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Book Aerodynamic Shape Optimization Via Discrete Adjoint Formulation Using Euler Equations on Unstructured Grids

Download or read book Aerodynamic Shape Optimization Via Discrete Adjoint Formulation Using Euler Equations on Unstructured Grids written by Bijoyendra Nath and published by . This book was released on 1998 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the optimization process, a constrained nonlinear programming package which uses a sequential quadratic programming algorithm is used. This study presents the process of analytically obtaining the exact discrete sensitivity derivatives and computationally cost-effective algorithms to efficiently use them in a design environment. Storage issues are circumvented by developing algorithms which perform matrix-vector operations during the construction itself. To validate the unstructured shape optimization procedure, an arbitrary symmetrical airfoil is optimized in an inviscid transonic flow regime.

Book Aerodynamic Shape Optimization of Complex Aircraft Configurations Via an Adjoint Formulation

Download or read book Aerodynamic Shape Optimization of Complex Aircraft Configurations Via an Adjoint Formulation written by James Reuther and published by . This book was released on 1996 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This work describes the implementation of optimization techniques based on control theory for complex aircraft configurations. Here control theory is employed to derive the adjoint differential equations, the solution of which allows for a drastic reduction in computational costs over previous design methods [13, 12, 43, 38]. In our earlier studies [19, 20, 22, 23, 39, 25, 40, 41, 42] it was shown that this method could be used to devise effective optimization procedures for airfoils, wings and wing-bodies subject to either analytic or arbitrary meshes. Design formulations for both potential flows and flows governed by the Euler equations have been demonstrated, showing that such methods can be devised for various governing equations [39, 25]. In our most recent works [40, 42] the method was extended to treat wing-body configurations with a large number of mesh points, verifying that significant computational savings can be gained for practical design problems. In this paper the method is extended for the Euler equations to treat complete aircraft configurations via a new multiblock implementation. New elements include a multiblock-multigrid flow solver, a multiblock-multigrid adjoint solver, and a multiblock mesh perturbation scheme. Two design examples are presented in which the new method is used for the wing redesign of a transonic business jet."

Book Optimization and Computational Fluid Dynamics

Download or read book Optimization and Computational Fluid Dynamics written by Dominique Thévenin and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Aerodynamic Shape Optimization Using Control Theory

Download or read book Aerodynamic Shape Optimization Using Control Theory written by James John Reuther and published by . This book was released on 1996 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Aerodynamic shape design has long persisted as a difficult scientific challenge due [sic] its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then [sic] by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions."

Book A Preconditioning Method for Shape Optimization Governed by the Euler Equations

Download or read book A Preconditioning Method for Shape Optimization Governed by the Euler Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-08-09 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations. The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level. The Hessian (second order derivative of the cost functional with respect to the shape variables) is approximated also at the continuous level, as first introduced by Arian and Ta'asan (1996). The approximation of the Hessian is used to approximate the Newton step which is essential to accelerate the numerical solution of the optimization problem. The design space is discretized in the maximum dimension, i.e., the location of each point on the intersection of the computational mesh with the airfoil is taken to be an independent design variable. We give numerical examples for 86 design variables in two different flow speeds and achieve an order of magnitude reduction in the cost functional at a computational effort of a full solution of the analysis partial differential equation (PDE). Arian, Eyal and Vatsa, Veer N. Langley Research Center NASA/CR-1998-206926, NAS 1.26:206926, ICASE-98-14 NAS1-19480; RTOP 505-90-52-01...

Book An a Posteriori Error Control Framework for Adaptive Precision Optimization Using Discontinuous Galerkin Finite Element Method

Download or read book An a Posteriori Error Control Framework for Adaptive Precision Optimization Using Discontinuous Galerkin Finite Element Method written by James Lu and published by . This book was released on 2005 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction: Aerodynamic design optimization has seen significant development over the past decade. Adjoint-based shape design for elliptic systems was first proposed by Pironneau and applied to transonic flow by Jameson . A review of the aerodynamic shape optimization literature and a large list of references is given in. Over the years much technology has been developed, allowing engineers to contemplate applying optimization methods to a wide variety of problems. In the context of structured grids, adjoint-based applications include multipoint, multi-objective airfoil design using compressible Navier-Stokes equations and 3D multipoint design of aircraft configurations using inviscid Euler equations. There have also been significant effort in applying adjoint methods to the unstructured grid setting. In this context, Newman et al., Elliot and Peraire were among the first to develop discrete adjoint approaches for the inviscid Euler equations.

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

Download or read book The Variational Method for Aerodynamic Optimization Using the Navier Stokes Equations written by and published by . This book was released on 1997 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book AIAA Journal

    AIAA Journal

    Book Details:
  • Author : American Institute of Aeronautics and Astronautics
  • Publisher :
  • Release : 2008
  • ISBN :
  • Pages : 1112 pages

Download or read book AIAA Journal written by American Institute of Aeronautics and Astronautics and published by . This book was released on 2008 with total page 1112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Least Squares Finite Element Methods

Download or read book Least Squares Finite Element Methods written by Pavel B. Bochev and published by Springer Science & Business Media. This book was released on 2009-04-28 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Book Aerodynamic Shape Optimization Techniques Based on Control Theory

Download or read book Aerodynamic Shape Optimization Techniques Based on Control Theory written by and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document serves as a final technical report for the AFOSR award F49620-95-1-0259. It reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in viscous compressible flow. The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wing-body combinations.