Aerodynamic Shape Optimization Research Articles

Disturbance observer-based fixed-time control for hypersonic morphing vehicles with uncertainties

Abstract The attitude-tracking problem of hypersonic morphing vehicles (HMVs) is investigated in this research. After introducing variable-span wings, the optimal aerodynamic shape is available throughout the entire flight mission. However, the morphing wings cause significant changes in aerodynamic coefficients and mass distribution, challenging the attitude control. Therefore, a complete design procedure for the flight control system is proposed to address the issue. Firstly, the original model and the control-oriented model of HMVs are built. Secondly, in order to eliminate the influence caused by the multisource uncertainties, an adaptive fixed-time disturbance observer combined with fuzzy control theory is established. Thirdly, the fixed-time control method is developed to stabilise hypersonic morphing vehicles based on a multivariable sliding mode manifold. The control input can be obtained directly. Finally, the effectiveness of the proposed method is proved with the help of the Lyapunov theory and simulation results.

Natural laminar flow airfoil design via adjoint-based transition onset delay

This work is focused on the aerodynamic shape optimization (ASO) of airfoils with the aim of attaining natural laminar flow (NLF) designs. The two-equation Amplification Factor Transport (AFT) model is utilized for an accurate prediction of the transitional boundary layer flows. The NLF designs are achieved by utilizing two different objective functions. In the first approach, the conventional drag minimization problem is solved with a target lift coefficient. In addition, a second approach is proposed in this work that directly aims at delaying the transition onset on both the pressure and suction sides, thus expanding the natural laminar flow region around the airfoil. It is shown that by utilizing a sigmoid fitting of the turbulence index profile, the transition onset locations can be accurately predicted in a differentiable and smooth fashion, which is essential to the adjoint-based sensitivity analysis of the RANS solver. The efficacy of the proposed technique for NLF design has been tested for NACA 0012 and RAE 2822 airfoils at moderate lift coefficients. Results have shown that a significantly lower drag count can be achieved by delaying the transition onset locations compared to the case where only a drag minimization is sought. Additionally, the transition onset locations on both sides of the airfoil are delayed using our proposed technique which results in a significant expansion of the natural laminar flow region.

An approach for formation design and flight performance prediction based on aerodynamic formation unit: Energy-saving considerations

The performance improvement of swarm drones through aerodynamic shape optimization may be challenging due to folded size constraints imposed by the specific launch approach. However, fixed-wing aircraft swarms can benefit from formation flight in terms of energy consumption. This study introduces the concept of the “aerodynamic formation unit”, which consists of two or three aircraft that form an inseparable unit of the formation. Considering the Unmanned Aerial Vehicle (UAV) distribution and wingtip vortex interference in the formation, two typical aerodynamic formation units are optimized by the variable-fidelity aerodynamic optimization method based on space mapping. The aerodynamic characteristics of the formation UAVs that affect flight performance, such as lift-to-drag ratio (L/D ratio) and static stability are analyzed by Computational Fluid Dynamics (CFD) simulations. The L/D ratio (cruising condition) of the following aircraft can be increased by 22.8% and 57.5% in the optimal units that involve two and three aircraft respectively. Moreover, this study conducts several CFD simulations for multi-aircraft formations formed by the units, which show that the average L/D ratio of the formation can be improved by more than 19%. These results verify the feasibility and effectiveness of the “aerodynamic formation unit” concept and the optimization framework for formation parameters.

Simultaneous surrogate modeling and dimension reduction using unsupervised learning. Application to parametric wing shape optimization

This paper presents a machine-learning-based approach that enables simultaneous surrogate modeling and dimension reduction and applies it to aerodynamic parametric shape optimization. Aerodynamic shape optimization is a crucial process in various industries, including aerospace, automotive, and renewable energy. It involves iteratively improving the properties of a system by evaluating an objective function and driving its minimization or maximization using an optimization algorithm. However, the evaluation of aerodynamic objective functions requires computationally expensive operations, such as solving complex fluid dynamics equations and calculating performance metrics like lift and drag coefficients. This computational cost becomes particularly burdensome when derivative-free optimization algorithms need to evaluate numerous samples per iteration. Additionally, when the design space dimension is high, the efficiency and effectiveness of the optimization process decrease. To address these challenges, the paper proposes combining surrogate modeling and dimension reduction. Surrogate modeling constructs a reduced order model that approximates the coefficients of interest in a cost-effective manner, while dimension reduction identifies the most relevant design space dimensions using techniques like Proper Orthogonal Decomposition. The paper suggests an integrative approach that employs Artificial Neural Networks (ANN) and Unsupervised Learning, specifically AutoEncoder networks, to simultaneously build a surrogate model and reduce the problem dimension. This technique is applied to optimize the shape of an airplane wing aerofoil under trans-sonic flight conditions. The wing shape is parameterized using Free Form Deformation (FFD). The paper demonstrates that the suggested approach enables rapid and effective shape optimization.

Robust shape optimization using artificial neural networks based surrogate modeling for an aircraft wing

Aerodynamic shape optimization is a very active area of research that faces the challenges of highly demanding Computational Fluid Dynamics (CFD) problems, optimization with Partial Differential Equations (PDEs) as constraints, and the appropriate treatment of uncertainties. This includes the development of robust design methodologies that are computationally efficient while maintaining the desired level of accuracy in the optimization process. This paper addresses aerodynamic shape optimization problems involving uncertain operating conditions. After a review of possible approaches to account for uncertainties, an Artificial Neural Network (ANN) model is used to approximate the aerodynamic coefficients when the operating conditions vary. Robust optimization problem-solving approaches based on deterministic measurements are used, inspired by the work of Deb [Deb K., Gupta H. Introducing robustness in multi-objective optimization. KanGAL Report 2004–2016, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, India (2004)]. The first procedure is a direct extension of a technique used for single-objective optimization. The second is a more practical approach allowing a user to define the desired degree of robustness in a problem. These approaches have been tested and validated in the case of the optimization of an aircraft wing profile in the transonic regime considering two uncertain variables: the Mach number and the angle of incidence.

Full Cross-section Aerodynamic Shape Optimization of a Triangular Cylinder using the surrogate model updating-based optimization framework

Full Cross-section Aerodynamic Shape Optimization of a Triangular Cylinder using the surrogate model updating-based optimization framework

Multifidelity aerodynamic shape optimization for airfoil dynamic stall mitigation using manifold mapping

Aerodynamic shape optimization for dynamic stall mitigation is computationally challenging, requiring multiple costly CFD evaluations. This work proposes a multifidelity modeling technique to efficiently mitigate dynamic stall over an airfoil, particularly manifold mapping (MM) within a trust-region-based optimization framework to find an optimal shape defined by six PARSEC parameters. The high-fidelity (HF) responses are modeled using the unsteady Reynolds-averaged Navier–Stokes equations with Menter’s shear stress transport turbulence model at a Reynolds number of 135,000, Mach number of 0.1, and reduced frequency of 0.05. The low-fidelity responses are acquired from the Kriging regression (KR) trained over the design space. The MM with the pattern-search algorithm is utilized to find optimal designs in two different test cases. The result yields two distinct optimal shapes with a higher thickness, larger leading-edge radius, and more aft camber than the baseline airfoil (NACA 0012), indicating the presence of multiple valid designs. Both designs delay the dynamic stall angle over 3 deg while mitigating peak lift and pitching moment magnitudes. The current approach delivers a computational saving of over 70% compared to HF-KR and Cokriging regression techniques. These findings present an efficient multifidelity strategy with potential application to other computationally expensive optimization problems.

Aerodynamic shape optimization of passenger car fender based on the FFD method

The research of this work focuses on optimizing the body fender of the CAERI AERO car model to decrease aerodynamic drag and improve aerodynamic performance. Five design regions of the body fender were selected and studied. The Free-Form Deformation (FFD) method was used to perform the mesh deformation process without re-modeling and re-gridding. The optimal Latin Hypercube Sampling method and Computational Fluid Dynamics (CFD) simulations are used to generate the sample points and obtain their responses. The relationships between the design variables and their responses, as well as the contributions of the main factors, were analyzed. After then, an optimization of decreasing drag using the Adaptive Simulated Annealing (ASA) algorithm was conducted based on the Radial Basis Function (RBF) model, and a set of convergent solution space sets is obtained. Finally, CFD simulations were performed on the ASA algorithm search results, and a comparison of the aerodynamic performance between the original fender and an optimal fender that selected from the solution spaces is presented. Using the FFD method and the surrogate model dramatically improves the computational efficiency in this study.

Aerodynamic shape optimization of gas turbines: a deep learning surrogate model approach

Aerodynamic shape optimization of gas turbines: a deep learning surrogate model approach

CFD based aerodynamic optimization design

The CFD technology based on the N-S equation plays an extremely important role in the detailed aerodynamic shape design of the complex surface of civil aircraft. In this paper, a consistent parameterization method, response surface model and numerical optimization method are used to conclude the optimization design. The aerodynamic optimization based on CFD, the commonly used CFD methods and free-form surface modeling technology are studied, and the challenges faced in the process of aerodynamic shape optimization of civil aircraft are analyzed. The adoption of a genetic algorithm based on the response surface increases the effectiveness of the entire optimization process.The results show that the adopted design method is effective in solving the problem of complex shape optimization using computationally expensive CFD codes. The advantage of the proposed method is that it can flexibly shape the wing body design and can quickly respond to changes in design requirements during the design process; the proposed method can be used in the design of a wider range of complex aerodynamic shapes.

Aerodynamic shape optimization of wind turbine rotor blades using the continuous adjoint method

Aerodynamic shape optimization of wind turbine rotor blades using the continuous adjoint method

Adjoint-based aerodynamic shape optimization with hybridized discontinuous Galerkin methods

We present a discrete adjoint approach to aerodynamic shape optimization (ASO) based on a hybridized discontinuous Galerkin (HDG) discretization. Our implementation is designed to tie in as seamlessly as possible into a solver architecture written for general balance laws, thus adding design capability to a tool with a wide range of applicability. Design variables are introduced on designated surfaces using the knots of a 2D spline-based geometry representation, while gradients are computed from the adjoint solution using a difference approximation of residual perturbations. A suitable optimization algorithm, such as an in-house steepest descent or the Preconditioned Sequential Quadratic Programming (PSQP) approach from the pyOpt framework, is then employed to find an improved geometry. We present verification of the implementation, including drag or heat flux minimization in compressible flows, as well as inverse design.

Aerodynamic shape optimization of the vortex-shock integrated waverider over a wide speed range

The vortex-shock integrated waverider over a wide speed range could significantly improve the aerodynamic performance of traditional waveriders by introducing the vortex effect at subsonic speeds. Therefore, it is promising to be widely used in the design of wide-speed-range aerospace vehicles. However, the design of the vortex-shock integrated waverider ignores the three-dimensional effect, the subsonic effect, and the viscous effect in the establishment of the reference flow field, which fails to obtain the expected ideal performance. Therefore, it is necessary to further improve the wide-speed-range performance of the vortex-shock integrated waverider by employing the aerodynamic shape optimization method. In this study, the wide-speed-range multipoint optimization of the vortex-shock integrated waverider is carried out using a gradient-based optimizer combined with adjoint gradient evaluations. The results show that the optimum configuration increases the subsonic lift and lift-to-drag ratio by 6.7 % and 7.1 %, while increasing the hypersonic lift-to-drag ratio by 1.4 %. The improvement of the aerodynamic performance at subsonic speeds is attributed to the enhancement of the leeward vortex effect. Also, the leeward surface near the leading edge is optimized to an inner concave region to further enhance the vortex lift, while guaranteeing against the volume decline. Furthermore, the Detached Eddy Simulation (DES) method and the Dynamic Mode Decomposition (DMD) method are used to analyze the vortex dynamic characteristics at subsonic speeds. By analyzing the first three modes, it is observed that the aerodynamic performance of the optimum configuration is improved mainly by the frequency reduction and the increase of the pressure difference between the windward and the leeward surface, which enhance the stability and strength of the vortex.

Multifidelity aerodynamic shape optimization for mitigating dynamic stall using Cokriging regression-based infill

Multifidelity aerodynamic shape optimization for mitigating dynamic stall using Cokriging regression-based infill

Sensitivity-Based Geometric Parametrization and Automatic Scaling for Aerodynamic Shape Optimization

Aerodynamic shape optimization has become well established, with designers routinely performing wing and full aircraft optimizations with hundreds of geometric design variables. However, increased geometric design freedom increases optimization difficulty. These optimizations converge slowly, often taking hundreds of design iterations. In addition, designers have to manually scale design variables through trial and error to achieve a well-behaved optimization problem, which is tedious and time-consuming. In this work, we propose a sensitivity-based geometric parametrization approach that maps the design space onto one better suited for gradient-based optimization while keeping the same optimization problem. At the same time, the process can automatically determine design variable scaling so that the new optimization problem can be solved more effectively. We demonstrate the approach on two aerodynamic shape optimizations and show improved terminal convergence trends compared to the traditional approach, without requiring manual adjustments to the design variable scaling.

Seamless morphing trailing edge flaps for UAS-S45 using high-fidelity aerodynamic optimization

The seamless trailing edge morphing flap is investigated using a high-fidelity steady-state aerodynamic shape optimization to determine its optimum configuration for different flight conditions, including climb, cruise, and gliding descent. A comparative study is also conducted between a wing equipped with morphing flap and a wing with conventional hinged flap. The optimization is performed by specifying a certain objective function and the flight performance goal for each flight condition. Increasing the climb rate, extending the flight range and endurance in cruise, and decreasing the descend rate, are the flight performance goals covered in this study. Various optimum configurations were found for the morphing wing by determining the optimum morphing flap deflection for each flight condition, based on its objective function, each of which performed better than that of the baseline wing. It was shown that by using optimum configuration for the morphing wing in climb condition, the required power could be reduced by up to 3.8% and climb rate increases by 6.13%. The comparative study also revealed that the morphing wing enhances aerodynamic efficiency by up to 17.8% and extends the laminar flow. Finally, the optimum configuration for the gliding descent brought about a 43% reduction in the descent rate.

Radial Basis Function Surrogates for Uncertainty Quantification and Aerodynamic Shape Optimization under Uncertainties

This paper investigates the adequacy of radial basis function (RBF)-based models as surrogates in uncertainty quantification (UQ) and CFD shape optimization; for the latter, problems with and without uncertainties are considered. In UQ, these are used to support the Monte Carlo, as well as, the non-intrusive, Gauss Quadrature and regression-based polynomial chaos expansion methods. They are applied to the flow around an isolated airfoil and a wing to quantify uncertainties associated with the constants of the γ−R˜eθt transition model and the surface roughness (in the 3D case); it is demonstrated that the use of the RBF-based surrogates leads to an up to 50% reduction in computational cost, compared with the same UQ method that uses CFD computations. In shape optimization under uncertainties, solved by stochastic search methods, RBF-based surrogates are used to compute statistical moments of the objective function. In applications with geometric uncertainties which are modeled through the Karhunen–Loève technique, the use on an RBF-based surrogate reduces the turnaround time of an evolutionary algorithm by orders of magnitude. In this type of applications, RBF networks are also used to perform mesh displacement for the perturbed geometries.

Aerodynamic shape optimization of bluff body for galloping-based wind energy harvester by the class function/shape function transformation technique

This paper presents an aerodynamic modification scheme by using the class function/shape function transformation (CST) method to determine the optimal shape of the bluff body and hence improve the performance of the associated galloping-based wind energy harvester (WEH). The CST method, accompanying with the Latin Hypercube sampling method, is used to generate 50 representative samples of galloping bluff bodies with varying sectional geometries, by using only four parameters to describe each sectional geometry. Wind tunnel tests are conducted to measure the output power of each WEH and the transverse wind force acting on the associated bluff body. A Kriging surrogate model is constructed based on the results from wind tunnel test, to determine the optimal shape in terms of the output power. Results show that the optimal shape has the tapered leeward side and concave windward side, which can double the output power compared to a square shape. The underlying mechanism for the high performance is explained by analyzing the measured transverse force in the wind tunnel and the vorticity contours of the flow field generated by CFD analysis. On the one hand, the tapered leeward side avoids flow attachment on the two lateral sides of the shape, providing considerable transverse force that sustains the unstable steady-state galloping. On the other hand, the concave windward side promotes the development of large circulation bubbles, causing significant asymmetry of wind flow and hence remarkable galloping. The findings of the research can guide the design for the bluff body of the galloping-based WEHs, and the CST method can be used as a powerful tool for aerodynamic shape optimization.

Surrogate-based cyber-physical aerodynamic shape optimization of high-rise buildings using wind tunnel testing

This study proposes a surrogate-based cyber-physical aerodynamic shape optimization (SB-CP-ASO) approach for high-rise buildings under wind loading. Three components are developed in the SB-CP-ASO procedure: (1) an adaptive subtractive manufacturing technique, (2) a high-throughput wind tunnel testing procedure, and (3) a flexible infilling strategy. The downtime of the procedure is minimized through a parallel manufacturing and testing (llM&T) technique. An unexplored double-section setback strategy with various cross-sections and transitions positions is used to demonstrate the performance of the proposed procedure. A total of 173 physical specimens were evaluated to reach the optimization convergence within the reserved testing window. Further analysis of promising shapes considering multiple design wind speeds is suggested to achieve target performance objectives at various hazard levels. Practical information on setback and cross-section modification strategies is discussed based on the optimization results. In comparison with a square benchmark model, the roof drifts for promising candidates with similar building volumes are reduced by more than 70% at wind speeds higher than 50 m/s. This procedure is expected to provide an efficient platform between owners, architects, and structural engineers to identify ideal candidates within a defined design space for real-world applications of high-rise buildings.

Biologically-inspired aerodynamic shape optimization for low Reynolds regimes

Biologically-inspired aerodynamic shape optimization for low Reynolds regimes