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2002 37th lntersociety Energy Conversion Engineering Conference (IECEC)
IECEC 2002 Paper No.
20176
NUMERICAL STUDY OF AERODYNAMIC INTERACTION
OF
COMPRESSOR AND COMBUSTOR FLOWS
K. Su
and C.
Q. Zhou
Purdue University Calumet
2200 169th Street
Hammond. Indiana46323
ABSTRACT
Numerical study of the aerodynamic interaction of
transient compressor and combustor flows has been
conducted using the KIVA-3V code. The simulation
was based
on
the solution of Navier-Stokesequations
with models of turbulence, sprays and chemical
reactions. A typical annular combustor, including the
diffuser, the secondary channels and the liner, was
modeled. The transient inflow was assumed by
specifying the pressure oscillation in a
form
of
sinusoidal function. Aeroacoustic characteristics of
the diffuser-liner flow were revealed. Three flow
patterns, namely the quasi-steady, transition and
steady patterns corresponding to the frequency
ranges of n
L
EO.
EO 5
n
5
320 and
n
2 320 Hz, were
classified. it is found that for the quasi-steady pattern,
combustion flow is in quasi-steady state with flow
properties dependent of time; for the steady pattern,
the combustion flow can be treated as
if
in steady
state, in which the influence of oscillation can be
ignored; and the flow in the transition pattern behaves
in-between. They significantly influence the gas
turbine combustion.
NOMENCLATURE
ap
amplitude factor
AM reference area
CO discharge coefficient
E
activation energy
H combustion heat
k turbulent kinetic energy; chemical reaction
constant
L length
M
Mach number
ma gas mass flow rate
m,
fuel mass flow rate
n oscillation requency
P pressure
P3 combustor inlet pressure
R
universal gas constant
S source term
st
Strouhal number
t
time
temperature
U , U velocity
ud droplet velocity
Z coordinate
P pressure difference
,$ variable
P density
r effective diffusivity
r droplet relaxation ime
INTRODUCTION
Offdesign conditions of compressor lead to
distortions, and moreover, reversing of gas flow at the
interface
of
compressor and combustor. During these
procedures, physical processes in individual
components of the gas turbine engine are strongly
coupled. Influences between connected components
such as compressor and combustor are important to
the engine performance. CFD simulation for gas
turbine combustor, from the compressor exit to the
combustor exit, is needed for investigation of the
interaction between the compressor and combustion
flows.
For a long time, diffuser and liner are simulated
separately due to the limitation of the capacity of
computers (Correa and Shyy, 1987; Tolpadi. 1995).
As the accuracy of physical models and the capacity
of computers increase, efforts
on
numerical simulation
of the whole combustor, including the diffuser,
secondaly flow channels and the liner. have been
made. Crocker et al. (1998) conducted the numerical
simulation of combustor flows from the exit of
compressor to the turbine inlet. Su and Zhou
(2000)
studied the effect of non-uniform nflow of the diffuser
on
combustion using the KiVA-3V code. Now it is
possible to numerically investigate the aerodynamic
interaction between compressor and combustor.
Aerodynamic interaction of transient compressor
and combustor flows is one of the most complicated
problems in gas turbine combustion. Most offdesign
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conditions are induced by unexpected compressor
behaviors. Among them, surge and stall are the most
common cases that would influence the durable
combustion performance and result in heavy
damages to the engine. Surge is a large-sale
reversed flow through the entire engine, including
compressor and combustor. Rotating stall is milder
situation that may occur just before the surge. In
rotating stall, pockets of stagnant air rotate around the
blade rows, causing local regions of flow blockage
and distortion. Because CFD codes at this stage
cannot deal with reversed flows at boundaries very
well, the effort in this study mainly focused
on
the
general and mild case, that is, the combustion with
transient distorted inflows from the compressor.
In this study, the aerodynamic mechanism of
interactions of transient compressor and combustor
flows was investigated through the numerical
simulation. Effects of the inflow oscillation
on
combustion were analyzed. These results will be
helpful in the development of the gas turbine
combustor.
THEORETICAL APPROACH
Compressible, threedimensional, transient
reacting flows in gas turbine combustor were solved
using a time-marching method with models of
turbulence, sprays and chemical reactions. Details of
the theory can be found in references (Amsden et al.,
1989; Amsden, 1993.1997).
Gas Phase Eauations
The governing equations are time-averaged,
threedimensional, transient Navier-Stokes equations.
Turbulence
is
modeled using the standard
k-E
model
along with the wall function treatment for near-wall
regions. The transient form of the three-dimensional
conservation equations may be written in general for
a conserved variable @as
where p is the fluid density, r the effective diffusion
coefficient, U the fluid velocity, and S he source term
which depends on the equation being considered.
Continuity, momentum, energy, turbulence and
species equations were solved, with the dependent
variable representing 1, velocity, internal energy,
turbulent kinetic energy and dissipation, and species,
respectively. The temperature field is obtained from
the thermochemical look-up table by linear
interpolation based on the calculated values of the
mixture fraction and its variance.
Chemical Reactions
For combustion, chemical reactions proceed
kinetically n the KIVA-3V code. The fuel was Jet-A in
a chemical formula of CIZH~~. A simplified kinetic
mechanism with 17-species and 23-step was
employed (Kundu et al., 1999). Chemical rate
expressions are evaluated by a partially implicit
procedure. The reaction rate constants are in the
form of Arrhenius
where
E
is the activation energy, and A is the
constant. With the reactions rates determined for the
mechanism, the chemical source terms in the species
equations were obtained. The mixing-controlled
turbulent combustion model based on the eddy-
dissipation was used for the turbulence combustion.
Liquid Phase Esuations
The Lagrangian method was used in the liquid
phase modeling. The fuel was assumed
to
inject into
the combustor as a fully atomized spray which
consists of spherical droplets. Liquid sprays are
represented by a discrete-particle technique, in which
each computational particle represents a number of
droplets of identical size, velocity, and temperature.
Droplet properties are determined by using the Monte
Carlo sampling method. The log-normal rule was
accepted to describe the droplet size distribution at
injection. The equation of motion of a spherical
droplet is given by the following equation
(3)
where ud is the droplet velocity and t he relaxation
time of the droplet. Physical properties of the gas
phase are calculated on the temperature averaged
between droplets and the surrounding gas.
The changes of mass, momentum and energy of
droplets from conservation equations are added into
the source terms of the governing equations. The
momentum exchange is treated by implicit coupling
procedures to avoid the prohibitively small time steps
that would otherwise be necessary. The accurate
calculation of mass and energy exchange is ensured
by automatic reductions in the time step when the
exchange rates become arge.
Turbulence effects on the droplet motion are
accounted for in the following way. When the time
step exceeds the turbulence correlation time,
turbulent changes in droplet position and velocity are
chosen randomly from probability distributions for
these changes. The interaction time between the
droplet and the eddy is taken as the minimum
of
the
eddy lifetime and the transit time required for the
droplet to cross the eddy.
NUMERICAL SCHEME
The gas phase solution procedure is based
on
a
finite volume method called the ALE (arbitrary
Lagarangian-Eulerian) method. The equations are
differenced in integral form with the volume of a
typical cell used as the control volume and with
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divergence terms transformed to surface integrals.
Spatial difference is formed on a finitedifference
mesh that subdivides the computational region into a
number of small cells that are hexahedrons. The
nodes may be arbitrarily specified functions of time,
thereby allowing a Lagrangian, Eulerian or mixed
description. Transient solution is marched out in a
sequence of time steps. The block-structured BFC
mesh is employed for the complex geometry of gas
turbine combustor. The discretization and the
numerical algorithm were described in references
(Amsden et al., 1989; Amsden, 1993,1997).
A typical gas turbine combustor was modeld in
this study. The combustor is annular with 12 domes
equally spaced along the circumferentialdirection. A
single dome sector of 30
span of the combustor,
which includes a swirler and a fuel nozzle and a set of
primary and secondary holes, was simulated with
periodic boundaly conditions on two sides. A grid of
80,000 cells for the entire combustor was used.
The computations were performed at the medium
power condition of the combustor with pressure
of
8.4
MPa and temperature of 600 K. The inflow was
simply assumed a sinusoidal function
e = [I + psin(&t)]
4
where ap is the amplitude factor of the oscillation and
ap = 0.01, n the oscillation frequency. Flow
oscillations with different frequencies in the combustor
are illustrated n Fig.1. Flows at the exhaust nozzle of
gas turbine engine usually are chocked during actual
operation. Therefore, pressure at the outlet of
combustor can be considered constant when inflow
distortion appears, which simplifies the simulation.
PrrannrnJaur
illha
-gl+mCtsrtB
Fig.1 Flow oscillations in the liner.
RESULTS
AND
DISCUSSIONS
Flow characteristics of combustor with diffuser
and the secondary flow channels were analyzed.
Time histories of pressure, mass flow rate, and heat
release rate were discussed.
Combustor
Flow
AnalvSis
Fig2 plots velocity distributions of combustor flow
at the longitudinal section. Airflow from the
compressor first enters the prediffuser where airflow
velocity reduces and the static pressure rises. It is
then split into three branches: the central stream that
supplies air to the combustor dome, and two streams
that feed the outer and inner annuli through the
diffuser dumps where flow velocity is further reduced
and static pressure rises. All the three flows then go
into the liner through penetration holes.
h,
. . .
Fig2 Typical combustor velocity field
Gas pressure becomes smaller when flows enter
the liner due to pressure loss through the
penetrations.
It
is more uniform than in diffuser
because of more straight and open flow channel and
the subsequent slowing down gas flow. Thereby,
physical and chemical processes in the combustion
flow can be considered to proceed under constant
pressure. There is a recirculation downstream of the
swirler where all the critical processes, such as fuel
injection, spray evaporation, turbulent mixing and
chemical reactions occur. For this reason pressure
and mass flow rate in combustion zone are typically
used in the analysis. Following is the dilution zone
where the fresh air enters the liner through
penetration holes, and mixes with the hot gas to
generate uniform exit temperature distributions. Mass
flow rate and pressure distributions are shown in
Figs.3 and 4. It is seen that the mass flow rate
increases along the axial direction due to the gas flow
accumulation from the swirler and penetration holes.
On the other hand, pressure drop along the axis is
small because of the low gas velocity in combustion
and dilution zones. and it becomes
a
little larger only
in the converging section near the exit where gas
velocity increases.
Previous researches only focused on either the
diffuser or the liner flow, but the influence of
compressor flow on combustion cannot be found this
way. Our effort is on the simulation of combustor flow
from the diffuser inlet to the exit of the combustor to
reveal the coupling of diffuser and combustor flows
under the inflow oscillation.
Aerodvnamic Characteristics
Figs.3 and 4 display the histories of pressures
and mass flow rates -at the diffuser inlet and In the
combustion zone of the liner with inflow oscillations of
n
= 80, 240 and
320
Hz. They clearly illustrate
pressure and mass flow rate oscillations under inflow
pressure oscillations. It is seen that amplitudes of
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pressure oscillations in the liner become smaller than
at the inlet for oscillations of
n
= 80 and 320 Hz. it
means that the pressure oscillation is dampened in
the flow and through the penetration holes. However,
for the inflow oscillation of n
=
240 Hz, the oscillation
is amplified. It indicates that some kind of resonance
happens
to
the combustion flow, which makes the
pressure oscillation stronger.
:~~
:
.2
1
*
-inlet
--cormustion
zone
7.8
I
0.000
O.OM 0.008 0.012 0.016
Tima
IS)
a) = 80 Hz.
8.4
e
6 0
0 000 04 0 008 0
012
r im 1
(b) = 240 Hz.
0
O W 4 0 8 0.012
rima
IS)
(c) = 320 Hz.
Fig.3 Pressure histones
I
I
-
P
.4
2
.
.2
O O W 0004 OW8 0012 0016
Time
I*
(a) n = 80 Hz.
0.000 0.004 0 008
0.012
rims 5 )
(b) = 240 Hz.
0 61
I
z
-inlet
--cormustion
zone
0
0.OW 0.003 0.006
O.OD9 0.012
r i m e IS
(c) = 320 Hz.
Fig.4 Mass flow rate histories.
Meanwhile, amplitude of mass flow rate
oscillation decreases as the frequency increases, as
indicated in Flg.4. It can be explained that the mass
flow rate oscillat ion is weakened by the forced mixing
resulted f he oscillation itself, and this effect is
intensified as the frequency increases. It is clear that
the mass flow rate oscillation in combustion zone is
much milder than at the liner exit. Usually the mass
flow rate
in
combustion zone is about
30
-
40
% of
the total mass flow rate. As mass flows accumulate in
the liner, fluctuations of mass flow rates gradually
become augmented. Please note that combustion
performance mainly dependson flow properties in the
combustion zone. Therefore, it mitigates the variation
of combustion performance. At the frequency of
n
=
240 Hz, pulsation n mass flow rate is stronger than at
the frequency of
n
= 80 Hz due to the resonance of
the flow.
When the oscillation frequency is lower than =
80 Hz, combustion flows can be considered in quasi-
steady state. Flow properties change through
convection relatively fast compared
to
the oscillation
itself, and at any instant the combustion can be
described as if it were in steady state. Due to
insulation of l iner walls and outflow boundary
condition, the combustion flow can only experience
less than 1/4 of the oscillation cycle while going
through the whole liner. Therefore, when the inflow
oscillation frequency 5 80 Hz, the combustion flow
can be dealt with using theoretical methods for the
steady combustion under the operating condition
changing with time.
On the other hand, when the oscillation
frequency is higher than n = 320 Hz, the combustion
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flow is like in steady state. From Fig.1, it is found that
the gas flow experiences more than one oscillation
cycle during residing in liner. Effective oscillation
along the axial direction is well developed. Because
the oscillation propagates at sonic speed in the gas
flow, flow properties can respond to the oscillation
quickly and be mixed up well in the liner. Therefore,
pulsations with flow properties could be moderated
comparatively for oscillation flows with frequencies of
2 320.
It
is seen that amplitude of mass flow rate
oscillation is about 5 % of time averaged value at
inflow oscillation of n = 320 Hz. Therefore, it is
reasonable to consider that the combustion flows with
inflow oscillation of
Z
320 Hz is in steady flow
pattern. Consequently,
all
the theory and analyses for
steady combustion can be applied. Unlike quasi-
steady combustion flow with
5 80
Hz, operating
conditions for this case can be considered constant.
Combustion flow with the inflow oscillation of 80 s
B
320 Hz can be classified as in transition flow
pattern. Combustion with the transition flow pattern
behaves in between that for quasi-steady and steady
flow patterns. In this frequency spectrum, effective
oscillation along the axial direction is gradually
established.
As
mentioned before, oscillations of flow
properties are gradually mitigated except at the
frequency around
n =
240 Hz when resonance
happens
to
the flow. Thus, the variation of
combustion flow in transition pattern is simply the
combination of the two aerodynamic processes, and
would be more complicated.
Forced combustion oscillation flows in the three
flow patterns, i.e., quasi-steady, transition and steady
flow patterns, have different effects on aerodynamic
characteristics and combustion performance.
Corresponding oscillation frequency, = 80 and 320
Hz, which are naturally called the quasi-steady
frequency and the steady frequency, are critical
to
the
combustion behaviors.
Fig.5 shows the ratio of amplitudes of pressure
oscillations at the inlet and in the liner. it is seen that
the pressure oscillation is dampened in transportation
in gas flow because of the viscosity of the flow and
the resistance of the flow channels between cold and
combustion regions. However, for the case with
n
=
240 Hz the amplitude of the pressure oscillation
becomes larger than at the diffuser inlet. Apparently,
aeroacoustic resonance occurs at the frequency of
240 Hz for the diffuser-liner system. Generally, the
damp of flow oscillation can protect combustor from
any undesirable impact of off-design conditions from
the compressor and make combustion more stable,
but it would also limit acceleration capability of the
engine and increase pressure
loss
in combustor.
However, aeroacoustic resonance intensities the flow
oscillation, and might result in deterioration of
combustion performance and lead to damage
to
combustor structure.
Fig.6 plots the amplitude of mass flow rate
oscillation in combustion zone. It is found that for the
frequency range of
5 80
Hz (quasi-steady flow
pattern), the amplitude of mass flow rate oscillation
remains about unchanged, but for 80 i i
320
Hz
(transition flow pattern) the amplitude decreases as
oscillation frequency n increases, and finally for 5
320
Hz
(steady flow pattern) the oscillation amplitude
becomes so weak that it can be ignored. Also, it is
obvious that the mass flow rate oscillation become
stronger when the resonance happens at the
frequency = 240 Hz. It will change the flow
properties in the combustion zone, and subsequently
affect the combustion performance.
Quasi-Steadv Flow Pattern n 5 80
As
discussed above, theoretical and empirical
analyses for steady combustion can be applied to
combustion flow with inflow oscillation in quasi-steady
flow pattern. Please note that flow properties oscillate
with time. Correspondingly, combustion performance
and aerodynamic characteristics can be achieved
through theoretical and empirical methods for the
steady combustion. Considering the combustor as a
simple flow channel, the mass flow rate of the
combustor can be obtained by
m,
=
C A , G
5)
where CO s the discharge coefkient, A,r the
reference cross section area,
p
the gas density, and
LIP the pressure difference throughout the flow
channel. In the simulation, temperature of the
transient inflow was simply assumed constant. Thus,
gas temperature mainly depends on the mass flow
rate in the combustor. Because the temperature rise
due to the combustion is more than 2000
K,
much
larger than the inlet temperature of the diffuser, then
the combustion temperature is obtained as
T
H,ml/m.,
where I is the fuel combustion heat.
Substituting it into Eq.(5) with the gas state equation,
then
Because amplitudes of pressure oscillations are
only
2 %
of the time-averaged or mean pressures,
gas flow throughout combustor can be considered
approximately at constant pressure. It is found that
the mass flow rate varies approximately with time in
an oscillatory trend of a sinusoidal function. With
Eq.(6). mass flow rate at any instant in an oscillation
cycle can be estimated. Please note that this
conclusion
is
only suitable for the inflow with the
oscillation frequency
S
80
Hz. For a constant
pressure flow process in gas turbine combustor, any
change in mass flow rate greatly influences the
combustion performance. Therefore combustion
performance will exhibit apparent oscillation trends in
case of oscillation frequency 5
80
Hz. Mass flow
rate oscillations are then approximated by
interpolating between that for quasi-steady and
steady patterns.
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iw *w YYI
w
5m
~ ~ i ~ t i m h e q u n c y n
mi
Fig.5 Ratios of oscillation amplitudes of
pressures in the liner and at the inlet.
Transition
Flow
Pattern (80 5 n 5 3201
Oscillation flows in transition flow pattem
(corresponding
to
inflow oscillation frequencies of 80
s i 320 Hz) exhibit two aerodynamic features: mass
flow rate oscillation dampens as inflow oscillation
frequency increases, while the pressure oscillation
keeps about the same: and oscillation resonance
happens to diffuser flows at the frequency around =
240
Hz. They have a combined influence on
combustion.
Effect of Pressure Oscillationon
Mass Flow Rate
It is interesting to notice one important feature of
inflow oscillation in Fig.6, i.e.. the amplitude of mass
flow rate oscillation decreases as the oscillation
frequency increases. One exception
is
at frequency
= 240 Hz where resonance occurs. Consider
simplified one-dimensional flow in a pipe of uniform
cross section with the oscillation inflow pressure.
Neglecting viscosity, mass diffusion and convection
terms, the onedimensional momentum equation
is
given as
7)
For one-dimensional flow with uniform cross section,
it can be found after integration,
where At is the amplitude of the mass flow rate
oscillation. As the frequency of inflow oscillation
increases, the amplitude of mass flow rate oscillation
decreases. It can be extended to explain combustor
flow oscillation in Fig.6. The amplitude of mass flow
rate oscillation in transition flow pattem can be
determined by interpolating between that for quasi-
steady and steady patterns corresponding to the
frequencies of = 80 and 320 Hz. Please note that,
at the frequency of
=
EO Hz the amplitude of mass
flow rate oscillation is obtained by Eq. 6); and when
= 320 Hz. the mass flow rate oscillation can be
ignored. It is seen that the abnormality happens for
inflow oscillations at the frequency of
=
240 Hz
because of the resonance. Since the oscillation
augment resulted by resonance is hard to predict at
this stage, the effect of resonance on mass flow rate
oscillation
cannot
be obtained quantitatively.
Fig.6 Oscillation amplitudes of mass flow
rates in combustion zone.
0
Resonance of Diffuser Flows
There are some kinds of self-sustained
oscillations with diffuser flows. Kwong and Dowling
(1994). and van Lier et al. (2001) studied flow
oscillations and resonance of the diffuser with gradual
divergence. According to aeroacoustics, the
instability of flow is incited when pasting a cavity such
as diffuser dumps shown in Fig.1 (Rossiter, 1964).
As it is forming, flow is directed into the cavity. Vortex
is shed from the leading edge of diffuser and ejected
in recirculations. The vortex shedding causes
boundaty layer to periodically separate mainstream.
When vortex shedding is strong enough. the feedback
will be able to influence mainstream, and the
mainstream will undergo pulsation, i.e., the self-
sustained acoustic oscillation. Variations of the
recirculation in the diffuser dumps at different times at
the resonance are shown in Fig.7.
a) Phase
0
b)
Phase
90'
(c) Phase
180
Fig 7
Instantaneous
recirculations
at different phases
in an oscillation cycle.
The first description of this feedback process was
credited to Rossiter (1964), who gave a semi-
empirical formula for the frequencies of oscillation
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where St = nUu s the Strouhal number corresponding
to frequency n, the cavity length, U and
M
the
mainstream velocity and Mach number, and K and
y
empirical constants with
=
0.25 and I/K
=
1.75.
Eq.(9) was originally developed for flows over a
rectangular cavity. It was applied to the diffuser flow.
Tab.1 lists oscillation the frequencies obtained from
Eq.(9) fo rm = 1 and 2, and the numerical simulation.
It
is
seen that there are many possible frequencies
corresponding to each m from Eq.(9). Block (1976)
indicated that the cavity would oscillate with a
characteristic frequency corresponding to
a
Strouhal
number
on
the order of St
< 1.
Oscillations or
St
z 1
can be ignored due to low power at high frequencies
in spectra. In this study, only the oscillation frequency
for m = 1 is considered effective. It is found the
frequencies from empirical formula for m
=
1 and the
simulation agree
to
each other reasonably.
Steady Flow Pattem
n
2
320
As discussed before, when the oscillation
frequency reaches about 320 Hz combustion flow will
be able to experience one complete oscillation cycle.
When the oscillation frequency is n 2 320 Hz, fast
oscillation makes flow properties well averaged, and
the mass flow rate oscillation well mitigated. It is
found that pulsation in mass flow rate is about 5 % of
the averaged value. Thereby, the influence of inflow
oscillation at this frequency can be ignored, and the
combustion flow treated as in steady state although it
is not real steady. Therefore, flow properties and the
combustion performance can be obtained based on
the constant operating condition using theoretical and
empirical approaches for steady combustion. It
makes the problem much simplified.
C NCLUSIONS
Aerodynamic interactions of transient compressor
and combustor flows were investigated through
numerical simulations. Following conclusions were
achieved:
(1) Three flow patterns, namely quasi-steady,
transition and steady patterns corresponding to
the critical frequency arranges of S 80, 80 2 n
2
320, and n 2 320 Hz, for gas turbine combustion
with inflow oscillations were summarized. The
three flow patterns have different effects on
combustion.
(2) Amplitude of mass flow rate oscillation decreases
as the inflow oscillation frequency increases due
to the mixing resulted from the flow oscillation.
Therefore, pulsations in flow properties are greatly
mitigated as the oscillation frequency increases.
(3) Resonance originating from the diffuser dumps
happens to combustion flows when the forced
inflow oscillation of n
=
240 Hz
is
applied to
combustor flows. Resonance leads to more
fluctuations in flow properties and combustion
oerformance.
ACKNOWLEDGEMENTS
The authors wish to thank the Department of
Energy for the support of this work under contract
#540-6288-1121 and A.A. Amsden of the Los Alamos
National Laboratory for all the help with the KIVA3V
code.
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