GROUP 1. Run title and other preliminaries TEXT(YX LAMINAR BACKWARD-FACING-STEP FLOW TITLE mesg( PC486/50 time last reported as 6.0 min DISPLAY Numerical Schemes validation example: 2-d x-y, Cartesian, steady, elliptic simulation The case considered is steady incompressible, laminar backward- facing-step flow, i.e. flow through a straight channel having a sudden asymmetric expansion. The flow is characterised by the step height H and the Reynolds number Re based on the bulk inlet inlet velocity and 2h, where h is the flow inlet height. The channel expansion ratio is 1.94, and the total length of the domain is 40H. A fully-developed parabolic velocity profile is prescribed at the inlet boundary located at the step. The calculation is made for Re=150 with the cubic upwind scheme, and the option exists to select the hybrid or van Albada scheme. ENDDIS This test problem is widely used for assessing the accuracy of numerical methods because of the dependence of the reattachment lengths X on Re. The flow has been studied experimentally by Armaly et al (J.Fluid Mech., Vol.127, p473 (1983)), and numerically in several papers, e.g.Gartling (Int.J.Num.Meth.Fluids Vol.11, p953 (1990)) and Freitas(ASME J.Fluids Engng, Vol.117, p208, (1995)), Gresho et al (Int.J.Num.Meth.Fluids Vol.17, p501 (1993))). The user is invited to perform 2 calculations for comparison with Armaly's data, namely Re=150 and Re=450. At Re=150, a primary recirculation zone develops immediately downstream of the step with X1/H=5.0. At Re=450, X1/H=9.5 and an additional separation cell forms on the upper wall of the channel. The measurements indicate that the separation point of this cell is located at X2/H=7.6 and the reattachment point at X3/H=11.3, yielding a cell length of DX/H=3.7. For Re > 450, the flow begins to exhibit 3d effects. The main results may be summarised as follows: Re=150 Data Hybrid Cubic-Upwind Van-Albada X1/H 4.2 4.17 4.24 4.25 Re=450 X1/H 9.5 8.79 9.13 9.06 X2/H 7.6 7.66 8.26 8.09 X3/H 11.3 11.14 11.39 11.52 DX/H 3.7 3.48 3.13 3.43 Although no grid-refinement studies have been performed, the results are in fairly good agreement with the data. It should also be mentioned that the foregoing results are better than those reported by Freitas(1995) for other general-purpose codes. The measurements indicate that for Re>450, 3d effects become significant, and for Re >6,600 the flow is 2d fully-turbulent. PHOTON USE P 0.20443E+04 0.15633E+04 CR gr ou z 1;mag gr 5 0.28838E+03 0.17522E+04 CR msg Reynolds number = 150 Cubic upwind scheme vec z 1 x 1 40 y 1 m sh STREAM 2D Z 1 X 1 40 Y 1 M -.699 0. 5 STREAM 2D Z 1 X 1 40 Y 1 M 0. 12. 8 msg pressto continue msg press to end pause ENDUSE AUTOPLOT USE file phi 5 d 1 u1 y 1;plot;div x .49 1 scale x 0 6;level y 0 msg Reynolds number = 150 Cubic upwind scheme msg horizontal (U1) velocity distribution along bottom wall msg reattachment point is where U1 crosses zero point msg press to continue msg press to end pause ENDUSE CHAR(SCHM);REAL(UIN,DY,HIN,HSTEP,YH,LENGTH,LENX1,RENO,DUM) REAL(UINAV,RLXFAC);INTEGER(NX1,NX2,NY1,NY2,NY2P1) ** All dimensions are based on: g, cm, sec HIN=0.52;HSTEP=0.49;LENGTH=40.0*HSTEP MESG(Enter Reynolds number - default 150 READVDU(RENO,REAL,150.) ENUL=0.16;UINAV=RENO*ENUL/(2.0*HIN) UINAV GROUP 2. Transience; time-step specification GROUP 3. X-direction grid specification was nx1=200 nx2=50 NX1=160;NX2=40;LENX1=0.666666*LENGTH NREGX=2;IREGX=1;GRDPWR(X,NX1,LENX1,1.0) IREGX=2;GRDPWR(X,NX2,LENGTH-LENX1,1.2) GROUP 4. Y-direction grid specification NY2=16;NY1=16;NREGY=2;IREGY=1;GRDPWR(Y,NY1,HSTEP,1.0) IREGY=2;GRDPWR(Y,NY2,HIN,1.0);DY=HIN/NY2 GROUP 5. Z-direction grid specification NZ=1;ZWLAST=0.01 GROUP 6. Body-fitted coordinates or grid distortion GROUP 7. Variables stored, solved & named SOLVE(P1,U1,V1) GROUP 8. Terms (in differential equations) & devices MESG( Enter required convection scheme MESG( Default: CUS - Cubic upwind MESG( The options are: MESG( CUS - Cubic upwind MESG( HYB - Hybrid scheme MESG( VAN - VAN ALBADA scheme READVDU(SCHM,CHAR,CUS) CASE :SCHM: OF WHEN CUS,3 + MESG(Cubic upwind scheme + SCHEME(CUS,U1,V1) WHEN FOU,3 + MESG(First-order upwind scheme + DIFCUT=0.5 WHEN VAN,3 + MESG(Van Albada scheme + SCHEME(VANALB,U1,V1) ENDCASE GROUP 9. Properties of the medium (or media) RHO1=1.2E-3 GROUP 10. Inter-phase-transfer processes and properties GROUP 11. Initialization of variable or porosity fields FIINIT(U1)=0.5*UINAV GROUP 12. Convection and diffusion adjustments GROUP 13. Boundary conditions and special sources ** Inlet velocity profile: u(y)/uav = {6y(hin-y)}/hin**2 umax/uav=1.5 at y=hin/2. The profile presumes a uniform mesh distribution. REAL(SAIN,SFIN,UBAR,FCON);FCON=RHO1*DY*ZWLAST;SAIN=0.;SFIN=0. DO JJ=1,NY2 + YH=0.5*DY+DY*(JJ-1);UIN=6.0*UINAV*YH*(HIN-YH) + UIN=UIN/(HIN*HIN);SAIN=SAIN+FCON;SFIN=SFIN+UIN*FCON + PATCH(IN:JJ:,WEST,1,1,NY1+JJ,NY1+JJ,1,NZ,1,LSTEP) + COVAL(IN:JJ:,P1,FIXFLU,RHO1*UIN) + COVAL(IN:JJ:,U1,ONLYMS,UIN);COVAL(IN:JJ:,V1,ONLYMS,0.0) ENDDO ** check on ubar UBAR=SFIN/SAIN ** Wall boundary conditions PATCH(TWALL,NWALL,1,NX,NY,NY,1,NZ,1,LSTEP);COVAL(TWALL,U1,1.0,0.0) PATCH(BWALL,SWALL,1,NX,1,1,1,NZ,1,LSTEP);COVAL(BWALL,U1,1.0,0.0) PATCH(STPWL,WWALL,1,1,1,NY1,1,NZ,1,LSTEP);COVAL(STPWL,V1,1.0,0.0) ** Outlet boundary PATCH(OUT,EAST,NX,NX,1,NY,1,NZ,1,LSTEP);COVAL(OUT,P1,10.0,0.0) GROUP 14. Downstream pressure for PARAB=.TRUE. GROUP 15. Termination of sweeps ** The number of sweeps required for convergence depends on the scheme used. Typically, 1000-2000 sweeps are required with the current mesh density. LSWEEP=100 GROUP 16. Termination of iterations LITER(U1)=10;LITER(V1)=10 GROUP 17. Under-relaxation devices ** The cubic-upwind & van-Albada schemes require RLXFAC to be halved as convergence is approached. RLXFAC=XULAST/(NX*UINAV) RELAX(P1,LINRLX,1.0);RELAX(U1,FALSDT,1.0*RLXFAC) RELAX(V1,FALSDT,1.0*RLXFAC) GROUP 18. Limits on variables or increments to them GROUP 22. Spot-value print-out TSTSWP =-1;IYMON=NY-3;IXMON=130 GROUP 23. Field print-out and plot control NPLT=20;ITABL=3 GROUP 24. Dumps for restarts