" User aust —S_|
~ TON
whe —-- 2 -- =
\
\

Upey Ls}, 62401 ns], 272 (Mig * Mya) Maa
3

10? (Mra = Menai | A
7

10°
0 0.05 ot 0.15 | 02
tis} tounsr=0.173S

Figure 17. Plots of Uyep dZ/dt,
and éZ/dt, Z/Z,, and of Mxz,

and Z/Z1, for t= 0
- Myra)! Myo for t

200 -—
2000
Par
% 1500 \
& \
a \
a® 1000 ~
a
500
0 1 .
0 02 04 06 08 | 1
t{s]} teyast=0.940S

and Pyy fort 2 0 and Do

Figure 18. Plots of Ppy
25x10"m", Toy: = TH

0.0005m; where Vit =

man

> tegpegs where Vir = 2-5x10%m, Do = 0.0005 Tpy, 294K) Pow = 34.47x105Pa (S00psi), Parr
= Typ = 294K, Ppys = 3447x10°Pa (S00ps!), Pera = 155.13x10Pa (2250psi), Pyursr = 4482x10°Pa (650psi).
155.13x10'Pa (2250psi), and Pgygst = 37-92x10"Pa
(550psi).
4
10 _' oo azrat
=
z pore eee
Fier ~ User
: ~
gabe mat) g a
= : 1
8 3 — Rio" ‘“
8 =
ra _ z \
= £
2 3 a \
2 10 \
= (Murs Muze)/Mwre 2027
o woo
1 10°
© 02 04 06 08 {1 0.935 0.945 0.95 0.955 0.96
tls} teunst=0.940s teunsr=0.9405. t{s}
Figure 19. Plots of User aud éZ/at fort = 0 and Do = Figure 20. Plots of Uyep 4Z/dt, ZZ and M2 -
0.000Sm; where Vip = 25x10%m’, Toy, = Tart Murs) Mya for 2 taurst and Dg = 0.0005m; where

294K, Poy, = 3447x105Pa (S00psi), Perma

155.13X10¢Fa (2250psi), Paypsr = 44-82x10°Pa (650psi).

548

Var = 2.5xi0%m", Toys
34.47x105Pa (S00psi), Perr

and Pypsr = 44.82x10°Pa (650psi).

‘HT 294K, Pov =
= 155.13x10°Pa (2250psi),


542

procedure which both 1) simulates de-pressurization of a field-deployed discharge vessel and 2) allows for acquisition of data,
including high speed photography, to chracterize adequately the discharge process. Second, to evaluate the discharge
characteristics of a wide range of alternative-agent/pressure-vessel configurations, thereby extending the slow and relatively
costly experimental method of making such evaluations. Finally, to predict exit flow conditions to be used to solve the
problem of agent dispersal outside of the discharge vessel. The model is based on the experimental configuration depicted
in Figure 1, and the solution method is capable of treating arbitrary choices of geometric parameters, material properties,
and initial conditions.

The model was used in example calculations which address the first of the applications, viz., the establishment of a robust
experimental design and procedure that would 1) simulate the discharge of field-deployed fire extinguishment systems useable

in US Air Force aircraft and 2) meet additional experimental constraints consistent with a program at NIST in support of
the US Air Force fire safety issues.

In the example calculations, the fixed parameters which characterized the system were a half-liter discharge vessel with a
circular exit nozzie/orifice of diameter 0.01905m half-filled with Freon 22 in the liquid phase at "room temperature,” 294K.

‘The deployed system was assumed to be pressurized with Nz to a total pressure of 41.37x10°Pa (600psi), where the exit
nozzle/orifice is closed with an explosive cap which is released "on demand." In the experimental system, the exit nozzle/orifice
is capped with a disk which ruptures at an a priori-unknown pressure, between '37.92x10°Pa (550psi) and 44.82x10°Pa
(650psi).

The experimental system, is brought to the rupture/ourst pressure, Paurst from an initial pressure Ppy, by a process of
pressurization by flow from the holding tank which is initially filled with N5 at some pressure, Pry). higher than Ppypst-
‘The holding tank communicates with the discharge vessel through a circular orifice of diameter Do-

The model was used to simulate the discharge of the deployed system and of the experimental system. Experimental
parameters that were varied were Poy {9.38x10°Pa (136psi or 34.47x10°Pa (500psi)};, Pim and the volume of the holding
tank {51.71x10°Pa (750psi) and 25xi0%m>, or 155.13x10°Pa (2250psi) and 25x10 ; and Do (0.005m, 0.001m, or
0.0005m).

Results of the simulations were presented in Figures 6 - 24.

Based on the model calculations it was determined that with Poy = 9.38x10°Pa (136psi) or 34.47x10°Pa (500psi) an
experimental configuration/design using the relatively low-pressure (51.7 '1x10°Pa (750psi)}, large-volume (2.5x103m?), holding
tank and the smallest-diameter (0.0005m) orifice ‘would accurately simulate the discharge of the field-deployed system.
Furthermore, it is expected that such a design is robust in the sense that it would also simulate well the field-deployed system
even when extended to a range of parameters and agent materials well beyond the scope of the present calculations.
Model calculations also indicated that an experimental design which uses the large-diameter orifice (0.005m) and/or the
relatively-high pressure small-volume holding tank (155.13x10°Pa (2250psi) and 2.5x10°°m3} would often not provide accurate
simulations of field-deployed discharges and would never be expected to be “robust.”

Validation of the model requires experimental confirmation of model predictions.

ACKNOWLEDGEMENT

The author acknowledges the support of the U.S. Air Force Wright Patterson Laboratory in carrying out this investigation.

REFERENCES
fy Shapiro, A.H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Volume 1, Ronald Press, New
York, 1953

(2) Model, M. and Reid, R.C., Thermodynamics and. Its Applications, Prentice Hall, Englewood Cliffs, NJ, 1983.
(3) Kim-E, M.E. and Reid, R.C., The Rapid Depressurization ‘of Hot, High Pressure Liquids or Supercritical Fluids,
Chemical Engineering at Critical Fluid Conditions, Paulaitis, M.E. et al, Eds., Ann Arbor Science, pp. 81-100, 1981.


where Cp o is the (compressible) flow coefficient for the orifice (1).

Flow Across the Nozzle/Orifice

~ CoAn[2atPpv - Pawn)? — if Pama & Psp
dMpyar/at = - (8)
~ CowAnl2ar(Ppv - Psp)] if Pama < Psp

Where Cp», is the flow coefficient for the nozzle/orifice and Pep is defined below. Assuming that Ax/Apy << 1 in discharge
vessels of interest here, in Eq. (8) the kinetic energy of the liquid upstream of the exit nozzle is neglected compared to the
Kinetic energy at, and immediately downstream of the nozzle.

DEFINITION OF Psp AND COMMENTS ON EQ. (8)

In Eq. (8) it is assumed that the liquid in the discharge vessel, at state (I; P] = {Tap Ppv > Psar(Tay)), flows into and
through the exit nozzle/orifice while moving along state paths of constant entropy. When the pressure of the liquid drops
below its saturation pressure, the liquid is assumed to initiate its movement into the “vapor dome” as a metastable super-
heated liquid.

For the generic pure material, the relevant P-V diagram which depicts the metastable states is sketched in Figure 2, This
includes the region of metastable super-heated liquid states and the correspording region of metastable subcooled vapor
states. For a pure material the metastable liquid or vapor state can only be maintained where (aP/8V) | < 0 [2], Le., only
outside the locus of points, referred to as the spinoidal curve, where (4P/aV)|-7 = 0. The spinoidal curve, sketched in Figure
2, passes through the critical state and has the superheated liquid region to its left and the subcooied vapor region to its right.

At any time during the discharge, Psp is defined as the particular pressure along the liquid-leg of the spinoidal curve of the
test agent associated with the intersection of the spinoidal curve and the above-mentioned, instantaneous, constant-entropy
paths. Since states along the spinoida! curve are states of unstable equilibrium where spontaneous nucleation will occur (2,
3}, ic. the constant-entropy metastable-state path of the tiquid cannot be sustained at the state defined by the intersection
point, it is conjectured that if Psp > Paygp violent flashing of the liquid jet occurs where and when its pressure reaches Pcp.
This would be upstream of a physically-unachievable, i.e., unstable, vena contracta at pressure Pawn.

If Pau is achieved prior to the Psp state then the top portion of Eq. (8) is used. For this circumstance the constant-entropy
State of the possibly metastable superheated tiquid at P, 'AMB !S a physically-admissible endpoint to the liquid-jet development
process. The situation is consistent with the idea that: 1) the endpoint state coincides with the vena contracta of the jet; 2)
the jet is convected for some distance downstream of this endpoint without substantial changes and at the vena coniracta
diameter; and 3) the jet eventually breaks apart due to fluid-dynamic and/or thermodynamic (flashing) instabilities. Note that
the upper Eq. (8)-description of the nozzle flow rate of a superheated liquid as an incompressible, non-flashing fluid, is
consistent with results reported in the literature, ¢.g., [4], for flow through sharp-edge orifices and short nazzles.

If Psp is achieved prior to Payg then flashing of the metastable liquid will be initiated immediately downstream of the
Position in space where the intercept occurs. In the latter case the incompressible flow calculation methodology is still
applicable at and upstream of the spinoidal-curve intercept point. This is indicated by the use of the bottom portion of Eq.
(8).

‘The above discussion is illustrated with CO . For stable and metastable liquid CO, a sketch from [3] of constant-entropy
paths in a P-T diagram is presented in Figure 3. In preparing this figure, the Peng-Robinson equation of state was uscd in
[3] to describe the metastable liquid CO2.

First assume that liquid CO, is in a Figure 1-type discharge vessel at Ppy = 70x10°Pa and Tay = 288K. In Figure 3 this
initial state is seen to lie on the s = s2 constant-entropy line, which has no positive P intercept with the spinoidal curve. As
the liquid CO. flows toward and then out of the vessel’s nozzle/orifice its state is assumed to move downward along the s2
curve of Figure 3. As can be seen, the P = Pany = 1x10°Pa intercept on this curve, corresponding to T ~ 277K, represents
an achievable metastable liquid state for the material. This is the metastable liquid state that is predicted by the present
model. It would be expected at, and for some distance downstream of, the jet’s vena coniracta.

533


2000 fy
= OT TY be
=
= \

1000
é \

Pow

500 eee

0 .

0 | 0.005 0.01 0.015 0.02 0.025

tauast#0.00173 ts}

Figure 21. Plots of Ppy and Pyp for t 2 0 and Do =
0.005m; where Var, = 2.$x10%m®, Toy: = Typ, = 294K,
Poy: = 34.47x10°Pa (500psi), Py, = 155.13x10°Pa
(2250psi), Paypsr = 37.92x105Pa (S50psi).

2500
2000
\
< \
z 1500 ve
a

w1000f =~

\
0
Q 0.005 0.015 0.02 0.025 0.03

teunsr=.00940s —t[s]

Figure 23. Plots of Ppy and Py for t = 0 and Dg =
0.005m; where Verp = 2.5x10m*, Toy, = Typ, = 294K,
Poy, = 34.47x10Pa (S00psi), Prt 155.13x105Pa
(2250psi), Paygst = 44.82x10Pa (650psi).

2

U sey [m/s], ZAK [m9], 272). (My ~ Myr) Mya g
a
T

tof | 7“ (Mae Mvee\/Maae

0 0.005 0.01 0.015 0.02 0.025

teunsr=0.00173s ts]

Figure 22. Plots of Uygp 4Z/dt, and Z/Zi, for t = 0
and dZ/dt, Z/Z,, and of (Myz-Myzg)/ Myog for t
2 tgupsrs Where Ver = 2.5x10%m’, Do = 0.005m, Thy,
= Tyr = 294K, Poy, = 34.47x105Pa (S00psi), Pyrry =
1S5.13x10°Pa (2250psi), aud Pgygsp = 37.92x10°Pa
(SSOpsi).

10?
z
A
= 10!
=
Soh Bl _
= ~~
Ss ~
8 107 MM
3 eo
+ ; y S (tha Mcallen
0 0.005 0.015 0.02 0.025 0.03

teursr=0.0094s t {s]
Figure 24. Plots of Uygp dZ/dt, and Z/Z1, for t 20
and dZjdt, Z/Zy, and of (Mx; - Myzg) Myag fort
2 tgupsri Where Visp = 2.5x10m?, Do = 0.005m, Thy,
= Tyry = 294K, Poyy = 34.47x10°Pa (500psi), Prey =
155.13x105Pa (2250psi), and Pyygsp = 44.82x10°Pa
(650psi).

349


546

Zz 10 dzidt

2

Bie} — 22

z Tae
3 a

= 107 ae \
2 7° Wra- Maas

2

2.

0 - 0.005 0.01 0.015 0.02 0.025

ttyuner [8]
Figure 9. Plots of Uyen aZ/dt, ZZ, and My:
Myzp)/Myop for t= taypsrs Where Vier = 2.5x10"m5,
Tov = Tas = 294K P, = Psar = 9-38x10°P8
(136psi), Prt = SL7ixioPe (750psi),  Pauast
37.92x10Pa (550psi) and Do = 0.005m.

2

. aziat

Pop - Hu

S10 User

= Tse

Z 9" ze ~ N

y

z 107 \

§ _

, _

— 3 °

% 10 a

rr LY (Mua * Mores) Mi2.8

10“
0 0.005 0.01 0.015 0.02 0.026

t- Guner (81

Figure 10. Plots of Ujep AZ/dt, Z/Z, and Mig
Myop)/Myog for t & tpupsrs Where Virr = 25x10",
Tova = Tam = 294K Pov = Pear = 9-38x10°Pa
(36psi), Pym, = SL7LL0°Pa (750psi), Paurst =
44.82x105Pa (6S0psi) and Do = 0.000Sm.

107 750 |
2 Wer
a ~ -- 700
= 10° dZiat 1.005
= 00
= - 7m P.001m —_gn0.0005m
= Zz 650
ath 2 :
£ = 600
3
8 1
= 10 -
3 A \ 550 —— Po |
3 Y (Maa > Mies Mw \ — — Px |
10? 500 a
0 0.005 0.01 0.015 0.02 0.026 0 0.5 1 1.5 2
t-tyuasr §] ¢<bounsr 5}

Figure 11. Plots of Ujey AZ/dt, Z/Zy and Mya >
Myzp)/Myap for t 2 taypori where Virr = 25x10" n°,
Tow = Tam = 294K, Pova = Psar = 9.38x10°Pa
(136psi), Pury = 51-71x10°Pa (7S0psi), Peurst =
4482x10°Pa (650psi) and Do = 0,005m.

Figure 12. Plots of Ppy and Pyy for 05 t = taurst and
Do = .0.00Sm, 0.001m, and 0.0005m; where Vert. =
2.5x10%m’, Toya = Tur = 294K: Pov = 34.47x105Pa
G00psi), Pyqy = S1-71x10%Pa (750psi), Paurst =
44.82x105Pa (650psi).


538

Vur = 2.5x10°3m? is chosen to be ten times larger than the initial gas volume in the discharge vessel and Pry, =
51.71x10°Pa (750psi) is chosen to be 6.89x10°Pa (100psi) greater than the maximum of the diaphragm burst pressure which
can fall within the range 37.92x10°Pa < Paypsr < 44.82x10°Pa (550psi < Paurst < 650psi).

‘The objective in the present choice of parameters is to provide for a pressurization process which is slow enough to minimize
disturbances of the liquid/gas interface, i.e. satisfy Eq. (15), but fast enough to be able to bracket clearly the time of the
subsequent discharge process to a known time interval of the order of 1s. The 1s time interval is required to guarantee timely
triggering of and photographic data acquisition from a high-speed camera during the discharge process. As mentioned above,
the fatter is expected to occur over a time interval of the order of 107s.

‘The relatively large volume of the holding tank would allow the pressurization/discharge process to be initiated either: 1) from
a relatively high-Ppy, state, somewhat below the minimum possible diaphragm burst pressure and with a relatively significant
initial mass of Nz in the discharge vessel; or 2) from a minimum-Ppy; state where there is no Nz in the discharge vessel (Le,
the discharge vessel initially contains only pure test agent at the saturation pressure Poy; = Psat, where Pear is significantly
below the Paupsr pressures under investigation).

Solution results are presented in Figures 6 - 13 and these are discussed below.
Initiating Pressurization/Discharge From the Agent's Saturation State; No N2 in the Discharge Vessel att = 0

Simulations were carried out for experiments where the pressurization/discharge processes were initiated at the test agent’s
saturation state, ie, at Ppyy = Psar(Tpvi = 294K) = 9.38x10°Pa (136psi), €.g, shortly after filling the evacuated vessel
with the test agent. In such experiments there is no Nz in the discharge vessel at t = 0, Le., Mpynaa = 0- Results of the
calculations are plotted in Figures 6 - 11.

The pressurization process. Figure 6 presents plots of Ppy and Py during vessel pressurization, 0 < t < tgupst- Results
are presented for the three orifice diameters, Do = 0.005m, 0.001m, and 0.0005m.

As seen in Figure 6, for the smallest orifice, Do = 0.0005m, the pressurization process, when Poy, S Ppy < Paursr takes
4.2s {for Paypst = 37:92x10°Pa (550psi)] 10 5.8s (for Ppurst = 44.82x10°Pa (650psi)]. For the intermediate-size orifice,
Do = 0.001m, the pressurization process takes 1.0s (for Ppurst = 5SOpsi) to 1.4s (for Paurst = 650psi). For the largest
orifice, De = 0.005m, the entire process takes place within 0.1s.

Upgr values corresponding to Figure 6 are presented in Figure 7. For the smailest orifice, Do = 0.0005m, Uyer Starts out
at approximately 4m/s and drops to 2 - 3m/s at tgupsr, the time of diaphragm bursting. For Dg = 0.001m, Uygy starts out
at approximately 8m/s and drops to approximately 4m/s at tgursT For Dog = 0.005m, User starts out at approximately
40m/s and drops to as low as approximately 16m/s [for Pp, = 44.82x10°Pa (650psi)} at tgurst

Based on the above results it is concluded that during the pressurization process and relative to the criterion of Eq. (15): 1)
use of the large orifice would lead to conditions which do not satisfy the criterion; 2) use of the intermediate size orifice would
Jead to results which are barely acceptable; and 3) use of the smalll orifice would lead to acceptable performance, provided
that pressurization times are consistent with timing requirements of the photographic data acquisition system.

The discharge process. Figures 8 - 11 present plots of Ujep, dZ/dt, Z/Z,, and (My - My2p)/Myop during the discharge
process. For the limiting burst pressures, Paupst = 37.92x10°Pa (550psi) and 44.82x10°Pa (650psi), results are presented
for the small- and large-orifice designs.

Figure 8 presents resuits for Parpsp = 37.92x10°Pa (550psi) and Do = 0.0005m. Once the discharge process is initiated,
the liquid is seen to drop from its initial elevation (Z/Z, = 1) and to be removed entirely from the vessel (Z/Z, -* 0) in
approximately 0.024s. Liquid discharge occurs at a relatively uniform rate with dZ/dt dropping from approximately 7.0 to
4.5 mis during the emptying process. During discharge ‘Uygr first rises slightly (because of relatively rapid reductions of Poy,
slow reductions of Pprr, and resulting increases in cross-orifice pressure difference) from approximately 3 ms, and then drops
(because of the significantly increased length along the jet axis between the source of the jet, at the orifice, and the elevation
at the gas/liquid interface - refer to Figures 1 and 2) to the final value of approximately 2m/s. As can be seen from the plot
of (My - My2p)/Myop, during the entire emptying process the total mass addition of Nz from the holding tank to the
discharge vessel is less than one percent of the initial N2 mass in the discharge vessel.



Uo = GMpyx2//Ao(MirpxyVi)] (2)
From (7]
UypUg = 0.96{0.066(2Z¢7/D.)+0.29] for 2Zyp7/Do > 10. (13)

When the ume-dependent solution for Mpyyp is available, Uygy can now be estimated from Eqs. (12) and (13) and the
significance of the jetting phenomenon can be assessed.

SOLVING THE MODEL EQUATIONS

A computer program was developed to solve the initial value problem of Eqs. (11) corresponding to an arbitrary choice of
geometric parameters, material properties, and initial conditions, and to determine the value of Uy_z from Eqs. (12) and (13).
‘The method of solution is based on the differential equation solver RKQC presented in [8]. The program was uscd in the
example calculations to follow.

EXAMPLE CALCULATIONS.
An Experimental Procedure to Simulate the Discharge of Field-Deployed Vessels

As mentioned in the introductory comments, the example calculations to be presented here focus on the establishment of
an experimental design and procedure, where vessel discharge closely simulates the discharge of a field-deployed vessel while
allowing for acquisition of data, including high speed photography, to characterize the discharge process.

Field-deployed systems use an explosive device to remove, “on demand," a cap covering the exit nozzle/orifice of a pre-
pressurized discharge vessel. Thus, the deployed system is characterized by a Figure 1-type configuration with no holding
tank component, i.¢., with Ag = 0.

‘The nature of the experimental program at NIST precludes the use of an explosive cap device. The experimental procedure
to be evaluated involves a vessel discharge process which is initiated, instead, by rupture of a nozzle/orifice diaphragm cap
ata high cross-diaphragm pressure difference. The pressurization of the discharge vessel from Ppy, to the diaphragm burst
pressure, Pyr-asp is achieved with the use of the holding-tank/orifice-flow feature of Figure 1.

As discussed earlier, an experimental run involves sequential processes of vessel pressurization and discharge. Initially, the
diaphragm cap prevents flow from the vessel to the outside environment. At t = 0* the orifice connecting the vessel and
the holding tank is opened and pressurization of the vessel is initiated. At the instant the pressure in the vessel reaches the
diaphragm burst pressure, the diaphragm ruptures. Nozzle/orifice flow and discharge of the vessel are then initiated. As
mentioned earlier, the pressurization and discharge processes of interest here are expected to occur over time intervals of
the order of 10s and 107s, respectively

Prior to any particular test run, Paypsr is only known to an accuracy of approximately ten percent. Also, the high speed
camera to be used to photograph the discharge process during the test procedure can record a total time interval no larger
than the order of a few seconds, including an initial interval of approximately 1s required to bring the camera up to its
Operating speed.

Criteria for Experimental Discharges to Closely Simulate Field-Deployed Discharges

One would hope to determine that an experimental discharge would closely simulate a field-deployed system discharge by
obtaining good agreement between results of mode! simulations of the two processes. The basic criterion would be good
reproduction of the predicted time-dependent values of Ppy and Mpvat-:

Since field-deployed discharges involve no addition of N, and no significant heat or mass transfer at the liquid/gas interface,
an acceptable Figure 1-type experimental procedure should similarly involve discharges with no significant addition of Ny.
In view of this, in addition to the above criterion two additional criteria must be satisfied if the experimental discharge is to
simulate closety a field-deployed discharge: 1) the experiment must include a discharge process during which the total mass

535


534

Now assume that liquid CO, in a discharge vessel is at P = Ppy = 60x10*Pa and T = Ta, = 291K. In Figure 3 this inital
state is seen to lie on the s = s3 constant-entropy line, which intersects the spinoidat curve at approximately Psp = 10x10°Pa
>> Payp: In this case, as the liquid CO2 flows through and out of the vessel nozzle/orifice the model predicts that it will
fash explosively when P = Psp. This will occur upstream of the position at which a fluid jet vena contracta would othenvise
occur; well within a distance of one nozzle/orifice diameter downstream of the vesset exit.

This nozzle/orifice flow model is consistent with a discharge process involving a smoothly time-varying Ppy, a constant T4;,
and an abrupt change in nozzle/arifice exit flow from a simple incompressible-fluid-jet type flow to an explosively flashing two-
phase flow. This kind of discharge phenomenon was clearly observed during recent Freon 22 discharge experiments at NIST
{5]. Note that the idea of using the condition of the existence of Pgp > Payyp a5 @ criterion for violent flashing of liquids
flowing through sharp-edged orifices or very short nozzle-like openings does not seem to have been proposed previously. Nor
has it been validated quantitatively.

REDUCED DIMENSIONLESS EQUATION SET - THE INITIAL VALUE PROBLEM

Eqs. (1) - (8) are made dimensionless by introducing a dimensionless time, 7, dimensionless mass of N2 and liquid agent in
the discharge vessel, x. and x3, respectively, and a combined variable, x,.

xy = ((1 + Agya(1 + Ax.) PpwPpvsZpwa - ¥3) + AA gC = 9)"
%2 = Mpvna/Myai %3 = Mpval/Mpvaii 7 = (Cp xAnl2Ppva/(MovantApv2y))?
Ay = (Myg/MpyacRyaRaa)s 42 = Prny/Ppw VM Merena,/Mn2)i

As = Ayrag = WY 15 Ag = (Wag - DY - DIM (Z,Apv) i

(9)

(10)

The initial values of the x’s are functions of the various parameters of the particular problem of interest. The dimensionless
initial value problem for an arbitrary Figure-1 configuration is

dxdt = 04; 0;=0,(%1, Xq X33 parameters of the problem); x,(0) specified, i = 1, 2, or 3 qa)

The reader is referred to the Appendix of [6] for definitions of the o; and for explicit equations to extract values of time-
dependent dimensional variables from a solution of Eqs. (11).

N, JET-DRIVEN MIXING IN THE DISCHARGE VESSEL - ESTIMATING THE RESULTING DISTURBANCE OF THE
LIQUID/GAS INTERFACE

The above model assumes that throughout the pressurization and discharge process the agent gas and the N2 in the discharge
vessel are fully mixed and in a state of thermodynamic equilibrium. It is also assumed that there is no significant heat or mass
transfer interactions at the gas/iquid interface, i.c., it is assumed that the interface is relatively quiescent.

In cases where there is no Nz flow from the holding tank (¢.g., the orifice is closed) the initial fully-mixed state of the gases
will persist throughout de-pressurization, the gas volume will be relatively quiescent, and the assumption of negligible interface
interactions is expected to hold. This is the case for actual field-deployed systems.

When there is N. flow from the holding tank, it is the Nz jet from the orifice that will drive gas mixing in the discharge vessel.
Refer to Figure 4. If jet velocities are too large, the liquid/gas interface disturbance of the jet can be violent enough to
invalidate the quiescent interface assumption.

For the configuration of Figures 1 and 4, the significance of the effect of the Nz jet impinging on the liquid surface can be
determined from an estimate of the axial velocity of the orifice jet at the liquid/gas interface. Such an estimate is obtained
here from the characteristics of an incompressible submerged jet (i.., analogous to the Nz orifice jet) in an unconfined space
(analogous to the gas volume of the discharge vessel). The estimate is also useful for other orifice orientations.

Let the velocity on the jet axis a distance Zypy = Zpy - Z from the orifice (i.e., at the elevation of the fiquid/gas interface)
be denoted by Ujpy and assume a uniform vetocity, Ug, across the orifice opening


‘3

40
0.005m
30
= 20
=
10 0.001m
Do#0.0005m
}—_Dor0 000°
0 3 2 a1 o 1
10 10 10 10 10

Us teurer (8)

Figure 13. Plots of Uygy for 05 t 5 tgypsp and Do =
0.005m, 0.001m, and 0.0005ua.; where Verr = 2.5110" m3,
Tova = Tm = 294K, Poy = 34.47x10%Pa (S00psi),
Pry = 51-71x105Pa (750psi), Pgupsr < 44.82x105Pa
(65Gpsi).

= = = PRESSURIZE FROM Yq = 2.510%m*
HOLDING TANK WITH Dg = 0.00050,
WHERE Pog » Paar 136964 Tou = 204K;

0.8 DISCHARGE WHEN Ppy RISES TO Prosar

DOISCHARGE WITH NO HOLDING TANK
AT Pees # Paonet = 600 pel, Toys = 204K

0.6
wv XX
0.4 QS
NG
Past = SS0pel
0.2 XY
XY
0
0 0.005 0.01 0.015 0.02 0.025

tehuner [5]

Figure 15. Plots of Z/Z, during discharge of: 1) field-
deployed vessel at Pgygsy = 41-37x105Pa (600psi) and
test configuration vessel [Vy = 2.510%m*, Do =
0.0005m, Poy: = Pear(294K) = 9.38x10°Pa (136psi)} at
2) Paursr = 37.92x10°Pa (S50psi) and 3) 44.82x10°Pa
(650psi).

700
— — — PRESSURIZE FROW Ve = 2x1 04m!
HOLDING TANK WH De» 0.0008
\ WHERE Pye = Pars £380 Toyy = 204K:
600 OISCHARGE WHEN Py, RISES TO Pau
DISCHARGE WITK KS HOLDING TANK
\ AT Pye = Prana = BEBE Ty = 264K
= 500
&
3
400
300
200

0 0.005 0.01 0.015 0.02 0.026

t= Gurer [5]
Figure 14. Plots of Ppy during discharge of: 1) field-
deployed vessel at Paygsy = 41-37x105Pa (600psi) and
test configuration vessel [Vy7 = 25x10%m3, Dg =
0.000Sm, Poy, = Psar(294K) = 9.38x10°Pa (136psi)] at
2) Pgupsr = 37.92x10°Pa (5S0psi) and 3) 44.82x10°Pa
(650psi).

2500
PS Pe
2000 ~_
1500
$1000
Pov
500 nN
0 .
0 0.05 O41 015 0.2
Us! teunsr=0.1738

Figure 16. Plots of Ppy and Pyp fort 2 0 and Dg =
0.0005m; where Vier = 2510m", Toya = Tyra = 294K,
Pov, = 3447x10°Pa (500psi), Py, = 155.13x10°Pa
(2250psi), Pyypsr = 37.92x10°Pa (§£0psi).

547


The parameters sets of Table 1 define simulations of 18 different experimental systems and the single simulation of the field-
deployed system. The parameters sets were used to define and solve the model's initial value problem. Solution resulis
Provide time-dependent histories of all model variables and the information necessary to determine whether or not the criteria
of Eqs. (14) and (15) are satisfied during the simulaticn. Sofution results will be presented and discussed below.

As indicated, the model simulations involve the agent CHCIF}. In solving Eqs. (11) and (12) the following thermodynamic
properties were used for this and for N.:

Properties of Chlorodifluoromethane/CHCIF, (Freon 22) [9].
Mol, Wt. = 86.469kg/(kg-mole); ar = Psar(294K) = 1209kg/m>; Crag = Cpag(300K) = 57(105)J/(kg-mole-K)
Par = 6895(T/R)C(F - (T/AR)JEF * TROMFTR) QA - BTR) + DETR) pa (16)

A=29.35754453; B=3845.193; C=7.86103122; D=0.002190939044; E=305.826813; F=686.1

Properties of Nitrogen {10}.

Mol. Wt. = 28.013kg/(kg-mole)
ay
Cpa = [7.440 - 3.24(10°3)(T/K) + 6.400(10%)(T/K)? - 2.790(10°°)(T/K}]41865/(kg-mole-K)

where T = Tpy, was used to estimate (a constant value for) Cera
Other Assumptions on the Model Parameters

‘The following completes the information used to fully define the mode! equations:

Flow coefficient for the nozzle/orifice (flow of test agent liquid from the discharge vessel to the outside environment).

Coy = 0.60 (is)

Spinoidal pressure. Use of Eq. (8) and the o, and c3 components of Eqs. (11) require values of Psp for isentropic paths from
the time-dependent liquid states in the discharge vesseL For the present calculation it is assumed that throughout the
discharge process Psp < Pany = 1.01x10°Pa (14.7psi), i.¢., spinoidal-curve type instabilities of the metastable exit liquid
stream do not occur during the major portion of the discharge-process time interval. This assumption is consistent with
previously mentioned Freon 22 discharge experiments at NIST [5]. However, as seen above in the discussion of COy, this
assumption can not be expected to hold in general, and actual estimates of Psp will have to be included in more generai
applications of the mathematical model.

Flow coefficient for the orifice (flow of No from the holding tank to the discharge vessel). Cp 0 for compressible flow through
sharp-edged orifices as a functicn of cross-orifice pressure ratio, Ppw/Puris provided in [11]. Data points for Cp o(PpwPyr)
are plotted in Figure 5. In the present calculations, values of Cpo are estimated by linear interpolation between these data
points.

Input value for Mpyac- To determine the constant mass of gaseous test agent in the discharge vessel it is assumed that
the process of filling the vessel included a time when pure test agent filled the entire vessel with gas and liquid volumes in
thermodynamic equilibrium with each other. The mass of gaseous agent at this time is taken to be Mopyac- In the presen:
calculations it is assumed that at this time of equilibrium the agent temperature was 294K. This is the value taken above
for the initial temperatures Tpy, and Ty

RELATIVELY LOW-PRESSURE LARGE-VOLUME HOLDING TANK
This section will present results for the pressurization/discharge sequence using a relatively low-pressure large-volume holding

tank. Note that experimental safety considerations motivate use of relatively low-pressures in the holding tank, especially
when it is of relatively large volume.

537


DISCHARGE OF FIRE SUPPRESSION AGENTS FROM A PRESSURIZED VESSEL:
A MATITEMATICAL MODEL AND ITS APPLICATION TO EXPERIMENTAL DESIGN*

Leonard Y. Cooper
Tire Modeling Group
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899
(301) 975-6880

Presented at the

Halon Alternatives Technical Working Conference 1993

May L1 - 13, 1993
Albuquerque, New Mexico

“Sponsored by the U.S. Air Force Wright Patterson Laboratory

529


where simulating tests would involve experiments where 37.92x10°Pa S Pyupst S 44.82x10°Pa (S50psi S Ppursr =
650psi)}. In Figures 14 and 15 calculated values of Ppy and Z/Z, for the deployed system simulation are compared with
the values of these variables obtained in the above test ‘simulations with Dg = 0.0005m. [The Ppvi = 9.3810°Pa (136psi)
results are presented in the figures since these compare somewhat {ess favorably with the field-deployed system results than
do the Ppy, = 34.47x10°Pa (S00psi) results.]

‘As can be seen in the figures, simulated field-deployed system results and simulated test results compare favorably.
Summary of Results of Simulations Involving the Relatively Low-Pressure Large-Volume Holding Tank
The above described model simulations fead to the following summary result:

A Figure 1-type test configuration with a 0.25x: 103m? holding tank and a 0.0005m, and possibly a 0.001m-diameter
orifice will provide experimental discharges which can be expected to simulate accurately the discharge of field-
deployed systems. Of the two orifice sizes the smaller orifice is preferable. Use of a 0.005m diameter orifice can
not be expected to adequately simulate field-deployed system discharges under the conditions studied.

It is expected that this result can be extended to a wide range of test parameters and test agents.
RELATIVELY HIGH-PRESSURE SMALL-VOLUME HOLDING TANK

This section will present results for the pressurization/discharge sequence using a relatively high-pressure small-volume holding
tank. Ver = 25x10°m? is chosen to be one tenth of the initial gas volume in the discharge vessel and Pyrpy = 155.13x10°Pa
(2250psi) is chosen to be large enough to insure that the amount of N, stored in the holding tank will rupture the diaphragm
even when Paypsr is at its maximum value, 44.82x10°Pa (650psi).

‘The objective of choosing this combination of parameters is to attain a pressurization/discharge sequence which is so rapid,
well within the above-mentioned 1s time interval, as to guarantee, without any significant timing considerations, successful
acquisition of high-speed photographic data of the discharge process. The feature of a relatively small initial volume and mass
of Nz in the holding tank is only consistent with test sequences with relatively high initial Ppyy’s, values close to the minimum
possible diaphragm burst pressure. Thus, the present test parameters would not be expected to be useful in initiating the

pressurization/discharge process from an initial state ‘where the vessel contained only pure test agent at its saturation pressure.
Here, Ppy, is again chosen to be 34.47x10°Pa (500psi), slightly below 37.92x10°Pa (550psi), the minimum value for Pgurst-

Solution results are presented in Figures 16 - 24.
Pressurization and Discharge for the Small Orifice, Do = 0.0005m
Simulation results for pressurization/discharge test using the small orifice design are presented in Figures 16 - 20.

For Pgurst = 37.92x10°Pa (550psi), plots of Phy and Pyry are presented in Figures 16 and plots of Uygy, dZ/at, ZZ,, and
(Myz - MyopV/Myop in Figure 17. Note that the latter variable is meaningful only during discharge when t = tgurst- AS
can be seen in these figures, for this case tgyuprst = 9-173s, ie., this is the time it takes for Poy to rise from Ppy; =
34.47x10°Pa (500psi) to the diaphragm rupture pressure. From Figure 17 it is seen that the liquid is nearty ail discharged
from the vessel (ie., Z/Z, is approaching zero) at approximately t = 0.2s. From Figure 17 it is also seen that during
discharge: the rate of liquid outflow is reduced to about half of its original value, with dZdt being reduced from 7.0m/s to
4.5m/s; Uygr is reduced from an initial pre-discharge value of approximately 4m/s to approximately 2m/s; and (My -
My2p)/Myz2z Mises from 0 to approximately 0.02, ic. at the end of the discharge the mass of No in the vessel is increased
from its value at tgypsr by a factor of approximately 0.02. The latter two results indicate that the criteria of Eqs. (14) and
(13) are both satisfied and, in this sense, as with the relatively large holding tank, the smalt orifice design can be expected to
adequately reproduce field-deployed discharges.

For Paurst = 44.82x10°Pa (650psi), plots of Poy and Pyrr are presented in Figures 18 and plots of Usgy and dZat are
presented in Figure 19. Plots of User SZ/at, Z/Z,, and (Mx - My2p)/My2p for the times of the discharge process are
highlighted in Figure 20. For this cas¢ tpupst = 0.94s. From Figure 18 it is'seen that the Pyry has almost been reduced
to Ppy at the time that discharge is initiated. Indeed, if the Pyrr had been much less than 155.13x10°Pa (2250psi), Py



Figure 9 presents results for Paypsyp = 37.92x10°Pa (550psi) and Dg = 0.005m. Based on an approximate extrapoiation
from t - tpursr = 0.020s, once the discharge process is initiated the liquid is seen to drop from its initial elevation and 10
be removed entirely from the vessel in approximately 0.023s. Liquid discharge occurs at a relatively uniform rate with Zt
dropping from approximately 7.0 to 5.Smys during the emptying process. During discharge Uypy first rises slightly from
approximately 30m/s, and then drops to the final value of approximately 20m/s. As can be seen from the plot of (My, -
My2p)/My2p, during the entire emptying process the total mass addition of N2 from the holding tank to the discharge vessel
is significant, approximately 45 percent of the initial N. mass in the discharge vessel.

Figure 10 presents results for Paursr = 44.82x10°Pa (650psi) and Do = 0.0005m. Here the discharge is completed in
0.023s. Liquid discharge occurs at a relatively uniform rate with dZ/dt dropping from approximately 7.5 to 5.0m/s during
the emptying process. During discharge Uygr first rises from approximately 1 to 2m/s, and then drops back to the final value
of approximatety Im/s. During the discharge the total mass addition of Nz from the holding tank to the discharge vessei is
less than one percent of the initial N2 mass in the discharge vessel.

Figure 11 presents results for Paypst = 44.82x10°Pa (650psi) and Dg = 0.005m. From this it is seen that discharge occurs
in approximately 0.021s. Liquid discharge occurs at a relatively uniform rate with dZ/dt dropping from approximately 7.5
to 5.5m/s during the emptying process. During discharge Uypy first rises from approximately 17 to 2Sm/s, and then drops
to the final value of approximately 20mys. During the discharge the total mass addition of N2 from the holding tank to the
discharge vessel is approximately 40 percent of the initial N2 mass in the discharge vessel.

Based on the above results it is concluded that during the discharge process and relative to the criteria of Eqs. (14) and (15}:
1) use of the large orifice would lead to conditions which violate both of the criterion; 2) use of the small orifice would lead
to acceptable performance.

Initiating the Pressurization/Discharge Sequence From a Ppy, Slightly Below Paupsr

Simulations were carried out for experiments initiated from a Ppy, which is slightly below Paupst- Since the minimum
possible Paugsr is 37.92x10°Pa (S50psi), Ppyy is selected to be 34.47x10°Pa (500psi).

The_pressurization process. Figure 12 presents plots of Ppy and Py during vessel pressurization. Results are presented
for the three orifice diameters, Do = 0.005m, 0.001m, and 0.0005m.

As seen in Figure 12, for the smallest orifice, Dg = 0.0005m, and for the diaphragm burst pressures under consideration,
the pressurization process, Poy, S Poy < Ppypsr takes 0.65 [Paupsr = 37.92x10°Pa (SSOpsi)] to 1.95 [Paurst =
44,82x10°Pa (650psi)}. For the intermediate-size orifice, Do = 0.001m, the pressurization process takes 0.1 (Paurst =
550psi) to 0.5s (Ppupsr = 650psi). For the targest orifice, Dg = 0.005m, the entire pressurization process takes place in
less than 0.02s.

Uyjgr values corresponding to Figure 12 are presented in Figure 13. For the smallest orifice, Do = 0.0005m, Uygr starts
Out at approximately 3.5m/s and drops to 2.0 - 2.5m/s at the time of diaphragm rupture. For Dg = 0.001m, Uygy starts out
at approximately 7m/s and drops to approximately 4.5m/s at the time of diaphragm rupture. For Dy = 0.005m, Uygy starts
out at approximately 33m/s and drops to as low as approximately 21ms [for Paygsr = 44.82x10°Pa (650psi)] at the time
of diaphragm rupture.

Based on the abave results it is concluded that during the pressurization process and relative to the criterion of Eq. (15), the
present results for Poy, = 34.47x10°Pa (S00psi) are similar to the earlier results for Poy, = Psat = 9.38x10°Pa (136psi).

The discharge process. In the present case where Ppvi = 34.47x10°Pa (500psi), results for the discharge process are very

similar to the earlier results where Poy, = Psat = 136psi and are qualitatively well represented by the plots of Figures 8 -
11 and the earlier discussion of these.

Comparing the Discharges of a Smail-Orifice Test Configuration and a Field-Deployed System

The model equations were also used to simulate the discharge of a field-deployed vessel filled with CHCIF, and pressurized

with N>. At the onset of discharge the temperature in the vessel was taken to be 294K and, corresponding to the above
calculations, the pressure in the vessel was taken to be 41.37x10°Pa (600psi) fi.e., a nominal Paypsr = 41.37x10°Pa (600psi),

539


of Nz delivered from the holding vesse! to the discharge vessel is small compared to the mass of No in the discharge vessel
immediately prior to the onset of discharge, ie.,

require (Myo - My2.p)My2B << 1 fort > tgyrsr . (14)
where Myog is the mass of Ng in the discharge vessel at tguRsti and 2) the addition of Nz during the entire pressuriza-
tion/discharge sequence does not lead to gas flows in the discharge vessel gas (where velocities will be of the order of Ujey)
which are so vigorous as to lead to significant heat or mass transfer at the liquid/gas interface. It is reasonable to expect that
interface surface interactions will not be significant if Uyer - AZ/dt never exceeds the order of a few m/s. Thus

require Uypy - dZ/dt < 5 to 10m¥/s fort = 0 (15)
Model Input Parameters
Sets of parameters representative of those a Figure-1-type experimental design are presented in Table 1. These are selected

to simulate discharge of a field-deployed system with a 0.5x10°3m? discharge vessel half-filled with liquid CHCIF, and
pressurized with N2 to 41.37x10°Pa (600psi). Parameters of the field-deployed system are included in the table.

agent Chlorodifluoromethane/CHCIF, (Freon 22)
Tova = 294K
Tym =
Dpv = 0.05m
Vov = 0.5x10°m?
MpvaLi= Par pyi2) = 0.302kg
Dy = 0.01905m
Vur = 25x10°m3 2.5x10°5m3 field simu-
(large holding tank) (small holding tank) lation
Pur = 51.71x10°Pa (750psi) 155.13x10°Pa (2250psi) :
Pov; = 34.47x10°Pa (500psi) 9.38x10°Pa (136psi) 34.47x10°Pa (500psi) 4137x
(Figs. 12 and 13) = Psa(Tpvi) 10°Pa
(Figs. 6 and 7) (600psi)
Paurst = 37.92 44.82x 37.92% 44.82x 37.92 44.82x 41.37x
10°Pa 10°Pa 10°Pa 10°Pa 10°Pa 10°Pa 10°Pa
(550psi) (650psi) (S50psi) (650psi) (S5Opsi) (650psi) (600psi)
(Figs. 14
and 15)
0.0005m, 0.0005m, 0.0005m 0.0005m 0.0005m 0.0005m
Do = 0.001m, 0.001m, Figs. 8, (Figs. 10, | (Fig 16 and | (Figs. 18, -
and 0.005m | and 0.005m | 14 and 15), | 14, and 17), 19, and
0.001m, 15), 0.001m, 20),
and 0,005m 0.001m, and 0.005m. 0.001m,
(Fig. 9) and 0.005m (Figs. 21 and
(Fig.11) and 22) 0.005m
Figs. 23
and 24)

Table 1. Characteristics of simulated discharges - model input parameters

536




532

For experimental systems of interest here taurst is expected to be of the order of 10s and the time interval of the discharge
process, (tp - tgurst): of the order of 10%. Prior to tp there is no gas mixture discharge from the vessel. The mass of
gaseous agent in the vessel therefore remains constant at its initial value Mpvac-

In view of the relatively short times of interest it is assumed that during an experimental run or field-deployed discharge there
is no heat or mass transfer across the liquid/gas interface. It is also ‘assumed that there is no heat or mass transfer across
the interface that contains the nitrogen and gaseous test ageat in the combined bolding-tank/discharge-vessel system, ¢.g.,
there is negligible heat transfer to the walls Of the vessel and holding tank. This is the basis of the assumption that both
Mopy,ac 2nd the total mass of Nz in the combined system, designated as Myp, are constant for all t,0 <t < tp. Myo is
determined from the initial conditions.

It is assumed that the gaseous test agent and the N2 can be modeled as perfect gases with constant specific heats and gas
constants, Cyag Cpac Rag 2nd Cynz Cpyz, Rua: The values of the specific heats, which depend on temperature, are
taken to be those which correspond to Tpyy-

THE MODEL EQUATIONS

‘Together with specified parameters, the unknown time-dependent variables of the problem that define the state of system.
at an arbitrary time are: Py, Pov, Mirena Movin Mpvav Tim Tov 2 Known/specified parameters would include:
the initial values of these variables, Pyrry, Pov» Mapa Movn2a Mpvane Tyr Tov and Z,, respectively, the
geometric parameters of the system, Ao: An Apv: Zow Vier material properties of the test agent and of N.; the constant
value Mpyvag; and nozzle/orifice discharge coefficients, to be introduced below. The equations governing the variables are:

Equations of State in the Holding Tank and in the Discharge Vessel and the Law of Partial Pressure in the Discharge Vessel

Perr = Murtya/Virr) Rater a
Pov = MpvyacRac + MpvnzRn2)Tpwl(Zpv - ZApvi rey
Conservation of Mass of No
Mpyn2 + Mirena = constant = My = Mpyyai + Mirna 8)
Relation of Z to Mpvar
MpvavPat = Apv@ @)
Pyrrf(Myrrya)” = constant = Pyrr/(Murewaa)” (5)
where 7 = Cpyo/Cyn2 = Rya/Cyne2 + 1
First Law of Thermodynamics for Entire Gas System
d(MpvacCvac + MovxzCva)Tpv + MerpnoCynaTrl/st = PpyApyiZiat 6)
Flow Across the Orifice
= CpoAoPartbRaaTaiuy + py * MT PH?
if PypPpy 2 [G + 1y2IK7-YI Ge, choked flow)
= CooAoP nr PovP an)! (21) - PowPaen) MG - DRyaTen dh? ”
if PypPpy <[G + 1277 -Pl (Le., ua-choked flow)

OMyrrn/tt =


[4] Benjamin, M.W. and Miller, J.G., The Flow of Saturated Water Through Throttling Orifices, Trans. Am. Soc. Mech,
Engrs., Vol. 63, pp. 419-429, 1941.
[5] Yang, J.C., private communication.
[6] Cooper, L.Y., Discharge of Fire Suppression Agents From a Pressurized Vessel: A Mathematical Model and Its
Application to Experimental Design, NISTIR, National Institute of Standards and Technology, Gaithersburg MD,
1993. .
17] Abramowitz, G.N., The Theory of Turbulent Jets, MIT Press, Cambridge, MA, p. 82-84, 1963.
{8} Press, WH. et al, Numerical Recipes - The Art of Scientific Computing, Cambridge University Press, 1986.
[9] Bracker, W. and Mossman, A-L., Matheson Unabridged Gas Data Book on Chlorodifluoromethane, ICHCIF,
Fluorocarbon-22), Matheson, Lyndhurst, NJ, 1974.
10} Reid,R.C. et al, The Properties of Gases and Liquids, Appendix A, 3rd Edition, McGraw Hill, 1977.
{11} Perry, J.A., Critical Flow Through Sharp-Edged Orifices, Trans. American Soc. Mech. Eng., 71, pp. 757-764, 1949.
NOMENCLATURE
Apv cross-section area of discharge vessel
Ax, Ag area of discharge nozzle/orifice, orifice from holding tank
Cox Coo flow coefficient of discharge nozzie/orifice, orifice from holding tank
Crag Cpn2 specific heat at constant pressure of agent gas, Nz
Cyag Cynr specific heat at constant volume of agent gas, Nz
Dpy; Dy diameter of discharge vessel, its exit nozzle/orifice
Do diameter of the orifice between discharge vessel and holding tank
Mpvac> Mpva mass of gaseous, liquid agent in discharge vessel
Mpvnz Mirex2 mass of No in discharge vessel, holding tank
Mpvn21 Mpvaca Mirgn21 Mpvx> Mpvau Mugy2 att = 0
N2 total mass of N, in discharge vessel and holding tank, see Eq. (3)
My2B mass of No in discharge vessel when the diaphram ruptures
P pressure
PaMB P of ambient environment
Ppurst P in discharge vessel when the diaphram ruptures
Pow Pur P in discharge vessl, holding tank
Pov Pim Pov. Pur att = 0
Psat P when liquid agent is at saturation
Psp P on agent spinoidal curve
Rag Ryo gas constants for gaseous agent, Ny
T temperature
Tat T of liquid agent
Tov: Tir T of gaseous agent in discharge vessel, N, in holding tank
Tove Tim Tpy. Typ at t= 0
t time from begining of experiment or from onset of discharge of field-deployed system
lpuRST (when diaphram ruptures
Ip 1 at completion of liquid discharge or when Ppy reaches Ps, during discharge
Ujen, Ug axial velocity Of orifice jet upstream of gasfiquid interface
Vow Virr volume of discharge vessel, holding tank
Xp Xa, XQ, variables of dimensionless initial value problem, Eq. (9)
elevation of gasfiquid interface above bottom of discharge vessel
Z, Zawc=0
Zpv length of discharge vessel
Zier Zpy -Z
7AG tatio of specific heats for N3, gascous agent
PAL density of liquid agent
PSAT density of saturated liquid agent
i dimensionsless parameters, i = 1 to 4, Eqs. (10)
a; functions of x; and parameters, i = 1, 2, 3, Eqs. (11)

dimensionless t, Eqs. (9)

543


0.9
t
0.85 by.
0.8
0.75 *
0.7
0.65
0.6
0 02 04 06

Pov/Pur

Figure 5. Discharge coefficient, Cp.o, for compressible
flow through a sharp-edged orifice as a function of cross-
orifice pressure ratio, Poy/Pyry [11].

40
0.05mi
30+
= 20
zt
10
001m
Do=0.0005m
0
10° 107 10" 10° 10°
{<tauner 5]

Figure 7. Plots of Ujey for 0 t = tgugsr and Do =
0.005m, 0.001m, and 0.000Sm; where Vip = 2.5x107% m3,
Tova = Tri = 294K, Poyy = Psat = 9.38x10°Pa
(36psi), Pug, = 51-71x10°Pa (750psi), Pgygst <
44.82x105Pa (650psi).

'<Guner (5)

Figure 6. Plots of Ppy and Pyry for O< t < tgypsr and
Do =.0.005m, 0.001m, and 0.000Sm; where Vir =
2.5x10%m>, Tpyr = Tur: = 294K, Poyr = Psar =
9.38x105Pa (136psi), Pry = S1.71x10°Pa (750psi),
Paursr = 44-82x105Pa (650psi).

10°

- — did

Sol User

= Te

= ~

= 10° zy ~N

gy \

= 10? \

a

2

= 10° “.

& 7 (Maa > Mua) Mva.8

=

to“
0 0.005 0.01 0.015 0.02 0.025

tuner {51

Figure 8. Plots of Ujepy dZ/dt, Z/Z,, and (My, -

Mxop)/Myzp for t = tgupsrs where Vyrp = 2.5x10%m3,
Tpvt = Tam = 294K, Pov; = Psar = 9-38x105Pa
(136psi), Py, = SL71x10°Pa (750psi), Paursr =
37,92x105Pa (550psi) and Dg = 0.0005m.

545


‘The experimental arrangement involves a right cylinder discharge vessel at pressure Ppy, which would contain N5-pressurized
test agent, and a holding tank filled with mass Mypyo of Nz at pressure Py. The discharge vesset is of height Zpy and
cross-sectional area Any. The volume of the holding tank is Vyzy.

‘The holding tank is connected via an orifice of area Ag to the discharge vessel. It is assumed that the flow path through
the orifice can be opened or closed with a relatively fast-acting solenoid vaive. If the path is open it is assumed that Pyrp =
Ppy, i.e. the flow is always from the holding tank to the discharge vessel. In the case of a field-deployed system there is no
hoiding tank and Ao is zero.

At the bottom of the vessel is a short-nozzle/orifice-type opening of area Ay. The agent will be Gischarged through this to
the outside ambient environment which is at Pressure Payp < Ppy. The discharge flow path is originally closed off by a cap
or diaphragm. When the cap is removed, the test agent liquid is driven out of the discharge vessel by virtue of the cross-
nozzle/orifice pressure difference.

The Procedure Prior to An Experimental Run or a Field-Deployed Discharge

‘The orifice and nozzle/orifice flow paths are closed and the discharge vessel is evacuated. The vessel is then filled completely
with a known mass of test agent. There will be a volume of liquid agent below and a volume of gaseous agent above and
the pressure will be Pcay, the saturation pressure at the agent temperature. The vessel is then pressurized with No. This
flows into the vessel from the holding tank or from some other relatively high-pressure N source. In general, the upper gas
volume is now a two-component mixture of Nz and test agent gas. Although some N, may be dissolved in the liquid volume,
it is assumed that the amount is always so small that throughout subsequent sequential (additional-)pressurization and
discharge processes to be studied here the properties of the liquid in the discharge vessel are well approximated by the liquid
properties of the pure test agent.

Now consider the system at the time, t = 0, when an experimental run or a field-deployed discharge is initiated. The
liquid/gas interface is a distance Z, above the bottom of the vessel. The mass of liquid in the vessel is Mpyar (the subscript
tefers to that portion of Discharge Vessel test Agent in the Liquid State) and, throughout the experimental run or field-
deployed discharge, the temperature and density of the liquid that remains in the vessel will be assumed to maintain their
Tespective initial values, Ty; and pay = Psat (T, "AL): As indicated, p 4, is estimated to be the density of saturated test agent
liquid at the saturation temperature T,;. The gas mixture is at an assumed uniform initial temperature Tpy, and the initial
masses of gaseous test agent and No ia the discharge vessel are Mpvag 2nd Mpywo1, respectively. Note that the pre-
pressurization process, prior to t = 0, may have been so rapid that the liquid and gas are not in thermal equilibrium with each
other. For this reason, Tpyz is not necessarily identical to Tay. The discharge vessel and the holding tank are at the
uniform pressures Ppva and Pir), respectively.

During an Experimental Run or Field-Deployed Discharge

During discharge of a Figure 1-type system, the flow path through the orifice is either open or closed at t = 0*. When the
orifice is closed the discharge will simulate discharge of a field-deplayed system which does not involve a holding tank. When
the onifice is open the discharge will simulate discharge of the experimental system where additional Ny pressurization during
the discharge is provided by the holding tank. The flow path through the nozzle/orifice at the exit of the discharge vessel is
either opened at t = O* (as in the field-deptoyed system, which uses an explosive cap to initiate discharge from an equilibrium
state at the specified Ppy,) or else it opens if and when Ppy rises to some specified diaphragm Tepture/burst pressure,
Paurst < Piri (as in the experimental system). The time when this latter flow path is opened is designated as tgurst-

Further Assumptions

For times and conditions of interest it is assumed that as long as liquid remains in the vessel Ppv > Psar(T az) and there
is no possibility of flashing (i.e, spontaneous change from a thermodynamically unstable liquid state to an equilibrium, two-
phase, tiquid/gas state) in the liquid volume. Future work will address the problem of removing this latter constraint from
the analysis. It is assumed that any N2 dissolved in the liquid that may come out of solution during the discharge process
is negligible.

‘The purpose of this work is to mathematically model the state of the system at any t > 0 up to tp, where tp is the smaller
of 1) the time when the discharge vessel is emptied of test-agent liquid, and 2) the time when Ppy is reduced to Pgar(T 1).

531


530

DISCHARGE OF FIRE SUPPRESSION AGENTS FROM A PRESSURIZED VESSEL: A MATHEMATICAL MODEL
AND ITS APPLICATION TO EXPERIMENTAL DESIGN

Leonard ¥. Cooper
Building and Fire Research Laboratory
National Institute of Standards and Technology

ABSTRACT

A mathematical model and associated computer program is developed to simulate the discharge of fire extinguishment agents
from N;-pressurized vessels. The model has three applications. First, to establish an experimental design and procedure
which closely simulates discharge of a field-deployed vessel; second, to evaluate the discharge characteristics of a wide range
of alternative-agent/pressure-vesse! configurations, thereby extending the slow and relatively costly experimental method of
making such evaluations; and finally, to predict vessel exit flow conditions to be used to solve the problem of agent dispersal
outside of the discharge vessel. The model is used in example calculations which address the first of these applications.

The field-deployed system, which forms the basis of the example calculations, involves a half-liter cylindrical discharge vessel
with a circular discharge nozzle/orifice of diameter 0.019m. The vessel is balf-filled with liquid Freon 22 and is pressurized
with No to 41.37x10°Pa (600psi). Vessel discharge is initiated by actuation of an explosive cap over the nozzle/orifice.

‘The simulating experimental configuration invoives a modified field-deployed system. A diaphragm with nominal 41.37x10°Pa
(600psi) rupture pressure [actual values between 37.92x10°Pa (550psi) and 44.82x10°Pa (650psi)] replaces the explosive cap.
The system is equipped with a high-pressure N2 holding tank connected to the discharge vessel via an orifice. An
experimental run begins with the onset of through-orifice Nz flow from the holding tank. The vessel is pressurized to the
point of diaphragm rupture and this is immediately followed by vessel discharge.

“The model is used to simulate discharge of the field-deployed system and pressurization/discharge of the experimental system.
Simulations of the experimental system involve holding tank volumes of 25x10%m° or 25x10°m*; orifice diameters of
0.005m, 0.001m, or 0.0005m; and initial vessel pressures of 9.3810°Pa (136psi) (the saturation pressure of Freon 22 at 294K)
and 34.47x10°Pa (500psi).

From the calculations it was determined that the 2.5x103m? holding tank with the 0.0005m orifice could be used to simulate
accurately the discharge of the field-deployed system and that it is reasonable to expect that this experimental design would
give good simulations even when extended to a range of parameters and agent materials well beyond the scope of the present
Calculations. Calculations also indicated that use of the 2.5x10"'m? holding tank and/or the 0.005m orifice would not be
consistent with an acceptable experimental design.

THE PROBLEM AND THE OBJECTIVE

This work formulates a mathematical model to simulate the discharge of Halon and Halon-alternative fire extinguishment
agents from N.-pressurized vessels. The ‘Objective is 10 develop a mathematical model which simulates agent-discharge
experiments under way at the Building and Fire Research Laboratory (BFRL) of the National Institute of Standards and
‘Technology (NIST). The experiments are part of a program to support advances in fire safety in aircraft of the US Air Force.

The model is expected to have three applications. First, it will be used to establish an experimental design and procedure
which closely simulates discharge of field-deployed vessels while allowing for acquisition of data, including high speed
photography, to characterize adequately the discharge process. Second, the model will be used to evaluate the discharge
characteristics of a wide range of alternative-agent/pressure-vessel configurations, thereby extending the slow and relatively
costly experimental method of making such evaluations. Finally, it will be used to determine the discharge vessel exit-flow
conditions for use in the simulation of agent dispersal outside of the vessel. After presenting the mathematical model, this
work will include example calculations which address the first of these applications. The analysis is based on the experimental
arrangement depicted in Figure 1.

THE EXPERIMENT AND THE MODEL ASSUMPTIONS
‘The Experimental Arrangement

Refer to Figure 1. This represents the arrangement associated with discharge experiments being considered at NIST The
Figure 1 arrangement can also be used to describe the phenomena of discharge from vessels under field conditions.


would not have risen to Paugsy and the discharge process would never have occurred! From Figure 19 it is seen that during
the pressurization process U;_r is reduces from approximately 4.0m/s to 1.5m/s. The liquid is nearly all discharged from the
vessel at 0,962s. During discharge: dZ/dt is reduced from 7.5m/s to 5.0m/s; Uygy rises to approximately 2.5m/s from its initial
value of 1.Sm/s and finally drops to approximately 2m/s; and (Myo - MyjnV/Myo9 Tises from 0 to approximately 0.005. The
criteria of Eqs (14) and (15) are again satisfied.

As noted, for both Paypsr = 37.92x10°Pa (5SOpsi) and 44.82x10°Pa (650psi) the above results indicate that both criteria
of Eq. (14) and (15) are satisfied with the small-bolding-tank/small-orifice design and that in this sense this design can be
expected to adequately reproduce field-deployed discharges. However, for the following three reasons the lacge-holding-tank
design is significantly more robust than the small-holding-tank design:

1. For a given maximum value for Pgupst: and discharge vessel volume, the minimum acceptable value for Pitt
[approximately 155.13x10°Pa (2250psi) for the present test parameters] is very sensitive to the original amount of
liquid in the vessel. For example, in the present simulations the vessel was assumed to be one-half full; but if it
were only one-quarter full, the minimum P;,y; that would lead to rupture of the 44.82x10°Pa (650psi) diaphragm
would have been approximately 206:84x105PS (3000psi).

2 The small-volume-holding tank configuration does not allow for the option of initiating tests from relatively-low
values of Poy, ¢.g. immediately after filling the vessel with the test agent, when Ppvi = Psat. To do so wouid
once again require highly variable and unreasonably large values of Pim

3. ‘The large-holding-tank design requires P,z7, values only slightly greater than the maximum Ppursr Value and it
suffers from neither of the above shortcomings.

Pressurization and Discharge for the Large Orifice, Do = 0.005m
Simulation results for pressurization/discharge test using the large-orifice design are presented in Figures 21 - 24.

For Paypsr = 37.92x10°Pa (550psi), plots of Ppy and Pyry are presented in Figures 21 and plots of Uygy, dZ/dt, Z/Z, and
(Myz - My2p)/Myo p in Figure 22. Note that the latter variable is meaningful only during discharge when t 2 tgypst- AS
can be seen in these figures, for this case tpypsp = 0.00173s, ic., this is the time it takes for Ppy to rise from Poy, =
34.47x10°Pa (500psi) to the diaphragm rupture pressure. From Figure 21 is seen that the Piry bas almost been reduced to
Ppy at t = 0.015s, at which time approximately 40 percent of the original amount of liquid is still in the vessel, ie. Z/Z, =
0.4 (Figure 22). Also, from Figure 22 it is seen that the liquid is nearly all discharged from the vessel (i¢., Z/Z, is
approaching zero) at approximately t = 0.023s. From Figure 22 it is seen that during discharge: the rate of liquid outflow
is reduced to about half of its original value, with dZ/dt going from 8my/s to 4m/s; Uygr is abways dropping, being reduced
from an initially large pre-discharge value of approximately 40m/s to approximately 4m/s; and (My - My p)/Mwop rises from
0 to 0.35, ie. at the end of the discharge the mass of Nz in the vessel is increased from its value at tgursr by a factor of
approximately 0.35. The latter two results indicate that the criteria of Eqs. (14) and (15) are not satisfied and, as when used
in conjunction with a relatively large holding tank, the large orifice design is not expected to adequately reproduce field-
deployed discharges.

For Paurst = 44.82x10°Pa (650psi), plots of Poy and Pyry are presented in Figures 23 and plots of Uygp, dZAAt, Z/Z,, and
(Myo - Mx p)/Myzg gy in Figure 24, The results are qualitatively similar to those discussed in the last Paragraph for Paupsy
= 37910 Pa (S50psi). The quantitative differences can be easily determined from the figures. For this case tgurst =
0.0094s. From Figure 23 is seen that the Pyrr has almost been reduced to Ppy at the time that discharge is initiated. Indeed,
if the Pyry1 had been much less than 155.13x10°Pa (2250psi), Ppy would not have risen to Paypsr and the discharge process
would never have occurred! The tiquid is nearly all discharged from the vessel at 0.03s. During pressurization process Uypy
drops from approximately 40m/s to 1Sm/s. During discharge: dZ/dt is reduced from 7m/s to Sms; Uygr is reduced from
15m/s to 3.Smv/s; and (My2 - Myo.)/Myop rises from 0 to 0.1. Although the criterion of Eq. (14) is satisfied, that of Eq.
(15) is not.

SUMMARY AND CONCLUSIONS

A mathematical mode! and associated computer program were developed to simulate the discharge of fire extinguishment
agents from No-pressurized vessels. The model is expected to have three applications. First, to establish an experimental

S41


HIGH PRESSURE N2
HOLDING TANK

OISCHARGE VESSEL

P [10°P2)

Figure 3. P-T diagram for metastable liquid CO, [3].

544

T= CONSTANT
SUPERHEATED METASTABLE LIQUIO
CAITICAL STATE

SATURATION CURVE

- SUBCOOLED METASTABLE GAS
SPINOIDAL CURVE

‘i——,

Figure 2. P-V diagram for a generic material; the spin-
oidal curve and regions of metastable liquid and vapor.

dZdt

Figure 4. Sketch of the orifice-driven N; jet flow in the
discharge vessel.