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%%%     Aeroacoustic source simulation for:
%%%
%%%     D. E. S. Breakey, J. A. Fitzpatrick, and C. Meskell,
%%%         "Aeroacoustic source analysis using time-resolved PIV in a free jet,"
%%%         Under review for Experiments in Fluids, 2012.
%%%
%%%     Copyright (c) 2012, David Breakey (breakeyd@tcd.ie)
%%%     All rights reserved.
%%%     
%%%     Redistribution and use in source and binary forms, with or without
%%%     modification, are permitted provided that the following conditions are met: 
%%%     
%%%     1. Redistributions of source code must retain the above copyright notice, this
%%%        list of conditions and the following disclaimer. 
%%%     2. Redistributions in binary form must reproduce the above copyright notice,
%%%        this list of conditions and the following disclaimer in the documentation
%%%        and/or other materials provided with the distribution. 
%%%     
%%%     THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
%%%     ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
%%%     WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
%%%     DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
%%%     ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
%%%     (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
%%%     LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
%%%     ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
%%%     (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
%%%     SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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%%%Experiment parameters
D       = 50;%mm,           Jet diameter
Uj      = 85000;%mm/s,      Jet velocity
Uc      = 0.7*Uj;%mm/s,     Convection velocity
f       = 1190;%Hz,         Oscillation frequency
c0      = 340000;%mm/s,     Speed of sound

fs      = 27000;%Hz,        Sample rate
xmic    = 7*D;%mm,          Mic location (x)
ymic    = 4*D;%mm,          Mic location (y)

%%%Model parameters
A       = 1;%unitless
C       = 1;%unitless
B       = C/10;%unitless
b       = 2*D;%mm
c       = 2*D;%mm
xs1     = 0;%mm
xs2     = 6*D;%mm
tc      = 0.001;%s

%%%Simulation parameters
xmax    = 10*D;%mm
dx      = D/10;%mm
tmax    = 18*D/Uc;%s
dt      = 1/fs;%s

%%%Dimension vectors
x       = (0:dx:xmax).';
t       = (dt:dt:tmax).';
t       = [-t(end:-1:1) ; 0 ; t(1:end-1)];          %symmetric t with even number of points for FFT
r       = sqrt((xmic-x).^2+(ymic-0).^2);

%%%Expand dimensions into grid
[xx,tt] = meshgrid(x,t);
rr      = sqrt((xmic-xx).^2+(ymic-0).^2);

%%%Source model                         (Eq.  9)
q       = A*cos(2*pi*f*(tt-xx/Uc)).*exp(-abs(tt-xx/Uc)/tc);

%%%Damping envelope model               (Eq. 10)
Df      = B*exp(-(xx-xs1).^2/b^2) + C*exp(-(xx-xs2).^2/b^2);

%%%Calculate far-field contributions    (Eq. 11)
nfft    = length(t);
freqFFT = [0:nfft/2-1 -nfft/2:-1]'*fs/nfft;
coef    = 1/4/pi./rr;
qshift  = ifft(fft(q,nfft,1).*exp(1j*2*pi*freqFFT*(-r'/c0)),nfft,'symmetric');
dq      = coef.*qshift.*Df*dx;

%%%Integrate far-field contributions    (Eq. 11)
p       = sum(dq,2);

%%%Perform correlation
Rqp     = ifft(conj(fft(q,nfft,1)).*repmat(fft(p,nfft,1),[1 length(x)]),nfft,'symmetric')/nfft;
Rqp     = [Rqp(nfft/2+1:end,:);Rqp(1:nfft/2,:)];    %move negative lags before positive
Rqp     = Rqp./repmat(std(q),[nfft 1])/std(p);      %apply scaling

%%%Plot results
contourf(xx/D,(tt-rr/c0)*Uc/D,Rqp,30,'linestyle','none');
colorbar
hold on
plot(x/D,0*x)
plot(x/D,(r(1)/c0-r/c0-x/Uc)*Uc/D)
hold off
xlabel('x/D')
ylabel('tau*Uc/D')