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 POLYMER MELT 2D PIPE FLOW msg Reynolds number = 1.E-4 Power index = 0.463 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 continue clear msg Bulk temperature profile da 1 tblk y m col3 1 pause msg press to end clear msg Nusselt number profile da 1 nusn y m col3 1 scale y -10 30. pause msg press to end pause end END_USE ************************************************************ IRUNN = 1 ;LIBREF = 113 ************************************************************ Group 1. Run Title TEXT(113 Heat transfer to molten polymer flow) ************************************************************ Echo save-block settings for Group 1 save1begin This case concerns heat transfer to steady molten polymer flow in a circular tube with a diameter of 0.25cm and a length of 800 diameters. The rheology of the melt flow is described by a power-law temperature-dependent non-Newtonian fluid. The fluid enters at 130degC with a bulk velocity of 0.15m/s and the pipe wall is held at a uniform temperature of 160degC along its entire length. A fully-developed velocity profile is specified at the inlet, but the inlet temperature is uniform. The power-law Reynolds number and Prandtl number are 1.E-4, 29.6E6, respectively. The Brinkman number is equal to 83, so that viscous dissipation has a significant effect on the temperature rise along the pipe. The physical properties of the polymer are assigned values for a typical high-density polyethylene melt. The fluid density is 794 kg/m^3, the specific heat is 2.51kJ/kgK, and the thermal conductivity is 0.255 W/m.K. The apparent dynamic viscosity is computed from: emu = K*G^(n-1)*Ft where G is the mean strain rate, n the flow-behaviour index, set to 0.453, and K the consistency set equal to 2.82e4 Pa.s^(n-1). The temperature function Ft is computed from Ft = exp( -B*n*(T-Tm) ) where B=0.024 K^-1 and Tm = 399.5K. The main tasks are to predict the temperature rise and asymptotic local Nusselt number, and then compare the results with the numerical results reported by: E.E.Agur an J.Vlachopoulos, Heat Transfer to Molten Polymer Flow in Tubes, J.Applied Polymer Science, Vol.26, 765-773, (1981). The following results are obtained: Tout (degC) Nuss PHOENICS 202.4 9.45 Agur & Vachopoulos 204.7 8.97 The PHOENICS results correspond to a Graetz number of Gr=0.27, whereas the target data are for Gz = 1.0. Therefore, improved agreement is likely if the simulated pipe length is increased by a factor of 4. save1end ************************************************************ Group 2. Transience STEADY = T ************************************************************ Groups 3, 4, 5 Grid Information * Overall number of cells, RSET(M,NX,NY,NZ,tolerance) RSET(M,1,20,60,8.333333E-05) * Cylindrical-polar grid CARTES=F ************************************************************ Group 6. Body-Fitted coordinates ************************************************************ Group 7. Variables: STOREd,SOLVEd,NAMEd * Non-default variable names NAME(128)=BIGZ ;NAME(129)=QLOC NAME(130)=SRM1 ;NAME(131)=SPH1 NAME(132)=TFNN ;NAME(133)=QWAL NAME(134)=NUSN ;NAME(135)=TBLK NAME(136)=LHTC ;NAME(137)=CNH1 NAME(138)=HTCO ;NAME(139)=THET NAME(140)=KOND ;NAME(141)=TEM1 NAME(142)=GRNO ;NAME(143)=WDIS 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,TEM1) * Stored variables list STORE(VISL,GEN1,WA,PA,BTAU,STRS,WDIS,GRNO) STORE(KOND,THET,HTCO,CNH1,LHTC,TBLK,NUSN,QWAL) STORE(TFNN,SPH1,SRM1,QLOC,BIGZ) * 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) SOLUTN(TEM1,Y,Y,Y,N,N,Y) ************************************************************ Echo save-block settings for Group 7 save7begin save7end ************************************************************ Group 8. Terms & Devices TERMS (TEM1,Y,Y,Y,Y,N,Y) NEWENL = T ************************************************************ Group 9. Properties TEMP0 =273.149994 RHO1 =794. ENUL = GRND4 ENULA =2.82E+04 ;ENULB =0.453 ;ENULC =0. CP1 =2510. DISWAL ENUT =1.0E-10 PRNDTL(TEM1)=-0.255 ************************************************************ Echo save-block settings for Group 9 save9begin REAL(RIN,DIN,WIN,DPDZ,REY,AN,POW2,BETA,ZETA,REYMR,FRIC) REAL(PLEN,CONSI,LDD,RGRENO,NUST,QIN,AWALL,AIN,MFIN,EFIN) REAL(PRNO,THKON,PECNO,PLPRNO,TIN,TWAL,EA,RGAS,CONS0,TREF,ACON) REAL(BRINKNO,ECKTNO) ENUL=GRND4; IENULA=0 ! Power-law rheology model RIN=0.00125;DIN=2.*RIN ! Pipe diameter PLEN=800.*DIN ! Pipe length WIN=0.15 ! Inlet velocity AIN=0.05*RIN*RIN AIN QIN=WIN*AIN QIN MFIN=RHO1*QIN MFIN TIN =130. ! Inlet temperature TWAL=160. ! Wall temperature EFIN=MFIN*CP1*(TIN+TEMP0) EFIN AN=0.453 ! Power-law exponent AN=1.0 ! Newtonian fluid DIN WIN PLEN AWALL=0.05*DIN*PLEN AWALL ! surface area of pipe wall ZETA=8; BETA=(3.*AN+1.)/(4.*AN) ZETA;BETA CONSI=28200.0 CONSI=100. ! Newtonian fluid REY=RHO1*WIN**(2.0-AN)*DIN**AN/CONSI ! Power-law Reynolds number CONSI;AN ENULA=CONSI ! Consistency index 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)) ** Thermal properties THKON=-1.*PRNDTL(TEM1) ! Thermal conductivity CP1 = 2510. ! Specific heat CP1 PLPRNO=CONSI*CP1*((WIN/DIN)**(AN-1))/THKON ! Power-law Prandtl number PLPRNO CP1 PRNO=PLPRNO/(WIN/DIN)**(AN-1) ! Prandtl number PRNO PECNO=RHO1*CP1*WIN*DIN/THKON ! Peclet Number = PLPRNO*REY PECNO REAL(GZNO,BIGZ) ! Graetz number Gz = z/(D*Peclet) GZNO=PLEN/(DIN*PECNO) GZNO BIGZ=4.*GZNO BIGZ ! ECKTNO=WIN*WIN/(CP1*(TWAL-TIN)) ! Eckert number ECKTNO BRINKNO=ECKTNO*PRNO ! Brinkman number BRINKNO *** Temperature-dependent consistency IENULB=2 IF(IENULB.EQ.2) THEN ! fT = exp(enulf*(T-enulg)) ENULF=-0.024*AN; ENULG=126.35 ! enulg = 399.5k ENDIF *** compute bulk fluid temperature (make1 TSUM IS 0.0) (make1 FSUM is 0.0) (make1 TSLB is 0.0) ** Start of IZ cycle DO II=1,NZ PATCH(PATCH:II:,CELL,1,NX,1,NY,:II:,:II:,1,1) (store1 TSUM at PATCH:II: is SUM(CNH1*TEM1)) (store1 FSUM at PATCH:II: is SUM(CNH1)) (store1 TSLB at PATCH:II: is TSUM/FSUM) (stored of TBLK at PATCH:II: is TSLB) ** End of IZ cycle ENDDO ** compute local Nusselt number, Graetz number, etc (stored of THET is (TEM1-:TWAL:)/(:TIN:-:TWAL:)) (stored of QWAL is HTCO*(:TWAL:-TEM1) with IF(IY.EQ.NY)) (stored of LHTC is QWAL/(:TWAL:-TBLK) with IF(IY.EQ.NY)) (stored of NUSN is LHTC*:DIN:/:THKON: with IF(IY.EQ.NY)) (stored of LHTC is LHTC[,,-1] with IF(IZ.EQ.NZ)) (stored of NUSN is NUSN[,,-1] with IF(IZ.EQ.NZ)) (stored of TBLK is TBLK[,,-1] with IF(IZ.EQ.NZ)) (stored of QLOC is QWAL*ANORTH with IF(IY.EQ.NY)) (stored of GRNO is ZG/(DIN*PECNO)) (stored of BIGZ is 4.*GRNO) ** print main parameters to inforout file (make1 tbo is 0.0) (make1 nuss is 0.0) (make1 grzn is 0.0) (make1 zbig is 0.0) (store1 tbo is TBLK[1,1,60]) (store1 nuss is NUSN[1,20,60]) (store1 grzn is GRNO[1,1,60]) (store1 zbig is BIGZ[1,1,60]) (print tb_out is tbo) (print nuss_no is nuss) (print greatz_no is grzn) (print big_z is zbig) save9end ************************************************************ Group 10.Inter-Phase Transfer Processes ************************************************************ Group 11.Initialise Var/Porosity Fields FIINIT(W1)=0.15 ;FIINIT(TEM1)=130. FIINIT(WDIS)=0.1 ;FIINIT(GEN1)=1.001E-10 FIINIT(VISL)=1.001E-10 PATCH(IINIT, INIVAL, 0, 0, 0, 0, 0, 0, 1, 1) INIADD = F ************************************************************ Echo save-block settings for Group 11 save11begin ** Use isothermal, analytical solution as an initial guess, simply to reduce the number of sweeps to convergence for this library case. (INITIAL of P1 at IINIT is -DPDZ*(ZG-:PLEN:)) (INITIAL of W1 at IINIT is WCON*(1.-(YG/RIN)^POW2)) save11end ************************************************************ Group 12. Convection and diffusion adjustments No PATCHes used for this Group ************************************************************ Group 13. Boundary & Special Sources PATCH(PATCH1, CELL, 1, 1, 1, 20, 1, 1, 1, 1) PATCH(PATCH2, CELL, 1, 1, 1, 20, 2, 2, 1, 1) PATCH(PATCH3, CELL, 1, 1, 1, 20, 3, 3, 1, 1) PATCH(PATCH4, CELL, 1, 1, 1, 20, 4, 4, 1, 1) PATCH(PATCH5, CELL, 1, 1, 1, 20, 5, 5, 1, 1) PATCH(PATCH6, CELL, 1, 1, 1, 20, 6, 6, 1, 1) PATCH(PATCH7, CELL, 1, 1, 1, 20, 7, 7, 1, 1) PATCH(PATCH8, CELL, 1, 1, 1, 20, 8, 8, 1, 1) PATCH(PATCH9, CELL, 1, 1, 1, 20, 9, 9, 1, 1) PATCH(PATCH10, CELL, 1, 1, 1, 20, 10, 10, 1, 1) PATCH(PATCH11, CELL, 1, 1, 1, 20, 11, 11, 1, 1) PATCH(PATCH12, CELL, 1, 1, 1, 20, 12, 12, 1, 1) PATCH(PATCH13, CELL, 1, 1, 1, 20, 13, 13, 1, 1) PATCH(PATCH14, CELL, 1, 1, 1, 20, 14, 14, 1, 1) PATCH(PATCH15, CELL, 1, 1, 1, 20, 15, 15, 1, 1) PATCH(PATCH16, CELL, 1, 1, 1, 20, 16, 16, 1, 1) PATCH(PATCH17, CELL, 1, 1, 1, 20, 17, 17, 1, 1) PATCH(PATCH18, CELL, 1, 1, 1, 20, 18, 18, 1, 1) PATCH(PATCH19, CELL, 1, 1, 1, 20, 19, 19, 1, 1) PATCH(PATCH20, CELL, 1, 1, 1, 20, 20, 20, 1, 1) PATCH(PATCH21, CELL, 1, 1, 1, 20, 21, 21, 1, 1) PATCH(PATCH22, CELL, 1, 1, 1, 20, 22, 22, 1, 1) PATCH(PATCH23, CELL, 1, 1, 1, 20, 23, 23, 1, 1) PATCH(PATCH24, CELL, 1, 1, 1, 20, 24, 24, 1, 1) PATCH(PATCH25, CELL, 1, 1, 1, 20, 25, 25, 1, 1) PATCH(PATCH26, CELL, 1, 1, 1, 20, 26, 26, 1, 1) PATCH(PATCH27, CELL, 1, 1, 1, 20, 27, 27, 1, 1) PATCH(PATCH28, CELL, 1, 1, 1, 20, 28, 28, 1, 1) PATCH(PATCH29, CELL, 1, 1, 1, 20, 29, 29, 1, 1) PATCH(PATCH30, CELL, 1, 1, 1, 20, 30, 30, 1, 1) PATCH(PATCH31, CELL, 1, 1, 1, 20, 31, 31, 1, 1) PATCH(PATCH32, CELL, 1, 1, 1, 20, 32, 32, 1, 1) PATCH(PATCH33, CELL, 1, 1, 1, 20, 33, 33, 1, 1) PATCH(PATCH34, CELL, 1, 1, 1, 20, 34, 34, 1, 1) PATCH(PATCH35, CELL, 1, 1, 1, 20, 35, 35, 1, 1) PATCH(PATCH36, CELL, 1, 1, 1, 20, 36, 36, 1, 1) PATCH(PATCH37, CELL, 1, 1, 1, 20, 37, 37, 1, 1) PATCH(PATCH38, CELL, 1, 1, 1, 20, 38, 38, 1, 1) PATCH(PATCH39, CELL, 1, 1, 1, 20, 39, 39, 1, 1) PATCH(PATCH40, CELL, 1, 1, 1, 20, 40, 40, 1, 1) PATCH(PATCH41, CELL, 1, 1, 1, 20, 41, 41, 1, 1) PATCH(PATCH42, CELL, 1, 1, 1, 20, 42, 42, 1, 1) PATCH(PATCH43, CELL, 1, 1, 1, 20, 43, 43, 1, 1) PATCH(PATCH44, CELL, 1, 1, 1, 20, 44, 44, 1, 1) PATCH(PATCH45, CELL, 1, 1, 1, 20, 45, 45, 1, 1) PATCH(PATCH46, CELL, 1, 1, 1, 20, 46, 46, 1, 1) PATCH(PATCH47, CELL, 1, 1, 1, 20, 47, 47, 1, 1) PATCH(PATCH48, CELL, 1, 1, 1, 20, 48, 48, 1, 1) PATCH(PATCH49, CELL, 1, 1, 1, 20, 49, 49, 1, 1) PATCH(PATCH50, CELL, 1, 1, 1, 20, 50, 50, 1, 1) PATCH(PATCH51, CELL, 1, 1, 1, 20, 51, 51, 1, 1) PATCH(PATCH52, CELL, 1, 1, 1, 20, 52, 52, 1, 1) PATCH(PATCH53, CELL, 1, 1, 1, 20, 53, 53, 1, 1) PATCH(PATCH54, CELL, 1, 1, 1, 20, 54, 54, 1, 1) PATCH(PATCH55, CELL, 1, 1, 1, 20, 55, 55, 1, 1) PATCH(PATCH56, CELL, 1, 1, 1, 20, 56, 56, 1, 1) PATCH(PATCH57, CELL, 1, 1, 1, 20, 57, 57, 1, 1) PATCH(PATCH58, CELL, 1, 1, 1, 20, 58, 58, 1, 1) PATCH(PATCH59, CELL, 1, 1, 1, 20, 59, 59, 1, 1) PATCH(PATCH60, CELL, 1, 1, 1, 20, 60, 60, 1, 1) EGWF = T ************************************************************ Echo save-block settings for Group 13 SAVE13BEGIN ** Inform for fully-developed velocity profile REAL(WCON) WCON=WIN*(1.+3.*AN)/(1.+AN) (SOURCE OF P1 at INLET is COVAL(FIXFLU,RHO1*WCON*(1.-(YG/RIN)^POW2)) with AREA) (SOURCE OF W1 at INLET is COVAL(ONLYMS,WCON*(1.-(YG/RIN)^POW2)) with AREA) SAVE13END ************************************************************ Group 14. Downstream Pressure For PARAB ************************************************************ Group 15. Terminate Sweeps LSWEEP = 5000 RESREF(P1)=5.0E-16 ;RESREF(V1)=5.0E-16 RESREF(W1)=5.0E-16 RESFAC =1.0E-05 ************************************************************ Group 16. Terminate Iterations LITER(P1)=200 ;LITER(TEM1)=50 ************************************************************ Group 17. Relaxation RELAX(P1 ,LINRLX,0.99 ) RELAX(V1 ,LINRLX,0.5 ) RELAX(W1 ,LINRLX,0.8 ) RELAX(TEM1,LINRLX,0.25 ) RELAX(LTLS,LINRLX,1. ) OVRRLX =1. ************************************************************ Group 18. Limits VARMAX(P1)=1.0E+12 ;VARMIN(P1)=-1.0E+04 VARMAX(V1)=100. ;VARMIN(V1)=-100. VARMAX(W1)=100. ;VARMIN(W1)=-100. VARMAX(TEM1)=3000. ;VARMIN(TEM1)=-204.862488 ************************************************************ Group 19. EARTH Calls To GROUND Station GENK = T PARSOL = F CONWIZ = T ISG6 = 2 ISG62 = 1 SPEDAT(SET,OUTPUT,NOFIELD,L,T) SPEDAT(SET,GXMONI,PLOTALL,L,T) SPEDAT(SET,RLXFAC,REFVEL,R,0.1) SPEDAT(SET,MAXINC,V1,R,2.5) SPEDAT(SET,MAXINC,W1,R,2.5) ************************************************************ Group 20. Preliminary Printout DISTIL = T ;NULLPR = F NDST = 0 DSTTOL =1.0E-02 EX(P1)=4.498E+08 ;EX(V1)=2.095E-05 EX(W1)=0.1748 ;EX(BIGZ)=0.5459 EX(QLOC)=7.833E-03 ;EX(SRM1)=249.199997 EX(SPH1)=2510. ;EX(TFNN)=0.5494 EX(QWAL)=1860. ;EX(NUSN)=3.458 EX(TBLK)=187. ;EX(LHTC)=352.700012 EX(CNH1)=4.573E-07 ;EX(HTCO)=607.5 EX(THET)=0.8912 ;EX(KOND)=0.255 EX(TEM1)=183.5 ;EX(GRNO)=0.1365 EX(WDIS)=4.316E-04 ;EX(STRS)=18.620001 EX(LTLS)=2.342E-07 ;EX(BTAU)=7.028E+06 EX(PA)=8.264E+08 ;EX(WA)=0.1706 EX(GEN1)=9.281E+04 ;EX(VISL)=2.178 ************************************************************ Group 21. Print-out of Variables OUTPUT(SRM1,Y,N,Y,N,Y,Y) OUTPUT(TBLK,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 = 16 ;IZMON = 50 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 )=4.498E+08 ; EX(V1 )=2.095E-05 EX(W1 )=1.748E-01 ; EX(BIGZ)=5.459E-01 EX(QLOC)=7.833E-03 ; EX(SRM1)=2.492E+02 EX(SPH1)=2.510E+03 ; EX(TFNN)=5.494E-01 EX(QWAL)=1.860E+03 ; EX(NUSN)=3.458E+00 EX(TBLK)=1.870E+02 ; EX(LHTC)=3.527E+02 EX(CNH1)=4.573E-07 ; EX(HTCO)=6.075E+02 EX(THET)=8.912E-01 ; EX(KOND)=2.550E-01 EX(TEM1)=1.835E+02 ; EX(GRNO)=1.365E-01 EX(WDIS)=4.316E-04 ; EX(STRS)=1.862E+01 EX(LTLS)=2.342E-07 ; EX(BTAU)=7.028E+06 EX(PA )=8.264E+08 ; EX(WA )=1.706E-01 EX(GEN1)=9.281E+04 ; EX(VISL)=2.178E+00 save24end GVIEW(P,-0.999988,4.999913E-03,0.) GVIEW(UP,4.999913E-03,0.999988,0.) GVIEW(VDIS,0.9005) GVIEW(CENTRE,6.239588E-05,6.25E-04,0.9375) > DOM, SIZE, 1.000000E-01, 1.250000E-03, 2.000000E+00 > DOM, MONIT, 5.000000E-02, 1.047191E-03, 1.716208E+00 > DOM, SCALE, 1.000000E+00, 5.000000E+01, 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, -60, 1.200000E+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. ,0.15 > OBJ, TEMPERATURE, 130. > 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, TEMPERATURE, T_AMBIENT > 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, SURF_TEMP, 0. ,160. STOP