TEXT(1D VERTICAL PNEUMATIC CONVEYING TITLE DISPLAY The problem considered is 1D vertical pneumatic conveying of solid particles in a pipe, as considered experimentally by Hariu and Molstad ( Ind.Eng.Chem, Vol.41,No.6, pp1148,1949 ). The solids mass inflow rate is 2.39g/s and the inlet gas superficial velocity is 5.2m/s. The pipe diameter is 13.5mm and the height of the riser is 1.368m. The particles are 503 microns in diameter and the solids density is 2643kg/m**3. The inlet solids volume fraction is estimated from the measured solids holdup of 0.0256g. The calculations employ the built-in particle- fluidisation drag model (CFIPD=7.), which for these void fractions ( i.e. > 0.8 ) uses a modified spherical-particle drag correlation suitable for pneumatic conveying. The task is to predict the gas and solids velocities, the voidage, the pressure drop and the solids hold-up. The PHOENICS predictions show fairly good agreement with the experimental data, as follows: pressure drop ( PHOENICS = 217 N/m**2 Data = 200 N/m**2 ); solids hold-up ( PHOENICS = 2.36g Data = 2.56g ). ENDDIS The solids holdup is calculated by summing the total mass of solids in the riser; this is achieved from the Q1 by solving for C2 and then introducing a PHASEM patch named HOLDUP for which CO=FIXFLU & VAL=1.0. The net-source printout near the end of the RESULT file will then print the solids holdup in kg. * CFIPD=7. selects the particle-fluidisation drag correlation REAL(CD,REYD,XLEN,UING,UINP,REYP,DIAMP,AREAD,MSOLID,FRIC) REAL(DIAMD,PI,UTERM,RING,RINP,FLOWG,FLOWP,dens,RHOG,DELRHO) XLEN=1.368;RHOG=1.23;dens=2643.0;PI=3.14159;DIAMD=0.0135; FLOWP=2.39E-3;UING=5.2;DELRHO=dens-RHOG;DIAMP=503.E-6 ENULA=1.8E-5/RHOG;AREAD=PI*DIAMD*DIAMD/4. ** estimate terminal velocity of particles REYP=UING*DIAMP/ENULA CD=24.*(1.+.15*REYP**.687)/REYP+.42/(1.+4.25E4/(REYP**1.16)) UTERM=(4.*9.81*DELRHO*DIAMP/(3.*RHOG*CD))**0.5 uterm ** estimate inlet solids volume fraction from experimental value of solids holdup, MSOLID MSOLID=2.56E-3;RINP=MSOLID/(dens*AREAD*XLEN) ** estimate inlet solids velocity and then gas inlet velocity and volume fraction UINP=FLOWP/(dens*AREAD*RINP);RING=1.-RINP;UING=UING/RING FLOWG=RHOG*RING*UING*AREAD GROUP 1. Run title and other preliminaries GROUP 2. Transience; time-step specification GROUP 3. X-direction grid specification YVLAST=AREAD;GRDPWR(X,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 ** C2 solved merely to avoid introducing ground coding to calculate solids holdup ONEPHS=F;SOLVE(P1,U1,U2,R1,R2,C2) Activate storage for printout of interphase drag properties STORE(REYN,VREL,CFIP,SIZE) GROUP 8. Terms (in differential equations) & devices GROUP 9. Properties of the medium (or media) RHO1=RHOG;RHO2=dens;ENUL=ENULA GROUP 10. Inter-phase-transfer processes and properties CFIPS=GRND7;VARMIN(R2)=1.E-10 ** CFIPA = minimum slip velocity CFIPB = particle size CFIPA=1.E-4;CFIPB=DIAMP;CFIPD=7. GROUP 11. Initialization of variable or porosity fields FIINIT(U1)=UING;FIINIT(U2)=UINP;FIINIT(R2)=RINP;FIINIT(R1)=RING GROUP 12. Unused GROUP 13. Boundary conditions and special sources INLET(IN,CELL,$1,$1,$1,$1,$1,$1,1,1) VALUE(IN,P1,FLOWG);VALUE(IN,U1,UING) VALUE(IN,P2,FLOWP);VALUE(IN,U2,UINP) OUTLET(OUT,CELL,%1,%1,%1,%1,%1,%1,1,1) ** use expected outflow velocities to allow for slip in the exit-cell outflow COVAL(OUT,P1,RHO1*UING*1.E2,0) COVAL(OUT,P2,RHO2*UINP*1.E2,0) REYD=UING*DIAMD/ENULA;FRIC=0.316/REYD**0.25 ** gas-phase wall friction PATCH(GFRIC,VOLUME,1,NX,1,NY,1,NZ,1,1) COVAL(GFRIC,U1,-0.5*RHO1*FRIC/DIAMD,0.0) ** gravity force PATCH(GRAVITY,PHASEM,1,NX,1,NY,1,NZ,1,1) COVAL(GRAVITY,U2,FIXFLU,-9.81*(1.-RHOG/dens)) ** introduce C2 patch which will compute solids holdup and print in RESULT file in net-source printout PATCH(HOLDUP,PHASEM,1,NX,1,NY,1,NZ,1,1) COVAL(HOLDUP,C2,FIXFLU,1.0) GROUP 15. Termination of sweeps LSWEEP=100 RESREF(P1)=1.E-12*(FLOWG+FLOWP) RESREF(R1)=1.E-12*FLOWG;RESREF(R2)=1.E-12*FLOWP RESREF(U1)=RESREF(R1)*UING;RESREF(U2)=RESREF(R2)*UINP GROUP 16. Termination of iterations GROUP 17. Under-relaxation devices REAL(DTF);DTF=XLEN/UING/NX RELAX(R1,LINRLX,0.5);RELAX(R2,LINRLX,0.5) RELAX(U1,FALSDT,DTF);RELAX(U2,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 OUTPUT(C2,N,N,N,N,N,N) OUTPUT(CFIP,P,P,P,P,Y,P);NXPRIN=1;NYPRIN=1;NZPRIN=1 GROUP 22. Spot-value print-out IXMON=NX/2;TSTSWP=-1 GROUP 23. Field print-out and plot control GROUP 24. Dumps for restarts