G. S. Dulikravich

The Pennsylvania Stale University, University Park, PA, USA

10.1 Introduction

Aerodynamic problems are defined by the governing partial differential or integral equauons, shapes and si/cs of the (low domains, boundary and initial conditions, fluid properties, and by internal sources and external inputs of mass, momentum and energy. In the case of an analysis (direct problem) we are asked to predict the details of a flow-field if the shapc(s) and size($) of the object(s) arc given In the case of a design (inverse or indirect problem) we are asked to de­termine the shape! s) and sizc(s)of the aerodynamic configuration! s) that will satisfy the govern­ing flow-field cquanon(s) subject to specified surface pressure or velocity boundary conditions and certain geometric constraints (ІЗОН 138). The entire design technology is driven by the in­creased industrial demand for reduction of the design cycle time and minimization of the need for the costly a posteriori design modifications.

Aerodynamic inverse design methodologies can he categorized as belonging to surface flow design and flow-field design. Surface flow design is based on specifying pressure. Mach number, etc. on the surface of the object, then finding the shape of the object that w ill generate these surface conditions. How-field design enforces certain global flow-field features (shock – free conditions, minimal entropy generation, etc.) at every point of the flow-field by determining the shape that will satisfy these constraints. An arbitrary distribution of the surface flow param­eters or an arbitrary field distribution of the flow parameters could result in aerodynamic shapes that either cross over ("fish tail" shapes) or never meet ("open trailing edge" shapes) These problems can be avoided by appropriately constraining the surface distribution of the flow parameters (139).

li should be pointed out that inverse methods for aerodynamic shape design are capa­ble of creating only point-designs, that is. the resulting shapes will hac the desired aerody­namic characteristics only at the design conditions. If the angle of attack, free stream Mach number, etc. in actual flight situations are different from the values used in the design, the aero dynamic performance will deteriorate sometimes quite dramatically. For example, when design­ing transonic shock-free shapes with a surface flow design method, the resulting configuration could have a mildly concave part of its surface locally covered by the supersonic flow indicating the existence of a "hanging shock" or a "loose-foot" shock [139) even at the design conditions. At off-design, the hanging shock attaches itself to the aerodynamic surface causing a boundary layer separation. Consequently, it is more appropriate to design shapes that have a weak family of shocks (140) since such designs have been found not to increase the shock wave strengths appreciably at off-design conditions.

In this chapter, we will focus on briefly explaining only these aerodynamic shape inverse design concepts that arc applicable to the design of three-dimensional (3-D) high speed configurations. An attempt will be made to focus on the techniques that have been found to be cost effective, reliable, easy to comprehend and implement, transportable to different comput­ers. and accurate.

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