Efficient polar optimization of transport aircraft in transonic RANS flow using adjoint gradient based approach

A major design requirement for transport aircraft is efficient cruise flight in the transonic region. From the aerodynamic viewpoint, this is achieved by favorable lift-to-drag ratio of the aircraft, both at the main design point and at off-design conditions. We therefore present a method to efficiently perform a multi-point optimization of a representative wing-body configuration. Designs are evaluated with RANS CFD simulations, the wing is parametrized using 40 free-form deformation control points, and a gradient-based method is used to drive the optimization. The gradient of cost functions is computed with a discrete adjoint approach, in which flow and mesh adjoint equations are solved. Compared to single-point optimization, with multi-point optimization we obtain a design with slightly lower best lift-to-drag ratio, but which has improved lift-to-drag polar over the whole range of practical lift coefficients compared to the baseline design

Unstructured mesh capabilities for supersonic wing design at low speed conditions

In this paper the reliability of using unstructured meshes for the CFD simulation of the flow over a low aspect-ratio wing in low speed configuration is investigated. It is intended to integrate such mesh strategy in a high-fidelity aerodynamic shape optimization loop for the design of high lift devices, so particular care is given to the set-up of a suitable meshing procedure usable in optimization context. Meshes are created using the grid generators Solar and Centaur; the CFD analysis is carried out using the DLR-TAU solver on the EPISTLE wing-body configuration with drop-nose slat. Results are compared to wind tunnel test data and to CFD results obtained on a structured mesh. It is shown that a grid of around 10 million points, if carefully conceived, is able to predict with reasonably good accuracy the aerodynamic loads and the overall flow features. Some discrepancies in the detection of vortical flow features are found, but they do not have significant influence on the computed loads. The application of the method at various Reynolds numbers confirms the importance of the prismatic layer thickness to accurately capture the vortical flow features

Application of multi-objective constraint optimization in aerodynamic high-lift design

This lecture deals with the application of numerical optimization for aerodynamic design of high-lift systems, which is a multi-objective constraint design problem. The applied mathematical fundamentals of numerical optimization are briefly outlined. A description of the design targets and constraints for high-lift wings is given, followed by a detailed analysis of the properties of the flow calculation for the use within optimization and the suitability of optimization algorithms for this type of design problem. Another focus is set on the practical issues resulting from a long time experience in applying numerical optimization to aerodynamic design. of high-lift systems for transport aircraft

Effect of Approximations of the Discrete Adjoint on Gradient-Based Optimization

An exact discrete adjoint of an unstructured nite-volume solver for the RANS equations has been developed. The adjoint is exact in the sense of being based on the full linearization of all terms in the solver, including all turbulence model contributions. From this starting point various approximations to the adjoint are derived with the intention of simplifying the development and memory requirements of the method; considered are many approximations already seen in the literature. The eect of these approximations on the accuracy of the resulting design gradients, and the convergence and nal solution of optimizations is studied, as it applies to a two-dimensional high-lift conguration

Engine Integration Based on Multi-Disciplinary Optimisation Technique

The paper presents the work related to the engine integration of a Rear Fuse-lage Mounted Engine configuration in the frame of the DLR/Onera project MDOrmec („Multi-Disciplinary Optimisation of Rear-fuselage Mounted Engine Configuration“). The developed multidisciplinary optimization process is based on a multi-level fidelity approach, where the aerodynamics is simulated using CFD methods while the weight and the handling qualities are assessed using preliminary design approach. Finally, the results of the optimisation are presented and discussed in detail

Adjoint Algorithms for the Optimization of 3d Turbulent Configurations

The solution of the discrete adjoint equations for an unstructured finite volume compressible Navier-Stokes solver is discussed. In previous work fixedpoint iterations taken from the non-linear method - suitably adjointed - were applied to the adjoint problem. Here it is seen that there are often situations in which these iterations can not be expected to converge. To address this the Recursive Projection Method is developed as a stabilizer, and then used to perform an eigenmode analysis of attached and separated flow on a single geometry, allowing identification of flow regions that were unstable under the basic iteration. Finally an adjoint based optimization with 96 design variables is performed on a wing-body configuration. The initial flow has large regions of separation, which are significantly diminished in the optimized configuration

Shape Optimization Using the Aero-structural Coupled Adjoint Approach for Viscous Flows

The aero-structural coupled adjoint approach here is an efficient approach to compute the gradients of the aerodynamic coefficients obtained from coupled fluid-structure simulations. These gradients can then be advantageously employed for gradient-based optimizations. In this study, the approach is extended for the first time to tackle viscous flows. After introducing the theory, the method is applied to optimize the flight shape of two realistic 3D configurations. In both applications, the coupled adjoint approach permits to decrease the drag at constant lift with limited computational effort

Efficient Algorithms for Solution of the Adjoint Compressible Navier-Stokes Equations with Applications

The complete discrete adjoint equations for an unstructured finite volume compressible Navier-Stokes solver are discussed with respect to the memory and time efficient evaluation of their residuals, and their solution. It is seen that application of existing iteration methods for the non-linear equation - suitably adjointed - have a property of guaranteed convergence provided that the nonlinear iteration is well behaved. For situations where this is not the case, a stabilization method based on the Recursive Projection Method is developed. The resulting adjoint solver is applied to 3D optimization of a turbulent wing-fuselage configuration, as well as to goal-oriented adaptation using an error representation formula

Investigation on Adjoint Based Gradient Computations for Realistic 3d Aero-Optimization

A discrete adjoint method for e�ciently computing gradients for aerodynamic shape op- timizations is presented. The chain itself involves an unstructured mesh Reynolds-Averaged Navier-Stokes solver, and is suitable for the optimization of complex geometries in three dimensions. In addition to the discrete ow adjoint the method introduces a second ad- joint equation for the mesh deformation. Using the adjoint chain it is possible to evaluate the gradients of a cost function for the cost of one adjoint ow solution and one adjoint volume mesh deformation, without performing any (forward) mesh deformation. By choos- ing a suitable mesh deformation operator, like linear elasticity, the chain may be readily constructed by hand. Furthermore, this adjoint chain can be subsequently used with pa- rameterized surface grids. The accuracy and the computational savings of the resulting procedure is examined for the gradient-based shape optimization of a wing in inviscid ow

Discrete Adjoint of the Navier-Stokes Equations for Aerodynamic Shape Optimization

A discrete adjoint of the Navier-Stokes equations has been developed in the unstructured finite-volume solver the DLR-TAU-code. The method consists of the explicit construction of the exact Jacobian of the spatial discretization with respect to the unknown variables allowing the adjoint equations to be formulated and solved. A wide range of the spatial discretizations available in TAU have been differentiated, including the Spallart-Almaras-Edwards one-equation, and the Wilcox k-omega two-equation turbulence models. The aim of this paper is to give an overview of the capabilities of the discrete adjoint to perform aerodynamic shape optimization in viscous flow. The strategy developed is extensively validated on 2D cases. The adjoint based design method is first validated by comparing the gradients of the drag, lift and pitching moment it produces with the approximate gradients obtained by finite-differences. Then the accuracy and efficiency of the approach are demonstrated for transonic airfoil design by considering geometric as well aerodynamic constraints, single- as well as multi-point design. Finally, the flap design of a multi-element airfoil in take off configuration confirms the capability of the discrete adjoint to solve wide range of aerodynamic problems