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Appendix A

A CFD Study of Air-fuel Mixing in a

Lean Premixed Combustor

The overall goal of the project titled ‘Analysis and Design Tools for Combustion Instabili-

ties’ (STTR AF00-T019 Phase I: Contract No. F49620-00-C-0056) was to develop an accu-

rate design tool for predicting and controlling oscillations in high-performance, gas-turbine

combustors. The sensitivity equation method (SEM) was developed by Aerosoft, Inc. (a

stand-alone commercial package called SENSE) to investigate turbulent flow sensitivities for

chemically reacting flows. The focus during Phase I was to develop a tool using the GASP

(Aerosoft’s CFD solver) and SENSE CFD software to study thermoacoustic instabilities

observed in a National Energy Technology Laboratory (NETL) lean premixed combustor.

The Phase I goal was to simulate a forced instability in a simplified geometry of the NETL

combustor. The inlet boundary condition for the combustor comprised of a planar jet profile

and the species mass fraction of air and fuel were specified as a function of the radial distance.

This profile was determined by solving the steady-state, axisymmetric flow equations for the

fuel nozzle alone. To determine the sensitivity profile, it was assumed that the mass-fraction

profiles can be approximated using a cubic Lagrange polynomial. Turbulent mixing of air

and methane in the nozzle was simulated using a two-equation model and a second moment

213

Appendix A: CFD Study of Air-fuel Mixing 214

closure Reynolds Stress Model (RSM). The baseline profile was made unsteady by imposing

a time-dependent sinusoidal fluctuation in velocity, where the amplitude and frequency were

obtained from experimental data.

Four different swirler configurations were attainable in the fuel-nozzle section of the NETL

combustor. In particular, the swirl vanes could be placed at different locations upstream

of the fuel-spoke injector in increments as shown in Figure A.1. The first case corresponds

to locating the swirl vanes 3.25 inches upstream of the combustor. Each successive case

corresponded to the vanes being located one inch farther upstream (i.e., to the left). One

of the design variables in the study was the swirler location relative to the fuel injection

location.

Figure A.1: The DOE NETL Combustor air-fuel mixing nozzle. The range of positions for

the swirling vanes are shown.

To determine the inlet to the combustor boundary profiles of velocity and species mass

fractions, three-dimensional mixing of air and fuel that takes place in the fuel nozzle was

simulated. The Fluent segregated CFD solver was used for the calculations and the grid was

generated using the Gambit preprocessor. Axisymmetric modeling of the air-fuel mixing

process was simulated by selecting the axisymmetric-swirl model in Fluent. The inlet air


was preheated to 578K and the fuel entered the flow domain at 300K. Both the RNG

k-ε and the Reynolds Stress Model (RSM) were applied for turbulence modeling. Air was

introduced at a swirl angle of 45◦ and the fuel was introduced at the location of the spoke

ring. Internal mass sources tuned for an equivalence ratio of φ = 0.74 were used to introduce

the fuel into the stream. The fuel nozzle exit mass-fraction profiles of CH4 and O2 are shown

in Figure A.2 and Figure A.3 respectively. The axial velocity at the exit of the fuel nozzle is

shown in Figure A.4.

Figure A.2: Mass fraction profile of CH4 at the exit of the fuel nozzle for different locations

of the swirler relative to the fuel injection location

As the swirling rings are located farther upstream of the combustion region, the swirl ratio

decreases at the spoke-ring location. As a result, the mixing in Case 4 is less than in Case 1.

The mass-fraction profiles for N2, O2 and CH4 were then applied as an in-flow profile for

the two-dimensional, chemically reacting simulation in the combustor. By running all four

swirler-ring cases, the sensitivity of the mass-fraction profiles to the swirler location was

formulated through a Lagrange polynomial.


Figure A.3: Mass fraction profile of O2 at the exit of the fuel nozzle for different locations

of the swirler relative to the fuel injection location

Figure A.4: Axial velocity profile at the exit of the fuel nozzle. The swirler location progresses

upstream in each of the four cases.

Appendix B

A CFD Study of Bluff-body Stabilized

Combustion in a Lean Premixed

Combustor

The overall goal of the ongoing project titled ‘Systematic Investigation of Bluff-Body Com-

bustion Instability’ (STTR AF00-T019 Phase II: Contract No. F49620-00-C-0048 STTR

AF00-T019) is to provide a sensitivity-analysis tool for the control of heat-release rate dis-

tribution in aeroengine combustors with emphasis on bluff-body type flame-holders. This

control is essential to attenuate the thermoacoustic instabilities of the combustors under lean

operating conditions. Previous studies on bluff body stabilized combustors have indicated

that such a configuration is susceptible to flow instabilities due to vortex shedding which

can hinder the study of thermoacoustic instabilities and their control. The importance of

this very internal flow boundary conditions is another issue addressed by the project.

The project includes both CFD investigation of bluff-body stabilized combustion and exper-

imental studies. For the experimental studies, a high pressure combustor has been designed

at VACCG. The combustor apparatus includes of a fuel-air impingement mixer section, fol-

lowed by a flow conditioning section; diffuser, plenum, and nozzle. Following the nozzle is

217

Appendix B: A CFD Study of Bluff-body Stabilized Combustion 218

the entrance to the combustor and the exit nozzle. The bluff-body flame stabilizer is placed

in the combustor. To support the combustor, high pressure air and natural gas supply setup

have been installed at the VACCG Laboratory. The goal of the test facility is to yield an

invaluable database that can guide the software computations and gage their limitations.

Since the project is focused on unstable combustion, its prediction, and active design method-

ology, designing the combustor was critical to the success of the project. Specifically, in the

case of bluff-body stabilized combustion strong coupling between the acoustics and shear

layer instabilities is expected. This manifests itself in the shedding of large scale structures,

which are typically straddled by the flame/combustion zone. To examine these structures

CFD simulations of cold flows were first undertaken using FLUENT 6. The geometrical con-

figuration was that of the coaxial bluff-body combustor shown schematically in Figure B.1.

Boundary conditions and numerical settings are listed in Table B.1.

10 mm

45

DL

6.35 mm

D

D

d

o

Figure B.1: Coaxial bluff-body combustor geometry used in the CFD simulation. The

dimensions of the bluff body are – D = 7.62 cm, d = 12D = 3.81 cm


Table B.1: Combustor domain dimensions, Boundary conditions and Numerical settings

Combustor dimensions

Diameter (D) = 7.62 cm

Downstream length (LD) = 3D = 22.86 cm (shown in Figure B.1)

Bluff-body top diameter, (d) = 12D = 3.81 cm

Reynolds number

39,124 (inlet velocity = 15m/s)

78,248 (inlet velocity = 30m/s)

Boundary conditions

Inlet: Uniform inlet velocity, no-free stream turbulence assumption (TKE = 0)

Outlet: Initial calculations performed by keeping the outlet at atmospheric pressure

Numerical settings

2D unsteady solution: second order accurate temporal discretization

RNG k-ε turbulence model

Second order accurate upwind spatial discretization

Time step: ∆t = 1 × 10−5 s (15 m/s), ∆t = 5 × 10−6 s (30 m/s)

The CFD investigation showed vortex shedding behind the bluff-body. A time series of

vorticity magnitude is shown in Figure B.2. Clearly seen are the alternating vortices shed.

The vorticity magnitude of the turbulent flowfield was collected at six locations that are

shown in Figure B.3. The resulting power spectra are shown in Figures B.4 and B.5 with a

magnification of spectra for Pt11 shown in Figure B.6. In both cases (15m/s and 30m/s) the

fundamental vortex shedding frequency corresponds to a Strouhal number of 0.3. It can be

noted from Figure B.2 that the time taken for one vortex to shed is approximately 8×10−3 s,

which corresponds to a frequency of 125Hz. The frequency calculated by FFT comes out

to be 120Hz (for the 15m/s case) which corresponds to a shedding time of approximately

8.33 × 10−3 s.


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t = 0 s t = 1 × 10−3 s t = 2 × 10−3 s

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t = 3 × 10−3 s t = 4 × 10−3 s

Vorticity magnitude contours (Uinlet = 15m/s)


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t = 8 × 10−3 s t = 9 × 10−3 s

Figure B.2: Vorticity magnitude contours (Uinlet = 15m/s)


Figure B.3: Locations where vorticity magnitudes were recorded


0 500 1000 1500−30

−20

−10

0

10

20

30

40

50

60

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Point 11Point 21

0 500 1000 1500−30

−20

−10

0

10

20

30

40

50

60

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Point 12Point 22

0 500 1000 1500−30

−20

−10

0

10

20

30

40

50

60

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Point 13Point 23

Figure B.4: Power spectrum plots of vorticity magnitude (Uinlet = 15m/s)


0 500 1000 1500 2000 2500 3000−40

−30

−20

−10

0

10

20

30

40

50

60

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Point 11Point 21

0 500 1000 1500 2000 2500 3000−40

−30

−20

−10

0

10

20

30

40

50

60

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Point 12Point 22

0 500 1000 1500 2000 2500 3000−40

−30

−20

−10

0

10

20

30

40

50

60

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Point 13Point 23

Figure B.5: Power spectrum plots of vorticity magnitude (Uinlet = 30m/s)


0 500 1000 1500−30

−20

−10

0

10

20

30

40

50

60

70

Frequency (Hz)

20lo

g 10(V

ortic

ityflu

c)

Uinlet

= 15 m/sU

inlet = 30 m/s

120 Hz 240 Hz

Figure B.6: Power spectrum plot of vorticity magnitude (Pt11; Uinlet = 15m/s and 30m/s)

Appendix C

Matlab Code for Frequency Response

Function Calculation

This code has been used to calculate the Frequency Response Function (FRF) between

unsteady velocity (u′, input) and the resulting unsteady heat release rate from the flame

(q′, output). The code has been used to compute the FRF for both laminar and turbulent

flames.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Matlab code for calculating the FRF between u’ and q’

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Number of frequencies at which the flame was excited

% is given by the variable ’freq’ which needs to be

% modified for every FRF calculation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;

226

Appendix C: Matlab Code 227

% sampling rate for the data

sam=10000;

% frequencies specified

freq = [15 20 25 30 35 50 75 100 200 300 500];

% number of frequencies

nfreq = length(freq);

% plus steady state value

nfreqf = nfreq + 1;

% creating strings for file name creation

siv = ’inletv_’;

srr = ’rr_’;

shz = ’Hz.out’;

% starting the for loop for FRF calculation

for i = 1:nfreq

% creating string from frequency vector

% to form final string for reading files

freq(i);

sfr = num2str(freq(i));

% reading velocities

fidv = fopen([siv sfr shz]);

a = fscanf(fidv,’%g %g’,[2 inf]); a = a’;


% velocity vector

vel = a(:,2);

% reading reaction rates

fidr = fopen([srr sfr shz]);

b = fscanf(fidr,’%g %g’,[2 inf]); b = b’;

% reaction rate vector

rr = b(:,2);

% comparing lengths of vel and rr vectors

len = length(vel);

lenr = length(rr);

if (len ~= lenr)

fprintf(’lengths of vel and rr not equal’)

break

end

% calculating mean

vel_mean = sum(vel)/len;

rr_mean = sum(rr)/len;

% calculating non-dimensionalized fluctuating components

vel = (vel - vel_mean)/vel_mean;

rr = (rr - rr_mean)/rr_mean;

% window size


win = len;

% cross spectrum between vel and rr

[P, F] = spectrum(vel,rr,len,0,hanning(win),sam,0.95);

% finding the magnitude of the transfer function

pm=abs(P(:,4));

% finding the phase of the transfer function

pp=(180.0/pi)*angle(P(:,4));

% calculating the resolution

res = sam/len;

% probing the frequency of interest from the cross spectrum

% since exact match is not always possible, the two

% frequencies closest to the frequency of interest are chosen

ifind = find(F > freq(i) - res & F < freq(i) + res | F == freq(i));

lenifind = length(ifind);

% finding the magnitude at the two frequencies

magvalues=pm(ifind);

% calculating magnitude for the frequency of interest

% by averaging the values obtained for the two frequencies

magn= sum(magvalues)/lenifind;

clear magvalues


% finding the phase at the two frequencies

phasevalues=pp(ifind);

% calculating phase for the frequency of interest

% by averaging the values obtained for the two frequencies

phase= sum(phasevalues)/lenifind;

clear phasevalues

clear ifind

mag(i) = 20*log10(magn);

pha(i) = phase;

clear magn phase

% closing the data files

fclose(fidv);

fclose(fidr);

% clearing variables no longer needed

clear vel_mean rr_mean

clear vel rr len lenr win P F pm pp

end

% steady state

freq(nfreqf) = 0;

mag(nfreqf) = 0;

pha(nfreqf) = 0;

% Computing the FRF


h=10.^(mag/20).*exp(j*pha/180*pi);

[num, den]=invfreqs(h(1:nfreqf),freq(1:nfreqf)*2*pi,2,2);

rden=roots(den)/2/pi

rnum=roots(num)/2/pi

hid=freqs(num,den,[1:1000]*2*pi);

% FRF magnitude plot

figure(1);

semilogx(freq,20*log10(abs(h)),’s’,1:1000,20*log10(abs(hid)))

axis([1 1000 -140 25]);

xlabel(’Frequency (Hz)’)

ylabel(’Magnitude (dB)’)

legend(’Computed Data Points’,’2nd Order Fit’,3);

grid on

% FRF phase plot

figure(2);

semilogx(freq,unwrap(angle(h))*180/pi,’s’,1:1000,unwrap(angle(hid))*180/pi)

axis([1 1000 -350 50]);

legend(’Computed Data Points’,’2nd Order Fit’,3);

xlabel(’Frequency (Hz)’)

ylabel(’Phase (deg)’)

grid on

% Calculating poles and zeros

re_rden=real(rden);

img_rden=imag(rden);

re_rnum=real(rnum);


img_rnum=imag(rnum);

% Pole-Zero plot

figure(3);

plot(re_rden,img_rden,’kX’,re_rnum,img_rnum,’kO’);

grid on;

xlabel ’Re’

ylabel ’Img’

legend(’Poles’,’Zeros’,2);

Vita

Prateep Chatterjee was born in the Darjeeling district of West Bengal, India in 1973. He

spent his childhood at the I.I.T. campus in Kanpur, Uttar Pradesh, India. He went to the

Campus School for his primary schooling and subsequently completed his high school ed-

ucation from Central School (Kendriya Vidyalaya), I.I.T. Kanpur in 1991. He pursued his

Bachelor’s degree in Mechanical engineering at the Zakir Hussain College of Engineering and

Technology, Aligarh Muslim University (AMU) and completed his degree in 1996. Between

October 1996 and August 1997, he worked at I.I.T. Kanpur as a Research Associate and

later as an Engineer Trainee at West Bengal Power Development Corp., West Bengal, India.

He started his graduate studies in Aerospace engineering at I.I.T. Kanpur in August 1997.

After completing the first semester of the Master’s program, he wrote a proposal for con-

ducting research in Germany. The German Academic Exchange Service (DAAD) awarded

him a fellowship to pursue his Master’s research at the University of Stuttgart, Germany.

The following ten months were spent at the Institute for Nuclear Technology and Energy

Systems (IKE) working under Prof. Manfred Groll. The thesis research conducted at IKE

involved experimental investigation of two-phase nucleate pool boiling over enhanced indus-

trial evaporative tubes. He defended his Master’s thesis at I.I.T. Kanpur in April 1999.

In the spring of 2000, he began his doctoral studies in Mechanical engineering at Viginia

Tech under the guidance of Dr. Uri Vandsburger. While pursuing his degree, he taught the

undergraduate heat transfer course three times. Upon successful completion of his Ph.D.,

he will begin working as a Senior Research Scientist at FM Global in Norwood, MA.

233

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