The traditional optimization of airfoils relies on, and is limited by, the knowledge and experience of the designer. As a method of intelligent decision-making, reinforcement learning can be used for such optimization through self-directed learning. In this paper, we use the lift–drag ratio as the objective of optimization to propose a method for the aerodynamic optimization of airfoils based on a combination of deep learning and reinforcement learning. A deep neural network (DNN) is first constructed as a surrogate model to quickly predict the lift–drag ratio of the airfoil, and a double deep Q-network (double DQN) algorithm is then designed based on deep reinforcement learning to train the optimization policy. During the training phase, the agent uses geometric parameters of the airfoil to represent its state, adopts a stochastic policy to generate optimization experience, and uses a deterministic policy to modify the geometry of the airfoil. The DNN calculates changes in the lift–drag ratio of the airfoil as a reward, and the environment constantly feeds the states, actions, and rewards back to the agent, which dynamically updates the policy to retain positive optimization experience. The results of simulations show that the double DQN can learn the general policy for optimizing the airfoil to improve its lift–drag ratio to 71.46%. The optimization policy can be generalized to a variety of computational conditions. Therefore, the proposed method can rapidly predict the aerodynamic parameters of the airfoil and autonomously learn the optimization policy to render the entire process intelligent.

Shock wave/boundary layer interaction (SWBLI) is a widespread phenomenon in supersonic flows and has received extensive attention. The boundary layer is generated due to viscous stress, which is a kind of macroscopic manifestation of molecular nonequilibrium motion, namely, nonequilibrium effects. In this paper, an investigation is conducted on SWBLI from the perspective of nonequilibrium effects. A method is proposed for studying nonequilibrium effects based on the Navier–Stokes (NS) equations and the Reynolds-averaged NS (RANS) equations. The SWBLI at Mach 2 and Mach 6 is concerned. The results show that nonequilibrium effects associated with the incident shock wave are weaker than that in the boundary layer for a Mach 2 incoming flow. Neither the separation shock wave nor the incident shock wave has an obvious interaction with nonequilibrium effects in the boundary layer. However, the nonequilibrium effects of the incident shock wave are stronger for a Mach 6 incoming flow, and it has an obvious interaction with the nonequilibrium effect in the boundary layer. We also discuss the relation between nonequilibrium effects and energy conversion in the boundary layer. The analysis reveals that changes in the gradients of total energy-related nonequilibrium effects contribute to the change in total energy by influencing the gradient of the heat flux and the power of viscous stress. Thus, this work provides the flow characteristics of boundary layer separation and energy conversion mechanism of SWBLI from the perspective of nonequilibrium effects, as well as the interaction of nonequilibrium effects between the shock wave and boundary layer.

The physical characteristics inside shock waves with nonequilibrium molecular motion are difficult to describe using conventional macroscopic methods. In this paper, nonequilibrium hydrodynamic and thermodynamic effects caused by the strong nonequilibrium molecular velocity distribution at a shock wave are studied using a mesoscopic kinetic approach. This approach is based on a lattice Boltzmann method and a kinetic nonequilibrium method. The former adopts a compressible double-distribution-function model with separated density and total energy distribution functions. The latter represents the nonequilibrium effects through nonequilibrium kinetic moments based on the nonequilibrium molecular velocity distribution. The nonequilibrium effects in the steady state and the process of the formation of a regular reflection shock wave are presented. Nonequilibrium effects inside the shock wave are further investigated. First, the curvature pattern during the formation of a regular reflection shock wave is addressed. The curvature characteristic leads to distinct features of nonequilibrium effects compared with the linear pattern. A vector-based approach for visualizing nonequilibrium effects is proposed to study the curvature pattern. Second, the influence of viscosity on nonequilibrium effects, which is related to the average collision time among molecules at the shock wave, is explored. The results obtained in this paper provide mesoscopic physical insight into the flow mechanisms occurring in shock waves.

A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann–Bhatnagar–Gross–Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem.