TEXT(2D 2-PHASE HILLS BUBBLE COLUMN TITLE DISPLAY The case considered is the bubble column studied experimentally by Hills [Instn.Chem.Engrs., Vol.52, p1, 1974], which has a diameter of 0.138m and a height of 1.37m. The column is initially filled with water, and air enters uniformly at the bottom with a superficial velocity of 0.038m/s. After about 25s steady-state conditions are obtained in which clockwise liquid circulation is observed, with upflow at the column centre and downflow at the outer wall. The task is to predict the gas holdup in the column, and to compare the predicted void-fraction and vertical liquid-velocity radial profiles at z=0.6m(i.e IZ=9) with the measurements. The calculation may be performed with one of 3 turbulence models, i.e. the Petersen SGS model, the Rice- Geary model, or a modified k-e model which accounts for bubble- induced turbulence production. The two-phase model accounts for interfacial drag, lift, pressure and virtual-mass forces. ENDDIS CHAR(CTURB) MESG( Enter the required turbulence model: MESG( SGS - Petersen subgrid-scale model MESG( RICE - Rice-Geary mixing-length model MESG( KE - k-e model (default) MESG( READVDU(CTURB,CHAR,KE) REAL(AREA,DIAMB,DIAMC,DTT,EMULIQ,EPIN,FLOWG,GRAVAC,PI) REAL(RADC,RGAS,RLIQ,RGINIT,STEN,TKEIN,VSLIPM,WSGAS,ZLENC) INTEGER(NT,TMODEL) BOOLEAN(LIFT,VMAS,INTP);LIFT=T;VMAS=T;INTP=T DIAMC=0.138;RADC=0.5*DIAMC;ZLENC=1.37;RGAS=0.14;RLIQ=1.-RGAS PI=3.14159;GRAVAC=-9.81;STEN=0.072;EMULIQ=1.E-3;RGINIT=1.E-4 WSGAS=0.038;DIAMB=7.61E-3;TKEIN=(0.05*WSGAS)**2 EPIN=0.1643*TKEIN**1.5/(0.1*RADC) GROUP 2. Transience; time-step specification ** The calculation should be run transient, and at least 500 time steps are required for the evolution of steady-flow conditions. STEADY=F DTT=0.05;NT=5;TLAST=DTT*NT;GRDPWR(T,NT,TLAST,1.0) GROUP 3. X-direction grid specification CARTES=F;XULAST=0.1;AREA=XULAST*0.5*RADC*RADC GROUP 4. Y-direction grid specification NY=10;GRDPWR(Y,NY,RADC,1.0) GROUP 5. Z-direction grid specification NZ=20;GRDPWR(Z,-NZ,ZLENC,1.4) GROUP 6. Body-fitted coordinates or grid distortion GROUP 7. Variables stored, solved & named ONEPHS=F;SOLVE(P1,V1,V2,W1,W2,R1,R2) SOLUTN(P1,Y,Y,Y,P,P,P) ** deactivate harmonic averaging SOLUTN(V1,P,P,P,P,P,N);SOLUTN(V2,P,P,P,P,P,N) SOLUTN(W1,P,P,P,P,P,N);SOLUTN(W2,P,P,P,P,P,N) SOLUTN(R1,P,P,P,P,P,N);SOLUTN(R2,P,P,P,P,P,N) STORE(VREL,CFIP,ENUT,LEN1,CD,REYN,WEB) GROUP 8. Terms (in differential equations) & devices GROUP 9. Properties of the medium (or media) PRT(R1)=0.5;PRT(R2)=0.5;RHO1=1.E3;RHO2=1.23 CASE :CTURB: OF WHEN SGS,3 + MESG(Petersen sgs turbulence model + TURMOD(SGSMOD);TMODEL=1 WHEN RICE,4 + MESG(Rice-Geary mixing-length turbulence model + TURMOD(MIXLEN-RICE);TMODEL=2 WHEN KE,2 + MESG(k-e turbulence model + TURMOD(KEMODL);TMODEL=3 + FIINIT(KE)=TKEIN;FIINIT(EP)=EPIN + PRT(R1)=0.75;PRT(R2)=0.75 ENDCASE ENUL=EMULIQ/RHO1 GROUP 10. Inter-phase-transfer processes and properties CFIPS=GRND7;CFIPD=4.0;VSLIPM=1.E-4;CFIPA=VSLIPM CFIPB=DIAMB;CFIPC=STEN;RLOLIM=1.E-3 IF(VMAS) THEN + CVM=GRND2;CVMA=0.5;STORE(VMSW,VMSV) ** penultimate argument activates spot value history + OUTPUT(VMSW,N,P,Y,P,N,P);OUTPUT(VMSV,N,P,Y,P,N,P) ENDIF IF(LIFT) THEN + CLIFT=GRND2;CLIFTA=-0.5 + INTSOR(LIFT,CLIFT,CLIFTA,RELAX,0.1) + OUTPUT(LISW,N,P,P,P,N,P);OUTPUT(LISV,N,P,P,P,N,P) ENDIF IF(INTP) THEN + CPIP=GRND2;CPIPA=0.25 + INTSOR(INTPL,CPIP,CPIPA,RELAX,0.1) + OUTPUT(IPSW,N,P,P,P,N,P);OUTPUT(IPSV,N,P,P,P,N,P) ENDIF GROUP 11. Initialization of variable or porosity fields FIINIT(R2)=RGINIT;FIINIT(R1)=1.0-FIINIT(R2);INIADD=F GROUP 12. Patchwise adjustment of terms GROUP 13. Boundary conditions and special sources ** Gas-phase mass-inflow boundary FLOWG=RHO2*WSGAS PATCH(IN,LOW,1,NX,1,NY,1,1,1,LSTEP) COVAL(IN,P2,FIXFLU,FLOWG);COVAL(IN,W2,ONLYMS,WSGAS) ** Gas-phase outflow boundary PATCH(OUTG,HIGH,1,NX,1,NY,NZ,NZ,1,LSTEP) COVAL(OUTG,P2,RHO2*1.E10,0.0) ** Liquid-phase 'pressure-relief' outflow cell PATCH(OUTL,HIGH,1,NX,NY,NY,NZ,NZ,1,LSTEP) COVAL(OUTL,P1,RHO1,0.0) ** Gravititional force relative to liquid phase PATCH(GRAVITY,PHASEM,1,NX,1,NY,1,NZ,1,LSTEP) COVAL(GRAVITY,W2,FIXFLU,GRAVAC*(1.-RHO1/RHO2)) ** Wall friction WALL(NWALL,NORTH,1,NX,NY,NY,1,NZ,1,LSTEP) ** Bubble-induced turbulence production IF(TMODEL.EQ.3) THEN + PATCH(KEDI,CELL,1,NX,1,NY,1,NZ,1,LSTEP);EL1A=0.01 + COVAL(KEDI,KE,FIXFLU,GRND3);COVAL(KEDI,EP,FIXFLU,GRND3) ENDIF GROUP 15. Termination of sweeps LSWEEP=100;TSTSWP=-10 GROUP 16. Termination of iterations SELREF=T;RESFAC=0.01 GROUP 17. Under-relaxation devices RELAX(V1,FALSDT,DTT);RELAX(V2,FALSDT,DTT) RELAX(W1,FALSDT,DTT);RELAX(W2,FALSDT,DTT) RELAX(R1,LINRLX,0.4);RELAX(R2,LINRLX,0.4) RELAX(CFIP,LINRLX,0.3) IF(TMODEL.EQ.3) THEN + RELAX(KE,LINRLX,0.3);RELAX(EP,LINRLX,0.3);KELIN=1 ENDIF GROUP 18. Limits on variables or increments to them VARMIN(R1)=1.E-12;VARMIN(R2)=1.E-12;LITER(P1)=30 GROUP 22. Spot-value print-out IYMON=1;IZMON=9 SPEDAT(SET,GXMONI,TRANSIENT,L,F) GROUP 23. Field print-out and plot control NPRINT=LSWEEP;NZPRIN=1;NYPRIN=1;IZPRF=11 NTPRIN=NT/4;NPLT=10 CSG1=H;IDISPA=NT/4 GROUP 24. Dumps for restarts