AUTOPLOT USE file phi 5 da 1 u2; da 1 uterm;screen msg 2nd-phase velocity & terminal velocity;col3 1;blb4 2 msg pressto continue pause cl;screen msg press to continue msg press e to END enduse TEXT(1D SETTLING OF PARTICLES UNDER GRAVITY TITLE DISPLAY The case considered is that of a particles falling through essentially stagnant air under gravity. The flow is steady, one dimensional and after a relatively short period of acceleration, the particles attain a uniform velocity under which the drag force balances the gravitational force. This velocity is called the terminal settling velocity, which is given by: Vset = [ 4.*{rho,p-rho,a}*g*diam,p/(3.*rho,a*Cd) ] ** 0.5 The density ratio is taken as 1000 and the particle Reynolds number as 2,000. The calculation may be performed in the x-, y- or z-direction with phase 1 as continuous (air) and phase 2 as dispersed (solid) or vice versa (CONPHS=2). The task is to calculate the terminal velocity of the particles. ENDDIS * CONPHS=1 selects 1st phase as the continuous ( gas ) phase and thus CFIPS=GRND7 * =2 selects 2nd phase as the continuous ( gas ) phase and thus CFIPS=GRND8 * VARLAM=T tests coding in GXCFIP when ENUL is variable BOOLEAN(VARLAM);INTEGER(CONPHS);VARLAM=T;CONPHS=1 * for 1dx calculation set: CH1=X;CH2=U1;CH3=U2 * for 1dy calculation set: CH1=Y;CH2=V1;CH3=V2 * for 1dz calculation set: CH1=Z;CH2=W1;CH3=W2 CHAR(CH1,CH2,CH3);CH1=X;CH2=U1;CH3=U2 CH1=Y;CH2=V1;CH3=V2 CH1=Z;CH2=W1;CH3=W2 REAL(XLEN,UGAS,UINP,UIN1,UIN2,R1IN,R2IN,REYP,DIAMP,DENRAT) REAL(USET,CD,RINP,VOLFP,FLOW1,FLOW2,RHOG,RHOS,ACON) REYP=2000;UGAS=1.E-3;UINP=1.E-3;DENRAT=1000.;ENULA=1.E-6 RINP=1.E-3;VOLFP=RINP*UINP;RHOG=1.0;RHOS=RHOG*DENRAT ** calculate expected particle settling velocity ACON=4.*(DENRAT-1.)*9.81/(3.*ENULA**2) CD=24.*(1.+.15*REYP**.687)/REYP+.42/(1.+4.25E4/(REYP**1.16)) DIAMP=(REYP*REYP*CD/ACON)**(1./3.);USET=REYP*ENULA/DIAMP cd uset diamp IF(CONPHS.EQ.1) THEN + UIN1=UGAS;UIN2=UINP;R2IN=RINP;R1IN=1-R2IN ELSE + UIN1=UINP;UIN2=UGAS;R1IN=RINP;R2IN=1-R1IN ENDIF GROUP 1. Run title and other preliminaries GROUP 2. Transience; time-step specification GROUP 3. X-direction grid specification XLEN=100.0;GRDPWR(:CH1:,20,XLEN,1.0) GROUP 4. Y-direction grid specification GROUP 5. Z-direction grid specification GROUP 6. Body-fitted coordinates or grid distortion GROUP 7. Variables stored, solved & named ONEPHS=F;SOLVE(P1,:CH2:,:CH3:,R1,R2) Activate storage for printout of interphase drag properties STORE(UTERM,REYN,VREL,CD,APRJ,CFIP,SIZE) GROUP 8. Terms (in differential equations) & devices GROUP 9. Properties of the medium (or media) IF(CONPHS.EQ.1) THEN + RHO1=RHOG;RHO2=RHOS ELSE + RHO2=RHOG;RHO1=RHOS ENDIF IF(VARLAM) THEN Use ENUL=ENULA+ENULB*TMP1 + STORE(TMP1);ENUL=LINTEM;ENULB=0.0;TMP1=CONST ELSE + ENUL=ENULA ENDIF GROUP 10. Inter-phase-transfer processes and properties IF(CONPHS.EQ.1) THEN + CFIPS=GRND7;VARMIN(R2)=1.E-10 ELSE + CFIPS=GRND8;VARMIN(R1)=1.E-10 ENDIF ** CFIPA = minimum slip velocity CFIPB = particle size CFIPA=1.E-3;CFIPB=DIAMP GROUP 11. Initialization of variable or porosity fields FIINIT(:CH2:)=UIN1;FIINIT(:CH3:)=UIN2 IF(CONPHS.EQ.1) THEN + FIINIT(R2)=VOLFP/USET;FIINIT(R1)=1.-FIINIT(R2) ELSE + FIINIT(R1)=VOLFP/USET;FIINIT(R2)=1.-FIINIT(R1) ENDIF FIINIT(UTERM)=USET GROUP 12. Unused GROUP 13. Boundary conditions and special sources FLOW1=RHO1*UIN1*R1IN;FLOW2=RHO2*UIN2*R2IN INLET(IN,CELL,$1,$1,$1,$1,$1,$1,1,1) VALUE(IN,P1,FLOW1);VALUE(IN,:CH2:,UIN1) VALUE(IN,P2,FLOW2);VALUE(IN,:CH3:,UIN2) OUTLET(OUT,CELL,%1,%1,%1,%1,%1,%1,1,1) ** estimate particle outflow velocity, and then use value so as to allow for slip in exit cell outflow IF(CONPHS.EQ.1) THEN + COVAL(OUT,P1,RHO1*UIN1*1.E2,0);COVAL(OUT,P2,RHO2*USET*1.E2,0) ELSE + COVAL(OUT,P1,RHO1*USET*1.E2,0);COVAL(OUT,P2,RHO2*UIN2*1.E2,0) ENDIF PATCH(GRAVITY,PHASEM,1,NX,1,NY,1,NZ,1,1) IF(CONPHS.EQ.1) THEN + COVAL(GRAVITY,:CH3:,FIXFLU,9.81*(1.-RHOG/RHOS)) ELSE + COVAL(GRAVITY,:CH2:,FIXFLU,9.81*(1.-RHOG/RHOS)) ENDIF GROUP 15. Termination of sweeps LSWEEP=100 RESREF(P1)=1.E-12*(FLOW1+FLOW2) RESREF(R1)=1.E-12*FLOW1;RESREF(R2)=1.E-12*FLOW2 RESREF(:CH2:)=RESREF(R1)*UIN1;RESREF(:CH3:)=RESREF(R2)*UIN2 GROUP 16. Termination of iterations GROUP 17. Under-relaxation devices REAL(DTF);DTF=3.*XLEN/USET/N:CH1: RELAX(R1,LINRLX,0.5);RELAX(R2,LINRLX,0.5) RELAX(:CH2:,FALSDT,DTF);RELAX(:CH3:,FALSDT,DTF) GROUP 18. Limits on variables or increments to them GROUP 19. Data communicated by satellite to GROUND GROUP 20. Preliminary print-out GROUP 21. Print-out of variables NXPRIN=1;NYPRIN=1;NZPRIN=1 GROUP 22. Spot-value print-out IF(:CH1:.EQ.X) THEN + IXMON=NX/2;IZMON=1;IYMON=1 ELSE + IZMON=NZ/2;IXMON=1;IYMON=1 ENDIF IF(:CH1:.EQ.Y) THEN + IYMON=NY/2;IXMON=1;IZMON=1 ENDIF TSTSWP=-1 GROUP 23. Field print-out and plot control GROUP 24. Dumps for restarts