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

Reduced order models for aerodynamic applications, loads and MDO

Reduced Order Models (ROMs) have found widespread application in fluid dynamics and aerodynamics. In their direct application to Computational Fluid Dynamics (CFD) ROMs seek to reduce the computational complexity of a problem by reducing the number of degrees of freedom rather than simplifying the physical model. Here, parametric nonlinear ROMs based on high-fidelity CFD are used to provide approximate flow solutions, but at lower evaluation time and storage than the original CFD model. ROMs for both steady and unsteady aerodynamic applications are presented. We consider ROMs combining proper orthogonal decomposition (POD) and Isomap, which is a manifold learning method, with interpolation methods as well as physics-based ROMs, where an approximate solution is found in the POD-subspace by minimizing the corresponding steady or unsteady flow-solver residual. In terms of the nonlinear unsteady least-squares ROM algorithm, we present the details of an improved accelerated greedy missing point estimation procedure which is usedin the online phase to select a subset of the unsteady residual for reasons of computational efficiency during the online prediction phase. The issue of how to best train the ROM with high-fidelity CFD data is also addressed. The goal is to train ROMs that yield a large domain of validity across all parameters and flow conditions at the expense of a relatively small number of CFD solutions. The different ROM methods are demonstrated on a wide-body transport aircraft configuration at transonic flow conditions. The steady ROMs are used to predict the static aeroelastic loads in the context of multidisciplinary optimization (MDO), where a structural model is to be sized for the (aerodynamic) loads. They are also used in a process where an a priori identification of the most critical static load cases is of interest and the sheer number of load cases to be considered does not lend itself to high-fidelity CFD. The unsteady nonlinear least-squares ROM approach is applied to modeling discrete gusts of different amplitude and length in the context of rapid evaluation of gust-induced air loads

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

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

Development of the Adjoint Approach for Aeroelastic Wing Optimization

In the context of gradient-based optimization techniques for multidisciplinary problems an efficient approach was sought to evaluate the gradient of the cost function with respect to the design variables; also called the sensitivities. The traditional approach to calculate the sensitivities, the finite differences, can become prohibitively expensive in high-fidelity optimizations. For this reason an existing adjoint approach was suggested to be further developed in order to suit coupled aero-structural systems. Then the developed approach was evaluated and tested. The results showed that the approach can provide accurate sensitivities in a very efficient way

An aeroelastic coupled adjoint approach for multi-point designs in viscous flows

As the wing flies, its structural elasticity interacts with the aerodynamic loads and the wing deforms. This deformation influences the aerodynamic flow over the wing. Hence, besides employing high-fidelity flow equations, considering the structural elasticity is necessary for an accurate prediction of the wing aerodynamic coefficients. Wing shape optimizations that consider high-fidelity aeroelastic effects are computationally costly and therefore the gradient-based algorithms are suitable for them. This study presents an efficient approach for computing the gradients required for such optimizations. An existing viscous flow adjoint approach is extended to include the structural elasticity effects. The contribution of this work is, to differentiate the flow-structure coupling methods and to implement the coupled adjoint equations in order to use it within industrially relevant wing-shape optimizations. The advantages of this coupled aeroelastic adjoint approach are that it computes the gradients accurately and nearly independently of the number of design parameters engaged in the optimization, hence it is possible to use high number of design parameters. This allows high-fidelity multipoint optimizations within acceptable computational time. In this context, it is found that the adjoint approach is saving more than 80% of the computational cost when compared to the conventional finite differences approach for computing the gradients. After successfully validating the gradients obtained with the developed approach, four optimization scenarios are performed on a wing-body configuration in a transonic flow regime. The effects of considering several flight points as well as considering some rough weight constraint are tested and this latter constraint shows beneficial results for aerodynamics as well as the structure of the aircraft

Exploring the Benefit of Engaging the Coupled Aero-Elastic Adjoint Approach in MDO for Different Wing Structure Flexibilities

By virtue of their efficiency, gradient-based algorithms can play a profound role in assessing wing designers overcome the challenges of decarbonizing the aviation industry. This role becomes more valuable when non-linearities increase in the corresponding physical discipline. The coupled aero-elastic adjoint approach, is used to efficiently compute the gradients of aerodynamic cost functions with respect to shape design parameters. This approach helps aerodynamic designers engage the effects of wing structure flexibility, earlier in the design process. To compute the gradients via the coupled aero-elastic adjoint approach, a fixed-point iteration between the aerodynamic adjoint equation and the structure adjoint equation is carried out. The cost of computing the coupled aero-elastic adjoint for a specific cost function is, hence, higher than that of computing the aerodynamic adjoint. In practice it costs three to ten times more, based on the structure flexibility. The aircraft industry tends currently to build wings with higher structure flexibility. This is the result of using composite materials instead of metal, in order to save structural mass, or advancing towards higher aspect ratio wings in order to improve the aerodynamic performance. These trends, which result in increased wing flexibility, motivate investigating the benefit of the coupled aeroelastic adjoint approach, over the aerodynamic adjoint approach. In the literature, some studies show the importance of employing the coupled adjoint, while others show barely any benefit for it. Hence, the aim of this study is to investigate, for the test case at hand, the relation between the wing flexibility and the necessity to employ the relatively costly, but ccurate, coupled aero-elastic adjoint approach. Five structure models were generated with different elasticities and were employed in two sets of optimizations; the first uses the aerodynamic adjoint to compute the gradients, and the other uses the coupled aero-elastic adjoint. This investigation was done for unconstrained as well constrained optimizations. The investigation showed that for the unconstrained optimization and for the design task at hand, a structure flexibility, that results in a normalized wing-tip deformation of 8% or higher, requires the use of the coupled aeroelastic adjoint. The normalized wing-tip deformation is defined, in this context, as the upward wing-tip deformation divided by half the wing span. For the constrained optimization, the investigation showed that the coupled aeroelastic adjoint always brought more improvements than the aerodynamic adjoint