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, Cf, 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:
Rex - current Reynolds number,
ro (x), U(x) - flow density and velocity along line EF,
tauwall(x) - wall shear stress.
Formula from CFX Theory documentation (ç4.4.4, formula 4.171) used for comparison is as follows:
Prof. Evgueni M.Smirnov, PhD Student A.M.Levchenya, March 10, 2003