Reaction rate data were collected for chemical reactions occurring at high temperatures during reentry of space vehicles. The principle of detailed balancing is used in modeling kinetics of chemical reactions at high temperatures. Although this principle does not hold for certain transient or incubation times in the initial phase of the reaction, it does seem to be valid for the rates of internal energy transitions that occur within molecules and atoms. That is, for every rate of transition within the internal energy states of atoms or molecules, there is an inverse rate that is related through an equilibrium expression involving the energy difference of the transition

Johnson, Richard E.

English

NASA Technical Reports Server

N87-25886
NON-EQUILIBRIUM EFFECTS IN HIGH
TEMPERATURE CHEMICAL REACTIONS
Richard E. Johnson, Ph.D.
Professor of Chemistry
LeTourneau College
Longview, Texas
ABSTRACT
Reaction rate data have been collected for chemical
reactions occuring at high temperatures during reentry of
space vehicles. Large differences in reaction rate data are
reported by various authors in the literature.
The principle of detailed balancing is used in modeling
kinetics of chemical reactions at high temperatures.
Although this principle does not hold for certain transient
or incubation times in the initial phase of the reaction,
it does seem to be valid for the rates of internal energy
transitions that occur within molecules and atoms. That
is, for every rate of transition within the internal energy
states of atoms or molecules, there is an inverse rate that
is related through an equilibrium expression involving the
energy difference of the transition.
Future goals include theoretical modeling to include
internal energy transitions into overall rate expressions
that can then be used to predict radiation heating effects
for reentry vehicles under non-equilibrium conditions.
NASA Colleague: Carl D. Scott, Ph.D., ED3, X4306
16-2
https://ntrs.nasa.gov/search.jsp?R=19870016453 2020-03-20T10:51:42+00:00Z
TABLE OF CONTENTS
Introduction
Chemical Reaction Rates
Detailed Balancing Principle
Master Equation Approach
Other Approaches to Nonequilibrium Rates
Summary
F'age
4
4
9
I0
13
15
Acknowledgements
Bibliography
Table i. Reaction Rate Data
17
18
b
16-3
INTRODUCTION
Data from Space Shuttle flights and experimental work
indicate that non-equilibrium radiation due to chemical
non-equilibrium in the shock layer of rentry vehicles may
result in a significant added heat load. (I,2,3) For OIV
and AOTV with higher reentry velocities, these non-
equilibrium effects may be even more significant. (4)
This work is a continuation of work from last summer which
will focus in on reaction rate data reported in the
literature and also consider furthur the principle of
detailed balancing as applied to transitions within the
internal energy states of molecules.
CHEMICAL REACTION RATES
At an altitude of 80-100 kilometers,
substances in the atmosphere include N , 0
the reactant
, N, 0, NO,
various positive ions and electrons. However, with these
few reactants, a multitude of reactions with various
interdependent relationships could possibly occur upon the
initiation of a shock wave by a reentry vehicle. The low
pressure at these altitudes and the high energy input due
to the shock wave from Mach 20-35 results in a region o÷
chemical non-equilibrium between the reentry vehicle's
surface and the shock front. This chemical non-
16-4
equilibrium is not just due to the progress of reactions
from reactants to products in the ordinary sense of
chemical reactions. A more significant and complicating
factor is that internal energies of atoms and molecules
also take a finite time to change with the rapid input of
energy. During this time of internal energy equilibration,
the ordinary rate constant of a chemical reaction is not
definable. This time of internal energy equilibration has
been referred to in the literature as an incubation time or
a pre-quasistationary time. (5,6,7)
The chemical reactions that could occur are many and some
of the representative ones are given on the next page.
Carlson and Rieper(8) considered only the first twelve
reactions given on the next page in their investigations on
medium shock waves(5-7 km/sec). Their numerical
predictions agreed with their experimental data on the
electron temperature variation in these shock waves.
16-5
Oi ÷ 0_20 + 0
0_. + 02_-_20 + 0 z
02 + M_- 20 + M
N2 + 0_- NO + N
02 + N4-_ NO + 0
N + 0_-NO _" + e
NO + M,_ N + 0 + M
N + N< -_ N 2 + e
.p
0 +0.-_ 0 z + e
N_.+ N_!_ 2N + N_.
N2+ N _ 2N + N
N2+ M _-_ 2N + M
NO + 0,_ N + 0 z
_" 0_o + o2_oz+
N 2+ N_-- _ N + N;
O + NQ_'_ NO + .0"e
N 2 + 0+_-_ O ÷ N;
N + NO_ NO + N+
02.+ NO+_--_ NO ÷ O_.
O + NO_ 02. + N ÷
NO + N_-_ 0 + N_Z
0 + e _ 0_ + e + e
N + e _ N_" + e + e
16-6
Chul Park(9,10) has used all of the above reactions in a
computer program (NEQAIR) to Calculate the extent of
reactions and radiation in the non-equilibrium zone for a
shock wave speed of iOkm/sec. At this higher shock speed,
calculated results did not fit the limited experimental
data from shock tube experiments.
There are still discrepancies in the literature for
reaction rate data as reported by various authors. Some of
these are given in Table 1 below.
Some of these differences in reaction rate data are small
in magnitude and would not affect the results of
computations drastically. However, many of the reactions
have orders of magnitude differences in the rate contants
and also differences in the temperature dependency of the
reactions. These include the nitrogen, oxygen and nitric
oxide dissociations as well as the impact ionization
reactions.
Further work on the effect of varying the rate constants
upon the output of computer programs would seem to be a
worthwhile effort. Better agreement with experimental data
may be obtained by adjusting rate parameters within the
computer program itself.
16-7
Reaction
Taole i. Reaction Rate Data
Rate Constant, k = AT e (co/mole-see)
A s B Ref.
Nz + N2_ N + N +Ni 3.7(21) 1.6 113,200 10
4.7(17) 0.5 113,200 ii
_.__(29)_ 3.5 113,200 12
N= + N_N + N + N 1.1(22) l.b 113,200 10
4.1(22) 1.5 113,200 ii
8.5(25) 2.5 113,200 12
0i + 02_ 0 + 0 + 0z 2.8 (19) 1. <) 59,500 10
i _' •
- (19) 1 0 59,5<_0 Ii
6.2(24) -.'_5 59,500 13
O2 + O _ 0 + O + O 8.3 (19) 1.0 59,500 Ic.)
0(19) I 0 59,5<_0 iii
4. <)(18) 1.0 59,500 13
N z + 0_N0 + N 3.2(13) 0.1 37,700 10
7. E (13) 0.0 38,000 11
1.8(14) 0.0 38,300 13
NO + M_ N + O + M
(M = O or N )
2.3(17) 0.5 75,500 i0
3.9(20) 1.5 75,500 II
1.4(14) 0.0 74,600 14
5.2(15) 0.0 75,800 15
NO + M_ N + O + M
(M = O,N or NO)
N + O_ NO + e
4.6(17) 0.5 75,500 10
7.8(20) 1.5 75,500 ii
3.0(14) 0.0 76,400 14
5.2(15) 0.0 75,80<) 15
i. 5 (10) -. 37 32,0<x) i0
1.4( 6) -1.5 31,900 ii
3.0(13) 0 5 3? 5<_<_ 16
N + N _ N z + e 1.8(10) -.77 67,500 10
0 U. ii
1.3XI0'T+3.3XI0 T -10 F) e'6_ 175 4X10 I+
0 + 0 _ 0_ + e 3.9(10) -.49 80,600 10
,3 ' _,1.6(17)(5_ .9_80,80<, ii1.9X10 T-_'(I+7.5X1C_ T+2.-.'X1 2) e- 17
16-8
DETAILED BALANCINGFRINCIPLE
For ordinary, one-step chemical reactions, the principle of
detailed balancing can be shown to follow from equilibrium
relationships. Consider the reaction
AB + M A + B + M
at equilibrium, k_ (AB) (M) = k_(A) (B) (M)
and therefore kd/k r = (A) (B)/(AB) = K, the equilibrium
constant.
Even away from equilibrium, _/k v = K because the k's
do not depend upon concentrations.
Usually _ and kyare not both available from experimental
data. Especially at high temperatures, _ is expressed as
/_ in computer programs and calculations involving these
rates of reactions.
Work last summer led to tde conclusion that this
relationship, _ /k_ = K, also called the principle of
detailed balancing, does not hold under certain conditions.
If a large, sudden change in temperature occurs in a system,
such as that generated by a high energy shock wave, then
the equilibration of energy into the internal states will
take a finite time and this time may become comparable to
the reaction time of the system. When this occurs, the
ordinary chemical rate constant is not well defined since
16-9
it usually represents an average rate of reaction over many
individual rates from internal energy states. There is
then an incubation time before the reaction rate reaches a
steady-state or defined value. During this incubation
time, the principle o÷ detailed balancing does not hold for
overall chemical reaction rates. (7)
During
become
these
Approach" which is shown diagramatically below.
the incubation time, internal energy transitions
important and the approach to considering all of
transitions is summarized in the " Master Equation
v=i _.
v=j
v=l
v--O
MASTER EQUATION APPROACH
AB.
1
| kji I AB. I i
I I ,,/
I ' /
i /
- I /
t / d [ABi_-
\ / dt
/
/
k°
+ M..Rq__AB; + M
k. Ji
J
l
ABi ._A + B
"-i
MASTER EQUATION
_.kji[M][AB"_- _ ki K.iJ J kij[M][AB i] - [ABi3 + _[8]
AB DISTANCE
f
16-10
This equation could be solved if all k_, , kd"_ ,k_" and W_" are
known. Approximations to this equation have been tried
using detailed balancing for the internal energy
transitions(kij and Wjl ), and also assuming a harmonic
oscillator. This development is shown in several references
such as "Introduction to Physical Gas Dynamics" by Vincenti
and Kruger. (18) This particular development is for
vibration levels only and is breifly, summarized below.
• ¢" Kj,_, _ _/_g
K,5. e -_T
KZj, = [_,_o
_o _.
t - e - _v/kr
a o:j
a _ = K_oE_iE_B_;j+(gH)E4BZ,,]+e. (-(,','O_q:]÷
v : - " _-_'_'-I
16-II
Probably the
principle of
states. At
best assumption in this development is the
detailed balancing for the internal energy
the molecular level, where elementary
collisions cause internal energy transitions, the exchange
from translational to vibrational energy or vice-versa in a
collisional process should be reversible in time by energy
conservation principles. Thus there is no reason to
suspect the failing of the principle of detailed balancing
at this elementary level unless some other energy
equilibration pr(_cedure is occuring that is not known.
Rotational energies are lower than vibrational energies_
but those transitions are assumed to occur very quickly
even at low pressures so that rotational energies and
translational energies are very quickly equilibrated. The
effect of annarmonicity of the vibrational mode within the
molecule is an effect that should be considered. This
effect becomes more pronounced at higher energies and it
is these higher energies that are important for
dissociation.
Thus the development of the Master Equation using detailed
balancing and harmonic oscillator assumptions is a valid
first approximation to calculation of rates of reaction in
high energy shock waves. However, other approaches are also
presently being worked on and these are summarized below.
16-12
OTHERAPPROACHESTO NON-EQUILIBRIUM REACTION RATES
Dove, et al have calculated the effects of coupling for the
internal modes upon the relaxation of internal energies for
hydrogen. (19) They concluded that at high rotational
energies (J 10), coupling between translational,
vibrational and rotational becomes almost as significant as
translational-roatational coupling and is greater than
translational-vibrational coupling. Thus at high rotaional
energies, equilibration in the internal energies occurs
through combined rotational-vibrational energy level
changes.
Koshi has calculated the effect of vibrational-dissociation
and dissociation-vibrational coupling(CVDV effect) and
compared it with experimental data on NO dissociation. (15)
His agreement is very good and indicates that as the
translational
temperature
the range
temperature increases, the vibrational
lags behind and seems to approach a limit in
of 5000K even though the translational
temperature is above 7500K. The CVDV effect is due to the
reduction of the dissociation rate due to the lack of
vibrational equilibration within the molecule and also the
coupled effect of a slower vibrational equilibration time
due to dissociation removing energy from the upper
vibrational levels and thus depleting them too rapidly.
• 16-13
This could result in a "bottle-neck" effect. That is, with
a very rapid and high energy input, such as that from a
high energy shock wave, the dissociation rate is limited by
internal energy transitions within vibrational levels and
not by the dissociation of the molecule from highly excited
vibrational energies into two atoms.
Carlson compared experimental results with calculations on
nitrogen in moderate shock waves studies and included the
CVDV efeect as well as electronic-vibrational coupling.
His clacul ated el ectronic temperature and the measured
values agreed well within experimental error for this
series of experiments. (8)
Finally, Chul Park has worked extensively on this problem
and has written a computer program for predicting the non-
equilibrium radiation in a shock front using available rate
data. (9,10) His approach utilizes a two or three
o
temperature model assuming different temperatures for
different internal modes of energy and also a translational
temperature. For some reactions, he uses the translational
temperature, for some, the vibrational temperature and for
others, the electronic temperature. Although this is an
interesting approach, the calculated distances in the shock
wave for peak and equilibrium temperatues, do not agree
with experimental data.
16-14
SUMMARY
The most significant finding this summer was that there are
large differences in important reaction rates as reported
in the literature by various authors. These large
differences could have significant effects on any computer
programs or calculations of chemically reacting systems
utilized in shock wave heat load predictions. It would be
worthwhile to try some of these other rates in present
computer programs and check the resulsts with known data.
The principle of detailed balancing is used widely in
calculations of reaction rates. It is not valid during
short incubation times in high energy shock waves in terms
of the overall dissociation or recombination rate
expressions. It does appear to be valid at the micro
energy level concerning transitions within molecules. These
transitions occur when translational energy is exchanged
for vibrational energy in a collision for example.
However, another significant find this summer is that in
collisional processes, multi-jump transitions in
vibrational levels can and do occur. This does not violate
the law of detailed balancing, but makes it more
complicated to take this into account.
Further refinements in calulation on these high energy
reactions would benefit from the use of coupling effects
16-15
such as some of those mentioned in this paper. These
include translation-vibration-rotational coupling,
electronic-vibrational coupling and vibration-dissociation,
dissociation-vibration coupling.
Future investigations should include models with limiting
expressions such as the vibrational temperature reaching a
limit and thus simplify the overall rate expressions. This
may or may not occur within a time period that is
insignificant in high energy shock waves. Approaches
utilizing partition _unctions and activated complex theory
also should be investigated. One final approach for future
work would include the information theory approach by such
authors as Levine to predict products of chemical reactions
on the basis of excess entropy. (20)
16-16
ACKNOWLEDGEMENTS
I would like to tlnank my NASA Colleague, Dr. Carl Scott for
the opportunity to work with him these past two summers on
this interesting and challenging problem. It has increased
my interest in the field of chemistry and in NASA.
I would also like to thank NASA and ASEE for these summer
program opportunities for faculty such as myself to enrich
our teaching and allow us to carry back some of this
enthusiasm to'our students who will become the engineers
and scientists o_ tomorrow.
16-17
BIBLIOGRAPHY
I. Scott, C. D.: "Catalytic Recombination of Nitrogen and
Oxygen oh High Temperature Reusable Surface Insulation," in
Aerothermodynamics and Planetary Entry, ed. by L. Crosbie,
Vol. 77 of Progress in Astronautics and Aeronautics, 1981,
pp 192-212.
2. Scott, C. D. :
on Shuttle Heat
Conference 1983.
"Effects of Nonequilibrium and Catalysis
Transfer," AIAA 18th Thermophysics
3. Blackwell, H. E., Scott, C. D., Hoffman, J. A., Mende,
S. B. and Swenson, G. P., "Spectral Measurements of the
Space Shuttle Leeside Shock Layer and Wake", AIAA/ASME 4th
Joint Thermophysics and Heat Transfer Conference, June 2-4,
1986, Boston MA.
4. Scott, C. D., Ried, R. C., Maraia, R. J., Li, C. F'. and
Derry, S. M.: "An AOTV Aeroheating and Thermal Protection
Study", in Thermal Design of Aeroassisted Orbital Transfer
Vehicles, ed. by H. F. Nelson,Vol 96, Progress in
Astronautics and Aeronautics, 1985, pp. 309-337.
5. Greene and Toennies, Chemical Reactions in Shock Waves,
Academic Press, NY, 1964, pp. 72-85.
6. Luther, K. and Troe, J.: "Influence of Temperature on
Unimolecular and Termolecular Reactions", in Reactions of
Small Transient Species, ed. by Fontijin and Clyne,
Academic Press, NY, 1983, pp. 65-76.
7. Troe, J. and Wagner, H. G.: "Unimolecular Dissociation
of Small Molecules", in Physical Chemistry of Fast
Reactions-Vol. i Gas Phase Reactions of Small Molecules,
ed. by B. P. Levitt, Plenum Press, NY, 1973, pp. 1-80.
8. Carlson, L. A. and Rieper, R. G.: "Electron Temperature
and Relaxation Phenomena Behind Shock Waves", O. Chem.
Phys. 57, 760-766, 1972.
9. Park, Chul: "Calculation of Nonequilibrium Radiation in
the Flight Regimes of Aeroassisted Orbital Transfer
Vehicles", Paper 84-0306 at AIAA 22rid Aerospace Sciences
Meeting, Reno, Nevada, Jan. 9-12, 1984.
16-18
10. Park, Chul: "F'roblems of Rate Chemistry in the Flight
Regimes of Aeroassisted Orbital Transfer Vehicles", Paper
84-1730 at AIAA 19th Thermophysics Conference, Snowmass,
Colorado, June 25-28, 1984.
ii. Kang, S. W. and Dunn, M. G.: "Theoretical and Measured
Electron Density Distributions for the RAM Vehicle at High
Altitudes", Paper 72-689, AIAA 5th Fluid and Plasma
Dynamics Conference, Boston, MA, June, 1972.
12. Kewley, D. J. and Hornung, H. G.: "Free-Piston Shock-
Tube Study of Nitrogen Dissociation", Chem. Phys. Letters
5, 531-536, 1974.
13. Oertel, H. Or.: "Regular Shock Reflection Used for
Study in Oxygen Dissociation", Modern Developments in Shock
rube Research-Proceedings of International Shock Tube
Symposium(1Oth), ed. Kamimoto, 605-612, 1975.
14. Myerson, A. L.: "Shock-Tube Atom Kinetics of Nitric
Oxide Decomposition" , Symposium (International) on
Combustion i4, 219-228, i973.
15. Koshi, M. et al: "Dissociation of Nitric Oxide in Shock
Waves", Symposium(Inizernational) on Combustion 17, 553-562,
1978.
16. Lin, S. C. and Teare, J. D.: Physics of Fluids 6,
1963.
355,
17. Wilson, J.: "Ionization Rate of Air Behind High-Speed
Shock Waves", Physics of Fluids 9, 1913-1921, 1966.
18. Vincenti, W. G. and Kruger, C. H. Or.: Introduction to
Physical Gas Dynamics, John Wiley and Sons, pp. 198-_L_,
1965, New York.
19. Dove, J. E. et al: "The Mechanism o÷ Vibrational
Relaxation of Molecular Hydrogen", J. Phys. Chem. 81, 2564-
2572, 1977.
20. Levine, R. D.: "Information Theory Approach to
Molecular Reaction Dynamics", in Annual Review of Physical
Chemistry, ed. B. S. Rabinovitch, Vol 29, pp. 59-92, Annual
Reviews Inc., Palo Alto, CA., 1978.
16-19


Non-equilibrium effects in high temperature chemical reactions

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