Analytical and computational techniques were developed to predict the stability behavior of liquid propellant rocket combustors using damping devices such as acoustic liners, slot absorbers, and injector face baffles. Models were developed to determine the frequency and decay rate of combustor oscillations, the spatial and temporal pressure waveforms, and the stability limits in terms of combustion response model parameters

Mitchell, C. E.

English

NASA Technical Reports Server

(NAS&-CR-162803} COMBUSTION STABILITX WITH _80-18128
B&FFLESw ABSORBERS AND VELOCITY SENSITIVE
COMBQSTION F_,tal Repoct, Dec. 1969 - Feb.
1980 (Colorado State Univ.) 9 p Unclas
HC AO2/MP A01 CSCL 21B G3/25 47326
COMBUSTION STABILITY WITH BAFFLES, ABSORBERS AND
VELOCITY SENSITIVE COMBUSTION
Grant NGR-06-O02-095
FINAL REPORT
Covering the Period December 1969 - February 1980
Research Conducted at Colorado State University
Fort Collins, Colorado 80523
Principal Investigator: C. E. Mitchell
, Department of Mechanical Engineering
Report Prepared for L% • _ ._.;L
National Aeronautics and Space Administration /_" %_'_% _!_
February 1980 _ ,"_ll_C_l_ :i_,
%
The NASATechnical Officer for this Grant
is Dr. R. J. Priam, NASALewis Research Cantor
1980009863
https://ntrs.nasa.gov/search.jsp?R=19800009863 2020-03-21T19:56:00+00:00Z
INTRODUCTION
The overall goal of this work was the development of analytical
and computational techniques for the prediction of the stability behavior
of liquid propellant rocket combustors using damping devices such as
acoustic liners, slot absorbers, and injector face baffles. The research
included development of predictive models for determining the frequency
and decay rate of combustor oscillations, determination of spatial and
temporal pressure waveforms, and the prediction of stability limits in
cerms of combustion response model parameters.
The work began with the development of a relatively simple predictive
model based on a simplified combustor. Tilis basic model was linear in
nature and ignored some features of real combustors. Nonetheless the
stability predictions based on this model proved qualitatively correct.
Sequential sophistication of the model followed, gradually including such
real combustor features as distributed combustion, nonlinear combustion,
nozzle and absorber responses, finite amplitude waveforms, and injector
face baffles.
In what follows brief summaries of the accomplishments in each of
the several areas of stability model development will be given. In
addition the reports, papers, publications and theses prepared with
grant support which document the work in detail in each area will be
cited. The reference numbers used refer to the comprehensive list of
grant-related publications which follows the text.
1980009863-002
SUMMARYOF RESEARCH
A. Basic Model
The basic analytical technique employed in all the work done under
this grant depends upon the use of an integral-iteration formulation
following the Green's function approach. The first application of this
technique was to a simplified combustor model. This model featured a
concentrated combustion zone at the injector which responded to the
combustor oscillations in a linear, pressure-sensitive way, a short nozzle,
linear (small amplitude) pressure oscillations, and either an acoustic
liner or an acoustic slot which served as a damping device.
References 1 and 2 give the earliest results obtained for this
model; these were presented at JANNAFcombustion meetings. The M.S. thesis
of W. R. Espander (Ref. 3) presents this early work in more detail. The
most comprehensive presentation of this basic model is given in two
contractor reports, References 4 and 5. The first of these makes use of
the iteration technique and simplified combustor model to make frequency
and decay rate predictions for several combustor configurations similar
to space shuttle main engine and preburners being proposed at that time.
The second presents results of calculations for the overall stability
behavior and pressure spatial waveforms in similar combustors. Both of
these reports include computer programs with user manuals and sample inputs
and outputs. A formal presentation of the mathematical technique as well
as a summary of results is given in a journal publication, Reference 6.
B. Effects of Distributed Combustion
Recognizing that, in fact, the combustion zone in liquid propellant
rocket engines is not concentrated at the injector face but rather is
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1980009863-003
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distributed along the motor axis, a considerable effort was made in order
to evaluate the effects of distributing the combustion on the stability
behavior of the combustor. The rest of the basic model remained the same
in this worK; that is, a short noz.le was assumed, either a partial length
acoustic liner or a slot absorber served as an acoustic damper, and small
amplitude pressure oscillations were assumed. Two approaches were used.
In the first of these the combustion distribution was modeled by a series
of planar sources. Details of the mathematical development and results
of stability calculations using this first approach appear in the M.S.
thesis of M. R. Beer (Ref.7). Some of the results of these calculations
were presented at the 9th JANNAF Combustion Meeting (Ref. 8) as well.
A formal journal presentation of the multi-zone approach is given in
Reference 9.
A second approach to the problem of distributed combustion allows
consideration of continuous distribution of combustion sources in the
axial direction. The mathematical sophistication is somewhat greater
than in the multi-zone approach mentioned above. Predictions of stability
behavior are similar qualitatively to those of the multi-zone approach,
though quantitatively the multi-zone predictions underestimate combustor
stability. Both approaches predict enhanced combustor stability and
simplificationof the overall stability picture with distributed combus-
tion. The continuous combustion approach is described in a JANNAF meeting
paper, Reference lO, and in a journal paper, Reference II.
C. Baffle Damping
In addition to the slot absorbers and partial length acoustic liners,
injector face baffles have been frequently used to stabilize liquid pro-
pellant combustors. A significant effort was made to develop a model
1980009863-004
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capable of exploring the mechanism through which these baffles work and
their impact on overall combustur stability. Two- and three-dimensional
geometries were investigated with the fundamental damping mechanism assumed
to be viscous dissipation near the tips of the baffle blades. Frequency
and decay rate predictions were found to be well-predicted using the
model. Because of the complex geometries involved (baffle cavities as
well as main chamber) the mathematical approach used in this part of the
wc_'k was somewhat different from that used in other phases of the work.
The Ph.D. thesis of M. R. Baer (Ref. 12) gives a presentation of the two-
and three-dimensional theory as well as results of calculations performed.
Some results are also to be found in Reference 13, which is a paper pre-
sented at the 12th JANNAFCombustion Meeting. A contractor's report
(Ref. 14) gives a summary of the theory and documents the computer program
used in calculations. A paper in the AIAA Journal (Ref. 15) summarizes
results of calculations and the analytical approach for three-dimensional
oscillations.
D. Nonlinear Effects
Modeling of nonlinear effects in two areas was pursued. The first
of these was the inclusion of nonlinear wave propagation effects in the
theory. That is, waves of finite amplitude instead of the vanishing
amplitude waves were to be considered. In this first part of the work
the boundary conditions at the combustion zone and acoustic absorber were
still taken to be linear, as before. Even with this simplified model
nonlinear effects such as triggering of oscillations and nonlinear stabil-
ity limits, as well as spatial and temporal pressure waveforms were
predicted. This theory was presented in the Ph.D. thesis o_ W. R. Espander
1980009863-005
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(Ref. 16) and subsequently in a contractor's report (Ref. 17) which
included the complex computer program.
A second area of effort in the modeling of nonlinear combustor
stability was the inclusion of nonlinear combustion responses and absorber
responses. Of primary interest here was to include velocity and wave
distortion dependent effects in the combustion response. Physically
this models a combustion process that is dominated by droplet vaporiza-
tion. Initially the work here assumed that nonlinear waveforms were
generated primarily by the combustion zone,and thus, nonlinear wave pro-
pagation terms in the partial defferential equations were ignored. Pre-
dictions based on this theory were presented at the 13th JANNAF Combustion
Meeting (Ref. 18) and indicated that wave distortion response mechanisms
could be significant, particularly if a characteristic time of combustion
was assumed to exist. The restriction ignoring wave propagation terms
was later relaxed using a successive approximationmethod. Both traveling
and standing waveforms were also included. This extended work is reported
in detail in the Ph.D. thesis of Yodchai Jotiban (Ref. 19).
E. Simplified Computer Models
The final effort under grant sponsorshipwas the development of a
simplified computer program which included the most important aspects of
the models and computer programs discussed previously. The idea here was
to produce a designer's tool which could be used simply and effectively
in making stability predictions at the design stage. Toward this end
many simplificationswere made both in the theory and in the computer
program so that a person without an extensive background in either
advanced mathematics or combustion stability could use the program and
1980009863-006
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understand input, output and the significance of the predictions. Basic
work was done in the development of both a linear and nonlinear program
of this type. These are discussed in the M.S. thesis of K. Eckert (Ref,
20). For the case of linear stability a particularly useful program
resulted. The nature of this program is discussed in a paper presented
at the 15th JANNAFCombustion Meeting (Ref. 21). The final form of the
program along with a user's manual and a simplified discussion of the
theory is presented in a "low number" I_ASAcontractor's report (Ref. 22).
1980009863-007
REPORTS,PAPERS, THESESAND PRESENTATIONS
I. "Analysis of Combustion Instability in Motors with Partial Length
Acoustic Liners," C. E. Mitchell, P. J. Wilbur, W. R. Espander,
Proceedings of the 7th JANNAFCombustion Meeting, CPIA Publication 204,
VoI. I, pp. 721-726, February ]971.
2. "A Study of tne Effects of Partial Length Acoustic Liners in Liquid
Propellant Rocket Motors," C. E. Mitchell, W. R. Espander, M. R. Baer,
Proceedings of the 8th JANNAF Combustion Meeting_,CPIA Publication 220,
Vol. I, pp. 795-805, November 1971.
3. "Partial Length Liners in Rocket Motors," W. R. Espander, M.S. Thesis,
Colorado State University, 1971.
4. "Determinationof Decay Coefficients for Combustors with Acoustic
Absorbers," C. E. Mitchell, W. R. Espander, M. R. Baer, NASA CR 120 836,
January 1972.
5. "Stability of Combustors with Partial Length Acoustic Liners," C. E.
Mitchell, W. R. Espander, M. R. Baer, NASA CR 120 889, March 1972.
6. "Stability of Combustors with Partial Length Acoustic Liners," C. E.
Mitchell, Combustion Science and Technology, Vol. 6, pp. 61-70, 1972.
7. "Combustion Instability in Rocket Motors with Distributed Combustion and
Acoustic Liners," M. R. Baer, M.S. Thesis, Colorado State University, 1972.
8. "Combustion Instability in Chambers with Distributed Combustion," C. E.
Mitchell, M. R. Baer, W. R. Espander, Proceedings of the 9th JANNAF
Combustion Meetin9, CPIA Publication 231, Vol. I, pp. 187_192, November
1972.
9. "Stabilityof Partially Lined Combustors with Distributed Combustion,"
M. R. Baer, C. E. Mitchell, W. R. Espander, AIAA Journal, Vol. 12, No. 4,
pp. 475-480, 1974.
lO. "Stability of Lined Combustors with Continuous Combustion Distributions,"
C. E. Mitchell, M. R. Baer, Proceedings of the lOth JANNAF Combustion
Meetin 9, CPIA Publication 243, VoI. II, pp. 255-271, December 1973.
II. "Stability Predictions for Combustors with Acoustic Absorbers and Continuous
Combustion Distributions," C. E. Mitchell, M. R. Baer, AIAA Journal, Vol. 13,
No. 8, pp. 1107-1109, August 1975.
12. "A Theoretical Evaluation of Rigid Baffles in Suppression of Combustion
Instability," M. R. Baer, Ph.D. Thesis, Colorado State University, 1975.
13. "Theoretical Evaluation of Rigid Baffles to Suppress Combustion Instability,"
M. R. Baer, C. E. Mitchell, Proceedings of the 12th JANNAF Combustion
Meeting, CPIA Publication 273, Vol. I, pp. 509-521, December 1975.
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14. "A Theoretical Evaluation of Rigid Baffles in Suppression of Combustion
Instability," M. R. Baer, C. E. Mitchell, NASA CR 134 986, March 1976.
15. "Theoretical Evaluation of Rigid Baffles in Suppression of Combustion
Instability," M. R. Baer, C. E. Mitchell, AIAA Journal, Vol. 15, No. 2,
pp. 135-137, February 1977.
16. "Acoustic Liner Suppression of Nonlinear Combustion Oscillations," W. R.
Espander, Ph.D. Thesis, Colorado State University, 1974.
17. "Suppression of Nonlinear Oscillations in Combustors with Partial Length
Acoustic Liners," W. R. Espander, Co E. Mitchell, M. R. Baer, NASACR
134 767, February 1975.
18. "Wave Distortion Effects on Vaporization Limited Combustion Stability,"
C. E. Mitchell, Y. Jotiban, Proceedings of the 13th JANNAFCombustion
Meetin 9, CPIA Publication 281, Vol. III, pp. _45-156, December 1976.
19. "Nonlinear Analysis of Wave Distortion Response," Yodchai Jotiban, Ph.D.
Thesis, Colorado State University, 1977.
20. "Computer Programs for Linear and Nonlinea _ Analysis of Rocket Engine
Stability" K.R. Eckert, M.S. Thesis, Colorado State University, 1978.
21. "Simplified Computer Program for Liquid Rocket Combustor Stability
Analysis," C. E. Mitchell, K. R. Eckert, Proceedings of the 15th JANNAF
Combustion Meetin 9, CPIA Publication 297, Vol. II, pp. 449-460, February
1979.
22. "A Simplified Computer Program for the Presiction of the Linear Stability
Behavior of Liquid Propellant Combustors," C. E. Mitchell, K. Eckert,
NASAContractor's Report 3169, August 1979.
1980009863-009


Combustion stability with baffles, absorbers and velocity sensitive combustion

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