Sangho Kim

Design Optimization of High-Lift Configurations Using a Viscous Continuous Adjoint Method

An adjoint-based Navier-Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-Averaged Navier-Stokes (RANS) equations are used as a flow model together with the Spalart-Allmaras turbulence model to account for high Reynolds number effects. Using a viscous continuous adjoint formulation, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite-difference methods. A study of the accuracy of the gradient information provided by the adjoint method in comparison with finite differences and an inverse design of a single-element airfoil are also presented for validation of the present viscous adjoint method. The high-lift configuration design method uses a compressible RANS flow solver, FLO103-MB, a point-to-point matched multi-block grid system and the Message Passing Interface (MPI) parallel solution methodology for both the flow and adjoint calculations. Airfoil shape, element positioning, and angle of attack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparisons with experimental data. Finally, several design results that verify the potential of the method for high-lift system design and optimization, are presented. The design examples include a multi-element inverse design problem and the following problems: C l maximization, lift-to-drag ratio, L/D, maximization by minimizing C d at a given C l or maximizing C l at a given C d (α is allowed to float to maintain either C l or C d), and the maximum lift coefficient, C l max , maximization problem for both the RAE2822 single-element airfoil and the 30P30N multi-element airfoil. A ERODYNAMIC shape design has long been a challenging objective in the study of fluid dynamics. Computational Fluid Dynamics (CFD) has played an important role in the aerodynamic design process since its introduction for the study of fluid flow. However, CFD has mostly been used in the analysis of aerodynamic configurations in order to aid in the design process rather than to serve as a direct design tool in aerodynamic shape optimization. Although several attempts have been made in the past to use CFD as a direct design tool, 1–5 it has not been until recently that the focus of CFD applications has shifted to aerodynamic design. 6–11 This shift has been mainly motivated by the availability of high performance computing platforms and by the development of new and efficient analysis and design algorithms. In particular, automatic design procedures which …

Viscous Aerodynamic Shape Optimization of Wings including Planform Variables

☞Introduction and Motivation➣While aerodynamic prediction methods based on CFD are now well established,accurate, and robust, the ultimate need in the design process is to find theoptimum shape which maximizes the aerodynamic performance.➣During the last decade aerodynamic shape optimization methods based oncontrol theory have been perfected for rigid wings with fixed planforms.➣Example: Redesign of the wing of a Boeing 747 with fuselage.

A Framework for Coupling Reynolds-Averaged With Large-Eddy Simulations for Gas Turbine Applications

Full-scale numerical prediction of the aerothermal flow in gas turbine engines are currently limited by high computational costs. The approach presented here intends the use of different specialized flow solvers based on the Reynolds-averaged Navier-Stokes equations as well as large-eddy simulations for different parts of the flow domain, running simultaneously and exchanging information at the interfaces. This study documents the development of the interface and proves its accuracy and efficiency with simple test cases. Furthermore, its application to a turbomachinery application is demonstrated.

Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method

An adjoint-based Navier‐Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-averaged Navier‐Stokes equations are used as a flow model together with the Spalart‐Allmaras turbulence model to account for high Reynolds number effects. When a viscous continuous adjoint formulation is used, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite difference methods. The high-lift configuration parallel design method uses a point-to-point matched multiblock grid system and the message passing interface standard for communication in both the flow and adjoint calculations. Airfoil shape, element positioning, and angle of attack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparison with available experimental data. Finally, several design results that verify the potential of the method for high-lift system design and optimization are presented. The design examples include a multi-element inverse design problem and the following optimization problems: lift coefficient maximization, lift-to-drag ratio maximization, and the maximum lift coefficient maximization problem for both the RAE2822 single-element airfoil and the 30P30N multi-element airfoil.

Reduction of the Adjoint Gradient Formula for Aerodynamic Shape Optimization Problems

We present a new continuous adjoint method for aerodynamic shape optimization using the Euler equations, which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral. The savings are particularly significant for three-dimensional aerodynamic shape-optimization problems on general unstructured and overset meshes. To validate the concept, the new gradient equations have been tested for various aerodynamic shape-optimization problems, including an inverse problem for three-dimensional wing configurations, and drag-minimization problems of a single-element airfoil and a three-dimensional wing-fuselage configuration

A gradient accuracy study for the adjoint-based Navier-Stokes design method

A continuous adjoint method for Aerodynamic Shape Optimization (ASO) using the compressible Reynolds-Averaged Navier-Stokes (RANS) equations and the Baldwin-Lomax turbulence model was implemented and tested. The resulting implementation was used to determine the accuracy in the calculation of aerodynamic gradient information for use in ASO problems. For completeness, the formulation and discretization of the Navier-Stokes equations and the resulting adjoint equations are discussed. However, the reader is referred to previous work for details of the derivations. The accuracy of the resulting derivative information is investigated by direct comparison with finite-difference gradients. In the process, shortcomings of the finite difference method for the calculation of derivative information are pointed out and discussed. The advantages of the use of an adjoint method become apparent because of the strict requirements that the finite difference method imposes on the level of flow solver convergence and the sensitivity of the value of the gradients with respect to the choice of step size. Design examples for both inverse and drag minimization problems are presented. A parallel implementation using a domain decomposition approach and the MPI (Message Passing Interface) standard is used to reduce the computational cost of automatic design involving viscous flows.

Two-dimensional High-Lift Aerodynamic Optimization Using the Continuous Adjoint Method

An adjoint-based Navier-Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-Averaged Navier-Stokes (RANS) equations are used as a flow model together with the Spalart-Allmaras turbulence model to account for high Reynolds number effects. Using a viscous continuous adjoint formulation, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite difference methods. A previous study of accuracy of the gradient information provided by the adjoint method, in comparison with finite differences and an inverse design of a single-element airfoil are also presented for validation of the present viscous adjoint method.tack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparisons with experimental data. Finally, several design results that verify the effectiveness of the method for high-lift system design and optimization, are presented. Firstly, C^ is minimized and Cf is maximized for a single-element airfoil. Secondly, a multi-element inverse design problem is presented that attempts to match a pre-specified target pressure distribution using the shape of all elements in the airfoil, as well as their relative positions. Finally, the lift-to-drag ratio of a multi-element airfoil is maximized with fixed Cj, or fixed Q. Introduction T HE motivation for this study is twofold: on the one hand, we would like to improve the takeoff and landing performance of existing high-lift systems using an adjoint formulation. On the other hand, we would like to setup a numerical optimization procedure that can be useful to the aerodynamicist in the rapid design and development of high-lift system configurations and that can also provide derivative information regarding the influence of various design parameters (gap, overlap, slat and flap deflection angles, etc.) on the performance of the system. The primary goal of an aerodynamic high-lift system is to increase payload capacity and reduce takeoff and landing distances by increasing both the lift coefficient at a given angle of attack and the maximum lift coefficient. Traditionally, high-lift designs have been realized by careful wind tunnel testing which is both expensive and difficult due to the extremely complex flow interactions. Recently computational fluid dynamics (CFD) analyses have also been incorporated to the high-lift design process. 1 In particular, automatic design procedures, which use CFD combined with gradient-based optimization techniques, have made it possible to remove the difficulties in the decision making process (traditionally taken by …

Aero-Structural Wing Planform Optimization Using the Navier-Stokes Equations

This paper describes the formulation of optimization techniques based on control theory for wing section and planform design in viscous compressible o w modeled by the Reynolds Averaged Navier-Stokes equations. Because the two disciplines that are relevant to this problem are aerodynamics and structures, an extension of a single to a multiple objective cost function is considered. A realistic model for the structural weight, which is sensitive to both planform variations and wing loading, is implemented. Results of optimizing a wing-fuselage of a commercial transport aircraft show a successful trade-o between the aerodynamic and structural cost functions, leading to meaningful wing planform designs. Results also indicate that large improvements in lift-to-drag ratio can be achieved without any penalty on the structural weight by stretching the span along with decreasing the sweep angle, thickening the wing-sections, and modifying the airfoil sections. Furthermore, by varying the weighting constants in the cost function, the Pareto front can be captured, broadening the design range of optimal shapes. I. Introduction

Enhancement of a Class of Adjoint Design Methods via Optimization of Parameters

CD = drag coefficient CL = lift coefficient Cp = pressure coefficient CW = structural weight coefficient F = design variable G = gradient G = modified gradient using Sobolev inner product i, j, k = cell indices in the three computational coordinate directions I = cost function M1 = freestream Mach number R = residual R = implicitly smoothed residual r = scaled spectral radii of the flux Jacobian matrices = angle of attack l = weighing coefficients in cost function = smoothing coefficient factor = variation = gradient smoothing coefficient = residual smoothing coefficient = step size = computational coordinate

Integrated Simulations for Multi-Component Analysis of Gas Turbines:RANS Boundary Conditions

The aero-thermal computation of the flow path of an entire gas turbine engine can be performed using multiple flow solvers, each specialized to a component of the engine. Here, we present an approach to integrate a Large Eddy Simulation (LES) solver and a Reynolds Averaged Navier-Stokes (RANS) solver. Challenges arise, when the LES solver is based on a low-Mach number approximation and can not deliver all variables needed for a compressible RANS solver. This study investigates the choice of boundary conditions applied to the RANS interface. We propose the use of inlet/exit boundary conditions and investigate the effect on simple pipe geometries.