Transonic Navier-Stokes wing solution using a zonal approach. Part 1: Solution methodology and code validation
Abstract : A fast diagonalized Beam Warming algorithm is coupled with a zonal approach to solve the three dimensional Euler/Navier Stokes equations. The computer code, called Transonic Navier Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin layer Navier Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method coded. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000 point mesh for a NACA 0012 wing. A three order of magnitude drop in the L2 norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.
Computational-experimental pressure distributions on a transonic, low-aspect-ratio wing
A generic, transonic, supercritical, low aspect-ratio wing was tested at design incidence of 5 deg at Mach numbers from 0.25 to 0.96. Oil-flow studies at the design Mach number of 0.85 showed local-flow separation, which, in retrospect, might have been avoided. At Mach 0.82 with unseparated flow, the surface-flow angles were less than 10 deg. Predictions with the FLO22 transonic potential code are good. Lift interference is strong without tunnel-wall suction. Evidence from this study shows that wings that are optimized for mild shock waves and pressure-recovery gradients generally have small, three-dimensional flow at conditions for unseparated flow.
Noniterative grid generation using parabolic difference equations for fuselage-wing flow calculations
A fast method for generating three-dimensional grids for fuselage-wing transonic flow calculations using parabolic difference equations is described. No iterative scheme is used in the three-dimensional sense; grids are generated from one grid surface to the next starting from the fuselage surface. The computational procedure is similar to the iterative solution of the two-dimensional heat conduction equation. The proposed method is at least 10 times faster than the elliptic grid generation method and has much smaller memory requirements. Results are presented for a fuselage and wing of NACA-0012 section and thickness ratio of 10 percent. Although only H-grids are demonstrated, the present technique should be applicable to C-grids and O-grids in three dimensions.