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 clear msg POWER-LAW-FLUID PIPE FLOW msg Reynolds number = 10 Power index = 0.5 msg Pressure (P1) profile msg Blue line --- PHOENICS solution msg crosses --- analytical solution pause 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 = 100 ************************************************************ Group 1. Run Title TEXT(100 2d pipe flow - Power-law fluid ) ************************************************************ Echo save-block settings for Group 1 save1begin This case concerns the steady laminar flow of a power-law pseudo-plastic non-Newtonian fluid in a circular pipe. The apparent viscosity of such a fluid is given by: emu = K*G^(n-1) where K is the consistency index,G is the mean strain rate, and n the flow-behaviour index. For pseudo-plastic fluids, n<1, so that emua decreases with increasing shear rate. Examples of pseudo-plastic fluids include rubber solutions, adhesives, polymer solutions or melts, and biological fluids. The bulk inlet velocity is 1m/s and the fluid density is 100 kg/m^3. The pipe diameter and length are 0.1m and 1m, respectively. The flow-behaviour index is set to 0.5, and the consistency K is set to define a power-law Reynolds number of 10. The power-law Reynolds number, defined by: Re = D^n*Win^(2-n)*rho/K where D is the pipe diameter, Win the mean velocity and Rho is the fluid density. 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. 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, John Wiley, (1967,and G.W.Govier & K.Aziz, The flow of complex mixtures in pipes, R.E.Kreiger Pub. Co.,Huntington, New York, (1977). 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 =100. ENUL = GRND4 ENULA =3.162278 ;ENULB =0.5 ;ENULC =0. CP1 =1. DISWAL ENUT =1.0E-10 ************************************************************ Echo save-block settings for Group 9 save9begin REAL(RIN,DIN,WIN,DPDZ,REY,AN,POW2,BETA,ZETA,REYMR,FRIC) ENUL=GRND4 ! Power-law rheology model REY=10.;AN=0.5;RIN=0.05;DIN=2.*RIN;WIN=1.0 ZETA=8; BETA=(3.*AN+1.)/(4.*AN) ZETA;BETA ENULA=RHO1*WIN**(2.0-AN)*DIN**AN/REY;ENULB=AN ENULA;ENULB * Generalised Metzner-Reed Reynolds number REYMR=REY/(ZETA**(AN-1.)*BETA**AN) REY;REYMR FRIC=2.*ZETA/REYMR FRIC DPDZ=(4.*RHO1*WIN**2/DIN)/REY*((2.+6.*AN)/AN)**AN DPDZ DPDZ=(2.*RHO1*WIN**2/DIN)*FRIC ! Alternative calculation DPDZ ** Analytical axial velocity profile POW2=(1.+AN)/AN (stored of WA is WIN*(1.+3.*AN)*(1.-(YG/RIN)^POW2)/(1.+AN)) ** 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)) save9end ************************************************************ Group 10.Inter-Phase Transfer Processes ************************************************************ Group 11.Initialise Var/Porosity Fields FIINIT(W1)=1. ;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,0.066667 ) RELAX(W1 ,FALSDT,0.066667 ) 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)=628.700012 ;EX(V1)=8.242E-03 EX(W1)=1.132 ;EX(WDIS)=0.01726 EX(SRM1)=39.82 ;EX(STRS)=0.01616 EX(LTLS)=3.746E-04 ;EX(BTAU)=125.900002 EX(PA)=623.799988 ;EX(WA)=1.145 EX(GEN1)=2614. ;EX(VISL)=8.749E-03 ************************************************************ Group 21. Print-out of Variables OUTPUT(STRS,Y,N,Y,N,Y,Y) 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 = 14 ;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 )=6.287E+02;EX(V1 )=8.242E-03 EX(W1 )=1.132E+00;EX(WDIS)=1.726E-02 EX(LTLS)=3.746E-04;EX(STRS)=1.616E-02 EX(SRM1)=3.982E+01;EX(BTAU)=1.259E+02 EX(PA )=6.238E+02;EX(WA )=1.145E+00 EX(GEN1)=2.614E+03;EX(VISL)=8.749E-03 save24end GVIEW(P,-1.,0.,0.) GVIEW(UP,0.,1.,0.) GVIEW(VDIS,0.482418) GVIEW(CENTRE,4.991671E-03,0.05,0.5) > DOM, SIZE, 1.000000E-01, 5.000000E-02, 1.000000E+00 > DOM, MONIT, 5.000000E-02, 3.780036E-02, 9.163948E-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, PRESSURE, P_AMBIENT > OBJ, VELOCITY, 0. ,0. ,1. > 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, 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 STOP