experimental pressure loss
1.6
1.4
P [bar]
1.2
1
0.8
0.6
0.4
0.2
0
10
20
30
40
50
60
3
70
80
90
100
110
Q[m /h]
Figure 6.8: Pressure loss experimental results.
It is seen that theoretical and experimental values are in good accordance. For the highest flow a
difference of 0.12 bar between the experimental and theoretical values is found. This is the highest
difference found in the experiment, nevertheless it lays in between the measurement uncertainty as
seen in figure 6.8.
The discrepancy between calculated and experimental values can be explained by the uncertainty in the local pressure loss coefficients (K) and by the different welding and plugs of the EBW
manufactured beam dump (see section 6.3.1) which can not be modelled accurately with the CHICA
code.
6.4
Film transfer coefficient measurement
6.4.1
PHETEN prototype
6.4.1.1
Description
A prototype to test the beam dump heat transfer coefficient value has been designed. This prototype with a total length of 1.2 m reproduces the geometry of a 131 mm long beam dump annular
cooling channel slice (corresponding to z = 1.135 m up to z = 1.266 m measured from the tip). All
106
6.4. Film transfer coefficient measurement
107
the parameters correspond to those of the beam dump (cooling channel diameter and thickness,
conical geometry with a slope of 3.43o , rugosity set to N9 which means a roughness of 6.3 µm). The
material employed in its fabrication is stainless steel 304L with a thermal conductivity of 14.6 W/mK
at 20 o C [99]. This material has been used instead of copper because:
II
I
III
IV
Flange 2
Flange 1
R UG O S IDAD
PROYECCION EUROPEA
0
DE
30
6
315
120
6
30
120
315
0.05
0.10
0.15
0.20
A
1000
Antigua
1000
Nueva
N12
N9
N6
6,30
0,60
N3
0.50
0.30
Ra (um)
50
0,10
Cotas a comprobar especialmente
MATERIAL
Letra
ESCALA
MODIFICACION
Fecha
Nº de piezas
Firma
Hoja Nº
PHETEN
FECHA
NOMBRE
Proyectado
OCT. 2010
A.GABRIEL
Dibujado
NOV. 2010
A.GABRIEL
(PROTOTIPO BD-IFMIF)
Sustituye a:
Sustituido por:
Verificado
Figure 6.9: PHETEN prototype scheme.
• Stainless steel diffusivity is more appropriate for a transient experiment to determine the heat
transfer coefficient, and at the time of the prototype manufacturing, this was the planned
method to measure the HTC (although finally discarded due to the difficulty in generating a
transient with the required time scale (see section 2.5)).
• The key factors affecting the heat transfer coefficient are the cooling channel geometry and
the material rugosity, hence employing copper or stainless steel does not make any difference.
• Stainless steel is cheaper and easier to machine than copper.
107
108
Figure 6.10: PHETEN prototype flanges.
Figure 6.11: PHETEN prototype partially assembled (left) and mounted in the hydraulic circuit (right).
In figure 6.9 the PHETEN prototype can be seen. It is divided in four parts:
• Section I corresponds to the PHETEN entrance, it consists of a 316 mm long cylindrical pipe
with a cone in its interior designed to accommodate the flow from a circular channel into an
annular one (left image in figure 6.11).
• Section II is a 600 mm straight section. The outer cylinder diameter is 168 mm with a thickness
of 5 mm, conforming together with the inner cylinder an annular cooling channel of 8.05 mm
width. The inner cylinder is also 5 mm thick and has an outer diameter of 142 mm.
• Section III is the film transfer coefficient testing section. It has identical dimensions as Section II. The heating element is embraced around the cylindrical section, where thermocouples
will be introduced in drills performed at different depths in the PHETEN surface to measure
temperature.
• Section IV is the 131 mm conical section where it was initially planned to perform the film
transfer coefficient measurement.
108
109
N6
Ø
N9
4
20
Ø
Aperture
Ø
18
3
10
M12
0
15
Ø
Ø285
14
Ø
Ø80
+ 0.15
-0
75
°
.)
ld
ta
Ø122
0
(1
Ø165
11
Ø165
Ø
Ø260
10
36°
.)
ld
ta
45°
2
(1
141,5
5
8,
8
1
0.
+ 0
-
6.5
Rib
20
3.9 ± 0.2
7.5°
N6
DETALLE DE CAJEROS (
)
RUGOSIDAD
PROYECCION EUROPEA
DE
0
6
30
A
6
30
120
315
0.05
0.10
0.15
0.20
315
120
1000
Antigua
1000
Nueva
0.30
N12
N9
N6
N3
6,30
0,60
0,10
0.50
Ra (um)
50
Cotas a comprobar especialmente
RELACION DE JUNTAS TORICAS ( EPIDOR )
MATERIAL
Letra
ESCALA
Codigo.- 305.886 ( Ø.122x5 ) 2 piezas
Nº de piezas
Fecha
MODIFICACION
BRIDA LADO DISTRIBUIDOR
Firma
Hoja Nº
PHETEN
Codigo.- 346.209 ( Ø.165x5 ) 2 piezas
FECHA
NOMBRE
Proyectado
OCT. 2010
A.GABRIEL
Dibujado
NOV. 2010
A.GABRIEL
Sustituye a:
Sustituido por:
Verificado
Figure 6.12: PHETEN entrance flange.
The design includes two flanges (see figures 6.9 to 6.12), one at the entrance and the other one
at the exit of the annular cooling channel. They are necessary to hold in place the inner and outer
cylinders. As shown in figure 6.12 the entrance flange has four apertures to allow the water passage.
The flange design tries to minimize the flow perturbation by maximizing the flange apertures for the
water flow, hence minimizing the rib size (space between the flange apertures).
6.4.1.2
3D simulation
A CFX simulation to study the influence of the two flanges on the flow has been performed. The
flow perturbation produced by the PHETEN flanges can affect the wall temperature measurement
in the heat transfer coefficient experiment creating flow areas with different velocities and therefore
different film transfer coefficients.
The whole PHETEN geometry has been modelled. A size element of 2 mm was chosen so that
the six inflation layers with a first layer thickness of 5 · 10−5 m, could perfectly fit in the 8 mm width
annular cooling channel. SST turbulence model has been employed in the simulation with a steady
temperature of 298 K, an inlet velocity of 1.53 m/s and an outlet pressure of 1.4 bar as boundary
conditions. A length of 700 mm downwards the exit of the second flange has been included in the
model so that no flow return through the outlet boundary occurred.
The simulation shows that the perturbation originated by the PHETEN entrance flange creates
109
110
Figure 6.13: Velocity profile in the testing section (zm ) plane.
flow sections with different velocities. In figure 6.13 such behaviour can be observed at the section
(zm ) where the film transfer coefficient experiment is carried out. There is a 1.744 m/s difference between the affected and non affected areas. Hence the temperature measurement in the heat transfer
coefficient experiment must be performed in the space in between the flange’s ribs.
Figure 6.14: Vector lines at the PHETEN entrance flange.
The vector lines around the entrance flange rib are seen in figure 6.14. It can be observed that
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111
the water flow impinges on the ribs and works it way around them accelerating the flow as a consequence of the transversal flowing area decrease. The rib creates a downstream area where reverse
flow with a maximum velocity around 2.9 m/s is found, leaving areas downstream the rib with no
cooling.
Figure 6.15: Streamlines downstream the PHETEN outlet flange.
In figure 6.15 the streamlines as water exits the flange into the 6” pipe are plotted. The flow perturbation can be observed including different velocity areas and reverse flow streamlines. Such flow
pattern is caused by the combination of a sudden change of the water flowing section, together with
the effect of the flange on the flow.
In conclusion, the ribs present in the flange perturb the water flow creating a non uniform velocity profile. The perturbation diminishes with flowing distance but inhomogeneities still remain
at the measuring section. Therefore the measurement to determine the heat transfer coefficient will
be performed in the non disturbed area between the ribs.
6.4.2
Experimental setup
6.4.2.1
Film transfer experimental determination
As it was explained in section 2.5, the procedure finally chosen for the heat transfer coefficient
determination is directly measuring the temperature difference between the fluid (Tb ) and the material at the fluid interface (Tsb ). Instead of heating the inner surface of the annular channel as it
happens in the beam dump, it is the outer surface of PHETEN the one that is heated (see figure
6.16). The temperatures at different radial positions are measured by means of thermocouples. If
the heat flux is known, then applying Newton’s equation the film transfer coefficient can be obtained
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(see equation 6.2).
h=
q/A
(Tsb − Tb )
(6.2)
Band heater
Band heater
Tout
Flowing water
Tb
Tmed
Tin
Tsb
Outer cylinder
Inner cylinder
Flowing water
Band heater
Figure 6.16: Schematic layout of the PHETEN heat transfer coefficient experiment assembly.
Needed data are the following:
• Heat flux (q/A).
• Tsb , the surface temperature in contact with the coolant.
• Tb , the bulk temperature.
In this experiment only the AB section of the hydraulic circuit is opened. The pump is started so
that water starts flowing through the prototype. Once it has reached the requested flow, the heater
is turned on until steady state is obtained.
6.4.2.2
Heating means
First step was finding an appropriate heating element that provided enough heating power to
cause a measurable temperature variation in the PHETEN testing section. A mineral insulated band
heater from Watlow manufacturer was chosen. The band heater has an internal diameter of 165 mm
and a width of 38 mm (effective heating width of 36.5 mm), delivering according to the manufacturer
data a maximum power of 1250 W (V = 240 V, R = 46 Ω), and thus a maximum average power density
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113
of 7.3 W/cm2 . No commercial band heater could be adapted to the conical test section. Therefore
it was decided to perform the experiment in the cylindrical section prior to the conical one (section
III). The band heater is mounted in the middle of this section and insulated with fibreglass wool so
that the maximum amount of heat is transferred to the cooling water. Assuming an average fibreglass wool conductivity of 0.034 W/mK and a thickness of 10 mm around the band heater, a thermal
resistance of 13.85 K/W is obtained. This value is much higher than the 0.019 K/W of the total thermal resistance between the fluid at nominal flow and the outer surface of PHETEN. Hence most of
the heat delivered by the band heater will be conducted to the flowing water.
The heater consists of two resistances internally assembled at each half of the cylindrical heater,
that deliver the heat by means of Joule effect. In figure 6.17 a picture of the employed band heater
is shown. The four prominent bolts seen in the picture are the terminals of each resistance (positive
and negative). In the space left between the two resistances one bolt is used to adjust the collar
around PHETEN.
Figure 6.17: Band heater.
The band heater power density was studied in order to check if it was heating in an uniform way.
It was concluded that the heater delivers the maximum power in a large central area of each of the
two resistances away from their ends. Hence the band heater position in the final setup is such that
temperature measurements are performed in this central area named Position I. The experimental
procedure followed to measure the power density shape and the obtained results are presented in
Appendix D.
6.4.2.3
Instrumentation
Thermocouple operation is based on the Seebeck electromotive force, which is the internal electrical potential difference between the terminals of any electrical conductor subjected to a temperature gradient [100]. The thermocouple consists of two dissimilar conductors which have a pre113
114
dictable and repeatable relationship between temperature and voltage. The two conductors are
welded at the so called hot or measuring junction, and at the other side their terminals (cold or
reference junction) are open so that they can be connected to extension wires, electrical measuring equipment or other configurations depending on the experimental setup (see figure 6.18). The
voltage difference between the two conductors is a function of the temperature difference between
the hot and the cold junctions. If a precise absolute value of temperature is required, the equivalent
voltage of cold junction temperature has to be calculated to correct the output voltage obtained.
The estimation of the cold junction temperature is the main source of errors in thermocouple temperature measurements (see [101] and [102]).
Type T Thermocouple
Copper wire
Reference junction
Hot junction
Constantan wire (Cu-Ni)
Figure 6.18: Type T thermocouple sketch.
Initially the experiments were performed with type K (chromel-alumel) thermocouples because
they are the most common for general temperature measurement purposes. However it was later
seen that type K thermocouple measuring range was too large for our purposes while type T (copperconstantan) range fitted much better our needs. Besides theoretical tolerance obtained in absolute
temperature measurements for class 1 type K thermocouples is ± 1.5 o C, while for class 1 type T is
± 0.5 o C. When it was finally decided that thermocouples would be in contact with water, as type
K voltage signal could be influenced by the cable vibration (see [103]), it was decided to change all
thermocouples to type T class 1.
The ten type T thermocouples to be employed in the heat transfer coefficient experiment were
calibrated following the procedure shown in Appendix A. However these calibrations were finally
dismissed because they contained errors due to difficulties with the temperature control and uni114
115
120
Standard calibration curve
y(x)
100
T [oC]
80
60
40
20
0
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
V [mV]
Figure 6.19: Standard type T calibration curve.
formity inside the oven.
Instead the type T thermocouple calibration defined by the IEC 60584-1 standard [104] has been
the one employed. This standard given by the National Physics Laboratory (NPL) of the United
Kingdom contains the reference tables of thermocouple electromotive force versus temperature for
a reference junction temperature of 0 o C. The polynomial functions given in such standard have
been employed in this thesis to convert the output voltage into temperature results. In figure 6.19
the standard calibration curve for type T thermocouples is shown.
The following recommendations from [100] have been followed in the thermocouple installation:
• Use the simplest possible installation to avoid perturbation errors.
• Bring the thermocouple wires away from the junction along an isotherm for at least 20 wire
diameters to reduce conduction errors. The use of thermocouple materials with low thermal
conductivity will also reduce this error.
• Locate the measuring junction as close to the surface as possible.
• Design the installation so that it causes a minimum disturbance on the fluid flow to avoid
changes in convective heat transfer.
Temperatures measured by thermocouples are processed with the Keithley 2000 model multimeter ( [105]). This device is connected by a GPIB port to a personal computer, where a LabVIEW
code [106] records the output voltage signals that are later employed in the heat transfer coefficient
calculation.
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116
Figure 6.20: Keithley 2000 data acquisition device.
6.4.3
Preliminary measurements
6.4.3.1
Introduction
The determination of the needed parameters to measure the heat transfer coefficient, especially
Tsb , turned out to be quite tricky. Many trial and error experiments were done with different configurations before arriving to the best setup. All these tests are briefly described in this chapter in a
chronological way. For the shake of clarity the different tests are described in the Annexes A to D,
and here only a summary is presented together with the main lessons learned from them.
6.4.3.2
First attempts. Measurement of temperature inside the wall
In a first series of tests the plan was determining the temperature at the water-material interface
extrapolating it from the measurement of the temperature inside the wall.
The bulk temperature (Tb ) was registered by a type K thermocouple, placed at the inlet of the
PHETEN. The water-material temperature (Tsb ) was measured indirectly employing a 1 mm diameter, type K mineral insulated thermocouple, placed inside a 4 mm deep, 1 mm diameter drill machined on the stainless steel (Tin in figure 6.16). Two more type K thermocouples were employed,
the first one to monitor the band heater temperature so that 350 o C are not exceeded, and the second one to measure the outer surface temperature (Ts ), in the space between the band heater and
the PHETEN at the same axial coordinate as Tsb . Knowing the outer temperature Ts and the temperature 1 mm away from the water-material interface Tin , Tsb can be extrapolated.
The experiments were repeated several times obtaining always too high values for the surface
and the water-material temperatures. It was planned to use the temperature difference between Ts
and Tin to obtain an experimental value of the amount of heat delivered by the band heater to the
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117
PHETEN. The theoretical temperature difference should be 19.95 K. However experiments showed
temperature differences in some cases over a hundred degrees. The first guess was that heat was
being transferred from the heater to the thermocouple through the air trapped in between the band
heater and the testing section. It was also seen that the presence of the thermocouple wires between
the heater and the PHETEN was reducing the thermal contact. Therefore to obtain a better adjustment of the heater to the surface, the thermocouple diameter was reduced down to 0.5 mm. No
improvement was obtained, so a stainless steel 304 L sleeve around the thermocouple measuring
Tin was installed. In such way the thermocouple-stainless steel sleeve set perfectly fitted the drill
without leaving air gaps. The Tin measurement showed a decrease of around 15 K.
The wall temperature measurements were not credible even after all the improvements performed in the setup, and hence different alternatives were tried.
As these problems came from the fact of having the heating element on top of the thermocouples, measuring in the small azimuthal space left between the two resistances was also tried. The
Tin values obtained were lower in this case but still incorrect. A thermal simulation with ANSYS was
performed trying to explain the experimental results. In figure 6.21 the temperature distribution in
the space between the two parts of the band heater is shown. The temperature footprint resembles
that of the deposited power showing that the temperature measurements taken in the space left between the resistances are not adequate to estimate the heat transfer coefficient. The reason is that
the heat transfer in this region is mainly 1D.
Temperature [ºC]
Figure 6.21: Thermal simulation of the band heater for a water heat transfer coefficient of 25000 W/m2 K.
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118
Tests were performed on a pipe (without water) to learn about the problems encountered measuring the wall temperatures and to find the best way to solve them. They are described in Appendix
B. The conclusions drawn from these tests were the following:
• The thermocouple in contact with the band heater does not provide a credible surface temperature measurement (Ts ) because it is affected by the heater. Therefore this thermocouple
will be suppressed.
• The temperature measurement in the wall with the 0.5 mm thermocouples improved significantly by using a 0.9 mm 304L stainless steel sleeve around them.
• The measurement improved even more by employing a thermal compound to fill any air space
between the PHETEN and the thermocouples.
• It was decided to back up the Tin thermocouple with a thermocouple placed in contact with
the flowing water.
After the tests performed on a pipe, modifications to the initial experimental setup were made in
the PHETEN. Three 1 mm diameter perpendicular drills were made. The depth of these drills was 2,
3 and 4 mm, corresponding to Tout , Tmed and Tin respectively (see figure 6.16) starting from the outer
surface of PHETEN. The thermocouples located in these drills were embedded in a 0.9 mm stainless
steel sleeve. Besides, the possible hollow space between sleeve, drill and thermocouple was filled
with Junpus DX1 thermal paste, with a thermal conductivity of 16 W/mK, close to that of stainless
steel 304L. As it is explained in Appendix C, the improved experimental setup configuration did not
solve the mentioned problems:
• The obtained wall temperature values were still too high despite the stainless steel sleeve and
the thermal paste.
• The presence of the wall thermocouples under the band heater provokes a poor adjustment
between the heater and the outer surface of PHETEN. As a consequence a lower heat flux is
transferred and its profile shows asymmetries in the azimuthal direction.
6.4.3.3
Direct measurement of temperature at the water interface
Two through holes were drilled on the PHETEN surface to pass two type T 0.2 mm diameter
thermocouples and measure the water-material temperature. The holes were drilled away from the
band heater position, see scheme in figure 6.16, so that the heater can be properly adjusted to the
outer surface of PHETEN. Guaranteeing an excellent thermal contact between the thermocouple
and the inner surface of PHETEN is essential in this experiment. The results of these experiments
are presented in Appendix C.B. The two thermocouples were initially fixed to the inner surface of
PHETEN by means of Araldit and duct tape. Araldit had a double function:
• Fixing the thermocouple to the inner wall.
• Isolating the thermocouple from the water flow, so that it measured the inner surface temperature instead of the water temperature.
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119
Thermocouples were also isolated with a 0.2 mm copper conducting tape. In general temperatures at the interface were very close to that of the water. It was observed that the use of tapes
covering the thermocouples modified the local heat flux giving higher wall temperatures.
Figure 6.22: Flat plate with thermocouples welded on it.
It was then decided to improve the thermal contact between the water-material thermocouples
and the inner surface of the PHETEN replacing the Araldit and duct tape by a weld joint. An Omega
TL-WELD thermocouple and fine wire welder was employed for the spot welding of the 0.2 mm type
T thermocouples. The welding process turned out to be extremely complicated due to the thermocouple wire diameter, its composition of pure copper in one of the terminals and Constantan
(Cu-Ni) in the other, and due to the position of the joint on the inner surface of the PHETEN outer
cylinder. In the first attempts the welded thermocouples gave temperature measurements which
were too low, denoting a bad thermal contact. Therefore different welding techniques were tried
using thicker thermocouples (0.5 mm diameter) in order to facilitate the welding process. Welding
tests were performed on a 304L stainless steel flat plate to learn about the best technique to be applied to the PHETEN. Thermocouples were welded employing two different welding machines, a
commercial one (the previously mentioned Omega TL-WELD) and a taylor made one at Ciemat. In
figure 6.22 an example of the different configurations tested on the flat plate is shown. To check the
quality of the thermal contact, the plate with the welded thermocouples on it was immersed in a
controlled temperature cask, where the flat plate was heated, then taken out, and the temperature
evolution measured by the thermocouples compared.
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120
The thermocouples welded on the plate were covered with Araldit, copper tape, and duct tape. It
was also decided to try welding each wire separately so that the two welding points could be handled
separately, using the right potential for each wire, therefore obtaining a more reliable contact point
with the PHETEN inner surface [100]. Appendix C.A includes a summary of the most relevant results.
T2
T3
T4
T1
Band heater
Outer cylinder
Inner cylinder
Annular channel
Figure 6.23: Cross sectional view of the PHETEN experimental setup.
From this testing the following conclusions were obtained:
• The 0.5 mm thermocouples were much easier to weld than its predecessors (0.2 mm). The
joint was more rigid and robust.
• Temperature measurements with thermocouples welded in different ways gave the same results giving us confidence on the welding technique employed.
• Covering the thermocouple tip with an insulating element delayed the thermocouple response.
After all this testing and preparation, a new setup with four 0.5 mm thermocouples welded to the
inner surface of PHETEN was prepared. The commercial welding machine was employed because
of the better voltage control in the spot welding process.
Three of the thermocouples were to be welded on the inner surface of PHETEN (T1, T2 and T4),
while T3 was welded in a small indentation on this surface of approximately 0.5 mm depth (see figure 6.24) and utterly covered with cold welding paste Pattex, Nural 21 (k = 0.17 W/m · K). Initially
thermocouples T1 and T2 were covered with Araldit, and T4 was covered with a copper tape (see
120
T4
121
T3
T2
T1
Figure 6.24: Thermocouples welded to the PHETEN inner wall (copper tape).
figure 6.24). While testing the thermocouples, it was seen that the copper tape in contact with the
two thermocouple bare wires was modifying the output voltage signal. The reason was that the electrically conducting tape was modifying the thermocouple electric circuit closing it where the copper
duct was placed. Therefore the output voltage was not representative of the real temperature on the
PHETEN inner wall, and it was decided to remove the copper tape and employ duct tape as it was
made in prior experiments (see figure 6.25).
In Appendix C.B.2 the results of the experiments performed with T1 and T2 covered with Araldit,
T3 embedded in the PHETEN wall and partially coated by a thin Araldit layer, and T4 covered with
duct tape, together with the experiments performed removing the Araldit layer from all thermocouples except for T1 are presented. The experiments were performed with and without the wall
thermocouples mounted.
The conclusions obtained from both sets of experiments are the following:
• The wall thermocouples definitely cause a temperature anisotropy due to the poor contact of
the band heater in the regions close to the thermocouples. Therefore they can not be employed
in the final experimental setup.
• Comparing the results with and without Araldit, it is seen that its presence is perturbing the
heat transmission in the thermocouple area obtaining higher temperature values than ex121
122
T4
T3
T2
T1
Figure 6.25: Thermocouples welded to the PHETEN inner wall (duct tape).
pected. Hence Araldit was removed from T2, T3 and T4 and in the setup to be employed in
the final campaign.
• The thermocouple weldings are now trustworthy. Their signals react in the expected way and
there is reproducibility in the obtained data. T2 and T4 are welded identically and under the
same boundary conditions reaching the same temperature values (see figure C.11).
6.4.3.4
Conclusions. Lessons learned
The conclusions from the temperature measurements inside the PHETEN wall are the following:
• The chosen setup is not correct because placing the thermocouples radially beneath the band
heater, despite their small diameter (0.5 mm), affects the heat delivered to the PHETEN outer
surface.
• The temperature measurement is not correct either because:
7 More importantly the thermocouples give higher temperatures than those expected. Installing the stainless steel sleeve and the thermal paste increases the thermal contact but
still does not turn the thermocouple into a part of the piece.
7 The reason for this is that the heat transferred from the band heater towards the outer
surface of PHETEN is also transferred partially by the copper constantan thermocouple
wires.
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123
• As a consequence the temperature measurement performed in this way does not represent
the real unperturbed wall temperature. If oblique drills had been performed on the PHETEN
surface these problems would have been partially solved.
From the temperature measurements at the material-water interface it was concluded that:
• Measuring the true material temperature at the surface in contact with water instead of a value
in between the one of the water and the one of the material is a difficult task. The thermocouple must be in close contact with the metal barely jutting out its surface. In this way the heat
transfer in the thermocouple area is exactly the same as it would be in any other part of the
metal surface.
• Covering the thermocouple tip so that it does not see the flowing water is not a good idea.
Although it guarantees that the thermocouple reaches the metal temperature, the thermal
impedance added by the covering layer (Araldit, duct or copper tape) disturbs the heat transfer
in the vicinity increasing the temperature and hence making such measurement not representative.
• In order to obtain a strong joint between the thermocouple and the metal wall, the following
is required:
7 Thick thermocouple (> 0.5mm).
7 Good quality welding.
7 The best option is welding each thermocouple wire separately. In such way the welding
size is minimized.
Other important lessons learned are the following:
• Spurious joints between the thermocouple wires must be avoided because if so happens the
thermocouple would be measuring the temperature of the faulty union. Therefore it must be
guaranteed that the bare thermocouple wires are not in contact between them or with the
stainless steel wall except at the measurement point.
• The band heater must be perfectly fitted to the outer surface of PHETEN. No elements can be
between the heater and such surface (not even the 0.5 mm thermocouples). To ensure a better contact the band heater must be adjusted while heated to compensate the heater thermal
expansion.
6.4.4
Final measurements. Results of HTC measurements
After all the trials described in the previous sections and Annexes, the experimental setup used
in the final measurements is:
• Thermocouples at the surface in contact with water:
7 T1 covered with Araldit.
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124
7 T2 and T4 uncovered and in direct contact with the flowing water.
7 T3 welded at approximately 0.5 mm from the inner surface of the PHETEN outer cylinder
and covered with cold welding paste.
• T5 measuring the water temperature.
The heater was placed at an azimuthal position such that the thermocouples (T1 to T4) are located in the middle section of one of the resistances (see figure 6.26).
Figure 6.26: Heat transfer coefficient experimental setup.
The experiment was performed applying a voltage of 256.2 V. The resistance was measured during the experiment with a multimeter giving a value of 46.5 Ω. Therefore a power of 1411.5 W was
delivered to the outside surface of PHETEN corresponding to a heat density of 73623 W/m2 . This
value is corrected accounting for the cylindrical geometry of PHETEN, obtaining a heat flux value at
the water interface of 78306 W/m2 . 1
The experiment was performed for three different water flows starting with 108 m3 /h until steady
state is reached, reducing then the flow to 60 m3 /h and ultimately to the lowest one of 25 m3 /h. The
circuit is pressurized up to 2.3 bar at the PHETEN inlet for the 108 m3 /h flow to reproduce a similar
condition to the one encountered in the beam dump.
In figure 6.27, T2, T4 and T5 temperature profiles for different water flows are presented. This
temperature profiles are corrected in two ways:
1. As raw millivolt data without cold junction temperature compensation is obtained from the
Keithley data acquisition system, the temperatures are corrected with the ambient temperature. In this case the correction is made with 22.6 o C.
2. As a consequence of the temperature gradient in the Keithley device, the different channels
(cold junctions) are at slightly different temperatures. Hence initial values of T2, T4 and T5 are
slightly different. All temperatures have been corrected by a constant shift in such a way that
1 The voltage and resistance values are slightly higher than the ones given by the manufacturer cited in section 6.4.2.2.
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125
T2
T4
T5
36
25 m3/h
34
60 m3/h
T [oC]
32
108 m3/h
30
28
26
24
22
0
20
40
60
80
100
120
140
Steps (x 15 seconds)
Figure 6.27: T2, T4 and T5 temperature profiles.
at the beginning of the experiment, before the heater is connected and the pump started, their
values are equal to that of T5. The correction needed has a value of 0.47655 o C for T2 and a
value of 0.36408 o C for T4.
Flow [m3 /h]
25
60
108
∆Ttheo [o C]
8.95
4.11
2.41
∆T2exp [o C]
6.49
3.82
2.57
∆T4exp [o C]
6.08
3.21
2.41
Table 6.2: Theoretical and experimental temperature difference values.
The water temperature increases during the experiment due to the heating produced by the
pump rotation (see figure 6.27). The slope decreases as the water flow is reduced due to the lower
friction caused by the pump (the vertical lines in figure 6.27 show the water flow change). With respect to the heat dissipated from the band heater, a few minutes after changing the water flow rate
steady state is obtained. This can be seen in figures 6.27 and 6.28 which show that the temperature difference between T2-T4 and T5 remains constant. Although T2 and T4 slightly differ in the
temperature measurement (for the 108 m3 /h case, the temperature difference between T2 and T4 is
around 0.15 o C, while for the 60 m3 /h and the 25 m3 /h cases the differences are between 0.4 o C and
0.6 o C), both of them are close to the theoretical values obtained using Petukhov-Gnielinski correlation (see table 6.2), especially in the 108 m3 /h and 60 m3 /h cases.
Table 6.3 shows the experimental heat transfer coefficients derived from T2 (hT 2 ) and T4 (hT 4 ),
together with the theoretical Petukhov-Gnielinski and Petukhov-Roizen HTC.
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126
Flow [m3 /h]
25
60
108
hT 2 [W/m2o C]
12061
20488
30467
hT 4 [W/m2 K]
13508
24379
32537
hgni [W/m2 K]
8745
19041
32482
hroiz [W/m2 K]
7546
16651
28405
Table 6.3: Theoretical and experimental HTC values.
T4 - T5
T2 - T5
8
25 m3/h
∆T [oC]
6
60 m3/h
4
108 m3/h
2
0
0
20
40
60
80
100
120
140
Figure 6.28: Temperature difference between inner surface and water.
Regarding the equipment calibration, the uncertainty in the measurement of all the equipment
employed has been taken into account except for the Keithley 2000 multimeter, whose uncertainty
is so low (0.001 K see [105]) that it is out of the measurement range. The Fluke 177 multimeter employed to measure the voltage and band heater resistance, hence the heating power, has an uncertainty in the AC voltage measurement of 2 %, and an uncertainty in the resistance measurement of
0.9 %. The type T thermocouples have an uncertainty in the absolute temperature measurement of
0.5 K in our range of temperatures. This is caused as explained in 6.4.2.3, by the difficulty in measuring an absolute temperature value at the cold junction. In our case raw millivoltage data with a cold
junction temperature of 0 o C is employed, so no correction is needed. This can be done because no
absolute temperature values are required for the HTC determination. Therefore an uncertainty of ±
0.1 K, which is the polynomial fit uncertainty given by the National Physics Laboratory (NPL) [104]
is employed. In the area calculation needed to obtain the heat flux value an uncertainty in the lineal
dimensions of PHETEN of ± 0.5 mm is employed, which is the typical average dimensional tolerance for a machined piece of these dimensions.
An error propagation study of the heat transfer coefficient indirect measurement is performed
taking into account all the previously mentioned measurement errors. In this case only the system126
127
atic errors due to the equipment uncertainty are considered because they are much higher than the
random ones.
The variables measured in this experiment are considered part of a stochastic process, that is
random and independent. Therefore the error associated can be calculated as a sum of the different
quadratic errors. Considering the heat transfer coefficient as a function of the heat flux (q” ), the
water temperature (Tb ) and the surface temperature (Tsb ):
s
δh =
∂h ”
δq
∂q ”
2
+
∂h
δTb
∂Tb
2
+
∂h
δTsb
∂Tsb
2
(6.3)
The heat flux is an indirect measurement, hence its uncertainty is calculated in the same way as
that of the heat transfer coefficient. The ones considered in the heat flux uncertainty calculation are
the voltage, the electric resistance of the heater and the fabrication dimensional tolerances of the
PHETEN piece and the band heater.
Theoretical HTC
Experimental HTC based on T2
Experimental HTC based on T4
35000
h [W/oC m2]
30000
25000
20000
15000
10000
5000
20
40
60
80
100
120
3
Flow [m /h]
Figure 6.29: Experimental and theoretical heat transfer coefficients with their associated uncertainty.
In figure 6.29 the experimental and Petukhov-Gnielinski theoretical heat transfer coefficient results with their respective uncertainties are plotted. It is seen that the heat transfer coefficients
calculated with T4 thermocouple are slightly higher than those obtained from T2. The difference
between the experimental value of the HTC and that obtained with the Petukhov-Gnielinski correlation is smaller than 10%.
The theoretical and experimental values for the heat transfer coefficient along with the obtained
uncertainty from the error propagation analysis are summarized in table 6.4.
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128
Flow [m3 /h]
25
60
108
htheo
8745
19041
32482
hT 2
12061
20488
30467
hT 4
13508
24379
32537
δhtheo
525
1142
1949
δhT 2
572
1149
2111
δhT 4
658
1485
2352
Table 6.4: Heat transfer coefficient values and their associated uncertainty.
6.4.4.1
Conclusions
7 The heat transfer coefficient has been successfully determined for different flows.
7 For flows lower than the nominal one, the obtained values of the HTC are up to 25 % higher
than the Petukhov-Gnielinski ones.
7 The values obtained at the nominal conditions differ from those considered in the beam dump
and its cooling system design (based on Petukhov-Gnielinski correlation) by less than 10 %.
128
CONCLUSIONS AND FUTURE WORK
The main objective of this thesis which was designing a cooling circuit for the LIPAc beam dump
has been accomplished. The main parameters obtained from this work are the following:
• Variable annular cooling channel geometry, designed to meet the heating needs throughout
the beam dump cooling channel by modifying the water velocity and hence the heat transfer
coefficient.
• Water flow of 30 kg/s, obtaining a temperature difference along the cooling channel of 9.14 o C.
• A beam dump rugosity value of 6.5 µm.
• Inlet pressure of 3.5 bar and a pressure loss in the whole beam dump of 1.5 bar.
The beam dump design has been performed solving the heat transfer equations assuming a 1D
heat conduction. Petukhov-Gnielinski correlation has been the chosen one for the heat transfer coefficient calculation. It has been checked that the nominal heat flux is at least 1.9 times lower than
the critical heat flux.
The 1D design has been complemented with 3D studies performed with the ANSYS CFX code in
the areas where 1D analysis is not valid. The main conclusions from these studies are the following:
• At least 1 m length of straight pipe is required prior to the beam dump entrance in order to
have a uniform flow.
• The beam dump tip has been shaped trying to minimize the impact on the flow.
• The heat transfer coefficient at the 180o water turn region was estimated and showed to be
sufficient for the required cooling needs.
• The effect of geometrical imperfections in the cartridge was assessed, concluding that for realistic manufacturing and mounting tolerances the heat transfer changes are not relevant.
• The influence on the flow of mounting 5 mm and 1 mm thermocouples was also analysed. 1
mm thermocouple was disturbing the flow in a much more moderate way than the 5 mm one.
129
Conclusion
• The heat transfer coefficient values obtained have been used in the mechanical simulations of
the beam dump as a contour condition.
An experimental campaign to validate some aspects of the beam dump design such as the pressure loss and the heat transfer coefficient value was designed. For this purpose a hydraulic circuit
that provides a water flow with the beam dump design conditions was constructed at Ciemat and
two prototypes were built.
The pressure loss validation was performed in a 1:1 beam dump prototype and it confirmed the
1.5 bar pressure loss between the inlet and outlet of the beam dump cartridge. For the heat transfer coefficient experiment, an stainless steel prototype reproducing the geometry of a beam dump
annular cooling slice was designed. An extensive experimental campaign eliminating the different
systematic errors was performed. The heat transfer coefficient was validated for three different water flows: 25 m3 /h, 60 m3 /h and 108 m3 /h. The experimental results have been compared with the
Petukhov-Gnielinski correlation and they show a high level of concordance, being the obtained experimental values a maximum of 25 % higher and therefore beneath the 40 % maximum allowed
uncertainty.
From a study of the literature about copper corrosion, the water quality requirements for the
beam dump were defined:
• pH in the range of 8 -8.5.
• Dissolved oxygen < 10 ppb.
• Conductivity in the interval 0.5 - 2 µS/cm.
A corrosion study with TRACT (TRansport and ACTivation code) for two different pH values (pH
= 7 and pH = 8.5) was undertaken, showing maximum corrosion rates of 0.9885 g/(m2 · year) and
0.01632 g/(m2 · year) respectively, thus confirming the choice of pH 8.5 for the beam dump cooling
water circuit.
The future work areas where the research activities developed in this thesis could be continued
are the following:
This thesis has contributed to the final design of the beam dump cartridge and of its cooling system. The final cartridge is already being manufactured whereas the cooling system will be procured
along 2015 so that the whole beam dump can be delivered to Japan in 2016.
Therefore the design work presented in this thesis is finished. However the tools developed and the
procedure employed to design the LIPAc beam dump shown in this thesis can be employed for other
beam dumps with annular cooling geometries, like the ones foreseen for the IFMIF accelerators.
The validation activities performed as part of this thesis could be improved and extended in
future projects in several ways:
130
Conclusion
• The experimental determination of the heat transfer coefficient could be improved by measuring the heat flux directly instead of inferring it from the heater parameters. This could be
done in two ways which imply some changes in the experimental setup:
7 Embedding thermocouples at different depths inside the PHETEN wall.
7 Placing two band heaters close to each other and leaving a small space between them
where thermocouples could be inserted (in this way the problems encountered measuring the temperature with thermocouples beneath the band heater would be avoided).
• The critical heat flux could be validated in the hydraulic circuit employed for the pressure loss
and heat transfer coefficient experiments.
• Experimental corrosion rate values could be obtained in the hydraulic circuit placing copper
samples in one of its branches.
131
APPENDICES
133
Appendix
A
CALIBRATION
One of the key aspects determining the heat transfer coefficient is having a trustworthy temperature measurement. This is crucial due to the low temperature differences measured between bulksurface and bulk thermocouples. It was seen that for the same absolute temperature, the different
thermocouples could differ 1o C in their measurement. Although all the thermocouples employed
in the experiment are type T with an accuracy of ± 0.5o C, each of them was calibrated so that an
individual temperature vs voltage response curve was obtained. Therefore the voltage signal of each
thermocouple can be processed individually and hence a more accurate temperature measurement
obtained.
Ten type T thermocouples were calibrated so that in case some of the them broke they could
quickly be replaced. The most important issue of calibrating them at the same time is that they are
all affected by the same boundary conditions, and hence any deviation in the response curves influences the ten thermocouples in the same way.
For such task the following material was employed:
• A tubular oven model Carbolite MTF 12/38/250.
• Ten type T thermocouples.
• Personal computer with LAbView software installed.
• Multimeter Keithley 2000.
• Calibrated temperature probe Rotronic AG Hygroskop A1 with a +- 0.3 K precision.
The ten thermocouples were bundled together and placed inside the oven (figure A.1), fixed in
the middle section so that no temperature differences in the measurement arose debt to temperature gradients in the oven (see figure A.2). The thermocouples were connected to the Keithley 2000
multimeter so that the voltage signal of each thermocouple could be recorded. A data acquisition
system was developed employing LabView. The Keithley multimeter was connected through the PCI
port to a computer running LabView software. LabView was programmed to control the triggering
135
Figure A.1: Calibration experimental setup.
signal sent to the Keithley, obtain the voltage signal and write it to a text file together with the external temperature obtained from the probe.
The calibrated thermocouples were connected to the ten measuring channels present at the
Keithley. They were distributed as follows:
• Channels 1 to 5 were the 0.5 mm mineral insulated thermocouples.
• Channels 6, 8 and 9 were the wire thermocouples (diameter of 0.2 mm).
• Channels 7 and 10 were the 1 mm mineral insulated thermocouples.
The obtained data was processed so that a response curve for each thermocouple could be obtained. The voltage and temperature data has been fitted with a fourth degree equation. In figure A.3
the temperature in Celsius degrees versus the voltage in millivolts for the different thermocouples
together with the standard calibration curve are plotted.
136
Figure A.2: Calibration thermocouple setup.
120
Therstd
y(x)
Ch1data
Ch2data
Ch3data
Ch4data
Ch5data
Ch6data
Ch7data
Ch8data
Ch9data
Ch10data
100
T [oC]
80
60
40
20
0
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
V [mV]
Figure A.3: Calibration curves of the ten type T thermocouples and the standard response curve.
137
138
Appendix
B
TEMPERATURE MEASUREMENTS
INSIDE THE PHETEN WALL
B.A
Different thermocouple configurations on a stainless steel pipe
Extremely high temperature measurements on the PHETEN wall (as seen in section 6.4.3) motivated an experimental campaign using 6” diameter stainless steel 304L pipe sections. The aim was
learning about the best way of performing the temperature measurements at different depths inside
the wall. The stainless steel pipe sections were tested with the band heater as it had been done with
the PHETEN device, but with air as cooling fluid. These pipe sections were much easier to handle
and besides that, carving, drilling or any other machining activity could be done on these sections,
while not in the PHETEN prototype.
t [min]
1
2
3
4
5
10
Ts [o C]
44.57
67.94
83.49
96.58
106.83
137.78
Tsb [o C]
22.72
39.83
54.80
67.56
78.34
112.92
Table B.1: Temperature measurement improvement # 1.
Three different pipe sections were employed. The tests were performed delivering 87.5 V to the
band heater, which means a heating power of 166 W. The first tests were performed on a 1.5 m pipe
section, carved with a longitudinal slot of 0.2 mm to accommodate the wall temperature thermocouple (Ts ), while the air-material Tsb temperature was directly measured on the inner diameter of
the pipe fixing the thermocouple with aluminium tape. The obtained results can be observed in
table B.1. The expected temperature difference was approximately of 1.2 o C.
139
Ts
Band heater
Tsb
6” stainless steel pipe
Air
Figure B.1: 2, 3 and 4 mm 304L stainless steel sleeves.
A stabilised temperature difference around 25 o C was observed. A second experiment was performed on the same pipe section, but this time the slot to accommodate the external surface thermocouple was increased up to 0.4 mm. The results can be observed in table B.2.
t [min]
1
2
3
4
5
10
Ts [o C]
39.28
58.13
72.96
85.72
96.70
133.34
Tsb [o C]
26.60
42.30
59.20
72.22
83.50
121.01
The temperature difference was reduced to 12-13 o C (see table B.2), which is better than the
results obtained in the first experiment, but still far away from the theoretical 1.2 o C temperature
difference. However it showed the trend to follow in the tests. It was concluded that the surface
temperature thermocouple when in contact with the band heater was measuring the band heater
temperature instead of the one of the material. Therefore the key to improve the setup concentrated
on ensuring a better contact between thermocouple and pipe.
The improvement on heating contact between thermocouple and pipe was tried with computer
thermal paste, usually employed to ensure a better conductivity between the processor and the
motherboard. Arctic Silver 5 thermal compound was the chosen one. It has a thermal conductivity around 9 W/mK according to the data sheet supplied by the manufacturer. The test was once
again performed on the 1.5 m pipe section, increasing the thermal conductivity by filling the 0.4 mm
140
t [min]
1
2
3
4
5
10
Ts [o C]
34.62
52.48
67.26
79.75
90.53
126.58
Tsb [o C]
26.46
43.57
58.13
70.70
81.49
117.27
slot with the thermal compound. The results can be seen in table B.3. The temperature difference
was reduced to 9 o C.
t [min]
1
2
3
4
5
10
Ts [o C]
27.43
44.45
58.80
70.69
80.50
117.36
Tsb [o C]
25.36
41.98
56.13
67.94
77.63
113.37
Next idea was measuring at a certain distance from the surface so that the effect of the heat provided by the band heater did not influence the surface temperature measurement. It was decided
to perform a 1 mm diameter, 2 mm deep perpendicular drill on a 0.5 m stainless steel 304L schedule 10s pipe section. A 0.5 mm type K thermocouple was introduced into the 1 mm diameter drill
obtaining the results of table B.4. The measured temperature difference was 3-4 o C, too high considering that the temperature shift at 1 mm from the inner surface of the pipe should be of 0.35 o C.
t [min]
1
2
3
4
5
10
Ts [o C]
24.07
38.43
52.03
64.08
74.44
111.22
Tsb [o C]
23.02
37.67
51.50
63.69
74.14
110.37
The next step was surrounding the 0.5 mm thermocouple with a 0.9 mm outer diameter and 0.5
mm inner diameter stainless steel 304L sleeve (figure B.2), and introduce it into the 1 mm diameter, 2
mm deep perpendicular drill, filling the space with thermal compound to increase the thermal conductivity. The results can be observed in table B.5. They agree with the theoretical values (around
0.35 o C temperature difference) until minute 5 of the experiment. It is seen how in minute 10 the
temperature difference has grown up to 0.85 o C, probably due to two dimensional heat transfer, con141
sequence of the 0.5 m length of the testing pipe.
Figure B.2: 2, 3 and 4 mm 304L stainless steel sleeves.
The conclusions drawn from these tests were the following:
• The thermocouple in contact with the band heater does not provide a credible surface temperature measurement (Ts ) because it is affected by the heater. Therefore this thermocouple
was suppressed.
• The temperature measurement in the wall with the 0.5 mm thermocouples improved significantly by using a 0.9 mm 304L stainless steel sleeve around them.
• The measurement improved even more by employing a thermal compound to fill any air space
between the PHETEN and the thermocouples.
• It was decided to back up the Tin thermocouple with a thermocouple placed in contact with
the flowing water.
B.B
Measurements with the bolt thermocouple
In order to improve the wall measurements a 4.5 mm deep, 3 mm diameter drill was performed
in the area below the band heater. The idea was introducing a bolt with a through hole in the centre
so that it could allocate a thermocouple. In figure B.3 the bolt geometry can be observed. The bolt
was screwed to the PHETEN prototype, and in the through hole a 0.5 mm thermocouple introduced
142
Figure B.3: 4 mm long, 3 mm diameter bolt.
to measure the wall temperature ensuring a good thermal contact. The thermocouple was fixed
to the bolt by means of a cold welding paste, fixing it and at the same time removing air from the
through hole.
60
T2
T3
T4
T5
50
50
T2
T4
T5
40
40
o
T [ C]
20
20
10
10
0
0
-10
-20
0
10
20
30
40
50
60 0
Steps
10
20
30
40
50
-10
60
Steps
Figure B.4: Thermocouple response with bolt in- Figure B.5: Thermocouple response without the bolt
stalled.
installed.
In figure B.4 the result of heating the PHETEN prototype with a voltage of 67.5 V is presented.
Thermocouples T2, T4 and T5 are the ones welded on the inner surface, whilst T3 corresponds to
the bolt thermocouple. It is seen how the temperatures reached by T3 are higher than the ones
expected. They should be pretty close to the ones obtained by T2, T4 and T5, because they are
separated by 0.5 mm. In figure B.5 where T3 was removed and the rest of the experimental setup
was maintained, the temperature values agree with the expected ones. The explanation of the temperature difference in figure B.4 between T4 and T5 with respect to T2, is that T3 creates an space
between the band heater and the outer surface causing an anisotropy in the heat conduction, where
143
T [oC]
30
30
T4 and T5 (separated by few milimiters) receive a higher heat flux than T2 which is separated from
T4 and T5 by some centimetres.
Conclusions from this setup are the following:
• The bolt does not measure the real temperature on the wall. The bolt presence affects the heat
transfer obtaining higher temperatures than the expected despite the thermal paste and the
manufacturing precision. Therefore it can not be employed as an alternative measurement for
the wall temperature.
• Any object between the band heater and the prototype creates an anisotropy in the heat flux
and hence careful attention must be paid if wall thermocouples are to be used.
144
Appendix
C
TEMPERATURE MEASUREMENTS AT
THE WATER-SURFACE INTERFACE
C.A
Transient experiments performed on a stainless steel plate
The relevant results of testing different welding procedures over a stainless steel plate and the
thermocouple response when covered with Araldit, duct and copper tape, are presented in this section.
70
Temp
T1
T2
T3
65
60
T [oC]
55
50
45
40
35
30
25
0
5
10
15
20
25
30
Steps
Figure C.1: Temperature evolution with T2 covered with Araldit and T1 and T3 with copper tape.
145
70
Temp
T1
T2
T3
65
60
T [oC]
55
50
45
40
35
30
25
0
5
10
15
20
25
30
35
Steps
Figure C.2: Temperature evolution with T2 covered with duct tape and T1 and T3 with copper tape
70
Temp
T1
T2
T3
65
60
T [oC]
55
50
45
40
35
30
25
0
5
10
15
20
25
30
35
40
45
Steps
Figure C.3: Temperature evolution with bare thermocouples.
Thermocouples T1 and T3 are welded with both wire ends together, while T2 wires are welded
separately on the flat plate. The plate is immersed in a controlled temperature cask filled with water.
Once the plate is in equilibrium, it is then taken out and temperature measurements are performed
registering the transient cooling on the plate. A temperature gauge (Fluke 177 with the 80TK ther146
mocouple module) is employed to have an independent measurement of the temperature evolution
on the plate.
In figure C.1 the temperature evolution with T2 covered with Araldit and T1 and T3 covered with
copper tape is presented. It is seen how T2 due to the low conductivity of the Araldit has a slower
response than T1 and T3.
In the next experiment Araldit was removed from T2 and was then covered with duct tape. T1 and
T3 remain as in the previous experiment. Figure C.2 shows the temperature evolution of the three
thermocouples. This time their evolution is quite similar because no isolating material is present on
the thermocouples tips.
It was then decided to test the thermocouples response without any cover on their tips. In figure
C.3 the evolution of the three bare thermocouples is presented. It is seen how they respond in the
exact same way, showing that any cover on the thermocouple tip alters its response.
70
Temp
T1
T2
T3
65
60
T [oC]
55
50
45
40
35
30
25
0
5
10
15
20
25
30
35
Steps
Figure C.4: Temperature evolution with T1 and T2 covered with duct tape and T3 uncovered.
In the last setup T1 and T2 thermocouples were covered with duct tape, while T3 was left uncovered. In figure C.4 no clear trend in the thermocouple response is observed. They do not show
the behaviour seen in figure C.3 where the tips of the thermocouples were left uncovered, neither
the one seen in figure C.1 where one of them was covered with Araldit and the rest uncovered. The
thermocouples respond approximately in the same way showing certain oscillations but nothing remarkable.
147
From this testing the following conclusions were obtained:
• The 0.5 mm thermocouples were much easier to weld than its predecessors (0.2 mm). The
joint was more rigid and robust.
• Temperature measurements with thermocouples welded in different ways gave the same results gaining confidence in the welding technique employed.
• Covering the thermocouple tip with an insulating element delayed the thermocouple response.
C.B
C.B.1
Experiments performed in PHETEN
Thermocouples fixed and covered with Araldit and duct tape
Tout
T2
T1
Band heater
Tmed
Tin
Outer cylinder
Inner cylinder
Annular channel
Figure C.5: Experimental setup scheme for T1 and T2 covered with Araldit and duct tape respectively.
This setup (see figure C.5) consists of three 0.5 mm mineral insulated thermocouples to measure
the temperature on the heated wall at different depths (2, 3 and 4 mm being Tout , Tmed and Tin ), two
0.2 mm wire thermocouples (T1 and T2) to measure the temperature of the material surface in contact with the water, and one mineral insulated 1 mm thermocouple for the bulk temperature (T5).
All the thermocouples employed are type T. In view of the results obtained in the tests performed on
a pipe (see Appendix B), the wall thermocouples were introduced into a 0.9 mm 304L stainless steel
sleeve, and filled when introduced into the 1 mm diameter drill in the PHETEN with thermal paste.
The 0.2 mm diameter for the T1 and T2 thermocouples were chosen so that they did not perturb
the water flow. These thermocouples were glued to the surface by means of Araldit and duct tape
respectively. The wires were fixed to the inner surface of PHETEN by means of duct tape (see figure
148
C.8). The through drills for the cables were filled with Araldit so that no water leaked through them.
T5 was placed prior to the entrance of the water flow in the PHETEN prototype. The whole setup is
covered with a fibreglass blanket to isolate it from the environment and favour the heat conduction
towards the water flow.
80
Tout
Tmed
Tin
T5
T1
T2
70
T [oC]
60
50
40
30
20
10
0
2
4
6
8
10
12
Steps
Figure C.6: Temperature readings of the different thermocouples for the 25 m3 /h water flow.
With such setup (see figure C.5) the experiment was performed for 25 m3 /h, 80 m3 /h and 108
m3 /h water flows and full power in the band heater. In figures C.6 and C.7 the temperatures are
plotted. It is seen that Tout , Tmed and Tin despite the improvements performed, still give higher temperatures than the theoretically expected ones. This is thought to be due to a bad thermal contact
between the thermocouple and the PHETEN material.
Once a steady state has been reached, an average value of the temperature difference between
T1 and T2 thermocouples with respect to T5 is obtained, and hence the heat transfer coefficient. 1
Flow [kg/s]
25
80
108
hpet [W/m2 K]
8745
19041
32482
hT 1 [W/m2 K]
6157
19144
31077
hT 2 [W/m2 K]
11436
15908
16544
Table C.1: Film transfer coefficient results based on T1 and T2.
In table C.1 the Petukhov, T1 and T2 based heat transfer coefficient calculations are presented. It
is seen how the T1 derived HTC agrees with the theoretical values quite precisely for the 80 m3 /h and
1 In the case of 25 m3 /h (figure C.6), only the last two points are considered.
149
100
Tout
Tmed
Tin
T5
T1
T2
90
80
90
80
70
60
T [oC]
T [oC]
70
Tout
Tmed
Tin
T5
T1
T2
100
50
60
50
40
40
30
30
20
20
10
10
0
2
4
6
8
10
12
0
2
4
Steps
6
8
10
12
Steps
Figure C.7: Temperature measured for the 80 m3 /h (left) and 108 m3 /h (right) water flows.
108 m3 /h flows, while in the 25 m3 /h case the results show a higher deviation. These results were
encouraging because they were pointing in the right direction. When they were repeated in order to
correct the non steady state of the 25 m3 /h experiment, it turned out that T2 broke at the beginning
of the experiment and hence no comparable data could be obtained. See figure C.8 where the T1
and T2 thermocouple state after emptying the hydraulic circuit is presented.
Figure C.8: 0.2 mm diameter thermocouples fixed with duct tape and Araldit
To sum up, fixing T1 and T2 to the inner wall of PHETEN showed to be a good solution for the
surface-material measurement, although it was seen that thermal contact had to be improved. Re150
14
garding the wall thermocouples, the stainless steel sleeve and the thermal paste improve the temperature measurement but the obtained values were too high compared with the theoretical ones.
Conclusions drawn from the different experiments carried out with this setup were the following:
• Covering the water-material thermocouples increased the thermal contact with the PHETEN
inner surface, hence effort would concentrate on such area.
• Thermal contact was better in T1 than in T2 (thermocouples fixed at the inner surface of
PHETEN). After analysing the state of the thermocouples when this campaign was finished,
it was observed that some Araldit was in between the stainless steel surface and the thermocouple, explaining the lower temperatures obtained by T2.
• Temperature measurements with Tout , Tmed and Tin were rethought in order to find a way to
improve them.
C.B.2
Thermocouples welded
In this section the experiments carried out with the thermocouples welded in the same way as
the final setup are presented. In figures C.9 and C.10 the experiment was carried out with the thermocouple tip in T1 and T2 covered with Araldit. T3 embedded in the PHETEN inner surface and
slightly covered by an Araldit film, and T4 covered with duct tape.
20
T4 - T5
T3 - T5
T2 - T5
T1 - T5
18
16
14
∆T [oC]
12
10
8
6
4
2
0
-2
0
10
20
30
40
50
60
Figure C.9: Temperature difference in the experiment performed with T1 and T2 covered with Araldit, T3
embedded and T4 covered with duct tape.
The experiment was performed with full band heater power (V = 256 V) and employing the fibreglass blanket to avoid heat losses. Three different flows were tested, 25 m3 /h, 60 m3 /h and 108 m3 /h,
151
and the circuit was set with an inlet pressure of 2.5 bar. In figure C.9 and table C.2 the results of the
experiment carried out with no wall thermocouples are presented, while in figure C.10 the results of
the experiment carried out with the wall thermocouples present can be observed. It is seen that the
temperature difference between the four wall thermocouples and the water is higher than it should
be (∆Ttheo ). T3 as expected because it was embedded in the PHETEN surface gives higher temperatures than the rest of the thermocouples. T1, T2 and T4 all of them with the tip covered reach similar
temperatures for the different flows tested.
∆Ttheo [o C]
8.95
4.11
2.41
Flow [m3 /h]
25
60
108
∆T 1exp [o C]
11.6
8.26
6.69
∆T 2exp [o C]
11.53
7.78
6.08
∆T 3exp [o C]
18.07
13.01
11.94
∆T 4exp [o C]
13.01
8.18
5.94
Table C.2: Theoretical and experimental temperature gradient values for the different thermocouples # 1.
20
T4 - T5
T3 - T5
T2 - T5
T1 - T5
18
16
14
∆T [oC]
12
10
8
6
4
2
0
-2
0
10
20
30
40
50
60
70
Figure C.10: Temperature difference in the experiment performed with T1 and T2 covered with Araldit,
T3 embedded, T4 covered with duct tape and the presence of the wall thermocouples.
The experiment carried out with the wall thermocouples installed between the band heater and
the PHETEN wall are presented in figure C.10 and table C.3. Due to the heat transfer anisotropy
caused by the presence of the wall thermocouples, the slope of the temperature difference is higher
than the one observed in figure C.9 (especially T4). Lower temperatures in T1, T2 and T4 derived
from the poor surface contact between the heater and the outer surface of PHETEN are obtained,
whereas T3 reaches slightly higher values than the ones of the experiment without the wall thermocouples. In any case the values obtained do not match the theoretical values (see table C.3).
152
∆Ttheo [o C]
7.20
3.67
2.26
Flow [m3 /h]
25
60
108
∆T 1exp [o C]
9.38
6.89
5.19
∆T 2exp [o C]
9.82
6.93
5.32
∆T 3exp [o C]
19.33
15.05
11.35
∆T 4exp [o C]
9.77
6.89
6.07
It was then decided to remove the duct tape from T4 and the Araldit from all thermocouples except from T1. The experiment was repeated under the same conditions of the previous one with the
duct tape and the Araldit. In this case Position 1 of the band heater was employed (see Appendix D).
Based on the previous results the experimental time at each water flow was increased to assure
that steady state was reached. In figure C.11 it is seen that T1 keeps behaving as in previous experiments, while T2 and T4 as they are not covered by any Araldit layer reach lower temperatures
than before. Even T1 which remained untouched, lowers its values because the isolating layer in its
vicinity was removed. This fact can be clearly observed in Table C.4, where the temperature results
are presented. The temperatures are much closer to the theoretical ones but still do not match the
expected values. If a heat transfer calculation is made for the water flow of 108 m3 /h considering
T2 and T4, taking the theoretical film transfer coefficient as valid, it comes out that half of the heat
power would be entering the PHETEN prototype.
12
T4 - T5
T3 - T5
T2 - T5
T1 - T5
10
∆T [oC]
8
6
4
2
0
-2
0
20
40
60
80
100
120
140
160
Figure C.11: Temperature difference in the experiment with no Araldit and no wall thermocouples.
The whole setup was checked because in the last experiment (see section C.B.2) performed it
was found that according to the thermocouple measurements of T2 and T4, which were by that time
reliable, half of the theoretical power was being delivered to the PHETEN. Therefore the fibreglass
blanket was removed and the voltage checked at the band heater pins. It was found that the heater
153
Flow [m3 /h]
25
60
108
∆Ttheo [o C]
7.20
3.67
2.26
∆T1exp [o C]
8.27
5.58
4.87
∆T2exp [o C]
3.28
1.58
1.09
∆T3exp [o C]
11.21
8.25
7.11
∆T4exp [o C]
3.34
1.57
1.04
was loosely attached to the PHETEN outer cylinder wall due to the heat expansion experienced by
the band heater. This situation was causing a deficient thermal contact and hence a lower input
power. It was solved by adjusting the band heater at full power.
154
Appendix
D
BAND HEATER POWER DENSITY
The band heater power density was studied because it was observed that depending on the position, thermocouples were being heated unequally. Therefore it was decided to perform an experiment turning the band heater approximately 55o each time, covering half of the band heater in three
turns. In figure D.1 the different band heater experimental positions are shown.
Band heater
Position 1
Position 2
Position 0
Figure D.1: Different band heater experimental positions.
The four thermocouples welded to the inner surface of PHETEN comprise approximately 45o .
Position 0 was taken as the closest point to the electric connectors of the band heater. The experiments are made with a voltage of 53 V with still air as cooling fluid, lasting four minutes by position.
155
15
T1-50o
T2-40oo
T3-15
T4-5o
10
T [oC]
5
0
-5
-10
1
2
3
4
5
6
7
8
9
Figure D.2: Thermocouple response at Position 0.
In figure D.2 Position 0 results are shown. The number accompanying the temperature in the
figure legend is the position in degrees of each thermocouple. It is seen how T4 and T3 give lower
temperatures than T1 and T2, which are placed closer to the centre position of the heater. 1
Position 1 temperature response is presented in figure D.3. It is the central part of the heater and
as seen the temperatures are quite uniform. Position 1 was the one chosen to carry out the rest of
the experimental campaign.
T1-110oo
T2-100o
T3-75o
T4-65
8
T [oC]
6
10
T1-170oo
T2-160o
T3-135o
T4-125
8
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
In figure D.4 Position 2 thermocouple responses are presented. In this case T4 and T3 reach
1 The
maximum temperature obtained by T2 and T1 is higher than the ones obtained in figure D.3 because in the first 15
seconds the power unit had to be regulated to 53 V, delivering a higher power during that time.
156
T [oC]
10
higher temperatures than T1 and T2 because they are closer to the middle section of the heater, exactly the opposite situation of Position 0.
Density
Power density [%]
100
80
60
40
20
0
0
20
40
60
80
100
120
140
160
180
o
Phi [ ]
Figure D.5: Power density percentage along the band heater.
The heating velocity has been calculated at each position. Steps 6 and 3 are taken for such calculation (see expression D.1). The heating rate for each position is normalized to the maximum
heating rate (see equation D.2).
∆T
T (t = 6) − T (t = 3)
=
∆t
∆t
%Pdensity =
∆T /∆t
(∆T /∆t)max
(D.1)
· 100
(D.2)
Figure D.5 shows the normalized power density results. It is seen that there is a wide section from
phi = 40o to phi = 135o where the power density delivered by the band heater is quite homogeneous.
Hence experiments are performed in this section, more specifically in Position 1.
157
158
Appendix
E
CHICA CODE
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# ! / usr / bin / python
# -* - coding : utf -8 -* # CHICA ( Cooling and Heating Interaction and Corrosion Analysis )
# 1 D Code developed to calculate the heat transmission and flud dynamics
aspects of the beam dump cartridge .
# Be aware : To run fipy library in subprocess ’ refrigeration - pot - Tran . py ’,
version 2.7 or higher of python is needed .
from math import *
import subprocess
# - - - - - - - - - - - - - - - - - - - - - - - - - - File definitions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -#
# Input files
iPot = open ( " curva de potencia1mm . txt " )
iKMat = open ( " conductividad termica Cu . txt " )
iCpRef = open ( " calor especifico refrigerante . txt " )
iKRef = open ( " conductividad termica refrigerante . txt " )
iDensRef = open ( " densidad refrigerante . txt " )
iPrandtl = open ( " numero de Prandtl . txt " )
iVisco = open ( " viscosidad dinamica refrigerante . txt " )
iSection = open ( " curva de seccion1mm . txt " )
iEb = open ( " ebullicion . txt " )
iSatRef = open ( " saturacion . txt " )
iXRef_02 = open ( " G_02 . txt " )
iXRef_015 = open ( " G_015 . txt " )
iXRef_01 = open ( " G_01 . txt " )
iXRef_005 = open ( " G_005 . txt " )
iPsat = open ( " Psat . txt " )
# Output files
oTempSI = open ( " temperaturesSI . txt " , " w " )
oVarsSI = open ( " variablesSI . txt " , " w " )
oPresSI = open ( " pressureSI . txt " , " w " )
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oRet = open ( " Ret . txt " , " w " )
oEsp = open ( " Espesor . txt " ," w " )
oQboil = open ( " Boiling . txt " ," w " )
oFricc = open ( " Fricc . txt " ," w " )
oInflu = open ( " Error . txt " ," w " )
oFilmlim = open ( " ENucleada . txt " ," w " )
oCrittab = open ( " CHFtab . txt " ," w " )
oLam = open ( " Laminar . txt " ," w " )
oTran = open ( " Transitional . txt " ," w " )
oFilm = open ( " HTC . txt " ," w " )
oData = open ( " Data_Refr . txt " ," w " )
oVarsSI . write ( " # z ( m )\ t Velocidad ( m / s )\ t Re \ t Re_epsi \ t h_gni ( W /( m ^2* C ))\
\ t Q_corrected ( W / cm ^2) \ t Bound_layer ( m ) \ n " )
oPresSI . write ( " # z ( m )\ t Pressure ( Pa ) \ t Pressure ( bar ) \ n " )
oTempSI . write ( " # z ( m )\ t Tbulk ( C ) \ t Tbulk after return ( C ) \ t Tsb ( C ) \ t \
Tsb after return ( C ) \ n " )
oRet . write ( " # z ( m )\ t Velocidad_ret ( m / s )\ t Re_ret \ t h_ret ( W / m ^2* C ) \ t \
Tbulk after return ( C ) \ t Shroud temp ( C ) \ t Q_tot ( W / m ^2) \ t Q_corr ( W / m ^2)\
\ t P_ret \ n " )
oEsp . write ( " # z ( m ) \ t Rint + Eint + esp ( m ) \ t Espesor ( m ) \ t Area ( m ^2) \ t \
1/ Area (1/ m ^2) \ Dh ( m ) \ n " )
oQboil . write ( " # z ( m ) \ t T_boil ( C ) \ t Q_boil ( W / cm ^2) \ t Q_dep ( W / cm ^2)\
\ t Eckert \ t X \ t Qcrit2 ( W / cm ^2) \ n " )
oFricc . write ( " # z ( m ) \ t Dynamic pressure ( Pa ) \ t Fricc ( Pa ) \ t \
Darcy - Weisbach friction parameter \ n " )
oInflu . write ( " # z ( m ) \ t h_gni ( W / m ^2 C ) \ t 1.06* h_gni ( W / m ^2 C ) \ t \
0.94* h_gni ( W / m ^2 C ) \ n " )
oFilmlim . write ( " # z ( m ) \ t Tlim ( C ) \ t hlim ( W / m ^2 C ) \ t h_gni ( W / m ^2 C ) \ n " )
oCrittab . write ( " z ( m ) \ t X ( adim ) \ t CHF ( W / cm ^2) \ t Ratio \ t Percentage \ n " )
oLam . write ( " z ( m ) \ t Bulk - surface temp ( C ) \ t h_shah ( W / m ^2 C ) \ n " )
oTran . write ( " z ( m ) \ t Bulk - surface temp ( C ) \ t h_levens ( W / m ^2 C ) \ n " )
oFilm . write ( " # z ( m ) \ t h_gni ( W / m ^2 C ) \ t h_Petukhov ( W / m ^2 C ) \ t \
h_roiz ( W / m ^2 C ) \ n " )
oData . write ( " # z ( m ) \ t Rint ( m ) \ t Rext ( m ) \ t Width ( m ) \ t v ( m / s ) \ t \
Q_bulk ( W / cm ^2) \ t Q_dep ( W / cm ^2) \ t Tb ( C ) \ t Tsb ( C ) \ t rho ( kg / m ^3) \ t \
mu ( kg / ms ) \ t Re \ t f \ t h_gni ( W /( m ^2* C )) \ t h_roiz ( W /( m ^2* C )) \ t \
P ( bar )\ t Psat ( bar ) \ t Tsat ( C ) \ t CHFtab ( W / cm ^2) \ t CHFbosc ( W / cm ^2) \ t \
Qboil ( W / cm ^2) \ n " )
# - - - - - - - - - - - - - - - - - - - - - - - - Parameter definition - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -#
h = 5E -3 # m , thickness
q_r = 30 # kg /s , Coolant mass flow
ref_type = " axial " # Refrigeration type
espesor_type = " fernando_1 "
spiral_tube = " rectangular " # A = a * b
g = 9.81 # Gravity
epsi = 0.0000065 # Rugosity value in m
epsi2 = 0.0000015 # Rugosity value in m
tp = 0.004 # Shroud thickness in m
sigma = 0.05891 # Water superficial tension in N / m
Tsat = 123.476 # Saturation temperature for P =2.28 bar
Hfg = 2272000 # Enthalpy of vaporization in J / kg
PM = 18 E -3 # Molar mass of water in kg / mol
R_ret = 0.198 # Cartridge radius in m
duty_cycle = 1 # Beam dump duty cycle
# - - - - - - - - - - - - - - - - - - - - - - - - - - Lists of data in files - - - - - - - - - - - - - - - - - - - - - - - - - -#
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kMat_0 = [] # temp in C
kMat_1 = [] # K in W ( m C )^ -1
cpRef_0 = [] # temp in C
cpRef_1 = [] # cp in J ( kg C )^ -1
kRef_0 = [] # temp in C
kRef_1 = [] # K in W ( m C )^ -1
pot_0 = [] # z in mm
pot_1 = [] # DP in W / cm ^2
densRef_0 = [] # temp in C
densRef_1 = [] # density in kg ( m )^ -3
prandtl_0 = [] # temp in C
prandtl_1 = [] # Prandtl number ( adimensional )
visco_0 = [] # temp in C
visco_1 = [] # dynamic viscosity in kg ( m s )^ -1
section_0 = [] # z in cm
section_1 = [] # r in cm
boil_0 = [] # P in kPa
boil_1 = [] # T in C
XRef_02 = [] # Interpolation parameters for CHF_tab calculation
Psat_0 = [] # Temperature value of the saturated pressure in C
Psat_1 = [] # Saturated pressure value in bar
CHF_2 = [] # Argument employed to call the boiling_tab function
T_boil = [] # Array used to calculate the saturation temperature
Boil = [] # Array empployed to calculate the boiling heat flux
Ra = [] # Array employed as dummy variable
Q_critot = [] # Array employed to keep the critical boiling heat value
PRef_0 = [] # Temperature reference for the saturation calculation
PRef_1 = [] # Temperature reference for the saturation calculation
R_d = [] # Adimensional density coefficient
rho_v = [] # Water vapor density
X = [] # Enthalpic quality
E_c = [] # Eckert number
B_oc = [] # Adimensional critical heat flux
B_oc2 = [] # Adimensional critical heat flux
Q_crit2 = [] # Alternative CHF value
friction = [] # Friction parameter
P_loss = [] # Pressure loss array
CHF_tab = [] # Tabulated critical heat flux value
# - - - - - - - - - - - - - Read files and store data - - - - - - - - - - - - - - - - - - - -#
for line in iSection :
data = line . split ()
section_0 . append ( float ( data [0])*1 E -3 )
section_1 . append ( float ( data [1])*1 E -3 )
for line in iKMat :
kMat_0 . append ( float ( data [0]) )
kMat_1 . append ( float ( data [1]) )
for line in iCpRef :
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cpRef_0 . append ( float ( data [0]) )
cpRef_1 . append ( float ( data [1]) )
for line in iKRef :
kRef_0 . append ( float ( data [0]) )
kRef_1 . append ( float ( data [1]) )
for line in iPot :
pot_0 . append ( float ( data [0])*1 E -3 )
pot_1 . append ( float ( data [1])*1 E4 )
for line in iDensRef :
densRef_0 . append ( float ( data [0]) )
densRef_1 . append ( float ( data [1]) )
for line in iPrandtl :
prandtl_0 . append ( float ( data [0]) )
prandtl_1 . append ( float ( data [1]) )
for line in iVisco :
visco_0 . append ( float ( data [0]) )
visco_1 . append ( float ( data [1]) )
for line in iEb :
boil_0 . append ( float ( data [0])*1 E3 )
boil_1 . append ( float ( data [1]))
for line in iSatRef :
PRef_0 . append ( float ( data [0]))
PRef_1 . append ( float ( data [1]))
for line in iXRef_02 :
XRef_02 . append ( float ( data [0]))
for line in iPsat :
Psat_0 . append ( float ( data [0]))
Psat_1 . append ( float ( data [1]))
# - - - - - - - - - - - - - List of temperatures and other string variables - - - - - - - - - - - - -#
T_ref = [0.0 for i in range ( len ( pot_0 ) ) ]
T_ref2 = [40.145 for i in range ( len ( section_0 ) ) ]
T_cext = [0.0 for i in range ( len ( pot_0 ) ) ]
T_ref3 = [0.0 for i in range ( len ( pot_0 ) ) ]
T_ref4 = [0.0 for i in range ( len ( pot_0 ) ) ]
T_aux = [0.0 for i in range ( len ( pot_0 ) ) ]
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T_metal = [0.0 for i in range ( len ( pot_0 ) ) ]
T_metal2 = [0.0 for i in range ( len ( pot_0 ) ) ]
T_aux2 = [0.0 for i in range ( len ( pot_0 ) ) ]
P_secc = [0.0 for i in range ( len ( pot_0 ) ) ]
P_ret = [2.48769072972 *1 E5 for i in range ( len ( section_0 ) ) ]
CHF_2 = [0.0 for i in range ( len ( pot_0 ) )]
T_boil = [0.0 for i in range ( len ( pot_0 ) )]
Ra = [0.0 for i in range ( len ( pot_0 ) )]
Boil = [0.0 for i in range ( len ( pot_0 ) )]
Q_critot = [0.0 for i in range ( len ( pot_0 ) )]
Q_crit2 = [0.0 for i in range ( len ( pot_0 ) )]
R_d = [0.0 for i in range ( len ( pot_0 ) )]
X = [0.0 for i in range ( len ( pot_0 ) )]
rho_v = [0.0 for i in range ( len ( pot_0 ) )]
E_c = [0.0 for i in range ( len ( pot_0 ) )]
B_oc = [0.0 for i in range ( len ( pot_0 ) )]
B_oc2 = [0.0 for i in range ( len ( pot_0 ) )]
pot_ret = [0.0 for i in range ( len ( pot_0 ) )]
pot_tot = [0.0 for i in range ( len ( pot_0 ) )]
Rug = [0.0 for i in range ( len ( pot_0 ) )]
friction = [0.1 for i in range ( len ( pot_0 ) )]
Hlim = [0.0 for i in range ( len ( pot_0 ) )]
P_loss = [0.0 for i in range ( len ( pot_0 ) )]
CHF_tab = [0.0 for i in range ( len ( pot_0 ) )]
T_ref [0] = 31.0 # Initial temperature , C
P_secc [0] = 3.5*1 E5 # Initial pressure value , Pa
T_ref3 [0] = 31 # Initial temperature , C
oPresSI . write ( str ( section_0 [0])+ " \ t " + str ( P_secc [0])+ " \ t " + str ( P_secc [0]*1 E -5)\
+"\n")
oTempSI . write ( str ( section_0 [0])+ " \ t " + str ( T_ref [0])+ " \ t " + str ( T_ref [0])+ " \ t " \
+ str ( T_ref [0])+ " \ n " )
# Definition of functions :
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Income - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -#
# Interpolation :
def interpolation ( list_0 , list_1 , value_0 ) :
for j in range ( len ( list_0 ) -1 ) :
if list_0 [ j +1] > value_0 :
return float ( list_1 [ j ] + ( list_1 [ j +1] - list_1 [ j ])/ \
( list_0 [ j +1] - list_0 [ j ])*( value_0 - list_0 [ j ]) )
# Over maximum value ...
return list_1 [ j +1]
# Inner cone thickness ( m ):
def Eint ( index ) :
if section_0 [ index ] <= 20 E -2 : return (1.7 E -2 - section_1 [ index ])
elif section_0 [ index ] <= 200 E -2 :
return 5E -3
elif section_0 [ index ] <= 2015 E -3 :
return 0.1*1 E -3 + Eint ( index -1)
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elif section_0 [ index ] > 2015 E -3 :
return 6.5 E -3
# Gap thickness ( m ):
def espesor ( index_in ) :
if espesor_type == " fernando_1 " :
if section_0 [ index_in ] <= 20 E -2 : return 2.3614*1 E -2
elif section_0 [ index_in ] <= 68.8 E -2 :
return ( 2.3614 + ( section_0 [ index_in ] - 20 E -2)*(1.212 -2.3614)/(68.8 E -\
2 -20 E -2) )*1 E -2
return ( 1.212 + ( section_0 [ index_in ] - 68.8 E -2)*(.7 -1.212)/(125.13 E -2 -\
68.8 E -2) )*1 E -2
elif section_0 [ index_in ] <= 200 E -2 :
return 0.7 E -2
return (0.7 E -2 - Eint ( index_in ) + 5E -3)
elif section_0 [ index_in ] <= 250 E -2 :
return (0.55 + ( section_0 [ index_in ] - 201.5 E -2)*(.7 -.55)/(250*1 E -2 -\
201.5*1 E -2) )*1 E -2
# Cooling water area ( m **2):
def a_r ( index_in ) :
if ref_type == " spiral " :
return a * b
elif ref_type == " axial " :
return pi *( ( section_1 [ index_in ]+ espesor ( index_in ) + Eint ( index_in ) )**2\
-( section_1 [ index_in ] + Eint ( index_in ))**2 )
# Hydraulic diameter ( m ):
def dh ( index_in ) :
# Hydraulic diameter
# Dh = 4 Area / wet perimeter
if ref_type == " spiral " :
return ((2* a * b )/( a + b ))
elif ref_type == " axial " :
return (2* espesor ( index_in ))
else :
print " WARNING : NOT IMPLEMENTED !!!!\ n "
return 1.
# Reynolds number ( Dimensionless ):
def rey ( index ) :
re = interpolation ( densRef_0 , densRef_1 , T_ref [ index ]) * vel ( index ) *\
dh ( index )/ interpolation ( visco_0 , visco_1 , T_ref [ index ])
return re
# Prandtl number ( Dimesionless ):
def pr ( index ) :
return interpolation ( prandtl_0 , prandtl_1 , T_ref [ index ])
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# Friction parameter for rough pipe ( Dimensionless ):
def fricc ( index ) :
a = 2/ log (10)
b = epsi /( dh ( index ) * 3.7)
d = ( log (10) * rey ( index ))/5.2
s = b * d + log ( d )
q = s **( s /( s +1))
g = b * d + log ( d / q )
z = log ( q / g )
Dla = ( g * z )/( g + 1)
Dcfa = Dla *(1 + z /(2*( g + 1)**2 + ( z /3)*(2* g - 1)))
friction = ( a * ( log ( d / q ) + Dcfa ))**( -2)
return friction
# Darcy - Weishbach linear loss height ( m ):
def carga ( index )
:
h_1 = ( fricc ( index ) * ( section_0 [ index +1] - section_0 [ index ]) *\
( vel ( index ))**2) / (2 * float ( g ) * dh ( index ))
return h_1
# Velocity ( m / s ):
def vel ( index ) :
return
q_r /( interpolation ( densRef_0 , densRef_1 , T_ref [ index ])* a_r ( index ))
# - - - - - - - - - - - - - - - - - - Film transfer coefficient correlations - - - - - - - - - - - - - - - - - -#
# Petukhov Nusselt number ( Dimesionless ):
def nusselt_rug ( index ) :
return ( ( fricc ( index )/8.)* rey ( index )* pr ( index )/(1.07+12.7*\
sqrt ( fricc ( index )/8.) * ( pr ( index )**(2./3.) -1)) )
# Petukhov film transfer coefficient ( W / m **2 K ):
def film_rug ( index ) :
hrug = nusselt_rug ( index )* interpolation ( kRef_0 , kRef_1 , T_ref [ index ])\
/ dh ( index )
return hrug
# Petukhov - Gnielinski with Sieder - Tate viscosity correction Nusselt number \
# ( Dimensionless ):
def nusselt_gni ( index ):
return nusselt_rug ( index )*(( rey ( index ) -1000)/ rey ( index ))*\
( interpolation ( visco_0 , visco_1 , T_ref [ index ])\
/ interpolation ( visco_0 , visco_1 , T_metal2 [ index ]))**(0.11)
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# Petukhov - Gnielinski with Sieder - Tate viscosity correction film transfer \
# coefficient ( W / m **2 K ):
def film_gni ( index ):
hgni = nusselt_gni ( index )* interpolation ( kRef_0 , kRef_1 , T_ref [ index ]) \
/ dh ( index )
return hgni
# Roizen with Sieder - Tate viscosity correction film transfer \
# coefficient ( W / m **2 K ):
def film_roiz ( index ) :
hrug = 0.86*(( section_1 [ index ] + espesor ( index ) + Eint ( index ))\
/( section_1 [ index ] + Eint ( index )))**(0.16)* nusselt_gni ( index )\
* interpolation ( kRef_0 , kRef_1 , T_ref [ index ])/ dh ( index )
return hrug
# Laminar film transfer coefficient ( W / m **2 K ):
def nusselt_lam1 ( index ) :
return 1.953*( rey ( index )* pr ( index )* dh ( index )/2.5)**(0.33)
def nusselt_lam2 ( index ) :
return 4.364 +0.0722*( rey ( index )* pr ( index )* dh ( index )/2.5)
def film_lam ( index ) :
if rey ( index )* pr ( index )* dh ( index )/2.5 >= 33.3:
return nusselt_lam1 ( index )* interpolation ( kRef_0 , kRef_1 , T_ref [ index ]) \
/ dh ( index )
else :
return nusselt_lam2 ( index )* interpolation ( kRef_0 , kRef_1 , T_ref [ index ]) \
/ dh ( index )
def nusselt_tran ( index ):
return 0.116*( rey ( index )**(0.66) - 125)* pr ( index )**(0.33)*\
( interpolation ( visco_0 , visco_1 , T_ref [ index ])\
def film_tran ( index ):
return nusselt_tran ( index )* interpolation ( kRef_0 , kRef_1 , T_ref [ index ]) \
/ dh ( index )
# - - - - - - - - - - - - - - - - - - - - - - Boundary layer calculation - - - - - - - - - - - - - - - - - - - - - - - - -#
# Boundary layer thickness ( m ):
def Bound ( index ) :
return 14.1* dh ( index )/( rey ( index )* friction [ index ]**(0.5))
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# Entry lenght ( m ):
def Entlength ( index ) :
return 1.359* dh ( index )* rey ( index )**(0.25)
def Entlength2 ( index ) :
return 0.0575* dh ( index )* rey ( index )
# Turbulence intensity
def inten ( index ) :
return 0.16* rey ( index )**( -0.124)
# - - - - - - - - - - - - - - - - - - - - - - - - - Critical heat flux calculation - - - - - - - - - - - - - - - - - - -#
def boiling ( index ):
T_boil [ index ] = interpolation ( boil_0 , boil_1 , P_secc [ index ])
Q_crit = film_gni ( index )*( T_boil [ index ] - T_metal2 [ index ])*1 E -4
Q_critot [ index ] = Q_crit + pot_1 [ index ]*1 E -4
# Boscary critical heat flux calculation :
if index == 0:
rho_v [0] = ( PM * P_secc [0]) / (8.31 * (350))
R_d [0] = interpolation ( densRef_0 , densRef_1 , T_ref [ index ])/ rho_v [0]
E_c [0] = vel ( index )**2 / ( interpolation ( cpRef_0 , cpRef_1 ,77)*\
( T_boil [0] - T_metal2 [0]))
X [0] = - interpolation ( cpRef_0 , cpRef_1 ,77) * ( T_boil [ index ] - 31) / Hfg
B_oc [0] = (0.025)* exp (( X [0])**2)*( E_c [0]**( -0.1428)* rey ( index )**( -0.25)\
* R_d [0]**( -0.25)*( - X [0])**(0.1))
Q_crit2 [0] = 1.25* interpolation ( densRef_0 , densRef_1 ,77)* vel ( index )* Hfg \
* B_oc [0]
else :
rho_v [ index ] = ( PM * P_secc [ index ]) / (8.31 * ( T_metal2 [ index ] + 273))
R_d [ index ] = interpolation ( densRef_0 , densRef_1 , T_ref [ index ])\
/ rho_v [ index ]
E_c [ index ] = vel ( index )**2\
/ ( interpolation ( cpRef_0 , cpRef_1 , T_metal2 [ index ]))\
*( T_boil [ index ] - T_metal2 [ index ]))
X [ index ] = - interpolation ( cpRef_0 , cpRef_1 , T_ref [ index ])\
* ( T_boil [ index ] - T_ref [ index ]) / Hfg
B_oc [ index ] = 0.025* exp (( X [ index ])**2)*( E_c [ index ]**( -0.1428)* rey ( index )\
**( -0.25)* R_d [ index ]**( -0.25)*( - X [ index ])**(0.1))
Q_crit2 [ index ] = 1.0* interpolation ( densRef_0 , densRef_1 , T_ref [ index ])\
* vel ( index )* Hfg * B_oc [ index ]
return T_boil , Q_critot , Q_crit2 , X
# Tabulated critical heat flux calculation :
def boiling_tab ( index ):
k_x = 0.81
k_p = 0.9
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G = q_r / a_r ( index )
T_boil [ index ] = interpolation ( boil_0 , boil_1 , P_secc [ index ])
X_2 = - interpolation ( cpRef_0 , cpRef_1 , T_ref [ index ])\
* ( T_boil [ index ] - T_ref [ index ]) / Hfg
if espesor ( index ) > 8.26*1 E -3:
k_esp = 0.75
else :
k_esp = 0.663 + 64.374* exp ( - espesor ( index )*1 E +3/1.242)
CHF_0_2 = interpolation ( XRef_02 , XRef_12 , G )
CHF_0_15 = interpolation ( XRef_015 , XRef_115 , G )
CHF_01 = interpolation ( XRef_01 , XRef_11 , G )
CHF_005 = interpolation ( XRef_005 , XRef_105 , G )
if abs ( X_2 ) <= 0.1:
CHF_tab [ index ] = k_x * k_p * k_esp * (( CHF_01 - CHF_005 )*( - X_2 - 0.05)\
/0.05 + CHF_005 )
else :
CHF_tab [ index ] = k_x * k_p * k_esp * (( CHF_0_2 - CHF_0_15 )*\
( - X_2 - 0.15)/0.05 + CHF_0_15 )
return CHF_tab
# - - - - - - - - - - - - - - - - - - - - - - - - - Return calculation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -#
# Cartridge - shroud geometry ( m ):
def geom ( index ) :
esp = R_ret - ( section_1 [ index ] + Eint ( index ) + espesor ( index ) + tp )
return esp
def Out_ret ( index ) :
return section_1 [ index ] + Eint ( index ) + espesor ( index ) + tp
def In_ret ( index ) :
return section_1 [ index ] + Eint ( index ) + espesor ( index )
# Cross sectional return area ( m **2):
def a_ret ( index ) :
return pi *( R_ret **2 - ( section_1 [ index ] + Eint ( index )\
+ espesor ( index ) + tp )**2)
# Return hydraulic diameter ( m ):
def dh_ret ( index ) :
return 2* geom ( index )
# Return velocity ( m / s ):
def vel_ret ( index ) :
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return q_r /( interpolation ( densRef_0 , densRef_1 , T_ref2 [ index ])*\
a_ret ( index ))
# Reynolds number ( Dimensionless ):
def re_ret ( index ) :
return interpolation ( densRef_0 , densRef_1 , T_ref2 [ index ]) \
* vel_ret ( index ) * dh_ret ( index )\
/ interpolation ( visco_0 , visco_1 , T_ref2 [ index ])
# Friction parameter in the water return ( Dimensionless ):
def fricc_ret ( index ) :
a = 2/ log (10)
b = epsi /( dh_ret ( index ) * 3.7)
d = ( log (10) * re_ret ( index ))/5.2
s = b * d + log ( d )
q = s **( s /( s +1))
g = b * d + log ( d / q )
z = log ( q / g )
Dla = ( g * z )/( g + 1)
Dcfa = Dla *(1 + z /(2*( g + 1)**2 + ( z /3)*(2* g - 1)))
friction = ( a * ( log ( d / q ) + Dcfa ))**( -2)
return friction
# # Darcy - Weishbach linear loss height in the return ( m ):
def carga_ret ( index ) :
return ( fricc_ret ( index ) * ( abs ( section_0 [ index -1] - section_0 [ index ]))\
* ( vel_ret ( index ))**2) / (2 * float ( g ) * dh_ret ( index ))
# Petukhov - Gnielinski with Sieder - Tate viscosity correction Nusselt number \
# in the water return ( Dimensionless ):
def nusselt_ret ( index ):
return ( ( fricc ( index )/8.)*( re_ret ( index ) -1000)* pr ( index )/(1.07+12.7\
* sqrt ( fricc ( index )/8.) * ( pr ( index )**(2./3.) -1)) )*\
( interpolation ( visco_0 , visco_1 , T_ref2 [ index ])\
# Return film transfer coefficient ( W / m **2 K ):
def film_ret ( index ) :
hret = nusselt_ret ( index )* interpolation ( kRef_0 , kRef_1 , T_ref2 [ index ]) \
/ dh_ret ( index )
return hret
# Reynolds roughness number ( Dimensionless ):
def re_epsi ( index ) :
return rey ( index )*( epsi / dh ( index ))*( fricc ( index )/8)**(0.5)
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# Function calculating power densities and temperatures in the water return :
def T_ret ( index ) :
T_cext [ i ] = ( film_ret ( i ) * Out_ret ( i ) * T_ref2 [ i ] + film_gni ( i ) *\
In_ret ( i ) * T_ref [ i ]) \
/ ( film_gni ( i ) * In_ret ( i ) + film_ret ( i ) * Out_ret ( i ))
pot_ret [ i ] = film_gni ( i )*( T_cext [ i ] - T_ref [ i ])
pot_tot [ i ] = pot_1 [ i ] + pot_ret [ i ]
T_ref3 [ i +1] = T_ref3 [ i ]+2.0*3.1416*( section_0 [ i +1] - section_0 [ i ])*\
( section_1 [ i ]+ Eint ( i ))* pot_tot [ i ] \
/ ( q_r * interpolation ( cpRef_0 , cpRef_1 , T_ref [ i ]))
return T_cext , pot_ret , pot_tot , T_ref3
# Pressure loss due to the section change ( m ):
k_tip = 1.05
h_tip = k_tip * ( vel (1)**2) * 0.5 / float ( g )
k_1 = 1 - ( float ( dh (200))**4) /( float ( dh (199))**4) # Friction parameter
hs_1 = k_1 * ( vel (200)**2) * 0.5 / float ( g )
hs_2 = k_2 * ( vel (688)**2) * 0.5 / float ( g )
hs_3 = k_3 * ( vel (1251)**2) * 0.5 / float ( g )
k_4 = 0.1127
hs_4 = k_4 * ( vel (2000)**2) * 0.5 / float ( g )
k_exit = 3.3
h_exit = k_exit * ( vel (2498)**2) * 0.5 / float ( g )
# - - - - - - - - - - - - - - - - - - - - Beginning of iterative procedure - - - - - - - - - - - - - - - - - - - - - -#
# Computing the temperature of refrigerant :
for i in range ( len ( section_0 ) -1 ) :
# adjust power density to outer surface :
pot_1 [ i +1] *=
duty_cycle * section_1 [ i +1]/( section_1 [ i +1]+ Eint ( i +1))
T_ref [ i +1] = T_ref [ i ]+2.0*3.1416*( section_0 [ i +1] - section_0 [ i ])\
*( section_1 [ i ]+ Eint ( i ))* pot_1 [ i ] \
/ ( q_r * interpolation ( cpRef_0 , cpRef_1 , T_ref [ i ]))
# Computing the temperature of interface :
if rey ( i ) > 10000:
T_metal [ i +1] = T_ref [ i +1] + pot_1 [ i +1]/ film_rug ( i +1)
T_metal2 [ i +1] = 40 # T_ref [ i +1] + pot_1 [ i +1]/ film_gni ( i +1)
T_aux = T_ref [ i +1] + pot_1 [ i +1]/ film_gni ( i +1)
elif 2300 < rey ( i ) < 10000:
T_metal2 [ i +1] = T_ref [ i +1] + pot_1 [ i +1]/ film_tran ( i +1)
T_aux = T_ref [ i +1] + pot_1 [ i +1]/ film_tran ( i +1)
oTran . write ( str ( section_0 [ i ])+ " \ t " + str ( T_ref [ i ] + pot_1 [ i ]\
/ film_tran ( i ))+ " \ t " + str ( film_tran ( i ))+ " \ n " )
else :
T_metal2 [ i +1] = T_ref [ i +1] + pot_1 [ i +1]/ film_lam ( i +1)
T_aux = T_ref [ i +1] + pot_1 [ i +1]/ film_lam ( i +1)
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oLam . write ( str ( section_0 [ i ])+ " \ t " + str ( T_ref [ i ] + pot_1 [ i ]\
/ film_lam ( i ))+ " \ t " + str ( film_lam ( i ))+ " \ n " )
j = 0
while abs ( T_metal2 [ i +1] - T_aux )
> 1E -8 :
T_metal2 [ i +1] = T_aux
T_aux = T_ref [ i +1] + pot_1 [ i +1]/ film_gni ( i +1)
j = j +1
# print j , i
# Calculation of the pressure profile along the beam dump \
# cooling channel :
if section_0 [ i ] <= 20 E -02 :
P_secc [1] = P_secc [0] - \
interpolation ( densRef_0 , densRef_1 , T_ref [0])* float ( g )\
* float ( h_tip )
P_secc [ i +1] = P_secc [ i ] +\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*0.5*\
( vel ( i )**2 - vel ( i +1)**2)\
+ interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*\
float ( g )*( float ( section_1 [ i ]) - float ( section_1 [ i +1]))\
- interpolation ( densRef_0 , densRef_1 , T_ref [ i ])* float ( g )\
* float ( carga ( i ))
P_secc [200] = P_secc [199] +\
interpolation ( densRef_0 , densRef_1 , T_ref [199])*0.5*\
( vel (199)**2 - vel (200)**2)\
+ interpolation ( densRef_0 , densRef_1 , T_ref [199])*\
float ( g )*( float ( section_1 [199]) - float ( section_1 [200]))\
- interpolation ( densRef_0 , densRef_1 , T_ref [ i ])* float ( g )*\
float ( carga (199) + hs_1 )
elif section_0 [ i ] <= 68.815 E -2 :
P_secc [ i +1] = P_secc [ i ] +\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*0.5*\
( vel ( i )**2 - vel ( i +1)**2)\
+ interpolation ( densRef_0 , densRef_1 , T_ref [ i ])* float ( g )\
*( float ( section_1 [ i ]) - float ( section_1 [ i +1]))\
float ( carga ( i ))
P_secc [688] = P_secc [687] +\
interpolation ( densRef_0 , densRef_1 , T_ref [687])*0.5*( vel (687)\
**2 - vel (688)**2)\
+ interpolation ( densRef_0 , densRef_1 , T_ref [687])* float ( g )*\
( float ( section_1 [687]) - float ( section_1 [688]))\
- interpolation ( densRef_0 , densRef_1 , T_ref [687])* float ( g )*\
float ( carga (687) + hs_2 )
elif section_0 [ i ] <= 125.13 E -2 :
P_secc [ i +1] = P_secc [ i ] +\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*0.5*( vel ( i )**2\
- vel ( i +1)**2)+ interpolation ( densRef_0 , densRef_1 , T_ref [ i ])\
* float ( g )*( float ( section_1 [ i ]) - float ( section_1 [ i +1])) -\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])* float ( g )*\
P_secc [1251] = P_secc [1250] +\
interpolation ( densRef_0 , densRef_1 , T_ref [1250])*0.5*\
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( vel (1250)**2 - vel (1251)**2)\
+ interpolation ( densRef_0 , densRef_1 , T_ref [1250])*\
float ( g )*( float ( section_1 [1250]) -\
float ( section_1 [1251]))\
- interpolation ( densRef_0 , densRef_1 , T_ref [1250])*\
float ( g )* float ( carga (1250) + hs_3 )
elif section_0 [ i ] <= 200 E -2 :
P_secc [ i +1] = P_secc [ i ] +\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*0.5*( vel ( i )**2\
- vel ( i +1)**2) + interpolation ( densRef_0 , densRef_1 , T_ref [ i ])\
* float ( g )*( float ( section_1 [ i ]) - float ( section_1 [ i +1])) -\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])* float ( g )*\
P_secc [2000] = P_secc [2000] +\
interpolation ( densRef_0 , densRef_1 , T_ref [2000])*0.5*( vel (2000)**2\
- vel (2001)**2) + interpolation ( densRef_0 , densRef_1 , T_ref [2000])*\
float ( g )*( float ( section_1 [2000]) - float ( section_1 [2001]))\
- interpolation ( densRef_0 , densRef_1 , T_ref [2000])* float ( g )* float ( carga ( i )\
+ hs_4 )
else :
P_secc [ i +1] = P_secc [ i ] +\
interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*0.5*( vel ( i )**2 -\
vel ( i +1)**2) + interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*\
float ( g )*( float ( section_1 [ i ]) - float ( section_1 [ i +1]))\
P_secc [2498] = P_secc [2497] -\
interpolation ( densRef_0 , densRef_1 , T_ref [2497])* float ( g )* float ( h_exit )
j = ( len ( section_0 ) -1) - i
P_ret [j -1] = P_ret [ j ] + interpolation ( densRef_0 , densRef_1 , T_ref [j -1])*0.5*\
( vel_ret ( j )**2 - vel_ret (j -1)**2) +\
interpolation ( densRef_0 , densRef_1 , T_ref [j -1])\
* float ( g )*( float ( section_1 [ j ]) - float ( section_1 [j -1])) -\
interpolation ( densRef_0 , densRef_1 , T_ref [j -1])* float ( g )*\
float ( carga_ret ( j ))
P_loss [ i +1] = P_secc [0] - P_secc [( len ( section_0 ) -1)]
# Critical heat Flux calculation :
CHF_2 [ i ] = boiling_tab ( i )
Boil [ i ] = boiling ( i )
Sh = pi * section_1 [2498]* sqrt ( section_1 [2498]**2 + 2.5**2)
Tlim = interpolation ( boil_0 , boil_1 , P_secc [ i ])
Hlim = pot_1 [ i ] / ( Tlim - T_ref [ i ])
oFilmlim . write ( str ( section_0 [ i ])+ " \ t " + str ( Tlim )+ " \ t " + str ( Hlim )+\
" \ t " + str ( film_gni ( i ))+ " \ n " )
# Return temperature calculation :
T_aux2 [ i ] = T_ret ( i )
jtot = 0
while ( T_ref3 [ len ( section_0 ) -1] - T_ref2 [ len ( section_0 ) -1]) > 1E -10 :
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T_ref2 = [ T_ref3 [ len ( section_0 ) -1] for i in range ( len ( section_0 ) ) ]
jtot = jtot + 1
print jtot
for i in range ( len ( section_0 ) -1):
T_aux2 [ i ] = T_ret ( i )
T_metal4 [ i +1] = T_ref3 [ i +1] + pot_tot [ i +1]/ film_gni ( i +1)
# Writing data to the output . txt files :
for i in range ( len ( section_0 ) -1) :
oRet . write ( str ( section_0 [ i ])+ " \ t " + str ( vel_ret ( i ))+ " \ t " + str ( re_ret ( i ))+\
" \ t " + str ( film_ret ( i ))+ " \ t " + str ( T_ref3 [ i ])+ " \ t " + str ( T_cext [ i ])+ " \ t " \
+ str ( pot_tot [ i ])+ " \ t " + str ( pot_1 [ i ])+ " \ t " + str ( P_ret [ i ])+ " \ n " )
oEsp . write ( str ( section_0 [ i ])+ " \ t " + str ( section_1 [ i ]+ Eint ( i )+ espesor ( i ))+\
" \ t " + str ( espesor ( i ))+ " \ t " + str ( a_r ( i ))+ " \ t " + str (1/ a_r ( i ))+ " \ t " + str ( dh ( i ))\
+"\n")
oVarsSI . write ( str ( section_0 [ i ])+ " \ t " + str ( vel ( i ))+ " \ t " + str ( rey ( i ))+ " \ t " \
+ str ( re_epsi ( i ))+ " \ t " + str ( film_gni ( i ))+ " \ t " + str ( pot_1 [ i ])+ " \ t " \
+ str ( Bound ( i ))+ " \ t " + str ( inten ( i ))+ " \ n " )
oTempSI . write ( str ( section_0 [ i +1])+ " \ t " + str ( T_ref [ i +1])+ " \ t " \
+ str ( T_ref3 [ i +1])+ " \ t " + str ( T_metal2 [ i +1])+ " \ t " \
+ str ( T_metal4 [ i +1])+ " \ n " )
oPresSI . write ( str ( section_0 [ i +1])+ " \ t " + str ( P_secc [ i +1])+ " \ t " \
+ str ( P_secc [ i +1]*1 E -5)+ " \ n " )
oFricc . write ( str ( section_0 [ i ])+ " \ t " \
+ str ( abs (0.5* interpolation ( densRef_0 , densRef_1 , T_ref [ i ])\
*( vel ( i +1)**2 - vel ( i )**2))*1 E -5)\
+ " \ t " + str ( interpolation ( densRef_0 , densRef_1 , T_ref [ i ])*\
float ( g )* carga ( i )*1 E -5)+ " \ t " + str ( fricc ( i ))+ " \ n " )
oInflu . write ( str ( section_0 [ i ])+ " \ t " + str ( film_gni ( i ))+ " \ t " \
+ str (1.06* film_gni ( i ))+ " \ t " + str (0.94* film_gni ( i ))+ " \ n " )
oQboil . write ( str ( section_0 [ i ])+ " \ t " + str ( T_boil [ i ])+ " \ t " \
+ str ( Q_critot [ i ])+ " \ t " + str (( pot_1 [ i ]*( section_1 [ i +1]+\
Eint ( i +1))/ section_1 [ i +1])*1 E -4)+ " \ t " + str ( E_c [ i ])+ " \ t " \
+ str ( X [ i ])+ " \ t " + str ( Q_crit2 [ i ]*1 E -4)+ " \ n " )
oCrittab . write ( str ( section_0 [ i ])+ " \ t " + str ( X [ i ])+ " \ t " \
+ str ( CHF_tab [ i ]*1 E -1)+ " \ t " + str ( Q_crit2 [ i ]/( CHF_tab [ i ]\
*1 E3 ))+ " \ t " \
+ str ( abs (100 - (100* CHF_tab [ i ]*1 E3 / Q_crit2 [ i ])))+ " \ n " )
oFilm . write ( str ( section_0 [ i ])+ " \ t " + str ( film_gni ( i ))+ " \ t " \
+ str ( film_rug ( i ))+ " \ t " + str ( film_roiz ( i ))+ " \ t " \
+ str ( film_gni ( i )/( interpolation ( visco_0 , visco_1 , T_ref [ i ])\
/ interpolation ( visco_0 , visco_1 , T_metal2 [ i ]))**(0.11))+ " \ t "
+ str ( film_rug ( i )*( interpolation ( visco_0 , visco_1 , T_ref [ i ])/\
interpolation ( visco_0 , visco_1 , T_metal2 [ i ]))**(0.11))+ " \ t " \
+ str ( film_roiz ( i )/( interpolation ( visco_0 , visco_1 , T_ref [ i ])/\
interpolation ( visco_0 , visco_1 , T_metal2 [ i ]))**(0.11))+ " \ n " )
oData . write ( str ( section_0 [ i ])+ " \ t " + str ( section_1 [ i ]+ Eint ( i ))\
+ " \ t " + str ( section_1 [ i ]+ Eint ( i )+ espesor ( i ))+ " \ t " \
+ str ( espesor ( i ))+ " \ t " + str ( vel ( i ))+ " \ t " + str ( pot_1 [ i ]*1 E -4)+\
" \ t " + str (( pot_1 [ i ]*( section_1 [ i +1]+ Eint ( i +1))/ section_1 [ i +1])\
*1 E -4)+ " \ t " + str ( T_ref3 [ i ])+ " \ t " + str ( T_metal4 [ i ])+ " \ t " \
+ str ( interpolation ( densRef_0 , densRef_1 , T_ref3 [ i ]))+ " \ t " \
+ str ( interpolation ( visco_0 , visco_1 , T_ref3 [ i ]))+ " \ t " + str ( rey ( i ))\
+ " \ t " + str ( fricc ( i ))+ " \ t " + str ( film_gni ( i ))+ " \ t " + str ( film_roiz ( i ))\
173
867
868
869
870
871
872
873
874
875
876
+ " \ t " + str ( P_secc [ i +1]*1 E -5)+ " \ t " \
+ str ( interpolation ( Psat_0 , Psat_1 , T_metal4 [ i ]))+ " \ t " \
+ str ( T_boil [ i ])+ " \ t " + str ( CHF_tab [ i ]*1 E -1)+ " \ t " \
+ str ( Q_crit2 [ i ]*1 E -4)+ " \ t " + str ( Q_critot [ i ])+ " \ n " )
subprocess . call ([ ’/ home / markus / Documentos / Beam Dump / Refrigeracion \
/ p r o g r a m a s _r e fr ig e ra c io n / Corrosion_Final / refrigeration - pot - Tran . py ’ ])
print P_loss [2498] , T_boil [2100]
print ( " SUCCESS !!! " )
174
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J00353 KI 90mm Premium GB

Oven Tracker® Thermocouple Range 1 A comprehensive range to

spraycool™ technology replaces fans and heat

Acson Moveo Catalogue 2015 (Online).compressed

TEA STAINED STAINLESS STEEL?