GROUP 1. Run title and other preliminaries TEXT(VAN DRIEST_1D DEVELOPED PIPE FLOW :T201 TITLE DISPLAY The case considered is the one-dimensional solution of fully- developed turbulent flow in a circular pipe at a Reynolds number of 1.E5. The turbulence is simulated by use of the Prandtl mixing length model with Nikuradse's prescription of the mixing length. The calculation integrates down to the wall by using van Driest's viscous- damping extension to the mixing length. The solution is performed by use of the single-slab solver with a prescribed pressure drop. A non-uniform grid is employed 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. The calculations yield a friction factor of f=0.018 which is in excellent agreement with the experimental value. ENDDIS The following AUTOPLOT use file produces two plots; the first is the axial velocity profile; and the second is the turbulent viscosity profile. AUTOPLOT USE file phi 5 da 1 w1;col3 1 msg Velocity (W1) profile msg Press RETURN to continue pause clear;da 1 enut col3 1 msg Press e to END ENDUSE BOOLEAN(VARLAM);VARLAM=F REAL(DIAM,WIN,REY,MIXL,FRIC,DPDZ,MASIN,DTF) REAL(DELT1,DELT2,DELT3,US) DIAM=0.1;WIN=1.0; REY=1.E5;FRIC=1./(1.82*LOG10(REY)-1.64)**2 REY FRIC DPDZ=FRIC*RHO1*WIN*WIN/(2.*DIAM);US=WIN*(FRIC/8.)**0.5 US GROUP 3. X-direction grid specification CARTES=F;XULAST=0.1 GROUP 4. Y-direction grid specification ENULA=WIN*DIAM/REY ** define first dely from wall and the grid-expansion factor Kfac which defines a constant ratio of lengths of two adjacent cells. DELT1=1.*ENULA/US REAL(KFAC,DELY);KFAC=1.1;DELY=DELT1/(0.5*DIAM) ** calculate NY from dely & Kfac REAL(AA) 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;INTEGER(JJM) DO JJ=NY,2,-1 + JJM=JJ-1 + YFRAC(JJM)=YFRAC(JJ)-DELY + DELY=KFAC*DELY ENDDO YVLAST=0.5*DIAM GROUP 5. Z-direction grid specification ZWLAST=0.1*DIAM GROUP 7. Variables stored, solved & named SOLVE(W1);STORE(ENUT,LEN1) GROUP 8. Terms (in differential equations) & devices TERMS(W1,N,N,P,P,P,P) GROUP 9. Properties of the medium (or media) ENUL=ENULA;ENUT=MIXLEN;EL1=NIKURPIP;GENK=T EL1A=0.14*YVLAST;EL1B=-0.08/YVLAST;EL1C=-0.06/YVLAST**3 ** activate van Driest correction to the mixing length IENUTA=5 ** test for ground-set enul IF(VARLAM) THEN + TMP1=CONST;TMP1A=0.0;ENUL=LINTEM ENDIF GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WIN GROUP 13. Boundary conditions and special sources WALL(WALLN,NORTH,1,1,NY,NY,1,NZ,1,1) PATCH(PFORW,VOLUME,1,1,1,NY,1,NZ,1,1);COVAL(PFORW,W1,FIXFLU,DPDZ) GROUP 15. Termination of sweeps LSWEEP=40;TSTSWP=-1;LITHYD=6 GROUP 16. Termination of iterations MASIN=RHO1*WIN*DIAM*DIAM/80.; RESREF(W1)=1.E-12*MASIN*WIN GROUP 17. Under-relaxation devices DTF=10.*ZWLAST/WIN;VARMIN(W1)=1.E-10;TSTSWP=-1 GROUP 22. Spot-value print-out IYMON=NY-2;NPLT=5;NZPRIN=1;NYPRIN=4;IYPRF=1 GROUP 24. Dumps for restarts RELAX(W1,FALSDT,DTF);WALPRN=T