On the Theory of Optimum Aerodynamic Shapes


Book Description

The physical models of interest in the theory of optimum aerodynamic shapes are reviewed. The corresponding mathematical models are illustrated for both problems involving one independent variable and problems involving two independent variables. Then, the solution process is considered. Finally, new trends in the theory of optimum aerodynamic shapes as well as problems of interest in the immediate future are outlined. (Author).



















Computational Algorithms for Aerodynamic Analysis and Design


Book Description

The goal of our research under AFOSR sponsorship is to develop mathematical procedures which can be used to arrive at optimum, or near optimum, aerodynamic shapes by merging techniques from computational fluid dynamics and control theory. With this in mind we have continued to work in two main topics: Development of high resolution shock capturing schemes with low numerical diffusion. Since last year the symmetric limited positive (SLIP) and upstream limited positive (USLIP) schemes have been improved by the introduction of a new flux limiter which guarantees positivity while maintaining good accuracy in smooth flow regions. A comprehensive theory has also been developed for design of numerical fluxes which guarantee stationary discrete shocks with a single interior point. Aerodynamic shape optimization by boundary control progress in aerodynamic shape optimization has been realized on two fronts. First the method has been successfully implemented for two-dimensional lifting potential flows using a general finite volume scheme with numerically generated grids. Secondly, the method has been successfully implemented for three-dimensional wing design using the Euler equations. (AN).




Theoretical and Applied Aerodynamics


Book Description

This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including: -The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics. - The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings to minimize wave drag. Unsteady flow is also briefly discussed. Numerical simulations based on relaxation mixed-finite difference methods are presented and explained. - Boundary layer theory for all Mach number regimes and viscous/inviscid interaction procedures used in practical aerodynamics calculations. There are also four chapters covering special topics, including wind turbines and propellers, airplane design, flow analogies and hypersonic (rotational) flows. A unique feature of the book is its ten self-tests and their solutions as well as an appendix on special techniques of functions of complex variables, method of characteristics and conservation laws and shock waves. The book is the culmination of two courses taught every year by the two authors for the last two decades to seniors and first-year graduate students of aerospace engineering at UC Davis.




Optimal Shape Design


Book Description

Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "shape" of some region. The main topics covered are: the optimal design of a geometrical object, for instance a wing, moving in a fluid; the optimal shape of a region (a harbor), given suitable constraints on the size of the entrance to the harbor, subject to incoming waves; the optimal design of some electrical device subject to constraints on the performance. The aim is to show that Optimal Shape Design, besides its interesting industrial applications, possesses nontrivial mathematical aspects. The main theoretical tools developed here are the homogenization method and domain variations in PDE. The style is mathematically rigorous, but specifically oriented towards applications, and it is intended for both pure and applied mathematicians. The reader is required to know classical PDE theory and basic functional analysis.