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.
Developments in computational methods for high-lift aerodynamics
Summary Viscous/inviscid interaction techniques for calculating the flow about multiple-element aerofoils have been under development in the UK for the last decade producing such programs as MAVIS and HILDA. These methods give reasonable predictions of the lift for viscous attached flow, but fail to give an estimate of the maximum lift and the associated flow separations on the aerofoils. The methods also fail to give adequate predictions of the drag for both attached and separated flow. The disappointing performance of the methods in predicting maximum lift stems primarily from the use of direct methods to solve the first order boundary-layer equations, whilst the poor drag predictions arise from inadequate methods for predicting the development of the flow over the flap. The assumption of incompressible flow could also be a contributory factor in both cases. Methods of overcoming the first restriction are described by using a more appropriate coupling between the inviscid and viscous flows which properly assigns the correct role to each partner in the coupling: this approach is illustrated by ‘semi-inverse’ and ‘quasi-simultaneous’ couplings of a finite-element method for the compressible inviscid flow with an integral method for the boundary layers and wakes. Some methods for calculating the compressible flow about multiple-element aerofoils are also reviewed. However these improvements do not give an adequate estimate of the drag so possible improvements to the calculation of the flow over the flap are discussed.
Experimental and Computational Investigation of a Swept-Wing Flow at Subsonic Speeds
The paper reports on an experimental and computational investigation of the flow on a portion of an aircraft swept wing in a wind tunnel at low speeds. The range of angle of attack covered the domain encountered by the aircraft, and the actual outer part of a wing was used for the tests. The experiments included static pressure distributions in the leading-edge region, as well as the rest of the chord; shear-stress measurements in the leadingedge region, obtained with heated film gages; and skin-friction measurements on the main part of the wing, obtained with modified Preston tubes. Velocity profile data across the boundary layer were taken in a smaller region, and some measurements of the turbulence characteristics at a few locations on the main wing were also taken. The pressure distribution was shown to be satisfactorily represented by patching a two-dimensional inviscid method in the leading-edge region and a three-dimensional panel method on the main wing. Starting from this, boundary-layer calculations were performed with Bradshaw's finite-difference program for straighttapered swept wings, where different spanwise stations were calculated separately. The results are encouraging, as the estimated skin-friction magnitude and trends with Reynolds numbers were predicted reasonably well.