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Dr. Neal T. Frink, Principal Investigator
NASA Langley Research Center
Co-Investigators: Dr. Shahyar Z. Pirzadeh, NASA Langley Research Center, and Dr. Paresh C. Parikh, Paragon Research, Inc.
Unstructured transonic Navier-Stokes (N-S) computations are presented for the complete F-16 aircraft configuration in an ongoing assessment of the Tetrahedral Unstructured Software System (TetrUSS) for aerodynamic analysis of very complex geometries and flow fields.
TetrUSS is a maturing unstructured-grid computational fluid dynamic (CFD) software system which is being used by a broad range of users for performing rapid aerodynamic analysis and design of complex configurations.
A thin-layered tetrahedral grid of 1,428,779 cells (255,959 nodes) was generated for a full F-16 aircraft configuration with the VGRIDns unstructured tetrahedral grid generator (see Figure 1). A companion "inviscid" grid of 1,111,762 cells (not shown) was also generated for comparison purposes. Grid sizes were kept small by utilizing anisotropic cell stretching which generally results in a third fewer cells than an isotropic grid with similar chordwise resolution. The initial viscous grid was completed within approximately 40 to 60 hours of labor.
Turbulent flow solutions were computed with the USM3Dns flow solver at angles of attack (AOA) of 0, 2, 4, and 8 degrees, Mach 0.95, and Reynolds number of 2 million based on mean aerodynamic chord. 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, a considerable savings in grid size, hence core memory, is achieved while retaining reasonable solution accuracy. The normal grid spacing was sized to yield a nominal midchord y-plus of 30 for the first node above the surface and 18 to 20 tetrahedra across the boundary layer.
Figure 2 depicts the overall surface pressure coefficient (Cp) contours for the N-S solution at AOA=4 degrees. The global pressure field is characterized by strong shock systems and interactions which are especially pronounced between the store components. Figure 3 portrays the Cp and "oil-flow" patterns on the outboard store and pylon. This figure reveals shock-induced flow separations on the store afterbody and aft-pylon region. Figure 4 compares the longitudinal distribution of Cp from Euler, N-S, and experimental data along the inboard and outboard sides of the store. As expected, the inviscid Euler shock is too strong and too far aft compared to data, whereas the N-S solution results in a softened expansion and brings the aft-shock into better agreement.
A typical N-S solution required 254MW of memory and 11 hours of CRAY C90 time. With a multitasking efficiency of 6 out of 10 processors, each case was completed in 2 wallclock hours.
The presented F-16 results serve to demonstrate the strong potential for tetrahedral-based Navier-Stokes methodologies to become a practical computational aerodynamic tool. The primary motivation for this new technology is rapid grid generation on the order of days with solution accuracies comparable to established structured-grid methodology.
Computations on a finer grid for the F-16 configuration are presently underway. The current focus is to continue validation of this upcoming capability for a broad range of complex geometries and flows in order to elevate user confidence.
Frink, N.T. and Pirzadeh, S.Z.: "Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations" , NASA/TM-1998-208961, December 1998, pp. 16, also presented at the 10th International Conference on Finite Elements in Fluids, Tucson, AZ, January 5-8, 1998. (To appear in Journal of Numerical Methods in Fluids.)
Figure 1: Viscous tetrahedral grid on complete F-16 aircraft with external
stores,
1,428,779 cells. Note thin-layer clustering on symmetry plane.
- 117k color jpg
Figure 2: Surface Cp contours for Navier-Stokes flow solution on complete
F-16 aircraft
with stores for Mach 0.95, angle of attack 4 degrees, and Re_mac=2 million.
red=low pressure and green=high pressure.
Figure 3: Surface Cp and "oil-flow" patterns on outboard store and pylon for
Mach 0.95,
angle of attack 4 degrees, and Re_mac=2 million. red=low pressure and
green=high
pressure.
Figure 4: Longitudinal distribution of surface pressure coefficient on
generic finned-store
body at Mach 0.95 and angle of attack 4 degrees. Store nose at x/L_store=0,
and
x/L_store=1 slightly aft of store fins.