FEATool Multiphysics  v1.16.1 Finite Element Analysis Toolbox
ex_swirl_flow3.m File Reference

## Description

EX_SWIRL_FLOW3 2D Axisymmetric Taylor-Couette (swirl) flow.

[ FEA, OUT ] = EX_SWIRL_FLOW3( VARARGIN ) Axisymmetric Taylor-Couette swirl flow in a tubular region where the inner cylindrical wall is rotating. Time dependent solution with periodic top and bottom boundaries.

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
rho         scalar {1}             Density
miu         scalar {1}             Molecular/dynamic viscosity
omega       scalar {300}           Maximum angular velocity (of inner wall)
tmax        scalar {3}             Maximum time
nstep       scalar {300}           Number of time steps
h           scalar {3}             Height of cylinder
sf_u        string {sflag1}        Shape fcn for velocity
sf_p        string {sflag1}        Shape fcn for pressure
iplot       scalar 0/{1}           Plot solution (=1)
.
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct


# Code listing

 cOptDef = { 'rho',      1;
'miu',      1;
'omega',    300;
'tmax',     3;
'nstep',    300;
'ri',       1.0
'ro',       1.5;
'h',        3;
'sf_u',     'sflag1';
'sf_p',     'sflag1';
'iphys',    1;
'iplot',    1;
'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) };

n = 16;
fea.grid = rectgrid( n, 6*n, [ri ro; -h/2 h/2] );

% Equation definition.
if ( opt.iphys==1 )

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 = [3 1 3 2];
fea.phys.sw.bdr.coef{2,end}{2,4} = sprintf( '%g*t/%g', opt.omega*ri, opt.tmax );

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 [] sprintf( '%g*t/%g', opt.omega*ri, opt.tmax ) ;
[]  0 [] 0 ;
[] [] [] [] };
fea.bdr.n = cell(size(fea.bdr.d));

end

% Fix pressure at p([r,z]=[ro,0]) = 0.
[~,ix_p] = min( sqrt( (fea.grid.p(1,:)-ro).^2 + (fea.grid.p(2,:)-0).^2) );
fea.pnt = struct( 'type',  'constr', ...
'index', ix_p, ...
'dvar',  'p', ...
'expr',  '0' );

% Parse and solve problem.
fea = parseprob( fea );
if ( opt.iphys==1 )
fea.bdr.n{1}{1} = @periodic_vel_bc_1_3;
fea.bdr.n{2}{1} = @periodic_vel_bc_1_3;
fea.bdr.n{3}{1} = @periodic_vel_bc_1_3;
else
[fea.bdr.n{1:3,1}] = deal( @periodic_vel_bc_1_3 );   % Set periodic BCs.
end
fea.sol.u = solvetime( fea, 'ischeme', 1, 'tstep', opt.tmax/opt.nstep, 'tmax', opt.tmax, 'tolchg', inf, 'fid', fid );

% Postprocessing.
if( opt.iplot )
subplot(1,2,1)
postplot( fea, 'surfexpr', 'sqrt(u^2+w^2)', 'isoexpr', 'sqrt(u^2+w^2)', ...
'arrowexpr', {'u' 'w'}, 'arrowcolor', 'w', 'arrowspacing', [8 48] )
title('In-plane velocity')

subplot(1,2,2)
postplot( fea, 'surfexpr', 'v', 'isoexpr', 'v' )
title('Azimuthal velocity')
end

out = [];
if( nargout==0 )
clear fea out
end

%