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 CROSS-FLUID PIPE FLOW msg Reynolds number =0.097 msg Velocity (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 end pause end END_USE ************************************************************ IRUNN = 1 ;LIBREF = 102 ************************************************************ Group 1. Run Title TEXT(102 2d pipe flow - Cross fluid ) ************************************************************ Echo save-block settings for Group 1 save1begin This case concerns the steady laminar flow of a Cross non-Newtonian fluid in a circular pipe. The apparent dynamic viscosity of such a fluid is given by: emu = emui+(emu0-emui)/[1+(T.G)^n] where emu0 is the low-shear viscosity, emui is the high- shear viscosity, T is the characteristic time scale, G is the mean strain rate, and n is the flow-behaviour index. The Cross rheology model finds applications in biological fluids and polymeric liquids. Semi-analytical solutions for the laminar flow of Cross fluids in circular pipes have been reported by: T.Sochi, Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits. Rheologica Acta, Vol.54, Issue 8, 745-756, (2015). The pipe diameter and length are 0.016m and 0.95m, respectively; and the rheology parameters are set to: emui=0.033 Pa.s; emu0=0.22 Pa.s; T=6.65s; and n=0.83. The task is to predict the pressure drop for fully- developed flow at the a given Reynolds number; and then compare the result with the semi-analytical solution of Sochi (2015). For this purpose, the inlet velocity is set to 0.2m/s, which equates to a volumetric flow rate Q of 4E-5 m^3/s,and a Reynolds number of 0.097. For these conditions, PHOENICS predicts a pressure drop of 797 Pa, which agrees well with the semi-analytical solution of 800 Pa reported by Sochi (2015). 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(143)=PA ;NAME(145)=WDIS NAME(146)=SRM1 ;NAME(147)=STRS NAME(148)=BTAU ;NAME(149)=GEN1 NAME(150) =VISL * Solved variables list SOLVE(P1,V1,W1) * Stored variables list STORE(VISL,GEN1,BTAU,STRS,SRM1,WDIS,PA) * 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 =0.22 ;ENULB =0.033 ;ENULC =0.83 CP1 =1. DISWAL ENUT =1.0E-10 ************************************************************ Echo save-block settings for Group 9 save9begin REAL(REY,RIN,DIN,WIN,AIN,DPDZ,QIN,PI) REAL(DPDZ,PLEN,TAUW) PI=3.14159265 RIN=0.008;DIN=2.*RIN ! Pipe diameter WIN=0.2 ! Bulk velocity PLEN=0.95 ! Pipe length AIN=PI*RIN*RIN;QIN=WIN*AIN QIN ! Volumetric flow rate ENUL=GRND4;IENULA=2 ! Cross fluid model ETA0=ENULA; ETAI=ENULB; AN=ENULC; TCONS=ENULD ETA=(ETAI+(ETA0-ETAI)/(1.+(TCONS*GAMDOT)**AN)) ENULA=0.22;ENULB=0.033 ENULC=0.83 ! ENULE Exponent ENULD=6.65 ! ENULD Time constant REY=WIN*DIN/ENULB ! Reynolds number REY DPDZ=800./PLEN ! From Sochi (2015) TAUW=0.5*RIN*DPDZ TAUW ** Semi-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)=0.2 ;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 = 2000 RESREF(P1)=5.0E-16 ;RESREF(V1)=5.0E-16 RESREF(W1)=5.0E-16 RESFAC =1.0E-04 ************************************************************ Group 16. Terminate Iterations LITER(P1)=200 ************************************************************ Group 17. Relaxation RELAX(P1 ,LINRLX,1. ) RELAX(V1 ,FALSDT,1.0E-02 ) RELAX(W1 ,FALSDT,5. ) 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) SPEDAT(SET,SOLPHI,P1,I,24) SPEDAT(SET,SOLPHI,V1,I,0) SPEDAT(SET,PREPHI,V1,I,0) SPEDAT(SET,SOLPHI,W1,I,0) SPEDAT(SET,PREPHI,W1,I,0) ************************************************************ Group 20. Preliminary Printout DISTIL = T ;NULLPR = F NDST = 0 DSTTOL =1.0E-02 EX(P1)=398.100006 ;EX(V1)=4.068E-04 EX(W1)=0.2388 ;EX(PA)=394.5 EX(LTLS)=9.573E-06 ;EX(WDIS)=2.76E-03 EX(SRM1)=56.029999 ;EX(STRS)=0.1658 EX(BTAU)=1.923 ;EX(GEN1)=3967. EX(VISL)=0.03537 ************************************************************ Group 21. Print-out of Variables OUTPUT(PA ,Y,N,Y,N,Y,Y) OUTPUT(BTAU,Y,N,Y,N,Y,Y) OUTPUT(VISL,Y,N,Y,N,Y,Y) ************************************************************ Group 22. Monitor Print-Out IXMON = 1 ;IYMON = 12 ;IZMON = 35 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 )=3.981E+02;EX(V1 )=4.068E-04 EX(W1 )=2.388E-01;EX(LTLS)=9.573E-06 EX(WDIS)=2.760E-03;EX(BTAU)=1.923E+00 EX(GEN1)=3.967E+03;EX(SRM1)=5.603E+01 EX(STRS)=1.658E-01;EX(PA )=3.945E+02 save24end GVIEW(P,-1.,0.,0.) GVIEW(UP,0.,1.,0.) GVIEW(VDIS,0.456404) GVIEW(CENTRE,3.993337E-04,4.0E-03,0.475) > DOM, SIZE, 1.000000E-01, 8.000000E-03, 9.500000E-01 > DOM, MONIT, 5.000000E-02, 5.340725E-03, 8.489994E-01 > DOM, SCALE, 1.000000E+00, 5.000000E+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. ,0.2 > 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