TEXT(ASM 1D SETTLING OF PARTICLES P112 TITLE DISPLAY The case considered is that of solid particles falling through stagnant liquid under gravity. A 1d unsteady simulation is performed with the algebraic slip model (asm), in which particles are released and allowed to fall under gravity. The particles eventually attain a uniform terminal settling velocity, under which the drag force balances the gravitational force. In the present case, the task is to calculate this velocity for which the theroretical value is 0.012m/s. The calculation may be performed in the x-, y- or z-direction with or without the liquid hydrostatic pressure included the solved-for pressure P1. ENDDIS PHOTON USE autoplot file phi 5 da 1 pt1; col3 1; level x .1469 key 0.62162E+03 0.17847E+04 a 0.17751E+04 0.17847E+04 l 0.17751E+04 0.17847E+04 x text 1 particles fall 0.147m in 13.26s 0.14610E+04 0.14330E+04 CR text 1 giving a settling velocity of 0.011m/s. 0.14610E+04 0.12962E+04 CR key 0.11599E+04 0.17456E+04 a 0.15637E+04 0.14069E+04 l 0.15637E+04 0.14069E+04 x text 1 PT1 0.29092E+03 0.25533E+04 C DIST(m) 0.31337E+04 0.15633E+03 c Theoretical terminal velocity = 0.012m/s 0.14610E+04 0.10878E+04 CR redr msg pressto continue msg press e to END ENDUSE BOOLEAN(BUOYANT) MESG(Extract hydrostatic pressure from P1? (default N)) READVDU(ANS,CHAR,N) IF(:ANS:.EQ.Y) THEN + MESG(Extract hydrostatic pressure from P1 + MESG(Gravity represented as a buoyancy force) + BUOYANT=T ELSE + MESG(Include hydrostatic pressure in P1 + MESG(Gravity represented directly + BUOYANT=F ENDIF CHAR(CH1,CH2) MESG( Enter the required 1d direction: MESG( X (default) MESG( Y MESG( Z MESG( READVDU(CH1,CHAR,X) CASE :CH1: OF WHEN X,1 + MESG(1DX simulation + CH2=U1 WHEN Y,1 + MESG(1DY simulation + CH2=V1 WHEN Z,1 + MESG(1DZ simulation + CH2=W1 ENDCASE REAL(XLEN,UGAS,UINP,UIN1,UIN2,R1IN,R2IN,REYP,DIAMP,DENRAT) REAL(USET,CD,RINP,VOLFP,FLOW1,FLOW2,RHOL,RHOS,ACON,RHOM) REYP=1.0; UGAS=1.E-3; UINP=1.E-3; ENULA=1.E-6 RINP=1.E-3; VOLFP=RINP*UINP; RHOL=1.027E3; RHOS=3.3E3 DENRAT=RHOS/RHOL RHOM=RHOL*(1.-RINP)+RHOS*RINP ** calculate expected particle settling velocity DIAMP=1.E-4 USET=DIAMP*DIAMP*(DENRAT-1.)*9.81/(18.*ENULA) REYP=USET*DIAMP/ENULA reyp XLEN=0.4 REAL(TIME); TIME=0.4*XLEN/USET CD=24./REYP cd uset diamp GROUP 1. Run title and other preliminaries GROUP 2. Transience; time-step specification STEADY=F GRDPWR(T,10,TIME,1.0) GROUP 3. X-direction grid specification GRDPWR(:CH1:,40,XLEN,1.0) GROUP 7. Variables stored, solved & named SOLVE(P1,:CH2:) SOLUTN(P1,Y,Y,Y,P,P,P) NAME(C1)=PT0; NAME(C2)=PT1 SOLVE(PT0,PT1); SOLVE(VFOL); STORE(DEN1,VISL,UTERM) GROUP 8. Terms (in differential equations) & devices GALA=T; TERMS(VFOL,N,N,N,N,P,P) GROUP 9. Properties of the medium (or media) RHO1=GRND; RHO2=RHOL; ENUL=GRND PHINT(PT1)=RHOS; CINT(PT1)=DIAMP PRNDTL(PT0)=ENULA; PRNDTL(PT1)=1.35E-6 GROUP 11. Initialization of variable or porosity fields FIINIT(PT0) = 1.000E+00 ; FIINIT(PT1 ) = 0.000E+00 PATCH(PT_INIT,INIVAL,1,1,1,1,1,1,1,1) INIT(PT_INIT ,PT0,ONLYMS,9.000E-01) INIT(PT_INIT ,PT1,ONLYMS,1.000E-01) GROUP 13. Boundary conditions and special sources PATCH(ASM_OUT,CELL,%1,%1,%1,%1,%1,%1,1,LSTEP) COVAL(ASM_OUT,P1,1.E3,0.0) PATCH(BUOYANCY,PHASEM,1,NX,1,NY,1,NZ,1,LSTEP) IF(BUOYANT) THEN + COVAL(BUOYANCY,:CH2:,FIXFLU,GRND2) + BUOYD=RHOL ELSE + COVAL(BUOYANCY,:CH2:,FIXFLU,GRND1) ENDIF IF(:CH1:.EQ.X) THEN + BUOYA=9.81 ENDIF IF(:CH1:.EQ.Y) THEN BUOYB=9.81 ENDIF IF(:CH1:.EQ.Z) THEN BUOYC=9.81 ENDIF GROUP 15. Termination of sweeps RESFAC=1.E-8 GROUP 16. Termination of iterations LITER(PT0)=2; LITER(PT1)=5 ENDIT(PT0)=1.E-8; ENDIT(PT1)=1.E-5 GROUP 17. Under-relaxation devices REAL(DTF); DTF=3.*XLEN/USET/N:CH1: + RELAX(PT0,LINRLX,0.3); RELAX(PT1,LINRLX,0.3) IF(:CH1:.EQ.Z) THEN + LSWEEP=120 + RELAX(:CH2:,FALSDT,DTF/50.) ELSE + LSWEEP=100 + RELAX(:CH2:,FALSDT,DTF) ENDIF RELAX(DEN1,FALSDT,0.5) GROUP 19. Data communicated by satellite to GROUND ASLP=T SPEDAT(SET,GXMONI,TRANSIENT,L,F) 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 24. Dumps for restarts DISTIL=T IF(BUOYANT) THEN + EX(P1 )=8.112E+00 ELSE + EX(P1 )=1.973E+03 ENDIF EX(PT0 )=9.978E-01; EX(DEN1)=1.032E+03 EX(U1 )=3.487E-12; EX(PT1 )=2.500E-03 EX(UTER)=1.000E-10; EX(VISL)=1.001E-06 EX(VFOL)=1.000E-10