GROUP 1. Run title and other preliminaries TEXT(2D Turb Duct Flow And Heat Trans TITLE DISPLAY The case considered is three-dimensional fully-developed, turbulent flow and heat transfer of an incompressible, constant-property fluid in a rectangular duct of aspect ratio alfa=0.5, where alfa=height/width. The calculations are performed for a Reynolds number of 1.E5, a Prandtl number of 3.0 and a constant temperature boundary condition is applied on all four sides ofthe duct. The solution exploits symmetry by performing the calculation over one quadrant of the duct cross section only. The flow Reynolds number is based on the hydraulic diameter of the duct. ENDDIS For data on the friction factor and Nusselt number the literature recommends that for most engineering calculations, it is sufficiently accurate to use the circular-tube correlations with the hydraulic diameter replacing the circular-tube diameter in the Reynolds number and Nusselt number ( see for example, 'Handbook of Heat Transfer Fundamentals', Ed. W.M.Rohsenow, J.P.Hartnett & E.N.Ganic', Chapter 7, McGraw Hill, 2nd Edition, ( 1985). For the Reynolds number and duct aspect ratio considered here, the data indicates that the friction factor f = 0.018 and the Nusselt number Nu = 392.0. The Petukhov correlation ( see below ) is used to estimate the Nusselt number. The PHOENICS prediction yields f = 0.017 and Nu = 373.0. These values agree fairly well with the data. It should be mentioned that no grid-sensitivity studies have been performed. It should be noted that the k-e turbulence model, which is used in the present calculation, is unable to predict the turbulence- driven secondary motions that are present in fully-developed turbulent flow in non-circular ducts. The present calculation predicts zero secondary flows, and one would have to resort to a suitable, but more complex turbulence model to capture the secondary motions, e.g. a Reynolds stress transport model. Finally, one may BFC=T with NONORT=T or F to verify that very similar results are obtained with the body-fitted-coordinates facility. BOOLEAN(HEAT);HEAT=T REAL(HEIGHT,WIDTH,ALF,HD2,WD2,WIN,DPDZ,REY,FRIC) REAL(US,DELT,AIN,DHYD,TKEIN,EPSIN,MIXL,FLOWIN) REAL(QIN,DTDZ,CP,COND,AWAL,TW,NUSS) ** ALFA = HEIGHT/WIDTH WIDTH=2.0;ALF=0.5;HEIGHT=ALF*WIDTH HD2=0.5*HEIGHT;WD2=0.5*WIDTH WIN=1.0 REY=1.E5;DHYD=4.*WIDTH*HEIGHT/(2.*HEIGHT+2.*WIDTH) ** compute expected pressure-drop for SATELLITE printout FRIC=1./(1.82*LOG10(REY)-1.64)**2 DPDZ=FRIC*RHO1*WIN*WIN/(2.*DHYD);US=WIN*(FRIC/8.)**0.5 FRIC DPDZ DHYD GROUP 3. X-direction grid specification AIN=HD2*WD2;ENUL=WIN*DHYD/REY DELT=2.*40.*ENUL/US NREGX=2;REGEXT(X,WD2) IREGX=1;GRDPWR(X,14,WD2-DELT,0.8) IREGX=2;GRDPWR(X,1,DELT,1.0) GROUP 4. Y-direction grid specification NREGY=2;REGEXT(Y,HD2) IREGY=1;GRDPWR(Y,14,HD2-DELT,0.8) IREGY=2;GRDPWR(Y,1,DELT,1.0) GROUP 7. Variables stored, solved & named SOLVE(P1,U1,V1,W1) TURMOD(KEMODL);KELIN=1;STORE(ENUT,LEN1) GROUP 8. Terms (in differential equations) & devices TERMS(W1,N,P,P,P,P,P) IF(HEAT) THEN + SOLVE(H1);TERMS(H1,N,P,P,P,P,P) + PRNDTL(H1)=3.0 ENDIF GROUP 9. Properties of the medium (or media) RHO1=1.0;FLOWIN=RHO1*WIN*AIN TKEIN=0.25*WIN*WIN*FRIC MIXL=0.09*DHYD;EPSIN=TKEIN**1.5/MIXL*0.1643 IF(HEAT) THEN ** prescribe energy flow from slab and fluid specific heat estimated from Dittus-Boelter Nu=0.023*Re**0.8*Pr**0.4 with (Tw-Tb)=5.0 + AWAL=(WD2+HD2)*ZWLAST + NUSS=0.023*REY**0.8*PRNDTL(H1)**0.4 + CP=1.0;COND=RHO1*CP*ENUL/PRNDTL(H1) + QIN=NUSS*5.0*COND/DHYD NUSS ** compute d(tbulk)/dz for input to single-slab thermal solver + DTDZ=QIN*AWAL/(CP*FLOWIN) + TW=10. ENDIF GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WIN;FIINIT(KE)=TKEIN;FIINIT(EP)=EPSIN IF(HEAT) THEN + FIINIT(H1)=0.5*TW ENDIF GROUP 12. Convection and diffusion adjustments PATCH(GP12CONH,CELL,1,NX,1,NY,1,NZ,1,1) COVAL(GP12CONH,U1,0.0,0.0);COVAL(GP12CONH,V1,0.0,0.0) COVAL(GP12CONH,W1,0.0,0.0);COVAL(GP12CONH,KE,0.0,0.0) COVAL(GP12CONH,EP,0.0,0.0) GROUP 13. Boundary conditions and special sources PATCH(WALLT,NWALL,1,NX,NY,NY,1,NZ,1,1) COVAL(WALLT,W1,LOGLAW,0.0);COVAL(WALLT,U1,LOGLAW,0.0) COVAL(WALLT,KE,LOGLAW,LOGLAW);COVAL(WALLT,EP,LOGLAW,LOGLAW) PATCH(WALLS,EWALL,NX,NX,1,NY,1,NZ,1,1) COVAL(WALLS,W1,LOGLAW,0.0);COVAL(WALLS,V1,LOGLAW,0.0) COVAL(WALLS,KE,LOGLAW,LOGLAW);COVAL(WALLS,EP,LOGLAW,LOGLAW) PATCH(RELIEF,CELL,NX/2,NX/2,NY/2,NY/2,1,NZ,1,1) COVAL(RELIEF,P1,FIXP,0.0);COVAL(RELIEF,H1,ONLYMS,SAME) FDFSOL=T;USOURC=T PATCH(FDFW1DP,VOLUME,1,NX,1,NY,1,NZ,1,1) COVAL(FDFW1DP,W1,FLOWIN,GRND1) IF(HEAT) THEN ** constant wall-temperature boundary condition + PATCH(FDFCWT,PHASEM,1,NX,1,NY,1,NZ,1,1) + COVAL(FDFCWT,H1,DTDZ,TW) + COVAL(WALLS,H1,LOGLAW,TW);COVAL(WALLT,H1,LOGLAW,TW) + COVAL(GP12CONH,H1,0.0,0.0) ENDIF GROUP 15. Termination of sweeps LSWEEP=50;LITHYD=1;LITER(W1)=15;LITER(H1)=10 GROUP 16. Termination of iterations RESREF(P1)=1.E-12*WIN*AIN RESREF(W1)=1.E-12*DPDZ*ZWLAST*AIN RESREF(U1)=RESREF(W1);RESREF(V1)=RESREF(W1) RESREF(KE)=RESREF(P1)*RHO1*WIN*TKEIN RESREF(EP)=RESREF(P1)*RHO1*WIN*EPSIN IF(HEAT) THEN + RESREF(H1)=1.E-12*QIN*ZWLAST*AWAL + QIN + COND=RHO1*CP*ENUL/PRNDTL(H1) + COND ENDIF GROUP 17. Under-relaxation devices REAL(DTF);DTF=5.*ZWLAST/WIN RELAX(U1,FALSDT,DTF);RELAX(V1,FALSDT,DTF) RELAX(W1,FALSDT,DTF);RELAX(KE,FALSDT,DTF) RELAX(EP,FALSDT,DTF) GROUP 22. Spot-value print-out IXMON=NX-2;IYMON=NY-2;TSTSWP=-1 GROUP 23. Field print-out and plot control NPLT=5;NYPRIN=3;NXPRIN=3 GROUP 24. Dumps for restarts YPLS=T ** compute expected Nusselt number from Petukhov correlation and printout from satellite REAL(XR) XR=1.07+12.7*(PRNDTL(H1)**.666-1.)*(FRIC/8.)**0.5 NUSS=REY*PRNDTL(H1)*FRIC/(8.*XR) NUSS