Aerodynamic Design Optimization Research Articles

Intuitive and feasible geometric representation of airfoil using variational autoencoder

Abstract Airfoil shape optimization is crucial for improving aerodynamic performance in advanced aircraft designs. Given the extensive functional evaluations required for optimization, surrogate modeling is widely used to alleviate computational burden. However, greater flexibility in airfoil parameterization often requires a larger number of design variables, leading to the challenge known as the curse of dimensionality in surrogate modeling. In recent years, generative models such as generative adversarial networks and variational autoencoders have shown potential to represent large design spaces with compact design variables. However, these models still exhibit limited feasibility and intuitiveness due to their high model capacity, which in turn degrades the efficiency of design optimization. To address this issue, we have developed a novel airfoil parameterization method using a variational autoencoder. The proposed method improves feasibility by using architecture modeling to separate the generation of thickness and camber distributions, resulting in smooth and nonintersecting airfoils. It also improves intuitiveness by using a physics loss function that aligns latent dimensions with geometric features of the airfoils. Notably, extensive comparative analyses validate the effectiveness of our method in terms of flexibility, parsimony, feasibility, and intuitiveness, leading to increased efficiency in aerodynamic design optimization.

Assessment of turbulence adjoint method in sensitivity calculation and aerodynamic design optimization of turbomachinery cascades

Adjoint-based optimization faces the challenges from sensitivity accuracy when applying in design optimization of turbomachinery cascades with strong turbulence flow. In the study, sensitivities of aerodynamic parameters of different cascades are calculated using the discrete adjoint method, which are then used for design optimization of the cascades. The principles of adjoint method are firstly introduced and the procedures of sensitivity calculation using discrete adjoint method are described. Aerodynamic sensitivities of a high-pressure-turbine cascade and a controlled-diffusion compressor cascade are calculated by both the turbulence adjoint and constant-eddy-viscosity (CEV) adjoint methods. Through comparisons against the sensitivities by finite difference method, the improved accuracy in sensitivity calculation by turbulence adjoint method is demonstrated. Moreover, at the off-design condition of the compressor cascade with intensified turbulence flow, more improvements in sensitivity accuracy are gained. Finally, aerodynamic design optimizations of these two cascades are conducted. The results illustrate that more gains in performance improvements can be obtained by turbulence adjoint method, especially in the optimization of compressor cascade at the off-design condition. The impacts of aerodynamic shape optimization on performance variations of the cascades are addressed.

Aerodynamics-guided machine learning for design optimization of electric vehicles

The transition to electric vehicles is driving a fundamental shift in the automobile design process. Changes in constraints afforded by the absence of a combustion engine create new opportunities for modifying vehicle geometries. Current approaches to optimizing vehicle aerodynamics require a vast amount of computational studies and physical experiments, which are expensive when performing parameter sweeps over conceivable geometric configurations, suggesting the need for more efficient surrogate models to assist analysis. Here we analyze a dataset of industry-quality automobile geometries with their associated aerodynamic performance obtained from experimentally validated, high-fidelity large-eddy simulations. We show that a relationship between these geometries and their respective aerodynamics can be extracted in a low-dimensional manner by leveraging a nonlinear autoencoder which is simultaneously trained to estimate the drag coefficient from the latent variables. We perform aerodynamic design optimization of vehicle designs by making use of the learned aerodynamic relationship in the low-order space obtained by the model. We demonstrate that the aerodynamic trends for the geometries produced from the optimization process show agreement with validation simulations. The findings of this work demonstrate the application of data-driven approaches to the analysis and design of vehicles in a production environment.

A Reformulated-Vortex-Particle-Method-Based Aerodynamic Multi-Objective Design Optimization Strategy for Proprotor in Hover and High-Altitude Cruise

An improved multi-objective design optimization framework is proposed for the efficient design of proprotor blades tailored to specific high-altitude mission requirements. This framework builds upon existing methods by leveraging a reformulated Vortex Particle Method (rVPM) and incorporates three key stages: (1) rapid determination of overall proprotor parameters using a semi-empirical model, (2) optimized blade chord and twist distribution bounds based on minimum energy loss theory, and (3) global optimization with a high-fidelity rVPM-based aerodynamic solver coupled with a multi-objective hybrid optimization algorithm. Applied to a small high-altitude tiltrotor, the framework produced Pareto-optimal proprotor designs with a figure of merit of 0.814 and cruise efficiency of 0.896, exceeding mission targets by over 15%. Key findings indicate that large taper ratios and low twist improve hover performance, while elliptical blade planforms with high twist enhance cruise efficiency, and a tip anhedral further boosts overall performance. This framework streamlines the industrial customization of proprotor blades, significantly reducing the design space for advanced optimization while improving performance in demanding high-altitude environments.

Airfoil Aerodynamic Optimization Design Using Ensemble Learning Surrogate Model

Airfoil Aerodynamic Optimization Design Using Ensemble Learning Surrogate Model

Improving transonic performance with adjoint-based NACA 0012 airfoil design optimization

This study delves into the discrete adjoint method, a powerful tool in high-fidelity aerodynamic shape optimization that efficiently computes derivatives of a target function for different design variables. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables. It is implemented to a NACA0012 airfoil at a transonic speed. This designated test case is qualitatively evaluated, considering specified Mach number and Reynolds number values of 0.7 and 15.96 million, respectively. The standard Spalart-Allmaras turbulence model is adapted to improve computational cost efficiency. The results validate the efficiency of Discrete Adjoint with OpenFOAM, showcasing its capability to generate optimal configurations. The achieved optimized performance is evidenced by minimizing the drag coefficient value (Cd) to an impressive value of 0.00871, 62.2 % lower than the previous studies, thus securing a novelty. While this research does not consider the post-processing of sensitivity calculations, it enables the potential for future research. The primary target of this paper is to assess the educational and training needs of researchers, engineers, and graduate students, offering a comprehensive introduction to discrete adjoint aerodynamic design optimization, presenting a novel methodology, and contributing to future advancements in the design optimization field.

Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

Aerodynamic optimization design and experimental verification of a high-load axial flow compressor

The performance and stable operating range of compressors are critical to the efficient operation of various turbomachinery systems. This paper proposes a multi-level optimization strategy combining the uni-uniform direct free deformation method, Linux partitioned CPU accelerated parallel computing technology, multi-objective particle swarm optimization algorithm and downhill simplex algorithm, which improves design efficiency. Numerical results show that after optimization design, the average value of peak efficiency and stall margin increases. The flow mechanism of compressor performance improvement after optimization lies in the reduction of a low-velocity separation zone in stator hub region. Moreover, the experiment study confirms the reliability and accuracy of the optimization design method and found that flow instability triggering mode, propagation characteristics of the stall cell, and surge frequency are changed after optimization design. Setting a probability distribution threshold for autocorrelation coefficient and cross-correlation coefficients can be used to predict the arrival of the surge condition.

Efficient Forced Response Minimization Using a Full-Viscosity Discrete Adjoint Harmonic Balance Method

A forced response induced by inlet distortion and blade row interactions can lead to high-cycle fatigue failure, especially when the unsteady excitation frequency is close to the natural vibration frequency of a blade. This paper presents the study of forced response sensitivity analysis and minimization using a full-viscosity unsteady discrete adjoint method. The goal is to improve the aeroelastic performances of turbomachinery blades and simultaneously constrain/improve aerodynamic performances. The decoupled modal reduction method is used to compute the forced response, which is considered the objective function in adjoint-based design optimization. To analyze aeroforcing and aerodamping flow and adjoint fields efficiently, the harmonic balance method and its adjoint counterpart developed by an automatic differentiation tool are applied. Two cases—the NASA Rotor 67 with inlet distortion and a three-row configuration with multiple fundamental frequencies in the second row—are used to demonstrate the effectiveness of the aerodynamic and aeroelastic coupled design optimization system developed in this work. For the latter case, the Fourier-transform-based method that first decomposes and then matches the time and space modes at two sides of an interface is used for interface coupling. The almost-periodic Fourier transform method is used to determine the time instances for cases with multiple fundamental frequencies.

Surrogate based design space exploration and exploitation for an efficient airfoil optimization under uncertainties using transition models

The pursuit of sustainable, zero-emission air travel is heavily dependent on the creation of energy-efficient aircraft. Key strategies for achieving this sustainability in aviation include reducing fuel consumption through low-drag designs harnessing laminar flow. However, designing aircraft with laminar flow characteristics is complex due to their sensitivity to environmental and operational factors. This study tackles the challenge of developing energy-efficient aircraft by using computational fluid dynamics models and sophisticated optimization techniques that account for uncertainty. Our approach demonstrates the effectiveness of surrogate-based optimization and uncertainty quantification in optimizing airfoil drag for a natural laminar airfoil (NLF) design. We use surrogate models, trained with data from detailed airfoil simulations, which include a boundary layer code coupled with a linear stability method and a newly developed transition transport model. Transition location predicted using transition models facilitate an accurate drag prediction used in the optimization process. The accuracy of these surrogate models is enhanced through active sampling strategies. Our robust optimization method considers uncertainties in environmental and operational conditions, offering a deeper insight into their effects on crucial design parameters. Unlike traditional deterministic aerodynamic design optimization, our findings highlight the efficacy and precision of uncertainty-based optimization in achieving robust NLF airfoil designs over large (exploration mode) and small (exploitation mode) design spaces. Investigating design space parameterization based on the size of design variables reveals significant differences in optimal airfoil configurations. The optimized designs we propose favor delayed transition, in contrast to deterministic designs which often result in significant loss of laminarity when facing uncertainties. This study represents a significant advancement in aerospace engineering, providing a practical and effective methodology for creating energy-efficient airfoil designs. The application of these advanced optimization and uncertainty quantification techniques shows great potential for the wider field of aerospace engineering, paving the way for more resilient and robust aircraft designs.

Aerodynamic Optimization Design of a Supergravity Centrifuge: A Low-Resistance Strategy

Wind resistance optimization is crucial for enhancing the rotational speed of supergravity centrifuges. We conducted a study using computational fluid dynamics on the Centrifugal Hypergravity and Interdisciplinary Experiment Facility (CHIEF) under construction at Zhejiang University and validated it experimentally using a ZJU400gt centrifuge. Our findings indicate significant reductions in wind resistance through structural modifications of the CHIEF. Reducing the outer radius from 4650 to 4150 mm decreased wind resistance by 16%, primarily due to reduced effective viscosity in the wake region’s gases. More substantial reductions were achieved by lowering the height of the outer wall from 2200 to 1400 mm, which cut wind resistance by 25%. This height reduction suppressed vortex shedding and Kármán vortex street development via the Venturi effect. Adjustments to the roughness height of wall surfaces further decreased wind resistance, with minimal impact from arm roughness. A critical roughness height was identified, below which no further reductions in wind resistance could be attained. Notably, using disc-shaped arms reduced wind resistance by approximately 73% because of their minimal pressure–resistance components and predominant frictional resistance, highlighting their potential in future high-speed centrifuge designs.

Self-Adaptive Evolutionary Info Variational Autoencoder

With the advent of increasingly powerful machine learning algorithms and the ability to rapidly obtain accurate aerodynamic performance data, there has been a steady rise in the use of algorithms for automated aerodynamic design optimisation. However, long training times, high-dimensional design spaces and rapid geometry alteration pose barriers to this becoming an efficient and worthwhile process. The variational autoencoder (VAE) is a probabilistic generative model capable of learning a low-dimensional representation of high-dimensional input data. Despite their impressive power, VAEs suffer from several issues, resulting in poor model performance and limiting optimisation capability. Several approaches have been proposed in attempts to fix these issues. This study combines the approaches of loss function modification with evolutionary hyperparameter tuning, introducing a new self-adaptive evolutionary info variational autoencoder (SA-eInfoVAE). The proposed model is validated against previous models on the MNIST handwritten digits dataset, assessing the total model performance. The proposed model is then applied to an aircraft image dataset to assess the applicability and complications involved with complex datasets such as those used for aerodynamic design optimisation. The results obtained on the MNIST dataset show improved inference in conjunction with increased generative and reconstructive performance. This is validated through a thorough comparison against baseline models, including quantitative metrics reconstruction error, loss function calculation and disentanglement percentage. A number of qualitative image plots provide further comparison of the generative and reconstructive performance, as well as the strength of latent encodings. Furthermore, the results on the aircraft image dataset show the proposed model can produce high-quality reconstructions and latent encodings. The analysis suggests, given a high-quality dataset and optimal network structure, the proposed model is capable of outperforming the current VAE models, reducing the training time cost and improving the quality of automated aerodynamic design optimisation.

A parallel variable-fidelity algorithm for efficient constrained multi-objective aerodynamic design optimization

Modern aerodynamic design optimization aims to discover optimal configurations using computational fluid dynamics under complex flow conditions, which is a typical expensive multi-objective optimization problem. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) combined with efficient global optimization is a promising method but requires enhanced efficiency and faces limitations in its application to multi-objective aerodynamic design optimization (MOADO). To address the issues, an efficient parallel MOEA/D assisted with variable-fidelity optimization (VFO) is proposed for solving MOADO, called the MOEA/D-VFO algorithm. Variable-fidelity surrogates are built for objectives and constraints, achieving higher accuracy using fewer high-fidelity samples and a great number of low-fidelity samples. By retaining more good candidates, the sub-optimization problems defined by decomposing original objectives are capable of discovering more favorable samples using MOEA/D, which prompts optimization convergence. A constraint-handling strategy is developed by incorporating the probability of feasibility functions in the sub-optimizations. The selection of new samples for parallel evaluation is improved by filtering out poor candidates and selecting effective promising samples, which improves the feasibility and diversity of solved Pareto solutions. A Pareto front (PF) can be efficiently found in a single optimization run. The proposed approach is demonstrated by four analytical test functions and verified by two aerodynamic design optimizations of airfoils with and without constraints, respectively. The results indicate that the MOEA/D-VFO approach can greatly improve optimization efficiency and obtain the PF satisfying constraints within an affordable computational budget.

Surrogate and Autoencoder-Assisted Multitask Particle Swarm Optimization for High-Dimensional Expensive Multimodal Problems

In practice, some optimization problems require expensive calculation and exhibit multimodal characteristics simultaneously. These problems are called high-dimensional expensive multimodal optimization problems. When addressing such problems, existing surrogate-assisted evolutionary algorithms (SAEAs) encounter the “curse of dimensionality," which severely affects their capability to search optimal solutions. Therefore, this study proposed a surrogate and autoencoder-assisted multitask particle swarm optimization algorithm. First, an autoencoder-embedded multitask evolutionary framework was established to transform a high-dimensional multimodal optimization problem into multiple low-dimensional subproblems or subtasks. Further, a multi-level surrogate model management mechanism combining mirror learning was proposed. An appropriate local surrogate model can be rapidly generated for each modality of the problem. Moreover, a dual-mode local exploitation strategy was developed to improve the capability of swarm to exploit each subtask. The proposed algorithm was compared with seven existing SAEAs on 33 benchmark functions and the aeroengine aerodynamic design optimization problem. Experimental results revealed that the proposed algorithm can obtain multiple highly competitive optimal solutions, including global optimal solutions.

Reduced order modeling for optimal aerodynamic design and operation of the industrial air-jet ejector

Reduced order modeling for optimal aerodynamic design and operation of the industrial air-jet ejector

A coupled fully implicit method for solving drag-adjoint equations of steady incompressible flows

Numerical instability is one of the main concerns when applying adjoint-based gradient computation in aerodynamic design optimization for a variety of engineering problems. An adjoint pressure-adjoint velocity-coupled fully implicit method for solving the adjoint equations of steady incompressible flows is developed in the present work, taking the aerodynamic drag as the optimization target. The finite volume method for cell-centered, collocated variables on unstructured grids is used for spatial discretization. A stabilization term based on pressure-weighted interpolation (PWI) of the adjoint velocity is added to the adjoint continuity equation to avoid spurious oscillations of adjoint pressure. All the terms of the continuous adjoint equations are discretized implicitly, including the adjoint transpose convection (ATC) term, which is regarded as one of the major sources of numerical instability. The resulting discretized equations are integrated into one linear system, and the adjoint fields can be obtained simultaneously. To prevent the diagonal element of the coefficient matrix of the linear system from getting too small, a singular value decomposition is applied to the diagonal block of the coefficient matrix, and a limiter is applied to the diagonal elements. The condition number of the coefficient matrix may be quite large, so a parallel sparse linear solver that effectively combines direct and iterative methods through a Schur complement approach is applied to solve the linear system. Compared to the staggered iterative solver, no damping or masking is needed for the ATC term in the proposed fully implicit method. There is no need to sacrifice numerical accuracy for numerical stability. This method has been tested in several benchmark cases, and the numerical results show good numerical stability and accuracy. The present method provides a sound basis for industrial applications of adjoint-based aerodynamic optimization methods.

Aerodynamic design of supersonic compressor cascade and vorticity dynamic diagnosis of flow field structure

High-load counter-rotating compressor plays a crucial role in reducing the axial length and weight of the compressor and increasing the thrust-to-weight ratio of the aero-engine. However, the boundary layer flow separation induced by shock waves in the channel of high adverse pressure gradient also brings more aerodynamic losses. This paper proposed a supersonic compressor cascade modeling method based on the unique inlet angle theory and the superimposing thickness on the suction surface method. It carried out aerodynamic optimization design of cascade with inlet Mach number of 1.85 combined with numerical optimization technology, vorticity dynamics diagnosis, and planar cascade experiment. The results show that multiple shock wave combination pressurization can be realized in the supersonic cascade channel. At the design point, the static pressure ratio is 3.285, and the total pressure recovery coefficient reaches 86.82%, and the experimental results of planar cascade also verify the correctness of the simulation method. In addition, the correlation laws between the distribution of the vorticity dynamic parameter, shock wave structure, and aerodynamic performance of cascade were analyzed by the vorticity dynamic flow field diagnosis method, which provides a beneficial reference for the subsequent compressor design.

Improving the energy efficiency and carbon dioxide reduction of a long-haul bus through aerodynamic design optimization

<p>Exhaustion of fossil fuel resources, inconsistent fuel costs and the difficulty of adopting electric vehicle technology in commercial vehicles support the idea that there is an opportunity for research in public transit regarding the correlation between energy efficiency and aerodynamic drag. The turbulent external airflow over a bus at high speeds impacts acceleration, speed, and fuel economy. The fundamental bus's design is intended to carry enough passengers for a reasonable run. Envisaging the factors influencing aerodynamic drag is defiant due to the convoluted relationship between the moving bus and the air. Consequently, a comprehensive numerical and experimental exploration is executed on the bodywork of a bus to improve its aerodynamic efficiency. The aerodynamic drag is directly proportional to the variations in the air density, frontal area, freestream velocity and the drag coefficient. Minimal design reforms are performed on a distinctive long-haul bus. The exertion aims to minimize the drag coefficient, thereby improving the flow characteristics of the bus's bodywork. Through the shape optimization of the bus's bodywork, the modified design has attained a forty-five percent reduction in the drag coefficient. This substantial reduction in drag coefficient directly impacts the reduction of drag force, energy efficiency improvement, and carbon emissions reduction.</p>

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.

Prescreening surrogate-model-assisted multi-objective aerodynamic optimization design of highly loaded axial compressor in heavy-duty gas turbine

To address the challenges of numerous design variables and high evaluation costs in the aerodynamic optimization of advanced highly-loaded axial compressors, this paper presents an axial compressor aerodynamic optimization platform based on directly manipulated free-form deformation (DFFD) parameterization method, a data-driven multi-objective differential evolution optimizer, and computational fluid dynamics. The DFFD method allows for direct geometric manipulation of the target compressor, enabling efficient parameterization of the blades and flow path and reducing the number of design variables. A prescreening surrogate-model-assisted multi-objective differential evolution (Pre-MODE) optimizer is developed to obtain competitive solutions within a limited number of iterations. The surrogate model in Pre-MODE conducts real evaluations only on selected individuals in each generation, thereby reduce evaluation costs while ensuring prediction accuracy. Additionally, a parallel task management system is integrated to improve optimization efficiency. To verify the effectiveness of the optimization platform, a 1.5-stage highly-loaded compressor is aerodynamically optimized. After optimization, the adiabatic efficiency at the design point and the surge margin are increased by 2.42% and 9.04%, respectively. These results confirm the effectiveness and speed of the aerodynamic optimization platform, promoting the establishment of an integrated optimization design system for axial compressors.