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Neal T. Frink
NASA Langley Research Center
April 1994
To 1) apply an emerging unstructured, viscous grid generation code to construct a tetrahedral, viscous grid around a delta wing, 2) obtain a laminar solution from an unstructured viscous-flow solver, and 3) validate the result against experimental data and a structured-grid computation.
An unstructured viscous grid of 730,454 tetrahedral cells was generated for a delta wing of aspect-ratio 1 by a version of the unstructured-grid generation code, VGRID, which was recently extended with the new Advancing-Layers method (ALM). Normal spacing is distributed near the surface to yield approximately 10 nodes (30 tetrahedra) in the mid-chord boundary layer for laminar flow. Anisotropic stretching, evident in the surface grid shown in the figure, is utilized to reduce the chordwise density of cells in the grid. This resulted in a 7-fold reduction in grid size compared to standard isotropic triangles.
A laminar flow solution was computed for a Mach number of 0.3, angle of attack of 20.5 deg., and Reynolds number of 900,000 using an unstructured Navier-Stokes flow solver, USM3D. A companion structured-grid computation was performed with the well established CFL3D code on a 65X65X33 (span-radial-chordwise) H-O grid for comparison.
The figure portrays the surface "oil-flow" pattern and a comparison of the spanwise distribution of pressure coefficient, C_p, at four chord stations. The coalescing and diverging streamlines in the computed flow patterns show evidence of the primary, secondary, and tertiary vortices. Good agreement is noted between the unstructured and structured solutions, and with the experimental data of Hummel. The computation required 133 megawords of memory and was fully converged in 3400 cycles and 21 hours on the Cray C-90. (Note: This performance has improved considerably since 1994).
This work represents a critical demonstration of a new totally unstructured 3-D viscous analysis capability. The primary advantage of unstructured grids comes from a greatly reduced grid generation time for complex configurations. It is anticipated that this methodology may lead to solving viscous-flow problems on complete aircraft geometries on the order of weeks, rather than months as with structured grids.
Work is underway to mature the VGRID/ALM code to the point that non-expert users can apply it effectively. A one-equation turbulence model has been installed in USM3D, and is undergoing testing. Additional validation studies are planned.
Pirzadeh, S.: "Viscous Unstructured Three-Dimensional Grids by the Advancing Layers Method", AIAA Paper 94-0417, January 1994.
Frink, N. T.: "Recent Progress Toward a Three-Dimensional Unstructured Navier-Stokes Flow Solver" , AIAA 94-0061, January 1994.
Comparison of computed and experimental data (solid line - USM3D, dashed line - CFL3D, circle - data), and surface triangulation and "oil-flow" patterns.
