The Variational Method for Aerodynamic Optimization Using the Navier-Stokes Equations


Book Description

This report describes the formulation of an aerodynamic shape design methodology using a compressible viscous flow model based on the Reynolds Averaged Navier Stokes equations. The aerodynamic shape is described by a set of geometrical design variables. The design problem is formulated as an optimization problem stated in terms of an aerodynamic objective functional which has to be minimized. The design scheme employs a gradient based optimization algorithm in order to obtain the optimum values of the design variables. The gradient of the aerodynamic functional with respect to the design variables is computed by means of the variational method, which requires the solution of an adjoint problem. The formulation of the adjoint problem is described which leads to a set of adjoint equations and boundary conditions. Using the flow variables and the adjoint variables, an expression for the gradient has been constructed. Computational results are presented for an inverse problem of an airfoil. It will be shown that, starting from an initial geometry of the NACA 0012 airfoil, the target pressure distribution and geometry of a best fit of the RAE 2822 airfoil in a transonic flow condition has been reconstructed successfully.










Optimization and Computational Fluid Dynamics


Book Description

The numerical optimization of practical applications has been an issue of major importance for the last 10 years. It allows us to explore reliable non-trivial configurations, differing widely from all known solutions. The purpose of this book is to introduce the state-of-the-art concerning this issue and many complementary applications are presented.




Aerodynamic Design Optimization Using the Drag Decomposition Method


Book Description

"The current work applies various drag decomposition methods in an adjoint-based aerodynamic shape optimization framework. In this thesis, the numerical solver based on the Reynolds-averaged Navier-Stokes (RANS) equations is briefly described. The drag decomposition methods, including a novel correction to the induced drag based on an objective vortex sensor, are presented and applied for the drag breakdown in inviscid and viscous flows. The adjoint-based optimization framework is described; particularly, the adjoint principle, the Radial Basis Function (RBF) mesh deformation scheme, and the optimization strategy. Special emphasis is also put on the implementation of the various decomposed drag components. Finally, the proposed approach is applied for the unconstrained and constrained drag minimization of several geometries, namely the DPW-W1 wing, the CRM isolated wing, and a pair of NACA 0012 profile wings, in subsonic-transonic inviscid and viscous flows." --




Optimum Aerodynamic Design & Parallel Navier-Stokes Computations ECARP — European Computational Aerodynamics Research Project


Book Description

This book is one of three volumes entitled "ECARP-European Computational Aerodynamics Research Project", which was supported by the European Union in the Aeronautics Area of the Industrial and Materials Technology Programme. This volume contains optimization techniques for a number of inviscid and viscous problems like drag reduction, inverse, multipoint, wing-pylon-nacelle and riblets (Part A); and methodologies for solving the Navier Stokes equations on parallel architectures for compressible viscous flows in two and three dimensions (Part B). The main objective of this book is to disseminate information about cost effective methodologies for practical design problems and parallel CFD to be used by computer scientists and multidisciplinary engineers.




Recent Development of Aerodynamic Design Methodologies


Book Description

Computational Fluid Dynamics (CFD) has made remarkable progress in the last two decades and is becoming an important, if not inevitable, analytical tool for both fundamental and practical fluid dynamics research. The analysis of flow fields is important in the sense that it improves the researcher's understanding of the flow features. CFD analysis also indirectly helps the design of new aircraft and/or spacecraft. However, design methodologies are the real need for the development of aircraft or spacecraft. They directly contribute to the design process and can significantly shorten the design cycle. Although quite a few publications have been written on this subject, most of the methods proposed were not used in practice in the past due to an immature research level and restrictions due to the inadequate computing capabilities. With the progress of high-speed computers, the time has come for such methods to be used practically. There is strong evidence of a growing interest in the development and use of aerodynamic inverse design and optimization techniques. This is true, not only for aerospace industries, but also for any industries requiring fluid dynamic design. This clearly shows the matured engineering need for optimum aerodynamic shape design methodologies. Therefore, it seems timely to publish a book in which eminent researchers in this area can elaborate on their research efforts and discuss it in conjunction with other efforts.







Engineering Design Optimization


Book Description

Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.