Numerical Study of Aerodynamic Interaction of Compressor and Combustor Flows

8/10/2019 Numerical Study of Aerodynamic Interaction of Compressor and Combustor Flows

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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

[email protected]

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.

REFERENCES

Amsden, A.A.. O'Rourke, P.J., and Butler, T.D., 1989,

KIVA-II: A Computer Program for Chemically

Reactive Flows with Sprays. Los Alamos National

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Amsden, A.A., 1993, KIVA-3: A KlVA Program with

Block-Structured Mesh for Complex Geometries,

LA-12503-MS.

Amsden, A.A., 1997, KIVA-3V: A Block-Structured

KlVA Program for Engines with Vertical or Canted

Valves, LA-13313-MS.

Block, P.J.W., 1976. Noise Response of Cavities of

Varying Dimensions at Subsonic Speeds, NASA

TND-9351.

Correa, S.M., and Shyy, W., 1987, Computational

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Crocker, D.S., Nickolaus D., and Smith, C.E., 1998,

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194.

Kundu, K.P., Penko, P.F., and VanOverbeke, T.J.,

1999, A Practical Mechanism for Computing

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2218.

Kwong, A.H.M., and Dowling, A.P., 1994, Unsteady

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of

Fluids

Engineering, Vol.116, pp.842-847.

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pp.695-703.

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Dequand. S., and Hirschberg, A., 2001,

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2002 Paoer No.20176-7

Documents

Numerical Study of Aerodynamic Interaction of Compressor and Combustor Flows