Aerodynamic Shape Optimization Using Unstructured Grid Methods

Two unstructured-grid Euler-based CFD codes, AIRPLANE and FLOWCART were coupled to a gradientbased quasi-Newton finite-difference optimization algorithm. These two optimization techniques were developed to provide detailed aerodynamic shape optimization methods for complete configurations with efficient grid generation methods. AIRPLANE utilizes a tetrahedral mesh whereas FLOWCART uses a hexahedral Cartesian mesh. Several codes were developed to facilitate aerodynamic shape optimization. These include developing surface grid perturbation methods with thickness constraint and overall surface overlap evaluations, used with both Euler codes, and adding a multigrid capability and a variety of mesh movement techniques to the AIRPLANE method. The AIRPLANE multigridding approach was proven to be accurate and effective, with typical speedup ratios of 3 to 5. The mesh movement techniques were effective in reducing the grid generation wall clock time by 70%. Detailed results of the AIRPLANE-based optimization technique are presented. The performance gains resulting from optimization are verified by computations with FLOWCART and OVERFLOW, and comparisons with experimental data on the baseline and optimized configurations. The low speed computational results of the baseline and optimized models were incorporated into an approach and landing simulation database. The controllability and handling qualities were good to excellent based on a piloted simulation in the NASA Ames Vertical Motion Simulator (VMS). FLOWCARTbased optimization was validated by comparing its gradients and design solutions with AIRPLANE’s on two separate optimization problems with identical design variables and objective functions. INTRODUCTION Aerodynamic shape optimization using structured grids was used successfully for several years at NASA Ames on High Speed Civil Transport designs. An adjoint method enabled rapid gradient computation, and efficient surface and volume mesh movement techniques were applied. However, these structured grid methods required start-up periods of a few months of labor to generate suitable meshes for complete configurations. The volume meshes consisted of many abutting zones, with points matching at abutting boundaries. For multigridding, each coarser mesh required half the number of points in each direction or one-eighth of the total grid points of the next finer mesh, matching alternate points in each direction. In addition to the full configuration mesh, another surface representation, consisting of sectional cuts, was required for rapid surface perturbations during optimization. Unstructured grid methods can establish the baseline surface and volume grid in far less time and more easily than for structured grid methods. Volume grid generation is completely automated for both Cartesian and tetrahedral approaches, independent of the geometric complexity of the configuration. These methods allow point insertion and deletion without introducing hanging nodes or extraneous points. Thus, the unstructured approach is well suited for the emergence or removal of surface components during optimization, or for adaptation to dynamic changes in flow field phenomena. Fig. 1. Baseline CTV Configuration. 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization 4-6 September 2002, Atlanta, Georgia AIAA 2002-5550 Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. 2 American Institute of Aeronautics and Astronautics Complete configuration multipoint numerical optimization can begin within a few days using unstructured methods. Optimization results can be obtained within a couple of weeks with a dedicated computer system, potentially before a structured-grid based optimization program could even begin. The negative side to using an unstructured optimization technique is that it is more expensive computationally and requires more memory. In addition, there is not currently an adjoint solver available, and the expense of finite-difference gradient computations severely limits the number of design variables that can be used simultaneously. In spite of these limitations, the reduced grid generation times for the unstructured methods may still tip the balance in their favor. Examples of the AIRPLANE based optimization process will be illustrated through the redesign of a Crew Transfer Vehicle (CTV) at multiple design points. NASA Ames Research Center personnel are conducting conceptual design studies of sharp-edged re-entry vehicles. The leading edges of the nose and wing will be composed of a new Ultra High Temperature Ceramic (UHTC) material to withstand the re-entry heat loads. These vehicles are being evaluated since they may improve the re-entry cross range capability and therefore the safety during abort mission scenarios. The planform, wing twist and dihedral have recently been modified since the publication of the original baseline to improve the low speed trim characteristics of the model. The modified baseline CTV is shown in Fig. 1. The stability and control of this class of vehicle is problematic since the vehicle must operate from hypersonic speeds during re-entry to subsonic speeds upon approach and landing, and trim must be achieved throughout this extensive Mach number range. AIRPLANE was used to conduct detailed simultaneous optimization at the landing speed of Mach 0.3, and the re-entry descent speed of Mach 6.0. The design objective was to trim the vehicle at the two conditions simultaneously while achieving the best L/D in the process. The results for the baseline and optimized CTVs from AIRPLANE based optimizations are compared with FLOWCART, OVERFLOW Navier-Stokes analyses, and experimental results from a low-speed wind tunnel. In addition NASA astronaut piloted time-histories from VMS flight simulation data for the baseline and optimized configurations for approach and landing will be presented. NUMERICAL OPTIMIZATION A gradient method was employed since it is well suited to detailed aerodynamic design. Gradient-based algorithms such as QNMDIF should require fewer function evaluations to find local minima or design improvements in contrast to non-gradient methods such as genetic algorithm (GA) techniques. QNMDIF is an unconstrained quasi-Newton finite-difference method that is capable of achieving a local minimum in a design space, but it is not guaranteed to find the true global minimum. The gradient calculations are somewhat expensive since they require two flow solutions for each design variable for forward and backward difference calculations. An AIRPLANE adjoint method is currently under development using techniques that have been successfully developed for aerodynamic design. 14 When this adjoint method is available it will reduce the CPU time for gradient computations to the equivalent of two flow solutions for any number of design variables. For the present methods, a limited number of design variables is recommended, unless many processors are available. QNMDIF is an unconstrained method with a single objective function, so constraints must be implemented by adding penalty terms to the objective function. QNMDIF calls a user-supplied function named FUN that returns the value of the objective for a prescribed set of design variables. An overview of the function FUN using AIRPLANE-based optimization is shown in Fig. 2. FUN controls surface shape perturbation, mesh movement or grid regeneration, and computation of the flow solution. This function is called repeatedly during the gradient and search steps of the optimization. The optimization code stops after a user-supplied number of design iterations is reached or when no further improvements can be made for the current design variables. The user supplies a range of values for each design variable to constrain the sizes of the perturbations. If the variables are outside of this range, a penalty function is returned to QNMDIF. If the design variables are in range, the code checks for a stored solution/objective function, matching the flow conditions and design variables. This is used to “restart” the optimization process by quickly retracing the steps of previous optimization runs. If no existing solution/objective function is found, the code will proceed to modify the surfaces of the configurations. APSHAPER perturbs the triangulated surfaces ensuring that the number of points and connectivity remain unchanged. It then computes surface vertical positions and thicknesses at userprescribed points and writes the information to a file. The AIRPLANE volume mesh of tetrahedra is deformed rather than regenerated using MESHMV. This code also preserves the number of points and connectivity of the original mesh. If the method should invert any tetrahedra, the entire mesh is automatically regenerated using MESH3D. Following this, the multigrid version of AIRPLANE is run. Then the surface vertical