TALK=T;RUN( 1, 1) ************************************************************ Q1 created by VDI menu, Version 2020, Date 13/01/21 CPVNAM=VDI; SPPNAM=Core ************************************************************ Echo DISPLAY / USE settings PHOTON USE AUTOPLOT file phida 3 cl msg ELLIS-FLUID LAMINAR FLOW msg Reynolds number = 2.75 msg Pressure(P1) profile msg Blue line --- PHOENICS solution msg crosses --- analytical solution da 1 p1 y 1;da 1 pa y 1 col3 1;blb4 2 redr pause msg pressto continue clear msg Velocity (W1) profile da 1 w1 z 35;da 1 wa z 35 col3 1;blb4 2 pause msg press to end pause end END_USE ************************************************************ IRUNN = 1 ;LIBREF = 106 ************************************************************ Group 1. Run Title TEXT(106 2d pipe flow - Ellis fluid ) ************************************************************ Echo save-block settings for Group 1 save1begin This case concerns the steady laminar flow of an Ellis non-Newtonian fluid in a circular pipe. The apparent viscosity of such a fluid is given by: emu = emu0/(1.+(tau/tau,1/2)^(alfa-1)) where emu0 is the low-shear viscosity, tau is the shear stress, tsu,1/2 is the shear stress at which emu=0.5*emu0 and alfa is a flow-behaviour index related to the power-law- fluid index n by alfa= 1=n. The shear stress tau = emu*G where G is the mean strain rate. The Ellis model has seen extensive use for modelling the rheologies of a wide range of polymeric solutions. Analytical solutions for the laminar flow of Ellis fluids in circular pipes have been reported by: A.H.P.Skelland, Non-Newtonian Flow and Heat Transfer, p110, p119-121, John Wiley, (1967). The bulk inlet velocity is 10m/s and the fluid density is 1 kg/m^3. The pipe diameter and length are 0.05m and 0.5m, respectively; and the rheology parameters are set to: emu0=0.185 Pa.s; alfa=2.42 and tau,1/2 = 1025 N/m^2. The flow Reynolds number based on emu0 is 2.75. The task is to predict the pressure drop and fully-developed axial-velocity profile for a given Reynolds number, and then compare the results with the analytical solutions. The inform facility is used to compute the analytical profiles of pressure and velocity, and the solutions are stored in PA and WA, respectively. save1end ************************************************************ Group 2. Transience STEADY = T ************************************************************ Groups 3, 4, 5 Grid Information * Overall number of cells, RSET(M,NX,NY,NZ,tolerance) RSET(M,1,20,40,8.333333E-05) * Cylindrical-polar grid CARTES=F ************************************************************ Group 6. Body-Fitted coordinates ************************************************************ Group 7. Variables: STOREd,SOLVEd,NAMEd * Non-default variable names NAME(142)=WDIS ;NAME(143)=SRM1 NAME(144)=STRS ;NAME(146)=BTAU NAME(147)=PA ;NAME(148)=WA NAME(149)=GEN1 ;NAME(150)=VISL * Solved variables list SOLVE(P1,V1,W1) * Stored variables list STORE(VISL,GEN1,WA,PA,BTAU,STRS,SRM1,WDIS) * Additional solver options SOLUTN(P1,Y,Y,Y,N,N,Y) SOLUTN(V1,Y,Y,Y,N,N,Y) SOLUTN(W1,Y,Y,Y,N,N,Y) ************************************************************ Echo save-block settings for Group 7 save7begin STORE(SRM1) ! = (GEN1)^0.5 save7end ************************************************************ Group 8. Terms & Devices ADDDIF = T NEWENL = T ************************************************************ Group 9. Properties RHO1 =1. ENUL = GRND4 ENULA =0.185 ;ENULB =2.4 ;ENULC =1025. CP1 =1. DISWAL ENUT =1.0E-10 ************************************************************ Echo save-block settings for Group 9 save9begin REAL(RIN,DIN,WIN,DPDZ,REY,BETA,ZETA,QIN,AIN,PI) REAL(PHI0,PHI1,ALFA,TAUHLF,EMUA,EMU0) REAL(ACON,BCON,CCON,FX,FXP,TAUW,TAUP) ENUL=GRND4; IENULA=9 ! Ellis rheology model ENULB=2.4 ; ENULA=0.185 ; ENULC=1025. EMU0=ENULA ! low-shear viscosity TAUHLF=ENULC ! shear stress at which emua=0.5*emu0 ALFA=ENULB ! indical parameter BETA=ALFA-1.0;ZETA=ALFA+1.0 PI=3.1415926 QIN=0.02 ! volumetric inflow rate RIN=0.025 ! pipe diameter DIN=2.*RIN; AIN=PI*RIN*RIN WIN=QIN/AIN WIN ENULA;ENULB * Reynolds number REY=WIN*DIN/ENULA REY ** Analytical pressure solution PHI0=1./ENULA PHI1=1./(ENULA*TAUHLF**BETA) PHI0;PHI1;BETA;ZETA DPDZ=8.*EMU0*WIN/RIN**2 ! Newtonian pressure drop DPDZ TAUW=0.5*RIN*DPDz ! Force balance in flow direction TAUW iterate for analytical wall shear stress ACON=0.25*PHI0*RIN BCON=(PHI1*RIN)/(3.+ALFA) TAUP=100.0 DO II=1,20 IF(ABS(TAUP).GT.1.E-3) THEN FX =ACON*TAUW+BCON*(TAUW)**ALFA-WIN FXP=ACON+BCON*ALFA*(TAUW)**BETA TAUP=-FX/FXP TAUW=TAUW+TAUP II TAUW TAUP ENDIF ENDDO TAUW DPDZ=2.*TAUW/RIN DPDZ ** Analytical pressure solution (make1 zgnz is 0) (store1 zgnz is zg with IF(IZ.EQ.NZ)) (print zgnz is zgnz) (stored of PA is -DPDZ*(ZG-ZGNZ)) ** Analytical axial velocity profile ACON=(PHI0*RIN*RIN/4.)*DPDZ CCON=(1.+ALFA)*(2.**ALFA) BCON=PHI1*(RIN**ZETA)*(DPDZ**ALFA)/CCON (stored of WA is ACON*(1.-(YG/RIN)^2)+BCON*(1.-(YG/RIN)^ZETA)) save9end ************************************************************ Group 10.Inter-Phase Transfer Processes ************************************************************ Group 11.Initialise Var/Porosity Fields FIINIT(W1)=10. ;FIINIT(WDIS)=0.1 FIINIT(GEN1)=1.001E-10 ;FIINIT(VISL)=1.001E-10 No PATCHes used for this Group INIADD = F ************************************************************ Group 12. Convection and diffusion adjustments No PATCHes used for this Group ************************************************************ Group 13. Boundary & Special Sources No PATCHes used for this Group EGWF = T ************************************************************ Group 14. Downstream Pressure For PARAB ************************************************************ Group 15. Terminate Sweeps LSWEEP = 1000 RESREF(P1)=5.0E-16 ;RESREF(V1)=5.0E-16 RESREF(W1)=5.0E-16 RESFAC =1.0E-05 ************************************************************ Group 16. Terminate Iterations ************************************************************ Group 17. Relaxation RELAX(P1 ,LINRLX,1. ) RELAX(V1 ,FALSDT,0.05 ) RELAX(LTLS,LINRLX,1. ) ************************************************************ Group 18. Limits ************************************************************ Group 19. EARTH Calls To GROUND Station GENK = T PARSOL = F ISG62 = 1 SPEDAT(SET,OUTPUT,NOFIELD,L,T) SPEDAT(SET,GXMONI,PLOTALL,L,T) ************************************************************ Group 20. Preliminary Printout DISTIL = T ;NULLPR = F NDST = 0 DSTTOL =1.0E-02 EX(P1)=5246. ;EX(V1)=0.1069 EX(W1)=11.87 ;EX(WDIS)=8.63E-03 EX(SRM1)=890.200012 ;EX(STRS)=13.25 EX(LTLS)=9.365E-05 ;EX(BTAU)=150.199997 EX(PA)=5335. ;EX(WA)=12.13 EX(GEN1)=1.021E+06 ;EX(VISL)=0.1727 ************************************************************ Group 21. Print-out of Variables OUTPUT(BTAU,Y,N,Y,N,Y,Y) OUTPUT(PA ,Y,N,Y,N,Y,Y) OUTPUT(WA ,Y,N,Y,N,Y,Y) OUTPUT(VISL,Y,N,Y,N,Y,Y) ************************************************************ Group 22. Monitor Print-Out IXMON = 1 ;IYMON = 15 ;IZMON = 36 NPRMON = 100000 NPRMNT = 1 TSTSWP = -1 ************************************************************ Group 23.Field Print-Out & Plot Control NPRINT = 100000 NYPRIN = 1 NZPRIN = 1 YZPR = T ISWPRF = 1 ;ISWPRL = 100000 No PATCHes used for this Group ************************************************************ Group 24. Dumps For Restarts ************************************************************ Echo save-block settings for Group 24 save24begin DISTIL=T EX(P1 )=5.246E+03;EX(V1 )=1.069E-01 EX(W1 )=1.187E+01;EX(WDIS)=8.630E-03 EX(LTLS)=9.365E-05;EX(STRS)=1.325E+01 EX(SRM1)=8.902E+02;EX(BTAU)=1.502E+02 EX(GEN1)=1.021E+06;EX(VISL)=1.727E-01 EX(PA )=5.335E+03;EX(WA )=1.213E+01 save24end GVIEW(P,-0.999988,0.,-4.999915E-03) GVIEW(UP,0.,1.,0.) GVIEW(VDIS,0.247512) GVIEW(CENTRE,1.247918E-03,0.0125,0.25) > DOM, SIZE, 1.000000E-01, 2.500000E-02, 5.000000E-01 > DOM, MONIT, 5.000000E-02, 1.994204E-02, 4.581974E-01 > DOM, SCALE, 1.000000E+00, 1.000000E+00, 1.000000E+00 > DOM, INCREMENT, 1.000000E-02, 1.000000E-02, 1.000000E-02 > GRID, RSET_X_1, 1, 1.000000E+00 > GRID, RSET_Y_1, 20,-1.040000E+00,G > GRID, RSET_Z_1, -40, 1.200000E+00 > DOM, T_AMBIENT, 0.000000E+00 > OBJ, NAME, INLET > OBJ, POSITION, 0.000000E+00, 0.000000E+00, 0.000000E+00 > OBJ, SIZE, 1.000000E-01, TO_END, 0.000000E+00 > OBJ, DOMCLIP, NO > OBJ, GEOMETRY, poldef > OBJ, TYPE, INLET > OBJ, WIREFRAME, YES > OBJ, PRESSURE, P_AMBIENT > OBJ, VELOCITY, 0. ,0. ,10. > OBJ, NAME, OUTL > OBJ, POSITION, 0.000000E+00, 0.000000E+00, AT_END > OBJ, SIZE, 1.000000E-01, TO_END, 0.000000E+00 > OBJ, DOMCLIP, NO > OBJ, GEOMETRY, poldef > OBJ, TYPE, OUTLET > OBJ, WIREFRAME, YES > OBJ, PRESSURE, 0. > OBJ, COEFFICIENT, 100. > OBJ, VELOCITY, 0. ,0. , SAME > OBJ, NAME, WALL > OBJ, POSITION, 0.000000E+00, AT_END, 0.000000E+00 > OBJ, SIZE, 1.000000E-01, 0.000000E+00, TO_END > OBJ, DOMCLIP, NO > OBJ, GEOMETRY, poldef > OBJ, TYPE, PLATE > OBJ, WIREFRAME, YES STOP