Calcolo dello Stato di Equilibrio

Transcription

CAMERA DI COMBUSTIONE DESCRIZIONE DELLA CHIMICA Calcolo dello Stato di Equilibrio CAMERA DI CO
In un processo di combustione adiabatico ed isobaro in cui la combustione
raggiunge uno stato di equilibrio chimico valgono le seguenti relazioni:
Vincolo stechiometrico (ponderale): Conservazione delle moli atomiche:
Condizione termodinamica di equilibrio chimico
(max entropia == min entalpia libera di Gibbs)
Conservazione dell’energia in termini di entalpia assoluta della miscela
Saturday, July 11, 15
TURBOGETTO SEMPLICE CICLO A PUNTO FISSO CICLO IN VOLO Ese. 5: Turbo-Getto TURBOFAN TURBO
COMBUSTORE
ANALISI A PUNTO FISSO: COMBUSTORE
EQ. ENERGIA (L̇s = 0, M ≪ 1): ∆h0 ≃ ∆h = ∆Q
ηb := Q̇/(ṁf Qf ) RENDIMENTO DI COMBUSTIONE
T4 : TEMPERATURA ALL’INGRESSO DELLA TURBINA (TIT)
ηpb := p4 /p3 RENDIMENTO PNEUMATICO DEL COMBUSTORE
f := ṁf /ṁa RAPPORTO COMBUSTIBILE/ARIA, O DI DILUIZIONE
ṁa h3 + ṁf hf + Q̇ = (ṁa + ṁf )h4
f ≪ 1 ⇒ ṁa h3 + Q̇ = ṁa h4 ⇒ ṁa cp (T4 − T3 ) = Q̇
Q̇ = ηb ṁf Qf
cp T3
cp (T4 − T3 )
=
f =
ηb Qf
ηb Qf
p4 = ηpb p3
!
T4
−1
T3
"
Processi chimicamente reversibili: congelati, in equilibrio
Processi chimicamente reversibili: congelati, in equilibrio
Irreversible processes
dS = dSext + dSint
1
p
dQext
dSext = dU + dV =
̸ 0
=
Non adiabatic system
T
T
T
1 !
µj dNj > 0
Chemically reactive system
dSint = −
T j
Internal (chemical) reversible processes
dSint
!
1 !
=−
µi dNi = 0
µj dNj = 0 ⇔ dG =
T j
i
Chemically frozen processes (air intake, compressor, turbine, nozzle)
∀j : dNj = 0 ⇒ Nj = const ⇒ ĉ(v,p) (T, Yi ) = const
if gas is calorically perfect
Processes in chemical equilibrium (combustion chamber)
!
µj dNj = 0 ⇒ M in [G (p, T, Nj )] ⇒ Nj = Nj∗ (p, T )
dG =
j
p,T given
Conservazione delle moli atomiche: stechiometria
Supponiamo che la miscela sia formata da 8 specie chimiche:
1
H2
2
O2
3
H
4
O
5
OH
6
H2 O
7
HO2
8
H2 O2
La conservazione delle moli atomiche si esprime con 2 equazioni algebriche
NH = 2n1 + n3 + n5 + 2n6 + n7 + 2n8
NO = 2n2 + n4 + n5 + n6 + 2n7 + 2n8
che in forma matriciale si scrive
Adn =
!
2
0
0
2
1
0
0
1
1
1
2
1
1
2
⎧
dn1
⎪
⎪
⎪
⎪
dn2
⎪
⎪
⎪ dn3
⎪
"⎪
⎨
dn4
2
dn5
2
⎪
⎪
⎪
⎪
dn6
⎪
⎪
⎪
⎪
dn7
⎪
⎩
dn8
⎫
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎭
=0
questo sistema lineare di 2 equazioni in 8 incognite ammette ∞6 = 8 − 2 soluzioni.
Le ∞6 soluzioni si trovano partizionando la matrice A ed il vettore dn:
⎧
dn3
⎪
⎪
⎪ dn4
⎪
!
"#
$
!
"⎪
⎨
2 0
dn1
1 0 1 2 1 2
dn5
=−
0 2
dn2
dn6
0 1 1 1 2 2
⎪
⎪
⎪
⎪
⎪
⎩ dn7
dn8
⎫
⎪
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎪
⎭
per ogni scelta delle componenti dnj , j = 3, 8 si troverà una ed una sola coppia
dnj , j = 1, 2 che soddisfa il sistema di due equazioni
come si possono scegliere le dnj , j = 3, 8 in modo di essere sicuri di averle prese
tutte ? si utilizza una base di vettori linearmente indipendenti ovvero:
#
$
, 1 se i = k
i
k = 1,8 - 2 = 6
ek = ek =
0 se i ̸= k
Con la scelta degli ek eﬀettuata utilizzando vettori linearmente indipendenti
consente di scrivere le ∞6 soluzioni in questo modo:
⎧#
$
!
"−1 !
dn1
2 0
1
⎪
⎨
=−
dn2
0 2
0
⎪
⎩
k
k = 1, 6
dn2+k = ek dξ
0
1
1
1
2
1
1
2
2
2
"
dn2+k
Tornando ad una rappresentazione per componenti si ottiene
⎫
1
1
dn1 = − 2 dξ ⎬
1
1
dn2 = 0
⇒ H2 = H
dξ assume valori compresi ≥ 0
⎭
2
dn = dξ 1
3
che indica che ogni ∞1 soluzioni rappresenta una reazione chimica virtuale
E qundi in una miscela con 8 specie formata da 2 elementi atomici si possono avere
al più 8-2=6 reazioni chimiche linearmente indipendenti
in forma compatta si può scrivere
dni =
$
k
νi dξ
k
k
Le 6 direzioni cosı̀ trovate individuano un sottospazio in R8 che in algebra lineare
viene chiamato: spazio nullo della matrice A ( NullSpace[A] in Mathematica ).
Lo spazio nullo è il sottospazio in cui, a partire da una composizione iniziale della
miscela assegnata, le reazioni chimiche trasformano la miscela in modo che il
numero di atomi iniziali si conservi
1
1 dξ
− 2 dt
dn1
dt
=
dn2
dt
=0
dn3
dt
=
dξ1
dt
dξ 1
1
1
1
:= r (p, T, Nj ) = rf − rb
dt
Reversible (zero entropy) process dG =
!
µj dNj = 0
j
Stoichiometric constraint dNj =
!
νjk dξk
k
⇓
dG =
!
µj
j
!
νjk dξk
k
=
!
k
dξk
!
µj νjk = 0
j
⇓
∀dξ k ̸= 0,
⎧
⎨!
⎩
j
⎫N reactions
⎬
µj νjk = 0
⎭
k=1
⇓
Free Enthalpy (Gibbs) is stationary ⇔ Chemical equilibrium
Legge di Azione di Massa
Legge di Azione di Massa
Equilibrium Condition
!
k
µj (T, pj ) νj = 0 k = 1,Nreactions
j
µj (T, pj ) := H̃j (T ) − T S̃j (T, pi ) Ŝj (T, pj ) :=
0
S̃j (T )
pj
− ℜLog(
)
pref
"
#
$
%
p
pj
j
0
0
0
µj (T, pj ) := H̃j (T ) − T Ŝj (T ) − ℜLog(
) = H̃j (T ) − T S̃j (T ) + ℜT Log(
) = µj (T )
pref
pref
"
#
#
&
'
!
!
!" 0
pj
pj
k
0
k
k
µj (T ) νj = −
ℜT Log(
) νj = 0 ⇒
) νj
µj (T ) + ℜT Log(
pref
pref
j
j
j
'
!
! k
!&
pj
pj νjk
0
k
) = −ℜT
Log(
)
H̃j (T ) − T S̃j (T ) νj = −ℜT
νj Log(
pref
pref
j
j
j
⎧
⎫
⎧
⎫
⎨
⎨!
' ⎬
1 !&
pj νjk ⎬
0
k
Exp −
H̃j (T ) − T S̃j (T ) νj
Log(
)
= Exp
⎩ ℜT
⎭
⎭
⎩
pref
j
j
.
/0
1
Kp (T )
k
Kp (T )
= Exp
⎧
⎨
⎩
Log
2
j
Law of Mass Action
⎫
k⎬
2 pj ν k
pj νj
(
)
) j
(
=
⎭
pref
pref
j
k
Kp (T )
=
2
j
pj νjk
)
(
pref
j
Ns + 2 incognite : composizione della miscela (NProducts
, j = 1, Ns ), Numero
totale di moli (Ntot ), e temperatura adiabatica di fiamma (TProducts )
Ns + 2 equazioni:
Conservazione delle moli atomiche:
i
N =
Ns
!
i
j
aj NReac =
j=1
Ns
!
i
j
i = Ne
aj NProducts
j=1
Condizione termodinamica di equilibrio chimico (Legge di azione di massa)
k
Kp (T )
=
"
j
pj νjk
)
(
pref
Nj
pj =
p
Ntot
k = Ns − Ne
Numero totale di moli
Ntot =
Ns
!
Nj
j=1
Conservazione dell’energia in termini di entalpia assoluta della miscela
j
j
H̃(TReac , NReac ) = H̃(TProducts , NProducts )
Risultati del Calcolo dello Stato di Equilibrio
Risultati del Calcolo dello Stato di Equilibrio
MISCELA H2 /O2
1.000
3400
0.500
3300
0.100
3200
0.050
3100
0.010
3000
0.005
2900
0.001
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Figure: Variazione Temperatura adiabatica
di equilibrio con rapporto di equivalenza
(p=1 e 10 atm); T reagenti = 300K.
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Figure: Variazione Composizione di
equilibrio con rapporto di equivalenza (p=1
e 10 atm); T reagenti = 300K.
FLUSSO ALLA RAYLEIGH
FLUSSO ALLA RAYLEIGH
Variazione di T0 e variazione di Mach in CC
#
$
!
"
2
2
2M 1 + δM (γ + 1)
T0
[M, γ] =
#
$2
⋆
2
T0 cal
1 + γM
!
T04
T03
%
T0
T⋆
0
&
[M4 , γ]
#
$#
$2
2
2
1 + δ M4 M4 + M3 M4 γ
cal
[M3 , M4 , γ] = % &
= #
$#
$2
2
2
T0
1 + δ M3 M3 + M3 M4 γ
cal
[M3 , γ]
T⋆
"
0
cal
Variazione di p0 e variazione di Mach in CC
!
!
p04
p03
"
p0
p⋆0
"
[M, γ] =
cal
%
[M3 , M4 , γ] = %
cal
p0
p⋆
0
1
#
$ γ
2 γ−1
(γ + 1) 1−γ
2 1 + δM
1 + γM2
&
[M4 , γ]
&cal
=
p0
[M3 , γ]
p⋆
0
cal
!
γ
1+
1+
2 " γ−1
δ M3
δ M24
1 + γ M24
1 + γ M23
RENDIMENTO PNEUMATICO
RENDIMENTO PNEUMATICO
Rapporto T04 /T03 in funzione della portata di combustibile f
!
"
f ηb Qf
cp (T4 − T3 )
cp T03 T04
T04
f=
≈
−1 ⇒
=1+
ηb Qf
ηb Qf T03
T03
cp T03
Numero di Mach in ingresso M3 della CC per assegnati Mach in uscita M4 e
rapporto T04 /T03
&
#
$
%$
%2
2
2
2 + M4 (γ − 1) M4 + M3 M4 γ
T04
== $
Solve
%$
%2 , M3
2
2
T03
2 + M3 (γ − 1) M3 + M3 M γ
4
Perdite di pressione p0 in funzione della variazione di Mach tra ingresso ed
uscita della camera
ηpb :=
!
p04
p03
"
[M3 , M4 , γ] =
cal
!
γ
2 " γ−1
1 + δ M3
1 + δ M42
1 + γ M42
1 + γ M23
Micro Combustion Chamber
M3 Test Bench - DLR
In Space Propulsion
ISP-1
FP7-SPACE-CALL-1
M3 chamber characterizes ignition behaviour, with varying
injection geometries and flow conditions
Mass flows are determined through Coriolis flow meters
Sonic nozzles set the correct mass flows
Sonic nozzles provide an effective separation between feed
lines and injector head, thus minimising low frequency
combustion instabilities
Space Propulsion Conference – Bordeaux – May 7-10, 2012
13
Model Equations for Unsteady CSTR with Energy Deposition
d( ρV )
= m! fuel [t,p] + m! oxid [t,p] − m! nozzle [p,T,Y]
dt
d( ρhV )
dp
!
= m! fuel [t,p]h fuel + m! oxid [t,p]hoxid − m! nozzle [p,T,Y]h[T,Y] + V
+ q[t]V
dt
dt
dY j
Wj
Yj
1
dρ
=
m! fuel [t,p]Y j + m! oxid [t,p]Y j − m! nozzle [p,T,Y]Y j +
ω j [p,T,Y] −
[p,T,Y]
dt
ρ[p,T,Y]V
ρ[p,T,Y]
ρ[p,T,Y] dt
1 d ρ 1 dp 1 dR 1 dT
p = ρ RT →
=
−
−
ρ dt p dt R dt T dt
R
dR
R dY j
R = ∑ U Yj →
=∑ U
dt
j Wj
j W j dt
p 0,fuel (t)Afuel
p
!
!
m fuel [t,p] = mred [
, ηfuel , γ fuel ]
dY j
dh
dT
p
(t)
R fuel T0,fuel
0,fuel
h = ∑ h jY →
= ∑ hj
+ Cp
→ C p = ∑ C j, pY j
dt
dt
dt
j
j
j
p 0,oxid (t)Aoxid
p
1 t −t 0
!
!
m
[t,p]
=
m
[
,
η
,
γ
]
oxid
red
oxid
oxid
Erg
ε [Joule] − 2 σ t2
Erg
p
(t)
R oxid T0,oxid
0,oxid
!
q(t)[
]
=
e
10[
]
Centimeter 3Second
4πσ r3σ t
Joule
p
p Aoxid
m! nozzle [p,T,Y] = m! red [ a , ηoxid , γ (T ,Y )]
p
R(Y)T
(
)
m! red [Πp , η, γ ] =
2γ 1
γ − 1 Πp
ISP-1 - September 22-23, 2011
γ
⎛
⎞
γ −1
η ⎜ 1 − Πp ⎟
⎝
⎠
γ
⎛
⎞
γ −1
1 − η ⎜ 1 − Πp ⎟
⎝
⎠
⎛ 2 ⎞
with Πp ≥ ⎜
⎝ γ + 1 ⎟⎠
γ
γ −1
Model Equations for Unsteady CSTR with Energy Deposition
dY j
(
)
R[Y ]T
m! fuel [t,p]Y j + m! oxid [t,p]Y j − m! nozzleY j
dt
pV
W jω j [ p,T ,Y ]
Yj
dρ
+
−
[ p,T ,Y ]
j = 1 , Ns
ρ[ p,T ,Y ]
ρ[ p,T ,Y ] dt
=
⎛ h − h[T ,Y ]
⎞
⎛ h − h[T ,Y ]
⎞
- m! nozzle [ p,T ,Y ] + m! fuel [t,p] ⎜ fuel
+ 1⎟ + m! oxid [t,p] ⎜ oxid
+ 1⎟
⎝
⎠
⎝
⎠
R[Y ]T
R[Y ]T
dT
=
dt
(Cp-R) p V
dY j
RU dY j
h
[T
]
-T
∑ j dt ∑ W dt
!
q[t]
j
j
j
−
+
(Cp[T ,Y ]-R[Y ])
ρ[ p,T ,Y ] (Cp[T ,Y ]-R[Y ])
dp p γ [T ,Y ] ⎛ γ [T ,Y ] − 1
=
dt
R[Y ]T ⎜⎝ γ [T ,Y ]
+
γ [T ,Y ]R[Y ]T
V
RU dY j ⎞
∑ h j [T ] dt + T ∑ W dt ⎟⎠
j
j
j
dY j
⎛
⎛ h fuel − h[T ,Y ]
⎞
⎛ hoxid − h[T ,Y ]
⎞⎞
!
!
!
m
[
p,T
,Y
]
+
m
[t,p]
+
1
+
m
[t,p]
+
1
fuel
oxid
⎜⎝ Cp[T ,Y ] T
⎟⎠
⎜⎝ Cp[T ,Y ] T
⎟⎠ ⎟⎠
⎜⎝ nozzle
1 t −t 0
Erg
ε [Joule] − 2
!
q[t][
]=
e
Centimeter 3Second
4πσ r3σ t
R
R[Y ] = ∑ U Y j
j Wj
ρ[ p,T ,Y ] =
σ t2
m! fuel [t,p] = m! red [
Joule
10[
]
Erg
m! oxid [t,p] = m! red [
p
p 0,fuel (t)
p
p 0,oxid (t)
m! nozzle [p,T,Y] = m! red [
p
R[Y ]T
h[T ,Y ] = ∑ h j [T ]Y j
j
dρ 1
=
m! fuel [t, p] + m! oxid [t, p] − m! nozzle [ p,T ,Y ]
dt V
(
)
m! red [Πp , η, γ ] =
, ηfuel , γ fuel ]
p 0,fuel [t]Afuel
, ηoxid , γ oxid ]
R fuel T0,fuel
p 0,oxid [t]Aoxid
R oxid T0,oxid
pa
p Aoxid
, ηoxid , γ (T ,Y )]
p
R[Y]T
2γ 1
γ − 1 Πp
γ
⎛
⎞
γ −1
η ⎜ 1 − Πp ⎟
⎝
⎠
γ
⎛
⎞
1 − η ⎜ 1 − Πp γ −1 ⎟
⎝
⎠
γ
⎛ 2 ⎞ γ −1
with Πp ≥ ⎜
⎝ γ + 1 ⎟⎠
Data
p0fuel = 2.5 patm; pfuel = p0fuel;
Tfuel = 290 Kelvin; T0fuel = Tfuel;
ηfuel = 0.8;
p0oxid = 5.0 patm; poxid = p0oxid;
Toxid = 290 Kelvin; T0oxid = Toxid;
ηoxid = 0.8;
radiusoxid = 0.11 Centimeter; Aoxid = Pi radiusoxid^2;
innerradiusfuel = 0.24 Centimeter;
outerradiusfuel = 0.30 Centimeter; Afuel = Pi (outerradiusfuel^2 - innerradiusfuel^2);
Lchamber = 16 Centimeter;
radiuschamber = 3 Centimeter;
Volume = Lchamber radiuschamber;
pa = 1 patm; p0a = pa;
Ta = 290 Kelvin; T0a = Ta;
radiusnozzle = 1 Centimeter;
Anozzle = Pi radiusnozzle^2;
ηnozzle = 0.8;
T0 = 300. Kelvin; p0 = 1. patm;
Inputs
5¥106
4¥106
3¥106
2¥106
1¥106
0.0
0.5
1.0
1.5
Total Pressures at Fuel & Oxygen Manifold in time
3.0 ¥109
2.5 ¥109
sigr = 1.0*10^-3 Meter;
sigt = 2.5*10^-4 Second;
eps = minimumEnergy ;
c1 = eps/(4 Pi sigr*sigr*sigr*sigt);
qdotSI = c1*Exp[-.5*((time - t0)/sigt)^2];
SItoCGS = 10;
qdot = qdotSI * SItoCGS
2.0 ¥109
1.5 ¥109
1.0 ¥109
5.0 ¥108
0
0.0
0.5
1.0
1.5
Energy deposition in time
Outputs: Methane/Oxygen System
Sensitivity of peak pressure on energy deposition time
2500
2000
1500
1000
500
1.8 ¥106
0.10
0.15
0.20
0.25
0.30
Temperature in time
1.6 ¥106
1.4 ¥106
1.8 ¥106
1.6 ¥106
1.2 ¥106
1.4 ¥106
1.0 ¥106
1.2 ¥106
1.0 ¥106
0.10
0.5
1.0
Peak pressure vs time lag
0.15
0.20
0.25
0.30
Pressure in time
•
•
•
•
•
•
short energy deposition time allow little reactants to fill the chamber -> lower total reactant mass yields a lower pressure
peak during ignition
short/long energy deposition time: ignition develop three/four stages
first stage[heating]: isobaric T growth due to energy addition
second stage[explosion] (kinetics >> convection): T increases due to fast kinetics, and P follows for inertial confinement
because the kinetics is faster than convection
third stage[relaxation] (kinetics ~ convection): T&P decrease because the higher P produces a larger outflow
fourth stage[near-equilibrium] (kinetics << convection): T&P increase following the arrival of reactants which are instantly
burned
1.5
Outputs: Methane/Oxygen System
Sensitivity of peak pressure on minimum energy deposition
1.63 ¥106
3500
1.62 ¥106
3000
2500
1.61 ¥106
2000
1.60 ¥106
1500
1000
1.59 ¥106
500
0.15
0.16
0.17
0.18
0.19
0.20
Temperature in time
1.58 ¥106
0.02
1.5 ¥106
•
•
•
•
1.4 ¥106
1.3 ¥106
1.2 ¥106
0.08
0.10
0.12
0.14
too low power levels cannot ignite the mixtures
higher power levels shorten the ignition times
less reactants can fill the chamber
peak pressure exhibits a max at ~50mJ
1.1 ¥106
0.16
0.17
0.18
0.19
0.20
Pressure in time
0.06
Peak pressure vs minimum energy deposition
1.6 ¥106
0.15
0.04
Objectives of ISP-1 WP 2.5
In Space Propulsion
ISP-1
FP7-SPACE-CALL-1
To check the ability of the physical models and prediction tools to reproduce:
• ignition model
• flame propagation
- kernel formation
- flame kernel evolution in a turbulent flow
• anchoring process
A dedicated experiment has been carried out at the M3 Test Bench (DLR Lampoldhausen) and has been
used as a reference test case to benchmark different numerical approaches
Ignition is triggered using a laser beam to control the ignition point location and energy release, in a
well controlled gas/gas injection configuration
This way a clean experimental configuration is obtained, allowing to check the ability of the numerical
tools to reproduce flame propagation and anchoring
Two test campaigns have been carried out:
•
•
ambient pressure
low pressure
20
Ignition Sequence
In Space Propulsion
ISP-1
FP7-SPACE-CALL-1
Test
case computed : 21.07.2011-7
An accurate selection of the ignition sequence is essential to avoid undesired peaks in the chamber pressure.
attached)
Accumulated unburnt masses prior to ignition determine the pressure rise during ignition and its overpressure.
τ r is the mean residence time in the chamber
τi
M
τ r :=
m! e
(ambient,
M
is the mass of gas inside the chamber
m! e
is the massflow rate of gases exhausted though the nozzle
is the ignition delay
The ignition overpressure (if all the quantity of propellant in the chamber prior to ignition is burnt instantaneously) can be found from:
pmax m! iτ i
=
pc
m! τ r
m! iτ i
is the mass of reactants in the chamber over the time
m! τ r
is the mass of propellants in the chamber at any time
τi
Decreasing the ignition delay decreases the overpressure during ignition.
These findings helped the selection of an ignition sequence of the test campaign able to minimize the overpressure.
- 117
-57
0 ignition
Time line ms
21
Micro Combustion Chamber
M3 Experiment - DLR
In Space Propulsion
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HOT FLOW
LASER-PULSE ON QUISCENT NITROGEN
COLD FLOW
Gaseous Oxygen, before ignition
Schlieren images of laser pulse (150 mJ);
Expanding blast wave; Sequence
sampled from multiple laser shots
therefore only an estimate for the timing
can be given; Time step ~ 50 µs
Coaxial Methane, before ignition, with Oxygen
Schlieren image sequence of laser
ignition of CH4/O2 gas/gas
22
Main experimental findings from DLR
In Space Propulsion
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Ambient pressure ignition
CC pressure rising due to heating
Excitation caused by heat release results in spontaneous emission of OH
radicals at ca. 305-309 nm
Spontaneous emission in the UV-range is recorded by an intensified highspeed CCD video camera
Complete chamber is visualised with a resolution of 512 x 256 pixels
A band-pass filter (310 nm ± 5 nm) selects only OH-radical emission
Flame lift-off length inversely proportional to chamber pressure
23
Motivations for CFD Analyses
In Space Propulsion
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Quantitative analysis of ignition can be done by a "Well-Stirred Reactor" (WSR) or "Continuously Stirred Tank Reactor" (CSTR) models
Both models assume infinitely fast and efficient mixing in the chamber
These models allow to readily carry out all the relevant sensitivity analyses
Why then making the costly and tedious CFD analyses ?
Because of the critical role of multi-dimensional phenomena !!
Blast Wave
Recirculation
Fuel Blockage
URANS & LES Modelling Options
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URANS MODELLING OPTIONS (CFD++ METACOMP Tech)
• Flow geometry 2D Axi-symmetric
• real gas, compressible equations
• Ideal gas equation of state
• multi-species with frozen/active detailed chemical kinetics
• viscous flow
• transient integration (time accurate, point implicit)
• second order space discretization
• turbulent modelling on: RANS two-eqns k-epsilon
• Ignition by « hot spot »
LES MODELLING OPTIONS (CEDRE ONERA)
• Flow geometry 3D
• real gas, compressible equations
• Ideal gas equation of state
• multi-species with a frozen/active global reaction mechanism
• viscous flow
• transient integration (time accurate)
• second order space discretization
• Smagorinski model for LES subgrid closure
• Ignition by « hot spot »
ICs:
• quiescent Nitrogen fills the chamber at T=290 K, and p=101325 Pa
ICs:
• quiescent Nitrogen fills the chamber at T=290 K, and p=101325 Pa
BCs:
• Walls are assumed isothermal, post tip and nozzle are considered
adiabatic
• Inflow: constant total pressure and temperature for both fuel and
oxygen
• Outflow: subsonic flow with prescribed ambient pressure
BCs:
• Walls are assumed adiabatic
• Inflow: ramped total pressure and temperature for both fuel and
oxygen
• Outflow: subsonic flow with prescribed ambient pressure
MESH: ~ 230K cells; block-structured
MESH: ~ 10M cells; unstructured
CHEMICAL KINETIC MECHANISM FOR CH4/O2+INERT NITROGEN:
• GRI3.0 (53 species) with Nitrogen kinetics removed involves 36
species
• Mechanism simplification (in-house tools) trimmed the mechanism to
15 species
CHEMICAL KINETIC MECHANISM FOR CH4/O2+INERT NITROGEN:
• Global kinetics (Jones and Lindstedt, adapted by Kim)
25
CFD Analyses
Inflow BCs for LES
In Space Propulsion
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Test case computed : 21.07.2011-7
(ambient,
• Step 1 : O2 cold flow
attached)
– Not the whole injector is meshed : to account for pressure losses in Ox tube, boundary condition pressure is Pi=9 bars
– To account for pressure increase vs time, relaxation is activated on the boundary condition
– From t=-117ms to -57ms
•
Step 2 : CH4 cold flow
– Along with stabilized O2 cold flow
– From t=-57ms to t=0ms
The filling process of the chamber by the cold
reactants needs to be accurately replicated
because the total mass of reactants at time T0
sets the total level of energy available for
combustion during the ignition start-up
26
How we trim the kinetics
Detailed (NS36) vs Simplified (NS15)
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GRI-Mech 3.0 (53 spcs and 325 reversible rcns) is used as reference mechanism
All N-containing species are removed, except N2, together with all N-related reactions, to yield a detailed mechanism with 36 spcs and
219 reversible rcns
Mechanism simplification done by in-house tools
A spatially homogeneous, iso-choric, adiabatic, forced ignition with gaussian energy deposition drives the simplification procedure
The selected simplified mechanism involves 15 species and 57 reactions
The fastest time scale of the simplified mechanism is two orders of magnitude larger than the one of the detailed (stiffnes reduction)
27
Test Case#07 Ambient Pressure
In Space Propulsion
ISP-1
Chamber pressure time evolution
FP7-SPACE-CALL-1
URANS & LES return similar chamber pressure histories
Both feature a larger-than-experiment chamber pressure peak value and growth rate
Chamber pressure peak exceeds fuel manifold pressure -> fuel blockage
Late pressure evolution exhibits oscillations tuned with chamber acoustics
NB: Chamber pressure growth rate proceeds as:
O
⇣
1 dp
p dt
⌘
⇡O
1 dT
T dt
+O
1 dR
R dt
+O
⇣
ṁF
⇢V
+
ṁOx
⇢V
ṁOut
⇢V
⌘
Massflows
In Space Propulsion
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FP7-SPACE-CALL-1
Test Case Values
Methane = 0.60 g/s
Oxygen = 2.26 g/s
Methane and oxygen inflows not fixed at their choked values when the pressure drop falls below the critical value
Hot products outflow eventually fixed by sonic condition at nozzle
Nearly constant massflows at late times suggest a nearly steady condition
URANS & LES fluxes are quite in agreement one to another (despite the slight different treatment of the inflow BCs)
Propellants Mach Number
In Space Propulsion
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Oxygen stream choked during cold flow injection (M>1)
Oxygen stream subsonic when chamber pressure peaks (M<1)
Methane stream never choked (M<1); tends to zero near chamber pressure peak
Blust Wave following Laser Pulse
•
•
•
In Space Propulsion
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A blast wave propagates spherically outward, reflects at the injector plate and at the wall, head-on collides
at the symmetry axis, propagates downstream towards the nozzle only to be reflected backward towards
the injector plate
The under-expanded oxygen jet gradually fades away when the flow becomes subsonic
Note the formation of transient traveling pressure peaks at the symmetry axis
Kernel initiation and flame propagation
•
The flame kernel propagates
downstream near the symmetry
axis as convected by the fast
central jet
•
The flame kernel propagates
across the recirculation region
away from the axis
•
When methane is not entering
the chamber anymore, the cold
oxygen jet is not consumed and
leaves the chamber unburned->
the temperature field at the axis
becomes very cold
•
Temperature
HCO
A significant amount of hot
products is still present in the
chamber ready to reignite the
propellants when the chamber
pressure is lowered by the mass
loss through the choked nozzle
In Space Propulsion
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Fuel blockage
In Space Propulsion
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Methane
•
•
•
Methane blockage is clearly monitored by this movie
Note the role of the cavity as an accumulator of the blocked methane
The blockage process exhibits fluctuations coupled with the chamber acoustics
Oxygen
In Space Propulsion
ISP-1
LES
Temperature iso-contour at T=2000K
FP7-SPACE-CALL-1
Overall LES dynamics
consistent with URANS
predictions
LES captures the non
symmetric flow evolution
triggered by the off-axis laser
pulse location
LES captures 3-D jet instabilities
LES captures a “breathing”
evolution of the flame front as
also noticed in experiments
LES captures the development
of cold unreacted pockets
URANS OH vs Experimental OH*
In Space Propulsion
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The comparison shows that the computed OH field is qualitatively exhibiting a similar shape and shape
evolution, moves downstream at about the right speed, and posses a brighter core region surrounded by
a darker halo, where locally the light intensity is proportional to the amount of OH
LES Temperature vs Experimental OH*
In Space Propulsion
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The shape and position of the OH∗ emission field is quite similar to the one of the temperature and reactive zones in the LES
computation
OH* emission field accounts for the integral contribution along the chamber cross-section, whereas both LES and URANS results
refer to cut-planes passing through the chamber axis
In Space Propulsion
ISP-1
Flame Index at “stationary” conditions
FP7-SPACE-CALL-1
FI = ∇yFuel ⋅ ∇yOxid
FI > 0 ⇒ fuel and oxidizer fluxes aim at same direction (pre-mixed nature)
FI < 0 ⇒ fuel and oxidizer fluxes aim at opposite directions (non pre-mixed)
Pre-heat, pre-mixed flame region
(Solid lines are HCO mass fraction lines)
Positive T Index
Premixed mixture
Fuel and oxidizer from both jet and
recirculation region mix here
llift −off ∼ v jetτ ign
v jet ∼
llift −off ∼
p0 − pCC
p0 − pCC τ ign
Negative T Index
Non-premixed mixture
Co-axial Jet Mixing layer
(nearly) stationary flame is: lifted, and pre-mixed
Conclusions
In Space Propulsion
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Lesson learned
•
URANS axi-symmetric calculations can be effectively able to provide a rather detailed picture of
the ignition events, albeit there remains a number of issues for the quantitative accuracy of the
URANS predictions
•
2D axi-symmetric URANS and 3-D LES provide predictions in satisfactory agreement, even
when rather different kinetic mechanisms have been adopted
•
CFD analyses offered interesting contributions in the understanding of a number of critical
ignition phenomena, which are difficult to appreciate on the basis of experimental diagnostics
alone
Main problem found
• Larger-than-experiment chamber pressure peak value and growth rate
Possible causes
(given that the pressure peak is mostly linked to the mass of CH4 and O2 in the chamber at T0)
•
neglecting nitrogen filling the propellant manifold at T0 (volume of pipe(s) between the probe and the
boundary conditions) realizes "too much" reactants in the chamber
•
supersonic oxygen jet spreads too quickly by numerical dissipation and causes an excess of oxidant
in the chamber at T0
Acknowledgements
In Space Propulsion
ISP-1
FP7-SPACE-CALL-1
This work has been carried out with the support of:
FP7 EU Grant no.218849, titled "In-Space Propulsion-1" (ISP-1)
M.Valorani acknowledges the support of:
CASPUR Competitive HPC Grant 2009
The URANS flow solver is:
CFD++ by Metacomp Technologies, Inc.
The LES flow solver is:
CEDRE, an ONERA in-house software package
39

Calcolo dello Stato di Equilibrio

Transcription

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