In recent years, deep learning technology has developed rapidly and has shown great potential in the optimization of complex systems. In aerodynamic shape optimization, traditional computational fluid dynamics and experimental methods are limited due to issues of efficiency and cost. In contrast, deep learning surrogate models have gradually become a new alternative to traditional methods due to their advantages in nonlinear modeling, efficient computation, and flexible design. These models offer novel approaches to optimization through methods such as data regression, automatic differentiation, and operator learning. This paper presents a comprehensive review of the latest research progress in the field of aerodynamic shape optimization based on deep learning surrogate models, focusing on key technologies, application cases, and future development trends. The article first elaborates on the importance and development context of airfoil and blade profile optimization, introducing the research background and motivation. Then, it discusses the key technologies and challenges faced in aerodynamic shape optimization. Subsequently, it introduces in detail the application of deep learning as a surrogate model, including data- and physics-drisven neural networks, such as Physics-Informed Neural Networks and Deep Operator Networks, and presents practical application cases of these networks in aerodynamic shape optimization. Finally, the article looks into the future of aerodynamic shape optimization, pointing out the advantages of Kolmogorov–Arnold Networks in improving model accuracy and interpretability, as well as the potential of new types of neural networks in aerodynamic optimization, and summarizes their development.

The coalescence-induced self-propelled droplet jumping on superhydrophobic surfaces has a large number of potential applications such as enhancement of condensation heat transfer, self-cleaning, and anti-icing, which becomes a current hotspot. At present, most of the research studies focus on the self-propelled jumping of two identical droplets; however, the jumping induced by unequal-sized droplets is much closer to actuality. In this paper, the coalescence-induced self-propelled jumping of binary unequal-sized droplets is simulated and all energy terms are studied. The normalized liquid bridge width induced by unequal-sized droplets is a function of the square root of the normalized time, and the maximum jumping velocity is a function of the radius ratio as well. The maximum jumping velocity descends with the decrease in the radius ratio and contact angle, and the critical radius ratio shows an upward trend with the decrease in the contact angle. Furthermore, all energy terms decline with the decrease in the radius ratio. The effective energy conversion rate of binary equal-sized jumping is very low, less than 3% in our results. This rate of binary unequal-sized jumping further reduces due to the existence of asymmetric flow. This work helps for a better understanding of the characteristics of coalescence-induced self-propelled droplet jumping.

The coalescence-induced self-propelled droplet jumping behaviors on superhydrophobic surfaces have attracted extensive interest, due to a huge application potential. The coalescence and jumping of two droplets with different radius ratios are numerically simulated, and the jumping velocity is theoretically analyzed. The jumping type changes from the vertical motion to the upward rotation motion, with the decrease of radius ratio. The droplet is not able to jump when the radius ratio is smaller than 0.4. The jumping velocity reaches several peak values when the radius ratio is smaller than 0.7. The maximum jumping velocities are theoretically predicted, which is based on the law of conservation of energy. The viscous dissipation energy which should not be ignored is the main and direct source of the errors.

Coalescence-induced self-propelled droplet jumping has attracted extensive attention because of its huge potential for enhancing dropwise condensation heat transfer, anti-icing, and self-cleaning. Most previous studies focus on binary droplet jumping, with little research on the more complex and realistic multi-droplet jumping. As a result, the effect of the droplet arrangement on the multi-droplet jumping phenomenon remains unclear. In this paper, the self-propelled jumping of three droplets with different arrangements (two droplets are fixed, and the location of the third one is changed) is numerically simulated, and energy conversion efficiency is studied. Based on two different forming mechanisms, region I (the coalescence between the lateral droplets forms the central liquid bridge) and region II (the changed interface curvature of central droplets turns into the central liquid bridge under surface tension) are defined in three-droplet arrangements. The liquid bridges exhibit different dynamic behaviors in two particular regions, even the jumping velocity is determined by the moving synchronicity of liquid bridges in each region. The critical distribution angle that leads to the overall nonmonotonic change of jumping velocities ranges between 110° and 120° (0.02 ≤ Oh ≤ 0.16). Compared with the symmetry of the droplet configuration, the geometry of the droplet arrangement plays a dominate role in the nonmonotonic change. The maximum energy conversion efficiency is just over 6.5% and the minimum is just under 3%. The findings of this study not only reveal how the arrangement affects ternary droplet jumping and explain the phenomenon that cannot be explained before, but deepens our understanding of multi-droplet jumping as well.

The coalescence-induced jumping of droplets on superhydrophobic surfaces is useful in engineering-related applications to enhance condensation-based heat transfer, self-cleaning, and anti-icing and, thus, has attracted extensive attention in research. Some researchers have claimed that superhydrophobic surfaces with protuberant structures can yield droplets with a higher jumping velocity. While the structure of the surface influences droplet dynamics, the concomitant energy transition also needs to be considered. The effects of the geometry on the mechanism of jumping and the energy transition need to be investigated. In this paper, an improved volume-of-fluid method is verified based on experiments and then applied to simulate the jumping behaviors of droplets on superhydrophobic surfaces with cuboid protuberant structures. The effects of repulsion caused by the contributions of the surface tension and the superhydrophobicity of the protuberance are crucial to enhancing the jumping of the droplets. The forces due to them provide a thrust oriented in the direction of jumping of the droplets to increase the value of the positive energy term, while reducing the area and duration of contact between the droplet and the substrate to reduce the negative dissipation term and enhance the efficiency of energy conversion. Surprisingly, an excessively tall structure leads to a sustainable increase in the velocity of jumping of the droplets under the effects of repulsion and the Laplace pressure after piercing the liquid bridge. The work here provides guidance to optimally combine a superhydrophobic substrate with special structures to enhance the jumping of droplets.

超疏水表面上液滴因聚并诱导而引起的自弹跳行为具有巨大的潜在应用价值, 因此有关问题引起了广泛关注. 目前液滴的物性参数对其自弹跳特性的影响却鲜有报道. 本文数值模拟了不同的液体物性参数下液滴的聚并自弹跳行为, 并利用灰色关联法研究了物性参数变化分别与液滴跳起时的真实弹跳速度及液滴和表面的真实接触时间的关联程度. 在无量纲的时间条件下, 液滴的聚并自弹跳的动力学特性仅受Oh数的影响. 在真实的时间条件下, 黏度变化与液滴聚并所需的真实时间无关, 而减小密度比会同时减少聚并过程和跳起过程中所需的真实时间. 无量纲的弹跳速度随着Oh数的增大而减小, 而减小黏度和密度都会增加液滴跳起时的真实弹跳速度. 根据灰色关联度的计算结果可知, 黏度的变化与真实弹跳速度的关联性更高, 密度的变化与真实接触时间关联性更高.