GROUP 1. Run title and other preliminaries TEXT(Boundary Layer Mixing-Length Model #cls TITLE DISPLAY Cases 190,191 and 192 concern steady, incompressible, turbulent plane flow along a smooth flat plate with zero pressure gradient. The plate is maintained at a constant temperature above that of the free stream. Pressure fixed at zero, velocity and temperature take on the prescribed values WFREE and TFREE Constant - - - - - - - - - - - - - - - - - - - - - - - - - - - specified mass-flux, velocity and temperature _____________________________________________________ profiles ///////////////////////////////////////////////////// Wall at constant temperature TWALL ^ y| |---> z #pause The calculations are started 0.487 metres downstream of the leading edge, corresponding to a length Reynolds number REx of 1.E6. The initial mean-velocity profile is taken from published experimental data, and the initial turbulence-energy profile is estimated from the local friction velocity by assuming a distribution compatible with that measured in the fully-developed boundary layer. The calculations are made with 20 grid cells across the jet and a forward step size of 30% of the local width of the boundary layer. 100 forward steps are taken so that the marching integration is terminated at a length Reynolds number of about 2.1E6. #pause In case 190, the Prandtl mixing-length turbulence model is used and the mixing-length distribution is prescribed according to the Escudier formulae, ie Lm=k*y for y/d<<0.09/k, and Lm=0.09*d for y/d>0.09. Here k is the von Karman's constant and y is the normal distance from the wall. The turbulent Prandtl number is set equal to 0.9 and the molecular Prandtl number to 0.71. #pause Experimental data indicate that the local skin friction coefficient Cf is fairly well described by the Schultz-Grunow correlation, i.e. Cf = 0.37*(LOG10(REx))**-2.58 where Cf = 2.*TAUW/(RHOFRE*WFREE**2). For gases with Prandtl numbers Pr in excess of 0.5, the local Stanton number St is quite well approximated by the following correlation: St*Pr**0.4 = 0.0295*REx**-0.2. For REx=2.1E6 these correlations yield Cf=3.17E-3 and St=1.84E-3, while the present PHOENICS predictions yield Cf=3.21E-3 and St=1.97E-3. The sensitivity of the solution to variations of the cross- stream grid-size and distribution and also to forward step size DZW1 should be assessed. ENDDIS #pause REAL(YINLET,WFREE,DELTIN,ZO,AK) REAL(CFEXPT,GPOWER,TFREE,TWALL,POW) YINLET=0.0115;WFREE=33.0;DELTIN=0.009923;ZO=0.487;AK=0.41 CFEXPT=3.381E-3;GPOWER=0.85;TFREE=5.;TWALL=10.;POW=0.2345 GROUP 4. Y-direction grid specification NY=22;YVLAST=YINLET YFRAC(1)=5.000E-02;YFRAC(2)=6.200E-02 YFRAC(3)=7.400E-02;YFRAC(4)=1.070E-01 YFRAC(5)=1.450E-01;YFRAC(6)=1.860E-01 YFRAC(7)=2.290E-01;YFRAC(8)=2.750E-01 YFRAC(9)=3.220E-01;YFRAC(10)=3.720E-01 YFRAC(11)=4.230E-01;YFRAC(12)=4.760E-01 YFRAC(13)=5.300E-01;YFRAC(14)=5.850E-01 YFRAC(15)=6.410E-01;YFRAC(16)=6.990E-01 YFRAC(17)=7.570E-01;YFRAC(18)=8.160E-01 YFRAC(19)=8.770E-01;YFRAC(20)=9.380E-01 YFRAC(21)=9.690E-01;YFRAC(22)=1.000E+00 AZYV=GPOWER;ZWADD=ZO GROUP 5. Z-direction grid specification PARAB=T;NZ=100;AZDZ=PROPY GROUP 7. Variables stored, solved & named NAME(H1)=TEMP;SOLVE(P1,V1,W1,TEMP);STORE(ENUT,LEN1) GROUP 8. Terms (in differential equations) & devices DIFCUT=0.0;TERMS(TEMP,N,Y,Y,Y,Y,Y) GROUP 9. Properties of the medium (or media) ENUL=1.5E-5 ** Select Mixing-Length Formula : Group 9/Sect. 5 of GREX3 EL1=MIXLENBL;ENUT=MIXLEN;EL1A=0.0;EL1B=AK PRT(TEMP)=0.86;PRNDTL(TEMP)=0.7 GROUP 11. Initialization of variable or porosity fields FIINIT(W1)=WFREE;FIINIT(TEMP)=TFREE GROUP 13. Boundary conditions and special sources ** South Wall Boundary WALL (WFUN,SOUTH,1,1,1,1,1,NZ,1,1) COVAL(WFUN,W1,LOGLAW,0.0) COVAL(WFUN,TEMP,LOGLAW,TWALL) **North Free Boundary PATCH(FREE,NORTH,1,1,NY,NY,1,NZ,1,1) COVAL(FREE,P1,1.E5,0.0) COVAL(FREE,W1,ONLYMS,WFREE);COVAL(FREE,V1,ONLYMS,0.0) COVAL(FREE,TEMP,ONLYMS,TFREE) ** Inlet Boundary PATCH(PROF,LOW,1,1,1,NY,1,1,1,1) COVAL(PROF,P1,FIXFLU,GRND3);COVAL(PROF,W1,ONLYMS,GRND3) COVAL(PROF,TEMP,ONLYMS,GRND3);COVAL(PROF,V1,ONLYMS,0.0) GROUP 14. Downstream pressure for PARAB=T IPARAB=1 GROUP 16. Termination of iterations LITHYD=8 GROUP 19. Data communicated by SATELLITE to GROUND ** Select strain-rate for use in Mixing-Length model DWDY=T;IDISPA=0 !!!!! The following use of TEMP0 is non-standard. When used in this way, it cannot be used for its usual purpose of converting temperatures to absolute values !!!!! TEMP0=TWALL;PROFA=CFEXPT;PROFB=DELTIN;PROFC=POW;PROFD=WFREE DZW1=0.3 EL1C = velocity fraction for layer-width calculation EL1D = free stream velocity for layer-width calculation EL1E = 0.0 for layer-width calculation EL1C=0.005;EL1D=WFREE;EL1E=0.0 GROUP 22. Monitor print-out NPRMON=4;IYMON=3;NPLT=1;IPLTL=LITHYD;TSTSWP=LITHYD/2 GROUP 23. Field print-out and plot control PATCH(IZEQNZ,PROFIL,1,1,1,NY,NZ,NZ,1,1);PLOT(IZEQNZ,W1,0.0,0.0) PLOT(IZEQNZ,TEMP,0.0,0.0);PLOT(IZEQNZ,LEN1,0.0,0.0) NYPRIN=2;NZPRIN=NZ;ORSIZ=0.4 GROUP 24. Dumps for restarts