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