FEATool Multiphysics
v1.17.1
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 ----------------------------------------------------------------------------------- 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 ----------------------------------------------------------------------------------- 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