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Numerical optimization is a little understood and even lesser used design tool which can have a significant effect on our efforts to reduce energy consumption, improve environmental quality and provide safer, more comfortable vehicles. Optimization is a numerical search method that can be applied to almost any engineering discipline where we perform computer analyses, whether structures, fluid dynamics or almost anything else. Though seldom taught in engineering colleges, these design methods and tools have been developed over the past forty years to a high level of maturity. The purpose of this paper is twofold. First, we will discuss the basic concept of design optimization. It will be seen that optimization can be coupled with almost any computer analysis and even experimental tests to change the important inputs to improve one or more outputs, with limits on other outputs. The second purpose will be to demonstrate that optimization works.

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the in viscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (i) adverse pressure-gradient minimization, (ii) pitching-moment minimization, and (iii) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.

Numerical optimization concepts are described with limited technical detail. The purpose is to provide the nonspecialist with sufficient information to judge the applicability of these methods to his particular design problem. The concepts are first described in physical terms to give a basic understanding of the iterative procedure employed by these methods. Next, the typical engineering task is presented and converted to a form ammenable to solution by numerical optimization. Basic algorithms for solving this problem are identified. Numerous applications are referenced, emphasizing the structural design discipline. The state of the art allows for the routine solution of nonlinear design problems of approximately 20 independent variables subject to 100 or more constraints. In many applications, much larger design problems may be solved. Selected references are provided which describe the methods and applications in more detail.

A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.

Recent applications of numerical optimization to the design of advanced airfoils for transonic aircraft have shown that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while the drag at the design Mach number is the objective function. Such a procedure doubles the computation time over that for single design-point problems, but the final result is worth the increased cost of computation. The ability to treat such multiple design-point problems by numerical optimization has been enhanced by the development of improved airfoil shape functions. Such functions permit a considerable increase in the range of profiles attainable during the optimization process.

Structural optimization has seen remarkable progress in recent years, and is now recognized as a practical design tool. The ingredients of a structural optimization computer code include finite element analysis, sensitivity analysis, and optimization. Each of these are now available, but are seldom contained in a single computer code. Notably, sensitivity analysis must often be calculated as a post-processing operation to the finite element analysis. These various aspects of structural optimization are discussed, with emphasis on sensitivity calculations. Examples are given to demonstrate the present state of the art. It is argued that, while experts in the field can now create this capability by combining existing software, this is still a major task. Thus, it is most desirable that general-purpose, commercial software be created at the earliest possible date in order that this technology be used to its potential.