Langley Research Center Turbulence Modeling Resource

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VERIF/2DTFP: 2D T3A SST-2003-LM2009 Results

Results are shown here from 2 compressible codes so that the user may compare their own compressible code results. Multiple grids were used so the user can see trends with grid refinement. Different codes will behave differently with grid refinement depending on many factors (including code order of accuracy and other numerics), but it would be expected that as the grid is refined the results will tend toward an infinite grid solution that is the same. Be careful when comparing details: any differences in boundary conditions or flow conditions may affect results.

Two independent compressible RANS codes, OVERFLOW and FUN3D, were used to compute this 2-D flat plate case with the Menter SST-2003 turbulence model and the Langtry and Menter 2009 transition model (see full descriptions on the SST-2003 and SST-2003-LM2009 pages). The full series of 8 grids were used. OVERFLOW is a finite volume, structured overset code and FUN3D is a node-centered, unstructured, finite volume code (FUN3D can solve on mixed element grids, so this case was computed on the same hexahedral grid used by OVERFLOW). Both codes used Roe flux splitting scheme. OVERFLOW utilized an SSOR implicit solution algorithm and FUN3D utilized a point-implicit procedure with implicit line relaxation. Both codes were run with the full Navier Stokes (as opposed to thin-layer), and both codes used first-order upwinding for the advective terms of the turbulence model. Details of each code can be found using the links below.

Additional OVERFLOW Information

Additional FUN3D Information

The following plots show the drag coefficient based on the integrated drag over the entire plate, as well as the local skin friction coefficient at three points, one within the laminar region, one within the transition region, and one within the fully turbulent region. In the plot the x-axis is plotting 1/N^1/2, which is proportional to grid spacing (h). At the left of the plot, h=0 represents an infinitely fine grid. Both codes go toward approximately the same integrated result on an infinitely refined grid. Note that the legend entries with hollow symbols (marked with an asterisk in the first figure) denote extrapoled (h=0) solutions based on the finest three mesh levels except for mesh level 8, i.e. meshes 5, 6, and 7. The filled diamond symbols represent extrapolated, (h=0) values based on mesh levels 6, 7, and 8..

Using the uncertainty estimation procedure from the Fluids Engineering Division of the ASME (Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., Coleman, H., Raad, P. E., "Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications"; Journal of Fluids Engineering, Vol. 130, July 2008, 078001, https://doi.org/10.1115/1.2960953), described in Summary of Uncertainty Procedure, the finest 3 grids yield the following:

The data files and meshes used to generate this data will be made available in the near future.

Profiles of the skin friction coefficient distribution obtained with OVERFLOW and FUN3D are also included in the figure below.

NOTE: The predictions of the SST-2003-LM2009 model (like all turbulence and transition model pairs) is sensitive both to the implementation of the transition model and the underlying turbulence model. The results included on this page utilize codes for which the implementation SST-2003 model has already been verified. It is highly recommended that coders ensure that the turbulence model is verified against the turbulent verification data (link to turbulence verification cases) before attempting to verify transition model implementations.

The results included on this page are provided in this reference: Venkatachari, B. S., Mysore, P., V., Hildebrand, N., Choudhari, M., M., and Denison, M., F., "Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D,", Journal of Aircraft 2024 Vo. 61 No. 2, pp. 345-364, https://doi.org/10.2514/1.C037445, which also includes a description of several other verification cases.

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