Guidelines for Applying Unstructured Navier-Stokes Code
Neal T. Frink
NASA Langley Research Center
Shahyar Pirzadeh
ViGYAN, Inc.
March 1996
Research Objective
To establish guidelines for the efficient application of a new
tetrahedral cell-centered unstructured Navier-Stokes capability to
high-Reynolds number, transonic, separated flows.
Approach
A matrix of eight thin-layered tetrahedral grids were generated
for the ONERA M6 wing with the VGRIDns unstructured tetrahedral
grid generator. Grid sizes ranged from 324,356 tetrahedral cells
where the midchord boundary layer (BL) is resolved by 12 tetrahedra,
to 463,968 cells with 30 tetrahedra resolving the BL. The matrix
was designed to 1) vary the number of tetrahedra spanning the BL
with a fixed initial grid spacing, 2) vary the initial grid spacing
for a fixed number of cells across the BL, and 3) vary the surface
grid density with a fixed normal distribution of cells across the
viscous layer.
Turbulent flow computations were performed at the transonic separated
flow conditions of Mach number = 0.8447, angle of attack = 5.06 degrees,
and Reynolds number = 11.7 million using the tetrahedral cell-centered
Navier-Stokes flow solver USM3DV. Turbulence is modeled in the
intermediate logarithmic layer of the boundary layer by the
Spalart-Allmaras one-equation model, and in the inner region by a
wall function. By exploiting the wall function, reasonable accuracy
is obtained on the present grids with a y+ greater than 50 at the
first node off the surface. As a point of reference, one fully grid
resolved case (no wall function) was computed with a y+ of
approximately 4.
Accomplishment Description
The first figure depicts the surface triangulation and "oilflow" patterns
obtained with a y+ of 70 and 18 tetrahedra resolving the midchord BL. A
significant shock-induced separated flow region is observed on the outboard
portion of the wing. The second figure portrays the longitudinal pressure
coefficient (Cp) distribution along two spanwise stations at 65- and
90-percent fractional semispan for the solution of Figure 1 and two others
with 12- and 30-tetrahedra resolving the midchord BL. Good agreement is
achieved with each case.
The computational matrix required from 59- to 104-megawords of memory.
Individual case run times on the Cray C-90 ranged from 3 to 16 hours.
The entire study utilized approximately 80 Cray C-90 hours.
Significance
This study represents a significant contribution toward establishing the
practical usability of viscous, unstructured grid methodology, and
promoting a more cost effective, long term utilization of NAS resources.
The established guidelines will result in major cost savings during future
applications of the unstructured N-S methodology to complex aerospace
vehicles.
Future Plans
A turbulent flow computation is presently underway on an advanced
subsonic transport configuration with a pylon/nacelle
(962,817 tetrahedra) using the established guidelines as a first
validation of the methodology on a complex configuration. Another
computation is being prepared for a high-speed civil transport
configuration with a focus toward satisfying milestone requirements
within the High Speed Research (HSR) Program.
Related Publications
Neal T. Frink,
Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous
Flows
34th AIAA Aerospace Sciences Meeting and Exhibit,
AIAA Paper No. 96-0292, Reno, Nevada, January 15-18, 1996, pp. 11 (527KB) .
Pirzadeh, S.: "Progress Toward A User-Oriented Unstructured
Viscous Grid Generator", AIAA Paper 96-0031, January 1996.
Figure 1. - Surface triangulation and "oilflow" patterns for ONERA M6
wing; magenta = low pressure and green = high pressure.
Figure 2. - Effect of normal grid density on Cp distributions for
ONERA M6 wing; Mach = 0.8447, angle of attack = 5.06 degrees, and
Reynolds number = 11.7 million.
