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