On performance of the low-Re k-omega based SST-model of turbulence implemented in CFX-TASCflow version 2.12.1.

Introduction

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.

1. Problem Definition

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.

Grid sketch (8 Kb)

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

2. Cases descriptions and computation aspects

Table 2

Case Grid dimensions Near-wall cell size ”Mean‘ 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

”Mean‘ y+ value was estimated at the plate“s 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.

3. Results

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.

Skin friction distributions for case 1 (3 Kb)

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

Skin friction distributions for case 1, picture 2 (3 Kb)

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

Skin friction distributions for case 3 (3 Kb)

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 (Á4.4.4, formula 4.171) used for comparison is as follows:

Formula from CFX Theory documentation (0.3 Kb)

4. Conclusions for the performance of the low-Re SST model

  1. Skin friction coefficient computed with the low-Re SST model and default parameters is unacceptably underpredicted in our computations.
  2. There are limitations on the lateral size of the near-wall cell like y+<0.8 or even less (see Table 2).
  3. 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