1. Lid driven flow in a cavity [Time: 1 h 30 ]

Transcription

1 Hands on computer session: 1. Lid driven flow in a cavity [Time: 1 h 30 ] Objects choice of computational domain, problem adimensionalization and definition of boundary conditions; influence of the mesh refinement (uniform mesh vs. near wall refined mesh, increasingly refined meshes); evaluation of different discretization schemes: accurancy and dissipative effects; identification of reference data, calculation of quantities to verify simulation accuracy (streamfunction, velocity profiles along vertical and horizontal midlines); Richardson extrapolation as a discretization error extimator. Physical problem A square cavity filled with flow; the top wall moves with a uniform velocity U: isothermal laminar incompressible problem; primary central vortex and secondary vortices at the corners; complex flow patterns at increasing Reynolds number; stability bounds for Central Difference Scheme. Centro Interdipartimentale di Fluidodinamica e Idraulica 1

2 Non dimensional data top wall velocity U = 1 cavity width L = 2 cavity height H = 2 Reynolds number Re = 1000 and Re = fluid adimensional density rho = 1 fluid adimensional viscosity mu = 2/Re Worksheet Mesh generation Boundary conditions Solution method Results mesh.4a: uniform mesh 20x20x1 cells; mesh.4b: near wall refined mesh 20x20x1 cells; mesh.4c: near wall refined mesh 40x40x1 cells; mesh.4d: near wall refined mesh 80x80x1 cells; create a subdomain (a quarter domain) with block structure grid create near wall refinement (uniform space factor) use CGEN-REFLECT to replicate subdomain regions use symmetry B.C. to set up a bidimensional simulation use Wall B.C.(slip option) at the top wall use Wall B.C.(no-slip option) at the bottom and side walls steady state simulation at Re=1000 (mesh 4a,4b,4c), solve for V, P steady state simulation at Re=10000 (mesh 4c,4d), solve for V, P use of differencing scheme (UD,CD,MARS) considerations over velocity field (velocity vectors and stream function contour plots) extraction of u and v velocity component profiles along the vertical and the horizontal midlines comparison to the literature results Richardson extrapolation References Ghia, U., Ghia, K. N., and Shin C.T., (1982), High-Re solutions for incompressible flows using the Navier-Stokes equations and a multigrid method, J.Comput.Phys, 48, Shon, J.L., (1988), Evaluation of FIDAP on some classical laminar and turbolent bench-marks, Int. J. Numer. Meth. Fluids, 8, Nonino, C., and Croce, G., (1997), An equal-order velocity-pressure algorithm for incompressible thermal flows, part 2: validation, Numer. Heat Transfer, 32, Centro Interdipartimentale di Fluidodinamica e Idraulica 2

3 Geometry and Results Figure 1: Refined grid 40x40 Figure 2: Streamfunction plot: right, Re=1000; left, Re=10000 [Ref.3] Figure 3: Streamfunction plot: right, Re=1000 (CDS); left, Re=10000 (MARS) Centro Interdipartimentale di Fluidodinamica e Idraulica 3

4 Re1000: u and v velocity components along vertical and horizontal midlines Figure 4: mesh with 20x20 cells: left,uniform mesh; right: near wall refined mesh.square[ref.3] Figure 5: Left: mesh with 20x20 cells; right: mesh comparison.square[ref.3]. Centro Interdipartimentale di Fluidodinamica e Idraulica 4

5 Re10000: u and v velocity components along vertical and horizontal midlines Figure 6: Meshes and discretization schemes comparison.square[ref.3]. Centro Interdipartimentale di Fluidodinamica e Idraulica 5

6 Reference values u components along vertical midline Re=1000 Re=10000 y u u v components along horizontal midline Re=1000 Re=10000 x v v Centro Interdipartimentale di Fluidodinamica e Idraulica 6

7 MACROS! Geometry.MAC *!!*** complete mesh generation by symmetry along x and y! get vmax mxve cset all cgen,2,vmax,cset,cset,1,vref,1,2 cset all cplot get vmaxnew mxve cgen,2,vmaxnew,cset,cset,1,vref,1,1 cset all cplot vmer all vcomp all ccomp all cset all cdirection,1,0,1,1,1 restructure,50000,,default, $y vset news vran 0,49000,1 vcomp all $y cset all cplot!umidplane-x0-gu.mac *!!*** y coordinate and u velocity component extraction on vertical midline to screen and to file.usr! vset subset gran ,,, greset y getv, None,SU gpost,vset,,,next frame,1,xreg,init,4 frame,1,xtitle,4.3,1.5 Y LOCATION frame,1,yreg,init,9 frame,1,ytitle,0.5,5.5 SU term,,x gdraw,1 rlabel,9,on SU Centro Interdipartimentale di Fluidodinamica e Idraulica 7

8 lint,9,9,3,1 symt,9,9,8,1 $rtab,9,y,y bart,9,9,90,1 gredraw oper,getv,x,1,1 oper,getv,y,1,2 oper,getv,z,1,3 oper,getv,su,4 savu,file.usr,both,user,vset I9,6X,4G16.9 close file.usr! Vmidplane-y0-GU.MAC *!!*** x coordinate and v velocity component extraction on horizontal midline to screen and to file.usr! vset subset gran,,, greset y getv, None,SV gpost,vset,,,next frame,1,xreg,init,3 frame,1,xtitle,4.3,1.5 X LOCATION frame,1,yreg,init,9 frame,1,ytitle,0.5,5.5 SV term,,x gdraw,1 rlabel,9,on SV lint,9,9,3,1 symt,9,9,8,1 $rtab,9,y,y bart,9,9,90,1 gredraw oper,getv,x,1,1 oper,getv,y,1,2 oper,getv,z,1,3 oper,getv,sv,4 savu,file.usr,both,user,vset I9,6X,4G16.9 close file.usr Centro Interdipartimentale di Fluidodinamica e Idraulica 8

9 ! U-V-midplane.MAC *!!*** comparison of u and v velocity profile from different file.pst! - load exe4-ud.pst greset y vset subset gran ,,, greset y numreg,100 getv, None,SU gpost,vset,,,1 sens dele all vset subset gran,,, getv, None,SV gpost,vset,,,12 frame,1,xreg,init,14,9 frame,1,yreg,init,20,4 frame,1,xrange,-1,1 frame,1,xtitle,4.94,1.6 U frame,1,yrange,-1,1 frame,1,ytitle,0.71,5.51 V rlabel,20,on SV lint,20,11,3,1 symt,20,20,8,1 $rtab,20,y,n bart,20,20,90,1 rlabel,4,on Y LOCATION lint,4,4,3,1 symt,4,4,8,1 $rtab,4,y,n bart,4,4,90,1 term,,x gdraw,1 load exe4mars.pst vset subset gran ,,, getv, None,SU gpost,vset,,,24 sens dele all vset subset gran,,, getv, None,SV Centro Interdipartimentale di Fluidodinamica e Idraulica 9

10 gpost,vset,,,36 frame,1,xreg,init,38,32,14,9 frame,1,yreg,init,44,27,20,4 frame,1,xrange,-1,1 frame,1,xtitle,4.94,1.6 U frame,1,yrange,-1,1 frame,1,ytitle,0.71,5.51 V rlabel,44,on SV lint,44,3,3,1 symt,44,44,8,1 $rtab,44,y,n bart,44,44,90,1 rlabel,27,on Y LOCATION lint,27,27,3,1 symt,27,27,8,1 $rtab,27,y,n bart,27,27,90,1 term,,x gdraw,1 Centro Interdipartimentale di Fluidodinamica e Idraulica 10