Joel Brezillon

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.

Eect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization

An exact discrete adjoint of an unstructured nite-v olume 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.

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.

Advanced High-Lift Design by Numerical Methods and Wind Tunnel Verification within the European Project EUROLIFT II

The design activity within the European 6th framework project EUROLIFT II is targeted towards an improvement of the take-off performance of a generic transport aircraft configuration by a redesign of the trailing edge flap. The involved partners applied different optimization strategies as well as different types of flow solvers in order to cover a wide range of possible approaches for aerodynamic design optimization. The optimization results obtained by the different partners have been cross-calculated in order to eliminate solver dependencies and to identify the best obtained design. The final selected design has been applied to the wind tunnel model and the test in the European Transonic Wind Tunnel (ETW) at high Reynolds number confirms the predicted improvements.

Development and application of multi-disciplinary optimization capabilities based on high-fidelity methods

The expected computational power that will become available in the next years and decades will allow the introduction of more accurate simulations at earlier aircraft design stages. It is thus mandatory to identify and consequently develop multi-disciplinary optimization capabilities based on high-fidelity methods enabling the design of the future aircraft. The paper will give an overview of the latest development conducted at DLR in this field. Three representative applications will demonstrate benefits and limitations of the capabilities developed.

Advanced Design by Numerical Methods and Wind-Tunnel Verification Within European High-Lift Program

The design activity within the European 6th framework project EUROLIFT II is targeted towards an improvement of the take-off performance of a generic transport aircraft configuration by a redesign of the trailing edge flap. The involved partners applied different optimization strategies as well as different types of flow solvers in order to cover a wide range of possible approaches for aerodynamic design optimization. The optimization results obtained by the different partners have been cross-calculated in order to eliminate solver dependencies and to identify the best obtained design. The final selected design has been applied to the wind tunnel model and the test in the European Transonic Wind Tunnel (ETW) at high Reynolds number confirms the predicted improvements.

Aerodynamic Inverse Design Framework Using Discrete Adjoint Method

The aerodynamic inverse design approach consists of finding the geometry that produces a desired (target) pressure distribution. Such design problem is here solved using optimization strategies based on CFD solver to minimize the pressure residual. It is observed that the key ingredients for solving this problem are the mesh point parametrization combined with the adjoint approach for efficient and reliable design. The resulting optimization framework is finally successfully assessed on representative 2D design problems ranking from viscous subsonic to inviscid supersonic flows.

Aircraft Wing Optimization Using High Fidelity Closely Coupled CFD and CSM Methods

The present paper describes a comprehensive MDO process chain to maximize the range of a transonic transport aircraft configuration. The parameterization incorporates wing plan form parameters and twist angles in four wing sections. The geometrical inputs for the disciplines CFD and CSM were generated by CATIA V5 based on those design parameters which were prescribed by a SUBPLEX optimizer. CFD is at first used to calculate the drag in cruise flight with RANS and secondly to provide aerodynamic forces from Euler solutions from certain maneuver cases for a structural sizing of the wing to yield the wing weight. As with the structural calculations the wing deformations are available, these are used to deform the CFD mesh and to evaluate drag and forces on the corresponding flight shapes. The fluid/structural-sizing procedure, which is performed in every optimization cycle, is repeated several times until a sufficient convergence of drag and wing mass is achieved. Both values are then used to compute the Breguet range, which represents the optimization objective. Finally two optimization runs have been conducted. While the first run lead to a consistent result, in the second run, which includes an additional load case, the best configuration was already found in the fifth cycle.

Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization

Abstract This paper presents a numerical method for aerodynamic shape optimization problems with state constraint. It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.

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.