GROUP 1. Run title and other preliminaries TEXT(1D Turb Pipe Flow & Heat Trans TITLE DISPLAY The case considered is fully-developed turbulent flow and heat transfer in a circular pipe at a Reynolds number of 1.E5 and a Prandtl number of 3.0. The tube wall is held at a constant temperature and calculations may be made with either a fully smooth or a fully rough surface with a relative sand-grain roughness of 0.015. Also, the calculation may be made with equilibrium (LOGLAW) or non-equilibrium (GENLAW) wall functions. Both types of wall function should produce the same results as the turbulence is in equilibrium for this flow. ENDDIS For fully-smooth conditions pipe-flow 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 = 0.018 and Nu = 393.0 with both LOGLAW and GENLAW type wall functions. These values agree very closely with the data. For fully-rough conditions pipe-flow data indicates that the friction factor f = 0.044 and the Nusselt number Nu = 786.0. The Petukhov correlation ( see below ) is used to estimate the Nusselt number. The PHOENICS prediction yields f = 0.041 and Nu = 767.0 with both LOGLAW and GENLAW type wall functions. These values agree fairly well with the data. The PIL variable WALPRN has been set to T, thereby activating printout of the local friction factor (sloc) and Stanton number (Stloc) in the RESULT file. In order to convert these values to f and Nu above, the following relations should be used: f = 8.*sloc*(W1(NY)/WIN)**2 Nu = REY*PRNDTL(H1)*Stloc*W1(NY)*(TW-H1(NY))/[WIN*(TW-TB)] where TB is the bulk temperature printed in the RESULT file. The energy equation may be solved via the H1 or TEM1 equation according to whether CH1 is set equal to H1 or TEM1. CHAR(CH1);CH1=TEM1 ** set ROUGH=F for a fully-smooth calculation BOOLEAN(ROUGH);ROUGH=T ** WALLFN used to test with GENLAW & LOGLAW wall functions INTEGER(WALLFN);WALLFN=2 REAL(DIAM,WIN,REY,TKEIN,EPSIN,MIXL,FRIC,DPDZ,MASIN,DTF) REAL(EPS,BCON,RIN,AIN,DELT,US,QIN,DTDZ,CP,COND,TW,AWAL) DIAM=0.1;WIN=1.0;REY=1.E5;RIN=0.5*DIAM ** set relative roughness & roughness height & then calculate expected friction factor IF(ROUGH) THEN + EPS=0.015;BCON=0.5/EPS;FRIC=1./(2.0*LOG10(BCON)+1.74)**2 ELSE + EPS=0.;FRIC=1./(1.82*LOG10(REY)-1.64)**2 ENDIF WALLA=EPS*DIAM ** compute expected pressure-drop for SATELLITE printout DPDZ=FRIC*RHO1*WIN*WIN/(2.*DIAM);US=WIN*(FRIC/8.)**0.5 DPDZ TKEIN=0.25*WIN*WIN*FRIC MIXL=0.09*RIN;EPSIN=TKEIN**1.5/MIXL*0.1643 GROUP 3. X-direction grid specification CARTES=F;XULAST=0.1;AIN=0.5*RIN*RIN*XULAST GROUP 4. Y-direction grid specification ENUL=WIN*DIAM/REY;DELT=2.*40.*ENUL/US NREGY=2;REGEXT(Y,0.5*DIAM) IREGY=1;GRDPWR(Y,29,0.5*DIAM-DELT,0.8) IREGY=2;GRDPWR(Y,1,DELT,1.0) GROUP 5. Z-direction grid specification ** AWAL is wall surface area per unit length AWAL=RIN*XULAST GROUP 7. Variables stored, solved & named SOLVE(W1,:CH1:);TURMOD(KEMODL);KELIN=1;STORE(ENUT,LEN1,GENK) GROUP 8. Terms (in differential equations) & devices ** deactivate convection terms TERMS(W1,N,N,P,P,P,P);TERMS(KE,Y,N,P,P,P,P) TERMS(EP,Y,N,P,P,P,P);TERMS(:CH1:,N,N,P,P,P,P) GROUP 9. Properties of the medium (or media) PRNDTL(H1)=3.0;MASIN=RHO1*WIN*AIN ** 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 REAL(NUSS);NUSS=0.023*REY**0.8*PRNDTL(H1)**0.4 CP=1.0;COND=RHO1*CP*ENUL/PRNDTL(H1) QIN=NUSS*5.0*COND/DIAM NUSS ** compute d(tbulk)/dz for input to single-slab thermal solver ; if TEM1 solved, multiply by CP IF(:CH1:.EQ.TEM1) THEN + DTDZ=QIN*AWAL/MASIN ELSE + DTDZ=QIN*AWAL/(CP*MASIN) ENDIF ** prescribe wall temperature TW=10. GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WIN;FIINIT(EP)=EPSIN;FIINIT(KE)=TKEIN FIINIT(:CH1:)=0.5*TW GROUP 13. Boundary conditions and special sources PATCH(WALLN,NWALL,1,1,NY,NY,1,NZ,1,1) CASE (WALLFN) OF WHEN 2 + COVAL(WALLN,W1,LOGLAW,0.0) + COVAL(WALLN,KE,LOGLAW,LOGLAW) + COVAL(WALLN,EP,LOGLAW,LOGLAW) + COVAL(WALLN,:CH1:,LOGLAW,TW) WHEN 3 + COVAL(WALLN,W1,GENLAW,0.0) + COVAL(WALLN,KE,GENLAW,GENLAW) + COVAL(WALLN,EP,GENLAW,GENLAW) + COVAL(WALLN,:CH1:,GENLAW,TW) ENDCASE ** activate pressure-drop calculation in single-slab solver FDFSOL=T;USOURC=T PATCH(FDFW1DP,VOLUME,1,NX,1,NY,1,NZ,1,1) COVAL(FDFW1DP,W1,MASIN,GRND1) ** temperature source/sink term for fully-developed flow PATCH(FDFCWT,PHASEM,1,NX,1,NY,1,NZ,1,1) COVAL(FDFCWT,:CH1:,DTDZ,TW) GROUP 15. Termination of sweeps LSWEEP=20;TSTSWP=-1;LITHYD=5 GROUP 16. Termination of iterations GROUP 17. Under-relaxation devices DTF=10.*ZWLAST/WIN GROUP 18. Limits on variables or increments to them VARMIN(W1)=1.E-10 GROUP 19. Data communicated by satellite to GROUND COND=RHO1*CP*ENUL/PRNDTL(H1) GROUP 21. Print-out of variables GROUP 22. Spot-value print-out IYMON=NY-2;ITABL=3;NPLT=2;NZPRIN=1;NYPRIN=1;IYPRF=1 NTPRIN=2 GROUP 24. Dumps for restarts RELAX(W1,FALSDT,DTF) RELAX(KE,FALSDT,DTF);RELAX(EP,FALSDT,DTF) ** use WALPRN for printout of near-wall y+ values & local friction factor & stanton number ;WALPRN=T;STORE(SKIN,STAN,YPLS,STRS) ** 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 IF(:CH1:.EQ.TEM1) THEN + STORE(PRPS);FIINIT(PRPS)=33; + ** mat no. rho enul cp kond expan ** 1 air CSG10='q1' MATFLG=T;NMAT=1 33 1. 1.E-5 1.0 3.333E-7 0 ENDIF