GROUP 1. Run title and other preliminaries TEXT(LAM-BRE K-E_2D PARAB BNDRY LAYER :T212 TITLE DISPLAY The case considered concerns steady, incompressible, turbulent plane flow along a smooth flat plate with zero pressure gradient ( see PHOENICS input Library case 192 for a complete problem description ). The plate is maintained at a constant temperature above that of the free stream. The calculations are started 0.487 metres downstream of the leading edge, corresponding to a length Reynolds number REx =1E6. The turbulent Prandtl number is set equal to 0.86 and the molecular Prandtl number to 0.71. The turbulence is simulated by use of the Lam-Bremhorst k-eps low- Reynolds-number turbulence model. The calculation integrates down to the wall with a non-uniform radial grid so as to concentrate cells very close to the wall. For this purpose a grid is generated which is a geometric progression with the property that the ratio of any two adjacent cell lengths is a constant. A forward step size of 30% of the local width of the boundary layer is used together with 100 forward steps. Consequently, the marching integration is terminated at a length Reynolds number of about 2.1E6. ENDDIS Experimental data indicates that the local skin friction coefficient Cf is fairly well described by the Schultz-Grunow correlation, i.e. Cf = 0.37*(LOG10(REx))**-2.58 where Cf = 2.*TAUW/(RHOFRE*WFREE**2). For REx=2.1E6 this correlation yields Cf=3.17E-3, while the present predictions yield Cf=3.87E-3. No grid optimisation studies have been conducted to discover the sensitivity of the solution to different mesh sizes.In order to resolve the streamwise changes in the viscous sublayer, it is advised that the maximum forward step size be restricted to a sublayer thickness, i.e. DZ=ENUL/US where US is the friction velocity. AUTOPLOT USE file phi 5 clear da 1 w1;col3;plot 1 @ 0.10254E+03 0.26250E+04 CR W1(m/s)@ @ 0.18969E+04 0.16284E+03 CR Distance from the Flat Plate (m)@ msg Press e to END ENDUSE REAL(YINLET,WFREE,ZO,CFEXPT,GPOWER,TFREE,TWALL,US) REAL(TKEIN,EPSIN,DELT1,DELY,KFAC,AA);INTEGER(JJM,JJJ) YINLET=0.0115;WFREE=33.0;ZO=0.487;GPOWER=0.85;TFREE=5.;TWALL=10. CFEXPT=3.381E-3;US=WFREE*(0.5*CFEXPT)**0.5 GROUP 3. X-direction grid specification CARTES=T GROUP 4. Y-direction grid specification ** define first dely from wall and the grid-expansion factor Kfac which defines a constant ratio of lengths of two adjacent cells. ENUL=1.5E-5;DELT1=0.5*ENUL/US;KFAC=1.08;DELY=DELT1/YINLET ** calculate NY from dely & Kfac AA=(1.0/DELY)*(KFAC-1.0)+1.0;AA=LOG(AA)/LOG(KFAC)+1.0001 NY=AA ** define uniform grid initially IREGY=1;GRDPWR(Y,NY,YINLET,1.0) ** compute expanding grid from south boundary over one half of the channel width YFRAC(1)=DELY DO JJ=2,NY + JJM=JJ-1 + DELY=KFAC*DELY + YFRAC(JJ)=YFRAC(JJM)+DELY ENDDO YFRAC(NY)=1.0;YVLAST=YINLET;AZYV=GPOWER;ZWADD=ZO;DZW1=0.3 GROUP 5. Z-direction grid specification PARAB=T;NZ=100;AZDZ=PROPY GROUP 7. Variables stored, solved & named SOLVE(P1,W1,V1,H1);STORE(ENUT);NAME(H1)=TEMP STORE(LEN1);TURMOD(KEMODL-LOWRE);KELIN=1 GROUP 8. Terms (in differential equations) & devices DIFCUT=0.0;TERMS(TEMP,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) RHO1=1.0;ENUL=1.5E-5;PRT(TEMP)=0.86;PRNDTL(TEMP)=0.71 GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=0.01*WFREE;FIINIT(TEMP)=TFREE TKEIN=WFREE**2*0.01;EPSIN=TKEIN**1.5/YVLAST FIINIT(KE)=TKEIN;FIINIT(EP)=EPSIN GROUP 13. Boundary conditions and special sources ** South wall boundary WALL(WFUN,SOUTH,1,1,1,1,1,NZ,1,100) COVAL(WFUN,TEMP,1.0/PRNDTL(TEMP),TWALL) **North Free Boundary PATCH(FREE,NORTH,1,1,NY,NY,1,NZ,1,1) COVAL(FREE,P1,1.E5,0.0);COVAL(FREE,TEMP,ONLYMS,TFREE) COVAL(FREE,W1,ONLYMS,WFREE);COVAL(FREE,V1,ONLYMS,0.0) COVAL(FREE,KE,ONLYMS,1.E-10);COVAL(FREE,EP,ONLYMS,1.E-10) ** Inlet Boundary: uniform profiles assumed PATCH(LOWIN,LOW,1,1,1,NY,1,1,1,1) COVAL(LOWIN,P1,FIXFLU,WFREE);COVAL(LOWIN,W1,ONLYMS,WFREE) COVAL(LOWIN,TEMP,ONLYMS,TFREE);COVAL(LOWIN,V1,ONLYMS,0.0) COVAL(LOWIN,KE,ONLYMS,TKEIN);COVAL(LOWIN,EP,ONLYMS,EPSIN) GROUP 14. Downstream pressure for PARAB=T IPARAB=1 GROUP 16. Termination of iterations LITHYD=20; RELAX(W1,FALSDT,1.E-3) RELAX(KE,FALSDT,1.E-3); RELAX(EP,FALSDT,1.E-3) RESREF(P1)=1.E-10*WFREE*YINLET RESREF(W1)=RESREF(P1)*WFREE; RESREF(V1)=RESREF(W1) RESREF(KE)=RESREF(P1)*TKEIN; RESREF(EP)=RESREF(P1)*EPSIN RESREF(TEMP)=RESREF(P1)*TFREE GROUP 18. Limits on variables or increments to them VARMIN(W1)=1.E-10;VARMIN(ENUT)=1.E-30 VARMIN(KE)=1.E-20;VARMIN(EP)=1.E-20;VARMAX(EP)=1.E6 GROUP 21. Print-out of variables OUTPUT(LEN1,Y,N,N,Y,Y,Y);OUTPUT(ENUT,Y,N,N,Y,Y,Y) GROUP 22. Monitor print-out NPRMON=20;IYMON=3;NPLT=5;IPLTL=LITHYD;TSTSWP=-1;ITABL=2 GROUP 23. Field print-out and plot control GROUP 24. Dumps for restarts