Kuo-Cheng Chang

Airfoils with separation and the resulting wakes

A viscous/inviscid interaction method is described and has been used to calculate flows around four distinctly different airfoils as a function of angle of attack. It comprises an inviscid-flow method based on conformal mapping, a boundary-layer procedure based on the numerical solution of differential equations and an algebraic eddy viscosity. The results are in close agreement with experiment up to angles close to stall. In one case, where the airfoil thickness is large, small difficulties were experienced and are described. The method is shown to be capable of obtaining results with large flow separation and quantifies the role of transition on the lift coefficient.

Further comparisons of interactive boundary-layer and thin-layer Navier-Stokes procedures

It is generally accepted that the Navier—Stokes equations correctly represent fluid-flow phenomena. Since the unsteady three-dimensional equations can generally be solved for flows where small-scale fluctuations are unimportant, emphasis has been placed on particular reduced forms such as those appropriate to regions of inviscid flow and boundary layers. In recent years, and with the application of numerical solution procedures in mind, attention has also been paid to the Reynolds-averaged Navier—Stokes equations and various further-reduced forms, including their so-called parabolized forms and the thin-layer Navier—Stokes (TLNS) equations.

Prediction of Post-Stall Flows on Airfoils

The calculation of the performance of airfoils requires the solution of the conservation equations, which, in general, can be accomplished in different ways. An important approach, where large scale computational facilities are available, is to solve the Reynolds-averaged Navier-Stokes equations or a reduced form such as the so-called parabolized and thin-layer Navier-Stokes equations. Two alternative and successful computational methods have been proposed by Maskew and Dvorak [126] and Gilmer and Bristow [79] in which an empirical inviscid flow model is used to represent the effects of flow separation with solutions of the boundary-layer equations in standard form up to the point of separation and a free surface assumption to model the separated flow region. The shape and the length of the separation are computed by satisfying a constant pressure boundary condition on the surface, and very good results have been obtained for airfoils over a wide range of angles of attack including stall and post-stall.

An Interactive Scheme for Three-Dimensional Transonic Flows

For reliable calculation of the flow over aerodynamic bodies, the viscous boundary-layer solution must be allowed to influence the inviscid-flow solution. This is the basis for the recent emphasis on the iterative coupling of the inviscid- and viscous-flow equations for aerodynamic problems. However, for a prescribed pressure distribution, the boundary-layer equations tend to become singular as separation is approached. This, in turn, has led to the development of procedures for solving the boundary-layer equations in an inverse form.

A general method for calculating three-dimensional laminar and turbulent boundary layers on ship hulls

Abstract : This report describes the progress made during the past year towards the development of a general method for computing three-dimensional incompressible laminar and turbulent boundary layers on ship hulls. The method employs an implicit two-point finite-difference method and an algebraic eddy-viscosity formulation. During the past year the efforts concentrated on the choice of an appropriate coordinate system; the calculation of the geometric parameters of this coordinate system; the numerical solution of the governing equation of the orthogonal curvilinear system; and obtaining preliminary results for simple ship forms. Further studies are in progress and will be reported in a forthcoming report.

Calculation of flow over multielement airfoils at high lift

An interactive boundary-layer procedure has been used to calculate the flow around three two-element airfoil arrangements. The procedure is known to be accurate, is seen as the foundation of a generally applicable calculation method, and is used here in comparatively simple form. The calculated results are in close agreement with measurements for angles of attack up to around 10 deg, with flap-deflection angles of up to 20 deg. The range of accuracy of the predictions can be extended by the incorporation of the wake, and this will be required to deal with high angles of attack, high flap deflection angles, and airfoil elements with smaller slot gaps than those considered here.

On the Turbulence-Modeling Requirements of Three-Dimensional Boundary-Layer Flows

Appropriate three-dimensional equations have been solved, in finite-difference form, and with boundary conditions corresponding to the infinite swept wing of van den Berg and Elsenaar and the full three-dimensional data of East and Hoxey. In the former case, results were obtained with an algebraic eddy-viscosity formulation and a two-equation model which allows for transport of turbulence kinetic energy and dissipation rate. The results show that both models yield similar mean-flow characteristics, provided the same wall boundary conditions are employed, and that these deviate from the measurements with increasing adverse pressure gradient. As with previous investigations of two-dimensional flows, the procedure used to generate the initial turbulence energy profile can significantly influence the calculated results. The calculations of the fully three-dimensional flow made use of the algebraic eddy-viscosity formulation and, in keeping with the previous results for two-dimensional flows and the swept wing, the agreement with measurements is excellent until the separation region is approached.

Physics of Unsteady Flows

Standard textbooks on aircraft aerodynamics either omit any discussion of unsteady aerodynamic effects or, at most, devote a. single chapter to it. A more detailed discussion of unsteady aerodynamics is usually found in textbooks on aeroclasticity. as for example in the books by Dowell et al. [1] and Bisplinghoff et al. [2]. This is because a complete understanding and analysis of aircraft flutter and dynamic response phenomena cannot be attained without the proper unsteady aerodynamic analysis methods. This state of affairs is somewhat unfortunate because it generates the impression that unsteady aerodynamics is a highly specialized discipline which is needed only for the prediction of aeroelastic phenomena.

Boundary-Layer Methods

This chapter is concerned with the solution of the boundary-layer equations of subsection 2.4.3 for boundary conditions that include a priori specification of the external velocity distribution either from experimental data or from inviscid-flow theory (called the standard problem), a priori specification of an alternative boundary condition which may be a displacement thickness distribution (called the inverse problem), or the determination of the freestream boundary condition by iteration between solutions of inviscid and boundary-layer equations (called an interaction problem).

The Differential Equations of Fluid Flow

The differential equations of fluid flow are based on the principles of conservation of mass, momentum and energy and are known as the Navier-Stokes equations. For incompressible flows and for flows in which the temperature differences between the surface and freestream are small, the fluid properties such as density ϱ and dynamic viscosity μ in the conservation equations are not affected by temperature. This assumption allows us to ignore the conservation equation for energy and concentrate only on the conservation equations for mass and momentum.