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.










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.







Scaling of Hybrid Wing-body-type Aircraft


Book Description

Unconventional aircraft configurations have the potential to reduce aviationâ s contribution to climate change through substantial reductions in fuel burn. One promising configuration which has received much attention is the hybrid wing-body (HWB). Due to the lack of design experience for unconventional configurations, high-fidelity design and optimization methods will be critical in their development. This thesis presents the application of a gradient-based aerodynamic shape optimization algorithm based on the Reynolds-averaged Navier-Stokes equations to the aerodynamic design of conventional tube-and-wing (CTW) and HWB aircraft. The optimal aerodynamic shapes and performance for a range of aircraft sizes including regional, narrow-body, midsize, and wide-body classes are found so as to characterize the aerodynamic efficiency benefits of the HWB configuration with respect to equivalent CTW designs. Trim-constrained drag minimization is performed at cruise, with a large design space of over 400 design variables. The smaller optimized HWBs, including the regional and narrow-body classes, while more aerodynamically efficient, burn at least as much fuel as to the equivalently optimized CTWs due to their increased weight, while the larger wide-body-class HWB has almost 11% lower cruise fuel burn. To investigate alternative configurations which may yield improved efficiency, exploratory optimizations with significant geometric freedom are then performed, resulting in a set of novel shapes with a more slender lifting fuselage and distinct wings. Based on these exploratory results, new lifting-fuselage configurations (LFCs) are designed. The slenderness of the LFC fuselage decreases with aircraft size, such that, for the largest class, the LFC reverts to a classical HWB shape. This new configuration offers higher aerodynamic efficiency than the HWBs, with the smaller classes seeing the largest benefit from the new configuration. This new lifting-fuselage concept offers 6% lower cruise fuel burn than the CTW in the regional class, and a marginal benefit in the narrow-body class. The effects of cruise altitude, stability requirements, and weight sensitivity are also examined.




Utilizing Direct Numerical Simulations of Transition and Turbulence in Design Optimization


Book Description

Design optimization methods that use the Reynolds-averaged Navier-Stokes equations with the associated turbulence and transition models, or other model-based forms of the governing equations, may result in aerodynamic designs with actual performance levels that are noticeably different from the expected values because of the complexity of modeling turbulence/transition accurately in certain flows. Flow phenomena such as wake-blade interaction and trailing edge vortex shedding in turbines and compressors (examples of such flows) may require a computational approach that is free of transition/turbulence models, such as direct numerical simulations (DNS), for the underlying physics to be computed accurately. Here we explore the possibility of utilizing DNS data in designing a turbine blade section. The ultimate objective is to substantially reduce differences between predicted performance metrics and those obtained in reality. The redesign of a typical low-pressure turbine blade section with the goal of reducing total pressure loss in the row is provided as an example. The basic ideas presented here are of course just as applicable elsewhere in aerodynamic shape optimization as long as the computational costs are not excessive. Rai, Man M. Ames Research Center NASA/TM-2015-218932, ARC-E-DAA-TN28338







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.