Theoretical, Numerical and Experimental Investigations of the Fundamental Processes
that Drive Combustion Instabilities in Liquid Rocket Engines – Program Abstract
Matt Quinlan, Yong Jea Kim, Martina Baroncelli, Ciprian Dumitrache, Hongfa Huo, Xingjian Wang, Vigor Yang and Ben T.
Zinn
Guggenheim School of Aerospace Engineering, Georgia Institute of Technology
C. K. Law and V. Akkerman
Department of Mechanical & Aerospace Engineering, Princeton University
September 13th, 2012
Introduction
Detrimental combustion instabilities have hindered the development of liquid rocket engines (LRE) for many
decades. To solve the problem, the mechanisms that drive these instabilities must be elucidated. This requires
development of experimental capabilities that would allow simulation of the oscillatory flow conditions
encountered in an unstable, full scale, LRE in a small scale rig at a reasonable cost. The development and
application of such a rig is the main objective of this program. Since this rig requires active control of its
boundaries impedances, it’s being referred to as the Actively Controlled LRE Simulator (ACLRES).
Since LRE often encounter spinning transverse instabilities that produce acoustic motions perpendicular to the
direction of the mean flow in the engine, this program is (initially) studying a two dimensional ACLRES, see
Figure 1, that can simulate transverse instabilities; i.e., the excited acoustic motions are perpendicular to the
direction of the mean flow (“out of the paper”). Figure 1a shows an injector array of a “full scale”, 2-D, LRE. To
study the driving of instabilities by the nine injectors shown in Figure 1b in a small scale rig, the acoustic
environment experienced by these injectors in the full scale engine must be reproduced in the small scale rig.
The ACLRES accomplishes this goal by using actively controlled actuators (e.g., speakers) to reproduce the
impedances experienced by the investigated injectors in the full scale rig, see Figure 1c. These impedances are
determined in “real time” by models that describe the unstable flow conditions in the regions on the left and
right sides of the section that is simulated in the ACLRES.
Figure 1: Description of the ACLRES concept.
This research program is divided into three tasks. The goal of Task I is to investigate and develop the ACLRES and
use it to elucidatethe mechanisms that drive LRE instabilities. Tasks II and III are using analytical models and
numerical simulations, respectively, to study the interactions between acoustic, fluid mechanical and chemical
processes that drive LRE instabilities. Close collaborations between these three tasks, performed by different
teams, should provide opportunities for determining what experiments to run and what measurements to
make. Additionally, these interactions should provide means for checking the fidelity of the investigated
analytical and numerical approaches that will be eventually incorporated into LRE design tools.
Currently, the ability of the ACLRES to simulate full scale LRE instabilities is being studied. Subsequently, the
ACLRES will be used to study the dependence of LRE instabilities upon LRE injection systems design, propellants
used and operating conditions. This task will also study how to use the ACLRES to determine the effect of design
changes upon the engine stability. The various flamefront instability modes of the premixed and diffusion flame
segments of the nozzle-generated triple flame ensemble, subjected to independent acoustic forcing, have been
analyzed and will be integrated with the chamber acoustic dynamics for a complete system combustion stability
analysis. In addition, comprehensive modeling and simulations based on large-eddy-simulation (LES) techniques
have been performed to provide direct insight into the behaviors of individual injectors and the collective
characteristics of the ACLRES assembly.
Task I: Development of Actively Controlled LRE Simulator (ACLRES) Rig
The main goal of this task is to develop the ACLRES rig discussed in the Introduction and apply it to elucidate
mechanisms that drive LRE instabilities. The ACLRES’ active control system requires capabilities for determining
the characteristics of the rig’s acoustics, the speakers’ Frequency Response Function (FRF) and the ability to
control the actuators in real time. To attain these capabilities, this task has developed an experimental facility
with needed diagnostic capabilities, an approach for determining the speaker FRF and a control algorithm that
employs the rig’s acoustics and the speaker FRF to determine the control signals for the speakers.
Development of Experimental Facilities
Figure 2 shows rigs and components developed under this task. The first (top left) shows the so called “Fullscale” engine. It consists of a combustor section attached to a variable length section on either side. By
adjusting the lengths of the sections on the left and right sides of the combustor section, instabilities with
different frequencies are spontaneously excited in the rig. To demonstrate the ACLRES concept, the variable
length section on the right of the combustor was replaced by a fixed length section that is attached at its (right)
end to a speaker. This speaker is actively controlled to simulate in the ACLRES the instabilities observed in the
so called “full scale” engine, simulating the effects of the “removed section”. Notably, both configurations have
a sensing section on the right-hand side of the combustor which employs acoustic sensors to determine the
characteristics of the excited acoustic oscillations. The combustor has a rectangular cross-section that allows
the use of flat windows that provide capabilities for good optical access.
Products
Acoustics
F+Ox
Figure 2: ACLRES rig configurations, gas/gas/liquid fuels injector schematic, and initial injector study
A counter-swirling gas-gas injector with an optional liquid fuel port, based on Russian injector designs, was
developed for initial testing of the rigs. This injector, see Figure 2c, allows for the adjustment of the heat release
distribution within the combustor by controlling the oxidizer flow rates in their two, counter-swirling, supply
paths. For example, supplying most of the oxidizer flow through path #1 with high swirl produces a short, wide
flame brush while supplying most of the oxidizer through path #2 with a lower swirl results in a longer narrow
flame.
Figure 3: Photo of rig and control schematic
Development of the Active Control System
To simulate full scale LRE instabilities in the small scale ACLRES rig, the acoustic impedance at, e.g., the interface
between the combustor and sensing section must be the same in both rigs. This is accomplished in the ACLRES
by active control of the actuator in a manner that reproduces the desired impedance at the specified location.
Figure 3b shows a schematic of the ACLRES control system. The acoustics of the rig are described by two plane
traveling waves, A and B that are determined from measured acoustic pressures in the sensing section. These
data are then used to determine the acoustic velocity of the speaker’s diaphragm. This information is supplied
to the speaker’s model that is then used to determine the control current to the speaker.
Acoustic development
The simple lossless 1-D wave equation in a constant area duct has the following solution
, and
.
Utilizing travelling wave solutions and requiring the impedance z at location xz of the ACLRES to equal the
impedance zL2 at the same location in the full scale engine (which is calculated by a separate model), the
following expression for the velocity of the speaker’s diaphragm was developed:
.
Speaker model
To actively control the ACLRES’ speaker, a model of the transfer function between the speaker’s diaphragm
velocity and current input was developed. Modeling the speaker’s dynamics as the following equation for a
damped harmonic spring mass system:
and relating the acoustic pressure at the diaphragm to the diaphragm’s velocity and impedance 𝑍𝑑 the following
expression for the speaker’s FRF was derived:
By performing experiments and analyzing the data, the required model constants, e.g., mass, were determined.
Figure 4: Speaker test bench and sample results
Results
When 𝐿1 = 0.89𝑚, 𝐿2 = 1.65𝑚, 𝑧𝐿1 = 𝑧𝐿2 >> 𝜌𝑐 in the full-scale engine rig, an instability spontaneously
occurred near 170Hz, as shown by the Power Spectral Density (PSD) in Figure 5a. Next, the ACLRES rig, see
Figure 2b, with its driver located at 𝑥𝑑 = 0.89𝑚, was operated with and without active control. With the
control off, the ACLRES exhibited a peak at 250Hz and practically no response at 170Hz, the full scale engine
instability frequency. However, when the ACLRES was actively controlled, the measured PSD, see Figure 5c,
shows spectral power similar to the full scale results at the frequency of interest. While the demonstrated
ability to excite the full scale engine instability of 170Hz in the small scale ACLRES was encouraging, the
continued excitation of an ACLRES natural acoustic mode (i.e., at 250Hz) was problematic. To address this issue,
current approaches for preventing the excitation of the ACLRES natural acoustic modes in actively controlled
experiments are under investigation.
Figure 5: PSD of full-scale, uncontrolled ACLRES, controlled ACLRES, and FFT of control signal
Including Combustion Effects in the ACLRES Controller
To date, the ACLRES controller neglected the effect of heat addition by combustion upon the acoustic
oscillations in the sections of the engine not simulated in the ACLRES. To improve the active control of the
ACLRES, the effects of mean flow and combustion in the “rest of the engine” upon the active control system
were also investigated in an annular combustor geometry, see Figure 6a. The developed model assumed that: 1.
“compact” combustion regions were “imbedded” in the annular engine and 2. A mean flow in the tangential
flow component could be present in the engine. To attain “real time” control, d’Alembert wave solutions were
used to describe the acoustic oscillations in the regions between heat sources and the full conservation
equations to describe the “compact combustion regions”. Preliminary results showed the presence of an
azimuthal mean flow may critically affect the instability characteristics. Specifically, when mean flow is absent,
an initial spinning wave disturbance is converted to a standing wave instability and an initial standing wave
disturbance is converted to a spinning wave instability when mean flow is present. Notably, the direction of the
spinning instability is in the direction of the mean flow. The latter results are in agreement with experiments
performed at NASA by Heidmann and Povinelli many years ago.
Figure 6: Acoustic/combustion modeling of simulated portion of chamber and preliminary results
Current efforts under this task are focusing on improving the ACLRES active controller. This work seeks to
prevent the excitation of the ACLRES acoustic modes in active controlled experiments. Additionally high-speed
(10 kHz) laser diagnostic techniques, including OH-PLIF and PIV, are being setup to provide capabilities for
studying the dynamics of the combustion processes in the ACLRES. Also, a multi-injector rig is being developed
to allow studies of injector to injector interactions. Lastly, the theoretical studies of the annular LRE are
continuing in an effort to attain “real time” control capabilities.
Task II: Theoretical Studies on the Role of Nozzle-Generated Triple Flame on LRE
Combustion Instability
Phenomenology
While previous studies on LRE combustion instability were primarily based on concepts related to diffusional
flame-sheet burning because of the high density of the medium which causes the associated reactions to occur
infinitely fast as compared to the heat and mass transport processes, recent studies of fuels chemistry and flame
structure have identified the significance of premixed burning that can further contribute to the instability. For
example, increasing the system pressure and temperature may not always facilitate the reaction rate as the
overall reactivity can be moderated by three-body termination reactions at higher pressure, while the negative
temperature coefficient (NTC) chemistry can affect the flame ignition, respectively. As such, a comprehensive
understanding of LRE instability must necessarily consider aspects of coupling involving both premixed and
diffusion flame segments of the triple-flame structure, downstream of the injector nozzle, which stabilizes the
entire flame ensemble.
The present component of the program therefore aims to theoretically study the coupling of flamefront
instabilities to externally applied acoustics. As listed in Table 1, the instability can be manifested in several
modes including: (i) the Rayleigh-Taylor (RT; body-force) instability for both premixed and diffusion flame
segments; (ii) the diffusional-thermal (DT; nonequidiffusive) instability, which is pervasive for premixed flames
and is relevant for near-limit diffusion flames, although its intensity diminishes with increasing pressure as the
flame thickness reduces; (iii) the Darrieus-Landau (DL; hydrodynamic) instability of premixed flames, which
intensifies with increasing pressure; and (iv) the Kelvin-Helmholtz (KH; shear-layer) instability, which can be
important for diffusion flames because of the inherently different properties of the fuel and oxidizer streams. In
addition, it is recognized that resonance can develop through acoustic coupling between the chamber dynamics
and the flamefront. Indeed, the sound wave generated in the LRE combustion chamber can affect the flame
dynamics in an essential manner: while the acoustics can stabilize or weaken the DL and RT instabilities and
modify the KH instability, they can also trigger the parametric instability.
Table 1: Intrinsic and acoustic flamefront instability modes
Instability Mode
Rayleigh-Taylor (RT)
Diffusional-thermal (DT)
Darrieus-Landau (DL)
Kelvin-Helmholtz (KH)
/////////////////////////
Acoustical / Parametric
Premixed Flame
Diffusion Flame
Yes
Yes
Pervasive, ↓ as p ↑
Near-limit situations
↑ as p ↑ and δ ↓
No
?
Yes
/////////////////////////// ////////////////////
Yes
Yes
Premixed Flame Instability
For the stability and acoustic coupling of the premixed flame segment, we have found that increasing the flame
thickness (δ) modifies the unstable regimes: first, it moderates the combustion instability due to thermal
stabilization of the DL instability; second, DT effects within a nonequidiffusive burning zone can also stabilize the
flame. The results were reported in the previous contractors’ meeting.
Formulation of Diffusion Flame Instability
We have now analyzed the stability of the diffusion flame segment, i.e. on the RT and KH instability modes. Let
us first consider a discontinuity surface of zero thickness (say, a flame sheet) or a transitional layer (of finite
thickness) separating two fluid media of different properties. Assume that this front is initially planar, but then it
becomes corrugated by weak, linear, 2D perturbations described by the function
z  F x, t    f i t coski x  .
(1)
The continuity and Navier-Stokes/Euler equations ahead and behind the front, the matching conditions across
the front, and the reaction evolution equation can be incorporated into a linear dispersion relation for the
perturbation amplitude f in the general form Iˆ f  0 , where the operator Iˆ describes the surface response to
the perturbation and couples the instability growth rate  to the perturbation wavenumber k , Iˆ  Iˆ( , k ) .
Within the linear approximation, there are two interacting frequency modes between the intrinsic instability and
the acoustic oscillations. The first is the resonant mode,    , which modifies and weakens the intrinsic
instability. The second is the doubling mode,   2 , which can excite the parametric instability through the
intrinsic-acoustic coupling if the sound is strong enough. We have applied this general formulation to the
particular cases involving the RT, DL, DT and KH instabilities.
Rayleigh-Taylor Instability
We start with the RT instability, inherent to any discontinuity surface, including both premixed and diffusion
flame segments, if the density gradient across the surface is directed oppositely to the acceleration field.
Specifically, we consider an infinitely thin front separating a heavy and a light mixtures, with the densities  h
and  l , respectively, subjected to a constant acceleration (gravitational or tractive) field g as well as a highfrequency
acoustic
velocity
field
u  U a sin  t  ,
producing
the
oscillating
acceleration
field
g a  U a cos t  . Analysis shows that RT instability develops if the acoustic amplitude is less than the cutoff
value
g 
 1
U RT  2 g 
 2 .
 Ak  
(2)
Regarding the parametric instability mode, it is excited if the amplitude U a exceeds the cut-off value
UP 
2g


.
 2 Ak
(3)
The analysis above can readily be extended to a transitional layer of small, but finite characteristic thickness,
extending the above results to,
~
 1 1  C1k
g 
U RT  2 g 
 2  ,
~
 Ak 1  C2 k  
~
UP 
~
2g
 1  C1k

.
~
 2 Ak 1  C2 k
(4)
~
where C 1 and C 2 are certain phenomenological or analytically-predicted dimensionless constants.
Kelvin-Helmholtz Instability
KH instability develops in a high-frequency acoustic filed, for a diffusion flame segment separating two flows
(fuel and oxidizer) of different properties, particularly the density, and move with a finite tangential velocity
differential. The dispersion relation,
2
 
1   1 U a2  2  1 g 





U k.
1  i
2
2
2
2  0
 1

2 U 0
 U0 k 


(5)
shows that an infinitely thin discontinuity is absolutely KH-unstable, independent of U a and g , hence
demonstrating the importance of the KH instability. In addition, KH–acoustic coupling can trigger the parametric
instability, which develops if
Ua

U0
2
2

1  
2 U 0 k 2 Ag 0 
4 2 
  2 
 
.


U 0    12 
A  2U 0 k   1 



(6)
Figure 7 shows the boundary with the density ratio   8 . It is noted that the above relation achieves its
minimum value when the oscillation frequency is in resonance with the characteristic frequency of the KH
~  2  /(  1)S k .
instability excited by a perturbation of the wavenumber k , 
L
Figure 7: Stability diagrams for KH instability of infinitely thin flamefront with density jump
8
We have also started investigation of the KH instability in the event of a boundary layer of small, but finite
thickness, k  1. Then the KH dispersion relation extends to
2
 
U0 
U 


 k 
2
  2 h k   ik 0  coth   
   ik
 1
2 
2 

 2 


2
U0 
U
 




ik
  2 l k 2    ik 0

 1
2 
2




 k
 coth 
 2


U 
 2

  A    ikU a a   Agk .
2 


2
(7)
which accounts for the viscosities of the heavy and light mixtures, v h and v l , respectively. Accordingly, the KH
instability is stabilized by acoustics and/or gravity/traction if
2
Ua 
2 gk coth k / 2   1 k 2  h   l  
 2 
 
.
U 0 U 0k 
 1 2
U 02

(8)
Summary and Synergy
We have now successfully analyzed the coupling of various intrinsic flamefront instability modes with an
imposed acoustic field, for both premixed and diffusion flame segments of the nozzle-generated triple flame.
The next and final step is to integrate the instability modes between the premixed and diffusion flames, and the
coupling between the diffusion flame segment and the chamber acoustics to arrive at the final LRE instability
boundaries. These boundaries will serve as useful guideline in the experimental and computational components
of the present program.
Task III: High-Fidelity Modeling and Simulation of LRE Combustion Instabilities
The primary purpose of this task is to perform high-fidelity modeling and simulations of the experiments
conducted in Task I. The basis is three-dimensional large-eddy-simulation (LES) codes developed for highpressure turbulent, chemically reacting, multi-phase flows. The work extends the existing capability for
cryogenic fluids to include a much broader range of fluid states, including gas/gas, gas/liquid and liquid/liquid
systems that simulate the pre-burner and main combustor environments of contemporary and future LRE.
Emphasis is placed on detailed flow structures, flame stabilization mechanisms, and combustion stability
characteristics.
The following tasks have been performed systematically.
1.
Further improvement of existing theoretical/numerical framework for treating liquid-propellant
combustion at both subcritical and supercritical conditions,
2.
Simulations of companion experiments in Task 1, and
3.
Development of guidelines for mitigating LRE combustion instabilities.
Results have led to the following papers for submission to Combustion and Flame for publication.
1.
“Subgrid-Scale (SGS) Dynamics for Large-Eddy Simulations of Supercritical Combustion of Liquid Oxygen
and Methane,” by H.-F. Huo and V. Yang;
2.
“Numerical Simulations of Supercritical Combustion of Gaseous Oxygen and Hydrogen of a Shear-Coaxial
Injector,” by H.-F. Huo and V. Yang;
3.
“S-Curve Responses of Counterflow Diffusion Flames for Real Fluids: Oxygen/Hydrogen Mixtures,” by H.F. Huo, X.-J. Wang, and V. Yang;
4.
“Flamelet and Flamelet-Progress-Variable Models Applied to Trans-critical Liquid Oxygen/Methane
Flames,” by H.-F. Huo, X.-J. Wang, N. Zong, G. Ribert, and V. Yang.
The major accomplishments made in each of the above three areas are summarized below.
Further Improvement of Theoretical/Numerical Framework for Treating Liquid
Propellants Combustion at Subcritical and Supercritical Conditions
A unified analysis incorporating fluid mechanics, thermodynamics, and transport phenomena has been
developed and implemented to study a variety of supercritical fluid and combustion problems. The purpose of
this subtask is to further improve the modeling and simulation capabilities, with special emphasis placed on the
subgrid-scale (sgs) dynamics.
The sgs modeling of unresolved terms in the filtered conservation equations is one of the central issues in largeeddy simulations (LES) and must be carefully treated. In the present AFOSR project, much effort was made to
assess and improve sgs models for LES of supercritical mixing and combustion. Two-dimensional quasi Direct
Numerical Simulations (DNS) of a liquid oxygen /methane flame stabilized by a splitter plate were performed as
a benchmark problem to provide the basis for the sgs model development. Exact values of the sgs terms in the
LES formulation were calculated by filtering the DNS data, and were compared with the values obtained with
various existing and proposed sgs models. All the sgs terms in the conservation equations and equation of state
were considered. It was found a modified gradient (GR) model is considerably more appropriate in modeling the
sgs terms than the Smagorinsky model.
Figure 8: Instantaneous temperature and shadowgraph fields for LOX/methane combustion
sgs
3
22 , 10 Pa
sgs
3
12 , 10 Pa
sgs
3
11 , 10 Pa
Figure 8 shows instantaneous temperature and
90
8
8
shadowgraph fields for a model problem involving
5
5
40
the mixing and combustion of methane (300 K and 60
2
2
m/s, upper stream), and liquid oxygen (120 K and 10
-10-1
0
1 -1-1
0
1 -1-1
0
1
m/s, lower stream) over a splitter plate with a
50
10
10
thickness of 0.3 mm. The environmental pressure is
0
0
0
10 MPa. The flame is anchored in the recirculation
-10
zone immediately behind the splitter plate, and
-50-1
0
1 -1
0
1 -10-1
0
1
spreads as the vortices roll up and develop
15
3
5
downstream. To examine the model assumptions
5
1
2
associated with the LES of supercritical mixing, the
sgs terms in the LES formulation are evaluated from
-5-1
0
1 -1-1
0
1 -1-2
-1
0
1
the DNS data by spatially filtering the data over a
y/
y/
y/
coarser grid ∆̅, which is typically several times larger
Figure 9: Modeled sgs shear stress compared with DNS data,
than the DNS grid size ∆. The filtered data represent
̅ = 𝟏𝟎∆.
black solid line: exact; blue solid line: modeled. ∆
the exact LES data for the corresponding filter size.
Then, the sgs terms calculated with various sgs models from the filtered data are compared with the exact data
to assess the accuracy of those sgs models. Figure 9 shows the modeled sgs shear stress and the exact data
obtained from DNS. The modified GR models accurately represent the sgs shear stress. Further analysis is
undergoing to systematically examine the various model assumptions in the LES of supercritical mixing and
combustion. The present analysis is expected to provide reliable guidance in developing sgs models for
supercritical reacting flows.
Simulations of Task I Experiments
The refined theoretical/numerical framework established in previous section will be applied to simulate the
experiments to be performed in Task I. The purpose is to investigate the detailed flow and combustion dynamics
in the experimental setup. The effects of various injector design attributes, inlet flow conditions, and chamber
operating condition on the overall flow characteristics will be examined systematically. Special attention will be
given to the response of the injector flow and flame dynamics to externally impressed oscillations at the
boundaries over a wide range of acoustic conditions.
In addition to the LES study of the chamber combustion dynamics, an analytical model will be established, to
provide direct insight into the near-field combustion characteristics, and to facilitate correlations of the LES
results in such a form that can be effectively used as a submodel in the injector and combustor design analysis.
The analytical model will extend the general inviscid flow theory described by Bazarov and Yang to include the
salient features of supercritical fluids. Furthermore, advanced data analysis techniques such as properorthogonal-decomposition (POD) techniques will be implemented to determine the spatial structures and
frequency contents of the entire oscillatory flowfields. The mutual coupling among the turbulent, acoustic, and
mean flowfields, as well as their collective interaction with the combustion process, will be studied
systematically.
Figure 10 shows a sample calculation of a bi-swirl injector. Liquid oxygen (LOX) and kerosene are introduced
tangentially into the swirling chamber and the annulus, respectively. The fuel and oxidizer temperature are 300
K and 120 K, respectively. The operating pressure is taken as 100 bar. A gaseous core forms in the center of the
oxygen injector and is acoustically connected with the downstream combustion flowfield. Thus any pressure
fluctuations will feed back to the interior of the injector and result in variations of the propellant mass flow rate.
LOX exits the injector nozzle as a cone-shaped film. With a recessed LOX post design, the liquid oxygen mixes
with the co-flowing kerosene around the exit of the fuel annulus. Between the two propellant streams, a thin
flame starts from the small recirculation zone behind the LOX post and continues to develop downstream as the
mixing of the two propellant streams proceed. Heated by combustion, and perturbed by strong turbulence,
propellants form a much lighter combustible mixture soon after the injection, and strong flames take place
surrounding the dense liquid propellant sprays.
Figure 10: Instantaneous temperature and density contours
Development of Guidelines for Mitigating Combustion Instabilities
In addition to provision of direct insights into the detailed flow and combustion dynamics in those experiments
conducted in Task I, a major goal of the overall research is to develop guidelines, both qualitative and
quantitative, for mitigating combustion instabilities in full-scale, practical LRE. To this end, physical rules
dictating the flame behavior and ensuing heat-release distribution under both steady and oscillatory conditions
will be explored. Their impact on combustion stability characteristics will be assessed. The present research
provides a precious opportunity to explore the fundamental mechanisms dictating the individual behavior of
injectors and their collective characteristics in a combustion chamber. The attributes of different injector types
(e.g., swirl vs. shear co-axial), propellant fluid states (gas/gas vs. gas/liquid or liquid/liquid), and local acoustic
properties (standing vs. spinning waves) will be examined systematically. Both high-level, qualitative design
guidelines and fundamental-level, quantitative information will be developed.