Aerodynamic Shape Optimization Research Articles

Efficient aerodynamic shape optimization using transfer learning based multi-fidelity deep neural network

Computational efficiency and precision pose a classic contradiction in aerodynamic shape optimization. To address this challenge, this study introduces an effective optimization framework based on multi-fidelity fully connected neural network (MFFCN). The framework utilizes transfer learning (TL) to train a multi-fidelity surrogate model that establishes direct mappings between geometric configuration parameters and aerodynamic performance by adaptively capturing linear or nonlinear relationships concealed between high-fidelity (HF) and low-fidelity (LF) information. The HF and LF data are derived from fine and coarse grids, respectively, evaluated using the same computational fluid dynamics (CFD) model. The MFFCN-TL framework is applied to optimize the National Advisory Committee for Aeronautics 0012 (NACA0012) airfoil (12 design variables) and the Office National d'Études et de Recherches Aérospatiales M6 (ONERA M6) wing (50 design variables). Simulation results demonstrate that the NACA0012 airfoil achieves a 69.47% enhancement in lift–drag ratio in 1.069 s, compared to a 12.76% gain over 24.8 h in single-fidelity CFD-based optimization. The ONERA M6 wing achieves a 24.66% reduction in drag coefficient in 694 ms compared to 18.37% over 237.3 h in the CFD model. Statistical results show that the MFFCN-TL framework can reduce optimization cost by more than 90% compared to the single-fidelity CFD-based model. These findings suggest that the MFFCN-TL framework significantly enhances optimization efficiency and provides superior feasible solutions over single-fidelity methods.

Adaptive Free-Form Deformation Parameterization Based on Spring Analogy Method for Aerodynamic Shape Optimization

An adaptive Free-Form Deformation parameterization method based on a spring analogy is presented for aerodynamic shape optimization problems. The proposed method effectively incorporates the gradients of the objective and constraint functions, achieving automatic control point adjustment based on variances in design variable components. To evaluate the performance of the adaptive FFD parameterization method, two 2D airfoil optimization design problems are examined. The optimization of the RAE2822 airfoil with 12, 18 and 24 design variables demonstrates superior results for the adaptive method compared to uniform parameterization. The adaptive method requires fewer iterations and achieves lower objective function values. Additionally, the optimization design from NACA0012 to RAE2822 airfoil with 18 design variables shows that the adaptive parameterization method achieves a lower drag coefficient while satisfying the optimization objective. This validates the method’s capability to finely adjust airfoil shapes and capture more optimal design points by exerting stronger control over local shapes. The proposed adaptive FFD parameterization method proves highly effective for optimizing aerodynamic shapes, offering stability and efficiency in the early stages of optimization, even with a limited number of design variables.

A new mesh deformation method using quaternion and displacement normal propagation for high quality and high efficiency

Mesh deformation technology is widely used in aerodynamic applications like unsteady flow, aeroelasticity, and aerodynamic shape optimization because of its low computational costs and consistent mesh connectivity. In order to raise deformed mesh quality and improve efficiency, a new mesh deformation method based on quaternion and displacement normal propagation (named QN method) is introduced in this paper. The boundary points propagate their displacements composed of translational vectors and quaternions to corresponding volume points along the normal direction under the control of the damping function, which preserves the mesh shape and guarantees the quality near boundaries, including orthogonality and normal size. It can also prevent the volume points from being interfered by other less relevant boundary points, so dealing with complex displacement fields effectively. In addition, it avoids complicated matrix and interpolation operations, thus saving lots of computational costs. For mesh with complex topology, a hybrid method combining the QN method and the radial basis function method (RBF method) is investigated to broaden application scenarios, which are applied to the mesh with normal correspondence inside the boundary layer and the mesh outside, respectively. Benefitting from effective handling for the near-wall elements by the QN method, the RBF interpolation part in the hybrid method requires minor support points to carry out valid large deformation, improving the deformation efficiency greatly compared to the individual RBF method. Five typical test cases with different deformation modes and mesh characteristics are implemented, showing better performance of the proposed method in deformed mesh quality and deformation efficiency.

Three-dimensional aerodynamic shape optimization with high-order direct discontinuous Galerkin schemes

Three-dimensional aerodynamic shape optimization with high-order direct discontinuous Galerkin schemes

Aircraft Ducted Heat Exchanger Aerodynamic Shape and Thermal Optimization

Abstract Interest in aircraft electrification and hydrogen fuel cells is driving demand for efficient waste heat management systems. Ultimately, most of the heat must be rejected to the freestream air. Ducted heat exchangers, also called ducted radiators, are the most common and effective way to do this. Engineers manually design ducted heat exchangers by adjusting the duct's shape and heat exchanger's configuration to reduce drag and transfer sufficient heat. This manual approach misses potential performance improvements because engineers cannot simultaneously consider all of the complex interactions between the detailed duct shape, heat exchanger design, and operating conditions. To find these potential gains, we apply gradient-based optimization to a three-dimensional ducted heat exchanger computational fluid dynamics (CFD) model. The optimizer determines the duct shape, heat exchanger size, heater exchanger channel geometry, and coolant flowrate that minimize the ducted heat exchanger's power requirements while rejecting enough heat. Gradient-based optimization enables the use of nearly 100 shape design variables, creating a large design space and allowing fine-tuning of the optimal design. When applied to an arbitrary, poorly performing baseline, our method produces a nuanced and sophisticated ducted heat exchanger design with five times less cruise drag. Employing this method in the design of electric and fuel cell aircraft thermal management could uncover performance not achievable with manual design practices.

PDE parametric modeling with a two-stage MLP for aerodynamic shape optimization of high-speed train heads

PDE parametric modeling with a two-stage MLP for aerodynamic shape optimization of high-speed train heads

Mathematical derivation of a unified equations for adjoint lattice Boltzmann method in airfoil and wing aerodynamic shape optimization

Unified equations of the adjoint lattice Boltzmann method (ALBM) are derived for five applicable objective functions in 2D/3D aerodynamic shape optimization problems. The derived equations include the adjoint equation, boundary condition, terminal condition and gradient of the cost function. In this research, firstly, these relations are extracted for each objective in details and then the general form of ALBM equations are presented for all defined practical aerodynamic objective function. Five applicable cost functions which are the most important objectives in optimization of aerodynamic geometries include desired pressure and viscous shear stress (VSS) inverse design, drag and moment at fixed lift and finally lift to drag ratio at fixed angle of attack. The new extracted relations are based on the circular and spherical function scheme, and are valid for viscous/inviscid, compressible/incompressible and 2D/3D flows in all continuous flow regimes. Proof of new extracted general relations have been performed by authors.

Aerodynamic shape optimization at low Reynolds number using multi-level hierarchical Kriging models

Aerodynamic shape optimization at low Reynolds number using multi-level hierarchical Kriging models

Aerodynamic shape optimization using a physics-informed hot-start method combined with modified metric-based proper orthogonal decomposition

Aerodynamic shape optimization based on computational fluid dynamics still has a huge demand for improvement in the optimization effect and efficiency when optimizing the unstable flow of airfoils. This article presents a physics-informed hot-start method combined with modified metric-based proper orthogonal decomposition (MPOD-ML-Phys). The data-based filtering strategy is a core step in the original metric-based proper orthogonal decomposition method (MPOD), but existing filtering strategies generate a significant amount of additional computational consumption. Therefore, this article applies machine learning methods to data-based filtering strategy in MPOD and establishes a modified MPOD method (MPOD-ML). In addition, during the MPOD-ML process, a lot of hidden physical knowledge that is beneficial for optimization will also be generated. This article combines Bayesian optimization to construct an MPOD-ML-Phys method, which fully utilizes the flow physical knowledge in MPOD-ML. The efficiency and effect of MPOD-ML and MPOD-ML-Phys are validated by two typical cases: inverse and direct design for airfoils. The results indicate that both MPOD-ML and MPOD-ML-Phys methods can effectively improve the overall optimization efficiency. However, the intervention of machine learning models has significantly reduced the robustness of the MPOD-ML method, while the embedding of physical knowledge makes MPOD-ML-Phys more robust. Meanwhile, the optimized airfoil obtained by MPOD-ML-Phys has better drag divergence characteristics, a later flow separation point, and better flow stability.

Aerodynamic shape optimization of aft propulsive fuselage concept using an internal/external integration model

Aerodynamic shape optimization of aft propulsive fuselage concept using an internal/external integration model

Efficient aerodynamic shape optimization by using unsupervised manifold learning to filter geometric features

Many aerodynamic shape optimization methods often focus on utilizing the end-to-end relationship between design variables and aerodynamic performance to find the optimal design, while overlooking the exploration of geometric knowledge of the shape itself. To fully use geometric knowledge to improve optimization efficiency, this paper proposes an efficient method by exploring the potential correlation between geometric features and aerodynamic performance at a low cost. We use unsupervised isometric feature mapping in manifold learning to capture geometric features that can distinguish the aerodynamic performance of different airfoils without embedding any tags. Then a filter criterion is establish based on the geometric features. During the optimization process, airfoils that deliver poor aerodynamic performance can be filtered out with a high probability before being precisely evaluated through computational fluid dynamics simulations. This helps improve samples quality to enhance the optimization efficiency. We applied the proposed method to the unconstrained and constrained optimizations of the Royal Aircraft Establishment (RAE) 2822 airfoil to validate its performance. The results demonstrate that the proposed method can improve the efficiency of optimization by over 50% compared with the original evolutionary optimization algorithm. It performs well across various optimization problems, demonstrating high engineering practical value.

Integrated Aerodynamic Shape and Aero-Structural Optimization: Applications from Ahmed Body to NACA 0012 Airfoil and Wind Turbine Blades

Integrated Aerodynamic Shape and Aero-Structural Optimization: Applications from Ahmed Body to NACA 0012 Airfoil and Wind Turbine Blades

Nacelle optimisation through multi-fidelity neural networks

PurposeAerodynamic shape optimisation is a complex problem usually governed by transonic non-linear aerodynamics, a high dimensional design space and high computational cost. Consequently, the use of a numerical simulation approach can become prohibitive for some applications. This paper aims to propose a computationally efficient multi-fidelity method for the optimisation of two-dimensional axisymmetric aero-engine nacelles.Design/methodology/approachThe nacelle optimisation approach combines a gradient-free algorithm with a multi-fidelity surrogate model. Machine learning based on artificial neural networks (ANN) is used as the modelling technique because of its ability to handle non-linear behaviour. The multi-fidelity method combines Reynolds-averaged Navier Stokes and Euler CFD calculations as high- and low-fidelity, respectively.FindingsRatios of low- and high-fidelity training samples to degrees of freedom of nLF/nDOFs = 50 and nHF/nDOFs = 12.5 provided a surrogate model with a root mean squared error less than 5% and a similar convergence to the optimal design space when compared with the equivalent CFD-in-the-loop optimisation. Similar nacelle geometries and aerodynamic flow topologies were obtained for down-selected designs with a reduction of 92% in the computational cost. This highlights the potential benefits of this multi-fidelity approach for aerodynamic optimisation within a preliminary design stage.Originality/valueThe application of a multi-fidelity technique based on ANN to the aerodynamic shape optimisation problem of isolated nacelles is the key novelty of this work. The multi-fidelity aspect of the method advances current practices based on single-fidelity surrogate models and offers further reductions in computational cost to meet industrial design timescales. Additionally, guidelines in terms of low- and high-fidelity sample sizes relative to the number of design variables have been established.

The continuous adjoint method to the γ−R˜eθt$$ \gamma -\tilde{R}{e}_{\theta t} $$ transition model coupled with the Spalart–Allmaras model for compressible flows

AbstractThe continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the transition model (in three, non‐smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in‐house, vertex‐centered finite‐volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of “frozen transition” (assumption according to which the adjoint to the transition model equations are not solved) or “frozen turbulence” (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities.

Aerodynamic shape optimization of NACA airfoils based on a novel unconstrained conjugate gradient algorithm

Airfoils are key factors in maximizing the efficiency of turbomachinery. The ideal configuration of the airfoil is engineered to produce significant lift while minimizing drag, all while adhering to specific structural limitations. In this investigation, an innovative algorithm based on unconstrained conjugate gradient techniques to optimize the aerodynamic shape of airfoils is proposed. NACA4412 and NACA2415 airfoils are chosen to be investigated in detail. Bézier parameterisation method is employed to define the design variables. Optimization is conducted utilizing a MATLAB code and the XFOIL panel method-based flow solver to attain the desired aerodynamic outcomes. The optimization process enhanced aerodynamic performance by increasing the lift-to-drag ratio and decreasing the angle of attack for maximum lift-to-drag ratio. An increase of 13.7 % in performance for the NACA 4412 airfoil and 32 % for the NACA 2415 airfoil was achieved. Comparisons with traditional methods demonstrated the efficiency and robustness of the proposed algorithm.

RANS-Based Aerodynamic Shape Optimization of a Wing with a Propeller in Front of the Wingtip

Accounting for propeller–wing interaction allows for the design of more efficient propeller aircraft through strategic propulsion integration. In this paper, the cruise drag of a wing with a propeller located in front of the wingtip is minimized using twist and airfoil-shape design variables. Reynolds-averaged Navier–Stokes computational fluid dynamics with an actuator-disk approach is used for the flow simulations, and a gradient-based algorithm is used for the optimization. Changing the rotation direction of the propeller and optimizing the twist and airfoil shapes of the wing are found to impact the aerodynamic performance significantly, as expected. However, optimizing the wing while accounting for the propeller slipstream during optimization provides little benefit over optimizing it without accounting for the propeller slipstream—a difference of less than one drag count.

Fuel consumption and trailing-edge noise tradeoff studies via mission-based airfoil shape optimization

Aerodynamic drag is often used as a proxy for fuel consumption in aircraft design. However, the aeroacoustic byproduct of airfoil design, such as trailing-edge noise (TEN), is yet to be considered in aircraft applications, despite its inclusion in wind turbine designs. To explore the impact of TEN in airfoil design for aircraft, we establish a mission-based aerodynamic shape optimization framework. A surrogate-based detailed flight mission analysis (that can simulate a flight mission from takeoff to landing) is incorporated into the optimization framework to obtain realistic flight conditions during takeoff and landing—which are important to assess TEN metrics—and calculate accurate fuel consumption, where both are used to evaluate the objective function. To assess its effectiveness, we compare the results against those of the conventional single-point optimization. Not surprisingly, the mission-based optimization simultaneously reduces fuel consumption and TEN, while the single-point optima (performed at the low Mach region) reduce TEN at the expense of higher fuel consumption. This is due to the tradeoff between aerodynamic performance in the transonic region and aeroacoustic performance in the low Mach region, which cannot be properly analyzed without including flight mission analysis in the optimization loop.

Data-driven aerodynamic shape design with distributionally robust optimization approaches

We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. DRO aims to minimize the worst-case expected performance in a set of distributions that is informed by observed data with uncertainties. Building on the findings of the work Gotoh, et al. (2018), we study the connections between a class of DRO and robust design optimization, which is classically based on the mean–variance (standard deviation) optimization formulation pioneered by Taguchi. Our results provide a new perspective to the understanding and formulation of robust design optimization problems. It enables data-driven and statistically principled approaches to quantify the trade-offs between robustness and performance, in contrast to the classical robust design formulation that captures uncertainty only qualitatively. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

The aerodynamic optimization of hypersonic vehicles with the proper-orthogonal-decomposition-based CST method

The flight performance of traditional hypersonic vehicles is limited to a specified incoming flow condition, their aerodynamic performance significantly deteriorates outside of the design condition. We construct a data-driven design framework for aerodynamic shape optimization of hypersonic vehicles, which can be used to improve the current flexibility of designing hypersonic vehicles based on the existing shockwave shape or flowfield. The framework uses a class function/shape function transformation to set parameters for the control sections of the vehicle, then the dimensions of the parameter matrix are reduced by using the proper orthogonal decomposition, and the surrogate model with improved expectations is combined to carry out the aerodynamic shape optimization of hypersonic vehicles. The hypersonic aerodynamic optimization design of NACA 0012 airfoil is conducted, which verifies the high efficiency of the optimization method. The single-point and multi-point aerodynamic optimization designs for the Hypersonic Technology Vehicle-2 (HTV-2) type are conducted. The correlation analysis to the fundamental modes of control sections and lift-to-drag ratio is performed, which verifies the accuracy of the design. Completed the single-point and multi-point optimized design of the entire vehicle considering 48 design variables and geometry restrictions with volume not less than 95% of the baseline. The single-point optimization increases the lift-to-drag ratio by 10.91%, and the multi-point optimization ensures that the aerodynamic performance is improved at all flight conditions and reduces the drag coefficient by 4.1% at the large angle of attack condition. The vehicle shape change rule that is controlled by the positively correlated and negatively correlated fundamental modes for the three control sections coincides with the optimized trend. The study demonstrated the effectiveness and practicality of the framework in the aerodynamic design of hypersonic vehicles.

Aero-Structural Comprehensive Nonprobabilistic Reliability-Based Optimization Method for High Aspect Ratio Wings

An aero-structural comprehensive reliability-based optimization method is proposed to construct the optimization framework of designing the high aspect ratio wing. There are three parts included in this method. 1) The ideal cruising shape is obtained by optimizing the geometrical parameters in the cruising conditions, where only the aerodynamic shape optimization is involved and the structural deformation is not considered. 2) The jig-shape optimization method is presented, where the aerodynamic performance of the wing structure with deformation is improved by adjusting the twist angle along the span direction to make sure that the shape with the aeroelastic deformation approaches the ideal cruising shape. 3) A nonprobabilistic reliability-based structural optimization is conducted by updating the thickness of composite layer, where the dispersion of mechanical properties of composite materials is considered and a nonprobabilistic reliability index according to strength and stiffness constraints is established. The global stiffness of the wing structure is changed after jig-shape optimization and structural optimization, and the jig-shape and structural scheme are modified alternately. The previously mentioned process needs to be repeated until the changes in the jig-shape and structural scheme in the iterations can be ignored. Finally, the effectiveness of this method has been verified through the numerical example followed by some conclusions.