FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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EX_SWIRL_FLOW4 2D Rotating swirling flow around a disk.
[ FEA, OUT ] = EX_SWIRL_FLOW4( VARARGIN ) Axisymmetric swirling flow around a rotating disk immersed in a container.
Accepts the following property/value pairs.
Input Value/{Default} Description ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- fea struct Problem definition struct out struct Output struct
cOptDef = { 'sf_u', 'sflag1'; 'sf_p', 'sflag1'; 'iphys', 1; 'iplot', 1; 'tol', 0.01; 'fid', 1 }; [got,opt] = parseopt(cOptDef,varargin{:}); fid = opt.fid; % Geometry and grid generation. fea.sdim = {'r' 'z'}; fea.geom.objects = { gobj_polygon([0 0;.03 0;.03 .05;.002 .05;.002 .02;.008 .018;.0085 .013;0 .013]) }; hmax = 2e-3; fea.grid = gridgen( fea, 'hmax', hmax, 'fid', fid ); % Equation definition. if ( opt.iphys==1 ) fea = addphys(fea,@swirlflow); fea.phys.sw.eqn.coef{1,end} = { 1.2e3 }; fea.phys.sw.eqn.coef{2,end} = { 2.3e-3 }; fea.phys.sw.sfun = [ repmat( {opt.sf_u}, 1, 3 ) {opt.sf_p} ]; fea.phys.sw.bdr.sel = [1 1 3 2 2 2 2 5]; [fea.phys.sw.bdr.coef{2,end}{2,4:7}] = deal('r*pi/6'); 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', 1.2e3 ; 'miu', 2.3e-3 ; 'Fr', 0 ; 'Fth', 0 ; 'Fz', 0 }; % Boundary conditions. n_bdr = max(fea.grid.b(3,:)); fea.bdr.d = cell(4,n_bdr); [fea.bdr.d{1,[1 2 5:7 8]}] = deal(0); [fea.bdr.d{3,[1 2 3 4:7]}] = deal(0); [fea.bdr.d{2,[1 2]}] = deal(0); [fea.bdr.d{2, 4:7 }] = deal('r*pi/6'); [fea.bdr.d{1:3,3}] = deal([]); fea.bdr.n = cell(size(fea.bdr.d)); % Fix pressure at p([r,z]=[0.03,0.05]) = 0. [~,ix_p] = min( sqrt( (fea.grid.p(1,:)-0.03).^2 + (fea.grid.p(2,:)-0.05).^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 ); % Postprocessing. if( opt.iplot ) postplot( fea, 'surfexpr', 'sqrt(u^2+v^2+w^2)', 'isoexpr', 'v', 'isolev', 15, 'isocolor', 'w' ) end % Error checking. [~,U_max] = minmaxsubd( 'sqrt(u^2+v^2+w^2)', fea ); out.err = norm( U_max - 4.445e-3 )/4.445e-3; out.pass = out.err < opt.tol; if( nargout==0 ) clear fea out end