In this paper we present evidence for the existence of multiple solutions of Reynolds– averaged Navier–Stokes equations (RANS) with the one–equation Spalart–Allmaras (SA) and two–equations Wilcox k − ω turbulence models on fixed grids in 3D and describe how they were obtained. The two major configurations considered are an ‘academic’ extruded 2D airfoil geometry and the trap wing, config–1 test case which is part of the AIAA CFD High Lift Prediction Workshop. The observed appearance of the multiple solutions seems to be closely related to smooth body separation (sometimes massive) routinely observed in flows over high lift configurations, especially near stall angles of attack. The results are obtained and cross–verified with two stabilized finite element codes (SUPG) which provide residual converged results for complex flows with second-order discretizations. In the paper, we describe the ways multiple solutions have been obtained, including such obvious ones as providing a different initial guess to the steady state solver as well as somewhat unexpected (in this context) techniques of using implicit residual smoothing while time-marching to steady state. We also discuss the phenomenon of the the so called ‘pseudo–solutions’, which we loosely define as solutions to the discrete system of equations having ‘sharp’ convergence behavior (sometimes up to 6–7 orders of the relative residual reduction) which however fail to achieve the stronger, machine–zero convergence criterion. We also present some numerical observations on the sensitivity of the obtained multiple solutions to the discretization and grid perturbations.

Over the next 20 years, Boeing will likely develop, manufacture, sell, and support many thousands of vehicles that fly. During this period, Boeing project aerodynamicists need access to tools that accurately predict and confirm vehicle flight characteristics. Thirty years ago, these tools consisted almost entirely of analytic approximation methods, Wind tunnel tests, and flight tests. With the development of increasingly powerful Computers, numerical simulations Of Various approximations to the Navier-Stokes equations have begun supplementing these tools. Collectively. these numerical simulation methods have become known as computational fluid dynamics (CFD). This chapter describes the algorithm issues and challenges associated with the development of reliable Navier-Stokes codes that can be used by a wide variety of project engineers who do not necessarily have a deep background in numerical methods.

Recent near-sonic and low-sonic boom transport aircraft development studies have sparked a renewed interest in the nature of the aerodynamics about configurations at near-sonic or low-supersonic speeds. The validity of the wind-tunnel test facilities and the computational methods are challenged by the flow characteristics at near-sonic speeds. Fundamental aerodynamic studies were conducted to assess the ability of the TRANAIR full potential code to predict pressure distributions, drag, and flow characteristics around a family of sting- mounted truncated parabolic bodies of revolution at near-sonic and low-supersonic speeds by comparisons with an extensive existing wind-tunnel database. The analyses included both inviscid and viscous coupled boundary layer analyses. The investigations also included assessments of wind-tunnel wall interference effects as influenced by the various body geometries and test conditions. Extensive test versus theory comparisons of surface pressure distributions, flowfield pressures, and drag forces are presented for subsonic through low-supersonic Mach numbers for the family of test configurations. An additional objective of these studies was to demonstrate the value of using existing and even rather historic experimental data. The experimental data used in the current studies were obtained from NACA wind-tunnel tests reported in 1958.

The mathematical description of a nacelle, body or airfoil having a round nose and pointed aft-end is a continuous but non-analytic because of the infinite slope at the nose and the corresponding large variations of curvature over the surface. Consequently, a large number of coordinates are typically required to describe the geometry. The general mathematical formulation necessary to describe an airfoil, axisymmetric body or nacelle, is defined in order to develop a fundamental geometric transformation technique. This method includes the introduction of a simple analytic and well behaved shape function” that describes the geometry. The “shape function” provides the ability to directly control key geometry parameters such as leading edge radius, trailing edge boattail angle, and closure to a specified aft thickness. A class function is defined that generalizes the method for a wide variety of geometries. The shape function and class function methodology provides a unified approach for describing rather arbitrary 2D and 3D geometries. Examples of using this approach to produce a variety of 2D and 3D geometries are shown to illustrate the versatility of this new methodology.

In this paper, we present the results of a numerical study of wind tunnel wall effects on the flutter characteristics of an airplane model. The airplane model corresponds to a twin engine airplane flying in the transonic range. The wind tunnel chosen is the Transonic Dynamic Tunnel (TDT) located at NASALangley Research Center. It is shown that while the slotted wind tunnel walls in the TDT have a relatively minor influence on the steady aerodynamics, their effects on the unsteady aerodynamics could be substantial. It is therefore important to take the wall effects into account, especially when the flutter frequencies are expected to lie in the same range as the tunnel acoustic natural frequencies.

We describe the use of solution adaptive local grid refinement in a numerical method for solving transonic flow problems about complex three dimensional aircraft configurations. The method is implemented in the TRANAIR code, which has been applied to help solve many practical engineering problems. Attention is focused here on the principal components of the solution adaptive grid algorithms currently being developed and on two applications that demonstrate the capabilities of the algorithms.

We present an approach to solve the full potential equation about arbitrary configurations. A hierarchical refinement of a globally uniform rectangular grid is superimposed over a boundary described by networks of panels. The finite element method is used to obtain discrete operators for irregularly shaped regions near the boundary. We describe the implementation of grid refinement and present some results obtained using this approach.

A new approach for solving certain types of boundary value problems about complex configurations is presented. Numerical algorithms from such diverse fields as finite elements, preconditioned Krylov subspace methods, discrete Fourier analysis, and integral equations are combined to take advantage of the memory, speed and architecture of current and emerging supercomputers. Although the approach has application to many branches of computational physics, the present effort is concentrated in areas of Computational Fluid Dynamics (CFD) such as steady nonlinear aerodynamics, time harmonic unsteady aerodynamics, and aeroacoustics. The most significant attribute of the approach is that it can handle truly arbitrary boundary geometries and eliminates the difficult task of generating surface fitted grids.

PANAIR uses high-order panel method to predict inviscid subsonic or supersonic flows about arbitrary configuration. Panel method solves linear partial differential equation numerically by approximating configuration surface with panels on which unknown singularity strengths are defined. PANAIR includes advanced software technology as well as advanced aerodynamic technology.