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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
Appendix A: CFD Study of Air-fuel Mixing 215
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.
Appendix A: CFD Study of Air-fuel Mixing 216
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
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 219
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.
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 220
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t = 3 × 10−3 s t = 4 × 10−3 s
Vorticity magnitude contours (Uinlet = 15m/s)
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 221
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t = 8 × 10−3 s t = 9 × 10−3 s
Figure B.2: Vorticity magnitude contours (Uinlet = 15m/s)
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 222
Figure B.3: Locations where vorticity magnitudes were recorded
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 223
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)
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 224
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)
Appendix B: A CFD Study of Bluff-body Stabilized Combustion 225
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’;
Appendix C: Matlab Code 228
% 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
Appendix C: Matlab Code 229
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
Appendix C: Matlab Code 230
% 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
Appendix C: Matlab Code 231
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);
Appendix C: Matlab Code 232
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