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TURBULENCE MODEL NUMERICAL ANALYSIS

3D ONERA M6 Wing Validation

SA-neg Model Results
 

Link to SA-neg equations

Preliminary results are shown for the 3D ONERA M6 wing, for the SA-neg variant of the SA model. Note that SA-neg is passive to the original (SA) model in well-resolved flowfields, and hence is expected to yield essentially identical results as SA for the cases here. For all results, the farfield value of the Spalart turbulence variable is \tilde \nu_{farfield} = 3 \nu_{\infty}. In all codes the Prandtl number Pr is taken to be constant at 0.72, and turbulent Prandtl number Prt is taken to be constant at 0.9. The dynamic viscosity is computed using Sutherland's Law (See White, F. M., "Viscous Fluid Flow," McGraw Hill, New York, 1974, p. 28). In Sutherland's Law, the local value of dynamic viscosity is determined by plugging the local value of temperature (T) into the following formula:

\mu = \mu_0 \left( \frac{T}{T_0} \right)^{3/2} \left( \frac{T_0 + S}{T+S} \right)

where \mu_0 = 1.716 \times 10^{-5} kg/(ms), T_0 = 491.6 R, and S = 198.6 R. The same formula can be found online (with temperature constants given in degrees K and some small conversion differences). Note that in terms of the reference quantities for this particular case, Sutherland's Law can equivalently be written:

\left( \frac{\mu}{\mu_{ref}} \right) = \left( \frac{T}{T_{ref}} \right)^{3/2} \left( \frac{T_{ref} + S}{T+S} \right)

where \mu_{ref} is the reference dynamic viscosity that corresponds to the freestream in this case, and freestream T_{ref} is 540R. This latter form may be more convenient for nondimensional codes. (Specific details regarding an implementation of Sutherland's Law in nondimensional codes can be found in handwritten notes describing Sutherland's Law in CFL3D and FUN3D.)

The results on this page have been reported in AIAA Paper 2018-1102, https://doi.org/10.2514/6.2018-1102. Also, many of the other papers from two special sessions at AIAA SciTech 2018 dealt with this case: see AIAA Papers 2018-1101 through 1104, and AIAA Papers 2018-1566 through 1570.
 

Case 2308, AoA=3.06 deg: Grid Convergence Behavior of Forces, Moment, and Maximum Eddy Viscosity

Plots are shown to illustrate grid convergence for the lift, drag, moment coefficient, and nondimensional maximum eddy viscosity for the ONERA M6 AoA=3.06 deg case. (Note: the moment is about the y-moment center.) The contributions to the drag coefficient due to the viscosity and pressure are also presented separately. For forces and moment, results from 4 different codes (on different versions of the grids) appear to be approaching nearly the same results as the grid is refined (i.e., as h approaches zero). CFL3D is a structured-grid code, while all others are unstructured-grid codes. For eddy viscosity, it is not as clear that all results are approaching the same answer; finer grids are likely required. Recall that all codes were run using SA-neg.

SA-neg - lift coefficient vs h for ONERA M6 alpha=3.06 SA-neg - drag coefficient vs h for ONERA M6 alpha=3.06

SA-neg - pressure drag coefficient vs h for ONERA M6 alpha=3.06 SA-neg - viscous drag coefficient vs h for ONERA M6 alpha=3.06

SA-neg - moment coefficient vs h for ONERA M6 alpha=3.06 SA-neg - maximum eddy viscosity vs h for ONERA M6 alpha=3.06

Results that generated the above plots can be found in the following data file: combined_forces_pitchmom_maxmut.dat.
 

Case 2308, AoA=3.06 deg: Surface Pressure and Skin Friction Coefficients

First, plots are shown to illustrate differences between three different CFD codes on the finest L1 grids (experimental data are also included for comparison). The "eta" refers to the span station (0=root, 1=tip), and the x-locations are nondimensionalized by local chord.

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.20 SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.20

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.44 SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.44

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.65 SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.65

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.80 SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.80

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.90 SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.90

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.96SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.96

SA-neg - Cp vs x/c for ONERA M6 alpha=3.06 at eta=0.99 SA-neg - Cfx vs x/c for ONERA M6 alpha=3.06 at eta=0.99

The following plots show grid convergence behavior of upper surface pressure coefficients and x-component of skin friction for individual codes (not available for USM3D yet), for eta=0.20, 0.80, and 0.99.

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20, using FUN3D on 4 grids SA-neg - Cfx vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20, using FUN3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20, using CFL3D on 4 grids SA-neg - Cfx vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20, using CFL3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80, using FUN3D on 4 grids SA-neg - Cfx vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80, using FUN3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80, using CFL3D on 4 grids SA-neg - Cfx vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80, using CFL3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99, using FUN3D on 4 grids SA-neg - Cfx vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99, using FUN3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99, using CFL3D on 4 grids SA-neg - Cfx vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99, using CFL3D on 4 grids

The following plots show grid convergence behavior of upper surface pressure coefficients near the trailing edge for each code, for eta=0.20.

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20 near TE, using FUN3D on 4 grids SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20 near TE, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20 near TE, using CFL3D on 4 grids

The following plots show grid convergence behavior of upper surface pressure coefficients near the minimum Cp location for each code, for eta=0.20.

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20 near min Cp location, using FUN3D on 4 grids SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20 near min Cp location, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.20 near min Cp location, using CFL3D on 4 grids

The following plots show grid convergence behavior of upper surface pressure coefficients near the shock intersection location for each code, for eta=0.80.

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80 near shock intersection, using FUN3D on 4 grids SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80 near shock intersection, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.80 near shock intersection, using CFL3D on 4 grids

The following plots show grid convergence behavior of upper surface pressure coefficients near the trailing edge for each code, for eta=0.99.

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99 near TE, using FUN3D on 4 grids SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99 near TE, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99 near TE, using CFL3D on 4 grids

The following plots show grid convergence behavior of upper surface pressure coefficients near the minimum Cp location for each code, for eta=0.99.

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99 near min Cp location, using FUN3D on 4 grids SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99 near min Cp location, using USM3D on 4 grids

SA-neg - Cp vs x/c for ONERA M6 upper surface alpha=3.06 at eta=0.99 near min Cp location, using CFL3D on 4 grids

Results that generated the above plots can be found in the following data files: FUN3D_OM6_A3p06_CPCF.dat, USM3D_OM6_A3p06_CP.dat, CFL3D_OM6_A3p06_CPCF.dat.

Sample input files are available for FUN3D and CFL3D: fun3d.nml_OM6_L2MIXcorrected, cfl3d_OM6sampleinput_L2.inp. (Note: it was discovered after-the-fact that FUN3D,FV was mistakenly run with conditions slightly different than those specified for this case. It used: reynolds_number=14.623131633937641e6, temperature=536R, area_reference=1.159316400000000, x_moment_length=0.801469910371319, y_moment_length=1.4844. However, these differences are believed to be small enough that the results, to plotting accuracy, would be very close. The incorrect values have been corrected in the input file provided here.)
 
 

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Recent significant updates:
04/17/2019 - added sample input files for FUN3D and CFL3D
06/22/2018 - added skin friction results from FUN3D and CFL3D

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Last Updated: 11/10/2021