Marco Berci

Multifidelity metamodel building as a route to aeroelastic optimization of flexible wings

High-fidelity aeroelastic simulations of the response of flexible wings to a sudden gust can result in a huge computing effort, making the search for the best wing design prohibitively expensive. As an alternative, a cost-effective multifidelity metamodelling-based optimization strategy, where a metamodel of a high-fidelity aeroelastic simulation response is built by tuning a lower fidelity aeroelastic simulation response, is proposed. In order to address and validate such an approach, both linear and non-linear aeroelastic equations for an aerofoil employing different levels of complexity for expressing the aerodynamic load are used for the high- and low-fidelity models. An aeroelastic gust response evaluation problem is formulated for the flexible wing of a small unmanned air vehicle, whose characteristic size makes it particularly susceptible to gusts. Three different approaches to tune the low-fidelity model, both explicit and implicit, are investigated and compared. Good agreement between the high-fidelity model and the corrected low-fidelity one shows that the proposed approach is indeed suitable for optimization of the aeroelastic gust performance of flexible wings.

Dynamic Response of Typical Section Using Variable-Fidelity Fluid Dynamics and Gust-Modeling Approaches—With Correction Methods

The gust response of a typical section is investigated in terms of both high-fidelity computational fluid dynamics (CFD) and low-fidelity semianalytical solutions of the aerodynamic flow, enabling the suitability of the two approaches in the preliminary design of a small, flexible-winged unmanned air vehicle (UAV) to be assessed. A sinusoidal vertical gust acts as the aerodynamic perturbation and the aeroelastic response is provided for different aerofoil shapes, spring stiffnesses, wind gust intensities, and modeling approaches. For attached flow, the predicted low-fidelity gust response is found to agree well with the corresponding high-fidelity gust response; for separated flow, the low-fidelity model is unable to predict the strong oscillation of the typical section, and suitable tuning of its response is needed. Three different methods are explored for correcting the low-fidelity results based on just a few high-fidelity ones. The good agreement found between the high-fidelity and the tuned low-fidelity results obtained shows that a multifidelity-metamodel-based strategy is suitable for efficiently correcting reduced-order models.

Metamodelling Based on High and Low Fidelity Models Interaction for UAV Gust Performance Optimization

The size of small flexible winged Unmanned Air Vehicles (UAVs) makes them particularly susceptible to gusts. Accordingly, a gust performance evaluation problem is formulated where the simulation of the gust response is treated as an aeroelastic problem. Generally, a high-fidelity simulation can result in a large computing effort that, being multiplied by a large number of calls for the aeroelastic simulation in the design optimization process, could make the latter prohibitively computationally expensive. Therefore, a multifidelity technique is employed, where a metamodel of the high-fidelity simulation response is built based on a tuned lower fidelity aeroelastic model. In order to address and validate such a multifidelity modelling approach, the linear aeroelastic equations of a 2D airfoil employing quasi-static aerodynamics are used for the lowfidelity model and solved analytically, whereas the nonlinear aeroelastic equations of a 2D airfoil employing unsteady aerodynamics are used for the high-fidelity model and solved numerically. Three different approaches to the low-fidelity model tuning are investigated and compared, both explicit and implicit. An application of the Moving Least Squares Method (MLSM) to the low-fidelity model tuning is also investigated. Good agreement between the high-fidelity model and the corrected low-fidelity model shows that a multifidelity model-based strategy is suitable for use in optimising the gust performance of small UAVs even in the presence of large structural deformations of their wings.

Subsonic Indicial Aerodynamics for Unsteady Loads Calculation via Numerical and Analytical Methods: a Preliminary Assessment

This study deals with generating aerodynamic indicial-admittance functions for the unsteady loads of aircraft wings via CFD and approximate analytical formulations. The novel aspects concern both a critical analysis of the CFD simulations process and an effective analytical synthesis of the CFD outcome based on sound physical grounds, where the main factors affecting the results’ accuracy are separately considered for both impulsive and circulatory parts of the flow response. Considering both thin aerofoils and elliptical wings in compressible subsonic flow, the first part of this work aims at understanding the best practice of generating aerodynamic indicial functions via CFD and numerical results of the lift build-up are obtained for several Mach numbers and aspect ratios. The second part of this work aims at investigating convenient semi-analytical means of approximating such aerodynamic indicial functions by modifying those available for incompressible flow, taking advantage of Prandtl-Glauert scalability for the circulatory part and piston theory for the non-circulatory part. Suitable tuning of the analytical expressions is also derived in order to mimic the CFD results and make proper comparisons between the two approaches. Results are finally shown and critically addressed with respect to the physical and mathematical assumptions employed for the aerodynamic load calculations, within a rigorous and consistent framework. Especially in the case of thin aerofoils, the correct limit behaviour and excellent agreement found between numerical and (tuned) analytical results (i) validate both, (ii) identify the best practice in setting up the CFD simulations and (iii) demonstrate the accuracy and robustness of the proposed analytical technique for approximating aerodynamic indicial-admittance functions efficiently.

Initial Investigation of Chordwise Flexible Flat Aerofoil

The size of small Unmanned Air Vehicles (UAVs) makes them susceptible to gusts, hence an evaluation of their aeroelastic performance is a necessary requirement. With advances in materials, new aircraft are ever lighter and more flexible, both in the span-wise and chord-wise direction. An experiment is set up to evaluate the aeroelastic performance of a 2D chord-wise aerofoil structure under gust loading, where the wing of a small Unmanned Air Vehicle (UAV) is considered by coupling a Finite Element (FE) structural model with a Doublet-Lattice Method (DLM) aerodynamic model; a new semi-analytical modelling approach is also described. The flexible aerofoil structure is then optimised by means of a genetic algorithm (GA) framework for the minimum weight, subject to aeroelastic constraints of flutter, divergence and structural displacement.

Multidisciplinary Multifidelity Optimisation of a Flexible Wing Aerofoil for Small UAV

The preliminary Multidisciplinary Design and Optimisation (MDO) of a flexible wing aerofoil apropos a small Unmanned Air Vehicle (UAV) is performed using a multifidelity model-based strategy. Both the passively adaptive structure and the shape of the flexible wing aerofoil are optimised for best aerodynamic performance under aero-structural constraints, within a coupled aeroelastic formulation. A typical flight mission for surveillance purposes is considered and includes the potential occurrence of wind gusts. A metamodel for the high-fidelity objective function and each of the constraints is built, based on a tuned low-fidelity one, in order to improve the efficiency of the optimisation process. Both metamodels are based on solutions of the aeroelastic equations for a flexible aerofoil but employ different levels of complexity and computational cost for modelling aerodynamics and structural dynamics within a modal approach. The high-fidelity model employs nonlinear Computational Fluid Dynamics (CFD) coupled with a full set of prescribed structural modes, whereas the low-fidelity one employs linear thin aerofoil theory coupled with a reduced set of the latter. The low-fidelity responses are then corrected according to few high-fidelity responses, as prescribed by an appropriate Design of Experiment (DOE), by means of a suitable tuning technique. A standard Genetic Algorithm (GA) is hence utilised to find the global optimum, showing that a flexible aerofoil is characterised by higher aerodynamic efficiency than its rigid counterpart.