GROUP 1. Run title and other preliminaries TEXT(LAM-BRE K-E_2D PARABOLIC PIPE FLOW :T211 TITLE DISPLAY The case considered is the two-dimensional parabolic solution of turbulent flow in a circular pipe at a Reynolds number of 1.E5 (see PHOENICS input Library case 175 for a problem description). The marching integration is carried out until the flow is fully- developed. The turbulence is simulated by use of either the Lam- Bremhorst k-e low-Re model or the 2-layer k-e low-Re 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 in which the ratio of any two adjacent cell lengths is constant. No grid optimisation studies have been conducted to discover the sensitivity of the solution to coarser meshes. 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. ENDDIS This low-Reynolds number demonstration library case is set to run for 20 slabs only (NZ=20). About 200 slabs are required for fully developed flow (NZ=200). 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 Pipe Centre (m)@ msg Press e to END ENDUSE BOOLEAN(TWOL);TWOL=F REAL(TIN,TWALL,GMIXL,CLEN,DIAM,WIN,RAD,REYNO) REAL(TKEIN,EPIN,US,DELT1,FRIC,KFAC,DELY,AA);INTEGER(JJM) REYNO=1.0E5;DIAM=0.1;WIN=1.;TIN=10.;TWALL=5. FRIC=1./(1.82*LOG10(REYNO)-1.64)**2;US=WIN*(FRIC/8.)**0.5 REYNO FRIC US GROUP 3. X-direction grid specification CARTES=F;XULAST=0.1 GROUP 4. Y-direction grid specification RAD=0.5*DIAM;ENUL=WIN*DIAM/REYNO ** define first dely from wall and the grid-expansion factor Kfac which defines a constant ratio of lengths of two adjacent cells. DELT1=1.*ENUL/US;DELY=DELT1/RAD IF(TWOL) THEN + KFAC=1.15 ELSE + KFAC=1.1 ENDIF ** calculate NY from dely & Kfac AA=(YVLAST/DELY)*(KFAC-1.0)+1.0;AA=LOG(AA)/LOG(KFAC)+1.0001 NY=AA ** define uniform grid initially IREGY=1;GRDPWR(Y,NY,YVLAST,1.0) ** compute expanding grid from north boundary YFRAC(NY)=1.0 DO JJ=NY,2,-1 + JJM=JJ-1 + YFRAC(JJM)=YFRAC(JJ)-DELY + DELY=KFAC*DELY ENDDO YVLAST=RAD GROUP 5. Z-direction grid specification PARAB=T;NZ=20;CLEN=70.*DIAM;GRDPWR(Z,NZ,CLEN*NZ/200.,1.0) GROUP 7. Variables stored, solved & named SOLVE(P1,W1,V1,H1);STORE(ENUT);NAME(H1)=TEMP STORE(LEN1) IF(TWOL) THEN + TURMOD(KEMODL-2L) + TEXT(2-LAYER K-E_2D PARABOLIC PIPE FLOW :T211 ELSE + TURMOD(KEMODL-LOWRE) ENDIF 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=WIN*DIAM/REYNO;PRT(TEMP)=0.86;PRNDTL(TEMP)=0.71 GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WIN;FIINIT(TEMP)=TIN TKEIN=0.25*WIN*WIN*FRIC;FIINIT(KE)=TKEIN GMIXL=0.09*RAD;EPIN=0.1643*TKEIN**1.5/GMIXL;FIINIT(EP)=EPIN GROUP 13. Boundary conditions and special sources ** North-Wall Boundary - Laminar at wall for low-Re model WALL(WFUN,NORTH,1,NX,NY,NY,1,NZ,1,1) COVAL(WFUN,TEMP,1.0/PRNDTL(TEMP),TWALL) ** Inlet Boundary: uniform profiles assumed PATCH(INLET,LOW,1,NX,1,NY,1,1,1,1);COVAL(INLET,P1,FIXFLU,WIN) COVAL(INLET,W1,ONLYMS,WIN);COVAL(INLET,TEMP,ONLYMS,TIN) COVAL(INLET,V1,ONLYMS,ZERO) COVAL(INLET,KE,ONLYMS,TKEIN);COVAL(INLET,EP,ONLYMS,EPIN) GROUP 16. Termination of iterations LITHYD=8 IF(TWOL) THEN + SELREF=F ENDIF REAL(MASIN);MASIN=RHO1*WIN*DIAM*DIAM/80. RESREF(P1)=1.E-12*MASIN/RHO1; RESREF(W1)=RESREF(P1)*RHO1*WIN RESREF(V1)=RESREF(W1); RESREF(KE)=RESREF(P1)*RHO1*TKEIN RESREF(TEMP)=RESREF(P1)*RHO1*TIN; RESREF(EP)=RESREF(P1)*RHO1*EPIN GROUP 17. Under-relaxation devices RELAX(W1,FALSDT,1.E3) RELAX(KE,FALSDT,1.E3); RELAX(EP,FALSDT,1.E3) GROUP 18. Limits on variables or increments to them VARMIN(W1)=1.E-10;VARMIN(KE)=1.E-10;VARMIN(EP)=1.E-10 GROUP 22. Monitor print-out IZMON=1;IYMON=NY-5;ITABL=2;IPLTL=30;NPLT=1;NPRMON=4 GROUP 23. Field print-out and plot control OUTPUT(LEN1,Y,N,N,Y,Y,Y);OUTPUT(ENUT,Y,N,N,Y,Y,Y) TSTSWP=-1;NZPRIN=50;NUMCLS=5 GROUP 24. Dumps for restarts