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planar.m
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% Planar surface vorticity code from
% Vortex Element Methods for Fluid Dynamic Analysis of Engineering Systems
% R. I. Lewis, 1991, Cambridge University Press, Ch. 4.
% This solver script expects some variables to be set as input before
% execution.
%
% There may be multiple input bodies/objects, each an item in a cell array.
%
% W % Freestream velocity
% Minf % Freestream Mach number for compressibility correction
% Sref % Reference area for calculating CD
% drawplots % Flag to draw plots and postprocess
% xlim % X Grid limits for velocity survey
% ylim % Y Grid limits for velocity survey
% nsurvey % Number of points in velocity survey grids
% nsl % Number of streamlines to trace
% ntstep % Number of streamtube relaxation steps
%
% names{nseg}; % Component names for output
% xepts{nseg}; % X Endpoints of panels (or initial streamtube)
% yepts{nseg}; % Y Endpoints of panels
% xuppts{nseg}; % X Endpoints of upper initial streamtube
% yuppts{nseg}; % Y Endpoints of upper initial streamtube
% xlowpts{nseg}; % X Endpoints of lower initial streamtube
% ylowpts{nseg}; % Y Endpoints of lower initial streamtube
% kuttas{nseg}; % Flags to apply Kutta condition to each body
% props{nseg}; % Flag to treat body as actuator disk
% deltaCP{nseg}; % Actuator disk pressure jump
% jtels{nseg}; % Index to TE lower panel
% jteus{nseg}; % Index to TE upper panel
% rads{nseg}; % Panel radius of curvature vector
% Vexs{nseg}; % Exact solution at panel endpoints for isolated body
%
gammagas = 1.4;
% Centrally set linewidth for figures that use it.
lw = 2;
nseg = length( xepts );
ydisk = cell(size(xepts));
for iseg = 1:nseg
if ( props{iseg} ) % Only check props
gammainf = - W * ( sqrt( deltaCP{iseg} + 1 ) - 1 );
gammas{iseg}=[];
gammasup{iseg} = gammainf * ones( size( xuppts{iseg} ) );
gammaslow{iseg} = gammainf * ones( size( xlowpts{iseg} ) );
else
gammas{iseg}=[];
gammasup{iseg}=[];
gammaslow{iseg}=[];
end
end
if ( drawplots)
figure( 1 )
clf
hold on
for iseg=1:nseg
plot( xepts{iseg}, yepts{iseg}, 'x-' );
end
hold off
axis equal
end
npan = 0;
% Process geometry
for iseg=1:nseg
if ( ~props{iseg} ) % 'Normal' components
xep = xepts{iseg};
yep = yepts{iseg};
dx{iseg} = xep(2:end) - xep(1:end-1);
dy{iseg} = yep(2:end) - yep(1:end-1);
ds{iseg} = sqrt( dx{iseg}.^2 + dy{iseg}.^2 ); % Panel arclength
theta{iseg} = atan2( dy{iseg}, dx{iseg} ); % Panel slope angle
xcp{iseg} = 0.5 * ( xep(2:end) + xep(1:end-1) ); % Panel x center point
ycp{iseg} = 0.5 * ( yep(2:end) + yep(1:end-1) ); % Panel y center point
dxup{iseg} = [];
dyup{iseg} = [];
dsup{iseg} = [];
thetaup{iseg} = [];
xupcp{iseg} = [];
yupcp{iseg} = [];
dxlow{iseg} = [];
dylow{iseg} = [];
dslow{iseg} = [];
thetalow{iseg} = [];
xlowcp{iseg} = [];
ylowcp{iseg} = [];
npans{iseg} = length( xcp{iseg} );
npan = npan + npans{iseg};
else % Actuator disk doesn't contribute panels
xep = xuppts{iseg};
yep = yuppts{iseg};
dxup{iseg} = xep(2:end) - xep(1:end-1);
dyup{iseg} = yep(2:end) - yep(1:end-1);
dsup{iseg} = sqrt( dxup{iseg}.^2 + dyup{iseg}.^2 ); % Panel arclength
thetaup{iseg} = atan2( dyup{iseg}, dxup{iseg} ); % Panel slope angle
xupcp{iseg} = 0.5 * ( xep(2:end) + xep(1:end-1) ); % Panel x center point
yupcp{iseg} = 0.5 * ( yep(2:end) + yep(1:end-1) ); % Panel y center point
xep = xlowpts{iseg};
yep = ylowpts{iseg};
dxlow{iseg} = xep(2:end) - xep(1:end-1);
dylow{iseg} = yep(2:end) - yep(1:end-1);
dslow{iseg} = sqrt( dxlow{iseg}.^2 + dylow{iseg}.^2 ); % Panel arclength
thetalow{iseg} = atan2( dylow{iseg}, dxlow{iseg} ); % Panel slope angle
xlowcp{iseg} = 0.5 * ( xep(2:end) + xep(1:end-1) ); % Panel x center point
ylowcp{iseg} = 0.5 * ( yep(2:end) + yep(1:end-1) ); % Panel y center point
dx{iseg} = [];
dy{iseg} = [];
ds{iseg} = [];
theta{iseg} = [];
xcp{iseg} = [];
ycp{iseg} = [];
npans{iseg} = 0;
end
end
AICs = cell( nseg, nseg );
for iseg=1:nseg
for jseg = 1:nseg
AICij = nan( npans{jseg}, npans{iseg} );
if ( ~props{iseg} && ~props{jseg} )
% i loop over panels implied by . operations
for j = 1:npans{iseg} % Loop over vortex j
[ uj, vj ] = ptvortex( xcp{iseg}(j), ycp{iseg}(j), xcp{jseg}, ycp{jseg} );
AICij(:,j) = ( uj .* cos( theta{jseg} ) + vj .* sin( theta{jseg} ) ) .* ds{iseg}(j);
end
if ( iseg == jseg )
C = 4.0 * pi * ycp{iseg} ./ ds{iseg};
curve = ds{iseg} ./ ( 4.0 * pi * rads{iseg} );
% Self influence term
AICii = -0.5 - ( log( 2.0 * C ) - 0.25 ) ./ C .* cos( theta{iseg} ) + curve;
% Excessively clever way to substitute the matrix diagonal.
AICij( 1 : npans{iseg} + 1 : npans{iseg} * npans{iseg} ) = AICii;
if ( kuttas{iseg} )
% Correction term for back-diagonal
for j = 1:npans{iseg} % Loop over column j
AICij(j,j) = - ( sum( AICij(:,j) .* ds{iseg}' ) - AICij(j,j) * ds{iseg}(j) ) / ds{iseg}(j);
end
end
end
end
AICs{iseg, jseg} = AICij;
end
end
% Assemble AIC from cell matrices.
AIC=[];
panidx=[];
segidx=[];
for iseg=1:nseg
AICrow = [];
for jseg = 1:nseg
AICrow = [AICrow AICs{jseg, iseg}];
end
AIC = [AIC; AICrow];
panidx = [panidx 1:npans{iseg}];
segidx = [segidx iseg*ones(1,npans{iseg})];
end
idx = [segidx; panidx; 1:npan];
% Apply Kutta condition to AIC
for iseg=1:nseg
if ( kuttas{iseg} )
jtelow = find( ( idx(1,:) == iseg ) & ( idx(2,:) == jtels{iseg} ) );
jteup = find( ( idx(1,:) == iseg ) & ( idx(2,:) == jteus{iseg} ) );
% Apply Kutta condition to AIC
AIC(jteup,:) = zeros( size( AIC(jteup,:) ) );
AIC(jteup,jteup) = 1;
AIC(jteup,jtelow) = 1;
end
end
opts = odeset;
opts = odeset( opts, 'Events', @planarmassevt );
opts = odeset( opts, 'AbsTol', 1e-8, 'RelTol', 1e-5,'MaxStep',1e-2);
optssl = odeset;
optssl = odeset( optssl, 'Events', @planarslevt );
optssl = odeset( optssl, 'AbsTol', 1e-8, 'RelTol', 1e-5,'MaxStep',1e-2);
for itstep=1:ntstep
yerr = 0;
gerr = 0;
% Setup & Assemble RHS
rhs = [];
for iseg=1:nseg
if ( ~props{iseg} ) % 'Normal' components
rhss{iseg} = -W * cos( theta{iseg} );
for jseg=1:nseg
if ( props{jseg} )
uad = zeros( size( xcp{iseg} ) );
vad = uad;
for j = 1:length( xcp{jseg} ) % Loop over vortex j
[ uj, vj ] = ptvortex( xcp{jseg}(j), ycp{jseg}(j), xcp{iseg}, ycp{iseg} );
uad = uad + uj * gammas{jseg}(j) * ds{jseg}(j);
vad = vad + vj * gammas{jseg}(j) * ds{jseg}(j);
end
[ uj, vj ] = tubevortex( xepts{jseg}(end), yepts{jseg}(end), xcp{iseg}, ycp{iseg} );
uad = uad + gammas{jseg}(end) * uj;
vad = vad + gammas{jseg}(end) * vj;
rhss{iseg} = rhss{iseg} - ( uad .* cos( theta{iseg} ) + vad .* sin( theta{iseg} ) );
end
end
rhs = [rhs rhss{iseg}];
end
end
% Apply Kutta condition to RHS
for iseg=1:nseg
if ( kuttas{iseg} )
jtelow = find( ( idx(1,:) == iseg ) & ( idx(2,:) == jtels{iseg} ) );
jteup = find( ( idx(1,:) == iseg ) & ( idx(2,:) == jteus{iseg} ) );
% Apply Kutta condition to RHS
rhs(:,jteup) = 0;
% % If actuator disk matches duct TE, apply gamma jump.
% for jseg=1:nseg
% if( props{jseg} )
% % Duct TE point
% xte = xepts{iseg}(1);
% yte = yepts{iseg}(1);
% % Disk leading point
% xd = xepts{jseg}(1);
% yd = yepts{jseg}(1);
%
% d = sqrt( ( xte - xd )^2 + ( yte - yd )^2 );
%
% if ( d < 1e-3 )
% rhs(:,jteup) = rhs(:,jteup) + gammas{jseg}(1);
% end
% end
% end
end
end
% Solve (gamma is tangental velocity at control points)
gamma = AIC \ rhs';
% Break gamma vector into per-body parts
for iseg=1:nseg
if( ~props{iseg} )
gam = gamma( idx(1,:) == iseg );
% Flip reversed panel velocities for plotting
gam = gam .* sign(dx{iseg})';
gammas{iseg} = gam';
end
end
xlownew = xlowpts;
ylownew = ylowpts;
xupnew = xuppts;
yupnew = yuppts;
gammalownew = gammaslow;
gammaupnew = gammasup;
% Update streamtube shape
for iseg=1:nseg
if( props{iseg} )
figure(15)
plot(xlowpts{iseg}, ylowpts{iseg}, xuppts{iseg}, yuppts{iseg})
hold on
axis equal
drawnow
% Place point at disk midpoint.
x0 = 0.5 * ( xlowpts{iseg}(1) + xuppts{iseg}(1) );
y0 = 0.5 * ( ylowpts{iseg}(1) + yuppts{iseg}(1) );
% Integrate streamline 1.5 tubelens downstream.
s0 = tubelen * 1.5;
[ tsl, Xsl ] = ode45( @planardX, [0, 10], [x0 y0 0], optssl, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, s0 );
% Extract streamline down center of disk slipstream.
xsl = Xsl(:,1);
ysl = Xsl(:,2);
ssl = Xsl(:,3);
% dssl = sqrt((xsl(2:end)-xsl(1:end-1)).^2 + (ysl(2:end)-ysl(1:end-1)).^2 );
% ssl = [0; cumsum(dssl)];
plot(xsl,ysl,'--');
drawnow
% Integrate mass flow at disk
x0 = xlowpts{iseg}(1);
y0 = ylowpts{iseg}(1);
xv = xuppts{iseg}(1) - x0;
yv = yuppts{iseg}(1) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
mass0 = inf;
% Integrate mass across 'lower' half.
% dm = planardm( eta, mass, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, len, mass0 );
[ tdist, mdist ] = ode45( @planardm, [0.0, 0.5], 0, opts, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, dlen, mass0 );
masslow = mdist(end);
% Integrate mass across 'upper' half.
[ tdist, mdist ] = ode45( @planardm, [0.5, 1.0], 0, opts, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, dlen, mass0 );
massup = mdist(end);
% Calculate vortex tube strength and eventual jet velocity
% gammainf = - W * ( sqrt( deltaCP{iseg} + 1 ) - 1 );
Wjad = W - gammainf;
% Set vortex tube height based on jet velocity and mass flow
hlow = masslow / Wjad;
hup = massup / Wjad;
if ( itstep < 0 )
if (true)
i = 1;
p = InterX( [xsl; ysl], [xlowpts{iseg}(i) xuppts{iseg}(i); ylowpts{iseg}(i) yuppts{iseg}(i)] );
x0 = p(1,:)';
y0 = p(2,:)';
% [u, v] = planarvel( x0, y0, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props );
xv = xlowpts{iseg}(i) - x0;
yv = ylowpts{iseg}(i) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
te = [];
tend = 3;
while isempty(te)
[tdist, mdist, te] = ode45( @planardm, [0, tend], 0, opts, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, 1, -masslow );
tend = 2 * tend;
end
xtest = x0 + xv * te;
ytest = y0 + yv * te;
plot(xtest,ytest,'x')
text(xtest,ytest,num2str(itstep));
xv = xuppts{iseg}(i) - x0;
yv = yuppts{iseg}(i) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
te = [];
tend = 3;
while isempty(te)
[tdist, mdist, te] = ode45( @planardm, [0, tend], 0, opts, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, 1, massup );
tend = 2 * tend;
end
xtest = x0 + xv * te;
ytest = y0 + yv * te;
disp([xtest ytest xuppts{iseg}(i) yuppts{iseg}(i)])
plot(xtest,ytest,'x')
text(xtest,ytest,num2str(itstep));
end
for i = 2:length(xlowpts{iseg})-1
p = InterX( [xsl; ysl], [xlowpts{iseg}(i) xuppts{iseg}(i); ylowpts{iseg}(i) yuppts{iseg}(i)] );
x0 = p(1,:)';
y0 = p(2,:)';
[u, v] = planarvel( x0, y0, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props );
xv = xlowpts{iseg}(i) - x0;
yv = ylowpts{iseg}(i) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
dm = ( u * yv + v * xv );
rlow = -masslow/dm;
xlownew{iseg}(i) = x0 + xv * rlow;
ylownew{iseg}(i) = y0 + yv * rlow;
xv = xuppts{iseg}(i) - x0;
yv = yuppts{iseg}(i) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
dm = ( u * yv + v * xv );
rup = massup/dm;
xupnew{iseg}(i) = x0 + xv * rup;
yupnew{iseg}(i) = y0 + yv * rup;
end
else
% Find streamtube by continuity
for i = 2:length(xlowpts{iseg})-1
p = InterX( [xsl; ysl], [xlowpts{iseg}(i) xuppts{iseg}(i); ylowpts{iseg}(i) yuppts{iseg}(i)] );
x0 = p(1,:)';
y0 = p(2,:)';
xv = xlowpts{iseg}(i) - x0;
yv = ylowpts{iseg}(i) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
te = [];
tend = 3;
while isempty(te)
[tdist, mdist, te] = ode45( @planardm, [0, tend], 0, opts, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, 1, -masslow );
tend = 2 * tend;
end
xlownew{iseg}(i) = x0 + xv * te;
ylownew{iseg}(i) = y0 + yv * te;
xv = xuppts{iseg}(i) - x0;
yv = yuppts{iseg}(i) - y0;
dlen = sqrt( xv^2 + yv^2 );
xv = xv / dlen;
yv = yv / dlen;
te = [];
tend = 3;
while isempty(te)
[tdist, mdist, te] = ode45( @planardm, [0, tend], 0, opts, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props, x0, y0, xv, yv, 1, massup );
tend = 2 * tend;
end
xupnew{iseg}(i) = x0 + xv * te;
yupnew{iseg}(i) = y0 + yv * te;
end
end
for i = length(xlowpts{iseg}) % (length(xlowpts{iseg})-1):length(xlowpts{iseg})
p = InterX( [xsl; ysl], [xlowpts{iseg}(i) xuppts{iseg}(i); ylowpts{iseg}(i) yuppts{iseg}(i)] );
x0 = p(1,:)';
y0 = p(2,:)';
xv = lowtube(1);
yv = lowtube(2);
xlownew{iseg}(i) = x0 + xv * hlow;
ylownew{iseg}(i) = y0 + yv * hlow;
xv = -lowtube(1);
yv = -lowtube(2);
xupnew{iseg}(i) = x0 + xv * hup;
yupnew{iseg}(i) = y0 + yv * hup;
end
[upts, vpts] = planarvel( xlowpts{iseg}, ylowpts{iseg}, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props );
ucp = ( upts(2:end) + upts(1:end-1) ) * 0.5;
vcp = ( vpts(2:end) + vpts(1:end-1) ) * 0.5;
Vcp = sqrt( ucp.^2 + vcp.^2 );
% Calculate vortex tube strength and eventual jet velocity
% gammainf = - W * ( sqrt( deltaCP{iseg} + 1 ) - 1 );
% Calculate new strength via: (vs*gamma)=const
gammalownew{iseg}(1:end-1) = ( gammainf * ( W - gammainf / 2 ) ) ./ Vcp;
% Force last two to equal tube strength
gammalownew{iseg}(end-1:end) = gammainf;
[upts, vpts] = planarvel( xuppts{iseg}, yuppts{iseg}, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props );
ucp = ( upts(2:end) + upts(1:end-1) ) * 0.5;
vcp = ( vpts(2:end) + vpts(1:end-1) ) * 0.5;
Vcp = sqrt( ucp.^2 + vcp.^2 );
% Calculate vortex tube strength and eventual jet velocity
% gammainf = - W * ( sqrt( deltaCP{iseg} + 1 ) - 1 );
% Calculate new strength via: (vs*gamma)=const
gammaupnew{iseg}(1:end-1) = ( gammainf * ( W - gammainf / 2 ) ) ./ Vcp;
% Force last two to equal tube strength
gammaupnew{iseg}(end-1:end) = gammainf;
yerr = max( yerr, max( abs( xlowpts{iseg} - xlownew{iseg} ) ) );
yerr = max( yerr, max( abs( ylowpts{iseg} - ylownew{iseg} ) ) );
yerr = max( yerr, max( abs( xuppts{iseg} - xupnew{iseg} ) ) );
yerr = max( yerr, max( abs( yuppts{iseg} - yupnew{iseg} ) ) );
gerr = max( gerr, max( abs( gammaslow{iseg} - gammalownew{iseg} ) ) );
gerr = max( gerr, max( abs( gammasup{iseg} - gammaupnew{iseg} ) ) );
end
end
xlowpts = xlownew;
ylowpts = ylownew;
xuppts = xupnew;
yuppts = yupnew;
gammaslow = gammalownew;
gammasup = gammaupnew;
yerrhist(itstep) = yerr;
gerrhist(itstep) = gerr;
% Re-process actuator disk geometry
for iseg=1:nseg
if( props{iseg} )
xep = xuppts{iseg};
yep = yuppts{iseg};
dxup{iseg} = xep(2:end) - xep(1:end-1);
dyup{iseg} = yep(2:end) - yep(1:end-1);
dsup{iseg} = sqrt( dxup{iseg}.^2 + dyup{iseg}.^2 ); % Panel arclength
thetaup{iseg} = atan2( dyup{iseg}, dxup{iseg} ); % Panel slope angle
xupcp{iseg} = 0.5 * ( xep(2:end) + xep(1:end-1) ); % Panel x center point
yupcp{iseg} = 0.5 * ( yep(2:end) + yep(1:end-1) ); % Panel y center point
xep = xlowpts{iseg};
yep = ylowpts{iseg};
dxlow{iseg} = xep(2:end) - xep(1:end-1);
dylow{iseg} = yep(2:end) - yep(1:end-1);
dslow{iseg} = sqrt( dxlow{iseg}.^2 + dylow{iseg}.^2 ); % Panel arclength
thetalow{iseg} = atan2( dylow{iseg}, dxlow{iseg} ); % Panel slope angle
xlowcp{iseg} = 0.5 * ( xep(2:end) + xep(1:end-1) ); % Panel x center point
ylowcp{iseg} = 0.5 * ( yep(2:end) + yep(1:end-1) ); % Panel y center point
end
end
end
for iseg=1:nseg
if( ~props{iseg} )
Cp{iseg} = 1 - gammas{iseg}.^2;
for jseg=1:nseg
if( props{jseg} )
xst = [fliplr(xlowpts{jseg}) xuppts{jseg}];
yst = [fliplr(ylowpts{jseg}) yuppts{jseg}];
xst = [xst(1)+30 xst xst(end)+30];
yst = [yst(1) yst yst(end)];
% Forces open polys to be closed
% Signed minimum distance -- negative is inside.
[dmin, x_d_min, y_d_min, is_vertex, idx_c] = p_poly_dist( xcp{iseg}, ycp{iseg}, xst, yst, true );
mask = dmin <= 0.0;
Cp{iseg}(mask) = Cp{iseg}(mask) + deltaCP{jseg};
end
end
end
end
if( drawplots )
figure(1)
hold on
for iseg=1:nseg
if( props{iseg} )
plot( xuppts{iseg}, yuppts{iseg}, 'o-', xlowpts{iseg}, ylowpts{iseg}, 'o-' );
end
end
hold off
% Post-process
figure(2)
clf
hold on
for iseg=1:nseg
if( ~props{iseg} )
plot( xcp{iseg}, gammas{iseg}, 'o' )
if ( length(xepts{iseg}) == length(Vexs{iseg}) )
plot( xepts{iseg}, Vexs{iseg} )
else
plot( xcp{iseg}, Vexs{iseg} )
end
end
end
hold off
ylabel('v/Vinf')
figure(3)
clf
hold on
for iseg=1:nseg
if( ~props{iseg} )
plot( xcp{iseg}, -Cp{iseg} );
end
end
hold off
ylabel('-C_p')
figure(4)
semilogy( yerrhist, 'x-' )
hold on
semilogy( gerrhist, 'o-' )
legend( 'Streamtube residual', 'Gamma residual' )
hold off
figure(25)
clf
subplot(2,1,1)
hold on
for iseg=1:nseg
if( ~props{iseg} )
plot( xcp{iseg}, -Cp{iseg},'k','LineWidth',1.5 );
end
end
hold off
ylabel('-C_p')
axis([-2 3 -1 5])
% set(gca,'xtick',[])
% axes('XColor','none');
ax1=gca;
ax1.XAxis.Visible = 'off';
subplot(2,1,2)
hold on
for iseg=1:nseg
plot( xepts{iseg}, yepts{iseg}, 'k', 'LineWidth', 1.5 );
end
for iseg=1:nseg
if( props{iseg} )
plot( xuppts{iseg}, yuppts{iseg}, 'k', xlowpts{iseg}, ylowpts{iseg}, 'k', 'LineWidth',1.5 );
end
end
hold off
axis([-2 3 -.5 1])
axis equal
axis off
end
drawnow
drawplots = drawmoreplots;
% Post-process velocity survey.
if( drawplots )
xv = [];
yv = [];
xomax = max( xlim );
xomin = min( xlim );
yomax = max( ylim );
yomin = min( ylim );
% Build component near-field survey points
for iseg=1:nseg
xmin = min( [xepts{iseg}, xlowpts{iseg}, xuppts{iseg}]);
xmax = max( [xepts{iseg}, xlowpts{iseg}, xuppts{iseg}]);
ymin = min( [yepts{iseg}, ylowpts{iseg}, yuppts{iseg}]);
ymax = max( [yepts{iseg}, ylowpts{iseg}, yuppts{iseg}]);
xomax = max( xomax, xmax );
xomin = min( xomin, xmin );
yomax = max( yomax, ymax );
yomin = min( yomin, ymin );
if( ~props{iseg} )
off = max( xmax - xmin, ymax - ymin ) * 0.2;
xgrd = linspace( xmin - off, xmax + off, nsurvey );
ygrd = linspace( ymin - off, ymax + off, nsurvey );
[xg, yg] = meshgrid( xgrd, ygrd );
xvi = reshape( xg, 1, [] );
yvi = reshape( yg, 1, [] );
yvi = yvi + rand(size(yvi))*.001-.0005;
xv = [xv xvi];
yv = [yv yvi];
xinterest = [xepts{iseg}(1) xepts{iseg}(end)];
yinterest = [yepts{iseg}(1) yepts{iseg}(end)];
if ( abs( xinterest(1) - xinterest(2) ) < 1e-3 )
imid = ceil( length( xepts{iseg} ) * 0.5 );
xinterest(2) = xepts{iseg}(imid);
yinterest(2) = yepts{iseg}(imid);
end
for i=1:length(xinterest)
xgrd = linspace( xinterest(i) - off, xinterest(i) + off, nsurvey );
ygrd = linspace( yinterest(i) - off, yinterest(i) + off, nsurvey );
[xg, yg] = meshgrid( xgrd, ygrd );
xvi = reshape( xg, 1, [] );
yvi = reshape( yg, 1, [] );
yvi = yvi + rand(size(yvi))*.001-.0005;
xv = [xv xvi];
yv = [yv yvi];
end
else
off = 0.1;
xgrd = linspace( min(xlowpts{iseg}(1),xuppts{iseg}(1)) - off, max(xlowpts{iseg}(1),xuppts{iseg}(1)) + off, nsurvey );
ygrd = linspace( min(ylowpts{iseg}(1),yuppts{iseg}(1)) - off, max(ylowpts{iseg}(1),yuppts{iseg}(1)) + off, nsurvey );
[xg, yg] = meshgrid( xgrd, ygrd );
xvi = reshape( xg, 1, [] );
yvi = reshape( yg, 1, [] );
yvi = yvi + rand(size(yvi))*.001-.0005;
xv = [xv xvi];
yv = [yv yvi];
xgrd = linspace( min(xlowpts{iseg}) - off, max(xlowpts{iseg}) + off, nsurvey );
ygrd = linspace( min(ylowpts{iseg}) - off, max(ylowpts{iseg}) + off, nsurvey );
[xg, yg] = meshgrid( xgrd, ygrd );
xvi = reshape( xg, 1, [] );
yvi = reshape( yg, 1, [] );
yvi = yvi + rand(size(yvi))*.001-.0005;
xv = [xv xvi];
yv = [yv yvi];
xgrd = linspace( min(xuppts{iseg}) - off, max(xuppts{iseg}) + off, nsurvey );
ygrd = linspace( min(yuppts{iseg}) - off, max(yuppts{iseg}) + off, nsurvey );
[xg, yg] = meshgrid( xgrd, ygrd );
xvi = reshape( xg, 1, [] );
yvi = reshape( yg, 1, [] );
yvi = yvi + rand(size(yvi))*.001-.0005;
xv = [xv xvi];
yv = [yv yvi];
end
end
% Build far-field survey points
xgrd = linspace( xomin, xomax, 31 );
ygrd = linspace( yomin, yomax, nsurvey );
[xg, yg] = meshgrid( xgrd, ygrd );
xvi = reshape( xg, 1, [] );
yvi = reshape( yg, 1, [] );
yvi = yvi + rand(size(yvi))*.001-.0005;
xv = [xv xvi];
yv = [yv yvi];
% Replace points near propwash with aligned points
for iseg=1:nseg
if( props{iseg} )
% First streamtube panel length
len = sqrt( (xlowpts{iseg}(2) - xlowpts{iseg}(1))^2 + (ylowpts{iseg}(2) - ylowpts{iseg}(1))^2 );
% Find minimum distance between any streamtube center point and
% any survey point.
dup = min( sqrt((xupcp{iseg}-xv').^2+(yupcp{iseg}-yv').^2), [], 2 );
mask = dup < ( len / 2.0 );
xv = xv(~mask);
yv = yv(~mask);
dlow = min( sqrt((xlowcp{iseg}-xv').^2+(ylowcp{iseg}-yv').^2), [], 2 );
mask = dlow < ( len / 2.0 );
xv = xv(~mask);
yv = yv(~mask);
xl = xlowpts{iseg};
xu = xuppts{iseg};
yl = ylowpts{iseg};
yu = yuppts{iseg};
xuv = xu-xl;
yuv = yu-yl;
luv = sqrt( xuv.^2 + yuv.^2 );
xuv = xuv./luv;
yuv = yuv./luv;
len = 0.2;
xl = xl - xuv * len;
xu = xu + xuv * len;
yl = yl - yuv * len;
yu = yu + yuv * len;
xst = [fliplr(xl) xu];
yst = [fliplr(yl) yu];
% xst = [xst(1) xst xst(end)];
% yst = [yst(1) yst yst(end)];
% Forces open polys to be closed
% Signed minimum distance -- negative is inside.
[dmin, x_d_min, y_d_min, is_vertex, idx_c] = p_poly_dist( xv, yv, xst, yst, true );
mask = dmin <= 0.0;
xv = xv(~mask);
yv = yv(~mask);
for i=1:length(xl)
% Add streamtube points
xv = [xv linspace(xl(i), xu(i), nsurvey)];
yv = [yv linspace(yl(i), yu(i), nsurvey)];
end
end
end
inv = zeros( size(xv) );
for iseg=1:nseg
if( ~props{iseg} )
xep = xepts{iseg};
yep = yepts{iseg};
% Forces open polys to be closed
% Signed minimum distance -- negative is inside.
[dmin, x_d_min, y_d_min, is_vertex, idx_c] = p_poly_dist( xv, yv, xep, yep, true );
% Loop to compare to nearby edge length. Velocity survey has
% problems within one edge length of body
for i=1:length( inv )
if ( idx_c(i) < length( ds{iseg} ) && idx_c(i) > 0 )
inv(i) = inv(i) | ( dmin(i) < ds{iseg}(idx_c(i) ) );
end
inv(i) = inv(i) | ( dmin(i) < 0 );
end
end
end
[uv, vv] = planarvel( xv, yv, W, nseg, xepts, yepts, xuppts, yuppts, xlowpts, ylowpts, xcp, ycp, xupcp, yupcp, xlowcp, ylowcp, gammas, gammasup, gammaslow, ds, dsup, dslow, dx, dxup, dxlow, props );
xv = xv( ~inv );
yv = yv( ~inv );
uv = uv( ~inv );
vv = vv( ~inv );
Cedg = [];
for iseg=1:nseg
if( ~props{iseg} )
nnext = length(xv) + 1;
mcon = length(xcp{iseg}) - 1;
xv = [xv xcp{iseg}];
yv = [yv ycp{iseg}];
uv = [uv gammas{iseg} .* cos( theta{iseg} ) .* sign(dx{iseg}) ];
vv = [vv gammas{iseg} .* sin( theta{iseg} ) .* sign(dx{iseg}) ];
Cedg = [Cedg [ nnext:nnext+mcon; nnext+1:nnext+mcon nnext ] ];
end
end
if( isempty(Cedg) )
DT = delaunayTriangulation( xv', yv' );
tri = DT.ConnectivityList;
IO = true( size( tri, 1 ), 1 );
else
DT = delaunayTriangulation( xv', yv', Cedg' );
tri = DT.ConnectivityList;
IO = ~isInterior(DT);
end
Vmagv = sqrt(uv.^2+vv.^2);
Cpv = 1 - Vmagv.^2;
for iseg=1:nseg
if( props{iseg} )
xst = [fliplr(xlowpts{iseg}) xuppts{iseg}];
yst = [fliplr(ylowpts{iseg}) yuppts{iseg}];
xst = [xst(1)+30 xst xst(end)+30];
yst = [yst(1) yst yst(end)];
% Forces open polys to be closed
% Signed minimum distance -- negative is inside.
[dmin, x_d_min, y_d_min, is_vertex, idx_c] = p_poly_dist( xv, yv, xst, yst, true );
mask = dmin <= 0.0;
Cpv(mask) = Cpv(mask) + deltaCP{iseg};
end
end
end % if( drawplots )
if ( drawplots )
verbose = 0; % flag to report progress
maxits = 1e4; % maximum number of iterations
Ltol = 0.01; % flowpath "out-of-triangle" tolerance
dLtol = 0.5; % flowpath "curvature" tolerance
ystl = linspace( min(ylim), max(ylim), nsl);
% ysl(1) = ysl(2) * 0.1;
xstl = min(xlim) * ones( size(ystl) ) + .01;
FlowP = TriStream( tri, xv, yv, uv, vv, xstl, ystl, verbose, maxits, Ltol, dLtol );
xcap = [];
ycap = [];
% for iseg=1:nseg
% if( props{iseg} )
% % Integrate mass flow at disk
% x0 = xepts{iseg}(1);
% mass0 = inf;
% [ ydist, mdist ] = ode45( @planardm, [yemin{iseg}(1), yepts{iseg}(1)], 0, opts, W, nseg, xepts, yepts, xcp, ycp, gammas, ds, dx, props, x0, mass0 );
% mass0 = mdist(end);
%
% % Find capture streamtube by continuity