Arguments are presented for the retention of vibrational equilibrium of species in the nozzle of the Space Shuttle Main Engine which are especially applicable to water and the hydroxyl radical. It is shown that the reaction OH + HH yields HOH + H maintains equilibrium as well. This is used to relate OH to H, the temperature, and the oxidizer-to-fuel ratio

Ford, D. I.

English

NASA Technical Reports Server

N88:15616 S/6"--2_
//_ 7/_"
7 ; r.
1987
NASA/ASEE SUMMER FACULTY RESEARCH FELLOWSHIP PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
EQUILIBRIUM RETENTION IN THE NOZZLE
OF OXYGEN HYDROGEN PROPULSION SYSTEMS
Prepared By:
Academic Rank:
University and Department:
NASA/MSFC:
Laboratory:
Division:
Branch:
NASA Colleague:
D. I. Ford
Associate Professor
LeTourneau College
Natural Science
Propulsion
Component Devices
Turbomachinery and
Combustion Devices
R. Eskridge
XVI
https://ntrs.nasa.gov/search.jsp?R=19880006234 2020-03-20T07:39:16+00:00Z
Abstract
Arguments are presented for the retention of vibrational
equilibrium of species in the nozzle of the space shuttle main
engine which are especially applicable to water and the hydroxyl
radical. It is shown that the reaction OH + HH -> HOH + H
maintains equilibrium as well. This is used to relate OH to H,
the temperature, and the oxidizer-to-fuel ratio.
XVl-i
EQUILIBRIUM RETENTION IN THE NOZZLE
O__FFOXYGm_HYDROG_ PROPULSION SY_
D. I. Ford
LeTourneau College
Summer Faculty 1987
Marshall Space Flight Center
Huntsville, AL 35812
INTRODUCTION
Spectroscopic examination of the exhaust gases of liquid oxygen-
hydrogen propulsion systems is currently being considered as a non-intrusive
method to perform engine diagnostics. (i) Emission or absorption methods
yield number densities for specific states and in some instances, rotational
vibrational and electronic "temperatures." Knowing which processes are at
equilibrium greatly facilitates the use of such data to calculate overall
species concentrations by use of the Boltzmann distribution for internal
states and equilibrium constants for the chemical reactions.
The most promising species for spectroscopic measurements is the hydroxyl
I
radical, OH. If complete equilibrium were maintained at the exit
i
plane, then the OH number density and rotational "temperature" which
can be deduced from its band structure could be used to calculate all
other species concentrations and ithe oxidizer-to-fuel mass ratio, (O/F).
It is well known, however, that Complete chemical equilibrium is not
maintained. It is the purpose of this report to identify those
processes which are expected to _ at or near equilibrium.
xvI- 1
Chemical Model
Typical combustion chamber and exit plane conditions are displayed in
Fig. 1 for the Space Shuttle Main Engine (SSME). It is generally assumed
that combustion is complete and total equilibrium is achieved in the
combustion chamber before the combustion products begin their expansion
through the throat and nozzle. Justification of such an assumption is
based on the high collision frequencies of the various species under the
chamber conditions of high temperature and pressure, along with a
relatively long resident time in contrast to the opposite conditions in the
.
nozzle. Computer codes for engine performance calculations use this
initial equilibrium assumption and perhaps spectroscopic studies can shed
some light as the the extent to which it is valid.
For fuelrich engines, the chemistry is described as follows: an initial
equilibrium mixture of high enthalpy water vapor and molecular hydrogen
(with about 4-7 percent of the dissociation products OH and H) is rapidly
expanded through the nozzle. The temperature and pressure dropping
rapidly, new conditions for equilibrium are established and the internal
and chemical states change to accommodate the new Boltzmann distributions
and equilibrium constants. These changes are rate processes and are
governed by the collision frequencies between the various species and the
probabilities for the individual collisions to produce a change.
xvI-2
Table 1 gives the typical number of collisions required for readjustment to
take place for the various types of energy modes at 300K. (2) As a "rule
of thumb" then, it is expected that equilibrium is achieved very fast for
rotation, more slowly for vibration and ever slower yet for chemical
reaction. However, it must be cautioned that these collision numbers have
a strong temperature dependence and may overlap depending on the specific
systems under consideration. In the following, each kinetic process will
be examined separately as it applies toward the hydrogen-oxygen reaction.
Translational - Rotational Relaxation
Translational and rotational equilibrium is generally thought to be
extremely rapid even in strong shock fronts. It is therefore safe to
assume that the rotational "temperature" of the OH bands will be the same
as the translational temperature at the exit plane. This temperature can
be determined by comparing various rotational transitions which occur
simultaneously with the electronic transition in the region of 280 to 340
nm for the OH radical.
Vibrational Relaxation
A significant amount of energy resides in the vibrational modes of the HH,
and OH molecules in the high temperature environment of the combustion
chamber. During expansion, the temperature drops and the vibrational
energy begins to relax toward a new equilibrium state dictated by the local
translational temperature. This again is a rate controlled process and
occurs almost exclusively during molecular collisions. Present cumputer
xvI-3
codes assume that this relaxation process is fast and that vibrational
equilibrium is maintained throughout the nozzle. At high expansion
rotations, it is known that for molecules with long relaxation times such as
N2, and CO 2, and CO, significant deviations from the Boltzmann
distribution can occur. (3) One approach that has been used to account for
the final rate of vibrational relaxation along with the chemical reactions
is to consider each vibrational state as a separate species. (3,4) There
are, however, several serious difficulties with this approach:
i. The number of states goes up drastically. Present codes can handle
effectively the kinetics of 150 to 250 species, but when each vibrational
state is considered separately, the number of species increases to
thousands instead of hundreds. This can be partially overcome by
the somewhat arbitrary grouping of states.
2. Rate constants of the various vibrational relaxation processes have,
for the most part, not been determined experimentally and theoretical
predictions are at best tentative.
3. The most serious difficulty is that no one has been able to model the
strong coupling which exists between the chemical reaction and the
vibrational relaxation. It is known, for example, that molecular hydrogen
in its first vibrationally excited state reacts with oxygen atoms 2600
times faster than hydrogen in the ground state at 300K. (5) Such data as
this is sparce and then it is only given for one temperature. Also, the
distribution of vibrational states among the newly formed products is
xvI-4
unknown except in some rather isolated cases.
In absence of a quantitative approach, we offer the following
qualitive arguments for retention of vibrational equilibrium during the
expansion of the exhaust gases of the liquid oxygen-hydrogen engines.
i. The vibrational modes of water are known to relax very rapidly -
comparable to its rotational relaxation. (6) This is generally true of
molecules which have large dipole movements. In contrast N2, CO2,
and CO have zero or small dipole movements and relax much slower than
water. As a rule, any strong intermolecular force assists vibrational
relaxation. (7) Water forms hydrogen bonds which are very strong
intermolecular forces.
(2) Water couples well with the other molecules present, OH and HH by
forming hydrogen bonds.
3. The three vibrational frequencies of HOH are 1600,3600 and 3760
i/cm. The vibrational frequency of hydroxyl, OH, is 3730 i/cm which
differs from the last frequency given for HOH by only 30 i/cm. Frequencies
within 50 l/c;, are said to be "resonant" and equilibrate quickly. (8) In
summary, the exhaust gases of liquid oxygen-hydrogen engines are much more
likely to be at vibrational equilibrium than hydrocarbon engines because of
the predominance of water in the former. This could be verified by the OH
spectrum. If non-equilibrium is observed it could indicate:
I. The above vibrational relaxation mechanisms, though fast, are not fast
enough.
XVl- 5
2. Chamber equilibrium may not be established. For example, the liquid
oxygen may not be fully dispresed before it makes it to the throat.
3. Secondary oxidation of the excess hydrogen with atmospheric oxygen in
the vicinity of the exit plane may have to be excluded or allowed for in
the data analysis.
XVl_
Chemical Relaxation
Computer programs are available which compute the performance of rocket
engines taken into account finite ratechemical reaction. (9) The results
of such a calculation are shown in Fig. 2 where number density is plotted
versus area ratio. Also shown are the number densities which would
result if chemical equilibrium had been maintained during the expansion.
It is seen that the concentrations of the minor components, OH, H, O and
0 2 are orders of magnitude different when finite rate chemistry is
used. The water and hydrogen gives essentially the same result whether
or not chemical equilibrium "is assumed. This is because only a small
amount of each was dissociated in the combustion chamber. The major
reactions taken plan during the expansion are the following:
i H + OH + M-> HOH + M
ii H + H + M-> _ + M
iii OH + _-> HOH + H
iv 0 + _-> OH + H
M is a third body required to dissipate the energy of the newly formed
water or hydrogen molecule and is likely to be either a water or hydrogen
molecule. It is known from the study of the chemistry of flames,
that away from the flame front, the exchange reactions iii and iv maintain
equilibrium while coupled to the recombination reactions, i and ii, which
are not at equilibrium. (i0) Since equilibrium relationships can relate
species concentrations to one other, it is worthwhile to examine whether iii
XVI- 7
and iv are in equilibrium in the nozzle expansion process as well.
The extent to which equilibrium is maintained is shown by comparing the
equilibrium constant Ke to the quantity K. K has the same form as Ke but
uses the prevailing partial pressures of the species of the reaction
instead of those that occur at equilibrium. Ke is a function of
temperature only and may be determined by the therm_lynamic relation:
-/kG ° - RT in Ke
and standard thermodynamic tables. K is calculated fram the mole fraction
and pressures computed at various area ratios using the NASA (X)K code
(9). Calculations were done-for two engines. The smaller RL-10 engine ham
a 5 inch diameter throat, a chamber pressure of about 400 psi and a chamber
temperature of about 3400K. The SSME has a i0 inch diameter thoat, a
chamber pressure of about 3000 psi and a chamber temperature of about
3400K.
Examination of Figs 3-8 shows that the exchange reactions iii and iv are
essentially at equilibrium i.e. K/Ke is close to one. Reaction iii
appears to be closer to equilibrium than iv. The exchange reactions i
and ii quickly fall out of equilibrium as is evidence by the rapid decline
of K/Ke to zero. Equilibrium is more persistent for the larger SSME
engine than for the smaller engine, presumably as a result of higher
operating pressures.
xvl- 8
One should use the ODK number densities and corresponding K/Ke values
with caution. They are based on rate constants which are in many cases
uncertain by an order of magnitude. Also, it appears that the smaller
number densities may suffer from "computational scatter" especially at the
large expansion ratios. I would suggest that they be used in a "soft"
fashion, that is, to demonstrate trends and qualitative behavior.
XVI- 9
Relating OH to Other Quantities
Using reaction iii as being essentially at equilibrium and the known
equilibrium constant Ke(T), [H] can be calculated from:
_OH] X [HH] where
[HI -
Ke(T) K [HOH]
UV absorption measurements can give [OH] and T. [HH] / [HOH] can
be calculated using the relation:
(O/F) - 8.0 x (I + [HH]/[HOH])"I
The last equation comes from conserving O and H atoms and recognizing that
at the exit plane, essential-ly all of the exhaust gas is HH and HOH.
Alternately, if [HI and [OH] are both known, then (O/F) could be calculated.
However, accurate temperatures must be used as Ke(T) is a strong function
of temperature. (See table 2 and Fig I0.) A similar analysis can be
made to estimate [O] from [OH] using reaction iv.
Fig. 9 shows how [OH] at the exit plan varies with (O/F). When (O/F)
changes from 5 to 7, (8 being stoichiometric) [OH] increases by a factor of
150. This suggests that the hydroxyl number density can be a sensitive
measure of the oxidizer-to-fuel ratio. Note also in Fig. 10, that the
teml_erature at the exit plan increases substantially as (O/F) increases.
xvI-10
Conclusion
Arguments are presented suggesting that equilibrium is substantially
maintained in the nozzle of the SSME with the exception of certain chemical
reactions, notably the recombination reactions. Reaction iii and iv will
maintain equilibrium enough to be used to estimate [H] and [0] from the [OH]
measurement. Accurate measurements of the absorption spectra of OH in the
exit plane will yield valuable information for engine monitoring and
verification of models employed in various computer codes in use to predict
rocket engine performance. The measurement of OH in the test study
environment is a challenging experimental and engineering problem with the
potential for giving a wealth of information.
xvl- 11
°°
°
°
.
6.
7.
°
9.
i0.
REFE_ENCE_
Cikanek, H. A.,
Shuttle Main
Results," Paper
Powers, W. T., and Eskridge, R., "Space
Engine Spectral Monitoring Preliminary
87-1792 at AIAA 23rd Joint Propulsion
Conference, San Diego, Ca., June 29-July 2, 1987.
Lambert, J. D.," Vibrational And Rotational Relaxation In
Gases," Clarendon Press, Oxford, 1977.
Limbaugh, C. C., "Vibrational Relaxation of C02 in High
Area Ratio Rocket Engines," Paper 85-1082 at AIAA 20th
Thermophysics Conference_ Williamsburg, Va., June 19-21,
1985.
Nickerson, G. R., "Nonequilibrium Radiation Model For
Exhaust Plumes," AFRPL-TR-74-74, March, 1975.
Light, G. C., J. Chem. Phys., 68, 1978, p. 2891.
Shin, H. K., J. Phys. Chem., 77, 1973, p. 346.
Kondrat'ev, V. N., "Chemical Kinetics of Gas Reactions,"
Pergamon Press, 1964, p. 378.
Ref. 2, p. 83 and Ref. 7, p. 377.
Nickerson, G. R., Dang, L. D. and Coats, D. E., "Two-Dimen-
sional Kinetic Reference Computer Program," NASA contract
no. NASA-35931, April, 1985.
Kaskan, W. E., J. Chem. Phys., 31, 1959, p. 944.
XVI-12
TABLE I -
I ii i
CO
OO
HH
HOH
Collisions required for energy transfers.
Z(I-0) vibrational to translational
Z(R) rotational to translational
T : 300 K
i i i i | i i I
Z(1-0) 1,000,000,000
Z(R) 2
Z(I-0) 100,000,000
Z(-R) 4
Z(1-O) 10,000,000
Z (R ) 200
Z(1-0) 50
Z(R) 4
T : 2000 K
I In
100,000
ii
10,000
10,000
XVI- 13
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Equilibrium retention in the nozzle of oxygen hydrogen propulsion systems

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