Using CFX-TASCflow version 2.12.1.beta and previous versions,
we performed computations of flat-plate compressible boundary
layers with the k-omega turbulence models.

There have been found problems when using the low-Re SST model.

The fluid used is a generic ideal gas (air at STP) with
molecular viscosity mu =1.88 x 10^{-5} kg m^{-1}
s^{-1}.

Boundary conditions are defined in Table 1.

Fig.1. Grid sketch (L=3.048 m, h=0.0762 m)

*Table 1 *

Region |
Condition |
Values |

AD | Inflow | Velocity: U=132 m/s, V=W=0 Temperature: static 300 K Turbulence: intensity (Tu) 0.25%, eddy length scale (L) 1.27x10 ^{-3} m |

CF | Outflow | Pressure: static 91715 Pa |

BC | Wall | Stationary, adiabatic |

AB, DE-EF | Symmetry | - |

The following initial conditions were used for all runs:

(U, V, W) = (132, 0, 0) m s^{-1}, Tu=2.5x10^{-3},
L=1.27x10^{-3 }m, P=91715 Pa, T = 300 K

*Table 2 *

Case |
Grid
dimensions |
Near-wall
cell size |
ÓMeanÔ y^{+}
value |
Maximum y^{+}
value |
Results (skin
friction distributions for two turbulence models) |

#1 | 121x43x3 | 1.62x10^{-6}
m |
0.4 | 0.87 | See Figure 2 and 3 |

#2 | 121x43x3 | 2.94x10^{-6}
m |
0.8 | 1.7 | No data for
SST model (overflow) |

#3 | 121x31x3 | 8.04x10^{-5}
m |
22 | 28 | See Figure 4 |

*ÓMeanÔ y*^{+}* value was estimated
at the plateÒs midpoint (x=1.524 m).*

Computations presented below were performed with CFX-TASCflow
version 2.12.1beta (solver build 2.12.1-558 for WinXP). Similar
results were obtained previously with versions 2.11, 2.12.0 and
2.12.1.alpha. Recommended values for computational parameters
are: DTIME=5x10^{-4}, KNTIME=100. All simulations were
started from the same initial guess as specified in the solver
parameter file. Computations with the Wilcox turbulence model
were carried out with parameter TWO_EQUATION_MODEL = 2, and for
the SST model special parameters were TWO_EQUATION_MODEL = 3,
ZONAL_KW_MODEL = 2, SST_TRANSITION_MODEL=F.

Figures 2, 3 and 4 shows variations of computed skin friction
coefficient, C_{f}, along the plate for the low-Re and
high-Re computations respectively.

Fig.2. Skin friction distributions for case 1 (low-Re calculations with parameter FIXED_WALL_DISTANCE_MODEL=T as is by default)

Fig.3. Skin friction distributions for case 1 (low-Re calculations with parameter FIXED_WALL_DISTANCE_MODEL=F manually set in PRM file)

Fig.4. Skin friction distributions for case 3 (high-Re calculations)

Formulas used for postprocessing are standard combinations of these quantities:

Re_{x} - current Reynolds number,

ro (x), U(x) - flow density and velocity along line EF,

tau_{wall}(x) - wall shear stress.

Formula from CFX Theory documentation (ç4.4.4, formula 4.171) used for comparison is as follows:

- Skin friction coefficient computed with the low-Re SST model and default parameters is unacceptably underpredicted in our computations.
- There are limitations on the lateral size of the
near-wall cell like y
^{+}<0.8 or even less (see Table 2). - There are no information in the documentation about the new solver parameter SST_TRANSITION_MODEL.

*Prof. Evgueni M.Smirnov, PhD Student
A.M.Levchenya, March 10, 2003*