47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
AIAA 2009-234
Experimental Study of High-Frequency Combustion
Instability in a Continuously Variable Resonance Combustor
(CVRC)
Yen C. Yu1, Loral O’Hara1, James C. Sisco 2, and William E. Anderson3
Purdue University, West Lafayette, IN, 47907
An experimental investigation of high-frequency longitudinal combustion instability
using a continuously variable resonance combustor (CVRC) is described. The continuously
variable resonance condition is provided by varying the length of a tube carrying oxidizer
into a combustor with a rearward-facing step. The acoustic length of the tube is varied
between a quarter- and half-wave resonator. The data are analyzed and compared with the
analytical results calculated using linearized Euler equations. As the tube length changes the
system transitions between stable and highly unstable operation, allowing the observation of
several unique stability behaviors. When the system transitions into instability, higher
harmonics appear simultaneously and instantaneously. The transition is accompanied by
transitory, unorganized, high amplitude, sub-harmonic pressure fluctuations. When the
system transitions into stability regime, the higher harmonics disappear sequentially, led by
the highest order. Small but measurable differences are measured in oscillation amplitude
depending on the direction of the sweep (½ wave to ¼ wave or vice versa). For gaseous fuel
experiments, the highest amplitudes of instability do not occur at the least damped acoustic
configuration suggested by classical acoustic models (½ wave, perfectly coupled resonance
condition). This indicates that the gas dynamic effects of the system on combustion is
important. Comparisons are made between the measured frequency and mode shape data
and results from a linearized Euler equation, indicating generally good agreement, but
highlight the need for an accurate combustion response submodel.
I. Introduction
C
ombustion instability due to a coupling between unsteady combustion and chamber gas dynamic modes creates
undesirable high amplitude pressure oscillations and enhanced heat transfer that are detrimental to hardware.
The underlying challenges that hinder the understanding and circumvention of combustion instability include the
high cost of conducting full-scale experiments, and the complexity of the involved physics. Although mechanisms of
combustion instability are not fully understood, the increase in computational power has rendered understanding of
the complicated dynamics possible. Experiments are crucial, both to validate computations and to provide
understanding.
Because of the coupling between the combustor modes and the unsteady reacting flowfield, experiments should
strive to represent the high-pressure acoustic environment in an actual combustion chamber. Observation and
measurement of an instability in the laboratory provide validation data, of course, and can also yield key insights.
Experimental difficulties associated with high-pressure operation should be evident, but the difficulties associated
with simulating the gas dynamic flowfield at full scale are more subtle. It is difficult to match the relatively large
acoustic scales and relatively low frequencies of the full scale combustion in the laboratory. For this reason subscale
test devices that can represent near full scale environments are critically needed.
The Continuously Variable Resonance Combustor (CVRC) experiment is a useful research tool for
combustion instability that provides important data and insights. The CVRC provides a continuous variation of gas
dynamic conditions during a test by providing a moving boundary at the combustor inlet. The CVRC was motivated
1
Graduate Research Assistant, School of Aeronautics and Astronautics, W. Stadium Ave., West Lafayette, IN
47907, and AIAA Student Member.
2
Postdoctoral Research Scientist, School of Aeronautics and Astronautics, 500 Allison Road, West Lafayette, IN,
47907, presently at Aurora Flight Sciences, Cambridge, MA, AIAA Member.
3
Associate Professor, School of Aeronautics and Astronautics, W. Stadium Ave., West Lafayette, IN, 47907, and
AIAA Senior Member
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Copyright © 2009 by Y. Yu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
by our previous experiments with fixed geometry combustors [1] with the goals of providing benchmarking data for
model validation and mechanistic combustion response submodels. Although the previous experiments covered
many discrete geometric combinations, the ability to continuously measure stability characteristics over a range of
gas dynamic modes was clearly desirable. Unique coupling configurations, transitions to highly non-linear behavior,
and hysteresis can be explored, along with a continuous map of combustion response to a range of frequencies that
can potentially be used for screening injection concepts. Limited information enabled by this capability is available
in the existing literature [2]. Morgan2 et al conducted an experimental study on longitudinal instability limit by
varying the chamber length during test operation.
Collaborations with CFD modelers [3,4] call for the use of gaseous fuel, so that liquid atomization and droplet
distribution do not have to be modeled. The change in fuel type from liquid JP-8 to gaseous methane in the current
experiment is a consequence of providing an experiment that matches the model. Another modification from the
prior experiments in reference [1, 5] includes the fuel injector design such that gaseous fuel flow is co-axial to the
oxidizer at interaction [6].
Unsteady heat release modeling has been the key issue for combustion instability. In simulations at all level of
fidelity, aside from LES, a model for unsteady heat release is a necessary input. Derivation of a mechanistic heat
release profile requires large number of test data. This can be achieved by conducting copious tests at various
conditions. The CVRC experiment provides an efficient way of generating a large number of data. The continuously
variable resonance condition is facilitated by translating the sonic inlet of the oxidizer injector during a test. This
alters the effective oxidizer injector tube length and changes the acoustic resonance conditions.
In our tests, the oxidizer tube is continuously changed between a ½ wave and ¼ wave resonator using an
analytical model based on Linearized Euler Equations (LEE) [7] as a design tool. The high frequency combustion
instability is designed to have a fundamental frequency on the order of 1400 Hz. The traverse motion is programmed
to be three orders of magnitude slower than the pressure perturbation, such that the system can be treated as quasisteady. The traverse is either in the forward or backward motion. Geometrically stationary experiments can also be
performed at desired oxidizer injector positions.
Recent results from CVRC experiments are presented in this paper. A brief description of the experimental
hardware is summarized first, followed by an overview of the tests that were conducted. Next, a general and visual
description of the stability behavior is provided by spectrograms calculated from the test data with full forward
sweep (oxidizer tube length of half-wave resonator to quarter-wave resonator) and the full backward sweep (quarterwave resonator to half-wave resonator). In both cases transitions between stability regimes are observed as the
effective oxidizer injector tube length varies. At an oxidizer tube length of 7.5-in, the system is marginally unstable
with two dominant modes apparent. As the length of the oxidizer injector approaches 6.5-in, the instability becomes
much more powerful and up to five higher harmonics appear simultaneously. With a continuing traverse toward a
more stable configuration, the higher harmonics disappear sequentially, higher order first. The inverse relationship
between frequency and the effective oxidizer injector tube length is also evident in the spectrograms.
Following this description of general instability characteristics, the full forward sweep test is chosen for
discussion of more detailed behavior. High-pass filtered pressure traces measured at various axial locations are
presented that show the onset to highly non-linear behavior is accompanied by transient pressure oscillations of nonresonant frequencies and high amplitude. Power spectral density (PSD) is calculated at various oxidizer tube lengths
and presented to indicate the distribution of signal power as a function of frequency. As the instabilities become
more powerful, sharpening of the gas dynamic resonances is clearly seen, as are differences between the energy
contained in the modes at various chamber locations. Finally the resonant frequencies and spatial mode shapes are
analyzed and compared to the analytical model developed using Linearized Euler Equations (LEE). Reasonable
agreements are attained in the comparisons between measured resonant frequencies and spatial mode shapes.
However, in order to distinguish the dominant mode from all the calculated resonance frequencies that satisfy the
computational criteria, using the predicted linear growth rates from LEE, an unsteady heat release is necessary.
II. Experimental Overview
The experimental design is devised from previous combustion instability experiments, details of which can be
found in reference [6]. The present experiment (Fig. 1) comprises an injector tube, an actuated shaft, an oxidizer
injector with a sonic throat inlet, and a highly instrumented rearward facing step combustor. The continuously
variable resonance conditions are provided by traversing the oxidizer injector axially during a test. Because of the
sonic (choked) condition provided by the inlet of the oxidizer injector, the effective acoustic resonance geometry is
changing continuously. A linear actuator (Parker ET Series ET050B02) is installed at the head end of the translating
shaft. The actuator is controlled by a Parker Gemini GV6K servo drive/controller.
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The warm oxidizer gas is produced by decomposing 90% hydrogen peroxide. The sonic throat in the
oxidizer injector is designed to mitigate the inherent shock structure and isolate pressure perturbations from the
oxidizer feed system. Gaseous fuel is injected radially through 36 equally-spaced sonic orifices to attempt to ensure
uniform circumferential distribution. A ‘collar’ is used to protect the fuel flow while it is turned axially. The gaseous
fuel only interacts with the warm oxidizer at 0.4-in upstream of the injector face. No external ignition source is
employed in the experimental setup; autoignition of a small amount (25mL, 0.1 second) of JP-8 prior to gaseous fuel
injection is used to initiate combustion. Propellant flowrates are controlled and metered using cavitating venturis for
the liquid oxidizer and sonic orifices for gaseous fuel. Mean pressures are measured using Druck pressure
transducers at a sampling frequency of 500 Hz.
To measure the high frequency pressure oscillations, seven Kulite pressure transducers, model WCT-312M3000A, are used and sampled at 200 kHz. As shown in Fig. 1, the high-frequency measurements are located at -3.0”
(labeled “1”), 0.5” (labeled “2”), 1.5” (labeled “3”), 2.5” (labeled “4”), 3.5” (labeled “5”) and 14.5” (labeled “6”)
with respect to the injector face. A Kulite pressure transducer, model XTEL-375M, is also installed in the fuel
manifold (labeled “Fm”).
Figure 1. Schematic of the Continously Variable Resonance Chamber. The chamber length is 15-in.
The length of the oxidizer post can be changed continuously from 7.5-in (half-wave resonator) to 3.75-in
(quarter-wave resonator) during a test to provide a wide range of gas dynamic conditions.
The continuously variable gas dynamic resonances in the CVRC are provided by varying the effective
oxidizer injector tube length by traversing the sonic oxidizer injector inlet. Prior to continuously varying the
resonance condition in the combustor, several preliminary tests were conducted at fixed geometry to finalize the
operating conditions. The preliminary tests were performed at an oxidizer injector length of 7.50-in and a chamber
length of 15.0-in for direct comparison to the substantial dataset obtained in previous tests [1, 5, 6]. The first set of
preliminary tests examined the stability of different gaseous fuels (hydrogen, ethylene, and methane) to determine
the fuels that would be used in the CVRC [6].
The second set of preliminary tests compared the combustion stability characteristics at a nominal designed
chamber pressure of 350 psia and a reduced designed chamber pressure of 250 psia. There are two primary reasons
to reduce the chamber pressure for CVRC. First, it reduces the structural loads on the actuating mechanism. Second,
it reduces the operating pressure in the fuel system below the critical pressure of the gas to eliminate the possibility
that slight variations in pressure or temperature could lead to large mass flowrate error. Chamber pressure was
decreased by reducing propellant flowrates.
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A consequence to
reducing
the
propellant
flowrate is unchoking the fuel
injector. At the reduced
chamber pressure condition,
gaseous methane is injected
5
6
6
5
with a mean Mach number of
0.8 at the orifice. Figure 2
shows the power spectal
b) Designed Pc = 250 psia;
a) Designed Pc = 350 psia;
density (PSD), calculated
Measured Pc = 200 psia
Measured Pc = 283 psia
during the limit cycle regime,
Figure 2. Power spectral density (PSD) calculated for stationary CVRC
using gaseous methane at
experiment with oxidizer injector tube length of 7.5-in and a chamber
different chamber pressures. It
length of 15.0-in at different chamber pressure a) Pc = 283 psia and b) Pc
is verified that the resonant
= 200 psia
frequencies and amplitudes are
independent
of
chamber
pressure at fixed geometry. Note that the measured chamber pressure was considerably lower than the design
chamber pressure in both cases; in all our gaseous fuel tests, cstar efficiency is generally poor, on the order of 0.8.
Inefficiency was more pronounced with higher levels of instability, a phenomena that was also observed with liquid
fuel tests [5].
The final operating conditions for all the CVRC experiments are: oxidizer (decomposed 90% hydrogen peroxide)
flowrate of 0.7 lbm/s; fuel (gaseous methane) flowrate of 0.1 lbm/s; and designed operating chamber pressure of 250
psia. Seven tests were performed and summarized in Table 1. The timing sequence for a typical test is as follows:
oxidizer flow starts at 5.0s and leads fuel flow by 3.5 s. The bi-propellant hotfire duration started at 2.5 s for the first
tests and was increased to 3.0 s for the subsequent tests. The traversing mechanism is actuated at 1.0 s into the bipropellant timing sequence (after the JP-8 autoignition transient). Tests CVRC-F01 and CVRC-B01 were the first
forward and backward translating test performed. To gain confidence on the traversing mechanism, the oxidizer
injector was only moved 2.0-in. After the integrity of the hardware was confirmed, the full sweep tests in both
forward and backward directions were conducted. Good repeatable data were also obtained for the forward actuation
tests (CVRC-F02, CVRC-F02r1 and CVRC-F02r2).
3
4
3
4
Table 1. Test summary for the translating CVRC experiment
Test ID
Effective Oxidizer Injector Traversing Velocity [in/s]
Tube length [in]
CVRC-F01
7.50” 5.50”
1.60
CVRC-B01
3.50” 5.50”
-1.60
CVRC-F02
7.50” 3.50”
2.00
CVRC-B02
3.50” 7.50”
-2.00
CVRC-F02r1
7.50” 3.50”
2.00
CVRC-F02r2
7.50” 3.50”
2.00
Bi-propellant
Duration [s]
2.5
3.0
3.0
3.0
3.0
3.0
Hotfire
III. Experimental Results
Figure 3. Measured mean flow parameters
as a function of time for a typical CVRC test
Measured mean flow parameters (chamber
pressure, propellant flowrates, and effective oxidizer
injector tube length) for test CVRC-F02 are depicted in
Figure 3. The propellant flowrates and the measured
oxidizer injector length correspond to the left y-axis and
the chamber pressure is related to the right y-axis. The
spike seen in the measured oxidizer injector tube length is
related tchange in voltage demaind caused by high
amplitude fluctuations, and does not indicate its actual
position.
In these tests the combustion instability characteristics
were measured using high frequency pressure
measurements. The measured pressure data are high-pass
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filtered around 100 Hz to eliminate any low frequency noise. Spectrograms for both forward and backward traverse
motion are presented to illustrate the spectrally-resolved pressure amplitude response to the continuously variable
gas dynamic resonances. The forward motion test, CVRC-F02, will be used as baseline for later more detailed
discussion of PSD’s, resonant frequencies, and spatial mode shapes.
The spectrograms presented in Figs. 4 and 5 are two-dimensional representations of the PSD in time. The
signal powers are represented using coloration, using red for high signal power and blue for low signal power. The
coloration scale is consistent between all the spectrograms. The spectrograms for test CVRC-F02 is shown in Fig. 4.
In both forward and backward sweep tests, the fuel main valve is actuated at 8.5 s into the timing sequence, and the
JP-8 ignition occurs between 8.7 and 8.8 s. The oxidizer injector remains stationary for 0.7 s after ignition, after JP-8
was exhausted and only methane is being injected into the chamber. The traversing mechanism is actuated at 9.5 s,
well after ignition transients have passed. The oxidizer injector moves 4.0-in in 2 s. As expected, the frequency
varies inversely with the effective oxidizer injector tube length. The comparisons between the measured frequency
and the calculated resonant frequencies from the multi-domain analytical model will be discussed in the analytical
results section. It is more interesting that the system transitions from a relatively stable regime into one of instability,
and then back to a stable regime, for both forward (Fig. 4) and backward (Fig. 5) traverse motion.
In the forward traversing
experiment (Fig. 4), relative
stability is observed at an
oxidizer tube length (Lop) of
7.50-in. No distinct spectral
content is observed in the
pressure measurements in the
oxidizer tube, (- 3.0-in,
upstream of injector face).
Other measurements in the
combustor show two faint
unstable modes near 1400 Hz
and 2800 Hz. Once the
oxidizer tube length shortens
to approximately 6.6-in, the
system transitions into a highly
unstable regime, with distinct
sharpening of the lowest two
modes
and
a
nearinstantaneous appearance of
higher order harmonics. This
highly unstable condition is
sustained through an oxidizer
tube length of 4.75-in. As the
tube length is reduced, the
system transitions back to a
relatively
stable
regime.
Unlike the instantaneous and
simultaneous appearance of the
higher harmonics when the
system transitions to the highly
unstable regime, as the system
Figure 4. Spectrograms calculated from measurements at different axial
transitions to a more stable
locations and measured oxidizer tube lengths as a function of time in the
condition the higher harmonics
forward full sweep test (CVRC-F02)
disappear sequentially, led by
the highest order.
It is also interesting to compare spectrograms obtained at different chamber locations. It is evident that the
spectrogram calculated at 0.5-in is cleanest, with highly resolved frequency contents and less noise. On the contrary,
a much noisier signal is seen in the measurements at 2.5-in and 3.5-in. A possible physical explanation is the
occurrence of combustion near these locations. A hypothesis regarding a vortex-shedding-controlled mechanism
whereby a vortex shed from the injector face impinges on the chamber wall at approximately five step heights
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downstream has been tested computationally [4] and experimentally [1] with positive results. The step height of the
current rearward facing combustor is 0.48-in and the vortex is expected to impinge at 2.4-in downstream of the
injector face, so it is possible that this noise is related to a local increase in unsteady combustion. It is quite
interesting to note the onset of unorganized pressure oscillations at less-than-fundamental frequencies (between
150Hz to 300Hz) coincident with the transition to the highly unstable, nonlinear region. These sub-harmonic
activities are most apparent in the measurement near the combustor head-end (0.5-in with respect to injector face)
and rear-end (0.5-in upstream of the chamber throat), both of which are in close proximity to a reflected boundary.
This effect is more apparent in the pressure trace and PSD plots which will be discussed briefly in the subsequent
section. Finally the spectrograms show the effects of the measurement location and respective mode shapes on
amplitude for specific modes.
It should be noted at this point that these instability characteristics are clearly dependent on effects other
than the acoustic geometry. For instance, a consideration of acoustics alone would lead to the conclusions that the
quarter-wave geometry provides the greatest amount of acoustic damping and that the half-wave resonator results in
the least amount of acoustic damping. However it is seen that both cases are relatively stable, and that the most
powerful instabilities are seen at an intermediate geometry. This should be clear evidence of the dominance of the
combustion mechanism that drives instability, and the effects that the gas dynamic modes can have on that
combustion mechanism.
The spectrogram for the backward traversing experiment (CVRC-B02) is shown in Fig. 5. The timing sequence
is kept identical to CVRC-F02, except that the tube length starts at 3.75-in and increases to 7.5-in. Similar to the
forward sweep, the system transitions between stable and unstable regimes. The backward motion experiment starts
off slightly more unstable, at an
oxidizer tube length of 3.75-in,
than the forward motion stability
level at an oxidizer tube length of
7.5-in. The overall instability level
during the backward traverse test
is also higher than the forward
traverse test. Similar to the
forward traverse, the spectral
content of the marginally unstable
system presents only two modes
prior to the traverse. Once the
oxidizer injector is tuned to the
driving geometry, all harmonics
appear instantaneously. As the
effective oxidizer tube length
continues
to
increase,
the
combustor becomes more stable,
and again the higher harmonics
disappear sequentially, with the
highest orders disappearing first.
Although general behavior
remains largely similar between
forward traverse motion and
backward traverse motion tests,
hysteresis-induced effects are also
noticed. For the backward full
sweep test, a higher level of
instability is noticed at the start of
the traverse. Also, as the oxidizer
tube length increases, the system
instability does not decay to the
same stable state that exists at the
Figure 5. Spectrograms calculated from measurements at different
beginning of the forward traverse.
axial locations and measured oxidizer tube lengths as a function of
For instance, the forward sweep
time in the backward full sweep test (CVRC-B02)
test indicates that oxidizer tube
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length greater than 6.6-in is a relatively stable region, when the system starts at marginally unstable. For the
backward sweep test, the instability level sustains, with higher harmonic present, until the oxidizer tube length has
increased to 7.5-in.
Spectrograms corresponding to
fuel manifold measurements are
shown in Fig. 6. At marginal
instability levels, at an oxidizer
tube length of 7.5-in, no distinct
spectral content is observed in the
fuel manifold. Inevitably, when
the system is highly unstable,
pressure perturbations propagate
to the fuel feed system. At an
oxidizer injector tube length of
b) Backward Full Sweep Test,
a) Forward Full Sweep Test,
3.75-in, (end of forward sweep
CVRC-B02
CVRC-F02
test, and beginning of backward
Figure 6. Spectrograms and oxidizer tube lengths as a function of time
sweep
test),
where
higher
for measurement in the fuel manifold, a) forward full seep test
instability level than marginal is
(CVRC-F02), and b) backward full sweep test (CVRC-B02)
observed, pressure oscillations are
also observed in the fuel feed
system. The presence of frequency contents
in the fuel manifold indicate the fuel
injector is becoming unchoked.
In the following discussions, the
forward motion test, CVRC-F02, is chosen
for more detailed examination. The highpass filtered pressure signal is presented in
Fig. 7. Similar to the spectrograms, it is
observed from the high-pass filtered
pressure data that the system transitions to
and fro from the unstable regime. The
peak-to-peak pressure oscillations differ
between axial locations. Highest pressure
fluctuations
are
observed
at
the
measurement located 0.5-in downstream of
the injector face, with maximum peak-topeak pressure fluctuations several times
greater than mean chamber pressure. Peakto-peak oscillations in other axial locations
are on the order of chamber pressure in the
unstable regime. As mentioned earlier,
significant
high-amplitude
pressure
fluctuations are measured during the
transition to highly unstable behavior; these
are strongest at 0.5-in and 14.5-in. These
pressure oscillations are unorganized subharmonic fluctuations at frequencies
between 150Hz to 300Hz (shown more
clearly in the PSD discussion in the later
Figure 7. High-pass filtered pressure trace for measurements
section). The sub-harmonic events are only
at different axial locations and oxidizer injector tube length
present in the transition between stable to
as a function of time in a forward full sweep test (CVRC-F02)
unstable region, once the unstable regime is
reached, the sub-harmonic events disappear.
To examine the frequency content in the pressure trace, a PSD is calculated over an interval of 0.1 s. The sample
rate of 200 kHz over this interval gives a frequency resolution of 10 Hz for the calculated PSD. Power spectral
density plots are presented for four distinct time intervals - , while the system is in stable regime (Lop = 7.5-in, Fig.
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Figure 8. Power spectral density calculated for various
axial locations in the marginally stable regime (Lop = 7.5in) during the forward full sweep test (CVRC-F02)
8); during the transition to the highly unstable
regime (Lop = 6.5-in, Fig. 9); during the limit
cycle (Lop = 4.5-in, Fig. 10); and prior to fuel
valve shutoff, while the system is stabilizing
(Lop = 3.75-in, Fig. 11).
The system is marginally stable at an
effective oxidizer tube length of 7.5-in. From
the PSD presented in Fig. 8, only two distinct
modes are noticed. At measurements in the
oxidizer tube (3.0-in upstream of injector
face), the second mode is dominant. The
factors determining the dominance of this
second mode could include spatial and
temporal distribution of the unsteady heat
addition, or the acoustic damping of the
system. As the instability level grows, the
fundamental mode is more energized and it
becomes the most dominant mode. Since the
fundamental mode has the widest spatial
distribution, the measurement at 3.5-in
downstream of the injector typically measures
higher amplitudes of this mode than any other
location.
During the initial portion of the traverse,
the system remains marginally stable.
However, as the oxidizer tube length reaches
6.5-in, the system transitions to a high level
of instability almost instantaneously. As seen
from the spectrograms, second order and
higher
harmonics
appear
nearly
simultaneously, and the instability level
grows by two orders of magnitudes. When
the system is highly unstable, the
fundamental mode is always dominant. In Fig.
9, the PSD’s are calculated during the
transition to the highly unstable regime. Some
high amplitude, unorganized pressure
fluctuations at sub-harmonic frequencies (150
Hz to 300 Hz) are observed at measurements
located at 0.5-in and 14.0-in. As mentioned
earlier these sub-harmonic events coincide
with the onset of higher harmonics and the
pressure spikes noted in the pressure trace
presented in Fig. 7. However, these subharmonic activities are transient and mostly
disappear after the transition to the unstable
regime has passed.
The most unstable geometric
combination in the forward full sweep test
occurs near an oxidizer injector tube length of
4.5-in. Distinct frequency contents, up to five
harmonics, are observed. The PSD presented
in Fig. 10 corresponds to the amplitude limit
cycle. Examination of the PSD beyond this
time, with further decrease in oxidizer
injector tube length, shows decrease in signal
8 at most
Figure 9. PSD calculated for various axial locations
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Institute
of
Aeronautics
test and Astronautics
unstable point (Lop = 6.5-in) in the forward full sweep
092407
(CVRC-F02)
Figure 10. PSD calculated for various axial locations at
most unstable point (Lop = 4.5-in) in the forward full sweep
test (CVRC-F02)
power. The decay is also noticeable in the
decreasing pressure trace presented in Fig. 7.
The sub-harmonic events present at the
transition are also non-existent. From the PSD
calculated from the measurement at 3.5-in, the
1st and 2nd harmonics are highly damped as this
location is near a spatial pressure node at those
frequencies.
The PSD’s depicted in Fig. 11 are
calculated prior to fuel shutoff (fuel shutoff at
11.5 s), at an oxidizer injector tube length of
3.75-in. The system has transitioned to a
marginally unstable region indicated by a
significant decrease in signal power and
disappearance of higher harmonics. The PSD
corresponding to a 3.75-in oxidizer tube length
at the beginning of the backward traverse
motion is also calculated using the backward
sweep test data depicted in Fig. 12. Figure 11
is calculated from forward sweep data, when
the system is decaying, and Fig. 12 is
calculated from backward sweep data when
the system is growing. The calculated PSD
looks largely similar except for the
measurement at 3.5-in. More thorough
examination indicates that the growing system
(Fig. 12) measures slightly higher magnitudes
than the decaying system.
IV. Experimental and Analytical Result
Comparisons
In this section the high frequency pressure
measurements are compared with results from an
analytical linearized Euler equation (LEE) model
[7] that includes mean flow and entropy wave
effects. It is derived for a multiple-domain
analysis and generalized for physically realistic
boundary and interface conditions. Once the
mean flow properties and the unsteady heat
release function are specified, the analytical
solution can be readily solved. The LEE model
calculates resonant frequencies and spatial mode
shapes. The resonant frequencies are complex,
with the real parts indicating the frequencies of
the resonant modes, and the imaginary parts
corresponding to the linear growth rates. To
correctly predict the linear growth rates and
distinguish the most unstable mode, a prescribed
unsteady heat release is necessary. The unsteady
heat release model is not included in the current
LEE results, and is the topic of an ongoing study.
A three-domain analysis is set up in LEE
with mean flow properties calculated using the
NASA Thermochemistry code (Chemical
Equilibrium with Application, CEA). A
Figure 11. Power spectral density calculated for various
9
axial locations when system has transitioned to stable
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region (Lop = 3.75-in) in the forward full sweep
test
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(CVRC-F02)
concentrated combustion profile is imposed
1.5-in downstream of the injector face. The
three computational domains consist of the
oxidizer injector tube; the sudden area
expansion at the injector face upstream of the
concentrated combustion plane; and the
chamber section consisting of combustion
products. A constant-mass-inflow with
constant enthalpy is used as the inlet
condition to represent the choked oxidizer
injector. The short nozzle admittance function
is used to approximate the exit condition.
The LEE model is used to calculate the
resonant frequencies and spatial mode shapes
as a function of oxidizer injector tube length.
Figure 13 summarizes the resonant
frequency
comparisons
between
the
analytical and experimental results for
frequencies up to 6000 Hz. System modes
including the effect of the tube and chamberonly modes are both seen. Chamber mode
frequencies are independent of tube length
whereas frequencies for the system modes are
highly dependent on tube length. To indicate
any pressure amplitude-related nonlinear
effects, the test data are discrimated
according to pressure oscillation amplitude.
Good agreements are achieved at most
geometry variations.
Figure 12. Power spectral density calculated for various
From the CVRC experiment, the
axial locations at oxidizer tube length (Lop = 3.75-in)
most unstable geometry does not correspond
corresponding to the PSD in Fig. 11 in the backward full
to the least acoustically damped case (½
sweep test (CVRC-B02)
wave), suggested by simple first order
analysis [8]. Even though unsteady heat
release is not included in the LEE model, the
Resonant Frequency vs Oxidizer Tube Length (Experiment & LEE)
linear growth rates predicted shows promising
trend. Using mean flow properties calculated
6000
with gaseous methane, the analytical linear
5500
growth rates indicate that the system is stable at
5000
an oxidizer tube length of 7.5-in, and unstable at
4500
3.75-in.
This improvement in predicting
4000
stability trend can be due to inclusion of mean
flow effects and the use more physically
3500
realistic boundary conditions.
3000
Spatial mode shapes are linear pressure
2500
perturbations with respect to axial locations. To
2000
compare calculated and measured mode shapes,
1500
the LEE model is used to calculate spatially1000
resolved pressure perturbations at different
3.5
4.5
5.5
6.5
7.5
instants of time. The LEE mode shapes shown
Oxidizer Tube Length [in]
in Fig. 14 is the spatial mode shape envelope,
Figure 13. Comparisons between measured and
which represents the maximum pressure
analytical resonant frequency at various oxidizer tube
perturbation at a fixed location in an oscillation
length
cycle. The experimental mode shapes are
computed amplitudes for the mode-of-interest
using
the
‘full-width,
half-maximum’
p' > 1 psia
1 psia <p'< 10 psia
Using High Frequency Pressure Measurement at x=2.5" w.r.t Injector Face
10 psia <p'< 50 psia
LEE
Resonant Frequency [Hz]
Cham
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American Institute of Aeronautics and Astronautics
092407
integration approach
[1]. For comparison,
experimental
amplitudes
are
normalized to the
highest
measured
peak-to-peak
oscillation, and, the
LEE mode shape
envelope
is
normalized by the
maximum amplitude
calculated within the
a)
b)
computational domain.
The measurement at
0.5-in
is
not
considered in the
spatial mode shapes,
as the measurement
generally
measures
two to five times
higher
pressure
fluctuations
than
measurements at other
locations. A good
agreement including
the 0.5-in location
c)
d)
may
only
be
achievable with an
Figure 14. Normalized experimental and analytical spatial mode shape
appropriate unsteady
comparisons at various oxidizer tube length using test data from forward full
heat release model.
sweep test (CVRC-F02): a) at marginally stable region (Lop = 7.5-in); b) at
Four experimental
transition from stable to unstable region (Lop = 6.5-in); c) at most unstable point
and analytical mode
(Lop = 4.5-in); and d) when system has transitioned to stable region (Lop = 3.75-in)
shape
comparisons
are shown in Fig. 14.
The cases correspond to the oxidizer injector tube lengths discussed in the PSD section: a) marginally stable regime
(Lop = 7.5-in), prior to traverse motion; b) at the transition from stable regime to unstable regime (Lop = 6.5-in); c) at
the most unstable location (Lop = 4.5-in), beyond which system starts to decay; and d) prior to fuel shutoff, where
system has stabilized (Lop = 3.75-in). Only two spatial mode shape comparisons are shown at an oxidizer tube length
of 7.5-inch, as the system is marginally stable and only two discernible frequencies are present. For other geometric
combinations, spatial mode shapes for the first three dominant modes are compared. Reasonable agreements are
attained between the analytical and experimental mode shapes. Spatial mode shapes will be used to determine the
unsteady heat release profile in the near future.
V. Conclusion
An experimental study of high frequency combustion instability under continuously variable resonance
combustor is presented.. The CVRC experiment is a useful research tool for combustion instability that provides
important insights to unique stability behavior. The CVRC experiment is configured to change the oxidizer injector
tube length between 7.5-in and 3.5-in, corresponding to an acoustic half-wave and quarter-waver resonator,
respectively. Both forward sweep and backward sweep tests are performed. Transition between stable regimes and
unstable regimes are observed in both traverse motions and the tuning of the oxidizer tube length allow the fine
definition of the most stable, most unstable, and transition geometries. At the onset of transition between marginally
stable to highly unstable regimes, unorganized sub-harmonic activities occur simultaneously with the instantaneous
appearance of higher harmonics. As the oxidizer tube length is moved into a stabilizing configuration, the higher
harmonics disappear sequentially led by the highest harmonics. Hysteresis induced effects are also noticed by
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American Institute of Aeronautics and Astronautics
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comparing test data in the forward and backward motion tests. Sweeps from quarter-wave to half-wave tube lengths
present higher amplitude instabilities, and the system requires longer time to decay to the stability levels measured
when the sweep starts at the half-wave length. Comparisons between the test results and an analytical model
developed using Linearized Euler Equations (LEE) show generally good agreements between resonant frequencies
and spatial mode shapes. To improve the agreement and to distinguish the dominant unstable modes according to
linear growth rates,, an unsteady heat release model is necessary. The CVRC experiment can generate large number
of test data at various geometric combinations in a single test that can be used for model validation data, generate
combustion response submodels, and provide fundamental insights into combustion instability.
Acknowledgments
The authors would like to express their gratitude towards numerous personnel and NASA. The project would not
be accomplished without the sponsorship by NASA Constellation University Institutes Project under NCC3-989,
with Claudia Meyer and Jeff Rybak as the project managers; Jim Hulka of Marshall Space Flight Center, for his
continuous support and technical discussions throughout the project; Stefan Koeglmeier for helping in
troubleshooting in the preliminary CVRC tests; Robert McGuire for his time and effort in hardware fabrication and
support; and Scott Meyer for his consultation in test operations.
References
1
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Morgan, C. J., Sokolowski, D. E., “Longitudinal Instability Limits with a Variable Length Hydrogen-Oxygen Combustor,”
NASA TN-D-6328, Washington, D. C., April 1972.
3
Smith, R., Ellis, M., Xia, G., Merkle, C., “Computational Investigation of Acoustic and Instabilities in a Longitudinal-Mode
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Yu, Y. C., Sisco, J. C., Anderson, W. E., Sankaran, V., “Examination of Spatial Mode Shapes and Resonant Frequencies
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8
Miller, K., “Experimental Study of Longitudinal Instabilities in a Single Element Rocket Combustor,” MS Thesis,
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