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

Comparison of optimizer-based and flow solver-based trimming in the context of high-fidelity aerodynamic optimization

This report compares two approaches for achieving a trimmed state of an aircraft configuration during an aerodynamic optimization. In the optimizer-based approach, balance equations are posed as direct constraints to the optimizer. In the flow solver-based approach, balance equations are satisfied within the flow solver evaluation. These approaches are applied to a flying wing case, where blended trailing edge deflection is used to control the pitching moment. The wing is treated as rigid, and lift and pitching moment balance equations are taken into account for trimming. Tests are performed with varying numbers of shape design parameters and with varying numbers of flight points. It is concluded that the flow solver-based approach performs more robustly, and thus should be preferred in general, even though it may take more time than the optimizer-based approach

Three dimensional large scale aerodynamic shape optimization based on shape calculus

Large scale three dimensional aerodynamic shape optimization based on the compressible Euler equations is considered. Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities. Special attention is paid to the applicability to large scale three dimensional problems like the optimization of an Onera M6 wing or a complete blended wing-body aircraft. The actual optimization is conducted in a one-shot fashion where the tangential Laplace-operator is used as a Hessian approximation, thereby also preserving the regularity of the shape

Adjoint gradient-based approach for aerodynamic optimization of transport aircraft

Aerodynamic design of transport aircraft has been steadily improved over past several decades, to the point where today highly-detailed shape control is needed to achieve further improvements. Aircraft manufacturers are therefore increasingly looking into formal optimization methods, driving high-fidelity CFD analysis of finely-parametrized candidate designs. We present an adjoint gradient-based approach for maximizing the aerodynamic performance index relevant to cruise-climb mission segment by modifying the aircraft wing shape. The test baseline geometry is a wing-body configuration based on the Do-728 regional jet, over which a hybrid structured-unstructured CFD grid is generated. For primal and adjoint aerodynamic analysis we employ the DLR TAU flow solver in RANS mode, with Spalart-Allmaras turbulence model. In each optimization cycle, multiple flight points are evaluated in order to make the final shape more robust to off-design flight conditions. Constraints are placed on pitching moment and wing root bending moment, to counter shape modifications unfavorable to trimming and structural mass. The wing shape is modified by free-form deformation (FFD), with positions of FFD control points being the design parameters. An SQP optimizer is used to drive the optimization

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

Drag Reduction of a 2D Airfoil with Constraints on Lift and Pressure Distribution using Adjoint Approach

The paper presents an alternative way to minimize the target pressure residual over parts where laminar flow should occur - typically some percent of the upper and lower front parts – and to perform a classical drag minimization at target lift and pitching moment at the same time. This approach allows 1) to ensure that the final geometry satisfies the target aerodynamic performance 2) to design a laminar profile with a low wave drag, without the use of laminar transition criteria in the optimization process

Comparison of Optimizer-Based and Flow Solver-Based Trimming in the Context of High-Fidelity Aerodynamic Optimization

This report compares two approaches for achieving a trimmed state of an aircraft configuration during an aerodynamic optimization. In the optimizer-based approach, balance equations are set as equality constraints to the optimizer. In the flow solver-based approach, balance equations are satisfied within the flow solver evaluation. These approaches are applied to a flying wing case, where blended trailing edge deflection is used to control the pitching moment. The wing is treated as rigid, and lift and pitching moment balance equations are taken into account for trimming. Tests are performed with varying numbers of shape design parameters and with varying numbers of flight points. Is is concluded that the flow solver-based approach performs more robustly, and thus should be preferred in general, even though it may take more time than the optimizer-based approach