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FEATool Multiphysics
v1.16.5
Finite Element Analysis Toolbox
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FEATool Multiphysics
v1.16.5
Finite Element Analysis Toolbox
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EX_SWIRL_FLOW1 2D Axisymmetric laminar swirl flow.
[ FEA, OUT ] = EX_SWIRL_FLOW1( VARARGIN ) Axisymmetric swirl for in tubular region where the inner cylindrical wall is rotating. Comparison with analytical solution.
Accepts the following property/value pairs.
Input Value/{Default} Description
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rho scalar {2} Density
miu scalar {3} Molecular/dynamic viscosity
omega scalar {5} Angular rotational frequency (of inner wall)
ri scalar {0.5} Inner radius
ro scalar {1.5} Outer radius
h scalar {3} Height of cylinder
sf_u string {sflag1} Shape function for velocity
sf_p string {sflag1} Shape function for pressure
iplot scalar 0/{1} Plot solution (=1)
.
Output Value/(Size) Description
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fea struct Problem definition struct
out struct Output struct
cOptDef = { 'rho', 2;
'miu', 3;
'omega', 5;
'ri', 0.5
'ro', 1.5;
'h', 3;
'sf_u', 'sflag1';
'sf_p', 'sflag1';
'iphys', 1;
'iplot', 1;
'tol', [];
'fid', 1 };
[got,opt] = parseopt(cOptDef,varargin{:});
fid = opt.fid;
% Geometry and grid generation.
fea.sdim = {'r' 'z'};
ri = opt.ri; % Inner radius.
ro = opt.ro; % Outer radius.
h = opt.h; % Height of cylinder.
fea.geom.objects = { gobj_rectangle(ri,ro,-h/2,h/2) };
fea.grid = gridgen( fea, 'hmax', (ro-ri)/8, 'fid', fid );
% Equation definition.
if ( opt.iphys==1 )
fea = addphys(fea,@swirlflow);
fea.phys.sw.eqn.coef{1,end} = { opt.rho };
fea.phys.sw.eqn.coef{2,end} = { opt.miu };
fea.phys.sw.sfun = [ repmat( {opt.sf_u}, 1, 3 ) {opt.sf_p} ];
fea.phys.sw.bdr.sel = [5 1 5 2];
fea.phys.sw.bdr.coef{2,end}{2,4} = opt.omega*ri;
fea = parsephys(fea);
else
opt.sf_u = 'sflag2';
opt.sf_p = 'sflag1';
fea.dvar = { 'u', 'v', 'w', 'p' };
fea.sfun = [ repmat( {opt.sf_u}, 1, 3 ) {opt.sf_p} ];
c_eqn = { 'r*rho*u'' - r*miu*(2*ur_r + uz_z + wr_z) + r*rho*(u*ur_t + w*uz_t) + r*p_r = r*Fr - 2*miu/r*u_t + p_t + rho*v*v_t';
'r*rho*v'' - r*miu*( vr_r + vz_z) + miu*v_r + r*rho*(u*vr_t + w*vz_t) + rho*u*v_t = r*Fth + miu*(v_r - 1/r*v_t)';
'r*rho*w'' - r*miu*( wr_r + uz_r + 2*wz_z) + r*rho*(u*wr_t + w*wz_t) + r*p_z = r*Fz';
'r*ur_t + r*wz_t + u_t = 0' };
fea.eqn = parseeqn( c_eqn, fea.dvar, fea.sdim );
fea.coef = { 'rho', opt.rho ;
'miu', opt.miu ;
'Fr', 0 ;
'Fth', 0 ;
'Fz', 0 };
% Boundary conditions.
fea.bdr.d = { [] 0 [] 0 ;
[] 0 [] opt.omega*ri ;
0 0 0 0 ;
[] [] [] [] };
fea.bdr.n = cell(size(fea.bdr.d));
% Fix pressure at p([r,z]=[ro,h/2]) = 0.
[~,ix_p] = min( sqrt( (fea.grid.p(1,:)-ro).^2 + (fea.grid.p(2,:)-h/2).^2) );
fea.pnt = struct( 'type', 'constr', ...
'index', ix_p, ...
'dvar', 'p', ...
'expr', '0' );
end
% Parse and solve problem.
fea = parseprob( fea );
fea.sol.u = solvestat( fea, 'fid', fid );
% Exact (analytical) solution.
a = - opt.omega*ri^2 / (ro^2-ri^2);
b = opt.omega*ri^2*ro^2 / (ro^2-ri^2);
v_th_ex = @(r,a,b) a.*r + b./r;
% Postprocessing.
if( opt.iplot )
subplot(1,2,1)
postplot( fea, 'surfexpr', 'sqrt(u^2+v^2+w^2)', 'isoexpr', 'v' )
subplot(1,2,2)
hold on
grid on
r = linspace( ri, ro, 100 );
v_th = evalexpr( 'v', [r;zeros(1,length(r))], fea );
plot( r, v_th, 'b--' )
r = linspace( ri, ro, 10 );
plot( r, v_th_ex(r,a,b), 'r.' )
legend( 'Computed solution', 'Exact solution')
xlabel( 'Radius, r')
ylabel( 'Angular velocity, v')
end
% Error checking.
if( ~got.tol )
if( opt.sf_u(end) == '2' )
opt.tol = 0.01;
else
opt.tol = 0.16;
end
end
r = linspace( ri, ro, 100 );
v_th = evalexpr( 'v', [r;zeros(1,length(r))], fea )';
out.err = norm( v_th - v_th_ex(r,a,b) );
out.pass = out.err < opt.tol;
if( nargout==0 )
clear fea out
end