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Pressure rise generated by combustion of a gas pocket
C O M B U S T I O N A N D F L A M E 3 8 : 3 2 9 - 3 3 4 (1980)
329
Pressure Rise Generated by Combustion of a Gas Pocket MERWIN SIBULKIN
Division of Engineering, Brown University. Providence,RhodeIsland, 02912
An analysis is presented for calculating the pressure rise in a vessel containingan inert gas and a pocket of combustible gas. The analysis gives results that are in reasonable agreement with experimental values. The theory confirms the experimental finding that the pressure rise for stoichiometric gas mixtures initially at atmospheric pressure is independent of the heating value of the fuel when the energyper unit container Volumeis the same. A generalizationof this result to nonstiochiometricmixtures is given. The available experimental results are shown to apply only when the system is initially at atmosphericconditions;the analysis allows the results to be extended to other initial conditions.
INTRODUCTION Accidental explosions of combustible gas mixtures are a continuing source of concern in many industrial operations. One aspect of the problem that has received relatively little attention is the calculation of the pressure rise due to the burning of a combustible mixture that only partially fills the confining structure. Experiments of this nature were conducted by Cubbage and Marshall [1] who were concerned with the consequences of explosions in manufacturing plants using gas-fired heaters. Recently, the possibility of the formation of combustible gas pockets in nuclear reactor containment vessels (Palmer et al. [2] ) has also directed attention to this problem. In the experiments of Cubbage and Marshall, stoichiometric mixtures of combustible gases were confined in a plastic bag and placed inside a pressure vessel. Both the combustible mixture inside the bag and the air outside the bag were initially at atmospheric pressure. After ignition, the measured pressure in the vessel reached a maximum value in about 50 ms and then slowly decreased as the gas cooled. Results were obtained for natural gas having a heating value of 1192 Btu/ft a (4.43 × 104 kJ/m a) and town gas having a heating value o f 498 Btu/ft a (1.85 × 104 kJ/ma). It was found that the results for both gases were correlated by a Copyright © 1980 by The Combustion Institute Published by Elsevier North Holland, Inc., 52 Vanderbilt Avenue, New York, NY 10017
single curve when the pressure rise Ap was plotted against Q/Vt where V t is the total volume of the reaction vessel and Q is the (calculated) total energy released by combustion, that is, the heat of reaction per mole of fuel times the number of moles of fuel in the combustible mixture. The authors did not attempt to predict this result from theory, and a literature search has not revealed any subsequent attempt to do so. In the present paper an analysis is made of the combustion of a gas pocket in a confining vessel. In particular, we are interested in determining (1) how the predicted pressure rise would vary if the initial pressure and temperature are not atmospheric and (2) whether the Ap versus Q/Vt correlation is predicted by theory. The analysis is based on equilibrium thermodynamics and does not consider the complex transient processes that occur during combustion. For a gas mixture that fills a spherical container, Bradley and Mitcheson [3] found that the final pressure rise given by their detailed transient calculation agreed closely with the thermodynamic pressure rise calculation. The analysis is also limited to small values of the relative pressure rise A p / p i which enables us to obtain a simple algebraic solution. Since many structures are designed to withstand only a small relative pressure rise, such results are of practical importance.
0010-2180/80/060329+06501.75
330
MERWlN SIBULKIN
ANALYSIS
tern due to its increase in volume is
A schematic drawing of the system is shown in Fig. 1 where V1 is the volume of the combustible mixture before burning, Vz is its volume after burning, and Vt is the total vessel volume. The basic simplifying assumptions made are: 1. The combustible and inert gas volumes are piecewise homogeneous before and after combustion. 2. The inert gas is compressed isentropically. 3. The perfect gas equation of state applies. 4. The pressure rise (/92 - Pl)/Pl ~ 1. The change in state of a closed system given by the first law of thermodynamics is E z - E a = Q - W, where E is the internal energy, Q is the heat added to the system, and W is the work done by the system. For the combustible gas mixture the heat added to the system due to chemical reaction is given by Q = - H r where the heat of reaction H r may be found from
Hr = E Npht,p - E Nth', r" p r Here hi, p is the heat of formation per mole of species p, Np is the number of moles of species p, and the subscripts p and r refer to products and reactants, respectively. The work done by the sys-
W=
fl
pdV.
It is assumed that the combustible gas mixture is a perfect gas for which E = NCoT. The resulting energy equation for the change in state of the combustible mixture is
N2Cv,2T 2 -N1Cv,IT1 = Q -
p dV,
(1)
where p is the pressure, T is the temperature, Cv is the specific heat at constant volume, and subscripts 1 and 2 refer to conditions before and after combustion. After combustion the pressure P2 in the reacted mixture is equal to the pressure in the inert gas and, of course, greater than Pl- We will, however, approximate, the work term in the energy equation by
l p dV ~- Pl (V2 - V1)"
(2)
This crude approximation greatly simplifies the analysis; it is justified by the fact that the energy represented by the work term is a small fraction of the energy released by combustion when use of the analysis is restricted to the case of small pressure rise [assumption (4)]. The approximation is on the conservative side since it will overestimate the pressure rise. Defining nondimensional variables
,I
(9=-- V/Vt,
P:-P2/Pl,
0 -- T2/T 1
and dividing by N 1Cv, 1 T1 gives
N2Cv 2 'O-1N1Cv,1
Vt
Q N1Cv,I T1 PlV1 ¢l_~a-1). Nx Cv,I T1
(3)
The change in state of the inert gas is given by
Vt-W2=P(_~_I) -1/'rx Fig. 1. Schematic drawing of system analyzed.
V t - Vl
'
(4)
PRESSURE RISE IN COMBUSTION
331
where 3'i is the ratio of specific heats of the inert gas. Again using assumption (4) to expand the right-hand side of Eq. (4) gives
where 3' = Cp,1/Co,1. Finally, combining Eqs. (5) and (8) to eliminate P gives as the equation for ¢2
1 -¢2 - - 1 - ¢1
1 -¢2_
1 (P-
1).
(5)
1
1
7i
-
-
1
¢1
1 ((H+_7)~11 7I \
C
(7-1))
¢2
1
.
C
This equation can be manipulated into the form In terms of the nondimensional variables, the equation of state p V = NR T takes the form
0 = NI¢2 P.
¢2 2
{(1-¢1)[C(3',+1)+(3'-1)]
1}¢2
(6)
N2¢1
- ((1 - ¢I)(H CI3' + 3')¢1 ) = 0.
Equations (3), (5), and (6) are a system of three equations for the three unknowns ¢2, 0, and P. We now define a heat addition parameter H-
+
The solution of Eq. (10) is ¢2 = K1 + (K12 + K2)1/2,
Q
(11)
(7)
N1Co,1T1
where
and C = Cv,2/Co,1. Then combining Eqs. (3) and (6) to eliminate 0 yields
} C 3 ' I K 1 --- 21 _-- {1 - (1-¢1)[C(3'I+1)+(3'-1)]
C¢2p=1+H-(3"-1)(~
K2 ~ /(1 - ¢1)" C(H+ 3 ' i7)¢1/
¢1
1) --
(8) '
/
1.4-
/
1.3 _
-
0.4
~ / ~ / t :
0.3
_
n,
y
,.2-
/
I.I 1.0
0
// I .01
.-'*,
_
/J~
/~//
o.z
.
o.i
I .02
(10)
I .03
I .04
0 .05
~j "vl / v t
Fig. 2. Pressurerise and expansionratio as functionsof initial combustiblevolumefraction (H = 13.1).
332
MERWlN SIBULKIN
Theory Experiments
[I]
1.4-
/ _
/•/"
~.s
g
/
II
a_
1.2
/./" //./
i.i
1.0 0
I
I
I
I
I
I
2
5
4
.5
Q/V t (Btu/ft I 0
I 50
3)
I I00 Q / V t ( k J / m 3)
I 150
I 200
Fig. 3. Comparison of theoretical pressure rise (H -- 13.1) with experimental results for natural gas and town gas.
After ¢2 is calculated, the pressure ratio P is f o u n d f r o m Eq. (8) rewritten in the forma P = (H + 3')¢1 1
(3' - 1)
C ¢2 C
(12)
The results obtained using these equations are discussed in the n e x t section.
RESULTS
value o f 3' = 1.4 was used. Calculation o f the parameter H for stoichiometric fuel-air mixtures gives H = 13.1 for CH 4 a n d H = 13.2 for H 2 taking T 1 = 3 0 0 ° K and Co,1 = 5 cal/mol K2. The natural gas used b y Cubbage and Marshall contained 78% CH 4 and their t o w n gas contained 52% H 2 and 32% CH4, so a value o f H = 13.1 was used in the calculations. A value o f C = 1.25 was chosen based on an after c o m b u s t i o n temperature o f 2 2 0 0 ° K and the specific heat variation o f nitrogen.
In order to calculate numerical results, values o f 3', H, and C must be specified for the combustible gas m i x t u r e and a value o f 7i for the inert gas. Calculations were made for a diatomic inert gas 3'I = 1.4. F o r fuel-air mixtures, the major species before and after c o m b u s t i o n is nitrogen and so a
2 That the values ofHfor stoichiometric fuel-air mixtures at T 1 = 300 ° K will be similar for hydrocarbon fuel gases can be seen by writing the parameter H in the form
1 The reader may be interested to note that in the limit ¢1 = 1, where the combustible gas fills the vessel, g 1 = 1/2 and K 2 = 0 giving the proper limit ¢2 = ¢1 = 1 and P = (1 + H)/C.
For hydrocarbon fuels, the heat of combustion per mole of oxygen Q/Nox does not vary greatly, and for stoichiometric fuel-air mixtures the ratio Nox/N 1 is dominated by the oxygen-nitrogen ratio in air.
O NICo, IT1
Q Nox Nox
1
N1 Cv,IT1
PRESSURE RISE IN COMBUSTION
333
The results of using these parameter values is shown in Fig. 2 for a range of ¢1 up to 0.05. In this range ¢2/¢1 --- 7 and P increases almost linearly with ¢1. The results are limited to P < 1.5 in keeping with assumption (4). In presenting their experimental results, Cubbage and Marshall [1] chose the parameter Q/V t. Using the perfect gas law, we find Q _ Q V: V1
V:
I 3.1
1.25 1.15
/ ~/~/~/ /
1.4
-
I/,, .//,
,.3 -
¢:,
N:RT1
C 1.35
6.55
Qp: - -
Vt
H 26.2
• Q.
giving 1.2
Q _ PlCv,1 - -
gt
He 1 .
(13)
R I.I
Since their tests were all conducted at P: = 1 arm and the value of H is nearly the name for both gases, our analysis does predict that the results for P versus Q / V t would be the same for natural gas and town gas, in agreement with the experimental findings. The theoretical and experimental results are compared in Fig. 3. 3 The predicted pressure rise exceeds the measured values. We attribute this primarily to the mathematical approximation made in Eq. (2) and the assumption of complete burning of the combustible gas mixture implicit in the calculation o f H . 4 The work of Cubbage and Marshall [ 1] was directed solely to the problem of accidental explosions in gas mixtures initially at atmospheric temperature and pressure. For other initial conditions (as in a nuclear reactor containment.vessel after a blowdown accident [2]) their experimental results are not directly applicable, since for a given composition and initial volume of the combustible gas the value of H depends on T 1 and the value of Q/V t depends on Pl. [1] extend, almost linearly, to Q/V t = 20 Btu/fta; the theoretical curve can also be extended, b u t the agreement between the two results is considered fortuitious in view o f the assumptions m a d e in the analysis. 4 It m a y be noted that taking C = 1, that is, neglecting the change in Cv, increases the value of P - 1 by approximately 15%.
1.0
0
I
I
I
0.2
0.4
0.6
He, Fig. 4. Effect of energy input parameter H on pressure rise.
Even for atmospheric values of T1, the values of H will vary if the fuel-oxygen ratio is not stoichiometric or the oxygen-nitrogen ratio differs from normal air. Calculations of pressure rise were made for three values of H and are plotted against the product H e 1 in Fig. 4. The results show that the pressure rise is nearly independent of H in these coordinates. Since Q/V t is proportional to H¢ 1 for fixed P: (see Eq. (13)), this result shows that the energy per unit container volume Q/V t controls the pressure rise even when the energy input parameter H varies.
3 The experimental results in Ref.
This work was partially supported by the HTGR Safety Division, Department o f Nuclear Energy, Brookhaven National Laboratory. However, any conclusions drawn in this publication are those o f the author and not o f the BNL.
334
REFERENCES 1. Cubbage, P. A., and Marshall, M. R., I. Chem. E. Symp. Series 33: 24-31 (1972). 2. Palmer, H. B., Sibulkin, M., Strehlow, R. A., and Yang, C. H., An Appraisal of Possible Combustion Hazards
MERWIN SIBULKIN Associated with a High-Temperature Gas-Cooled Reactor, NUREG-50764, Brookhaven National Laboratory, Upton, N.Y., 1978. Bradley, D., and Mitchson, A., Combust. Flame 26: 201-217 (1976).
329
Pressure Rise Generated by Combustion of a Gas Pocket MERWIN SIBULKIN
Division of Engineering, Brown University. Providence,RhodeIsland, 02912
An analysis is presented for calculating the pressure rise in a vessel containingan inert gas and a pocket of combustible gas. The analysis gives results that are in reasonable agreement with experimental values. The theory confirms the experimental finding that the pressure rise for stoichiometric gas mixtures initially at atmospheric pressure is independent of the heating value of the fuel when the energyper unit container Volumeis the same. A generalizationof this result to nonstiochiometricmixtures is given. The available experimental results are shown to apply only when the system is initially at atmosphericconditions;the analysis allows the results to be extended to other initial conditions.
INTRODUCTION Accidental explosions of combustible gas mixtures are a continuing source of concern in many industrial operations. One aspect of the problem that has received relatively little attention is the calculation of the pressure rise due to the burning of a combustible mixture that only partially fills the confining structure. Experiments of this nature were conducted by Cubbage and Marshall [1] who were concerned with the consequences of explosions in manufacturing plants using gas-fired heaters. Recently, the possibility of the formation of combustible gas pockets in nuclear reactor containment vessels (Palmer et al. [2] ) has also directed attention to this problem. In the experiments of Cubbage and Marshall, stoichiometric mixtures of combustible gases were confined in a plastic bag and placed inside a pressure vessel. Both the combustible mixture inside the bag and the air outside the bag were initially at atmospheric pressure. After ignition, the measured pressure in the vessel reached a maximum value in about 50 ms and then slowly decreased as the gas cooled. Results were obtained for natural gas having a heating value of 1192 Btu/ft a (4.43 × 104 kJ/m a) and town gas having a heating value o f 498 Btu/ft a (1.85 × 104 kJ/ma). It was found that the results for both gases were correlated by a Copyright © 1980 by The Combustion Institute Published by Elsevier North Holland, Inc., 52 Vanderbilt Avenue, New York, NY 10017
single curve when the pressure rise Ap was plotted against Q/Vt where V t is the total volume of the reaction vessel and Q is the (calculated) total energy released by combustion, that is, the heat of reaction per mole of fuel times the number of moles of fuel in the combustible mixture. The authors did not attempt to predict this result from theory, and a literature search has not revealed any subsequent attempt to do so. In the present paper an analysis is made of the combustion of a gas pocket in a confining vessel. In particular, we are interested in determining (1) how the predicted pressure rise would vary if the initial pressure and temperature are not atmospheric and (2) whether the Ap versus Q/Vt correlation is predicted by theory. The analysis is based on equilibrium thermodynamics and does not consider the complex transient processes that occur during combustion. For a gas mixture that fills a spherical container, Bradley and Mitcheson [3] found that the final pressure rise given by their detailed transient calculation agreed closely with the thermodynamic pressure rise calculation. The analysis is also limited to small values of the relative pressure rise A p / p i which enables us to obtain a simple algebraic solution. Since many structures are designed to withstand only a small relative pressure rise, such results are of practical importance.
0010-2180/80/060329+06501.75
330
MERWlN SIBULKIN
ANALYSIS
tern due to its increase in volume is
A schematic drawing of the system is shown in Fig. 1 where V1 is the volume of the combustible mixture before burning, Vz is its volume after burning, and Vt is the total vessel volume. The basic simplifying assumptions made are: 1. The combustible and inert gas volumes are piecewise homogeneous before and after combustion. 2. The inert gas is compressed isentropically. 3. The perfect gas equation of state applies. 4. The pressure rise (/92 - Pl)/Pl ~ 1. The change in state of a closed system given by the first law of thermodynamics is E z - E a = Q - W, where E is the internal energy, Q is the heat added to the system, and W is the work done by the system. For the combustible gas mixture the heat added to the system due to chemical reaction is given by Q = - H r where the heat of reaction H r may be found from
Hr = E Npht,p - E Nth', r" p r Here hi, p is the heat of formation per mole of species p, Np is the number of moles of species p, and the subscripts p and r refer to products and reactants, respectively. The work done by the sys-
W=
fl
pdV.
It is assumed that the combustible gas mixture is a perfect gas for which E = NCoT. The resulting energy equation for the change in state of the combustible mixture is
N2Cv,2T 2 -N1Cv,IT1 = Q -
p dV,
(1)
where p is the pressure, T is the temperature, Cv is the specific heat at constant volume, and subscripts 1 and 2 refer to conditions before and after combustion. After combustion the pressure P2 in the reacted mixture is equal to the pressure in the inert gas and, of course, greater than Pl- We will, however, approximate, the work term in the energy equation by
l p dV ~- Pl (V2 - V1)"
(2)
This crude approximation greatly simplifies the analysis; it is justified by the fact that the energy represented by the work term is a small fraction of the energy released by combustion when use of the analysis is restricted to the case of small pressure rise [assumption (4)]. The approximation is on the conservative side since it will overestimate the pressure rise. Defining nondimensional variables
,I
(9=-- V/Vt,
P:-P2/Pl,
0 -- T2/T 1
and dividing by N 1Cv, 1 T1 gives
N2Cv 2 'O-1N1Cv,1
Vt
Q N1Cv,I T1 PlV1 ¢l_~a-1). Nx Cv,I T1
(3)
The change in state of the inert gas is given by
Vt-W2=P(_~_I) -1/'rx Fig. 1. Schematic drawing of system analyzed.
V t - Vl
'
(4)
PRESSURE RISE IN COMBUSTION
331
where 3'i is the ratio of specific heats of the inert gas. Again using assumption (4) to expand the right-hand side of Eq. (4) gives
where 3' = Cp,1/Co,1. Finally, combining Eqs. (5) and (8) to eliminate P gives as the equation for ¢2
1 -¢2 - - 1 - ¢1
1 -¢2_
1 (P-
1).
(5)
1
1
7i
-
-
1
¢1
1 ((H+_7)~11 7I \
C
(7-1))
¢2
1
.
C
This equation can be manipulated into the form In terms of the nondimensional variables, the equation of state p V = NR T takes the form
0 = NI¢2 P.
¢2 2
{(1-¢1)[C(3',+1)+(3'-1)]
1}¢2
(6)
N2¢1
- ((1 - ¢I)(H CI3' + 3')¢1 ) = 0.
Equations (3), (5), and (6) are a system of three equations for the three unknowns ¢2, 0, and P. We now define a heat addition parameter H-
+
The solution of Eq. (10) is ¢2 = K1 + (K12 + K2)1/2,
Q
(11)
(7)
N1Co,1T1
where
and C = Cv,2/Co,1. Then combining Eqs. (3) and (6) to eliminate 0 yields
} C 3 ' I K 1 --- 21 _-- {1 - (1-¢1)[C(3'I+1)+(3'-1)]
C¢2p=1+H-(3"-1)(~
K2 ~ /(1 - ¢1)" C(H+ 3 ' i7)¢1/
¢1
1) --
(8) '
/
1.4-
/
1.3 _
-
0.4
~ / ~ / t :
0.3
_
n,
y
,.2-
/
I.I 1.0
0
// I .01
.-'*,
_
/J~
/~//
o.z
.
o.i
I .02
(10)
I .03
I .04
0 .05
~j "vl / v t
Fig. 2. Pressurerise and expansionratio as functionsof initial combustiblevolumefraction (H = 13.1).
332
MERWlN SIBULKIN
Theory Experiments
[I]
1.4-
/ _
/•/"
~.s
g
/
II
a_
1.2
/./" //./
i.i
1.0 0
I
I
I
I
I
I
2
5
4
.5
Q/V t (Btu/ft I 0
I 50
3)
I I00 Q / V t ( k J / m 3)
I 150
I 200
Fig. 3. Comparison of theoretical pressure rise (H -- 13.1) with experimental results for natural gas and town gas.
After ¢2 is calculated, the pressure ratio P is f o u n d f r o m Eq. (8) rewritten in the forma P = (H + 3')¢1 1
(3' - 1)
C ¢2 C
(12)
The results obtained using these equations are discussed in the n e x t section.
RESULTS
value o f 3' = 1.4 was used. Calculation o f the parameter H for stoichiometric fuel-air mixtures gives H = 13.1 for CH 4 a n d H = 13.2 for H 2 taking T 1 = 3 0 0 ° K and Co,1 = 5 cal/mol K2. The natural gas used b y Cubbage and Marshall contained 78% CH 4 and their t o w n gas contained 52% H 2 and 32% CH4, so a value o f H = 13.1 was used in the calculations. A value o f C = 1.25 was chosen based on an after c o m b u s t i o n temperature o f 2 2 0 0 ° K and the specific heat variation o f nitrogen.
In order to calculate numerical results, values o f 3', H, and C must be specified for the combustible gas m i x t u r e and a value o f 7i for the inert gas. Calculations were made for a diatomic inert gas 3'I = 1.4. F o r fuel-air mixtures, the major species before and after c o m b u s t i o n is nitrogen and so a
2 That the values ofHfor stoichiometric fuel-air mixtures at T 1 = 300 ° K will be similar for hydrocarbon fuel gases can be seen by writing the parameter H in the form
1 The reader may be interested to note that in the limit ¢1 = 1, where the combustible gas fills the vessel, g 1 = 1/2 and K 2 = 0 giving the proper limit ¢2 = ¢1 = 1 and P = (1 + H)/C.
For hydrocarbon fuels, the heat of combustion per mole of oxygen Q/Nox does not vary greatly, and for stoichiometric fuel-air mixtures the ratio Nox/N 1 is dominated by the oxygen-nitrogen ratio in air.
O NICo, IT1
Q Nox Nox
1
N1 Cv,IT1
PRESSURE RISE IN COMBUSTION
333
The results of using these parameter values is shown in Fig. 2 for a range of ¢1 up to 0.05. In this range ¢2/¢1 --- 7 and P increases almost linearly with ¢1. The results are limited to P < 1.5 in keeping with assumption (4). In presenting their experimental results, Cubbage and Marshall [1] chose the parameter Q/V t. Using the perfect gas law, we find Q _ Q V: V1
V:
I 3.1
1.25 1.15
/ ~/~/~/ /
1.4
-
I/,, .//,
,.3 -
¢:,
N:RT1
C 1.35
6.55
Qp: - -
Vt
H 26.2
• Q.
giving 1.2
Q _ PlCv,1 - -
gt
He 1 .
(13)
R I.I
Since their tests were all conducted at P: = 1 arm and the value of H is nearly the name for both gases, our analysis does predict that the results for P versus Q / V t would be the same for natural gas and town gas, in agreement with the experimental findings. The theoretical and experimental results are compared in Fig. 3. 3 The predicted pressure rise exceeds the measured values. We attribute this primarily to the mathematical approximation made in Eq. (2) and the assumption of complete burning of the combustible gas mixture implicit in the calculation o f H . 4 The work of Cubbage and Marshall [ 1] was directed solely to the problem of accidental explosions in gas mixtures initially at atmospheric temperature and pressure. For other initial conditions (as in a nuclear reactor containment.vessel after a blowdown accident [2]) their experimental results are not directly applicable, since for a given composition and initial volume of the combustible gas the value of H depends on T 1 and the value of Q/V t depends on Pl. [1] extend, almost linearly, to Q/V t = 20 Btu/fta; the theoretical curve can also be extended, b u t the agreement between the two results is considered fortuitious in view o f the assumptions m a d e in the analysis. 4 It m a y be noted that taking C = 1, that is, neglecting the change in Cv, increases the value of P - 1 by approximately 15%.
1.0
0
I
I
I
0.2
0.4
0.6
He, Fig. 4. Effect of energy input parameter H on pressure rise.
Even for atmospheric values of T1, the values of H will vary if the fuel-oxygen ratio is not stoichiometric or the oxygen-nitrogen ratio differs from normal air. Calculations of pressure rise were made for three values of H and are plotted against the product H e 1 in Fig. 4. The results show that the pressure rise is nearly independent of H in these coordinates. Since Q/V t is proportional to H¢ 1 for fixed P: (see Eq. (13)), this result shows that the energy per unit container volume Q/V t controls the pressure rise even when the energy input parameter H varies.
3 The experimental results in Ref.
This work was partially supported by the HTGR Safety Division, Department o f Nuclear Energy, Brookhaven National Laboratory. However, any conclusions drawn in this publication are those o f the author and not o f the BNL.
334
REFERENCES 1. Cubbage, P. A., and Marshall, M. R., I. Chem. E. Symp. Series 33: 24-31 (1972). 2. Palmer, H. B., Sibulkin, M., Strehlow, R. A., and Yang, C. H., An Appraisal of Possible Combustion Hazards
MERWIN SIBULKIN Associated with a High-Temperature Gas-Cooled Reactor, NUREG-50764, Brookhaven National Laboratory, Upton, N.Y., 1978. Bradley, D., and Mitchson, A., Combust. Flame 26: 201-217 (1976).