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