GROUP 1. Run title and other preliminaries TEXT(CK KE_1D PIPE POWER-LAW FLUID :T304 TITLE DISPLAY The problem concerns the steady fully-developed turbulent flow of a power-law pseudo-plastic non-Newtonian fluid. The apparent viscosity of such a fluid is given by: enul = K*[(dw/dy)**(n-1.)] /rho, so that enul decreases with increasing shear rate. Here, K is the fluid consistency index and n the flow-behaviour index. The turbulence may be simulated by means of one of the following low-Reynolds-number two-equation models: the 2-layer, Chen-Kim or Lam-Bremhorst k-e models, or the k-omega model. ENDDIS AUTOPLOT USE FILE PHI 5 D 1 W1;COL3 1 PAUSE CL;D 1 KE;COL6 1 PAUSE CL;D 1 ENUT;D 1 VISL;COL6 1;COL9 2 PAUSE CL;D 1 EP;COLF 1 PAUSE ENDUSE INTEGER(TMODEL);CHAR(CTURB,TLSC) REAL(RIN,DIN,WIN,AIN,DPDZ,FLOWIN,REYST,REYPLS,AN,REYFAC) REAL(FRIC,A1,A2,A3,AA,BB,GR,EPSPLS,TKEIN,EPSIN,US,GYPLUS) REAL(GWPLUS,KFAC,RECN,TMN,YPLSW,DELT1,DELY) INTEGER(JJM1,JJM) RIN=0.1;DIN=2.*RIN;WIN=1.0;AIN=RIN*RIN/2. MESG(Enter Reynolds number - default 1.158E4 READVDU(REYST,REAL,1.158E4) MESG(Enter Power Index - default 0.525 READVDU(AN,REAL,0.525) RECN=1./AN;TMN=2.-AN REYFAC=8.**(AN-1.); REYFAC=REYFAC*(0.25/AN+0.75)**AN REYPLS=REYST*REYFAC ENULA=WIN**(2.0-AN)*DIN**AN/REYPLS ENULB=AN FRIC=1./(1.82*LOG10(REYST)-1.64)**2 DPDZ=FRIC*RHO1*WIN*WIN/(2.*DIN);US=WIN*(FRIC/8.)**0.5 A1=4./AN**0.75;A2=0.4/AN**1.2;A3=1.-0.5*AN DO JJ=1,20 + BB=FRIC**A3;BB=REYST*BB;AA=LOG10(BB) + BB=A1*AA-A2;FRIC=1./(BB*BB) ENDDO FRIC DPDZ=FRIC*2.*RHO1*WIN*WIN/DIN;US=WIN*(FRIC/2.)**0.5 DPDZ ** estimate initial values from K+=2 & EP+=1./(ak*Y+) EPSPLS=1./(0.41*100.); RIN=0.5*DIN TKEIN=2.*US*US;EPSIN=EPSPLS*US**4/ENULA MESG( Enter the required turbulence model: MESG( LAMB - Low-Re Lam-Brem. k-e model MESG( CHEN - Low-Re Chen-Kim k-e model MESG( TWOL - Low-Re 2-layer k-e model MESG( KO - Low-Re k-omega model (default) MESG( READVDU(CTURB,CHAR,CHEN) CASE :CTURB: OF WHEN LAMB,4 + TEXT(LB KE_1D PIPE POWER-LAW FLUID :T304 + MESG(Low-Re Lam-Bem. k-e turbulence model + TMODEL=1;TLSC=EP WHEN CHEN,4 + MESG(Low-Re Chen-Kim k-e turbulence model + TMODEL=2;TLSC=EP WHEN TWOL,4 + TEXT(2L KE_1D PIPE POWER-LAW FLUID :T304 + MESG(Low-Re 2-layer k-e turbulence model + SELREF=F;TMODEL=3;TLSC=EP WHEN KO,2 + TEXT(KO KE_1D PIPE POWER-LAW FLUID :T304 + MESG(Low-Re k-omega turbulence model + TMODEL=4;TLSC=OMEG + STORE(EP);EPSIN=EPSIN/(0.09*TKEIN) ENDCASE GROUP 2. TRANSIENCE; TIME-STEP SPECIFICATION CARTES=F GROUP 4. Y-direction grid specification NY=50;GRDPWR(Y,NY,RIN,0.8) ** define first dely from wall MESG(Enter Grid KFAC - default 1.05 READVDU(KFAC,REAL,1.05) YPLSW=1.0 DELT1=YPLSW*ENULA/(US**TMN);DELT1=(DELT1)**RECN;DELY=DELT1/RIN ** 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=RIN GROUP 5. Z-direction grid specification GROUP 7. Variables stored, solved & named SOLVE(W1);STORE(VISL) CASE (TMODEL) OF WHEN 1 + TURMOD(KEMODL-LOWRE);KELIN=3;STORE(REYN,FONE,FMU,FTWO) WHEN 2 + TURMOD(KECHEN-LOWRE);KELIN=3;STORE(FMU,REYN,FONE) WHEN 3 + TURMOD(KEMODL-2L);KELIN=3;STORE(FMU,FTWO,REYN,REYT) WHEN 4 + TURMOD(KOMODL-LOWRE);STORE(FMU,REYT,FONE,FTWO) ENDCASE STORE(ENUT,GEN1) GROUP 8. Terms (in differential equations) & devices GROUP 9. Properties of the medium (or media) ENULA=WIN**(2.0-AN)*DIN**AN/REYPLS ENULB=AN ** enul = enula*(dwdy)*[0.5*(enulb-1)] ENUL=STRAIN GROUP 11. Initialization of variable or porosity fields FIINIT(:TLSC:)=EPSIN;FIINIT(KE)=TKEIN REAL(YPLS1);YPLS1=11.5**AN ** use log-law for initial W profile DO JJ=1,NY +PATCH(IN:JJ:,INIVAL,1,NX,JJ,JJ,1,NZ,1,1) +GR=0.5*YFRAC(JJ) IF(JJ.NE.1) THEN + JJM1=JJ-1 + GR=YFRAC(JJM1)+0.5*(YFRAC(JJ)-YFRAC(JJM1)) ENDIF +GYPLUS=YVLAST*(1.-GR)*US/ENULA +GWPLUS=LOG(GYPLUS)*RECN/0.41+5.25*RECN IF(GYPLUS.LE.YPLS1) THEN + GWPLUS=GYPLUS**RECN ENDIF +INIT(IN:JJ:,W1,ZERO,GWPLUS*US) ENDDO GROUP 13. Boundary conditions and special sources WALL(TOPW,NORTH,1,NX,NY,NY,1,NZ,1,1) ** activate fully-developed-flow pressure adjustment FLOWIN=RHO1*WIN*AIN FDSOLV(FLOW,FLOWIN) GROUP 15. Termination of sweeps LSWEEP=120;LITHYD=5 GROUP 16. Termination of iterations GROUP 17. Under-relaxation devices REAL(DTF);DTF=0.1*ZWLAST/WIN RELAX(W1,FALSDT,DTF) IF(TMODEL.EQ.4) THEN + RELAX(W1,FALSDT,DTF) + RELAX(KE,FALSDT,DTF); RELAX(OMEG,FALSDT,DTF) ELSE + RELAX(KE,LINRLX,0.3); RELAX(EP,LINRLX,0.7) ENDIF GROUP 22. Spot-value print-out IYMON=NY-4;TSTSWP=-1 GROUP 23. Field print-out and plot control ITABL=3;NPLT=1;NYPRIN=1;NZPRIN=1 GROUP 24. Dumps for restarts WALPRN=T;OUTPUT(ENUT,Y,N,Y,N,Y,N)