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NASA NTRS2003

Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry

The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.

Nemec, Marian↗
NASA NTRS1996

Aerodynamic shape optimization using control theory

Aerodynamic shape design has long persisted as a difficult scientific challenge due 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 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.

Reuther, James↗
NASA NTRS2001

Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic and Structural Design Optimization (SASDO) is shown as an extension of the Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) method. It is extended by the inclusion of structure element sizing parameters as design variables and Finite Element Method (FEM) analysis responses as constraints. The method aims to reduce the computational expense. incurred in performing shape and sizing optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, FEM structural analysis and sensitivity analysis tools. SASDO is applied to a simple. isolated, 3-D wing in inviscid flow. Results show that the method finds the saine local optimum as a conventional optimization method with some reduction in the computational cost and without significant modifications; to the analysis tools.

Gumbert, Clyde R.↗
NASA NTRS2006

Reentry-Vehicle Shape Optimization Using a Cartesian Adjoint Method and CAD Geometry

A DJOINT solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (e.g., geometric parameters that control the shape). Classic aerodynamic applications of gradient-based optimization include the design of cruise configurations for transonic and supersonic flow, as well as the design of high-lift systems. are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric computer-aided design (CAD). In previous work on Cartesian adjoint solvers, Melvin et al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the two-dimensional Euler equations using a ghost-cell method to enforce the wall boundary conditions. In Refs. 18 and 19, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm were the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The accuracy of the gradient computation was verified using several three-dimensional test cases, which included design variables such as the free stream parameters and the planform shape of an isolated wing. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Factors under consideration include the computation of mesh sensitivities that provide a reliable approximation of the objective function gradient, as well as the computation of surface shape sensitivities based on a direct-CAD interface. We present detailed gradient verification studies and then focus on a shape optimization problem for an Apollo-like reentry vehicle. The goal of the optimization is to enhance the lift-to-drag ratio of the capsule by modifying the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design.

Nemec, Marian↗
NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗
NASA NTRS1988

An exact inverse method for subsonic flows

A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.

Daripa, Prabir↗
NASA NTRS2001

Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) for a 3-D Flexible Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) are extended from single discipline analysis (aerodynamics only) to multidisciplinary analysis - in this case, static aero-structural analysis - and applied to a simple 3-D wing problem. The method aims to reduce the computational expense incurred in performing shape optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, Finite Element Method (FEM) structural analysis and sensitivity analysis tools. Results for this small problem show that the method reaches the same local optimum as conventional optimization. However, unlike its application to the win,, (single discipline analysis), the method. as I implemented here, may not show significant reduction in the computational cost. Similar reductions were seen in the two-design-variable (DV) problem results but not in the 8-DV results given here.

Gumbert, Clyde R.↗
NASA NTRS2001

Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) for a 3-D Flexible Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) are extended from single discipline analysis (aerodynamics only) to multidisciplinary analysis - in this case, static aero-structural analysis and applied to a simple 3-D wing problem. The method aims to reduce the computational expense incurred in performing shape optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, Finite Element Method (FEM) structural analysis and sensitivity analysis tools. Results for this small problem show that the method reaches the same local optimum as conventional optimization. However, unlike its application to the rigid wing (single discipline analysis), the method, as implemented here, may not show significant reduction in the computational cost. Similar reductions were seen in the two-design-variable (DV) problem results but not in the 8-DV results given here.

Gumbert, Clyde R.↗
NASA NTRS1986

Tactical missile aerodynamics

The present conference on tactical missile aerodynamics discusses autopilot-related aerodynamic design considerations, flow visualization methods' role in the study of high angle-of-attack aerodynamics, low aspect ratio wing behavior at high angle-of-attack, supersonic airbreathing propulsion system inlet design, missile bodies with noncircular cross section and bank-to-turn maneuvering capabilities, 'waverider' supersonic cruise missile concepts and design methods, asymmetric vortex sheding phenomena from bodies-of-revolution, and swept shock wave/boundary layer interaction phenomena. Also discussed are the assessment of aerodynamic drag in tactical missiles, the analysis of supersonic missile aerodynamic heating, the 'equivalent angle-of-attack' concept for engineering analysis, the vortex cloud model for body vortex shedding and tracking, paneling methods with vorticity effects and corrections for nonlinear compressibility, the application of supersonic full potential method to missile bodies, Euler space marching methods for missiles, three-dimensional missile boundary layers, and an analysis of exhaust plumes and their interaction with missile airframes.

Hemsch, Michael J.↗
NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗
NASA NTRS1993

Aerodynamic analysis of Pegasus - Computations vs reality

Pegasus, a three-stage, air-launched, winged space booster was developed to provide fast and efficient commercial launch services for small satellites. The aerodynamic design and analysis of Pegasus was conducted without benefit of wind tunnel tests using only computational aerodynamic and fluid dynamic methods. Flight test data from the first two operational flights of Pegasus are now available, and they provide an opportunity to validate the accuracy of the predicted pre-flight aerodynamic characteristics. Comparisons of measured and predicted flight characteristics are presented and discussed. Results show that the computational methods provide reasonable aerodynamic design information with acceptable margins. Post-flight analyses illustrate certain areas in which improvements are desired.

Mendenhall, Michael R.↗
NASA NTRS1999

Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) for a 3-D Rigid Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) is presented and applied to a simple 3D wing problem. The method aims to reduce the computational expense incurred in performing shape optimization using state-of-the-art CFD flow analysis and sensitivity analysis tools. Results for this small problem show that the method reaches the same local optimum as conventional optimization methods and does so in about half the computational time.

Gumbert, Clyde R.↗
NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗
NASA NTRS1976

Computer method for design of acoustic liners for turbofan engines

A design package is presented for the specification of acoustic liners for turbofans. An estimate of the noise generation was made based on modifications of existing noise correlations, for which the inputs are basic fan aerodynamic design variables. The method does not predict multiple pure tones. A target attenuation spectrum was calculated which was the difference between the estimated generation spectrum and a flat annoyance-weighted goal attenuated spectrum. The target spectrum was combined with a knowledge of acoustic liner performance as a function of the liner design variables to specify the acoustic design. The liner design method at present is limited to annular duct configurations. The detailed structure of the liner was specified by combining the required impedance (which is a result of the previous step) with a mathematical model relating impedance to the detailed structure. The design procedure was developed for a liner constructed of perforated sheet placed over honeycomb backing cavities. A sample calculation was carried through in order to demonstrate the design procedure, and experimental results presented show good agreement with the calculated results of the method.

Minner, G. L.↗
NASA NTRS2002

Flexible-Wing-Based Micro Air Vehicles

This paper documents the development and evaluation of an original flexible-wing-based Micro Air Vehicle (MAV) technology that reduces adverse effects of gusty wind conditions and unsteady aerodynamics, exhibits desirable flight stability, and enhances structural durability. The flexible wing concept has been demonstrated on aircraft with wingspans ranging from 18 inches to 5 inches. Salient features of the flexible-wing-based MAV, including the vehicle concept, flexible wing design, novel fabrication methods, aerodynamic assessment, and flight data analysis are presented.

Ifju, Peter G.↗
NASA NTRS1991

Design of 3-dimensional complex airplane configurations with specified pressure distribution via optimization

A subcritical panel method applied to flow analysis and aerodynamic design of complex aircraft configurations is presented. The analysis method is based on linearized, compressible, subsonic flow equations and indirect Dirichlet boundary conditions. Quadratic dipol and linear source distribution on flat panels are applied. In the case of aerodynamic design, the geometry which minimizes differences between design and actual pressure distribution is found iteratively, using numerical optimization technique. Geometry modifications are modeled by surface transpiration concept. Constraints in respect to resulting geometry can be specified. A number of complex 3-dimensional design examples are presented. The software is adopted to personal computers, and as result an unexpected low cost of computations is obtained.

Kubrynski, Krzysztof↗
NASA NTRS1998

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Nielsen, Eric J.↗
NASA NTRS1977

Supercritical cascade design

The use of the method of complex extension to achieve better aerodynamic designs for supercritical cascades applicable to transonic turbomachinery is discussed. The method permits the computation of analytical solutions to elliptic, hyperbolic or mixed second-order partial equations in two dimensions. Boundary value problems formulated to develop an airfoil shape having a prescribed speed distribution for subsonic flow and a nearby speed distribution in the transonic case are also considered. Computing times necessary to run the blade design program are described as acceptably short.

Korn, D. G.↗