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An analysis of hydrogen-oxygen chemical reaction kinetics in rocket engine combustion, focusing on induction and postinduction times. The study calculates reaction times and concentration histories for various rocket engine conditions, identifying the importance of temperature and oxidant-fuel weight ratios on induction times. The document also discusses the limitations of the analytical method and the significance of chemical reaction times in rocket combustion.
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HYDROGEN-OXYGEN CHEMICAL
REACTION KINETICS I N
ROCKET ENGINE COMBUSTION
by Martia Hersch
Lewis Research Center
Cleveland, Ohio
N A S A TN D-
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COPY: RETURN TC
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https://ntrs.nasa.gov/search.jsp?R=19680002174 2020-05-13T23:31:04+00:00Z
By M a r t i n H e r s c h
L e w i s R e s e a r c h C e n t e r C l e v e l a n d , Ohio
For s o l e by the Cleoringhouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.
I I I I I 11.11 I ,^111.^ I.^ ,,...-.,-^ I .I.^. .I^ ..^.^ ..^ ..^.^.^.^ -^.^ .._..^.^ ..^ ..^ ..
invalid.
H + O2 = O + OH I
0 + H2 = H + OH 11
H + OH + M = H20 + M Iv
H2 + OH = H + H 2 0 (^) VI
where M is any third body.
a n analytical solution for reactions I, 11, VI, VII, and VIII (ref. 9), shows that the
HO2 + H2 H202 + H VII
eight reactions.
H2 + O2 - 2 OH is also considered with the use of the analytical technique.
species, and temperature change during reaction. The analytical method is restricted to constant H2 and O2 concentrations, nonreversible reactions, and constant temperature.
The numerical method considers reversible reactions, concentration changes of all
the reaction are also shown. Calculations were made for initial temperatures ranging
C A LC U LAT I ON S
Numerical Solution
(1) The mixture is one of thermally perfect gases. (2) Flow is inviscid throughout. (3) Transport properties can be neglected.
(5) The law of m a s s action applies throughout. Backward r a t e s a r e calculated, with microscopic reversibility assumed, from the
state a r e solved simultaneously with the differential equations for specie concentration changes due to chemical reactions.
similar unpublished Lewis data.
integration program a r e
Equations of mass, energy, and
Input data for the numerical program are temperature, pressure, species concentra-
The reactions, including those proposed by Brokaw (ref. 9), used for the numerical
0 + H2 = H + OH (^) IIn
2 H + M = H 2 + M IIIn
H + O H + M = H 2 0 + M N n
2 0 + M =02 + M (^) Vn
H2 + OH = H + H 2 0 VIn
H 0 2 + H2 = H + H
H + 0 2 + M (^) H 0 2 + M
VIIn
VIIIn
A n a l y t i c a l S o l u t i o n
An analytical solution is obtained with isothermal conditions and constant reactant
H + 0 2 -0^ K1 + OH
0 + H2& H + OH
0 2 + M - 2 0 + M Kg
la
IIa
IIIa
Va
Ha + OH -HKg + H 2 0 VIa
HOa + H2- K7 H + H202 (^) VIIa
H + 0 2 + M-H02+ K8 M VIILa
and induction radical formation is of concern. Reaction lVn is omitted from the analyti-
period. Reaction VLTI is considered in both directions in the analytic solution.
(for the case of reaction VIII in the forward direction)
--dCH - - K I C O p H + K Z C H C O+ 2K3CHpM dt
H02 = - K C 7 H a C (^) H 0 2 + K 8 C 0 2c cM H
dC
d t
hit
i= 1
hit c H = Bie + bH i= 1
hit = C Cie +- 'H H02 i= 1
hit COH = Die + dOH i= 1
constant with dimensions of second-'. The t e r m s a,, bH, cH02, and dOH, which result from initiation reactions, are
1111 I 11111111111 l I I I I I
solid and dashed curves represent numerical and analytical results, respectively. The
and radicals. The curves then show the relatively long induction period characterized by constant exponential growth under isothermal conditions. The numerical results show
10
(^0) YIW 0
Y m? (a) Temperature, 1400° K.
-8 -6 -4 -2 0 2x10- Time, see (b) Temperature, 1600" K. Figure 1. - OH growth and temperature rise.
500-
400
300
200
100- Q
10-
10-
10-
10-
10-l
10-16-10 -8 -6 -4 -2 0 2
3 V
$ 10-
;10-
al CL I-^ al^ V cO 0 10-
10-
100 10-l
(c) Temperature, Moo" K.
-3 -2 -1 0 1 2 3xW Time, sec (d) Temperature, 2500" K, numerical solution. Figure 1. - Concluded.
cases, well into the region of temperature increase. In this study the induction period is considered ended when the atom and radical concentrations deviate from constant exponential growth. This deviation can be determined, in this study, by the numerical method only. Although the analytical assumptions are violated when the system is
Numerical computation times increased drastically with decreasing temperature.
in figure 1 (a). The induction period is often considered ended when the OH concentration reaches the threshold of experimental detectibility, 10" gram-mole per cubic centi-
9
t
meter (ref. 9). This criterion appears to be suitable only for a n initial temperature near 1500' K. The induction time may now be determined by using these limits of OH concentration shown in figure 2.
portant, the postinduction time must also be investigated. Some idea of the post- induction time may be obtained from the curves of figure 3, which shows the temperature
seconds.
10-
10- U av), .-^ ai^ E
10-
10- 1200
\
\
1400 1600
. , , ,. I I. , Time.. Sdlution Oxidani-'fuel ratio, 01 F Induction Numerical 1
1800 2000 2 m Temperature, "K Figure 4. - Effect of initial temperature on induction and postinduction time.
and analytical methods show nearly identical results for the induction time. initial temperature higher than about 1700° K, the induction time is small in comparison with the postinduction time and therefore may be neglected. At lower temperatures the
time. The induction time increases rapidly with decreasing temperature for temper - a t u r e s below 1600' K. In this region the induction time increases exponentially with the reciprocal of initial temperature. The effect of O/F on induction time was investigated by determining the OH con-
atures were not made because of the long computational times. The OH concentration
For a n
imately the same for both O/F conditions.
c 0 c^ mL c al U c 0 U a 5 l CL^ m al
Initial temperature, "K (a) Numerical solution.
ized t o OH concentration).
(b) Analytical solution. Figure 5. - Relative product species d u r i n g induction period (normal-
induction, however, the relative concentrations remain nearly constant with time.
numerical program cannot be started with zero atom and radical concentrations. The effect of starting numerical calculations with arbitrary atom and radical concentrations
concentrations were calculated analytically. The solid curves a r e concentration
ll11llll1l11 I 1 I 1 I I I I 1 II I
0
1
Temperature, "K
o n t i m e to attain a r b i t r a r y OH concentra-
f u e l ratio. 1.
SIGNIFICANCE OF CHEMICAL REACTION
TIMES IN ROCKET COMBUSTION
Liquid -propellant rocket -engine combustion involves many steps, atomization,
steps will be more important than the rapid ones. The combustion dead time, a n in-
operating conditions. High-frequency instability must also be considered. Reference 1 shows that wave times for high-frequency instability range from about 0.1 to 1 milli- second. Thus, the time range of interest in liquid rocket combustion ranges from 0. to several milliseconds. Therefore, if chemical reaction times become greater than about 0.1 millisecond, they must be considered in studying rocket combustion.
ing reactant temperatures if the temperature is below about 1700° K. At 1600' K the
time increases to about
The slower
second and thus enters the region of interest in rocket
tors a r e substantially heated soon after injection by convection, radiation, and recircu- lation. The results of this study indicate that if the unreacted propellants are rapidly
(2. OX106 N/sq m).
s u r e gradients. If the instability wave reduces the temperature to below about 1500' K, then reaction times would greatly increase and become approximately equal to the wave period. Under these conditions the reaction kinetics could become an instability driving force.
Combustion instabilities, however, are known to cause large temperature and pres -
S U M M A R Y OF RESULTS
Hydrogen-oxygen reaction times and concentration histories were calculated for rocket combustor conditions. Calculations were made for oxidant-fuel weight ratios
chamber pressure of 20 atmospheres (2.0~10 N/sq m).^ A numerical integration pro-
were obtained:
1200' K. Since processes requiring times less than milliseconds can be neglected in determining performance efficiencies o r combustion characteristics this study indicates
approximately 1400' K.
of the oxidant-fuel mixture ratio on induction time increased with increasing temper- ature.
8. Zupnik, T. F. ; Nilson, E. N. ; and Sarli, V. J. : Investigation of Nonequilibrium Flow Effects in High Expansion Ratio Nozzles. Computor Program Manual. Rep. No. UACRL-C910096-11 (NASA CR-54042), United Aircraft Corp., Sept. 15, 1964.
Thermodynamic Properties to 6000' K for 210 Substances Involving the First 18 Elements. NASA SP-3001, 1963.
NASA-Langley, 1961 - 21 E-4010 17
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