Stage of a Nuclear Fireball - CSIRO Research Publications Repository

Transcription

A Numerical Model of the
Late (Ascending)Stageof
a Nuclear Fireball
I. E. Galbally, P. C. Manins, L. Ripari and R. Bateup
D[VISION OF ATMOSPHERIC RESEARCH TECHI\ilCAL PAPER No. 16
COMMONWEALTH SCIENTIFIC AND INDUSTRIAL
1987
AUSTRALIA
RESEARCH ORGANISATION,
A Numerical Model of the
Late (Ascending)Stageof
a Nuclear Fireball
By I. E. Galbally, P. C. Manins, L. Ripari and R. Bateup
Division of Atmospheric ResearchTechnicalPaper No. L6
CommonwealthScientificand Industrial
ResearchOrganisation,Australia
1987
A NUMERICAL MODEL OF THE LATE (ASCENDTNG)
STAGE OF A NUCLEAR FIREBALL
r.E.
Galbally,
P.C.
Manins,
L.
Ripari
and R. Bateup
ABSTRACT
a nuclear
of
ascending
stage
the
late
A numeri.cal
model
of
equations
covering
the
The model is based on five
firebatl
is presented.
loss,
the
buoyancy,
radiative
entrainment,
of mass including
conservation
relationship.
The
distance
and the velocity
energy balance of the fireball
pressure,
and
volume
and temperature
gas
to
relate
law
is
used
ideat
the
(1971) free energy minimization
scheme is used to calculate
Erikssonrs
The
air.
model
the
fireball
of
enthalpy
composition
and
molecular
and the
of selected
behavior
dependent
of the time
Parameters
simulations
data from mid latitude
with
available
heights
compare favourably
rise
final
physical
for
only
this
mode1, suitable
of
A simplification
explosions.
in an appendix.
is discussed
calculations,
CONTENTS
1.
fntroduction
)
Tnitial.
2.L
2.2
J .
Ambient atnospheric
conditions
Energy partitioning
following
near-surface
nuclear
explosion
FirebaIl
3.L
3.2
3.3
3.4
3.5
3.6
A
Conditions
a
description
Conservation
of mass ancl entrainment
Conservation
of momentum
Composition
and enthalpy
Radiative
loss
Energy balance
Sufiunary of model equations
Characteristics
of
the
Fireball
Model
Conclusion
6.
Acknowledqements
7.
References
^nnanAi
nac
A.
A simpler
model of
stage of a nuclear
B.
Fireball
model
flow
C.
Fireball
model
code
the late
fireball
diaqrams
(ascending)
F
1.
TNTRODUCTION
in the study of nuclear
has been renewed interest
there
Recently
(Ambio L982).
There have been
impact on the atmosphere
explosions
and their
releasing
postfires
explosion
effects
of
the
about
new discoveries
concerning
and the more well known questions
pollutants
into
the atmosphere,
burning
and
pu1se,
flash
electromagnetic
radioactivity,
oxides,
nitrogen
(Pittock
1986).
However while
et al.
strock wave darnage have been reexarnined
is known,
fireball
very little
by the nuclear
are generated
these processes
about these fireballs.
the open literature,
within
of
nuclear
impact
of
the
environmental
to
analyses
As an aid
of a nuclear
stage
ascendi.ng,
moclel of the 1ate,
a numerical
explosions
the shock wave has
This model conmences after
firebatl
has been developed.
the
concerning
and thus cannot address questions
from the fireball
separated
flash
intensity,
radiation
oxides,
The production
of nitrogen
shock wave.
the
be examined with
can all
debris
of the radioactive
of rise
and height
fireball
questions
concerning
other
Furthermore
presented
here.
model
can be addressed with this model.
composition
(e.g. erode and Bjork,
1960) and
models do exist
Complex numerical
to
Howeverr according
detail.
in great
explosions
nuclear
these describe
of
(1968),
and mid tjme histories
the early
only
.1964\ and Brode
Bethe
- are
- before
begins
rj se of the hot vapour
buoyant
development
fireball
been
at fate times has apparently
The behaviour
considered
by these models.
but no information
(Glasstone
and Dolan L977, Fiq.10,p158)
at length
studied
is
presented
results
provide
for
basis
the
which
the
models
about
forthcoming.
the
with
dealing
report
accessible
as we know, the only
As far
is singularly
fireball
is by Waltman (1975) and the model presented
rising
The dynamlc model presented
observed behaviour.
in simulating
unsuccessful
associated
and
reactions
(i.e.,
the
chemical
without
the
model
here
presented
by
to
that
similar
superficially
processes)
is
thermodynamic
input
identical
with
models
the
two
However
when
waltman
og75).
After
obtained.
are
results
differing
widely
p
arameters
are
compared,
-detailed
numerical
the
to
understdnd
still
unabLe
we are
examination
presented
in Waltman (1975).
solutions
of the new
the basis
is to document
Report
of this
The purpose
of the
description
a detailed
rise,
to provide
fireball
model of nuclear
present
to
it'
may
utilize
others
that
so
model
the
implements
code which
and to demonstrate
available
data,
with
of model output
comparisons
limited
It
is not intended
assumptions.
of the model to various
the sensitivity
problems:
these
ne$/ research
deal with
significant
should
that
the Report
elsewhere.
of papers to be presented
are the subject
2.
INITIAI,
fireball
entrained
fireball
AND AMB]ENT CONDITTONS
case where the
the
represents
nuclear
explosion
A near-surface
is
material
and no surface
surface
earth's
touch
the
does not
as a clean
be described
subsequently
This will
the fireball.
into
be those from ambient air.
present
will
and the only constituents
2
nuclear
i-s that
of a surface
here,
Another
case, not considered
of
fitebal.I
and the composition
It may be described
as a dirty
explosion.
during
the
from the surface
entrained
materials
would include
the fireball
early
stage of the explosion.
2.1
Ambient
(l,gg5)
in mid
11km.
atmospheric
conditions
atmospheric
conditions
used by Manins
slandard
The ICAO (1964)
and
is taken to be at mean sea level
The surface
are employed here.
(t30o to +70o latitude)
of
the tropopause
is at an altitude
latitudes
prevail
conditions
assumes hydrostatic
The ICAO standard
atmosphere
:E
dz
(1.|
0 q
g is acceleration
due to gravity'
pressure,
0 is the
where p is atmospheric
The
conditions.
denotes
ambient
leve1
subscript
density
z and the
at
pressure
from
and density
of tempetature,
vertical
distributions
standard
The
of 40kn as given in ICAO (1964) are used.
to an altitude
the surface
from
in Table 1 and has been adapted
is given
composition
of the atmosphere
into
account recent data for Co, and water vapour.
Va11ey (1965) taking
(up to 200
is so large
fireballs
The rate of rise of thermonuclear
,
may be
of the fireball
the influence
of anrbient winds on growth
* s-')
that
of
and transport
spread
the
subsequent
determine
Wj-nds will
ignofed.
of rise.
height
at the ultimate
fireball
material
2.2
Energy
partitioning
following
a near-surface
nuclear
explosion
The
is uncertainexplosion
in a nuclear
The energy partitioning
(and
fission
from the
amount of
can be calculated
energy
release
total
and
to Glasstone
According
has taken place.
that
fusion
if
appropriate)
the
beJ-ow 40,000 ft'
p.7,
nuclear
explosion
for
a fission
Dolan
G977)
initial
358, air
shock 50t.
radiation
thermal
into
is partitioned
enerqy
10*.
The residual
radiation
nuclear
radlation
54, and residual
nuclear
ylelcl
a nuclear
of
energy
included
when the
not
radiation
is
nuclear
Hence the yield
in terms of the TNT eguivalent.
is stated,
e.g.,
explosion
95* of the total
fission-fusion
fission
en€irgy .(or
9Ot of the
total
is
-.
partitioning
Thus the energy
as a
for
explosion)
a thermonuclear
energy
explosion
would be thermal- radiation
W, for
a fission
function
of yieId,
5t.
llowever two details
radiation
nuclear
air
ancl initial
39t,
shock 56t,
loss'
source of energy
picture.
there
is another
this
Firstly
complicate
of this
and buoyant
rise
entrainrnent
energy
dissipated
via
is
the
this
to
Furthermore
accordingr
later.
this
will
be discussed
fireball
and
explosive
for various
classtone
and Dolan (\97'7) p3L3, the thermai partition
(39E) clerived
to the 0.39
yields
is 0.35,
in contradiction
at sea leve1
above.
1
ryield',
W,
The total
energy,
or
expressedo in Mt of TNT equivalent.
4.18 x 10- MJ of energy.
is
of a thermonuclear explosion
releases
1 Mt of TNT equivalent
Tab1e 1:
(a)
of
The composition
ATMOSPHERIC I4IXING RATIO FOR DRY AIR
ambient
(V,/V)
Mixing Ratio
species
(b)
air
(V,/V)
N.
0. 780836
o2
coz
o.209487
Ar
0. 009343
0. 000340
VJATERVAPOUR MIXING RAT]O AS FUNCTTON OF HEIGHT
Height
ltcm)
l4ixing
Ileight
Ratio
(km)
(v /v)
Mixing
Ratio
(v/v)
0. 0L0129
2.O
0.006110
4.O
0.003055
6.0
0.oo7447
8.0
0.000434
1 0 .0
0.000059
0 . 0 0 0 0 37
1-4.0
0. 00001-6
1 6 .0
0.00001,4
1 8 .0
0. 000010
20.o
0.000010
22.O
0.000010
24.O
0.00001-0
26.O
0.000010
28.0
0.000010
30.0
0.000010
31.0
0.000010
0.0
1 t
n
Actual mixing ratio
ory mixing ratio
of species
(apart
frorn Hro) is:
x (l - Water vapour mixing ratio)
4
while
acknowledging
the
of
that
efficiency
a blast
depends
(weakly) on bomb design, Brode (1968) in a review of nuclear
Ueapons effegts
gives a formula for thermal yielil,/total
yield i= 0.4 + (0.06w''\/\t
+ O.5w-'))
where W is in Mt.
This indicates
that the thermal partition
fraction
is
generally greater than 0.4 and equals O.44 for a 1 Mt yield explosion.
Some
early
measurements of the thermal
radiation
from a nuclear
detonation
(Broido et a1. 1953) indicate
in the range 0.34 to
thermal efficiencies
0.45, decEl-sing with increasing yield over the range 1kt to 30 kt.
There is some uncertainty
about the
Theoretical
around 0.40 t 0.05 are appropriate.
(Taylor 1950a) suggest that half the energy is
wave and the other half remains behind the shock
in the case of nuclear explosions is the firebal1.
but values
thermal yield,
studLes of large explosions
partitioned
into the blast
wave as wasted hot air that
This energy partitioning
is essentially
the time integral
over the
(^,1 min) of the energy used in a particular
lifetime
of the explosion
process as a fraction
of the total energy releaseil by the hreapon at the time
The sequence of events in such an explosion is described.
of the explosion.
Initially,
a nuclear explosion generates a massive quantity of soft x-rays
which are imrnediately absorbed by the surrounding few metres of atmosphere
(Glasstone
1977).
and Dolan
A hot
isothermal
bubble
of
spherical
It
dissociated
air
and bomb products
at very high pressure
is formed.
by radiative
expands primarily
transfer.
A blast wave propagates outward,
shocking surrounding
air to high temperature and pressure and for a short
period of time this shock wave is opaque. For definiteness,
consider a 1 Mt
expJ-osion.
As witnessed- from afar,
the temperature
of the explosion
decreases rapidly
but wlthin
a few tenths of a second the blast wave has
expanded so far away from the directly
heated gases (the fireball)
that the
air in the shock wave is no longer shocked to high enough temperature to be
opaque. The fireball
is then visible
through the shocked air and begins to
(Brode 1968).
The
to the far field
cool rapidly by emission of radiation
supply of radiant
energ'y can be thought of as coming from a cooling wave
propagating
of the
into the fireball,
and is manifest by a slow shrinking
(Bethe l-964).
However, to an observer,
the apparent
radiating
surface
temperature of the fireball
at first
begins to rise
as the much hotter
The shock wave
fireball
becomes visible
through the clearing
shocked air.
fireball
and this
is
then moving ahead of the central
stage is termed
rbreakawayr.
By about 0.9s after
detonation of the device the 'second
The temperature of the fireball
thermal maximumr is reached.
stabilizes
at
a value between 6000K and 10,000K, independent of device yield,
before
Bethe (1964) indicates that the second thermal maximum for a
again.
falling
near surface expJ.osion occurs when the fireball
is at a pressure of 500 kPa.
However the shock wave expands quickly
and the fireball
rapidly
relaxes to
presented in Brode (1968) show that
Model calculations
arnbient pressure.
from a 1 Mt explosion
while a fireball
in near surface air reaches its
second thermal maximurn at 0.9 secoRds (120*) the fireball
has relaxed to
The maximum radius
ambient pressure
at some tine
around 1.3 seconds.
(a parameter
observed around this
d:r
to be used in the model
time,
presented
to ambient
here)
will
oicur
w1len the fireball
has relaxed
pressure.
is most intense, but
At this stage the radLation to the far field
decreases to below a
it decays rapidly
to zero thereafter
as the tenperature
has temporariLy ceased to
few thousand K.
Also at this time the fireball
Soon after,
hydrodynamic forces start to
expand and even begins to shrink.
begins to rise
and grow again by entrainment
of
dominate, the fireball
ambient air.
5
We take the time just after
the second thermal maximum when the
(tine t=0) for the
pressure has relaxed to ambient as the initial
state
model to be presented here.
The fireball
is treated
as a hot isothermal
spherical
thermal of radius a and characteristic
density
the
P. Actually
proximity
fireball
initially
is distorted
by its
to the ground and by
reflected
blast
waves, and later
by the development of a strong internal
circulation
Its
density
and stem-cLoud.
also varies
due to radiative
The thermal is assumed to be at a.mbient
effects
and incomplet-e rnixing.
pressure throughout the model calculati.ons.
The temperature of the initial
T., is set at 8000K in conformity with the data of Glasstone and
state,
Dolan (1977).
Independence of this
initial
temperature
on device yield
implies
that the volume of the fireball
then is proportional
only to the
yie1d.
The initial
excess energy of
(above ambient conditions)
is
E,
=
t
8x4.18x1015xw (J)
the whole flreball
or
thermal,
E.,
(2)
,
of the initial
W, (in Mt) remaining
where B is the fraction
explosive yieId,
in the firebal-I at time t=0.
If at t=0, 0 ls density, and V = 4/3n a.3 is
the volume of the sphere, E. is given by the enthalpy
excess of the
{rne specific
p.V{h(T. ) -h(T-) }.
fireball,
enthaLpy of the fireball
is
represented'by
h(t)
where T is. tenperature
and the subscripts
i and 6
(fireball)
represent initial
and anibient conditions
and a variabLe without a
subscript
is that variable
for the fireball.
Note that initially,
at least,
gases
some of the energy is stored as chemical energy in the dissociated
making up the fireba1l.
This is discussed further
when the thermodynamic
We have
equation for the thermal is presented.
î" fr
=
^
gx|.tsxto"
1 5 4
]:|r.9. {n (ri) -h (r_) }
.
(3)
(L950a).
Observational
This scaling is the same as that used by Taylor
(1950b),
characteristics
is presented in Taylor
evidence about firebalL
The avail-able data on
Glasstone (1962) , Brode (1968) and waltman (1975).
initial
fireball
radius for bombs ranging from 1kt to 1Mt are summarised in
Table 2.o Fron_rthis table a representative
value of a.37'W is approximately
t
0.5 x 1-0" m3Mt
and by application
of Eq.(3) this co-rresponds to a B of
(To calculate
O.44.
the enthalpy
at T. = 8000K does require
the full
procedure discussed in Section 3.3).
The constraint
that B = 0.44 is used as the standard case in model
As tine
increases
most of the energry initially
in the
calculations.
fireball
subsequently
radiated
to the far
field
and the rest
is
is
dissipated
as it rises.
we note
by mixing of ambient air into the fireball
lost to the far field
is radiated before
that 20* of the ther,mal radiation
As the model
the secontl thermal
maximum (Glasstone
and Dolan 1977).
presented here cornmences just after
the second thermal maximum, then the
loss must be increased by 25t to account for this
calculated
total
radiant
early radiant loss.
7
FTREBALL DESCRIPTION
There
are
.
.
five
processes
which
Conservation
the
firebal-l.
These are:
conservation of mass including
entrainment
conservation of rnomentum
variation
of chernical composition and enthalpv
with temperature
radiative
loss
conservation of energy
These processes are described
3.1
describe
in the following
sections:
of mass and. entrainment
Followingr Baines and Hopfinger (1984), we assume that the rate of
gtowth of the thermal depends only on its gaseous mass, m, momentum (which
implicitly
contains the speed and density of the thermal) and the density
qives
To lowest
of the ambient air, p_
order
this
dm
dt
oo
^r"r[kJ"'
t4l
The growth due to influx
of ambient air occurs at a rate proportional
to
the surface area, A, the mean speed, u, of the rising
thermal,
and the 2/3
power of the ratio
This latter
of densities
of thermal and ambient air.
growth when the
term accounts for the difficulty
of effecting
turbulent
density
across the sheared interface
of the very light
thermal is large
(Batchelor 1954).
The constant of proportionality
e, is an entrainment
coefficient:
its constancy depends on an assumption of self-similarity
of
the thermalrs
which takes a few thermal radii
structure
of rise height to
develop.
Since the density difference
is stilI
large during that tine,
from Eq. (4), is sma1l and little
entrainment,
error can arise from the
assumption.
The initial
organisation
of
the
thermal
is
an
important
(Turner 1957).
determinant of the value of the entrainment coefficient
A
thermal with littIe
disorganized
initial
density difference
has an o of
O.25, while
a buoyant vortex
ri-ng - a very organized thermal- - has an
entrainment coefficient
which, while almost always less than 0.25, increases
with buoyancy force and decreases as the square of the irnparted circui-ation.
(7973) , reviewing
Escudier
and Maxworthy
the
situation,
come to
the
conclusion that d is rarely
subject to precise specification,
even under
Values in the range 0.01- and 0.35 can be expected.
laboratory conditions.
Mantrom and Haigh (1973) present
data for a "1ow yield,
J.ow
altitude
event" from which a value of q, can be derived.
Probably based on
these same data, Waltman (1975) quotes values of q in the range 0.13 to
O.26 from nuclear tests.
The data of Mantrom and Haigh are plotted
in
Fig.1 as height of the centre of the firebalI,
z, vs. Iateral half-width
of
by the half-width
the cloud, a, both nondimensionalized
of the fireball
when
a,.
By considering available
evidence on rise
it commences buoyant rise,
(e.9.,
time to reach altitride
fireball
diameters
heights,
and initial
18
Weapons data
( scaled to equivalent
sphere)
16
a=0.05 I
,
14
/
I a=0.10
I I
V/
/
12
weaponsdata
./ (toroidal
shape)
u=O.15
z 1 0
=0.20
2ai
I
a=O.25
6
4
2
1
2
3
4
a
5
6
7
qi
Figrure 1:
entrainment
varying
with
calculations
model
of
Comparison
and Haigh
from Mantrom
data
weapons
coeificients,
or with
of
half-width
against
is plotted
(l-973).
of centre
Height
h
a
l
f
w
i
d
t
h
'
i
n
i
t
i
a
l
t
h
e
b
y
b
o
t
h
s
c
a
l
e
d
firebalL
9
Glasstone and Do1an 7977), we conclude that the data presented by Mantron
and Haigh are actually
for an event with yield near J. Mt.
Thus in Figure 1
we compare the prototype observations
from the model developed
rrith results
here for several values of a for a 1 Mt explosion.
Note that the range of q
quoted by Waltman (1975) is in agreement with our simulations
of the Mantrom
and Haigh (l-973) data.
However, closer
Figure 1 shows that
study of
the fireball's
l-ateral extent at first
increases more strongly
than the dianeter
of model
thermals,
and this is due to the development of a toroidal
shape, probably
with
a hollow
centre
and certainly
with
a strong
circulation,
in the
(Glasstone and Dolan 1977) and laboratory
prototype
analogn:e (Mantrom and
Haigh 1973).
In view of the discussion above it would be quite surprising
to find an entrainment coefficient
near 0.25 since this characterises
a
glance crudely
disorganized
fits
thermal,
and at first
the observations
presented
for
in Figure 1.
Recognizing
that,
a sphere of equivalent
surface
area to the prototype
toroidal
structure,
the radius
will
be
significantly
less than the l-ateral extent of the toroid,
we find that the
best agreement throughout the range of heights is obtained if the observed
values of a are reduced by a factor
of 7.75 to faII
along the line
characterised
The correspondence shown in Figiure 1by a = 0.1 in the model.
is then particularly
The factor of 1.75 was determined by trial
close.
and
error.
It incorporates
a deal of information
about toroid
structure
which
prototype
Its
is
unavailable
for
fireballs.
constancy
implies
self-similarity
in the fireball
structure
and this is required by the model.
We take q = 0.1 as the standard case in model calculations.
3.2
Conservation
Escudier
of momentum
and Maxworthy
(1973) presented
the momentum equation
for
a thermal:
d
ilt
. .
L \P
+
kp_)uVl
=
v(p_ - p)g
(s)
(5),
In
Escudier
setting
down equation
and Maxworthy have made the
relatively
minor assumption that
there is no loss of momentum from the
thermal to a wake, :1.e., that there is no drag force on the thermal.
The
j-nertia
kp_ due to
of the thermal
in Eq. (5) is enhanced by a factor
displacement of the surrounding air.
The added mass coefficienl,
k, is
assumed to be that for a sphere in potential
flow, viz I/2 (Lanb 1952).
The
buoyancy of the thermal relative
to its surroundings changes the momentum of
the upward-moving air.
3.3
Composition and enthalpy
has two components.
The elemental
composition
of the fireball
Firstly
at the moment of cornmencement of the model vre define a fireball
of
moist
composition,
which for
a clean
explosion
consists
air
of
The fireball
composition app'ropriate at the earthrs
surfacei
see TabLe 1.
composition is specified
according to the number of atoms (in mole amounts)
material.
During the running of the
of each element per kg of fireball
rnodel additional
mass of ambient air is entralned
into the fireball.
The
10
is defined
of this
air
composition
the
so that
kept for each element,
known at any time.
according
elemental
A mass balance
to Table 1.
of the firebal-I
composition
is
is
record,
there
are
elemental
composition
this
Accompanying
firebirll
the
and its
of
composition
chemical
tikely
of the
calculations
A limited
set
temperatures.
range of fireball
for the appropriate
enthalpy
according
to
their
50 are
chosen
Iess
than
chemical
species
of
range
of
elemental
for
fireball
the
in
the
occurring
likelihood
of
minimization
scheme
of
A free
energy
being
considered.
compositions
(1971) is used to calculate
composition
and enthalpy
the chemical
Eriksson
of the fireball
the elemental
conposition
having
mixture
of an equilibrium
liquiil
solid'
This scheme can handle
and pressure.
for a given
temperature
elements
in
each
of
up to ten
phases
species,
and charged
and gaseous
is drawn from a
species
for
the various
data
Thermochemical
calculation.
(Turnbutl
and Wadsley 1984).
library
of information
computer-based
(1'971') procedure'for
version
of Eriksson's
The efficacy
of this
in two ways.
A
equilibria
is tested
chemical
high
temperature
calculating
(1955)
the
Gilmore
of
that
of
to
duplicate
!{as performed
calculation
in
is presented
of dry air at 8OOOK. The comparison
composition
equilibrium
good
though
slightly
in
agreement,
are
all
The
3 (a) .
results
table
properties
of !.hermodynamic
values
due to changes in the accepted
different
the
currently
is
0 , where
to
this
The one exception
the
species.
of
(JANAF 1971) is approximately
70 kcal,/nole
higher
heat of formation
accepted
(1955).
than the value used bv Gilmore
Z
coefficients
the dissociation
comparing
invol-ves
The second test
specific
air
at STP) and the
of
(= moles
state/moles
air
in heated
of
by
program with
those presented
in the present
h(T) as calculated
enthalpy
(Table 3(b))
comparable,
are closely
(1965).
the
results
Again
Reynolds
values
of thermomight be due to changes in accepted
that
differences
with
dynamic properties.
predicted
the
but
is
fireball
of
the
enthalpy
Because
the
mode1,
an iterative
in
the
step
at
each
time
is
unknown
temperature
procedure
the fireball
In this
temperature.
procedure
is used to calculate
are used to
temperature
pressure
and an estimated
composition,
elemental
against
the
compared
is
enthalpy
calculated
The
enthalpy.
calcufate
with
is repeated
a
the calculation
and if necessary
model enthalpy
fireball
A quadratic
agree.
the two enthalPies
until
of temperature
further
estimate
is calculated
and
range
in the desired
versus
temperature
fit
of enthalpy
process.
this
used to facilitate
state
for
the
The volume
of
gas
an ideal
pV
=
firebal-l
is
calculated
from
the
of
(6)
nRoT
and n is
for
air
where R^ is the gas constant
gaseous"chemical.species
in the fireball.
The density of the firebal_l
considering al1 species - solid, liquid
mass.
equation
the
total
number
of moles of
using this volurne but
is calculated
of
and gaseous - for the calculation
tl
rable
3 (a) :
Comparison of equilibrium
composition
at 8000 Kelvin
and
(ratioed
varying density
to ilensity of air at STp) for the
Eriksson
procedure
and the RAND calculations
of Gilmore
(1955) .
Units
moles/(mole
air
at STP) .
The syrribol e
represents free electrons.
Iog10(density
Species
Eriksson
procedure
co"
NO;
o -
Cd
9. 088-10
3.39E-09
-')
N-+
NO
NO+
-t
"t
9.59E-11
? oqF-1n
l_.40E-10
3.7 AF.-]-O
4.
bb.H;--t-J
4. L0E-o5
7.46E-O7
1-.388-05
1.37E-05
9. 05E-08
1. 65E-01
l - "0 7 E - 0 4
2.45E-O3
7.A7E-O4
1.00E-10
1. b5.Ei-Ul
6.99E-O2
8.308-05
9.00E-04
5.31E-O4
A
?
J . U5.E;-U5
1 lE-nq
3.22E-O3
2.728-04
N
1.23E+00
N+
N++
N+++
z - zYL-v
oo
o+
o++
o+++
1.788-06
J
4. .LbE-UJ.
9.04E-06
o
1.1-1E-04
2.37E-O3
8.40E-04
I3r;-u I
I. b5.E;-U5
Ne
Ne+
AT
Ar+
Ar++
! . 5 Z!;-UY
+. ozE- !z
t.
c
Eriksson
procedure
4.l_6E-05
CO+
N,
1og1-0(density ratio)
-2.O
ratio)
??F-n?
7.72E-06
9.928-06
4.54E-O7
J.348-UJ
2.63E-04
1.47E-05
1.23E+00
2.03E-03
8.36E-41
1.94E-O6
4. 16E-01
5.38E-04
9.44E-20
L.77E-4A
3.98E-05
9.34E-03
7.05E-06
4.968-1.7
O'7F-r))
8.64E-05
8.728-04
5.69E-O4
3.92E-l-L
9.72E-06
3.27I.-07
O. UJTJ-UJ
2.85E-04
3. 1_68-05
7.42E+OO
4. 868-03
9 -728-07
4. 188-01_
1.67E-05
o
??F-n?
1.428-05
2.778-O4
2.85E-05
1.42E+00
4-34E-O3
6. 138-40
1.05E-06
4.Lt}1-VL
9.998-04
3.27Ij-19
7.098-47
3.98E-05
L.268-7I
9.34E-03
1. 308-05
1.69E-16
z'
coefficients'
Cornparison of dissociation
and specific enthalpy' h(T), of heated dry
(1965;
and Reynolds
air fron this study
Fig.B.9) at 1 atm. units of h(T) are MJ/kg.
Table 3(b):
Reynolds (1965)
This study
Temp.
z
h (r)
h (r)
z
N
8000
7000
6000
5000
4000
3000
2000
1000
248
1.88
1. 60
L.32
L.2I
1. l_5
L.02
L.00
L.00
1: 00
2?
2
zJ.d
15.0
o o
' 7 4
3.8
2.O
rr'7
0.o
l_.90
1-..58
1.35
L .
Z L
7.r2
L. 06
1.03
1. 00
1.00
38.5
26.O
15.7
1 0 .3
1
i
4.3
2.3
1.L
0.3
3.4
the
Radiative
loss
Radiation
Stefan-Boltzmann
of a thennal
from the surface
as
law which can be written
K
=
4
is
expressed
4
eoA(r- - T-)
in
terms of
(7)
opacity,
of
the
or more correctly
the
effective
emissivity,
where e is
The
fireball
composition
is
a function
of
it
thermal:
_gnd _$:mp;:rature.
-K n
and A is the
o' has the value 5.67 x tO'w
constant,
Stefan-Boltztnann
radiation
In
Eq. (7)
the
environmental
firebaIl.
the
area
of
surface
level
of
the
at the
ambient
temperature
the
is
taken
as T-r
temperature
to a complex situation.
approximation
This is an unimportant
thermal.
heated
air
opacity
of
the
discussions
of
There
are
detailed
1964) and radiation
7961, Gifmore
7960, Armstrong
et a1.,
et aI.,
(gethe 1964, Brode 1968).
details
are
Certain
fireballs
loss
from nuci.ear
of
be opaque at temperatures
wil]
The air
the fireball
within
known.
well
1000 to
around
lower
temperatures
at
and transparent
6000 K and above
probably
be opaque at all
will
within
the fireball
The bomb debris
2OOO K.
(Gilmore
of the fireball
to the opacity
and thus
contributes
temperatures
burst
we use
for
a near-surface
effects
these
To accommodate both
1.964).
with
an
as a opaque sphere
acts
fireball
that
the
assumption
the
simple
procedure.
by the following
calculated
surface
at the outer
emissivity
(Meyerott
Planck
mean
absorption
(1964)
of
provides
table
a
Gilmore
The
and air density.
of temperature
of heated air as a function
coefficient
(1964) as
by GiLnore
P, is defined
coefficient,
Planck mean absorption
P =
(1964)
Thus we use Gilmorels
in Eq. (7) where
e
=
table
--*
of
-RPa
1-e
(8)
^
i/aoer4
.
P to
derive
the
effective
emissivity
e
(e)
of a transformed table
interpolation
The values of P are derived by linear
and
coefficient
scales of PLanck mean absorption
logarithmic
involving
The value of P is extrapolated
scale for temperature.
density and a linear
The
down to L000K using the same transformed scales as for interpolationThese data
value of P is held at that for 1000K for alt lower temperatures.
are presented in Table 4(a).
the loss of energy by
factor
which affects
There is a further
rnust
The atmosphere surrounding the firebatl
from the fireball.
radiation
is lost from the
so that the emitted radiation
transparent
be sufficiently
is absorbed in the
If the radiation
and its imrnediate surrounds.
fireball
(i.e.,
radius
distances << a fireball
of the fireball
inunediate vicinity
will
from the surface) then the air which has been heated by the radiation
fn this case the radiative
and be entrained into it.
rise with the fireball
to the buoyant
system and contributes
energy is not lost from the fireball
rise of the fireball.
I4
Table
4(a):
Planck mean absorption
for highcoefficient
-.
(Gilmore 1964) Units:
temperature
air
cm
Temperature
Ratio*
Density
(K)
10
1 0 -
1 0 -
_A
1 0 -
10
2000
5.4E-05
1".7E-06
5.48-08
I.7E-O9
3000
1.3E-03
4.4F'-05
1.6E-06
7.0E-08
2.7E-O9
7.1E-11
4000
1.0E-02
5.78-04
2.6E-O5
7.78-07
2. 1E-08
6. 7E-l-0
6000
1.8E-01
6.1E-03
7.9D-O4
6.6E-O6
J.5E-Ul
r.d-Ei-ut
8000
4.5E-01-
1.4E-O2
5.1E-04
l-.9E-05
5.9E-07
1.8E-08
: Density
ratio
*
Table
4(b):
Fraction,
the 0.25
= density
heated
248
air
at
STP
Tr, of black
body
radiation
emitted
in
1976).
Lo 2.5 pm window (Paltridge
& Platt
i2.5um
a^cltrlot4
Jo. zsuro
Temperature
(K)
1000
air/density
0
u. rol
2000
0.634
3000
o. 834
4000
0.9L4
5000
o.946
6000
0.954
7000
o.944
8000
0.919
15
the
the
its
The factor
to be considered
is what
field?.
fireball
can be lost
to the far
transmission
of fireball
radiation
through
immediate
surrounds
to the far fieId.
fraction
of the
We define
this
air
at ambient
radiation
from
factor
as T*,
temperature
in
distances
radiation
absorbed at short
by
Ultraviolet
is strongly
bands of 0^ at all
absorption
the
Schumann-Runge
temperatures.
Complete
-metres
within
of
of
the
thermal
is
assumed for
all
a distance
several
l
e
s
s
t
h
a
n
0
.
2
5
u
m
.
wavelengths
tr
processes
but the
At longer
wavelengths
there
are many absorption
rnost important
of these insofar
the transmission
of radiation
as determining
from the thermal
to some distance
is due to water
vapour
and carbon dioxide
greater
There are many absorption
in the atmosphere.
bands for wavelengths
than 2.51m (Paltridge
and Platt
1976).
We assume cornplete absorption
for
| > 2.51m.
'
range
0.25pm < \ < 2.5pm the
atmosphere
surrounding
the
In the
The transmission
for
black
factor
fireball
is assumed to be transparent.
of temperature
from the fireball
is computed
as a function
body radiation
parameters
Paltridge
and Platt
tabulated
in e.g.,
using the Plank function
(1976, Table 2.2) to evaluate
the integral
rr
=
12.5pm
4
B.dtlor|
Jo . 2 5 u m A
Tt
Table 4 (b) .
The resuLts
in
are presented
constant at a value
transmission
is practically
temperatures above 5000 K but below that temperature
peak thermal emission moves to longer wavelengths.
at the lower temperatures.
3.5
(10)
that
the
is
evident
of 0.95 for fireball
it fa1ls rapidly as thE
Tr o TApproximately,
Energy balance of the thermal
growth and rise
process
over a tirne
for thermal
A two-stage
a mass dm of
Firstly'
the thermal entrains
increment ilt is considered.
ambient air which is at the same pressure p as the thermal at the level z.
The
expanding against the enveloping air.
fhe thermal then rises further,
to the far field.
only heat loss from the thermal, dQ' is due to radiation
So we have
d Q =
- R d t
clH =
dQ+vdp+dH'
and
of
Here H is the enthalpy
due to entrainment
thermal
dHt = h_ dm and so
the thermal,
of ambient
dHr
air
of the
is the change in enthalpy
h_.
Thus
of specific
enthalpy
I6
dH
dt
=
h
"-
dm
dt
*
rrdP-e
dt
alh
-'dr
An
An
- + \ / : r 1
m -
o[
- R
oz
(11)
sl-nce
dz.
(12)
c1t
The thermodynamic
unique
solution
for
the
temperature
for
any given
l-ikelv
chemical
srrecies are
relations
described
in Section
3.3 provide
a
relationship
bet-ween
fireball
enthalpy
and
(provided
fireball
elemental
compositionr
the
known and ideal
behaviour
is assumed).
Theories
of (non-radiating)
thermals
rising
into
stably
stratified
atmospheres
are usually
expressed
in terms cf the buoyancy of the thermal,
- p),
(e.9.,
gv(prather
than the thermal
energy
Morton et al,_ L956).
Eq. (11) can be rewritten
in terms of the buoyancy utilizing
the equation
of
Eq. (6).
If
state,
dissocation
and temperature
dependence of the specific
(c^ = (ahlaT)^),
heat,
could
be neglected,
Eq. (11)
would
reduce
to
a
Y
familiar
Torm:
dt
lgv(P- - P)l
-
-P- *"
-
ô
f,r_
(13)
The buoyancy of the thermal changes due to its
motion relative
to
given in terms of N(z), the Brunt-Veis;f;
ambient thernal stratification
frequency, and by radiative
loss of heat to its surroundings.
In
equation
wake.
3.6
it
both
the thermodynamic
and buoyancy
formulations
has been assumed that
there
is no loss of internal
Sunmary
put
F* = gV*(l-pr).
of
model
d
,if
i
of the above
energy to a
equations
gt = e/e_ = m*/v*,
m* = ga3,
v* = p_a3,
Then the working equations can be written
dz
alt
the
n
[(P'+
-
(.r4)
I4*/V*
k)M*]
?
M* = p@a-u
as
=
F*
f l ql
and
I7
dm*
i+
= 3 ' l 5 l@ ' ) 2 / 3
dh /T\
In (r) -tr(r_) ]
- 3 T e o
(16)
?fr
lulp'-1-/3
{.n4-n 4 }
t
-
g!/P'
(17)
ap
enthalpy
and a new specific
integrated
These four equations
are numerically
the fireball
each time
for
after
composition
are predicted
and elemental
procedure
equilibrium
is then used in the thermodynamic
An iterative
step.
(see Section
chemical
the fireball
temperatur:e,
3.3),
to calculate
module
and
elemental
the
enthalpy
volume
to
corresponding
composi tion
and
process
of numerical
and the
This
one tirile
step
completes
composition.
The numerical
integration
with
is performed
integration
is conrmenced again.
(Margenau
1956).
The
Murphy
and
Runge
Kutta
method
fourth
a
order
for numerical
and it was found that
stabifity
integration
scheme was tested
produced on average an increase
of 4t in
in timesteps
a factor
of 8 increase
runs,
by, on separate
values.
The scheme was also tested
the final- variable
q, g and o to
The model behaviour
was in
zero.
the
constants
setting
for these
from the simplified
set of equations
agreement with that predicted
z = 0 at
from th.e level
from rest
The thermal
commences to rise
T. of 8000K, and
temperature
are an initial
t = 0.
The standar<l conditions
c = 0.1,
The entrainment
coefficient
radius a. given by Eg.(2).
an initial
opacity
and
the
enthalpy'
k = 1/2,
and
c-oefficient
the
mass
added
described
in
calculations
by
the
are
specified
transmission
function
are those of the mid-latitude
The ambient conditions
3.3 and 3.4.
sections
(section
2.1).
TCAo standard
atmosphere
A
CHARACTERISTICS OF THE FIREBAI,L MOTJEL
comes
from
about
firebal-ls
published
information
Most
of
the
against
which
form the standard
These data will
1 Mt explosions.
that
ft
is
not
the model merely
be judged.
sufficient
the
model will
fireball,
balance
the
The
of
energy
rise
heights.
correct
reproduce
period,
high-temperature
nust be reasonably
particularly
during
the critical
(and hence chemical
is
composition)
history
the ternperature
accurate
so that
well
simulated.
rclean'
a 1 lvlt
behaviour
of
2 presents
simulated
temporal
the
Figure
from rest at a rate very close
initially
accelerates
The thermal
explosion.
in a dense
spherical
bubble
for
rate
a weightless
the theoretical
to 2'g,
by
(Mi1ne-Thonpson
until'
builds
up_,, speeC
1967).
The
thermal
fluid
-.
Thereafter
the
of 164 m s
19 s, it
is rising
at a rate
approximately
dominate.
air
of ambient
and acceleration
as entrainment
speed decreases
buoyancy
rise
its
neutral
overshoots
Eventually,
by about 2!O s, the thermal
in
A damped oscillation
again.
to fal1 back, overshooting
height
and begins
370 s,
period
close
to the buoyancy
of
ensues with
and height
velocity
to
rise
height
altitude.
We take the final
period
at that
of the atmosphere
material
extent
of fireball
maximum and the vertical
be equal
to the first
to
span
this
level
and the
subsequent
minimum.
E
o
o
o- 15
o hrop
I Mt observations
(Glasstone and
Dolan 1977)
o U
o
h r o p/ 1 , 0 o 0
F
a,
s 1 0
o
o
q
:
G
0.6 ?
2
c
o.4 8
oo
5
F
o.2
to
F
' t o
o
o.o
t
-o.2
-5
o.1
Figmre 2(a):
1.O
100
10
Time (sec)from Tmax
The height of the top of the fireball,
h*^-,
its rate of
rise,
u, its
temperature T and its
dianefdf
D(=2a), as a
function of time for a 1 Mt - yield nodel simulation
compared
with observations
from classtone anal Dolan (1977\.
1.O
o.g
F
x
o
t
0.6 :E
o
o
o.4 3
F
o.2
0
.e,
.G
1.O
Figure
2(b):
100
10
Time(sec)from Tr"t
The temperature,
radiant
scalecl to radiant
loss at
loss
time=O, A/R^, integrated
loss scaled to fireball
radiant
energy at tYme t=0, !Rdt/H^ and the fraction
of the black
*fireballbody radiance lost from the
at each stage, ExTr, see
text.
I9
this
because
grow by entrainment
thennal
cannot
At
first
the
However the
and atmosphere.
thermal
between
velocity
relative
requires
by
responds
which
sphere,
the
coolinq
raciate
strongly,
does
thermal
takes
but it
is sJight
The shrinkage
Figure 2(a).
<lecreasing in diameter,
coolinqt
growth
over radiative
to dominate
entrainment
seconcls for
several
As maximum
drops.
as the temperature
in irnportance
decreases
which rapidly
would
grows rapidly
anc in practice
the thermat
hej qht is approached
rise
by the ambient wind.
carried
spread horizontally'
rnaximum
thermal
second
the
3 s from
approximately
After
percent
of
Ninety
to 42OO K.
has dropped
of the thennal
temperature
lost,
and
been
has by then
the
thermal
from
radiated
energy
total
strength.
initial
flux
is only 48 of its
radiative
the
the
the
decay may be compared with data presented
radiative
Tbe predicted
As shown by Figure 2(b) the agreement
and Dolan (!91'7, Ch.7).
by classtone
simulated
is well
In particular
it may be noted that the timescale
i's good.
The predicted
rise
must also be satisfactory.
variation
so the temperature
report'ed
observations
is also in good agreement with
of tine
as a function
is
s1i9ht1y
height
rise
but
the
ultimate
Do1an,
and
classtone
by
of
data on the rate
reported
with
The model agrees well
underestimated.
by as
the maximum velocity
times,
but perhaps overestimates
at later
rise
much as 128.
t = 0 is
fireball
at
the
in
energy
the
81t
of
Ultimately,
of the device
Since the fraction
to the far field.
predicted
to be radiated
after
to be 44t (see discussion
is predicted
in the thermal
yi.ta
i.titially
to
is expected
emitted
radiation
thermal
Eq.3 above) , and 2Ot of the total
(Glasstone
and
the model conmences to be relevant
before
have been lost
is
model description
in this
energy
radiated
the total
Dolan 1977, Ch.1),
the thermal- partition
than
higher
w.
This
is
yield,
the
device
45t of
and Dolan and is in good agreement
of f = 35t, quoted by Glasstone
fraction
f = 444, quoted by Brode (1969).
with the fraction
in
at t=0 is dissipated
About 19* of the energy in the firebalf
with
this
corresponds
of the fireball:
rise
via the buoyant
mixing
turbulent
loss of
This
way.
in this
being dissipated
about 8% of the weapons yield
(Glasstone
and Dolan 1977, Brode
texts
in classical
energy is not discussed
for in
accounted
energy is erroneously
Vle can only presume that this
1968).
as it
is unlikely
partition".
The latter
the shock wave or in the "thermal
and the
results
our modelling
between
discrepancy
a serious
woul-d create
in
of the energy
fraction
whereas as far as we know the exact
observations,
known.
the shock wave is l-ess accurately
Itwouldbeasimplemattertofine-tunethernodelbyvarying
fireball
of
detail
published
of
lack
the
view
of
in
but
parameters
study
s
e
n
s
i
t
i
v
i
t
y
o
f
a
I
n
s
t
e
a
d
,
r
e
s
u
l
t
s
n
o
t
w
a
r
r
a
n
t
e
d
.
t
h
i
s
i
s
Lehaviour,
the
setting
it
can be seen that
From the Table
in Table 5.
are presented
value of
to a constant
of the air
and transmission
of the firebatl
op..ity
does not have a great
temperature
it to vary with
of allowing
instead
unity
radiates
The thermal
behaviour.
of fireball
on the major indicators
effect
the
than
rapidly
more
litt1e
a
so
cools
and
field
far
to
the
more energy
Neglecting
by 5*'
of rise,
is a lovrer height
The result
case.
standard
20
Table 5:
model
of the present fireball
The sensitivity
standard
of parameters from the
to variation
cdse. (T. = 8000K, 0 = 0.11 B = O.44, molespecified
Tr and e all
cular com$osition,
Units are MKS.
functions of temperature).
T @3.5s
@ t
u
max
top
G t
D
m1n
IR avno
5 /5
0.81
1,7925 2L5
570
0.84
30567
20r
796
0.00
! IbY)
Z!
5Zr
0.81
19
198L4
20'7
ozr
0.81
159
77
18054
2L5
J3
3804
-Lu5
ZZ
22379 20L
o = 0.05
3998
229
26
27354
cl = 0.15
3 t t6
136
15
L6Z
J5 /J
L
ZL
2L380
Standard
3878
164
79
ta82'7
€ x Tr = 1.0
3872
161
76
e x Tr = 0.0
7 451.
232
35
U.JJ
3767
f,f,5
!
A
39A2
1,71
T 1, = 1 0 0 0 0 K
56ZO
T. = 6000K
P
=
Q _
RR
t
2LL
r
I
A A A
74A
0. 58
189
trf,f,
0. 84
Z+J
587
n 7 q
277
781
u. of
l_
Composition
fixed
TJ
I I
2I
(by
quite
e = 0 or
T* = 0)
losses
is
radiative
entirely
setting
The thermal does not cool correctly
and th6 maxinum velocity
unacceptable.
The physically
realistic
lower bound to
and rise height are far too high.
losses involves using the opacity of heated air alone (Gilmore
the radiative
Tn fact
low
7964) as is
done here.
the opacity
may be higher
at
temperatures due to the presence of bomb debris (Gilrnore L964).
Variation
in the energy
of the fraction
of device yield initially
radius of the thermal at
to varying the initial
of the thermal (equivalent
proportional
temperature)
response in
constant
causes an almost directly
ft also has a large effect on the fraction
of enerqy
ultimate rise height.
(Note the fractlon
radiate$.
of the device yield
radiated
is equal to
1-.25 BIRdt/H^.')
This comes about because the fraction
of device yield
in
and the
only between energy radiated
the thermal" can be partitioned
thermal.
Reducing B by 258
of kinetic
dissipation
energy by the rising
it
drops the radiated energy to only 33t of device yie1d, while increasing
Both extremes
by 20t increases the radiated energy to 568 of total yielil.
(and
fireball
in the initial
are unacceptable, so the energy partitioning
Note
is constrained
to be close to that proposed here.
thus its radius)
that the ratio of radius to bomb yield derived for the standard case is that
observed from nuclear explosions (Section 2.2).
is
not a sensitive
The initial
thermal
temperature
of
the
parameter, but a value as low as 6000 K does lead to a rj.se height which is
(onIy
because not enough energy is lost by radiation
too large, prirnarily
temperature used in the standard case is
32* of device yield).
The initial
that observed from nuclear explosions.
A 50* lower entrainment coefficient
is much too low, with maximum
the
due to
reduced
retardation.
and rise
too
high
velocity
height
a to 0.15 is less drastic but the enhanced mixing does lead to
rncreasing
The comparison
of
height
than
observed.
lower
rise
a significantly
diameter to rise height for the model, and a real event, have been
fireball
presented in Fig.L.
was held at that for
Finally,
if the composition of the fireball
allowed,
i.e. N^, o^, Ar, CO^' Hô, and no dissociation
ambient conditions,
zpartitionfng
the fireball
has
f.s maintained,
.tr.fgy
then when the initial
The initial
has a
fireball
guite clifferent
behaviour to the standard case.
14t higher and loses only 34t of the total
diarneter, rises
36* larger
Initially
the fixed composition fireball
explosive energy as radiant 1oss.
This arises
one.
than the dissociated
falls
in temperature more rapidly
for
four times higher
at 8000K is nearly
because the specific
enthalpy
air,
whereas by 3O0OK the
compared with
the undissociated
dissociated
difference is only 35*.
We conclude from the sensitivity
study that it is not possible to
from the proposed parameter values in the
have a great deal of variation
behaviour are to
major indicators
of fireball
standard model if realistic
parameters except the
This is very satisfying
since all
be obtained.
to
of the necessity
coefficient
were chosen independently
entrainment
performance.
predict ultimate
fireball
50
Modol top
^40
E
g
----.-.
Mid latilude top
I from Chinesetests
Mid latilude bottom, (Telegadas 1979)
g
o
'6
30
+...'..) Chinese 3 Mt tests (Bauor 1979)
E
E
5
-9
/,/
Model
/'bottom/
o
E 2 0
.g
o
.o
9ro
II
o
o.o1
o.oo1
Figure
3(a):
10
1.O
o.1
Bombyield (Mt)
100
and fron
from the rnodel simulations
heights
Fireball
rise
as described
in rnid latitudes
various atmospheric explosions
in the text' where the explosions'were near mean sea level.
E
! 2
.
o
Mid latitude top
I
Mid latituda bottom .l
individual U.S. tests in Nevada
(Glasstone 1962)
E
.9
o
.c
o
a
E
a o
o
=
I
t
o 1
t
'
(!
Model
toP
a
o
Model
bottom
c
=
o
.o
o
.:
lr
e
qo
o
o.oo1
o.ol
o.1
Bomb yield (Mt)
Figure
3(b):
Fireball
rise
heights
atmospheric explosions
the nodel calculations
took place
explosions
level "
ancl from
from the model simulations
in Nevada, uSA, (Glasstone 1962) h'here
are referenced to, and the atmospheric
2 km above nean sea
at, approximately
of
rise
with
variation
height
show the
rigures
3 (a)
and 3 (b)
testing
has
nuclear
Most of the atmospheric
yield
device
for
the model.
(2-17'N)
by the USA and in pol-ar
latitudes
in equatorial
been conducted
(75oN) by the USSR (Bauer 1979).
The main data from mid latitudes
latitudes
this
to be good agreement
between
There appears
comes from Chinese
tests.
(1979) and Bauer
by Telegadas
of the Chinese tests
model and the analysis
(1979) as shown in Fig.r:re 3(a),
ranges from 0.001 to 10 Mt.
with overlapping
mid latitude
nuclear
presents
heights
from other
cloud
classtone
0962)
tests
were
of burst
in these
The helghts
in north-eastern
Nevada.
tests
on
which
in
turn
is
400m above the
local
surface,
approximately
300 to
level,
leading
to
an
2 km above
mean sea
less
than
average
slightly
These data are
of around 2 km above sea Ievel.
approximate
height
of burst
where the
frorn nodel calculations
cloud heights
3(b) with
compared in Figure
rt
that
the
sea
level.
appears
2 km above
height
of
explosion
is
is
the
cloud
top
calculations,
but
the
model
bracket
observations
of 0.01 to 0.1 Mt whereas it is
in the model for bomb yields
underestimated
qlightly
for bomb yields
of 0.001- Mt.
overestimated
from this
simple
heights
of cloud
Overall
the predictions
for most bomb yields
obs;:rvations
within
the scatter
of the actual
lie
0.001.Mt to 10 Mt, a dynamic range of l-0-.
model
from
CONCLUSION
(ascending)
fireball
has
stage of a nuclear
A model of the late
parameters
has
in basic
to variations
and its
sensitivity
been presented
permitting
little
The model has been shown to be robust,
been presented.
with
by comparison
values
established
parameters
of
avtay from
variation
observations.
independent
The model is sufficiently
- to address issues
many extensions
oxide
nitric
and elemental
of radiactive
bursts.
6.
complex
such as:
to
be
useful
as
the
basis
for
soot
by fireballs,
into
the stratosphere
injection
injection
from "dirty"
explosions'
carbon injections
of air
radar
signature
into
the atmosphere,
isotopes
ACKNOWT,EDGE}4ENTS
and Mr. Mike Wadsley for supplying to
we thank Dr. Alan Turnbull
(1971) chemical composition
and
us the code implementing the Eriksson
procedures.
This work would not have been possible
enthalpy calculation
We thank Professor Paul Crutzen for discussions that stimulated
without it.
Year of Peace,
We also thank the Committee of the International
this work.
for financial
support for Lou Ripari and the
Department of Foreign Affairs
proj ect.
2l+
7.
REFERENCES
(1982):
Reference
Anrlcio advisers
Ambio 1L, 94-99.
fought.
Armstrong,
(1984):
Thermals
Hopfinger
1"8, 1051-1057.
Atmos.Environ.,
density
G.K.
(1979):
E.
be
rnight
e r v v v .
(l-954):
Q.J.Roy.Met.Soc.'
Bauer,
war
nuclear
Meyerott
J.Quant.
E.J.
W.D. and
difference.
Batchelor,
a
D.H. Holland and R.E.
R.W. Nicho1ls,
B.H., J. Sokoloff,
air.
(1"961):
properties
temperature
of high
Radiative
qna^fr^qn-P,adiant
L, 1-43-162.
Transfer,
v g v v
Baines,
How
scenario:
ozone,
and
Heat convection
80, 339-358.
large
with
in
effects
buoyancy
on
influences
of perturbing
A catalogue
84, 6929-6940J.Geophys.Res.,
7955-1975.
fluids.
stratospheric
Bethe,
Alamos
scientific
Los
fireball.
the
Theory
of
H.A. (1964):
New Mexico'
Los Alamos,
California,
of
University
Laboratory,
85pp.
LA-3064, UC-34, PHYSTCS, TrD-4500 (30th Ed.),
Brode,
H.L. (1968):
18'
Sci.,
Brode,
(l-960):
from a megaton
Cratering
R.L.
H.L. and Bjork,
Memorandurn RM26O0, The Rand Corporation,
Research
USA' 60PP.
Broido,
Review of
753-202.
weapons
nuclear
Ann.Rev.
effects.
Thermodynamic
G. (197L):
ACTA Chemica Scandinavica,
Escudier,
M.P.
and
thermals.
Maxworthy
T.
Mech.
J.Fluid
(1973):
On
541-552.
equilibr5.a'
temperature
of high
studies
25, 265L-2654.
61,
surface
burst.
Monica'
santa
and
s.B. Martin
from
a
Nuclear
U.S. Naval
8.3].
NTIS AD-8951 585.
Hillendahl'
R.w.
Day,
R.P.
Butler'
A., C.P.
(1953):
Radiation
Thermal
A.B. Willoughby
Tumbler-Snapper
lProject
Operation
Detonation.
san Francisco.
Defence Laboratory,
Radiological
109pp.
Eriksson,
motion
the
Nuclear
of
turbulent
Gilmore,
properties
and thermodynamic
(1955):
composition
Equilibrium
F.R.
RM-1543 ASTTA Document No. AD84o52' The Rand
to 24,0o0K.
of air
68PP.
Santa Monica.
CorPoration'
Gilmore,
properties
of
radiation
Approximate
F.R. (1964):
(ARPA Order
Memorandurn RM-3997-ARPA
and 8OO0K.
Santa Monica.
Rand Corporation,
Gl-asstone,
The effects
S. (1962):
730PP.
Office,
Printing
Glasstone,
S. and Do1an, P.J.
Government Printing
(]-977) z
Office,
of
nuclear
The effects
653pp.
air between
No.189-61-).
weapons.
of
nuclear
us
2000
The
Government
weapons.
us
25
Manual
ICAO (1954):
32 kilometres
nv rr aYrsnr r f z q e
i f zv r rr+t
i nn
rMr ^v n. r+er a
r v: s 4 .
extended
to
atmosphere
standard
civil
Aviation
International
ICAo
Edn).
the
(2nd
of
l
D.R. Stull
and
2nd
ed.
Tables
Thermochemical
JANAF (1971), JANAF
Bureau of
National
of Standard Reference Data'
H. Prophet,
Office
ser. '
Nat.Bur.
Nat.Stand.Ref.Data
D.C.,
Washington
Standards,
(U.S.),
37, 1]-47p. plus 1976 and 1982 supplements.
stand.
Lamb, Sir
Manins,
H. (1952):
738pp.
6th Edn.
Hydrodynamics.
(l-973):
entrainment
Fireball
w.W.
D.D. and Haigh,
Final
Calif.
Beach,
Redondo
Group
Systems
september 1973, NTIS-AD-780 L92.
18895-6004-RU-OO.
Margenau,
(1956):
Murphy,
H. and G.M.
Van Nostrand Co.,
Chemistry.
Meyerott,
R.w.
and
R.E.,
J.
Sokoloff
Geophysies
of air.
coefficients
Air
Research
Division,
Research
Massachusetts.
Bedford,
Morton,
pittock,
Reynolds,
Taylor,
study.
Report
1l-1pp.
of
The Mathematics
USA, 604pp.
Princeton,
Physics
TRw
No.
and
(1960) :
Absorption
Nicholls
Force
Air
Research Directorate,
Command.
USAF'
and Development
(1956):
gravitational
Turbulent
Taylor
and J.S. Turner
8.R., G.I.
sources.
- Proc.Roy.
and instantaneous
from maintained
convection
Soc. A., 234, 7-23.
(1967) z
L.M.
Milne-Thompson,
Macmillan.
660PP.
paltridge,
Press.
resulting
injections
and stratospheric
t9, I245-t255.
Atmos.Env.
Cloud heights
P.C. (19e5):
t^'ar.
from a thermonuclear
Mantrom,
Carnbridge University
G.W. and c.M.R.
and climatology.
Theoretical
5th
hydrodynamics.
(1976):
Radiative
Platt
318pp.
Ansterdam.
process
in
Edn.
meteorology
C.S. Shapiro
M.C. Maccracken,
crutzen,
P.J.
Ackernan,
A.8.,
T.P.
(1986):
consequences of nuclear
The environmental
and R.P. Turco
John Wiley
and
effects,
and atmospheric
Vo1ume 1, Physical
war'
UK' 359PP.
Sons, Chichester,
w.C.
(1965):
(1950a) :
G.I.
explosion.
159-17 4.
Thermodynamics.
The formation
Theoretical
I.
McGraw-Hi1l,
a blast
of
discussion.
Ne\'7York,
458pp.
wave by a very
Proc.Roy.Soc.,
intense
A. 2W,
Taylor,e.I.(1950b):Theformationofablastwavebyaveryintense
Proc.Roy.Soc',
of 1945.
The Atomic Explosion
Tr.
explosion.
2O1-,175-L86.
A'
26
atmospheric
Estimation
of maximum credible
TeJ-egadas, K. \979t
from nuclear
and dose rates
concentrations
activity
Atnos.Env., L3, 327-334.
Turnbull,
-
(1984):
of
Thermodynamic Modelling
A.c.
and M.w. Wadsley
Processes by the CsIRO-SGTE Thermodata system.
Metallurgical
Proc.slzmp. on Extractive Metal-Lur9y, Aqs.f.M.M. Nov. 1984. p79-85.
Turner, J.s.
valley,
radiotests.
(1957):
Buoyant vortex rings.
Proc.Roy.Soc., A. 42,
S.t. (ed.) 1965, Handbook of geophisics
Mccraw-Hill, N.Y., USA, 683PP.
and
6I-75.
space environments.
Waltman, D.D. (1975): A simple description of an ascending nuclear fireball
of
Air Force Institute
M.Sc. thesisr
solution.
and a fortran
78pp.
Technology, Ohio, USA. NTIS AD-A017 780/7.
A
simpler
model
If the only purpose
of
and no detail
behaviour
can be greatly
computation
for heated air,
retationship
Fig.B.9) in place of the free
in code
reduction
substantial
factor
of 2 to 10 depending
scheme.
chemical equilibria
of
the
Late
(ascending)
stage
of
a
nuclear
model is to examine physical
of the fireball
required
then the
model is
the chenical
by using an enthalpy,/temperature
simplified
such as may be obtained from Reynolds (1965t
energy minimization scheme. This leads to a
(tu 309) and the running time is reduced by a
in the
on the nurnber of species evaluated
is computed for the same
relationship
rf the enthalpy,/temperature
species and air of the same elemental composition in the simple and the full
parameters
are (by
of other physical
model then the model predictions
indistingr:ishable.
def inition)
Appgndix
B:
Fireball
Model
Flow Diagrams
*rnitialize
rnitialize_Output
Differential
Equations
ambient
l4ass Balance
*see
next
page
Update
enthalpy
Initialize
Dif f erential
Equations
ambient
Mass_Balance_Update
enthalpy
29
PROGRAM OUTLINE
-T.
Read initial
conditions
and open output
files
from
read
"D.fil"
in
data
r_T
rnitialize
all variables and set
esuations
up simultaneous differential
Write
headers
the
nine
Write
data to output
files
Determine
to
time
step
output
if
files
required
fnitialize
t
T
Initial
ize_Output
T
Output Data
value
-f
adjustrnents
to DErs using
Calculate
Runge Kutta
and then solve
order
4th
Find the temperature that
corresponds to the known enthalpy
Momentum stop
Runge Kutta
_L
ri"f r
I_
criterion?
Time
stop
Output data to files
for last step
less than
time?
Output
T Data
!
I
30
rnitialize
Subroutine
variables
Initialize
T
CLEAN FIREBAI,L
molar fraction
Calculate
ambient air gases
I
I
T
GRAM ATOM
nurnber of moles of
Calculate
air
element per kg fireball
I
I
pressure
and density
temperature'
calculate
height
air for initial
of anbient
ICAO Air
data for each
Read thermochemical
from "NEWDATA.DAT"
in fireball
read
of
enthalpy/kg
temperature
calculate
initial
I
species
T
in_CHNOS
I
I
air
fireball
TI
for
I
I
I
scramble
Ca1cu1ate
mole
all
suns of
in
species
data for
Read thermochemical
from "A-t'lB.AIR"
of enthalpy
1 kg
air
ambient
fireball
calculations
II
air
I
T
read_amb_air
T
Calculate
enthalpy
of
ambient
for
air
the
by dividing
mass of fireball
Calculate
of
by the enthalpy,/kg
of fireball
enthalpy
enthalpy
minus ambient
temperature
initial
and height
temperature
Initialize
differential
number of
total
Calculate
air
species in fireball
equations
moles
for
height
initial
enthalpy
ambient
I _
initial
air
at
at initial
variables
each
elemental
T
Set
up differential
equations
Equations
Differential
t-
Subroutine
-
(hite,
CLEAN FIREBAIL
calculates
the
Water
molar
vapour
MFH2O, MFN2' IvlFo2, !1FCO2, I4FAC)
vapour,
fractions
of
aribient
gases
air
Set molar fraction
HÔ to zero
z
included?
molar fraction
Calculate
of Hô for given heiqht
calculate molar fractions
of ambient air qases
of molecules
Check that mole fractions
H.o'
including
making up ambient air,
very close to unity
Function
:
is
MF H2o(z)
returns
the
molar
fraction
Set
of
index
Hro
variable
IncremenE.
Height
at
(I)
j
the
given
(I)
to
zero
(I=Ifa,
g z < Height
Calculate
the molar
at given height,
z,
interpolation
height
(I+1) ?
of
fraction
uslng linear
Hro
-
of
JZ
GRAM-ATOM (tlFH2O, MFN2, MFO2, IrfCO2' I{FAr' nN' nO, nH, nC, nAr)
Subroutine
-
calculates
fractions
the number of noles
per
of the molecoles
of each element given
kg of ambient air
Calculate
molecule
the number of moles of
per kg of ambient air
the number of moles
Calculate
element per kg of ambient air
ambient-enthalpy
Subroutine
-
calculates
the
enthalpy
molar
of
each
each
(z,tenp)
of
the enthalpy
Calculate
air at
rnake up ambient
Calculate
molar
weight
molecular
the relative
Calculate
of ambient air
the
new ambient
air
composition
molecules
for all
given
temperature
which
air
gases
of
fractions
ambient
T
ENTH
l_
T
CLEAN
FIREBALL
-L
molecular
relative
Calculate
air composition
ambient
Calculate
Function
the
enthalpy
of
weight
1 kg
of
of
new
ambient
air
ENTH (I,T)
by
indexed
air
species
of the ambient
the enthalpy
calculates
This function
T where T is up to 60O0"K.
I for the temperature
been read in from the
has already
data used for this
The thermodynamic
and stored into the arrays ER(6), which is the heat of
file'amb.air'
and C(6,6) which contains
at 298.15oK for each of the six species,
formation
heat at
of specific
the variation
that describe
the numeric coefficients,
needed for the calcufation
pressure
as a function
of temperature,
constant
of
enthalpy.
33
Subroutine
-
fCAO-Air
calculates
the given
(2, temp,pressurerdensity)
temperature,
height
of the
Set
pressure
fireball
variable
index
rncremenE
leve1
Calculate
fireball
(J)
J,
and density
(J)
to
of
the
ambient
air
zero
(J=J+-L,
5 z < level
(J+1) ?
the temperature
of the
interpolation
using linear
lapse (J) = 9z
and
calculate
the pressure
by
density
of the fireball
a given set of equations
SET A
the pressure
and
Calculate
of the fireball
density
by
a given set of equations
SET B
for
JLI
Subroutine
-
scramble
(temprpressure)
molar amounts for
uses the output of CHNOS3, stores all f i n a l
various
in rHoldn' array and calculates
species in fireball
properties
of the cornposition of the f i r e b a l l
Calculate the enthalpy per kg of fireball
and
air gtiven the pressure, temperature,
molar arnounts of each element in the fireball
molar amounts for each
array
in the 'Holdnr
Store aII
in fireball
final
air
Calculate
per kg of
the mole
fireball
sum of
air
all
gaseous
Calculate
per kg of
the mole
fireball
sum of
air
all
solid
Calculate
of fireball
the mole
air
sum of
all
species
species
species
species
per
kg
Calculate
the nole sum of
species per kg of firebaLl
positively
all
air
chargted
the mole sum of
Calculate
species per kg of fireball
all
negatively
air
charged
Calculate
per kg of
the mole
fireball
sum of
air
a1I
charged
species
T
CHNOS3
I
35
Subroutine
-
CITNOS3 ( t e m p , p r e s s u r e ,
caLculates
the
enthalpy
holding
Set array
element per kg of
aN, aO, aH, aC, aAr, aS, aE, Enthalpy
per
kg of
fireball
molar amounts
fireball
air
per
kg)
air
for
each
calculate
Gibbs free energy
air
in fireball
soecies
for
each
per mole
air
for
each
T
I
ENTR
T
I
CENTH
enthalpy
Calculate
species in fireball
gn:ess of the number of
Set initial
of each species per kg of fireball
the number of moles of
Calculate
air
species per kg of fireball
I
moles
air
each
T
I
I
Cafcufate
fireball
the
air
enthalpy
per
kg of
36
Subroutine
-
finds
Find-T
the
temperature
that
less
counter
than
T
scramble
I
I
enthalpy
temperature
CaIculate
enthalpy
for gn-ress temperature
Update temperature and
enthalpy pairs used for
quadratic fit
enthalpy
compare calculated
with known enthalpy
Error > 0.01t?
4?
Use quadratic fit to
guess temperature
corresponding to
enthalpy
Approximate guess temperature
corresponding to enthalpy
using linear fit method
CaIculate
for guess
a known enthalpy
to
corresponds
enthalpy
Compare calculated
with known enthalpy
Error > 0.1t?
Difference
temperature
temperature
between guess
and previous
used in fit
< 1.0?
Add or subtract 1.0 fron this
guess temperature so that the
pairs used for the fit are at
least 1"K apart
TI
matrix
I
37
Subroutine
-
matrix
A 2nd order
temperature
Have
fit
Polynonial
corresponding
used by Find
to enthalpy
.F
o2
a
z
2
le:
-1
"a
T to
approximate
f,
x = T
guess
need to solve
for
x
,F
-2
"2
.F
-3
-3
J
in
variables
lnitialize
and in T matrix
matrix
F
Reduce F to an uPPer
natrix
triancrular
solve for :!, that
for a, b arid c
Function
CENTH (I
T)
and Function
is
ENTR (r,T)
and entropy
respectively
the enthalpy
The functions
CENTH and ENTR calculate
T.
T, for any temperature
and any fireball
species,
has already
been
for these calculations
The thermodynamic
data required
'newdata.dat'
HR(50), the heat
in the arrays
and stored
read from the file
the enthalPy
of the species at
of species at 298.15K, sR(50),
of formation
298.15K, cl(50,5) , c2(5o,5), c3(50,5), c4(50,5), TM(50'5) and HH(50,5)-which
the variation
of specific
describe
contain
that
the numeric
coefficients
pressure
of temperature.
heat at constant
as a function
Subroutine
-A
Runge-Kutta
(Nrt)
approximation
4th order
Runge Kutta
numerical
equations.
differentiaL
the time by the
This subroutine
increnents
to
the
tinestep.
solution
of
the
N
38
Subroutine
Dif f erential_Equations
- recalculates
differential
ecruations
Update variables
equations
solved
based on differential
in 'Runge Kuttar
Calculate temperaturer
of the arnbient air for
Calculate
fireba1l.
increase
T
pr€ssure and density
the new heioht
i.n mass of
atoms
in
the
ICAO Air
I
I
T
t
r
l
l
l4ass Balance_Update
Calculate
the new number of moles of
per kg of fireball
species in fireball
Update the volume, radius,
buoyancy of the fireball.
Calculate
the
arnbient air.
enthalpy
Ca1culate
the energy
due to radiation.
Recalculate
differential
of
lost
each
air.
l
1
speed and
the
to
entrained
far
field
ambient
Tenthalpy
Loss
T
Radiant
1
ecruations.
39
Subroutine
-
(oLD MASS' BMass,
Mass-Balance-Update
the
calculates
present
time
in
increase
mass of
in
atoms
hite)
fireball
and updates
for
T
calculate
air gases
the
for
fractions
molar
the given height
number of moles of
Calculate
air
element per kg ambient
number
fireball
new total
Calculate
in
of each element
number of moles
Calculate
element per kg of fireball
Subroutine
-
(T,
Loss-Radiant
the
calculates
energy
lost
rad.
to
r
of
of
anbient
CLEAN FIREBALL
I
T
GRAM ATOM
each
f
moles
of each
air
amb)
far
field
due to
radiation
by cthich ever
transmissivity
Calculate
temperature
for current
is valid
fornula
Sum of
Set opacity
to 1.0
of
all
condensed
species
of fireball
opacity
Calculate
using P1anck Mean Absorption
coefficient
fireball
product
Calculate
and transmissivitv
> 3x10 -?
of
energy lost
Calculate
field
due to radiation
opacity
to
far
T
I
I
PMAC
I
I
40
Function
-
returns
PMAC (r
the
fb)
Planck
Mean Absorption
First
Coefficient
tine?
fnitialize
the table
of
coefficients
to the values
(1964)
given by Gilmore
Ca1culate
density
ratio
given
by density
of fireball/density
of ambient
air
Linearly
interpolate
table
using
logarithmic
density
ratio
sca1e,
temperature
scale and logarithmic
PMAC scale
Subroutine
-
Initialize_Output
sets initial
output
files
information
in
headers
Initialize
for
a1I
data
character
Write
header
output
files
information
write
labels
column
to
output
to screen and
variables
to
each
all
file
9
4T
Subroutine
-
outputs data to the screen and output files.
five timesteps and for the final timestep
Subroutine
-
reads
opens
Subroutine
-
data
thermochemical
for
called
ambient
air
every
the
gases
from
read-in-CHNOS
read-in-data
the
the
initial
outPut
conditions
files
Do-enth-halt
and other
input
data
from
"D.FTL"
and
-
it is
message subroutine,
is an error
this
per
Equations
if the enthalpy
Differential
enthalpy.
fireball
greater
than the initial
of the Program
and stops execution
Subroutine
-
is only
the thermoand all
from "D.FIL"
reads the species in the fireball
from "NEWDATA.DAT". Counts the nunber
data for these species
chemical
gases and condensed species and sets up the atoms matrix
of elements,
for use in the Eriksson
Procedure
Subroutine
-
It
read-amb-air
the
reads and stores
trAMB.AIR"
the file
Subroutine
-
output-Data
from the subroutine
called
mass is
kg of fireball
message
It prints
an error
Show-Status
from the subroutine
which is called
message subroutine
error
another
is less than zero
of the fireball
temperature
Find T if the calculated
message and stops
out an error
It prints
than 10r000"K.
or gieater
of the Program
execution
42
Appendix
I,IST
9:
Tireball
Model
Code
OF VARIABI,ES USED IN PROGRAI'I
VARIABI.E
TYPE
aXX
Real
Character*80
anXX
ReaI
atirfle
ReaI
Atnos
b(0:3)
beta
Bllass
Character*20
ReaI Array
ReaI Constant
Real
c ( 0 : 3)
ReaI Array
c(5,5)
ReaI Array
cala
calb
calc
ch
ReaI
Character*1
DESCRIPTION
- U s e t l i n " C H N O S 3 " .M o l a r
amount value for entity XX
per kg fireball.
XX : Ar,C,E,H,N,0,S
- Used in "reacl_in_CHNOS3".
Reads a line of clata frout
"D.FIte".
- Calculated in "GRAM-ATOM"
and
used in "Hass_BaIance-Uptlate".
Molar amount of XX per kg of
anbient air.
XX: Ar,C,E,H,N,0,S
- Used in "Output_Data".
Program calculatecl time.
- Used in "reail_in-data"
antl
TYpe of
"Initialize-Output".
atmosphere usecl.
- Used in "Runge-Kutta".
Coefficient array used in
Runge Kutta integration
scheme.
- Read fron "D.FfIre" and usecl
Fraction of
in "Initialise".
at
bombyield in fireball
start tine. For 8000 Kelvin
at start teurp, beta has value
of 0.443942345.
- Dunny variable (same as
Mass). used in
"!lass_Balance_Update". Mass
of firebalt air. Unit : kg.
- Used in "Runge_Kutta".
Coefficient array used in
Runge Kutta integration
schen6.
- Used in "read-amb-air" to
store the numeric
fron "AMB.AIR"
coefticients
allowing the calculation of
entropy anil enthalpy.
- Usecl in "Find T" antl
"Hatrix". Coefficient of
enthalpy/ tenperature
polynornial calculated in
"Matrix", used in "Find-T" to
estimate tenperature given
enthalpy.
_
l
l
l
r
l
l
-
l
t
l
t
r
l
- Used in "read_in-CHN0s"anal
"read_in-clata". Readsa
character from "D.FILe".
chan z
Real
Charged
Logical
counE
I nt eger
counter
Integer
cVol
ReaI
D aurbient
ReaI
D_grouncl
ReaI
D_1og
ReaI
d. file
File Nane
DL
ReaI
nt
ReaI
Ddash
ReaI
Delta Enth
Real
delta nass
Real
43
- U s e di n
"Dif f erential Equatons".
Difference in height between
current anil previous tine
srep.
- s e t i n " r e a d i n C H N O Su"s e d
i n " C H N O S 3a"n d " 0 u t p u t - D a t a " .
- U s e r li n M a i n p r o g r a ma n d
"output_Data". It counts the
n u m b e ro f t i n e s t h a t t h e n a i n
progran loop is cycletl and
allows the output alatato be
sent to the output file every
five cycles.
- U s e di n " I n i t i a l i s e " a n d
" F i n c l T " . H o l c l st h e n u n b e r o f
ture
Enthalpy/ Ternpera
calculations clone.
- U s e di n
"Dif f erential Equations".
volune ot the tireball.
Unit : cu metre.
- Useclin
"Diff erential Equations".
A m b i e n tD e n s i t y .
Unit : kg ,l tn*r'3'
- U s e di n " P M A C "D
. ensitY
ambientat groundlevel.
Unit:kg/m**3.
- U s e d i n " P i l A C " .L o g t o t h e
base ten of the ratio of
required density to ground
density.
- The naneof the file which
contains the fireball
specifications to be entered
into the "Bonbs" program and
run.
- U s e c li n " L o s s R a d i a n t " .
Interpolatecl log base ten
density tor lower
tenperature.
- Usedin "l,oss Racliant".
Interpolatecl log base ten
density for upper
tenperature.
- U s e di n
"Di f f erent iaI-Equations " .
Ratio of fireball tlensitY to
D arnbient.
- Usedin "Fincl T". Is a
n e s s u r e o f t h e c l o s e n e s so f
the enthalpy, calculated for
a given temperature,to the
required enthalpy.
- U s e di n
.
"Hass_BaIance_Uptlate"
Difference in nass between
current and Previous tine
steps.
44
Den
Real
density
ReaI
Density
ReaI
df
ReaI Array
ReaI Array
dm
ReaI
D},IFXX
ReaI
Dratio
Real
att
Real
Et
Real
E2
rl
Elsqr
E2sqr
E3sqr
E1nu1
E2nu1
E3nuI
ENTII
r
ReaI
enth anbient
Real
enth_fb3er_l{ass
Real
EnthaI
U s e d i n " P M A C " .R a t i o o f
required density to ground
density.
Dunnyvariable (saureas
D_aurbient) usetl in
"ICAO_Air".Density of
anbient air. Unit : kg/n**3.
U s e di n
".
" Dif f erent i a1_Equations
Density of fireball.
Unit : kg/6**3.
Usedin
' r D i ff e r e n t i a l E q u a t i o n s " .
Array of ilifferential
eguations qhich alescribes
fireball behaviour.
Useclin "P!{AC".Log to the
base ten of the density ratio
taken from Gilnore.
Usedin
Increnent in nass of
Fireball. Unit : kg.
R e a df r o n " D . F I L e " a n d u s e d
i n " C 1 e a n _ F i r e b a l 1 " .D r y n o l e
f r a c t i o n o f a m b i e n ta i r X X .
XX : Ar,COz,N2,02
Usetl in "Pl,tAC".Ratio shich
irill aIlow interpolation of
1og to the base ten density.
Used in Main progran antl
" R u n g e _ K u t t a " .T h e t i m e
increment. Unit : second
U s e c li n " M a t r i x " . V a r i a b l e s
used in natrix inversion.
t
i
l
l
r
l
r
l
l
I
tl
rr
:
ReaI Array
lr
:
:
ll
,
:
:
U s e d i n ' E N T H " .E n t h a l p y .
Unit:cal/rro1e
Calculatetl in
"ambient_enthalpy_". Enthalpy
of anbient air.
Unit:.Ioule/nole.
Usealin
Enthalpy per kg fireball
nass.
Usedin "Intialize" and
"Find_T". Enthalpy per hg of
fireball air.
Unit:iloule/mole.
45
ENTHAI.
ReaI Array
enthalpy
Real Array
Enthalpy3er_kg
entrain
ReaI
ReaI Constant
ER
ReaI Array
f new
Real Array
f old
Real Array
Real Array
ReaI
Fb
file
name
G
G
GilivR
C h a r a c t e r * 2 2A r r a y
ReaI Constant
Real Array
ReaI Constant
HEIGHT
Real Array
Holiln
Real Array
Read in "read-anb-air" and
used in "anbient_enthalpy".
Holds enthalpy per nole of
g i v e n a m b i e n tg a s .
Unit:Joule/mole.
U s e d i n " C H N O S 3 "A. r r a y o f
enthalpy per nole values for
species in fireball air.
Unit:Joule/mo1e.
U s e c li n " I n i t i a l i z e ' , " C H N O S 3 "
and "Fincl_T". Enthalpy per kg
of fireball air.
Unit:Joule/kg
R e a df r o n ' ! D . F I L e " a n d u s e d
in "Dif f erential_Equations".
N o r r n a l l y , e g u a lt o 1 . 0 , i t i s
fireball entrainnent
coefficient or the fraction
of the fireball nass
entrained.
Read f ron "ADIB.AIR"antl holtls
heat of fornation at 298.15
KeIvin.
U s e di n " R u n g e _ K u t t a " .
Equations used to clescribe
ilifferent f ireball behaviour
processing.
after Runge_Kutta
U s e c li n " R u n g e _ K u t t a " .
E q u a t i o n su s e d t o d e s c r i b e
different fireball behaviour
before Runge_Kutta
processing.
U s e di n
"Diferential Equations".
E q u a t i o n su s e d t o d e s c r i b e
ilifferent fireball behaviour.
Used in
"Dif erential Equations".
Firebal.l Buoyancy/ (A / 3 x
pi). Unit : kg n / s*t,z
R e a df r o m " D . F I L e " a n d h o l i l s
output file nanes.
Read tron "D.FILe" and used in
Geopotential constant equals
9 . 8 0 5 5 5m / s t * 2 .
U s e t l i n " C H N O S 3 "G. i b b s
nininization energy of
species.
Used in "ICAO_Air".
= 0.034164d0.
Useil in function "MF-H2O".
Array of height in metre
above ground corresponding to
$ater vapour IIATERp.which
contains nole fraction of H20
in anbient air.
Useil in "scramble" as a
holcler for the nole nunber of
species per kg firebaIl.
40
Integer Array
IN
initial
dt
Real Constant
Ini t i a I_fb_enthal py
Real
init iaI_fb_tenp
R e a1
initial
mornentun
Real
initial
radius
Real
initial
z
ReaI
ISN
Integer Array
Tn I adar
.lunk
Character*5
ReaI
1_density
ReaI Array
l3ress
ReaI Array
I_tenp
ReaI Array
Iapse
last count
ReaI Array
Integer Constant
level
ReaI Array
I ine
Character*80
R e a c lf r o m " D . f I L e " . I N ( , 1 )
contains the positlon number
i n t h e " N E I I D A T A . D A Tf i"l e o f
the thermochemical data for
species J.
Read fron "D.FILe" and used
in "Initialize".
Initial
timestep Unit : Second
Used in "Initialize".
Equal
to 44l- of energy in fireball
at t = 0 for initial
fireball
temperature equal to 8000.0
K e l v i n . R e c l u c e sl o 2 2 4 f . o r
initial
fireball temperature
equal to 5000 kelvin.
Unit : Joule.
Reatl from "D.FILe" and usetl
in "Initialize".
Start time
temperature. Unit : Kelvin.
Used in "InitiaIize".
Start
time monentun. Unit : kg m/s.
Used in "InitiaIize".
Start
tine radius. Unit : Metre.
R e a c lf r o n " D , F I L e " a n c l u s e t l
in "Initialize".
Start tirne
height. Unit : Metre.
Numeric order representation
of ambient gases as present
in "AMB.AIR".
Read f ronr "D.FILe". 'JI holds
a value which tel1s "CHNOS3"
the Ith orcler that an entity
tuas reatl . This allols
thd
array variable "B" in
" C H N o S 3 "t o r e a d t h e c o r r e c t
entity mole value. "f" ranges
from 1 to 10.
Used to read unused data from
"AMB.AIR" to allow reading of
u s e f u l d a t a o n s a m el i n e .
Read from "D.FILe" and used
in "Dif ferential_Equations".
A d d e d : m a s sc o e f f i c i e n t .
Used in "ICAO-Air". Density
at given level. Unit : kg/ITl**3.
Usetl in "ICAO_Air". Pressure
at given level. Unit : Pascal.
Usecl in "ICAO_Air".
Tenperature at given 1eve1.
Unit : Kelvin.
Used in "ICA0 Air",
Read trom "D.FILe" and used
in Main program and
"0utput_Data" . Maxinum nunber
of time steps.
Usetl in "ICAO_Air". Height at
given 1eve1, Unit : netre.
Usetl in "read_anb_air" to
read lines of data fron
"AllB.AIR" which are not useil.
4t
M
Real
Mdate
Character
l{t im
Character
Mass
MFXZ
ReaI
ReaI
rnonentun_stop
Logical
M<
Integer
nwa
n1
n2
n3
NEIIDATA.DAT
ReaI
Real
- U s e di n
MornentumUnit : kg rn / s.
- U s e di n " I n i t i a l i z e _ O u t p u t " .
Date progran run.
- U s e c li n " I n i t i a l i z e _ O u t p u t " .
Timeprogran run.
- M a s so f f i r e b a l l a i r . U n i t : k g .
- Calculated in "CLEANFIREBALL"
and useil in
"ambient-enthalpy" ancl
"GRAltAT0M". Hole traction of
arrbient XZ.
X Z = A r , H 2 0, C O z , N 2 , O z
- Used in llain program,
deternines whether lhere is a
time stop or a nonentunlstop
criterion on the run.
- R e a df r o n " D . F I L e " . M S i s t h e
nunber of species making up
the fireball air.
- Molecularweight of air.
- U s e di n " l { a t r i x ' l . V a r i a b l e s
used in natrix inversion.
_
tl
Input File
nxx
ReaI
nxz
ReaI
nfXX
ReaI
NgasS
Integer
NNS
Integer
NOM
Character Array
NPS
Tnteger
_
i
l
[
l
i
l
l
l
t
l
l
- U s e c l i n " C H N O S 3 " .C o n t a i n s
thernocheurical clata for
species in firebal1.
- Used in "anbient_enthalpy".
Ilole nunber of XX per kg
fireball
air at 298 Kelvin.
X X : A r , C , H 2 0 ,H 2 , C 5 H 5 . C 8 H 1 8 , 0 2
- Dunny variable (same as anXX)
used in "GRAMATOl,l". Mole
nunber of XZ per kg of
ambient air.
X Z : H 2 0 ,N 2, Q 2, C O 2 , A r, Q ,N , C , H
- Used in
"l,lass_EaLance_Update". MoIe
number of XX per Kg fireball
air. XX : Ar,C,E,H.N,O,S
- Reatl fron "D,FILe". NgasS is
the nunber of gaseous species
in the firebalI.
- R e a c lf r o n " D . F I t e " . N N S i s
the nunber of negatively
charged species in the
fireball.
- Read fron "D.FILe". NOM(J)
contains the character
discription
for the
"Output_Data" subroutine for
species il.
- Read fron "D.FILe". NPS is
the nunber of possitively
chargetl species in the
fireba1l.
48
TID
fnt eger
NsolS
Integer
nTotalCharged
Number of des
Real
Thl6dar
-..evYvr
OLD I,IASS
Real
0p_fb
Real
OpTr
ReaI
P ambient
ReaI
Readfrom "D.FILe". NS is the
number of gaseous uncharged
species in the fireball air.
R e a c lf r o m " D . F I L e " . t t r s o l S i s
the number of condensed
species in the fireball.
Used in "scramble" as the sum
of all chargecl species.
Used in l,lain program and
"Runge_Kutta". Nunber of
Sirnultaneous Dif f erential
Equations.
Used in
Equations" and
"Differential
" M a s s _ B a l a n c e _ U p d a t e " .M a s s
from previous time step.
Used in "Loss Racliant".
Opacity of Fireball.
Uni.t : cm**-L.
Used in "l,oss Radiant"
0pacity x Transmission
coef f icient .
Used in
"Dif f erential Equations"
Anbient Pressure.
Unit : PascaI.
pgrn
pii
PMAC
PMAC_IJog
C h a r a c te r
Real Constant
Real
ReaI Array
PHAC_1o910
ReaI
pressure
Real
REAI
K
rad
ReaI Constant
neal
Usetl in "Initialize_Output"
3.14159d0
Useil in "PMAC". Planck Hean
Absortion Coefficient of
for given
fireball
tenperature. Unit : crn**-1.
Used in "PMAC".Log to the
base ten of Planck Mean
Absortion Coefficients at
iliffering densities and
temperatures.
U s e c li n " P M A C " . L o g t o t h e
base ten of Planck Mean
Absortion Coefficients at
required density and
tenperature.
Dunny variable (same as
P_anbient) used in "ICAO_Air"
representing ambient pressure
at given 1evel.
Unit : Pascal.
U s e d i n " C H N o S 3 "P. r e s s u r e
Unit : Atnosphere.
U s e d i n " C H N O S 3 "G. a s
constant.
Units : callKelvin/mole.
(=1.98?1?).
Dunnyvariable ( s a n e a s
radius) used in
" L o s s R a d i a n t " . Radius of
firebalI. Unit : metre.
L A
rad loss0
Real
Radiant Loss
ReaI
RadInCM
Real
radius
ReaI
RATIO
Real
RltI{
ReaI
Setting_up
srgma
Logical
Real
Species_nun
TnladAr
SR
ReaI Array
SR
ReaI Array
start
tine
ReaI Constant
SUMPS
Real
SU}INS
ReaI
t
ReaI
T
Real
T anbient
Real
Used in "Initialize"
ancl
"Output_Data". Radiation lost
to far field at time zero.
Racliant Fireball
flux at t=0.
Used in "Loss Radiant" and
"Differential
Eguations". The
energy lost as radiation to
the f ar f i.elil. Unit : Joule.
Used in 'iloss Racliant".
Radius of fireball.
Unit : cm.
Used in
"Dif f erentail Eguations".
Radius of Fireball.
Unit : metre.
Used in "MF H20". Useil to
interpolate for the rnole
fraction of H20 in ambient
air given the height.
Used in "anbient_enthalpy"
and "GRAI'I_ATOM".
Relative
molecular weight of arobien!
air. Unit : gram / mole.
Used in function "PMAC".
Allows the function to read
the data, require<I for
calculation, only the first
time that the function is
entered.
R e a c lf r o m " D . F I L e " a n d u s e i l
in "Loss Radiant". StefanBoltznann contant.
Used in "scramble".
Read from "D.FIIre" as number
of species in fireba1I.
Calculated in "read_in_CHN0s"
and used in ENTR. Enthalpy of
fireball species at 298.15
Kelvin.
Used in "read_amb_air" to
read fron "AMB.AIR" the
entropy at 298.15 Kelvin.
Used in "Initailize"
as time
that progran starts at.
Unit : second.
Used in "scramble" as the sum
of the possitively charged
spec].es.
Used in "scramble" as the surn
of the negativeLy chargecl
species.
Used in "Runge_Kutta" as time
variable. Unit : second.
Used in "ENTH",
"Loss_Radiant " . Teroperature.
Unit : Kelvin.
Usecl in
"Dif ferential Equations".
Anbient Temperature.
Unit: Kelvis.
ReaI
ReaI
Used in
"Dif f erentail Equations",
"Loss_Radiant". Temperature
of Fireball. Unit : Kelvin.
Used in "Matrix". Variables
usecl in matrix inversion.
tl
tl
Real
ReaI
tenper
Elme
Time
E].mes_up
nt
TI,
TMT
Tnum
TNT_equivalent
ReaI Array
Real
Real Constant
Real
Real Array
Real
Integer
ReaI Constant
TotalGasllole
Real
TotaIHoIe
ReaI
TotalnfXX
Real
Tot al Sol idl'loIe
Real
Tr
ReaI
Used in "C1ean FirebalI".
Sun
of dry rnole fractions of
molecules rnaking up anbient
air.
Dumrnyvariable (sane as
T_ambient) used in
"fCAO Air"and
"arnbj.ent_enthalpy" .
Tenperature at given level.
Unit : Kelvin.
Usetl in "Intialize"
and
"Finil_T". Temperature
corresponding to enthalpy per
kg of fireball.
Unit:Joule/mole.
Current tine. Unit : seconcl.
Read fron "D.FILe" and used
in Main program to stop the
program when the tine reaches
"tines_up". Unit : seconcl.
Used in
, "CENTH" and
"ENTR". Temperature lower
Iimit. Unit: Kelvin.
Used in "PMAC".Array of
tenperatures corresponding to
P M A Cv a l u e s g i v e n b y G i l n o r e .
Used in "Clean Fireball".
Sum
of rnole fractions of
molecules making up ambient
air Iincluding H201.
Read from "D.FIIre" as nunber
of gases in ambient air.
U s e c li n " I n i t a l i s e "
as
conversion factor for energy
in joule of given size bomb.
Unit:,Ioule/Megaton
( 4 . 1 8 5 e 1 5j o u l e p e r n e g a t o n ) .
Used in "scramble" as the
mole sum of all gaseous
species per Kg fireball.
Used in "scramble" as the
mole sun of all species per
kg fireball.
Usecl in "Mass_Balance_Update"
as the total fireball
mole of
XX.XX: Ar,C,E.H,N,0,S
Used in "scranble" as the
mole sun of all condensed
species per kg firebalI.
Used in "l,oss_Racliant".
Transnissivity.
)I
Tratio
R ea I
TU
ReaI
u
R ea I
V
R e aI
vapour
ll
water
liATERp
water include
weight
Y
Logical
ReaI Constant
Character*3
ReaI Array
r ^-i ^^f
!u9 ru4r
ReaI
Real Array
Real
zfb
Real
Zdsh
Real
- U s e d i n " P M A C " .T e n p e r a t u r e
ratio which will allow for
interpolation of Iog to base
ten of PMAC.
- Used in "ENTH"."CENTHa
" nd
"ENTR". Temperature upper
limit. Unit : Kelvin.
- Usetl in
"Diff erential Eguations".
S p e e do f F i r e b a l l .
Unit:metre/second.
- Used in
Dirnensionless rrass of
fireball.
- D u m m yv a r i a b l e ( s a m e a s
water include) used in
"CIean Fireball". Deterrrines
whether water vapour to be
includetl in ambient air.
- Read trom "D.fILe" and used
Yield of
in "Initialise".
blast in }legaton.
Unit: Megaton.
- Used in "Initialise-OutPut"'
Allows the output to state
whether $ater vapour included
in the systen.
- Used in "MF-H20". ArraY of
mole fractions of H20 in
arnbient air. Corresponds to
array variable HEIGHTiihich
contains the height above
ground in metre.
- Read from "D.FILe" and
determines whether water
vapour is to be included in
the calculations.
- Used in "Runge-Kutta".
- Used in "scramble" as the
number of rnole of the species
per kg fireball.
- Used in "ICAO-Air", "MF-H20".
Height above ground.
Unit : Metre.
dissociation coeff icient.
dissociation coef f icient.
Forrnula : TotalGasMole * mwa
/ 1000.0d0
ccccccccccccccccccccc
N
0.00
0.44
9.80665
0.10
0.01
8000.0
0.00000
N
R
D. F t L E
ccccccccccccccccccccc
stop
Tine stop else l,lomentun
tine for run
beta
9 . 8 0 6 6 5G r a v i t . y ; M e t r e p e r s e c o n ds q u a r e d .
e n t r a i n ( n o r a m a l l y0 . 1 )
Initial increnent in tirne (nornalIy 0.02)
Initial tireball tenperature
Initial <letonation height
k
IJast count
MoIecular lleight 0f Ambient Air
0 . 5 5 7 i 1 - 0 7s i g m a : S t e f a n - B o l t z n a n nc o n s t a n t
Type of atmosphereusetl
file name 1 )
file nane 2 )
30000
28.9607
0.567ar-0?
N2/02/Ar/HZo/CoZ
fBouBsSl.dat
FBoilBS82
. dat
FBOUBSS3.dat
f i l e n a m e 1',|
F B o M B S 8d4a.t
file name 4 )
FBol.lBs85
. dat
file_name q l
FBOIIBSS6.
file naure b ,
dat
FBOIIBSST.
dat
file_nane 1 l
FBoMBs88
. dat
file name 8 )
FBOI{BS89.
dat
: file nane q l
1.00
: B o m bs i z e ( H t )
Y
: llater vapou r i n c l u d e d i n a m b i e n t a i r c a l c u l a t i o n s [ Y / N ]
) MFN2 ; clry nole fraction ot N2
0.780835
: (0.78084D
) Mf02 ; dry mole fraction of 02
0.209481
: ( 0 . 2 0 9 4 8D
)
: ( 0 . 0 0 0 3 4 Dl'lFCO2
0.000340
; dry mole fraction of C02
)
0.009343
: ( 0 . 0 0 9 3 4 3Dl,lFAr
t dry mole fraction of Argon
49
: T o t a l n u m b e ro f s p e c i e s .
48
: Total nunber of gaseous species.
3 4 1 . . . n C H . . .3 . . n c ( c ) . . 6 . . n C H 2 . . 1. 0 . . . n C N . . .1 2
. .4
1 4 . . . n C O . . .1 5 . . n C O z . . .1 9 . . . n C 2 . . 2 I . . n C 2 t 1 2 2
2 7 . . . n C 3 . . .2 9 . . . n C 4 . . .3 1 . . . n C 5 . . .3 2 . . . n H . . . . 3 3
3 4 . . n H N O . . .3 5 . n H N O 2 g 3
. .6 . n H N 0 2 g 13.8 . . . n H O . . . 3 9
4 1 . . . n H 2 . . . 4 2 . . n H 2 N . . .4 4 . . n H 2 O . . .4 5 . . n H 2 0 2 . 5
. 0
5 1 . . . n N O . . .5 2 . . n N O 2 . . .5 5 . . . n N 2 . . . 5 5 . . n N 2 0 . . .5 0
6 1 . . . n 0 .. . . 6 4 . . . n 0 2 . . 5 6 . . . n o 3 . . L 2 2 . . . n A r . . .
: T o t a l n u m b e ra n d d e s c r i p t i o n o f u n c h a r g e ds p e c i e s .
: chargealspecies incLudeil [Y/N]
1 0 8 5 . . n N O +. . 9 7 . . . n H + .. . 9 8 . . n A r + .. . 9 9 . . . n C + . .
1 0 4 . . . n N + . . . 1 0 5 . . n N 2 + . . .1 0 6 . . . n 0 + . . . 1 0 ? . . n 0 2 + . . . 1 1 1
114 ..nHO+...
: Total numberancl description of possitively chargetl species.
4 9 3 . . . n 8 - . . . 9 5 . . . n 0 - . . . 1 0 0. . . n N - . . . 1 0 1. . n N 2 - . . .
: T o t a l n u n b e r a n d d e s c r i p t i o n o f n e g a t i v e l y c h a r g e ds p e c i e s .
1 89 ..nC(s)..
: TotaL nunber and clescription of non gaseous species.
C = l H = 2 N = 3 0 = 4 S = 7A r = 5 E = 5 : C = l , H = 2 , N = 3 , 0 = 4 , $ = $ , | 6 = S , f , = ( + , - ) = 7
: Order of introduction of the different entities.
5 1 2 3 4 5
: F r o m " N 2 . d e t " . A n b i e n t a i r g a s e o u ss p e c i e s .
: Fractional part of H2 in H2O
0.000
53
c c c c c c c c c c c c c c c c c c c c c c c ccc0 M M 0 N . P UcTc c c c c c c c c c c c c c c c c c c c c c c c c
LoGICALCharged
LoGICALwater include, Setting-up, nonentum-stop
count, Nunber-of-des, TYPE
INTECER
, counter
I N T E G ES
Rp e c i e s - n u n , N S , N P S , N N s , N s o l S , N g a s S , l ' t S
Atnos*20
f ite_nane*22,NOI{*9,
CHARACTER
R E A L * 8i n i t i a l _ d t , i n i t i a L _ f b _ t e n p , i n i t i a 1 _ 2 , k
REAL*8Initial-tb-enthalpy, MtC
c o l l l { o N/ O n e A / f i l e - n a n e ( 9 ) , t i n e s - u p , T Y P E , l { t c
col{t{oN
/ O n e / c o u n t , d(f5 ) , d t , f ( 5 ) , k , L a s t - c o u n t , Mr ,a d - I o s s 0
COUI{ON
/two/chan_2,cVol, Dtlash,Density, Fb,u, G
COI{MON
/ three / ini tial-tlt, init ial-f b-tenp, ini t i al-z
C O I { l { O/ f}of u r , / b e t a , D - a n b i e n t , e n t r a i n , I n i t i a l - f b - e n t h a l D y ' 9 i i , . T , n t { a
COlll{oN/ f ive / enth-anb i ent, Tot alMoI'e, Nunber-of -des
COlllloN/six/atiue, Mass,P-anbient. radius, T-anbient, T-f b, z, Z -tb
COI{MON
/ s even/enth-f b3e r-l{as s, EnthalpyJter-kg
cot'tMoN
/eight/Charged, Setting-up, nonentun-stop
c o M M O/N
u n o / T o t a l n f N ,T o t a l n f 0 ,T o t a I n f H, T o t a I n f C
ColilMON
/rlue/Tot alnf Ar, Tota1nfS,Totalnf E
coltUON
/ q u a t / n f N ,n f 0 , n f A r , n f C ,n f S ,n f H ,n f E
COllltON
lB / Op-fb,Tr, Radiant Loss,signa
COl{l{oN/h2o/ watet-include,Atrnos
c o l ' t M o/Nc c c/ p r ( 2 o ) , P T o r ,T , Y ( 5 0) , Y O( 5 0) , Y F( 5 0) , Y T O (T2 0)
C O I { } I O/ hNo l / H o l d n( 5 0 ) , T o t a l G a s M o l e , T o t a l S o I i i l M oZl e<' l s h
, g a s sI,N ( 5 0) , M S
, N SN, s o l S N
Col{}toN
/ n s l / S p e c i e s - n u nN, O t({5 0) , N s ,N P SN
, ,n02,nTotalCharged
C o l { l , l o/No u t / n N , n N O , n Nn2O
col'lMON
/output/opTr
c o l t i l o N/ U s E / E n t h a(I2 0 0 0 ) ,t e m p e r( 2 0 0 0 ) ,c a l a , c a 1 b ,c a l c , c o u n t e r
)4
BOI'1BS
PROGRAM
CC****************************rt*****t(*****t<*****tt******Jr***ttr(***CC
nanely D.FILe'
CC
CC
- whether or not a stop tine is set for the run and
CC
CC
rC
the value of the stoP time.
- the values of the following constants :
- beta, the fraction ot bombyield in the
at start time
firebatl
- k, the atlded-rnass coetficient
- entraln. the fireball
entrainnent coefficient
- G, gravity
- signa, Stefan-boltznann constant
- nwa, the molecular weight of anbient air
- t h e maximum
b e carried
out
t o be
carrie
o f tirne
s t e p s to
t i n e steps
m a x i m u mnunber
n u n b e r of
CC
- the bomb size,
CC
CC
T h i s p r o g r a mr e q u i r e s t h r e e i n p u t f i l e s ,
CC
CC
and AMB.AIR.
NEIIDATA.DAT
The file D.FILE contains the following
cc
:
- whether or not water vapour is to be included in
the anbient air calculations
- the type of aturosphereusecl
- the nine output file names
initial
detonation height,
initial
CC
CC
fireball tenperature and initial time increnent
- t h e d r y m o l e f r a c t i o n s o f a m b i e n ta i r g a s e s
(.(.
- lhe total nuuber of species, the number'of gaseous
and non-gaseous species
- whether or not charged species are included
- the total nunber and description of uncharged,
possitively charged and negatively charged species
- the order of introcluction of the different species
CC
CC
cc
CC
cc
cC
- the nurnberof anbient gases and their nunerical
o r d e r a s p r e s e n t i n t h e A M B . A i Rd . a t af i l e .
cc
Cc
cc
CC
T h e f i l e s N E W D A T A . D AaTn d A M B . A I R c o n t a i n t h e t h e r n o an<l the CC
chenical data for all the species in the fireball
ambient air gases respectively.
CCt!**tr**t(*****tr**********r.rrr!**J,***********Jr*********************CC
(A-H,M-Z)
PRECISION
IMPI,ICITDOUBIJE
include 'conrnon.put'
Nunber_of_des
= $
CaII read-in_data
CaII Initialize
CalI Initialize_Output
count = 0
2 0 i f ( n o a l ( c o u n t , 5 .)E Q . 0 . O R . c o u n t . E Q . l a s t - c o u n t ) C a 1 1
*Output_Data
(atine .cT. 0.299) dt = 0.025d0
if
(atine.cT.2.99) dt = 0.25d0
if
(atine .cT. 49.99) dt = 0.5i10
if
( a t i r n e. c T . 9 9 . 9 9 ) d t = 1 . 0 d 0
if
(Number_of
Call Runge_Kutta
_des,atine)
CaIl Find T
count=count+1
( m o m e n t u m - s t o P )t h e n
if (M .GE. 0) go to 20
else
if (atime .1,T. tines-uP) go to 20
endif
Cal1 Output-Data
D o 2 5 I = 1 ' 9
if
1I+1)
"ro."
25 continue
Stop
END
Initialize
SUBROUTINE
PRECrsroN(A-H'l{-z)
rMPLrCrr D0UBLE
. Put '
inclutle ' comnon
R e a l * 8 i n i t i a l - m o m e n t u n ,i n i t i a l - r a d i u s
counter
initial nomentum
initial ratlius
TNT-equivalent
start tine
Setting-up
pii
C
C
C
= Q
= 0.0d0
= 0.0d0
= 4.186d15
= 0.0d0
=.true.
= 3.14159d0
This sets up the 'lata
CLEAN-FIREBAII,Ca1I to SUBROUTINE
g o i n g i n t o " C H N O S 3f o" r a n o n - s u r f a c e b l a s t c o n c l i t i o n '
A l s o s e t c o n c l i t i o n s f o r c o m p o s i t i o no f t h e a t n o s p h e r e '
f
caII CLEAN_FIREBALL(initial_z,water-incIutle,MFH20,l{fN2,t(loz,}1FC02'
,,IIFAr)
c
C
C
C
c
c
c
C
c
c
C
c
This returns the nunber of
GRAM-AToMS.
Call to SUBRoUTINE
rnote of the of each elenent, N,O,H,C antl Ar given the mole
fractions of the nolecules per kilogram oi ambient air'
(HFH2O.
MfN2,MfO2,I{FCO2,HFAr, nf N, nf 0, nf H' nf C' nf Ar )
CALL GRAM-ATOM
= 0.0d0
nfS
= 0.0d0
nfE
= 0-0d0
enth-fb3er-Mass
= initial-z
z
= initial-radius
ratlius
= initial-dt
dt
= start-time
atime
CALL IcAo-Air ( ini t ial-2, T-ambient, P-ambi ent, D-anbi ent )
It 1s necessary to calculate the enthalpy of the species ' which
at ambient enthalpy. This will be
will nake up the fireball,
temperature.
fireball
subtracted tron the enthalpy at initial
given the
riilI
be
calculated,
of
fireball
Mass
the
the
llence
energy.
fireball
knowledge of the initial
T-fb = initial-fb-tenp
r i r i t e ( 0 , 4 ) n f N , n f o , n f C ,n f H , n f A r , n f S ,n f E
56
Call read_in_CHNOS
CaII scramble(T_fb, P_arnbient
)
CaIl read_anb_air
C a I l a u b i e n t _ e n t h a l p y( i n i t i a l _ 2 , T _ a r n b i e n t )
write (0,15) enth_ambient
= beta * ll * TNT-equivalent
Initial-fb-enthalpy
= initial_fb_tenp
t e n p e r( 1 )
= Initial_f b_enthalpy/ (Enthalpyjer_kg-enth_arnbient)
l{ass
= Initial-fb-enthalpy / Mass
Enthal(1)
= initial z
f (1)
= initial-monenturr
f (2)
= 3 . 0 d 0 * M a s s/ 4 . 0 d 0 / p i i
f(3)
= Entbalpy_per_kg
f ({)
f (5) ts energy radiated fron fireball.
C
a s s u n e dz e r o a t s t a r t
= 0.0d0
f (s)
w r i t e ( 0 , 1 0 ) M a s sI,n i t i a l _ f b _ e n t h a l p y , E n t h a l p y 3 e r _ k g
=Mass*nfN
TotalnfN
write (0,12) TotalnfN
=Mass*nfO
TotalnfO
prite(0,12) TotaLnfo
=Mass*nfC
TotalnfC
write (0,12) TotaInfC
=Mass*nfH
TotalnfH
write(0,12) TotalnfH
= l,tass* nfAr
TotalnfAr
write(0,12) TotalnfAr
=Mass*nfS
Totalnfs
w r i t e ( 0 . 1 2 )T o t a l n f s
=l{ass*nfE
TotalnfE
write (0,12) TotalnfE
C a 1 1D i f f e r e n t i a l _ E q u a t i o n s
r a d _ I o s s O= d f ( 5 )
C------AI,IJ THS FORMAT
STATEMENTS
c
4 F o r n a t ( ' n f N= ' , d 1 0 . 4 , ' n f O= ' , d 1 0 . 4 , ' n f C = ' , d 1 0 . 4 ,
*' nfH=',d10.4,' nfAr=',d10.4,, nfS=',d10.4,' nfE=',d10.4)
1 0 F o r n a t ( ' M a s s= ' , d 1 2 . 6 , ' k g
f B E N T H= ' , D 1 2 . 6 , ' , J e n t h / k g = , ,
t d . L z. 6 , ' . I / k g ' )
!z
F o r m a t ( 'I T = ' , d 2 0 . 1 4 )
F o r n a t ( ' e n t h _ a n b i e n=
t ',4114.8)
RETURN
END
57
S U B R O U T I NCEI . E A N - T I R E B A L I , ( h i t E ' V A P O U T , M F H 2 O . M F N 2 ' l T O z ' M F C O 2 ' I , I F A T )
c
the nolar fractions of anbient air gases for a
c.......Calculates
c.......non-surface blast condition.
c.......DIIF indicates nolar fraction of species in dry air.
PRECISION(A-H't'l-Z)
IIIPLICIT DOUBIJE
Logical vapour
conmon /now/ nMrl2,D!lF02,DHFCo2'DMFAT
(vapour) THEN
M F H 2 0= M F - H 2 0 ( h i t e )
ELSE
I.IFH2O = 0.000D0
ENDIF
= Dl,lFN2't (1.0D0 - $fHzO)
UFN2
= D l { F 0 2 * ( 1 . 0 D 0- M r H 2 0 )
MFO2
IF
urco2
= D M F C o*2 ( 1 . 0 D 0 - [ ! F H 2 O )
= DHFAr * (1.0D0 - l'tFlt2O)
l{FAr
=
+
TMF l,lFH2o ltFN2 + t{F02 + MfC02 + ilFAr
i f ( d a b s( 1 . 0 d 0 - T t ' l F ) . G 8 . . 1 . 0 d - 5 ) t h e n
write (0,4) TMF,MFH2O,ltFN2,MF02'llfCOZ'MfAr
StoP
endif
C-----AI,I,
THE FORMATSTATEI,IENTS
4 F o r m a t ( ' T M F s h o u l c le q u a l 1 . 0 0 , b u t i n s t e a c l i t e q u a l s ' , D 2 0 . 1 4 , ' . '
*,/,'This
program is now terrninatetl. check the data file "d.file".
* , , / , ' M F I I 2 O = ' , , d L 4 . 8 , ' l ' l F N 2=
l ' l F O =2 . , a I 1 4 . 8 , / '
'
,
d
1
4
.
8
)
,
.
d
1
4
.
8
,
'
=
* ' M F C O =2
MFAr
"d14.8,J
RETURN
END
c
c---------c
(Z)
DOUBLEPRECISIONFUNCTIONI'IF-H2O
I
c.....Returns the volunetric nixing ratio (v/v) or rrolar fraction of
c.....H20 at a givenheight.
a
II.{PLICIT DOUBI,EPRECISION (A-H ' I{-Z )
( 1 ? ) , t { A T E R (p1 7 )
D I H E N S I o NH E I G H T
INTEGERI
, . 0 D 3 ,8 . 0 D 3 ,1 0 . 0 D 3 ,1 2 . 0 D 3 '1 4 . 0 D 3 '
0 .O 1 D 32,. 0 D 3 ,4 . O D 3 6
D A T AH E T G H T / O
* 1 6 . O D 3, 1 8 . O D 3, 2 0 . O D 3 2
, 2 . 0 D 3, 2 4 . 0 D 3, 2 5 . 0 D 3 ,2 8 . 0 D 3 ,3 0 . 0 D 3, 3 1 - 0 D 3/
DATA l{ATERp
/t}t29 .OD-6, 6110.0D-5 , 3055- 0D-6 ,1447 '0D-5 ,434 ' 0D-5 '
* 5 9 . O D - 5 ,3 ?. O D - 6 ,1 6 . O D - 6 ,1 4 . O D - 6, 1 0 . O D - 6 ,1 0 . 0 D - 6 ,1 0 . 0 D - 6 ,1 0 . 0 D - 6,
* 1 0 . o D - 6 ,1 0 . O D - 5 1
, 0 . 0 D - 6 ,1 0 . 0 D - 6 /
IF (z .GT.
!tF-lI2O =
RETURN
ENDIF
IF (z .LE.
MF H2O=
RETURN
ENDIF
I = 0
31.0d3) THEN
10.0D-6
HEIGHT(1)) THEN
10129.0D-5
58
1 I = I + 1
I F ( z . L T . H E I G H T ( I+ 1 ) ) T H E N
R A T I O= ( z - H E I G H T ( I ) ) / ( H E I G H T ( I+ 1 ) - H E I G H T ( ] ) )
= I , I A T E R p ( I )+ ( R A T I O * ( i l A T E R p ( I + 1 ) - W A T E R p ( I ) ) )
I'!F_H2O
RETURN
ELSE
IF (I.I,T.15) THEN
GOTO1
EIJSE
WRITE(0,2)
(' ERROR
2
FORI{AT
IIRONGIN DB FUNCTIONMT H2O ')
SOI1THING
STOP
ENDIF
ENDIF
RETURN
END
( MFH2O,
SUBRoUTINE
GRAI,I_AToM
MFN2,MF02,ilFCO2,MFAr,nN, n0, nH, nC, nAr )
c
C.....Returns the nunber of noles of each of the elenents N,O,H,Cand Ar
C.....given
the nole fractions of the molecules per kilograrn of ambient
C.....air.It
first calculates the relative molecular weight of the
C.....system,
c
II,IPLICIT DOUBI,EPRECISION(A-H.M-Z)
* 2 8 . 0 1 4 D 0 +) ( M r O 2 ' t 3 1 . 9 9 8 D 0 )
R M t [ = ( l , t F H 2*o 1 8 . 0 1 5 D 0+) ( M F N 2
+ ( H F C O '2t 4 4 . 0 0 9 D 0 )+ ( M F A i l t 3 9 . 9 5 0 D 0 )
1
nH2O= MFH20,, 1000.0D0/ Rl'lll
nN2 = MFN2 't 1000.0D0/ Rl,ltl
n02 = llF02 ,, 1000.0D0/ Rt{W
nCO2= I{FCO2* 1000.0D0/ R]'liI
nAr = MFAr * 1000.0D0/ RMI{
n O = n H 2 0+ ( 2 . 0 d 0 * n C 0 2 )+ ( 2 . 0 d 0 * n 0 2 )
nN =2.0d0*nN2
nC = nC02
nH =2.0d0*nH20
nAr = nAr
RETURN
END
ambient-enthalpy ( z, temp)
SUBRoUTINE
C....,Calculates relative molecular weight of new ambient air
c. . . . . conposition and enthalpy of lkg ainbient air .
c
P R E C I S I O N( A - H , I { - Z )
IMPLICIT DOUBLE
Locrical water include
integer Tnun, Number-of-cles
C H A R A C T EARt m o s * 2 0
COMIION
/ f ive / enth-ambi enL, To t al}tole, Nurnber-of-tles
common/h2o/ water-include,Atnos
c o n m o n/ a m b / T n u mI,S N ( 5 ) , E N T H A L ( 6 )
Save
Do40J=l,Tnun
D o 5 0 I = 1 , 6
if (1sN(J) .EQ. I) then
E N T H A(L, J ) = E N T H( . 1 ,l e m p ) * 4 . 1 8 6 D + 0 0
endif
50 continue
40 continue
c
c
( z, wat er-inc lude, t'lfHZO,llFN2,HFO2,MFC02']'lFAr)
Ca11 CLEAN-FIREBALL
R l { l i = ( M F H 2 o * 1 8 . 0 1 5 D 0+) ( M f N 2 * 2 8 ' 0 1 4 D 0 )+ ( M F 0 2 * 3 1 . 9 9 8 D 0 )
+ ( l ' t F c o 2* 4 4 . o o 9 D 0 ) + ( M F A r * 3 9 . 9 5 0 D 0 )
nlt20 = I4FH2O* 1000.0D0 / RMIf
nN2 =MFN2 *1000.0D0 lRl'Iil
n02 = MF02 * 1000.0D0 / R}lll
nCo2 = I'lFcO2* 1000.0D0 / RMH
nAr = l'lFAr * 1000.0D0 / RMW
nH2 = 0.0d0
e n t h a m b i e n t = ( E N T H A L ( 1 )* n N 2 ) + ( E N T H A L ( 2 )* n O 2 ) +
( E N T H A L ( 3 )* N A T ) + ( E N T H A I , ( 4 )* N H 2 O )+
1
( E N T H A L ( S )* n C 0 2 ) + ( E N T H A L ( 5 )* n H 2 )
2
I2O RETURN
END
1
60
c
FUNCTION
ENTH(I,T)
C . . . . . C a l c u 1 a t e st h e e n t h a l p y o f t h e a u b i e n t a i r s p e c i e s f o r t e n p e r a t u r e
C . . . . . T , w h e r eT i s u p t o 5 0 0 0K e l v i n .
c
c
IMPIJICIT DOUBI,EPRECISION(A-H,O-Z)
Connon /det/
E R ( 6 ), C r c , 6 )
(I)
ENTH=ER
I F ( T . L T . 2 9 8 . 1 5 )T H E N
TL = 298.15
T U = T
E N T H = E N T+H ( C ( I , 1 )
+ C(I,2)r,Tt
I
+ C(I,3)*TIJ*TL
2
+ c(r,4)*(?L:**(-2.0)))*(Tu-TL)
3
RETURN
ENDIF
TL=298.15
TU=T
E N T H = E N T H(+I ,C1 ) * ( T U - T L )
+ C ( I , 2 ) t r ( T U r . T U - T L * T/ I2I .)
1
+c(I,3)*(TU*TUiiTU-TL*TL*TL)/3.
2
-c(r,4)*(1./TU-l./TL)
3
RETURN
END
c
c---------c
c
SUBROUTINE
ICAO_Air( z, t ernp,pressure, tlensity)
c . - - . . c a l c u L a t e s t h e t e m p e r a t u r e ,p r e s s u r e a n d i l e n s i t y o f t h e a m b i e n t
C.....air frornthe height of the fireball.
(A-H,O-Z)
II{PIJIC]TDOUBI'E
PRECISION
R e a l * 8l e v e l ( 5 ) , l a p s e ( 5 )I,_ t e m p ( 6 ) , I j r e s s( G ) , 1 _ d e n s i t y ( 5 )
Datalevel/ 0.0000,11000.0,20000.0,32000.0,4?000.0,51000.0/
D a t a l a p s e / - 0 .0 0 5 50, . 0 0 0 ,0 . 0 0 1 ,0 . 0 0 2 8 0, . 0 0 0 ,- 0 . 0 0 2 8 /
D a t a l _ t e n p / 2 8 8 . t 5 0 , 2 L 6 . 6 , 2 L 6 . 6 , 2 2 8 . 6 , 2 7 0 . 6 , 2 '/1 0 . 6
D a t a l j r e s s / L 0 L 3 2 5 .2, 2 6 3 0 . 35, 4 7 5 0. 0 ,8 6 7 .9 2 1 ,1 1 0 .9 8g , 6 6 . 9 2 O
1/.
D a t a l _ d e n s i t y / 1 . 2 2 5 4 + 03, . d 39 4 d - 1 ,8 . 8 0 3 d - 2 ,t . 3 2 2 5 d , - 2t ., A Z j' td , - 3 ,
*8.515d-4/
= 0.034164d0
GilivR
J = 0
10, J=iI +1
i f ( z . c E . l e v e 1( , t + 1 )) g o t o 1 0
t e m p= I _ t e n p ( . I ) + l a p s e ( J ) * ( z - I e v e l ( J ) )
if (Iapse(.t).eq. 0.0) then
p r e s s u r e= I j r e s s ( J ) * d e x p ( - G d i v R * ( z - I e v e 1 ( J ) ) / l _ t e n p ( t ) )
density = I_density(,t) * pressure / I1lress(J)
else
p r e s s u r e= l j r e s s ( . I ) * ( ( t e n p / I _ t e n p ( J )) * ' , ( - G d i v R / l a p s e ( ,)t))
d e n s i t y = I _ < l e n s i t y ( , t ) * ( ( t e n p / ] _ t e m p ( . 1) )t * ( - ( ( G d i v R / 1 a p s e ( .)t+) 1
1 . 0 )) )
endif
RETURN
END
6l
S U B R O U T I NsEc r a m b l e ( t e m p ,p r e s s u r e )
c
C.....Stores atl final molar amountsfor species in fireball in Holtln
C . , . . . a r r a y a n d c a l c u l a t e s t h e s u r no f a l l g a s e o u s s p e c i e s , a l l s o l i d
all species, all negatively charged species and all
c.....species,
c h a r g e ds p e c i e s .
c.....positively
L
P R E C I S I O N( A - H , M - Z )
IMPLICIT DOUBLE
include
c
' c o m m o np. u t '
C a I l C H N O S( t3e m p ,p r e s s u r e , n f N , n f o . n f H , n f C , n f A r , n f S , n f E ' E n t h a l p y 3 e
i r_kg)
c
L4
ilo 14 1=l,Species-num
Holdn(I) = Y(I)
TotalcasMole = 0.0d0
Do16I=l,Ngass
15 TotalGasl{ole = Tota]GasMole + y(I)
Zdsh = TotalGasMole * mwa/ 1000.0d0
TotalSolidl'lole = 0.0d0
Do 1g I = lrfg6sg+l,species_num
18 TotalSolidMole = TotalSolidMole + Y(I)
Totaluole = TotalGasuole + TotalSolidMole
Z tb = TotalGasMole * mi{a / 1000.0d0
= 0.0d0
SUMPS
= 0.0d0
SUMNS
Do24I=NS+L,NS+NPS
2 4 S U I { P S= S U U P S+ Y ( I )
Do 25 I = NS+NPS+I,NS+NPS+NNS
26 SUI'INS= SUI{NS+ Y(I)
nTotalCharged = SUMPS- SUI'INS
RETURN
END
S U B R 0 U T I NC
EH N O3S( t e m p ,p r e s s u r e , a N , a O ,a H ,a C ,a A r , a S. a E ,E n t h a l p y 3 e r
*-kg )
C,.,..Calcu1ates the enthalpy per kg of fireball air given the pressure,
C . . . . . t e m p e r a t u r e a n d m o l a r a m o u n t so f e a c h e l e m e n t i n t h e f i r e b a l l a i r .
TEST PROGRAM
T'ORFREE ENERGYMINIMIZATIONROUTINE
a
I } I P L I C I T D O U B I JPER E C I S I O N( A - H . O - Z )
DIMENSIONenthalpy ( 50)
c
C o M M 0 N / A A A( 5/ A0 , 1 0 ) , A K T( 5 0 ) , A K T F( 5 0 ) , B ( 1 0 ) , B 0 ( 1 0 ) . c ( 5 0 )
c o M M o N / B BrBV/A R K
, H( 2 0) , L , L 1 , M ,I , t 1t,l A ,M B ,M p ,M S ,l l F ( 1 5 ) , M L( 1 5)
c o M M o N / c c c / p(r2 0 ) , p T o T ,T , y ( 5 0 ) , y 0 ( 5 0 ) , y r ( 5 0 ) , y T o T( 2 0 )
comnon /xaa/ I'lc,MR
C O I , I M O N / N/ IJNTE,J 2 , J 3 , J 4 , J 5 , J 6 , J 7
ENTERGM ATOMSOF ELEMENTS
c
B(Jl)
B(J2)
B(J3)
B(J4)
B(J5)
B(J5)
B(,I7)
=
=
=
=
=
=
=
aC
aH
aN
a0
as
aAr
aE
c
ENTERTEMPERATURE,
PRESSURE
e
(\
c
a
c
c
= tenp
T
P T O T= p r e s s u r e / 1 0 1 3 2 5 . 0 d 0
CAI.CUI.ATE
GIBBS ENNRGIESOF SPECIES
R=1.98717
D0 70 I=I,MS
(1.T) ) /R/T
G ( I ) = ( C E N T(HI , T ) - T * E N T R
The value of CENTH(I.T) has units Kcal/rnole.
Ilowever enthalpy(I) needs to have units of J/mote.
It is then necessary to multiply CENTH(I,T)
by 4.185D+00 to convert ca}/mole to ,I/rnole.
enthalpy(I)
= 4 . 1 8 5 D + 0 0* 6 E N T H ( I , T )
7 0 CONTINUE
c
a
c
ENTERINITIAIJ GUESS
YTOT(1)=HG
D0 ?5 I=I,MS
Y(I)=1.
7 5 CONTINUE
CALI, GAUSS
IF (U. GT. MP) TIIEN
r{RrTE(0,117) M,},tP
stop
ENDIF
63
= 9.969
Enthalpy3er-kg
D0 80 I=1,MS
Enthalpy3er-kg = Enthalpyjer-kg
80 CONTINUE
RETURN
',I3,'
MP= ',I3,/'
1 1 ? F O R I I A T ( 1' 1=
END
+ (enthalpy(I)
* Y(I))
EQUILIBRIUN
MO T A T T A I N E D ' )
c---------c
Find-T
SUBROUTINE
a
C.....Finds the tenperature that corresponds to the enthalpy.
c
(A-II,}1-Z)
PRECISION
II{PLICIT DOUBI,E
put '
inclutle 'cornnon.
counter=qqunfsl+1
if (counter .I"T. 4) then
Enthal (counter) = enth-fb-Per-l'tass
2 0 C a l I s c r a n b l e( T - f b , P - a n b i e n t )
DeIta-Enth = (enth-fbjer-l'lass-Enthalpyjer-kg) /
* (enth-f b3er-l'lass)
i f ( d a b s ( D e l t a - E n t h ). G T . 0 . 0 0 0 1 d 0 )t h e n
T _ f b = T - f b * s q r t ( ( D e l t a - E n t h+ 1 . 0 D 0 ) )
goto 20
else
temper(counter)=T-fb
endif
else
40 CalI matrix
T-fb = cala * (enth-fbjer-Mass 't enth-fbjer-Mass) + calb *
r.enth-fbJer-l{ass + calc
I f ( T - f b . 1 , T . o o o . o i l o . o R . T - f b . G T . 1 0 0 0 0 . 0 d 0 )c a l l s h o w s t a t u s
C a I l s c r a m b l e( T - f b , P - a m b i e n t )
tenper (counter)=T-fb
EnthaI (counter) =EnthaIpyJer-kg
Delta-Enth = (enth-fbjer-Mass - EnthalpyJer-kg)
*
/ (enth-fb3er-Mass)
i f ( i l a b s ( D e I t a - E n t h ). c r . 0 . 0 0 1 ) t h e n
) . 1'0) then
i f ( d a b s ( t e r , p e r ( c o u n t e r ) - t e m p e r ( c o u n t e r -. lL) T
i f ( ( t e m p e r ( c o u n t e r - 2 ) - t e n p e r ( c o u n t e r) - l.)G E . 0 . 0 ) t h e n
t e m p e r ( c o u n t e r=) t e n p e r ( c o u n t e r - 1 )- 1 . 0
else
tenper(counter) = tenperlq6unlss-l) + 1.0
endif
CalI scranble (tenper (counter),P-anbient)
Enthal (counter) = EnthalpyJer-kg
enilif
counter=counter+1
goto 40
endif
endif
RETURN
END
SUBROUTINE
natrix
C . . . . . 4 2 n d o r d e r p o l y n o n i a l f i t used by Find_T to approxinate guess
C . . . . . t e n r p e r a t u r e c o r r e s p o n i l i n gt o e n t h a l p y .
c
(A-H, !r-Z )
IMPLICITDOUBI,E
PRECISION
Integer counter
R e a L * 8T 1 .T 2 ,T 3 ,8 1 , E 2 , 8 3E, 1 s q r E
, 2 s q rE
, 3 s q rE
, 1 n u lE
, 2 n u 1E, 3 n u I
R e a l * 8 c a 1 a ,c a I b , c a l c , t e r n p e r , E n t b a l
R e a l r , 8n l , n 2 , n 3
C o n n o n/ U S E / E n t h a(I2 0 0 0 ) ,t e m p e r( 2 0 0 0 ) ,c a 1 a , c a l b , c a l c ,c o u n t e r
=tenper(counter-3)
T1
=tenper(counter-2)
TZ
=temper(counter-1)
T3
Elsqr = Enthal(counter - 3) ** 2.0d0
= E n t h a l ( c o u n t e r- 3 ) , , * 1 . 0 d 0
E1
E l n u l = E n t h a l ( c o u n t e r- 3 ) t * 0 . 0 d 0
E2sqr = Enthal(counter- 2) ** 2.0d0
= E n t h a l ( c o u n t e r- 2 ) * * 1 . 0 d 0
E2
E 2 n u l = E n t h a l ( c o u n t e r- 2 ) * * 0 . 0 d 0
E3sqr = Enthal(counter- 1) 't* 2.0d0
= E n t h a l ( c o u n t e r- 1 ) * * 1 . 0 d 0
E3
E3nul = Enthal(counter- 1) ** 0.0d0
=E2sqr/Elsqt
n1
=E3sqr/E1sqr
n2
E 2 s q r= 0 . 0 d 0
=E2- (n1*E1)
E2
E2nul = E2nul - (n1 * Elnul)
E3sqr = 0.0c10
=E3-(n2*El)
E3
E 3 n u 1= E 3 n u I - ( n 2 * E L n u l )
=T2- (n1*T1)
T2
=T3-(n2*T1)
T3
=E3/E2
n3
=E3-(n3*82)
E3
E 3 n u 1= E 3 n u l - ( n 3 * E Z n u I )
=T3-(n3*T2)
T3
calc =T3lE3nuI
c a l b = ( T 2 - ( E 2 n u 1* c a l c ) ) / E z
ca1a = {T1 - (E1 * calb) - (Elnul * calc)) / nlsqr
RETURN
END
65
CENTH(I,T)
FUNCTION
c
C.....Calculates
the enthalpy of any fireball
species at any tenperature
II{PLICIT DOUBI,EPRECISION(A-H,O-Z)
50
, 1) ,c 2( 5 0 ,5 ) ,c 3( 5 0 ,5 ) ,C 4( 5 0 ,5 )
c o u r . { o N / D A( T
/ c5
( 5 05
,)
(5 0 ) ,H H(5 0 ,5 ) , T M
c o l , r M o N / D A(5T0/ )H,SRR(5 0 ) , N R
c
(I )
cENTH=HR
N=NR(I)
IF (T.I,T.298.15) THEN
U
-
I
TL = 298.15
T U= T
+ T(HC 1 ( I , J )
CENTH=CEN
+ C2(r,J)*TL
1
+ c3(r,,t)*TL'tTL
2
+ C4(I,J)*(TL**(_2.0)))*(TU_TIr)
3
CENTH=CENTH+HH(I,.t)
ELSE
D0 30 'J=1,N
TL=298.15
I F ( J . G T . 1 )T L = T M ( I , . i - 1 )
TU=T
I F ( T . G E . T l t ( r , ,)I ) T U = T M ( r , . t )
* (TU-TL)
)1
C E N T H = C E N T(HI ,+JC
+ C 2 ( I ' , 1 ) *( T U * T U - T L * T/I2J.)
1
+ C 3( I , J ) * ( T U , , T U * T U - T L * T L /*3T.L )
2
-C4(r,J)*I./TV-r./TL)
3
r F ( T . L T . T l t ( r , J )) G O T O
40
CENTH=CENTH+HH(I,,I)
3O CONTINUE
Itr' (T . GT. TI.1(I,N)) THEN
TL = TM(I,N)
T U = T
= CENTII+ (C1(I,N)
CENTH
+ C 2( r , N )* T L
1
+ C 3( I , N ) * T L * T L
2
+ C4(I,N)r!(TL**(_2.0)))*(TU_TIJ)
3
ENDIF
ENDIF
40 RETURN
END
66
TUNCTION
ENTR(I,T)
c
C.....Calculates
c
the entropy of any fireball
species at any temperature.
II'IPIJICIT DOUBIEPRECISION(A-H,O-Z)
c
( 5/ C
0 ,15 ) , C 2( 5 0 ,5 ) , C 3( 5 0 ,5 ) , c 4 ( 5 0 ,5 )
col,tMoN/DAT
( 5/ H
coMr'toN/DAT
0 )R,s R( 5 0 ) ,N R( 5 o ) ,H H( 5 0 ,5 ) , T M( 5 0 ,5 )
(I )
ENTR=SR
N = N (RI )
I F ( T . I , T . 2 9 8 . 1 5T) H E N
iI =1
TL = 298.15
T U=T
E N T R = E N+T R( C 1 ( I , J )
+ C2(I,J)*TL
L
+ C 3( I , , 1 )* T L * T L
2
3
+ C 4( I , . 1 ), ,( T I J * *( - 2 . 0 ) ) ) * D L O(GT U I T L )
( I, J) /Tl,l( I.,t )
ENTR=ENTR+HH
ELSE
D O3 0 J = 1 , N
TL=298.15
If (,t.cT.1) TL=TI{(I,.1-1)
TU=T
I F ( T . G E . T(lI1, . 1 )) T u = T l I ( I , J )
(I, J) *LOc(TU/TL)
ENTR=ENTR+C1
+C2(I..t)*(TU-TIr)
1
z
+ C 3( I , . I ) * ( T U * T U - T 6 * T/L2,.
- c 4 ( r , . r ) * ( 1 . / T U / T U - I ./ t L / T L I 2 .
/
I F ( T . L T . T l , l ( I , , t)) G O T O
40
I ,H
. tH
) / T M( I , , t )
E N T R = E N T R( +
3O CONTINUE
IF (T .GT. TM(I,N)) THEN
TL = TM(I,N)
T U = T
E N T R = E N T+R ( c l ( I , N )
1
2
3
ENDIF
ENDIF
40 RETURN
END
+ C 2( f , N ) , t T I r
+ c 3 ( I , N )* T L , r T L
+ c 4 ( I , N )r 3( T L * *( - 2 . 0 ) ) ) * D L O G ( T U / T t )
o t
GAUSS
SUBROUTINE
c
t h e n u m b e ro f m o l e s o f e a c h s p e c i e s i n f i r e b a l l
c.....calculates
C.....kilogram of fireball ai.r.
c
C
c
c
air
ERIKSSONFREE ENERGYMINIMIZATIONROUTINE
P R E C I S I O N( A - I T ' O - Z )
IMPLICIT DOUBI,E
( 5/ 0A,1 0 ) ,A K T( 5 0 ) ,A K T (F5 0 ) ,B( 1 0 ) ,B 0( 1 0 ) ' c ( 5 0 )
collMoN/AAA
. F( l ' 5 ) . M L( 1 5)
, AM
. BI.' t PI,' l SM
c o M M o N / B B B / r v; KAH
R( 2 0 ) ,t . 1 1 ,M ,M 1 M
2 r0 ) ,P T o TT, ,Y ( 5 0 ) ,Y 0( 5 0) ' Y F( 5 0 ) ,Y T o r( 2 0 )
c o M t { o N / c c c /(P
c
D r u E N S r oFN( 5 0 ) , r F A S ( 1 0 ) , 1 S O L ( 1 0 ) , N S U M ( 2 0 0 ) ' 0 P r ( 2 0 )
( 2N0 .2 1 ) , Y r r o r( 2 0 ) ' Y x ( 5 0 )
D T M E N S TRO
I5=-I
MSUM=0
NG=0
1 ISUt'l=O
l,lSA=0
rr (us . GE. Itl ) TI{EN
D0 2 I=Ml'HS
) [N
r r ( Y ( r ) . N E . o r. H
MSA=MSA+l'
I S O L( M S A=) I
I S U M = I S U H + 2 *( I*+ M p - M l)
ENDIF
2 CONTINUE
ENDIF
3 MPA=0
NG=NG+1
I F ( N G . 8 Q . 5 0 1 )N G = t
=ISUI'I
NSUII(NG)
YSUM=0.
D0 4 M=1,MP
) HEN
I F ( Y T O T ( H ) . N E . O .T
llPA=MPA+1
IFAS(MPA)=M
(Nc) +2** (}t-1)
NSUI{(NG)=NSUM
(M)
YSUM=YSUM+YToT
ENDIF
4 CONTINUE
) E . I S . A N D . T T P A + } I S A . I . EG
.G
. tO
, ) T O1 1
IF (NSUM(NG
5 IS=IS+2
DO 6 N=l,MPA
M = I F A S( N )
Y T O T( M )= 0 .
6 CONTINUE
ISUM=0
MPA=L
YTOT(1 ) =1 .
I F ( I { S A . N E . O )T H E N
DO7 N=I,MSA
I = I S O L( N )
Y(I)=0.
? CONTINUE
MSA=0
ENDlF
IF (IS.NE.1) THEN
IT=IS
8 M=0
9 l'l=M+1
I T ( 2 * * M . I . E . I T ) G O T O9
IF (M.I,E.ilP) TIIEN
MPA=MPA+1
IFAS (MPA)=lt
Y T o T( t { )= 1 .
HA=MF(il)
(M)
HB=MI,
D0 10 I=ilA,MB
Y(I)=YsUlI
1O
CONTINUE
EIJSE
I=}l+ML(MP)-ltp
IF(I.GT.MS)RETURN
HSA=MSA+1
I S O L( M S A=) I
I S U i l = I S U M + 2 *(*H - 1)
Y(I)=YSUil
ENDIF
IT=IT-2** (tt-1)
r r ( r T . E Q . 1c) o T o8
IF (}IPA+MSA.GT.L)GOTO5
ENDIF
I F A S( 1 ) = 1
IF (NsUlI(NG).GT.Is)NG=NG+I
NSUII(NG)=IS
1 1 I F ( N G . N E . 1 )T H E N
DO 12 K=2,NG
r F ( N S U r , t ( N c ) . E Q . N S U M ( K) - 1G) O T O5
L2 CONTINUE
I F ( N s u l ' l ( l l c - l ) . E Q . M S U MN
( N c - j . )= - N S U M ( N G - 1 )
) SUM
( N c - 2) . N E .- M S U I , I . O R . N S( U
r F ( N c .L T . 3 . 0 R . N S U M
NM
C ). E Q . M S U MG
) O T O1 3
NSUH(NG-2) =-Nsul,t(NG-2)
ENDIF
1.3LX=0
t4 D0 15 ,I=l,L
B 0 ( , t ) = B( , J )
1 5 CONTINUE
D0 18 M=l ,lIP
(M)
MA=MF
!18=lIL(11)
I F ( Y T O T ( M ) . I , 8 . 0 . )T H E N
DO 15 I=l'lA,MB
AKT(I)=0.
AKTF(I)=1.
Y(I)=0.
YF(I)=0.
CONTINUE
EIISE
D0 17 I=l{A,}18
I F ( Y ( I ) . L T . 1 . E - 8 )y ( I ) = 1 . E - 8
AKTF(I)=1.
L1
CONTINUE
CAI,L ABER
r F ( Y T O T ( M ) . E Q . 0 . )G O T O3
ENDIF
18 CONTINUE
69
D M I N = 1E. - 6
IVAR=0
IVAR.I=ML( 1) -l{S
LS1=L+l{PA+MSA
LS=LS1-1
tr5!=l,g+2
1 9 D 0 2 0 J = 1, L S 1
D0 20 K=\],LSZ
R ( , 1, K ) = 0 .
2 0 CONTINUE
D0 24 N=I,MPA
LL=L+N
M = I F A S( N )
!,tA=l{F(M)
MB=I{L(M)
D0 23 I=MA,MB
IF (Y(I).NE.O.) THEN
F ( I ) = G( I ) + L o c ( A K T( I ) )
R ( L l , L S 2 ) = R( L l , t S 2 )+ F ( I i * y ( I )
DO 22 J=L,L
r F ( A ( r , . r ) . N E . 0 .) T H E N
AY=A(I,J)*Y(I)
R (.t , L1) =R(!T, IJl ) +Ay
R ( . t , L S 2 )= R( J , L S Z )+ A y * F( I )
DO 21 K=.LII
R (.1. K) =R('J,K) +AY*A( I , K)
2T
CONTINUE
ENDIF
22
CONTINUE
ENDIF
23 CONTINUE
D0 24 J=l,L
R ( , t ,L S 2 )= R( . t ' L S 2 )- R ( , t ' L 1 )
24 CONTINUE
I F ( M S A . N E . O . )T H E N
D0 25 N=1,llSA
I=IsoL (N)
K=L+l{PA+N
R(K,tS2)=G(I)
DO25 J=1.L
R(J'K)=A(I',1)
25 CONTINUE
ENDIF
D0 25 .I=2,1,S1
N=J-1
D0 26 K=1,N
s 1 g. K 1 = x( K , J )
26 CONT]NUE
DO 28 K=l,L
I T ( K H ( K ) . N E . O )T H E N
D 0 2 7 . I = 1, L S 1
R ( J , L S 2 )= R( , t , t S 2 ) - P I ( K ) / , R( . 1, K )
CONTINUE
27
ENDIF
R ( K ,L S 2) = R( K , L S 2) + 8 0( K )
28 CONTINUE
DO 32 K=1,IrS
I F ( K H ( K ) . E Q . O )T H E N
ELMAX=O.
70
D0 29 J=K,LSI
I F ( A B S ( R ( . ' , K)). I J E . E L H A X . O R . K H .(N
J )E . O ) G O T O2 9
MROli=J
(R(,t, K) )
ELIIAX=ABS
29
CONTINUE
IF (EI.I'IAX.tE.O.) THEN
r F { B 0 ( K )) 5 , 3 2 , 5
ENDIF
IF (}IROI{.NE.K)THEN
D0 30 N=K,LS2
(l,lROI{,N)
RADBYT=R
{ ,) = R( K . N )
R ( M R O IN
R( K , N )= R A D B Y T
30
CONTINUE
ENDIT
KA=K+1
D0 31 .I=KA,LSI
, 1, r ) 7 p 1 1 , 6 1
R K V O T =(R
DO 31 N=KA,LS2
R ( . t , N ) = R( . 1, N ) - R K V O T * R
( K ,N )
31
CONTINUE
ENDIF
32 CONTINUE
D0 34 N=l,LSl
K=LS2-N
I F ( K H ( K ) . E Q . O )T H E N
r F ( R ( K , K ). E 9 . 0 . . A N D . R ( K , r , S.2E)Q . O ). T H E N
P r ( K )= 0 .
K=K-L-MPA
I F ( K . I , E . O ) G O T O3 4
I = I S O L( K )
Y(I)=0.
GOTO1
ENDIF
P I ( K )= R( K , L S 2) / R ( K , K )
KA=K-1
I F ( K A . N E . O )T H E N
D0 33 J=1,K4
33
R(.t,LS2)=R(,I,LS2)-pI(K)*R(.r,K)
ENDIF
ENDIF
34 CONTINUE
r F ( I V A R . E Q . 0 . 0 R . M R . t . G E . 0 . O R . S t A l r . t T . o . 1c) o T o 4 5
D0 35 J=1,L
I F ( A B S( P I ( J ) ) . G T .1 . E - 8 . A N D . A B(SO P I( J ) / P I ( J ) - 1 . ) , G T . D M I N ) G O T O4 4
35 CONTINUE
NR=0
IF (NG.NE.1) THEN
D0 35 K=2,NG
I F ( N s u M ( N c .)E Q . - N s u l ' t ( K - 1) N R = N R + I
36 CONTINUE
ENDIF
D0 38 M=I,MP
I F ( Y T O T( M ) . I , E .O . ) T H E N
HA=MF
{M)
(M)
MB=ML
CAIJLXEER
YFTOT(M)=0.
DO 37 I=tlA,MB
(M)+Yr ( r )
YFTOT(M)=YFTOT
Yx(I)=YF(I)
A K T( I ) = 0 .
YF(I)=0.
3 7 CONTINUE
Ir (u.E9.1) YFToT(l{) =YFToT(H) /PToT
ENDIF
3 8 CONTINUE
3 9 DIFM=1.
D0 40 l{=1 ,HP
) T . O . . O R . Y F T O T (.II{. )E . D I T M )coTo 40
I F ( Y T O T ( M. G
KA=M
DIFII=YFTOT(M)
40 CONTINUE
I F ( D I F M . N E . 1 . . )T H E N
I F ( N R . N E . O )T H E N
NR=NR-1
YFTOT(KA)=1.
coro 39
ENDIF
(NG)
MSUtI=NSUI{
YTOT(KA)=1.
MA=Mf(KA)
(KA)
MB=ML
DO
41
I=}IA.MB
.Y
I ) / Y F T O T( K A )
( I ) = Y S U M * Y(X
4L CONTINUE
GOTO3
ENDIF
IT (}IS.GE.Ml) THEN
DIFM=0.
D0 43 I=MI,MS
IF (Y(I).I.8.0.) THEN
PIA=-G ( I )
D0 42 il=l ,Ir
PIA=PIA+A(I, J) ,,PI ('J)
42
CONTINUE
IF (PIA.GE.DIFM)THEN
KA=I
DIFM=PIA
ENDIF
ENDIT
43 CONTINUE
IF (DIFM.NE.O.) THEN
Y (KA)=YSUM
GOTO1
ENDIF
ENDIF
IVAR'J=0
GoTO 46
44 DO45 J=1,L
0PI (J)=PI (.t)
45 CONTINUE
46 SLAM=I.
DO 48 N=I,MPA
L1=L+N
- I{=IFAS(N)
!tA=!lF (t{)
(M)
ME=ML
72
DO 48 I=MA,MB
I T ( Y ( I ) . N E . O .) T H E N
P I A = F( I ) - p I ( 1 1 )
D0 47 J=l,L
P I A = p I A - A( I , J ) * p I ( , t )
47
CONTINUE
YX(I)=PrA*Y(r)
IF (PIA.cT.SLAM) SLAI{=pIA
ENDIF
48 CONTINUE
IF (stAM.cT.1. ) SLAM=0.9/stAil
I F - ( M S A . N E . OT) H E N
DO 49 N=l,!lSA
I = I S O L( N )
K=[+l,lpA+N
IF (Pr(f).LT.0.) [1=0
y (or T
)o
r F ( r v A R . E g . 0 . 0 R . p r ( K ) . c T ). - G
49
) T O4 9
I F ( S L A M . L T . 1 . . A N D . - P I ( K ) / Y S U M . I , T . 1 , EG8O
Y(I)=0.
GOTO1
49 Y(I)=ABS(PI(K))
ENDIF
DO 50 ,I=1,L
B 0 ( J ) = B( , I )
50 CONTINUE
YSUM=O.
D0 52 N=1,l,lpA
I.l=IfAS(N)
MA=I{F(M)
MB=IIL(M)
D0 51 I=MA,MB
IF (Y(I).NE.O.) THEN
Y(I)=Y(I)-sLAM*yX(I)
I F ( Y ( I ) . r , T . 1 . E - 1 0 )Y ( r ) = 9 .
ENDIF
51 CONTINUE
CALI, ABER
r r ( Y T o T ( U ) . E 0 . 0c.o) T o3
(t{)
YSU}I=YSUH+YTOT
52 CONTINUE
IVAR=IVAR+1
IF (MR.EQ.25.OR.MR.EQ.50) DMrN=100.*DMrN
rF (MR.E9.?5) coTo 5
I F ( r v A R J . L T . 0 . O R . L l . E g . 0 . o R . S L A M . L T .)1 .C O T O1 9
IVAR,J=IVARJ+1
IF (IVARJ.NE.10) THEN
DO 53 N=I,MPA
M=IFAS(N)
MA=IIF(M)
ltB=ML(H)
DO 53 I=MA,MB
IT (Y(I).GT.O.) THEN
r F ( A B S ( y X ( r ) ) / y ( r ) . G T . 1 . E - 6 )G O T O1 9
ENDIF
53 CONTINUE
ENDIF
73
D0 54 N=I.,MPA
l.l=IFAS(N)
(M)
MA=MF
MB=ML(M)
CAIL XBER
DO 54 I=MA,$B
IF (Y(I).tE.O.) THEN
Y ( I ) = Y T O T( M )* Y F( I )
) 0 T 05 4
r r ( Y ( r ) . 1 T . 1 . E - 1 0 . 0 R . 1 X . E 0 . 1G
r v-l
!A-
I
GoTO 14
ENDIF
54 CONTINUE
IF (IVARJ.EQ.10)t't=O
RETURN
END
c---------SUBROUTINE
ABER
CAIJCULATE
ACTMTIES
C
c
0F SPECIES FROUMOLEFRACTIONS
IMPITICIT DOUBLEPRECISION(A-H'O-Z)
c
c o u i l o N / A A A( 5
/ A0 ,1 0 ) ,A K T( 5 0 ) ,A K T r( 5 0 ) ,B ( 1 0 ) ,B 0( 1 0 ) ,G( 5 0 )
c o l t M o N / B B B / r v A R , K I l ( 2 0 ) , ,LM
, L, l1, t,l l l A , l ' l B , l l P , M s , t t F ( 1 5 ) , l ' t l ( 1 5 )
, , Y ( 5 0 ) ,Y O( 5 0 ) ,Y r ( 5 0 ) ,Y T O(T2 0 )
c o t t M o N / c c c /(P2 r0 ) ,P T o r T
c
2
4
6
8
Y T O T( M )= 0 .
D0 2 I=MA,ilB
YTOT(M)=YToT(M)+Y (I)
CONTINUE
I F ( Y T O T ( H ) . I . T . 1 . 8 - 8 )T H E N
Y T O T( M )= 0 .
ELSE
If (l,l .eq. 1) YToT(1) = YTOT(1)/PToT
DO 5 I=MA,I{E
YF (I ) =Y ( I ) /YToT (l'l)
CONTINUE
DO 8 I=MA,!{B
AKT(I) =AKTF(I) *YF (I)
CONTINUE
ENDIF
RETURII
END
XBER
SUBROUTINE
c
C
c
CAITCUTATE
MOLEFRACTIONSOF SPECIES fROll ACTMTIES
(A-H.O-Z)
PRECISION
IMPLICITDOUBI,E
( 5 0 ) ,B( 1 0 ) ,B 0( 1 0 ) ,G( 5 0 )
( 5/ 0
coilMoN/AAA
A,1 0 ) ,A K T( 5 0 ) ,A K T F
- col{l{oN/BEB/
l{A,llB,UP,}lS,l{F( 15), ML( 15)
rvAR,KH( 20), L, t1, M,}.11,
( 2 0)
, , Y ( 5 0 ) ,Y O( 5 0 ) ,Y F( 5 0 ) ,Y T o T
c o l t M o N / c c c l(p2r0 ) ,P T o r T
OYF(50)
DII{ENSION
74
(PTOT)
PLOG=LOG
I F ( P I r O C . L T . 1 0). P L 0 G = 1 0 .
D0 5 I=l{A, MB
IF (Y(I).I.E.0.) THEN
PIA=-G ( I )
D0 2 J=L,L
I F ( A ( I , . ' ) . N E . O .) T H E N
I F ( P r ( , r ) . 8 0 . 0 . ) G 0 T 04
P I A = P I A + A( I , J ) * p I ( J )
ENDIT
2
CONTINUE
IF (PIA.GT.PL06) PIA=PLOG
IF (PIA.I,T.-200.) GOTO 4
A K T( I ) = E X P( P I A )
YF(I)=AKT(I)
GOTO 6
4
A K T( I ) = 0 .
YF(I)=0.
ENDIF
6 CONTINUE
IVAR=0
8 IVAR=IVAR+I
D0 10 I=MA,MB
o Y F( I ) = Y F( I )
Y F ( 1 ) = A K T( I ) / A R T F( I )
TO CONTINUE
DO 12 I=MA,MB
IT (YF(I).GT.O.)THEN
I F ( A B s ( o Y F ( I ) / Y F ( I ) - 1 . ) . c T . 1 . E - 4 )c o T o
ENDlT
12 CONTINUE
RETURN
END
8
v
c---------c
SUBROUTINE
Runge_Kutta (N, t)
C . . . . . 4 t h o r d e r R u n g e - K u t t af o r s o l v i n g d i f f e r e n t i a l
c
equations.
(A-H,O-Z)
IIIPLICIT DOUBI.E
PRECISION
Integer count
R e a l * 8k , H
D i n e n s i o n f _ n e w ( 1 0 ) f, _ o l r l ( 1 0 )
D i n e n s i o nc ( 0 : 3 ) , b ( 0 : 3 )
D a t a c / 0 . 0 d 0 ,0 . 5 d 0 , 0 .5 d 0 ,1 . 0 d 0 /
Data b/1.0it02
, . 0 d 0 ,2 . 0 4 1 0
1 ,. 0 a 1 0 /
C o n n o n/ O n e / c o u n t , d f( 5 ) , d t , f ( 5 ) , k , l a s t _ c o u n t , l ',fr a d _ l o s s 0
Do 10 ,l = 1,N
f -new(.t) = f (.I)
f_o1d(J) = f(J)
10 continue
Do40I = 0 ,3
del_t=c(I)*dt
w e i g h t = b ( I )* d t / 9 . 0 d 0
Do20J=1 ,N
f (.t) = f _old (rt) + del_t * df (.t)
20 continue
/)
CaIl Dif f erential-Eguations
Do 30 ,J = 1.,N
f _new(J) = f_nes(.I) + weight * df (J)
30 continue
40 continue
D o 5 0 J = l . N
f (.I) = f -nev (.I)
50 continue
1 = t + d t
RETURN
END
c
c---------c
Dif f erential-Equations
SUBROUTINE
I M P I , I C I T D O U B I JPER E C I S I O N( A - H , M - Z )
inclutie
' common
. Put '
= f(1) - z
chan*z
= t[l
z
= f (4)
enth-fb3er-Mass
call Do-enrh-hart
rnitial-fb-enthalpy)
rf (enth-fbjer-Mass'GT'
CaI1 ICAo-air (z,T-ambient,P-anbient,D-arnbient)
OLD'MASS= Mass
= f (3) * 4.0d0 / 3.0d0 * pii
I'tass
S, l'lass, z )
Cal l Mass -Ba1ance-Update (OLD-fiAS
= l l a s s * T o t a l G a s M o l e* 8 . 3 1 4 3 * T - f b / P - a n b i e n t
cVol
= ( ( c V o I * 3 . O d O/ ( 4 . 0 d 0 ' t p i i ) ) * * ( 1 . 0 d 0 / 3 . 0 d 0 ) )
radius
= (radius ** 3.0d0) * D anbient
v
=f(31 /Y
Dtlash
= D c l a s h* D - a m b i e n t
Density
= t ( 2 ) / ( D d a s h+ k )
Itl
= M / V
u
=G*V*(1.0d0-Ddash)
Fb
= 3 . 0 d 0 * e n t r a i n * d a b s ( M / r a d i u s ) * D d a s h * * ( 2 . 0 d 0/ 3 . 0 d 0 )
tlrn
Ca1I anrbient-enthalpy ( z , T-anbient )
= u
df(1)
= Fb
df (2)
= dm
df (3)
CaIl Loss-Radiant (T-fb, radius, T-anbient )
= Radiant-l,oss
df (5)
=- (f(4) -enth-anbient) *dn*4.0d0
/ 3.0d0*pii/Uass
df(4)
- df (5) / Mass
1
- (G'*u/Ddash)
2
RETURN
END
to
SUBROUTINE
Mass_Ba1ance_Upclate ( OID_MAS
S, BMass, hi te )
c-.-..calculates
the increase in nass of atoms in firebalr
C.....for present tine.
and uodates
(A.H,I,I-Z)
I}TPLICIT DOUBIJE
PRECISION
include'con$on.put'
a
a
The "an" stands for the arnount per kilograrn of ambient air.
Thus "anN" means the amount of atomic nitrogen, in mole,
per kilogran of anbient air.
These values are returnetl frorn the GRAMATOMSUBROUTINE.
Cal1 CI,EAN_FIREBALI,(hite,water_incIude,llFH20,MFN2,MFO2.MFCO2,MfAr)
(l{FH20,MFN2, MFO2, MFCO2
CALI GRAM_ATOI'I
, }lFAr , anN, anO, anH, anC, anAr )
= BMass - OLD_MASS
delta nass
= 0.0d0
nfS
= 0.0c10
nfE
= 0.0ct0
anS
= 0.0d0
anE
= T o t a l n f N + (tlelta_nass *
TotaLnfN
= Totalnf0
+ (delta_nass *
Totalnfo
= T o t a 1 n f H + (delta_urass*
Totalnfll
= T o t a l n f C + ( d e l t a _ m a s s*
TotalnfC
= T o t a l n f A r + (tlelta_nrass*
Tota1nfAr
= Totalnfs
+ (delta_nass*
TotalnfS
= T o t a l n f E + ( d e l t a _ n a s s*
TotalnfE
nfN =Tota1nfN/BHass
nfo = TotalnfO ,/ Bl{ass
nfH =TotalnfH/BMass
nfAr=TotalnfAr/BMass
nfC =TotalnfC/Bl,lass
nfS =TotalnfS/BMass
nfE =TotalnfE/8Mass
RETURN
END
anN)
ano)
anH)
anC)
anAr)
anS)
anE)
77
SUBROUTINE
Loss_Radiant (T, rad, T_anb)
c
C.....Calcu1ates the energy lost to far field
clueto radiation.
L
(A-H,O_Z)
IHPLICIT DOUBI.E
PRECISION
R e a l * 8 I n i t i a l _ f b _ e n t h a l p ym
, wa
ConnonloutputlopTr
Connon/f our /beta, D_arrbient,ent rain. f ni t ial_f b_enthalpy,pi i, tl, mwa
C o r n n o/nh o l / H o l d n( 5 0 ) , T o t a l G a s M o l e , T o t a I S o l i d M oZI ed,. s h
C o m n o /nB / O p _ f b , T r , R a d i a n tL o s s , s i g n a
i f ( T . c T . 3 0 3 5 . 0 d 0 t)h e n
T r = 0 . 9 5 4 d 0- 1 . 0 d - 8 * ( ( T - 6 0 0 0 . 0 d 0 )* * 2 . 0 d 0 )
eLse
i f ( T . c T . ? 0 4 . 0 d 0 )t h e n
T r = 0 . 5 3 5 d 0* d l o g ( T ) - 3 . 5 0 7 7 d 0
else
Tr = 0.0d0
endif
endif
If (TotalSoIidltole .cT. 3.0d-05) then
op_fb = 1.0d0
else
RadInCM=100.0d0*rad
o p - f b = 1 . 0 d 0 - D e x p ( - 4 . 0 d 0 ' t 2 . 0 d O * R a d I n C l l * P M)A C ( T )
endif
= op-fb * Tr
0pTr
= 4.0d0 rt pii r, (rad * rad)
Radiant Loss
1
* OpTr * sigma * ( (T ,, T) + (T_anb * T_amb)
)
,, (T t T_amb) * (T - T_anb)
2
RETURN
END
a
c
Function PMAC(T
fb)
C.....Returns the Planck llean Absorption Coefficient (PI{AC)
I
(A-H,M-Z)
IUPIJICITDOUBIJE
PRECISION
L o g i c a l C h a r g e d , S e t t i n g _ u p , m o t n e nst ut omp
C o n n o n/ t v o / c h a n _ 2c, V o l . D d a s hD, e n s i t y , F b , u ,G
Comnon/ eidtrt /ctrirged, Set t i ng-up, mornen
tun-s top
C o m m o/ n
Din/ DL(4),TL(7),PMAC_Log(8,4)
If (Setting_up) then
Setting-up = .false.
D_grounal= 1.225D+00
T L( 1 ) = 0 . 0 i l 0
TIr(2) = 1000.0d0
TL(3) = 2000.0d0
TL(4) = 3000.0d0
TL(5) = 4000.0d0
TL(6) = 6000.0d0
TL(7) = 8000.0d0
D L ( 1 )= 0 . 0 d 0
D L( 2 ) = - 1 . 0 a 1 0
DL(3) =-2.0d0
DL(4) =-3.0d0
P M A c _ L o(g1 , 1 ) =
P I I A CL o s ( 2 , L ) =
P M A C _ l r o g ( 3 , 1=)
PI.IAC_Log(4,1=
)
P M A C _ l , o g ( 5 , 1=)
P M A CL o g ( 6 , 1 ) =
P M A CI J o g ( 7 ' 1 ) =
P M A CL o g( 8 , 1 ) =
P l , l A CL o g ( 1 , 2 \ =
P M A CL o g ( 2 , 2 1 =
P M A CL o s ( 3 , 2 ) =
P M A C _ L o( 4
g, 2 \ =
P l ' l A C _ L o( g5 , 2 1 =
P I l A C _ L o(g6 , 2 1 =
P M A C _ L o(g1 , 2 ) =
P l ' l A CI J o g $ , 2 ) =
P M A C _ l r o g ( 1 , 3=)
P M A CI r o g ( 2 , 3 ) =
P M A C _ L o s ( 3 , 3 =)
P M A CL o g ( 4 ' 3 ) =
P M A c _ L o g ( 5 , 3 )=
Pl,lAC
Log(6,3) =
P I I A CL o g ( 7 , 3 ) =
P l ' l A C _ I r o g ( 8 , 3=
)
(1'4) =
PHAC-Log
P M A CL o g ( 2 , 4 ) =
P H A CL o g ( 3 , 4 ) =
P M A CL o g [ , a ) =
P M A C _ l , o g ( 5 , 4 )=
P M A CL o g ( 5 , 4 ) =
P M A C _ L o(g1 , a \ =
PuAc-Los(8'A) =
endif
D1os10(5.4d-08)
DtosL0(5.4d-08)
D l o g 1 (01 . 7 d - 0 6 )
D l o g 1 0( 4 . 4 d - 0 5)
(5.7d-04)
DlosL0
D 1 o s 1(06 . 1 d - 0 3
)
D l o s l 0( 1 . 4 d - 0 2 )
D 1 o s L(01 . 4 d - 0 2)
D I o g 1 0( 1 . 1 d - 0 9
D l o g 1 0( 1 . 7 d - 0 9
D 1 o s 1 0( 5 . 4 d - 0 8
D l o g 1 0( 1 . 6 c 1 - 0 6
Dlogl0 (2. 6d-05
D I o g 1 0( 1 . 9 d - 0 4
DIog10(5.1d-04
D1og10(5.1d-04
D 1 o s 1(05 . 3 d - 1 1 )
DIoslO(5.3d-11)
D I o g l O( 1 . ? d - 0 9)
D1og10(7.0d-08)
D1og10(7.7d-07)
D1os10(6.6d-05)
Dlos10(1.9d-05)
DloglO(1.9d-05)
DIog10(1.7d-12)
D 1 o s 1(01 . 7 d - 1 2)
D 1 o g 1(05 . 3 d - 1 1 )
D1os10(2.7d-09)
D l o s 1 0( 2 . 1 d - 0 8)
Dlos10(3.3d-07)
D I o s l O( 5 . 9 d - 0 7)
D1os10(5.9d-07)
Den=Density/D_ground
D - I o g = D I o g 1 0( D e n )
D o1 I = 1 , 3
I f ( D _ 1 o g . L E .D L ( I ) . a n d . D _ l o g . G E . D L ( I + 1 ) ) K = I
Continue
DoZ I =L, 7
r f ( T f b . G E .T t ( r ) ) ' J = I
Contlnue
Dratio = (D-log - Dt(K) | / (DI'(K+1) - DL(K))
D l . = P M A C - L o g ( . I , K )+ ( D r a t i o " ( P t { A C - L o g ( J , K + l ) - P M A CL o g ( , t ' K ) ) )
D 2 = P H A C _ L o g ( J +, 1K ) + ( D r a t i o * ( P I ' l A C _ L o g ( J + 1 , K + l )(.t+1, K) ) )
I
PMAC_Log
T r a t i o = ( T - f b - T L ( , 1 )) / ( T l "( , t + 1 ) - T L ( J ) )
P M A C _ 1 o 9 1=
0 D 1 + ( T r a t i o * ( D 2 - D 1 ))
P}IAC= 10.0d0 ** PMAC_Iog10
RETURN
END
t9
f nitialize-OutPut
SUBROUTINE
c
c . . - . . s e t s i n i t i a l i n f o r n a t i o ni n h e a d e r sf o r c l a t ao u t p u tt o s c r e e n
C.....and output files.
c
I}4PL1CIT DOUBI,EPRECISION(A-H.M-Z)
inclucle 'conmon.put'
Character water*3, pgrn*25
C h a r a c t e r * 8 M t i m ,l l d a t e
Character*13 sub,sub2
Character*50 Forn, Forml
pgrm
if(water include) then
water = 'Yes'
else
water = 'No '
endif
='FB10.F0R L'I/L1/L986'
CalI Date(Mdate)
CalI Tine (Mtin)
D o 1 0I = 2 , I 0
w r i t e ( I , 2 ) l { , t t da t e , f i l e - n a m e ( I - 1 ) , M ti u t , p g r n , S p e c i e s - n u n , A t n o s ,
* beta, Z_fb, T_fb, entrain, t irnes_upG
, , s i g m a ,i { a L e r
10 continue
write(3,4)
write (4,6)
?'-fb '
TGasMole Tsoll'lole TotalMol
T-fb
Form = ' Tirne
I
K
nrole/kg rnole/kg rnole/kg
s
Fornl='
(
C
h
a
r
g
e
d
)
then
If
If (Species-nurn .I,E. 6) then
' TotChargetl'
w r i t e ( 5 , * ) F o r n ,( N O l 4 ( I ) , , , , I = T , S p e c i e s _ N u m ) ,n
' I=1, Species-num) ' nrole/kg'
wtite (5, *) Forrrl, ( ' roole/kg
,
,
else
w r i t e ( 5 , * ) F o r n , ( N o M ( I ) I, ' , f = 1 , ? )
w r i t e ( 5 , * ) F o r m l ,( ' m o l e / k g
endif
"r=1,7)
endif
If( .not. Charged) then
if (Species-nurn.LE. ?) then
w r i t e ( 5 , * ) F o r m ,( N o l { ( I ) , " , f = l , S p e c i e s - n u n )
w r i t e ( 5 , * ) F o r m l ,( ' m o l e , / k g ' , I = l , S p e c i e s - n u n )
else
w r i t e ( 5 , i ) F o r n , ( N o t ' l ( I,)' ' , f = 1 , ? )
'
w r i t e ( 5 , * ) F o r m 1 ,( ' m o l e / k g
,I=1,7)
endif
enilif
write(6,7)
Time Tfb'
sub =r
K '
s
sub2='
Do 20 .IK = 1'3
( ( . I K - 1 )* 1 1 ) - 1
J = 8 *
If(Species-num .GT. 'J-1 .and. Charged) then
if(Species-num .LE. ,t+10) then
w r i t e ( J K + 5 ,* ) s u b , ( " , N O M ( I ) , I = r J + l ,S p e c i e s - n u r n ) , ' n T o t C h a r g e c l '
write(JK+5,*) sub2,(' nole/kE',t=il{l,Species-nurr+l)
else
w r i t e ( J K + 5 , i) s u b , ( , ' , N 0 1 { ( I ) , I = J + l , i 1 + 1 1 )
w r i t e ( , l K + 6 , * ) s u b 2 ,( ' n o l e / k g ' . I = , 1 + 1 , J + l 1 )
endif
endif
i f ( S p e c i e s _ n u m . G T . , l . a n ( l. . n o t . C h a r g e d ) t h e n
i f ( S p e c i e s _ n u m. l r E . J + 1 1 ) t h e n
write (JK+5,
sub, ( ",NOM (I), I=J+l. Species_num)
")
w r i t e ( J K + 5 ,* ) s u b 2 , ( '
r n o l e / k g ' , I = r l + L .S p e c i e s _ n u m )
e 1s e
w r i t e ( , l K + 5 *, ) s u b , ( '
,1=J+1,,1+1.L)
w r i t e ( J K + 6 , * ) s u b 2 ,( ' " NnooM
l e( /I k) g ' , I = J + 1 , . 1 + 1 1 )
endif
endif
20 Continue
I f ( S p e c i e s _ n u r n. G T . 3 9 . a n d . C h a r g e d ) t h e n
i f ( S p e c i e s _ n u m. L E . 5 0 ) t h e n
w r i t e ( 1 0 , * ) s u b . ( ' ' , N O l l ( I ) , I = 4 L , S p e c i e s _ n u m ) ,n' T o t C h a r g e d '
w r i t e ( 1 0 , * ) s u b 2 ,( ' n o l e / k g r , I = 4 1 , ,S p e c i e s _ n u u r + 1 , )
else
write (0,1)
Stop
endif
endif
i f ( S p e c i e s _ n u m. G T . 4 0 . a n d . . n o t . C h a r g e d ) t h e n
i f ( S p e c i e s _ n u m. L E . 5 1 ) t h e n
w r i t e ( 1 0 , * ) s u b , ( ' ' , N O (MI ) , I = 4 7 , S P e c i e s - n u m )
w r i t e ( 1 0 , * ) s u b 2 (, '
else
w r i t e( 0 , 1 )
mole/kg',1=4L,Species_num)
Stop
endif
endif
w r i t e ( 0 , 8 ) i l , M d a t e ,M t i m ,p g r n , b e t a , Z _ fb , T _ f b , e n t r a i n
RETURN
C--------AI,IJ
THE FORMATSTATEMENTS
c
1 Forrrat('There are too manyspecies in the system lmore than 51]
* ',/, ' See Initialize_Output
S U B R O U T I N EP.r o g r a m n o w T e r m i n a t e c l . '
'
!
)
2 F o r n a t ( t 7 . 4 , ' M e g a t o n B o n r bY i e t d .
Date data taken on ',A8,/,'
Th
*is clata was storecl in file : ',AL2,' at time ',A8,/,' Data generat
*ed from program : ',A25,/.'
Input data read by program frorn file
:
* D.file
Inclutles ',f2,'
S p e c i e s . T y p e o f a t m o s p h e r e, , , A 2 0 , / ,
*' Beta = ',f5,3,' Init Z = ',f.6.4,' Init Tf = ',f6.1.' Entrain = '
t , f 4 . 2 , / , ' T i n r ef o r r u n : ' , f 5 . L , '
* G r a v i t y : ' , t 7 . 5 , ' S i g n a : ' , d 9 . 3 , ' l f a t e r v a p o u r i n c l u r l e c l: ' , A 3 )
4 Forrrat(47x,'f(1) alf(1),u',/,'
Time T_fb
H_top H_bot raal
* cVol
z
speed
ch_z OpTr
R
TotR/ii R/Ro Zdsh
*',/,'
s
K
m
ITr
m
n**3
m
n/s
* m
J/s')
'
6 F o r n a t ( 1 5 x , ' i l f( 1 ) , u ' , 3 3 X , ' d f ( 2 ) , f b
Tirne T_fb speecl
,/ ,'
*cVo1
llass
Den Ddsh Buoyancy
P_amb T_amb fb_N
fb_O
*
fb_H
fb_Ar fb_C TotalHole' , /,
*r
s
* P a
K
m/s
n**3
kg
kS/m3
kg.rn/s2
K rnol/kgnoI/kg nol/kg nol/kg mol/kg nole/kg')
81
df (1) df(2),fb
f (3)',7X,'t(4)
7 F o r m a t ( 1 5 x , 'l f) ' , L z X , ' t Q )
*
T _ a m b M( D d + k )
V.Ddash
e
tlf (3\' , / ,'
Tinre T_tb
z
*nth_fb
dt
enth-amb
Ent
u
Bouyancy
dm
df (4)
*hperkg',/,'
Jou
K
kg
s
n
kg.m/s
K
*Ie
J/s
s
Joule/kg
Joule/
m/s
ks/ s
kg.n/s2
*kg' )
8 F o r n a t l K , f ? . 4 , ' M e g a t o n B o m bY i e l c i . D a t e t l a t a t a k e n o n ' , A 8 , / , ' T
*his data uas stored in files : d?.dat at tirne ',A8,/,'
Data gener
* a t e d f r o m p r o g r a m: ' , 4 2 5 , / , ' B e t a = ' , f 5 . 3 , ' I n i t Z = ' , f 5 . 4 , ' I n
*it Tf - ' ,f6.1,/,'
e n t r a i n = ' , f 4 . 2 , / , 4 6 x , ' f ( L l d f ( 1 ). u '
* , / ,'
z
speed c
Time
cVoI
T_fb H_top H bot rad
*h_z opTr
n
n**3
s
K.
m
n
Ro , ,/ ,,
')
-*
lo
m/s
m
Jls
END
;---------a
SUBRoUTINE
0utput_Data
C...,.Outputs data to screen and output files.
c
IMPIJICIT DOUBI'EPRECISION(A-H.I{-Z)
include 'connon.put'
C h a r a c t e r F o r r u 2 * 4 7F
, o r m 3* 4 1 , F o r m 4 * 4 5 ,F o r m 5* 3 9
w r i t e ( 0 . 1 ) n T o t a l C h a r g e d c, o u n !
r r r i t e ( 3 , 4 ) a t i m e , T _ f b . z i r a d i u s , z - r a d i u s , r a d i u s , c V o 1 ,z . u , c h a n _ Z ,
* O p T r ,R a d i a n t I J o s s ,f ( 5 ) / I n i t i a l _ f b _ e n t h a l p y , d f ( 5 ) / r a d _ l o s s 0 , Z d s h
i { r i t e ( 4 , 5 ) a t i r n e , T _ f b , u , c V o l , l , l a s s ,D e n s i t y , D d a s b ,F b , P _ a n b i e n c ,
* T _ a m b i e n t, n t N , n f O i n f l { , n f A r , n f C , T o t a l M o l e
F o r m 2= ' ( F 6 . 2 , F 7 . 1 , 3 D 1 0 . 3 , X , F 5 . 3 /, '/ c h a x ( S p e c i e s _ n u +
m4 8 )/
*/'D10.3,d10.3)'
F o r m 3= ' ( F 6 . 2 , F 7 . 1 , 3 D 1 0 . 3 , X , F 5 . 3 , 7 D 1 0 . 3 ) '
If (Charged) then '
If(Species_nurn .LE. 5) then
w r i t e ( 5 , F o r m 2 ) a t i m e , T _ f b ,T o t a l G a s M o l e , T o t a l S o I i d M o l e , T o t a l M o l e
* , Z _ f b , ( H o l d n ( I ) , I = 1 , S p e ci e s _ n u m ), n T o t a l C h a r g e d
e 1s e
w r i t e ( 5 , F o r m 3 ) a t i n e , T _ f b , T o t a l G a s f i o l e ,T o t a l S o l i d M o l e , T o t a I M o l e
* , 2 - f b , ( H o l d n( I ) , I = 1 , 7 )
endif
endif
If (.not. Charged) then
if(Species_nun .1,8. ?) then
write (5,6) atine,T_fb,TotalGasMoIe,TotaISolidMole,TotalMole,
* Z _ f b , (H o l d n ( I ) , I = 1 , S p e c i e s _ n u n )
eI se
w r i t e ( 5 , F o r m 3) a t i m e , T _ f b , T o t a l G a s M o l e ,T o t a I S o I i d l 4 o 1 e , T o t a l M o l e
* , 2 _ f b , ( l t o l d n( I ) , I = 1 , 7 )
endif
endif
82
w r i t e ( 6 , 7 ) a t i r n e ,T _ f b , z , T _ a n r b i e n tf, ( 2 ) , f ( 3 ) , f ( 4 ) * M a s s ,u , F b ,
* d f ( 3 ) , d f ( 4 ) , d t , e n t h _ a m b i e n t f, ( 4 )
Do 10 ilK = 1,4
J=8+((,tK-1) ',11)
I f ( S p e c i e s _ n u u r . G T . J - 2 . a n a l . C h a r g e c l. a n d . S p e c i e s _ n u m. L E . J + 9
* ) then
L =Species_num-,J+2
L L = I r - 9
write(0,2) L,LL,J,.tK
if (u..GE.1) then
F o r m 4= ' ( X , F 5 . 2 , F 6 . 0 , 9 d 1 0 . 3 , ' , / / c h a(rt L + 4 8 ) / / ' , d L 9 . 3 , D 1 0 . 3 ) '
else
F o r r n 4= ' $ , f 6 . 2 , F 6 . 0 , ' / / c h a r ( t + 4 8 )/ / ' d L } . 3 , D 1 0 . 3 ) '
endif
, o r m 4 ) a t i n e , T _ f b , ( H o l d n ( I ) , I = J , S p e c i e s _ n u n ) ,n T o t a I C
write (.IK+6F
*hargetl
enilif
IF(Species_num .GT. J-1 .ancl. .not.
't LE. J+10) then
L =SpeCies_nun-.t+1
Charged .and. Species_nun .
L . L = . L - v
if (tL.GE.1) then
F o r m 5= ' ( X , 1 6 . 2 , F 5 . 0 , 9 d 1 0 . 3 , ' / / c h a r ( L t + 4 8 )/ / ' d l l . 3 ) '
else
F o r m 5= ' ( X , F 6 . 2 , F 5 . 0 , ' / / c h a r( L + 4 8 )/ / ' d 7 0 . 3 \ '
endif
write(JK+5,Form5) atime,T_fb, (Ho1dn(I),I=J,Species_nurn)
endi f
If(Species_nun .GT. ,J+9 .and. Charged)
* then
w r i t e ( J K + 5 , 3 ) a t i r n e , T _ f b ,( H o I d n ( I ) , I = J , J + 1 0 )
endif
IF(Species_nun .cT. J+10 .and. .not. Charged ) then
$ r i t e ( J K + 5 ,3 ) a t i m e , T _ f b , ( H o l < I n ( l ) ,I = J , J + 1 0 )
endif
10 Continue
w r i t e ( 0 , 8 ) a t i m e , T _ f b , z + r a d i u s , z - r a d i u s , r a a l i u s ,c V o l , z , u , c h a n _ 2 ,
*OpTr,Radiant Loss
RETURN
c
C=--------ALL
THE FORMATSTATEI1ENTS
1 F o r n a t ( ' O n T o t a l C h a r g e d= ' , D 1 0 . 4 , ' c o u n t = ' , 1 3 )
2
F o r m a t ( 'L = ' , 1 3 , ' L L = ' , 1 3 , ' , J = ' , 1 3 , ' J K =
3
F o r m a t( X .f 5 . 2 , F 6. 0 , 1 1 d 1 0 . 3)
4 F o r m a( tX , t 6 . 2 , f 6 . 0 , t .70 , f 7. 0 ,f 7 . 1 . D 1.14 , f 8 . L , f 7. 2 , f 5 . 1 ,
* f 6 . 3 , D 1 0 . 3 , X . F 5 . 4 , X ,41, 6
1 .5 3
. )
5 F o r m a(tF 7. 2 , f ' 1 .1 , F ? .2 , 2 D I 0 3. , 2 F 6 3. , D 1 0 3. ,F 9 .1 , f 5 . 1 , 5 F 7 3
. ,D 1 0 3. )
5
F o r m a(tF 6 . 2 , F .7L , 3 D 1 03., X , F 53. , ? D l 0 3
. )
f o r m a (t X , F 62. ,F 6 .0 , F 8 .1 , F 5 1. , " , D 1 03. ,D 1 03. , " , D 1 03. , "
',
'
*r5.1,' ',2D10.3.'
,F4.2,'
,DLo.3)
8 r o r n a t( x ,F 5. 2 , F ?. 1" D
, FL?.00.,3F ,7'. 0 . F 5 . 0, " " ,DD190.3., 3
F ,8' .L , F ' .I 2 , 8 6. 1 ,
1F6.2,'"09.3)
END
83
read amb air
SUBRoUTINE
c
C . . . . . R e a d s a n d s t o r e s t h e t h e r m o c h e r n i c a ld a t f o r t h e a m b i e n t a i r
C . . . . . c a l c u l a t i o n s o f e n t h a l p y f r o r nt h e f i I e A l ' l B . A I R -
c
T ] ' I P L I C I TD O U B L EP R E C I S I O N( A - H , M - 2 ,
Logical water-inclucle
i n t e g e r T n u m , N u n b e r - o-f d e s
u n k * 5 ,l i n e * B 0 , A t m o s * 2 0
C H A R A C T EJ R
c o m m o n/ d e t / E R ( 6 ) . c ( 5 , 6 )
r -o f -des
COM)'ION
/ f i ve / en th-ambi ent, TotalMo I e, Numbe
c o m m o n/ h 2 o / w a t e r - i n c l u d e , A t n o s
c o m m o n/ a m b / T n u m ,I S N ( 5 ) , E N T H A(L6 )
SR(6)
DIMENSION
30
20
10
write(0,101)
r e a d ( 1 2 ,* ) T n u n .( I s N ( I ) , I = 1 . T n u m )
w r i t e ( 0 , * ) T n u m (, r s N( r ) , 1 = l , T n u m )
w r i t e ( 2 , * ) T n u n , ( 1 S N( I ) , I = l , T n u m )
Do10I=l,Tnum
'amb.air',status='old')
O p e n ( u n i t= L l , f i l e =
Do 20 J = 1,5
if (IsN(I) .EQ. J) then
r e a d ( 1 1 , 1 0 2 )J u n k . E R ( I ) , S R ( I )
w r i t e ( 0 , 1 0 3 ) . I u n k , E R ( I .) S R ( I )
r e a c l ( 1 1 , 1 0 4 )l i n e
w r i t e ( 0 , 1 0 5 )l i n e
r e a d( 1 1 . 1 0 4 ) l i n e
' * r r i t e( 0 . 1 0 5 )l i n e
r e a d ( 1 1 , 1 0 6 () c ( I , K ) , R = L , 6 )
w r i t e ( 0 , 1 0 7 )( c ( I , K ) , R = l , 6 l
r e a d( 1 1 , 1 0 4 ) l i n e
w r i t e ( 0 , 1 0 5 )l i n e
E N T H A L ( I )= E N T H ( I , I C M P )* 4 . 1 8 6 D + O O
w r i t e ( 0 ,1 0 8 ) T , E N T H A L ( r )
else
d o 3 0 K = 1 , 5
read(11,104)line
continue
endif
continue
close (unit=L1)
conti.nue
RETURN
C-------ALI.
c
STATE}IENTS
THE FOR}TAT
'
1 0 1 F o r m a (t ' E n t e r t h e n u m b e ro f g a s e o u sm o l e c u l e s t o b e e n t r a i n e d ,' )/
*
,' followetl by the nolecule nunber lseparatedby spaces] .. 1 0 2 F o r r n a(tA 5, r 1 1. 2 , F 8. 3)
L 0 3 F o r m a(tX , 4 5 , F 1 12 ., F 8 .3 )
1 0 4 F o r m a (t l )
1 0 5 F o r r n a(tX ,A )
1 0 5 F o r n a t( 4 D 1 2 . 62, F 1 02. )
2 ,F f 0 . 2 )
1 0 ? F o r m a(tX , 4 D 1 2 . 5
1 0 8F o r m a t ( E
' N T H A L ( ' , f l ,=
' )' , d 2 0 . 1 4 )
END
84
SUBROUTINE
reaal_in_CHNOS
l.
C . . . . . R e a d s a n c l s t o r e s a l l t h e t h e r n o c h e r n i c a ld a t a f o r t h e s p e c i e s
C.....in the fireball from the file NEIIDATA.DAT.
c
IMPIJICIT DOUBI,EPRECISION(A-H,O-Z)
c
c
Logical Chargecl,Setting_up, momen!um_stop
C H A R A C T EERL A * 2 , E I J F * 2 , E L N * 2 , A N F * 8 0 , N O U * 9 , c h
Tnteger Species_num
DIHENSIOE
N L A( 5 0 , 6 ) , A T A( 5 0 , 6 ) , N E A( 5 0 ) , E L N( 5 0 )
D I M E N S I OD
N A( 5 , 6 ) , E I . F( 5 0 ) , A T F( 5 0 )
DIMENSION
IN(50)
( 5/ A
c0Hr,r0N/AAA
0 , 1 0 ) , A K T( 5 0 ) , A K T F( s 0 ) , B ( 1 0 ) , B 0( 1 0 ) . C ( 5 0 )
C O M I . I O N / BIBVBA/R ,K H( 2 O) , t , 1 1 , I ' I ,} I 1 ,M A ,M B ,M P ,M S ,M F( 1 5) , I , I L( 1 5)
C o D 1 M O N / C C(C2l0p)r, p T o T ,T , y ( 5 0 ) , y o ( 5 0 ) , y r ( 5 0 ) , y r o r ( 2 0 )
C o H H o N / D A T (/ 5
C01, 5 ) , C 2( 5 0 ,5 ) , c 3 ( 5 0 ,5 ) , c 4 ( 5 0 ,5 )
50
C 0 I { M o N / D A T /(H
R) , S R( 5 0 ) , N R( 5 0 ) , H H( 5 0 , 5 ) , T M( 5 0 , 5 )
C o m n o n/ m s l / S p e c i e s _ n u m , N O l , l ( 5 0 ) , N S , N P S , N N S , N s o I S , N g a s s
connon /xaa/ MC,tlR
connon /eight/Charged, Setting_up,nonentum stop
CoMI{oN/NIN
J L , J 2 , J 3 , J 4 , , J 5 ,J 6 , J 7
/E
a
C
( U N I T = 1 3F
. ] L E = ' N E I . I D A TDAA. T S T A T U S = ' O L )D '
OPEN
"
ENTERTHE SPECIESTO BE USED
I
c
C
C
C
C
w r i t e ( 0 , 1 0 1)
The input data is read on all species. MS j,s the total number of
species to be reaal. NS is the number of non charged species. NpS
is the number of possitively charged species. NNSis the nunber
of negatively charged species.
READ(12,*)MS
( 1 2 ,* ) N g a s S
READ
(J),J=l,NS)
R E A (DL 2 , ' t )N S ,( I N ( , I ) , N o M
R e a d( 1 2 , 1 0 2 )A N F
Read(12,*)ch
T{RITE(2,103)MS
IIRITE(2,104)NgasS
w R r ? E ( ? *, ) N S , ( r N ( . t ) , N o M ( , r ) , J = ,1N S )
n r l t e ( 2 , 1 0 2 )A N F
w r i t e ( 2 , 1 0 5 )c h
C h a r g e d= . f a 1 s e .
if (ch .eq. 'y' .or. ch .eq. 'y') then
Charged = .true.
( , t ) , J = N S + LN, S + N p S )
R e a d( 1 2 , * ) N P S ,( I N ( J ) , N O M
I { R I T E( 2 , * ) N P S ,( I N ( J ) , N 0 1 { ( . I ) , J = N S + 1 , N S + N P S )
R e a d( 1 2 , 1 0 2) A N F
write (2,102)ANF
( . 1 ) ,i t = N S + N p S +N
R e a d( 1 2 , ' t ) N N S ,( I N ( , t ) , N O M
1S
, + N p S + N )N S
(J ) , , I = N S + N P S + N
I I R I T E( 2 , * ) N N S ,( I N ( , 1 ) ,N O M
1 ,S + N P S + N)N S
Read(12,102)ANF
w r i t e ( 2 , 1 0 2) A N F
endif
if(ch .eq. 'n' .or. ch .eq. 'N') then
R e a d ( 1 2 , 1 0 5 )N P S , N N S
85
I I R I T E ( 2 , 1 0 5 )N P S , N N S
write(0,10?) NPS,NNS
endif
( , I ) , J = N S + N P S + N N SN+S
R e a d( 1 2 , * ) N s o I S , ( I N ( , t ) , N O M
I ,+ N P S + N N S + N s o I S )
I { R I T E( 2 , * ) N s o I S , ( I N ( . t ) , N o M( J ) , r I = N S f N P S + N N SN
+S
1 ,+ N P S + N N S + N S) o I S
Read(12,102)ANF
I { R I T E( 2 , 1 0 2 ) A N F
I F ( N S + N P S + N N S + N S o. INSE . M S ) t h e n
w r i t e ( 0 , 1 0 8)
stop
endif
R E A D ( 1 21 ,0 9 ) , J 1 , , t 2 J, 3 ,J 4 , J 5 , J 6 , J 7
l { R r T E ( 2 L, L 0 ) J L , J 2 , J 3 , J 4 , J 5 , J 6 , J 7
READ(12,102)ANF
I{RITE(2, 102) ANF
w r i t e ( 0 , * ) l { s , ( I N ( , t ) , N 0 l .( 1. 1 ) , J = 1, } I s )
Species_nun = MS
REI{IND13
NREC=0
10 REID(131
, 11.END=35)NE,NN,ND,DH,DS
NREC=NREC+1.
) T F ( J ) ' , 1 = 1' N E )
R E A D ( 1 3 ' 1 1 2()E I , F ( . 1' A
( 1 3 , 1 1 3 )A N F( 1 : N N )
READ
D0 15 .I=1,ND
15
R E A D ( 1 3 , 1 1 4( D
) A ( , t , K,)K = 1 , 6 )
C
STORESPECIES DATA IN }IE$ORY
c
20
D0 30 I=1.I{S
I F ( N R E C . E Q . I N ( I ) )T H E N
D0 20 J=1,NE
ELA(I,J)=ELF(J)
ATA(I,.I)=ATF(J)
CONTINUE
NEA(I) =NE
HR(I)=DH
s R( I ) = D s
25
N R( I ) = N D
DO 25 .I=1,ND
C l ( I , J ) = D A( J , 1 )
C2(I,,J)=DA(,I,2)
C 3( I , . I ) = D A ( J , 3 )
C 4( I , J ) = D A( J , 4 )
TM(I,J)=DA(J.5)
111
s 1 ,g ) = p A( J , 6 )
CONTINUE
coTo10
ENDIF
3O CONTINUE
GoTO 10
86
e
COUNTELEMENTS,GASESAND CONDENSED
SPECIES
35
L=0
l,lG=0
MR=0
D0 50 I=1,MS
I F ( E I , A ( I , N E A ( I ).)8 9 . ' G ' ) T H E N
MG=MG+1
EI,SE
MR=MR+1
ENDIT
N=NEA(I)-1
D0 45 J=l,N
IF (L.Eq.O) THEN
t=L+1
E L N( L ) = E L A( I , J )
c0T0 45
EIJSE
D O 4 0 K = 1 ,L
r F ( E r . A ( r , J ) . E Q . E r N ( K )c) o T o 4 5
40
CONTINUE
L=L+1
E t N ( t) = E L A ( I , . I )
END]F
45
CONTINUE
5O CONTINUE
LL=L+1
H1=MG+L
MP=1
MF(1.)=1
Mt(1)=Mc
I { R I T E( 0 , 1 1 5 ) t , M G , M R
C
c
SET UP ATOMMATRIX
D0 55 I=1,MS
DO 55 K=I,L
55 A(I, r) =9.
D0 55 I=I,MS
N=NEA(I)-1
D0 50 ,I=l,N
DO 60 K=1,L
I F ( E L A ( I , . t ) . E g . E t N ( K) ) A ( r , K ) = A T A ( r , J )
5 0 CONTINUE
I { R I T E ( 0 , 1 1 6 )I , ( A ( I , K ) , K = l , L )
5 5 CONTINUE
close(13)
RETURN
C--------AIIJ
THE FOR},IAT
STATEffENTS
1 0 1 F o r n a t( ' E n t e r t h e n u m b e ro f s p e c i e s t o b e p r o c e s s e d ,f o l l o w e d ' , /
* , ' b y t h e s p e c i e s n u m b e ra c c o r t l i n g t o t h e N E I T D A T A . Dt aAbTl e , , , / ,
* ' a l l n u n b e r s i n i n t e q e r f o r m a n d s e p a r a t e db y
a space. ',/,
* l
r \
1 0 2 F o r n a t( x , A )
1 . 0 3F o r n a t ( ' M S= ' , 1 2 , '
1 0 4 F o r m a t ( 'N g a s S= ' , T . 2 , '
1 0 5 F o r m a(tx , A 1 ,'
: Total species nunber. ')
: T o t a l g a s e o u ss p e c i e s n u n b e r . ' )
: C h a r g e ds p e c i e s i n c l u d e d [ y / N ] . ' 1
6t
1 0 5 F o r m a(tI 3 , / / , ! 3 , / )
',13)
' P S= ' , 1 3 , ' N N S=
1 0 ?F o r m a t ( N
1 0 8 F o r r n a t ( ' T h e c h a r g e da n d n o n - c h a r g e ds p e c i e s ' l o n o t s u m t o " M S' ,"/' '
* ' 1 , / , ' 1 t h e n u m b e ro f t o t a l s p e c i e s . C h e c kD . f i l e , t h i s p r o g r a m
* ' i s n o wt e r m i n a t e d . ' )
1 0 9 F o r n a t( ? ( 4 x ,I 1 ) )
F o r m a t (C
' = ' , 1 1 , 'l l = ' , 1 1 , 'N = ' , 1 1 , '0 = ' , 1 1 , ' S = ' , 1 1 , 'A r = " 1 1 " E
1.10
*=,,11)
3 r 2 ,F 1 1 .2 , F 8 .3 )
1 1 1 -r O R l t A( T
1 12 F O R M (A1T0( A 2 ,F 5 . 3) )
113 FORUAT(A)
( 4TF 1 2 . 02, F 1 0 . 0 )
114FORUA
',12,' CONDENSED
',12,' GASES
1 1 5 F O R ] ' I A T (E/ 'L E I ' I E N T S
(
2
X
,
(
I
X
,
I
2
,
1
0
3
)
F5. )
"12)
115FORMAT
END
c---------read-in-data
SUBRoUTINE
C.....Readsalt the initial
conditions fron the input file D'FIL'
t.
P R E C I S I O N( A - H ' M - Z )
IMPLICIT DOUBI,E
inclucle
' comnon.
Put
'
C h a r a c t e r * g M t i m , l { d a t e ,c h i l
DMFAr
DMF02,DMFCo2,
Comrnon/now/ DMFI'I2,
'd.file',Status = 'old')
o p e n ( 1 2 , f i 1 e=
Reuind 12
R e a d( 1 2 , 1 ) c h , t i m e s - u p , b e t a , G , e n t r a i n , i n i t i a l - a l t '
w r i t e ( 0 , 2 ) c h , t i m e s - u p , b e t a , G ,e n t r a i n . i n i t i a l - d t '
nolfientun-stop = .true.
i f ( c h . E 9 . ' Y ' . o R . c h . E Q . ' y ' )t h e n
monentun-stop = .false.
else
) ' then
if (ch.NE.'N'.AND.ch.NE.'n
write (0.3)
stop
endif
endif
ini tial-f
initiaL-f
z,k,last-count,mwa,signa'Atnos
Read(12,3) initial
write(0,4) initial-z,k,1ast-count,nwa,signa,Atnos
write (0, 5) Number-of-cles
D o 1 0 0 1 = L , 9
R e a d ( 1 2 ,6 ) f i I e - n a m e( 1 )
write (0,7) I,fi1e-name (I)
' n e w ' , R E C L= 1 3 0 )
open(I+1,file = file-name(I),Status =
100 continue
b-tenp
b-temp
C a l I D a t e( l l d a t e )
C a I l T i m e( M t i m )
write(2,8) Mtim,Mdate
w r i t e ( 2 , 2 ) c h ,t i r n e s _ u pb, e t a , c , e n t r a i n , i n i t i a l _ d t , i n i t i a l _ f b _ t e n p
write (2,4) initial_z,k,Iast_count,rnwa,sigma,Atmos
w r i t e ( 2 , 5 ) N u n b e ro f c t e s
do 110i=1,9
write(2,7) I,fiIe
110 continue
r e a d ( 1 2 , 9 )l i
write (0,10) i{
w r i t e( 2 , 1 0 ) l i
narre(I)
vrite (0,11) initial_f b_ternp
R e a d ( 1 2 , 6c) h
write(2,12)ch
write(0,12)ch
water_include= .true.
if (ch .eq. 'N' .or. ch
w a t e r _ i n c l u d e= . f a 1 3 e .
else
if (ch .ne.
w r i t e ( 0 , 1 3)
'n' ) then
.and. ch .ne. 'Y') then
stop
endif
enilif
write(0,15) initial z
Read( 12, 19) Dl,lFN2
DMFCo2,
DMFAr
, DMF02,
write (0,20) DMFN2,DMFO2,DltFCo2,DMfAr
w r i t e ( 2 , 2 0 ) D M F ND
2 ,M F o 2
D,M F c o 2 , D M F A r
TDHF= Dl'lFN2+ DMF02+ DMFCO2
+ Dl,lFAr
i f ( T D M F. N E . 1 . 0 d 0 ) t h e n
write(0,21) TDI4F
Stop
endif
RETURN
1 F o r n a (t / x , A l , / x , f 5 . L , / x , f 4 . 2 ,/ x , f j . 5 , / x , t 4 . 2 , / x , f 4 . 2 ,/ x , f 6 . I )
F o r n a t ( ' T i m e s t o p e l s e n o n e n t u rsnt o p [ y / N ] : , , A L , / ,
1 ' C o m p u t esrt o p t i n e : ' , f 5 . 1 , / x , ' b e t a ' , 1 G x , , : ,, , f 4 . 2 ,
2 / x , ' G t a v l t y ' , 1 3 x ,: '' , f 7 . 5 , / x , ' E n t r a i n c o e f f i c i e n t : , , t 4 . 2 , / x ,
3 ' I n i t a i l _ i l t ' , 1 0 x , 'z ' , t 4 . 2 , / x , ' I n i t i a l _ f b _ t e m p5' ,x , ' : ' , f 6 . 1 )
3 F o r m a(tx , f 7 . L , / x , f . 3 . 1 /, x , I 5 , / x , F 8 .5 , / x , d 9 .3 , / x , A 2 0 )
4 F o r n a t ( I' n i t i a l _ z ' , L L x , ' : ' , f 7 . L , / x , , k , , 1 9 :x' , 'f 3 . 1 ,
I / x , ' I a s t _ c o u n t ' , 1 . 0 x , '' :, I 5 , / x , ' M l r w e i g h ta i r , , G x , ' : , , F 9 . 5 ,
2 / x , ' s i g n a ' , 1 5 x:,' ', d 9 . 3 , / x ' A t n o s p h e tr ye p e ' , 5 x , :' ' A 2 0 )
5 F o r n a t ( ' N u n b e r _ o 1 _ 6=s'5, 1 1 )
b F o r n a t( x , A )
I F o r m a t ( x ' 0 u t p uF
t i l e N a r n *e' , 1 1 , ' : ' , A 1 2 )
I F o r r n a t ( 2 0 X , ' F b o m b s 8 1 .:d a
Cto p yo f i n p u t f i l e ' , D . f i I " . p r o d u c e da t
1 'rA8,' on 'rA8)
9 Fornat(x,f6.3)
1 0 F o r n a t ( x , ' B o nsbi z e
, ',t6.3,' Mt. ')
1 1 F o r n a t( ' i n i t i a l _ f b _ t e m p = ' , d 1 4 . ' 8 )
12 Fornat(X.41.15x,': llater vapour inclucledin anbient air calculatio
*ns [Y/N] ')
1 3 F o r m a t ( ' C h e c k" d . f i l e " a s a " y " o r " N " d o e s n o t a p p e a r c o r r e c t l y
*,)
1 5 F o r n a(t'
B o r n db e t o n a t i o nh e i g h t i s ' , d 1 0 . 4 , ' m e t r e .
')
89
1 9 F o r m a t ( x , f 8 . 6 ,/ x , f . 8 . 6 , / x , f 8 . 5 , / x , f 8 . 6 )
set of dry air
20 Forroat (' the nole fractions of the CI,EAN-FIREBALL
* ate:.',f,
'DMFN2
*
,D16.10 ,/,
'DMF02
*
,D15.10 ,/,
' DMFCo2
*
....
,/,
' DMFAr
i
. . . . '",DD1156..1100 )
2L Fornat('TDMF should equal 1.00, but instead it equals',D15.10,'.
')
* This program is now terminated. Check the data fiIe "d.fiIe".
END
c---------c
SUBROUTINE
DO_enth_halt
write (0,10)
' Enthalpy Error
10 Fornat (
StoP
RETURN
END
')
c---------c
ShowStatus
SUBROUTINE
(A-H,}'I-Z)
IMPIJICITDOUBIJE
PRECISION
Integer counter
c o n n o n/ s i x / a t i m e , l l a s s ,P _ a m b i e n tr,a d i u s , T _ a m b i e n tT, _ fb , z , Z _ t b
common
, nthalpyJer_kg
/ s e v e n / e n t h _bf 3 e r _ M a s s E
c o n m o n/ U S E / E n t h a( 2l 0 0 0 ) , t e n p e(r2 0 0 0 ) , c a l a , c a l b , c a l c , c o u n t e r
w r i t e ( 0 , 1 0 ) T _ fb , e n t h _ fb 3 e r _ M a s s / M a s s
D o 3 0 I = ( c o u n t e r- 1 0 ) , e o u n t e r
w r i t e ( 0 , 2 0 ) I , E n t h a l( I ) , I , t e m p e r( I )
30 continue
w r i t e ( 0 ,4 0 ) E n t h a l p y j e r - k g
St o p
RETURN
1 0 F o r m a t ( 'T _ f b = ' , D 1 0 . 3 , ' e n t h = ' , D 1 0 . 3 )
2 0 F o r m a t (E
' nthal(',13,'=
) ' , D 1 0 . 3 , 'T e n p e r ( ' , 1 3 , '=) ' , D 1 0 . 3 )
4 0 F o r n a t ( ' E n t h a l p y 3 e r - k g= ' , D 1 0 . 3 )
END

Stage of a Nuclear Fireball - CSIRO Research Publications Repository

Transcription

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