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Pressure distribution is important information for engineers during an aerodynamic design process. Pressure Distribution Oriented (PDO) optimization design has been proposed to introduce pressure distribution manipulation into traditional performance dominated optimization.In previous PDO approaches, constraints or manual manipulation have been use...
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... However, in practical design processes, the design focus for airfoils typically does not seek the airfoil with the highest lift-to-drag ratio. Instead, the focus is on stability considerations, and specific characteristics such as pressure distribution coefficient, drag divergence Mach number, etc. (Li et al. 2018;Wang et al. 2025) are selected as performance indicators. For example, a three-stage design based on WGAN was proposed by Lei (Lei et al. 2021) and Deng et al (Deng and Yi 2023), using the pressure feature as a specified condition for generating the corresponding airfoil. ...
... The method consists of three main steps: first, the transonic pressure coefficient (CP) distributions are captured through the diffusion model according to the six pressure performance features such as the suction peak and pressure gradient. The diffusion model provides enhanced physical interpretability, facilitating better integration with the requirements of aerodynamic performance (Li et al. 2018;Yang et al. 2023a). Next, the mapping model is utilized to extract the physical information from the CP distribution and accurately reconstruct the corresponding airfoil geometry, ensuring that the generated airfoil adheres to the specified pressure features. ...
... Consequently, the performance-oriented design of the airfoil can be indirectly guided by imposing constraints on key pressure distribution characteristics, thereby improving the overall efficiency of the design process. Building upon previous works (Li et al. 2018), this paper uses six distinctive pressure coefficient features widely recognized in the field of supercritical airfoil aerodynamic design, as shown in step 7 in Fig. 5 and described as follows: ...
Inverse design approach, which directly generates optimal aerodynamic shape with neural network models to meet designated performance targets, has drawn enormous attention. However, the current state-of-the-art inverse design approach for airfoils, which is based on generative adversarial network, demonstrates insufficient precision in its generating and training processes and struggles to reveal the coupling relationship among specified performance indicators. To address these issues, the airfoil inverse design framework based on the classifier-free guided denoising diffusion probabilistic model (CDDPM) is proposed innovatively in this paper. First, the CDDPM can effectively capture the correlations among specific performance indicators and, by adjusting the classifier-free guide coefficient, generate corresponding upper and lower surface pressure coefficient distributions based on designated pressure features. These distributions are then accurately translated into airfoil geometries through a mapping model. Experimental results using classical transonic airfoils as examples show that the inverse design based on CDDPM can generate a variety of pressure coefficient distributions, which enriches the diversity of design results. Compared with current state-of-the-art Wasserstein generative adversarial network methods, CDDPM achieves a 33.6% precision improvement in airfoil generating tasks. Moreover, a practical method to readjust each performance indicator value is proposed based on global optimization algorithm in conjunction with active learning strategy, aiming to provide rational value combination of performance indicators for the inverse design framework. This work is not only suitable for the airfoils design, but also has the capability to apply to optimization process of general product parts targeting selected performance indicators.
... Methods based on potential flow [4] are also widely applied for transonic aerodynamic shape optimization, including the BLWF code [6], which uses an iterative quasi-simultaneous algorithm to solve the strong viscous-inviscid interaction of the external potential flow and boundary layer on lifting surfaces. These methods can quickly estimate the wing surface pressure distribution but cannot precisely predict the shock wave pattern and separation, which are crucial for evaluating the aerodynamic performance of transonic wings [7,8]. ...
Machine-learning-based models provide a promising way to rapidly acquire transonic swept wing flow fields but suffer from large computational costs in establishing training datasets. Here, a physics-embedded transfer-learning framework is proposed to efficiently train the model by leveraging the idea that a three-dimensional flow field around wings can be analyzed with two-dimensional flow fields around cross-sectional airfoils. An airfoil aerodynamics prediction model is pretrained with airfoil samples. Then, an airfoil-to-wing transfer model is fine-tuned with a few wing samples to predict three-dimensional flow fields based on two-dimensional results on each spanwise cross section. Sweep theory is embedded when determining the corresponding airfoil geometry and operating conditions, and to obtain the sectional airfoil lift coefficient, which is one of the operating conditions, the low-fidelity vortex lattice method and data-driven methods are proposed and evaluated. Compared to a nontransfer model, introducing the pretrained model reduces the error by 30%, whereas introducing sweep theory further reduces the error by 9%. When reducing the dataset size, less than half of the wing training samples are need to reach the same error level as the nontransfer framework, which makes establishing the model much easier.
... Methods for optimizing the wing surface and the airfoils that form it to improve aerodynamic characteristics are considered in [5,6,7]. ...
The influence of tail surface irregularities on the aerodynamic drag and fuel efficiency of the aircraft is considered. The problem of eliminating oscillations of the airfoil curvature graph is considered. The influence of eliminating unintended concavities of the airfoil on its aerodynamic characteristics is investigated.
... Methods based on potential flow [6] are also widely applied for transonic aerodynamic shape optimization, including the BLWF code [8], which uses an iterative quasi-simultaneous algorithm to solve the strong viscous-inviscid interaction of the external potential flow and boundary layer on lifting surfaces. These methods can quickly estimate the wing surface pressure distribution but cannot precisely predict the shock wave pattern and separation, which are crucial for evaluating the aerodynamic performance of transonic wings [9]. Thus, they can only be used in the preliminary design stages. ...
Machine learning-based models provide a promising way to rapidly acquire transonic swept wing flow fields but suffer from large computational costs in establishing training datasets. Here, we propose a physics-embedded transfer learning framework to efficiently train the model by leveraging the idea that a three-dimensional flow field around wings can be analyzed with two-dimensional flow fields around cross-sectional airfoils. An airfoil aerodynamics prediction model is pretrained with airfoil samples. Then, an airfoil-to-wing transfer model is fine-tuned with a few wing samples to predict three-dimensional flow fields based on two-dimensional results on each spanwise cross section. Sweep theory is embedded when determining the corresponding airfoil geometry and operating conditions, and to obtain the sectional airfoil lift coefficient, which is one of the operating conditions, the low-fidelity vortex lattice method and data-driven methods are proposed and evaluated. Compared to a nontransfer model, introducing the pretrained model reduces the error by 30%, while introducing sweep theory further reduces the error by 9%. When reducing the dataset size, less than half of the wing training samples are need to reach the same error level as the nontransfer framework, which makes establishing the model much easier.
... In addition, when using machine learning methods to model aerodynamic parameters, there are many hidden physical knowledges that are beneficial for optimization. Knowledge mining of these physical knowledge can not only make machine learning models more in line with physical needs , but also improve optimization effectiveness and efficiency (Li et al., 2018). Li et al. (2018) developed a pressure distribution guidance (PDG) method using shock wave information from the pressure coefficient distribution on airfoil surfaces to achieve better pressure distribution manipulation while maintaining optimization efficiency. ...
... Knowledge mining of these physical knowledge can not only make machine learning models more in line with physical needs , but also improve optimization effectiveness and efficiency (Li et al., 2018). Li et al. (2018) developed a pressure distribution guidance (PDG) method using shock wave information from the pressure coefficient distribution on airfoil surfaces to achieve better pressure distribution manipulation while maintaining optimization efficiency. However, if the selected physical knowledge is inappropriate, it can actually reduce the robustness of the optimization process. ...
... into the optimization process. For example, the drag of supercritical airfoils is related to shock waves (Li et al., 2018), wing flutter phenomenon is related to the surface friction coefficient distribution (Li et al., 2022c), and the pitch moment of transonic airfoils is related to the surface pressure coefficient distribution (Zhao et al., 2016). ...
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.
... The important flow structures of wing flow fields, such as shock waves and separations, can also be indicated with distributions, which will be helpful for wing design. 28,29 When establishing the database, the pressure can be directly obtained from every surface grid point on the wing, and the friction at every surface grid point is additionally calculated from the gradient of the tangential velocity between the first and second grid layers. The friction is decomposed into a streamwise part C f,s in the x-y plane and Physics of Fluids ARTICLE pubs.aip.org/aip/pof a spanwise part C f,z in the z-direction, as shown in Fig. 8. ...
With their development, machine learning models can be used instead of computational fluid dynamics simulations to predict flow fields in aerodynamic optimization. However, it is difficult to construct a prediction model for swept wings with various planform geometries because too many samples are required to cover the parameter space. In the present paper, a new model framework is proposed to predict wing surface pressure and friction distributions with fewer samples. The distributed geometry parameters along spanwise are used as model inputs instead of the global planform parameters, and processors are designed to help the model better learn the local effect of geometric variation. The model is trained and tested on simple swept wings with single segment and linear twist distribution, where it outperforms the global input model by 57.6% in terms of lift coefficient prediction errors on small dataset sizes. The distributed input also enables the model to be transferred from single wings to more engineering-practical yet complex kink wings. After fine-tuning with a few samples, model accuracy for kink wings can be similar to that of simple wings, which proves the model for wings with complex planform geometries can be efficiently built with the proposed method.
... In addition to stating the relation between the thickness, drag divergence Mach number, and lift coefficient, Korn's equation [11] also explains how the shock wave grows in response to the free-stream Mach number. According to Oswatitsch's theorem, wave drag [12] can be estimated and optimization efficiency increased by using the wall Mach number in front of a shock wave [13]. To alter the length of the laminar flow area, Zhang et al. [14] adjusted the pressure gradient of the suction plateau on supercritical natural laminar flow airfoils. ...
... This method is easy to extend to most existing CNN architectures, and has certain advantages such as mesh resolution independence. [1] ，开启了人工智能在学术界和工业界的研究浪潮。作为新一 代信息技术的代表，人工智能广泛应用于科学、社会、经济的方方面面 [2] 。近年来，人 工智能在围棋和蛋白质折叠等众多科学领域取得重大进展，使其成为引领新一轮科技革 命和产业变革的核心驱动力之一。利用先进的人工智能方法，推动经典学科在智能化时 代诞生新的突破性成果， 现已成为全球科技工作者的研究热点 [3] 。在 本轮研究浪潮当中， 利用人工智能技术解决流体力学问题最为迫切 [4 , 5 ] 。相关学者致力于流体力学智能化方 向的发展，以期进一步推动对流动机理更深层次的认识 [6,7] 。 现代流体力学的进步得益于高精度试验测量技术 [8 ] 和高保真度数值仿真方法 [9 ] 的广 泛使用，丰富精细的流场数据对复杂构型流动机理的研究，以及多尺度湍流结构的深入 分析， 提供了基础和支撑 [10,11] 。 但是， 获得高保真度高维流场数据的计算资源消耗巨大， 对于气动优化和流固耦合等工程问题，借助人工智能实现复杂流场信息的快速获取成为 不可或缺的技术手段。全球诸多航空航天大国都在探索前沿人工智能与传统流体力学的 有效结合，在集中/分布载荷建模、风洞智能控制、颤振主被动抑制、飞行器优化设计等 方面，人工智能得到越来越广泛的应用 [12,13] 。基于深度学习等人工智能方法发展面向复 杂流场结构的特征提取与表征，以及面向流体力学的深度学习创新框架，并推广到多场 耦合仿真和流动控制等场景，进一步挖掘流体力学的理论和模型，成为流体力学从业者 关注的重难点问题 [14,15] 。 流场信息的快速获取又称为流场建模，是基于数据驱动的建模方法，利用有限的高 精度流场数据样本，建立高效高准确度的代理模型或降阶模型，代替耗时和昂贵的流场 求解器。 在深度学习之前， 传统机器学习技术在流体力学问题中已被证明是有效的 [16,17] 。 代表性的方法包括多层感知器(Multi-Layer Perceptron，MLP)、Kriging 模型 [18] 、径向 基函数(Radial Basis Function，RBF)神经网络，以及随机森林 [19] 等。Li 等人 [20] 综述了 机器学习方法在气动优化研究中的应用。机器学习是人工智能领域的核心技术之一，通 过数学模型和算法从数据中学习规律，涉及概率论、统计学、逼近论、凸分析等多门学 科。但是，传统机器学习方法应用于高维流场建模面临两大挑战 [21,22] 型 [23] ，因其独有的局部连接和权值共享特性，可以高效充分提取空间结构信息，具备强 大的非线性映射能力，在流体力学领域得到极大关注 [24] 。相关研究已将该方法广泛应用 于湍流建模 [25] 、 流场重构 [26] 和不确定性分析 [27,28] [67] 和 ESRGAN [68] 的重构性能进行了全 面的研究和比较。 流场建模的重要应用场景之一是面向飞行器的气动优化设计和反设计。 陈等人 [69] 认 为专家在型号设计中对物理信息的利用方式并不只关注气动性能参数，更重要的是针对 流场结构进行观察分析，通过修型实现对这些结构的调控来获得更全面均衡的性能。对 于经典的 Kriging 代理模型 [70] ，构造的代理优化方法仅能适合于集中载荷建模，在处理 大规模样本数据，以及建立高维特征映射方面还存在不足。李等人 [71,72] 使用深度学习增 强流场结构，将压力分布引入传统的性能主导优化中，提出了模拟"人在回路"的合理 行为和作用机制，以深层次利用信息和知识来改善优化的实用性和效率。Chen 等人 [73] 利用高保真度数据集对基于 U-Net 的深度神经网络模型进行训练以推断流场，然后作为 代理模型进行形状优化问题的求解，显示出解决一般气动设计问题的前景。Du 等人 [74] 针对某型涡轮静叶端壁型线的设计优化问题，提出了一种串联卷积神经网络结构，能够 提供丰富的流场信息和性能参数，显著优于高斯过程回归模型。流场建模能够给出更丰 富的高密度信息，包括旋涡、附面层、尾迹、激波等，非常适合开展融入先验知识的优 化框架，以兼顾流场结构和总体性能指标。 这些研究验证了卷积神经网络对流场空间信息优秀的表征能力。CNN 模型不仅可 以预测流场，还可以获得满足工程标准的气动力，对于解决气动设计问题具有广阔的前 景。由于 CNN 模型通常需要均匀分布的像素化数据，因此当前研究大都采用了将流场 数据投影到均匀笛卡尔网格的数据预处理方法 [75] 。 此类建模方法不能表征边界层的细节 [76] ， 导致模型预测的近壁区流场和变量分布不平滑。 为了用于不规则计算域的流场预测， [79] 。高维数据集通常位于低维流形上，所在低维流形的维度就是 该数据集的本征维度 [80,81] 。数据降维思想是通过降阶方法，在保留全阶系统主要信息的 前提下，获取高维数据的低维空间。通过建立高维空间与低维空间之间的映射关系，可 以实现在较低维空间近似描述全阶系统 [82] 。ROM 作为一种模型识别方法，是降低动力 学系统复杂性和大规模的有力工具，最具代表性的 POD [83] 和动态模态分解 [84] 等方法在 亚临界圆柱涡致振动 [85] 、翼型跨声速抖振模态分析 [86] 、压气机叶栅分离流动 [87] 、高超声 速边界层转捩 [88] 等方面得到应用。 Lario 等人 [89] 使用循环神经网络建模谱 POD 潜在空间 的时间依赖系数，所提出的模型能够对复杂的统计平稳数据进行低秩预测。但是，这些 研究大多基于线性或弱非线性假设，难以高准确度重构流场中激波附面层干扰的流动细 节。为增强并拓展传统方法，已有研究通过在一般模型中嵌入伽利略不变性 [90] ，或 使用 神经网络对湍流系统进行降阶建模 [91 , 92 ] [144,145] ， 并在流场建模方面已经取得应用 [146,147] 。 Brandstetter 等人 [148] 基于神经信息传递， 用反向优化的神经函数近似器代替计算图中所有启发式设计的组件，研究证明神经信息 传递求解器代表性地包含一些经典方法，如有限差分、有限体积和 WENO 格式。但是， GNNs 在训练过程中会存在计算成本高、深层不稳定和过平滑等问题 [149] 。Hao 等人 [150] 设计新颖的异构归一化注意力层，提出了可扩展且有效的基于 Transformer 的算子学习 框架，该模型能够灵活地处理多输入函数和不规则网格。You 等人 [151] 将神经网络解释为 1 1 Pr Pr [158] 和两方程的剪应力输运 (Shear-Stress Transport)SST k-ω 模型 [159] 应用最为广泛，本文使用这两种湍流模型进行亚声速 和跨声速的流场仿真。 ,, [164,165,166] ...
The rapid acquisition of high-fidelity flow field information is of great significance for the study of physical mechanisms such as flow separation and multi-field coupling, and is an indispensable technical means for the development of engineering problems such as aerodynamic optimization and fluid-structure interaction (FSI). A series of deep learning models represented by Convolutional Neural Networks (CNNs), which have good representation ability for spatial structure information, have become an important method in the field of flow field modeling. However, because the convolution operator is limited to uniform discrete data, and the model architecture does not make full use of the prior information of the flow field structure, it is difficult for CNN to effectively solve the modeling of complex flows such as wall turbulence with multi-scale and strong nonlinear characteristics, as well as the generalization of mesh density. The neural operator network of nonlinear mapping in infinite dimensional function space has mesh resolution independence and interpretability. However, there are still some shortcomings such as low modeling accuracy and data format constraints in the modeling of high Reynolds number flow field in the field of aviation engineering. Inappropriate data processing methods and training strategies make the unsteady flow field modeling weak in generalization and significant in error accumulation, which makes it difficult to give long-term stable dynamic response in multi-field coupling solution.
Therefore, this paper focuses on the subsonic / transonic flow field modeling of high Reynolds number airfoils and wings, and uses deep learning methods to establish efficient and accurate flow field surrogate models and reduced-order models to accurately characterize the non-uniform multi-scale turbulence field with strong nonlinearity such as shock wave discontinuity and flow separation. The deep learning model architecture design, physics-guided neural operator development, data dimensionality reduction and dynamic modeling are carried out, and the aerodynamic optimization and aeroelastic simulation framework are built based on the flow field prediction model. The main research contents are as follows:
(1) The method of flow field modeling based on CNN from the perspective of transform domain is proposed. The coordinate transformation is used to transform the flow field from the non-uniform physical plane to the uniform discrete calculation plane, and the metric coefficient is constructed to characterize the geometric characteristics. For the subsonic / transonic flow field modeling case of the airfoil shape-based, U-Net can accurately characterize the whole flow field variables and the flow details in the near-wall region. The prediction results are highly consistent with CFD, and the relative errors of the flow field variables are less than 1%. The CAU-Net with channel attention mechanism can characterize the dramatic changes of flow parameters in the shock wave region with high accuracy, which greatly improves the generalization of the model. For the subsonic / transonic flow field modeling case of the wing shape-based, the flow field contour and surface variable distribution predicted by the model coincide with the CFD, and the relative errors of the integral force coefficients are less than 1%. The CAU-Net model has the scalability of millions of mesh nodes and the ability to learn complex three-dimensional effects. The CAU-Net feature map contains the flow information of the shock region of different shapes and the stagnation region of the leading edge of the airfoil, which retains the interpretability of the POD mode. Based on the transform domain convolution flow field modeling, a hybrid optimization design / inverse design framework is built to realize the pressure distribution-oriented optimization design task integrated with prior knowledge.
(2) A mesh convolution Mesh Conv method for modeling steady flow field on non-uniform mesh is proposed. Through the Green function transformation, based on the approximation of the integral operator of the partial differential equation, the standard convolution elements are decomposed and combined with the specific data type of the flow field, and the local weight concept is introduced to embed the data structure information. The geometric field features such as distance, slope and curvature are designed, and the difference between the operator and the standard convolution operator and the graph convolution operator is clarified. For data sets using a single base mesh, the training and testing MSE of the Mesh-Net model is reduced by 30% and 26%, respectively, compared with the CNN model, indicating that the non-uniform structured data considering local weights can greatly improve the modeling accuracy. For the mixed data set using two base meshes, the training and testing MSE of the Mesh-Net model are reduced by 63% and 55%, respectively, compared with CNN. Mesh Conv makes full use of the characteristics of CNN and structured mesh of flow field, and draws on the neighbor aggregation characteristics of the graph convolution. This method is easy to extend to most existing CNN architectures, and has certain advantages such as mesh resolution independence.
(3) A mesh operator Mesh Operator method with permutation invariance for steady flow field modeling is proposed. Based on the integral operator approximation of partial differential equations, the continuous convolution weight function is constructed based on the anisotropy of wall turbulence, and the differences and connections among Mesh Operator, Mesh Conv and Conv are expounded. The MeshONet architecture designed using group convolution and channel weight greatly saves model memory and improves operating efficiency. For the S809 airfoil shape-based separation flow case, a mixed resolution data set is constructed based on five different mesh topologies, and the modeling results of FNN-1, FNN-2, DeepONet, CNN, Mesh Conv and MeshONet are compared and analyzed in detail. The model loss of MeshONet can be reduced by 1-2 orders of magnitude compared with other models, and the relative errors of the integral force coefficients are less than 2%. Mesh Operator can be extended to general flow field data format. For the 30P30N three-segment wing multi-block mesh case, the model loss of MeshONet is reduced by two orders of magnitude compared with FNN-2 and DeepONet, and the relative errors of the integral force coefficients are less than 1%. The similarity with the integral form of the solution operator enables MeshONet to capture the long-range dependencies in the computational domain, and the continuous processing of the interaction between nodes makes the resolution of MeshONet independent and has the versatility of the general flow field data structure.
(4) An unsteady flow field modeling method for subsonic / transonic forced response of airfoils and wings is proposed. Using data dimensionality reduction technology and deep learning methods, random signals and chirp signals are designed to construct data samples. For the case with weak nonlinearity, POD is used to extract the flow modes, and the time-dynamic evolution of POD coefficients modeled by ARX and RRBF methods is compared. The results show that the error accumulation problem of unsteady flow field inferring can be overcome by constructing training samples with broadband excitation signals. For cases with strong nonlinearity, a reduced-order model is established based on CAE and LSTM. The relative errors of the flow field variables are less than 5‰, and the relative errors of the integral force coefficients are less than 1%. The complex limit cycle behavior of sinusoidal samples with wide amplitude and frequency range can be predicted accurately. The CAE-LSTM method is extended to the unsteady forced response modeling of the subsonic wing. The flow field contour of the wing surface and the variable distribution at different spanwise positions predicted by the model are in good agreement with CFD. The unsteady response basically coincides with CFD in the entire time domain, which verifies the strong learning ability and generalization of the unsteady three-dimensional effect. The FSI simulation framework is built based on CAE-LSTM, and the time series response of pitch displacement and moment coefficient of the airfoil at different reduce frequencies of subsonic / transonic condition is given with high efficiency and high accuracy.
... In the engineering design of airfoils and wings, the pressure distribution is closely related to aerodynamic performance and is the most important concern for engineers during the aerodynamic design process [32]. In general, designers acquire design experience from pressure distribution to efficiently guide the optimization process. ...
... The rest of the samples are used as the testing set. The minibatch size is 8,8,8,16,16,16,32,32 for the eight different training set sizes. The number of training epochs for 1D-CAE is 5000, and that for two FMLPs is 2000. ...
... The rest of the samples are used as the testing set. The minibatch size is 8,8,8,16,16,16,32,32 for the eight different training set sizes. The number of training epochs for 1D-CAE is 5000, and that for two FMLPs is 2000. ...
Traditional optimization methods usually perform aerodynamic design by manipulating geometry shapes, which would ignore useful information in flowfields. In order to improve the defect, a novel pressure-based optimization (PBO) method is developed in this study to conduct the design of airfoils using deep learning techniques. In this method, a one-dimensional convolutional auto-encoder (1D-CAE) is employed to extract representative features from the pressure distributions. With these latent features as inputs, two multilayer perceptrons are constructed to predict airfoil profiles and forces, respectively. Furthermore, these deep learning models are combined with the genetic algorithm to minimize the drag of the RAE2822 airfoil. Finally, two data mining techniques are implemented to investigate the optimization mechanisms. Results show that, after the latent dimension reaches 12, the reconstructed pressure distributions by 1D-CAE agree well with the original ones. The predicted forces are close to the observations, with the mean absolute relative error below 0.21% for [Formula: see text] and 0.69% for [Formula: see text] on the testing set. Meanwhile, the predicted airfoils show a good match with the true profiles, and the root mean square error is less than 0.08% for all the testing samples. Optimized results show that, compared with several state-of-the-art optimization approaches, the proposed PBO method achieves a lower drag coefficient and has the potential to provide better airfoil designs. In addition, the discovered mechanisms indicate that the pressure distributions could be manipulated by varying pressure features to achieve drag reduction of airfoils.
... The aerodynamic shape design of civil transport aircraft is strongly constrained by the transonic buffet boundary [1]. At high subsonic Mach numbers or high angles of attack, periodic shock motion with large amplitudes can be observed on the wings. ...
At transonic flight conditions, the buffet caused by the shockwave/boundary-layer interaction can degrade aircraft performance and even threaten their safety. In this paper, a closed-loop control using an active shock control bump (SCB) has been proposed to suppress the buffet on a supercritical airfoil flying at transonic speeds. A closed-loop control law is designed by using the lift coefficient as the feedback signal and using the bump height as the control variable. The unsteady numerical simulations show that the buffet can be effectively suppressed by an optimal combination of the parameters of the control law, namely the gain and the delay time. Furthermore, the buffet control effectiveness is still acceptably constrained by a prescribed maximum bump height, which is believed to be practically important. In addition to being able to achieve both wave drag reduction and buffet alleviation, the active SCB is less sensitive to the parameters of the control law and has a shorter response time in comparison with the reference active trailing edge flap.
