FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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EX_SWIRL_FLOW2 2D Axisymmetric swirl flow in step domain.
[ FEA, OUT ] = EX_SWIRL_FLOW2( VARARGIN ) Axisymmetric swirl for in tubular step region where the inner cylindrical wall is rotating.
Accepts the following property/value pairs.
Input Value/{Default} Description ----------------------------------------------------------------------------------- omega scalar {100} Angular rotational velocity (of inner wall) 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 = { 'omega', 100; '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'}; fea.geom.objects = { gobj_rectangle(0.5,1.5,0,3) gobj_rectangle(1.0,1.5,1.5,3,'R2') }; fea = geom_apply_formula( fea, 'R1-R2' ); fea.grid = gridgen( fea, 'hmax', 0.1, 'fid', fid ); % Equation definition. if ( opt.iphys==1 ) fea = addphys(fea,@swirlflow); fea.phys.sw.eqn.coef{1,end} = { 1 }; fea.phys.sw.eqn.coef{2,end} = { 1 }; fea.phys.sw.sfun = [ repmat( {opt.sf_u}, 1, 3 ) {opt.sf_p} ]; fea.phys.sw.bdr.sel = [1 1 5 2 1 1]; fea.phys.sw.bdr.coef{2,end}{2,4} = opt.omega; fea.phys.sw.prop.artstab.ps = isequal(opt.sf_u,opt.sf_p); fea = parsephys(fea); if( isfield(fea,'constr') ) fea = rmfield(fea,'constr'); end 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 ; 'miu', 1 ; 'Fr', 0 ; 'Fth', 0 ; 'Fz', 0 }; % Boundary conditions. fea.bdr.d = { 0 0 [] 0 0 0 ; 0 0 [] opt.omega 0 0 ; 0 0 0 0 0 0 ; [] [] [] [] [] [] }; fea.bdr.n = cell(size(fea.bdr.d)); end % Fix pressure at p([r,z]=[ro,h/2]) = 0. [~,ix_p] = min( sqrt( (fea.grid.p(1,:)-1.5).^2 + (fea.grid.p(2,:)-1.5).^2) ); fea.pnt = struct( 'type', 'constr', ... 'index', ix_p, ... 'dvar', 'p', ... 'expr', '0' ); % Parse and solve problem. fea = parseprob( fea ); fea.sol.u = solvestat( fea, 'maxnit', 50, 'fid', fid ); % Postprocessing. if( opt.iplot ) postplot( fea, 'surfexpr', 'sqrt(u^2+v^2+w^2)', 'isoexpr', 'v' ) end % Error checking. out.ref = [ -6.1 10.5 73 1.25 ]; if( ~got.tol ) if( opt.sf_u(end) == '2' ) opt.tol = 0.05; else opt.tol = 0.3; end end [u_min,u_max] = minmaxsubd( 'u', fea ); out.val = [ u_min u_max intsubd('v',fea) intsubd('w',fea) ]; out.pass = mean(abs(out.val-out.ref)./abs(out.ref)) < opt.tol; if( nargout==0 ) clear fea out end