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ex_navierstokes9.m File Reference

Description

EX_NAVIERSTOKES9 2D Axisymmetric jet impingement with heat transfer.

[ FEA, OUT ] = EX_NAVIERSTOKES9( VARARGIN ) Sets up and solves stationary axisymmetric flow of a jet impacting in a thin constrained region with a coupled heat transfer mode. Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
Re          scalar {100}           Jet Reynolds number
igrid       scalar 1/{0}           Cell type (0=quadrilaterals, 1=triangles)
hmax        scalar {0.2}           Max grid cell size
sf_u        string {sflag2}        Shape function for velocity
sf_p        string {sflag1}        Shape function for pressure
iplot       scalar 0/{1}           Plot solution and error (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = { ...
   'Re',       100; ...
   'igrid',    0; ...
   'hmax',     0.2; ...
   'sf_u',     'sflag2'; ...
   'sf_p',     'sflag1'; ...
   'iplot',    1; ...
   'fid',      1 };
 [got,opt] = parseopt( cOptDef, varargin{:} );
 fid       = opt.fid;


% Geometry definition.
 r = 10;   % Radius.
 l = 3;    % Length.
 gobj = gobj_polygon( [0 0; r 0; r l; 1 l; 0 l] );
 fea.geom.objects = { gobj };
 fea.sdim = { 'r' 'z' };   % Space coordinate names.


% Grid generation.
 if ( opt.igrid==1 )
   fea.grid = gridgen( fea, 'hmax', opt.hmax, 'fid', fid );
 else
   fea.grid = rectgrid( round(r/opt.hmax), round(l/opt.hmax), [0 r;0 l] );
   if( opt.igrid<0 )
     fea.grid = quad2tri( fea.grid );
   end
   ic = fea.grid.b(1,:);
   ii = fea.grid.b(2,:);
   jj = mod(ii,size(fea.grid.c,1)) + 1;
   p1 = fea.grid.p( :, fea.grid.c(sub2ind(size(fea.grid.c),ii,ic)) );
   p2 = fea.grid.p( :, fea.grid.c(sub2ind(size(fea.grid.c),jj,ic)) );
   pm = [ p1 + p2 ]'/2;

   ix4 = find( (pm(:,1)<1) .* (abs(pm(:,2)-3)<eps) );
   fea.grid.b(3,ix4) = 4;

   ix5 = find( pm(:,1)<=eps );
   fea.grid.b(3,ix5) = 5;
 end


% Boundary specifications.
 i_plate    = 1;
 i_inflow   = 4;
 i_outflow  = 2;
 i_symmetry = 5;
 inflow_bc  = -opt.Re;


% Problem definition.

% Add Navier-Stokes equations physics mode.
 fea = addphys( fea, {@navierstokes 1} );
 fea.phys.ns.eqn.coef{1,end} = { 1 };
 fea.phys.ns.eqn.coef{2,end} = { 1 };
 fea.phys.ns.sfun            = { opt.sf_u opt.sf_u opt.sf_p };


 fea.phys.ns.bdr.sel(i_inflow)   = 2;
 fea.phys.ns.bdr.sel(i_outflow)  = 3;
 fea.phys.ns.bdr.coef{2,end}{2,i_inflow} = inflow_bc;
 fea.phys.ns.bdr.sel(i_symmetry) = 5;

% Add heat transfer physics mode.
 fea = addphys( fea, {@heattransfer 1} );
 fea.phys.ht.eqn.coef{4,end} = fea.phys.ns.dvar{1};
 fea.phys.ht.eqn.coef{5,end} = fea.phys.ns.dvar{2};
 fea.phys.ht.sfun            = { opt.sf_u };

 fea.phys.ht.bdr.sel(:)         = 3;
 fea.phys.ht.bdr.sel(i_inflow)  = 1;
 fea.phys.ht.bdr.sel(i_plate)   = 1;
 fea.phys.ht.bdr.sel(i_outflow) = 2;
 fea.phys.ht.bdr.coef{1,end}{1,i_inflow} = 1;

% Parse physics modes.
 fea = parsephys(fea);


% Parse and solve problem.
 fea       = parseprob( fea );   % Check and parse problem struct.
 jac.form  = {[1;1] [1;1] [] [];[1;1] [1;1] [] []; [] [] [] []; [] [] [] []};
 jac.coef  = {'r*rho_ns*ur' 'r*rho_ns*uz' [] []; 'r*rho_ns*wr' 'r*rho_ns*wz' [] []; [] [] [] [];[] [] [] []};
 fea.sol.u = solvestat( fea, 'fid', fid, 'jac', jac );


% Error checking.
 u = evalexpr( 'u', fea.grid.p, fea );
 w = evalexpr( 'w', fea.grid.p, fea );
 out.err(1) = (max(u) - 75.9)/75.9;
 out.err(2) = (min(u) +  9.8)/(-9.8);
 out.err(3) = (max(w) -  7.9)/7.9;
 out.err(4) = (min(w) +  106)/(-106);
 out.pass   = all( out.err<0.05 );


% Postprocessing.
 if( opt.iplot>0 )
   figure
   subplot(1,2,1)
   postplot( fea, 'surfexpr', 'sqrt(u^2+w^2)', ...
                  'arrowexpr', {'u' 'w'}, 'arrowspacing', [60 20], ...
                  'isoexpr', 'sqrt(u^2+w^2)' )
   title( 'Velocity field' )

   subplot(1,2,2)
   postplot( fea, 'surfexpr', 'T', 'isoexpr', 'T' )
   title( 'Temperature' )
 end


 if( nargout==0 )
   clear fea out
 end