AUTOPLOT USE file phi 5 da 1 u2; da 1 uterm screen col3 1;blb4 2;scale y 0 .2;redr msg 2nd-phase velocity msg blue PHOENICS + analytical msg pressto continue pause cl screen msg press to continue msg press e to END enduse TEXT(1D RISING OF AIR BUBBLES IN WATER TITLE DISPLAY The case considered is that of a cluod of air bubbles rising through essentially stagnant water. The flow is 1D steady and after a relatively short period of acceleration, the bubbles attain a uniform velocity under which the drag force balances the buoyancy force. This velocity is called the terminal rise velocity, which is given by: Vrise = [ 4.*{rho,l-rho,b}*g*diam,b/(3.*rho,l*Cd) ] ** 0.5 The calculation may employ any one of three built-in bubble-drag correlations, as selected by CFIPD=4., 5. OR 6. with CFIPS=GRND7. CFIPD=4. allows for distortion of the bubble shape; CFIPD=5. assumes spherical bubbles in dirty water; and CFIPD=6. assumes ellipsoidal bubbles in clean water. The calculation may be performed in the x-, y- or z-direction with phase 1 as continuous (water) and phase 2 as dispersed (air) or vice versa (CONPHS=2). The task is to calculate the terminal rise velocity of the bubbles. 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 CFIPD=4. * reg1, reg2, etc identify each of the regions of the CFIPD=4. interphase drag correlation; for each calculation one region is selected to test the appropriate coding in GXFIPS. BOOLEAN(REG1,REG2,REG2B,REG4,REG5) REG1=F;REG2=T;REG2B=F;REG4=F;REG5=F * 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,ULIQ,UINB,UIN1,UIN2,R1IN,R2IN,REYB,DIAMB,DENRAT) REAL(URISE,CD,RINB,VOLFB,FLOW1,FLOW2,RHOL,RHOG,ENULIQ) REAL(WEBER,WEBMAX,EOTVOS,MORTON,STEN,DELRHO,ACON) ENULIQ=1.E-6;ULIQ=1.E-5;UINB=1.E-3;DENRAT=1000. RINB=0.01;VOLFB=RINB*UINB;RHOG=1.0;RHOL=DENRAT*RHOG STEN=0.072;DELRHO=(RHOL-RHOG) ACON=4.*9.81*DELRHO/(3.*RHOL*ENULIQ**2) ** calculate expected particle settling velocity IF(CFIPD.EQ.4.) THEN IF(REG1) THEN + REYB=0.2;CD=16./REYB + DIAMB=(REYB*REYB*CD/ACON)**(1./3.);URISE=REYB*ENULIQ/DIAMB ENDIF IF(REG2) THEN + REYB=50.;CD=20.68/REYB**0.643 + DIAMB=(REYB*REYB*CD/ACON)**(1./3.);URISE=REYB*ENULIQ/DIAMB ENDIF IF(REG2B) THEN + REYB=150.;CD=6.3/REYB**.385 + DIAMB=(REYB*REYB*CD/ACON)**(1./3.);URISE=REYB*ENULIQ/DIAMB ENDIF IF(REG4) THEN + WEBER=4.0;CD=WEBER/3. + DIAMB=((0.75*WEBER*STEN*CD)/(9.81*DELRHO))**0.5 + URISE=((WEBER*STEN)/(RHOL*DIAMB))**0.5 + REYB =URISE*DIAMB/ENULIQ ENDIF IF(REG5) THEN + WEBER=10.0;CD=8./3. + DIAMB=((0.75*WEBER*STEN*CD)/(9.81*DELRHO))**0.5 + URISE=((WEBER*STEN)/(RHOL*DIAMB))**0.5 + REYB =URISE*DIAMB/ENULIQ ENDIF WEBER=RHOL*URISE**2*DIAMB/STEN;WEBMAX=2065.1/WEBER**2.6 ENDIF IF(CFIPD.EQ.5.) THEN + REYB=150.;CD=6.3/REYB**.385 + DIAMB=(REYB*REYB*CD/ACON)**(1./3.);URISE=REYB*ENULIQ/DIAMB ENDIF IF(CFIPD.EQ.6.) THEN + EOTVOS=10.;CD=0.622/(1./EOTVOS+0.235*RHOL/DELRHO) + DIAMB=((STEN*EOTVOS)/(9.81*DELRHO))**0.5 + URISE=(4.*DELRHO*9.81*DIAMB/(3.*RHOL*CD))**0.5 + REYB=URISE*DIAMB/ENULIQ ENDIF reyb cd diamb urise weber webmax EOTVOS=9.81*(RHOL-RHOG)*DIAMB**2/STEN MORTON=9.81*(RHOL*ENULIQ)**4*(RHOL-RHOG)/(RHOL**2*STEN**3) eotvos morton IF(CONPHS.EQ.1) THEN + UIN1=ULIQ;UIN2=UINB;R2IN=RINB;R1IN=1-R2IN ELSE + UIN1=UINB;UIN2=ULIQ;R1IN=RINB;R2IN=1-R1IN ENDIF GROUP 1. Run title and other preliminaries GROUP 2. Transience; time-step specification GROUP 3. X-direction grid specification XLEN=1.0;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) IF(CFIPD.EQ.6) THEN + STORE(EOTV) ELSE + STORE(WEB) ENDIF GROUP 8. Terms (in differential equations) & devices GROUP 9. Properties of the medium (or media) IF(CONPHS.EQ.1) THEN + RHO1=RHOL;RHO2=RHOG ELSE + RHO2=RHOL;RHO1=RHOG ENDIF IF(VARLAM) THEN Use ENUL=ENULA+ENULB*TMP1 + STORE(TMP1);ENUL=LINTEM;ENULA=1.E-6;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 = bubble size ** CFIPC = surface tension for gas-liquid CFIPD set above CFIPA=1.E-4;CFIPB=DIAMB;CFIPC=STEN GROUP 11. Initialization of variable or porosity fields IF(CONPHS.EQ.1) THEN + FIINIT(U1)=UIN1;FIINIT(U2)=URISE + FIINIT(R2)=VOLFB/URISE;FIINIT(R1)=1.-FIINIT(R2) ELSE + FIINIT(U2)=UIN2;FIINIT(U1)=URISE + FIINIT(R1)=VOLFB/URISE;FIINIT(R2)=1.-FIINIT(R1) ENDIF FIINIT(UTERM)=URISE 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*URISE*1.E2,0) ELSE + COVAL(OUT,P1,RHO1*URISE*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.-RHOL/RHOG)) ELSE + COVAL(GRAVITY,:CH2:,FIXFLU,-9.81*(1.-DENRAT)) 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=0.5*XLEN/URISE/N:CH1: RELAX(R1,LINRLX,0.3);RELAX(R2,LINRLX,0.3) RELAX(:CH2:,FALSDT,DTF);RELAX(:CH3:,FALSDT,DTF) RELAX(CFIP,LINRLX,0.4) 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 OUTPUT(CFIP,P,P,P,P,Y,P);NXPRIN=1;NYPRIN=1;NZPRIN=1 OUTPUT(CD,P,P,P,P,Y,P) 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