One major problem in the development of hypersonic vehicles is severe aerodynamic heating; thus, the implementation of a thermal protection system is required. A numerical investigation on the reduction of aerodynamic heating using different thermal protection systems is conducted using a novel gas-kinetic BGK scheme. This method adopts a different solution strategy from the conventional computational fluid dynamics technique, and has shown a lot of benefits in the simulation of hypersonic flows. To be specific, it is established based on solving the Boltzmann equation, and the obtained gas distribution function is used to reconstruct the macroscopic solution of the flow field. Within the finite volume framework, the present BGK scheme is specially designed for the evaluation of numerical fluxes across the cell interface. Two typical thermal protection systems are investigated by using spikes and opposing jets, separately. Both their effectiveness and mechanisms to protect the body surface from heating are analyzed. The predicted distributions of pressure and heat flux, and the unique flow characteristics brought by spikes of different shapes or opposing jets of different total pressure ratios all verify the reliability and accuracy of the BGK scheme in the thermal protection system analysis.

To improve the capacity for utilizing a higher number of design variables and handling complex geometries in the class-shape-transformation parameterization method, this paper introduces an alternative for the shape function that employs radial basis functions to interpolate the deformations of the control points throughout the entire shape function. Two representative airfoils are parameterized first, and the results indicate that the presented method can avoid the ill-conditioning problem encountered when using high-order Bernstein polynomials in the traditional method. Moreover, it is more effective in parameterizing complex geometries. A comprehensive test on a database containing 1433 airfoils reveals that the presented method can cover a larger design space with an increase in the number of design variables. The presented method is further employed and validated in two typical aerodynamic shape optimization tasks: an airfoil inverse design and a benchmark problem for drag minimization in transonic viscous flow. The results suggest that the presented method has potential advantages in gaining better optimized results when more design variables are employed.

Dynamic stall in clean air flow has been well studied, but its exploration in air–particle (air–raindrop or air–sand) flow is still lacking. The aerodynamic performance loss of aircraft (NACA0012) and wind turbine (S809) airfoils and their differences during the hysteresis loop at different pitching parameters are also poorly understood. As shown in this paper, the reduced frequency has little effect on the value of the maximum lift coefficient increment caused by particles, but a larger one can enhance the hysteresis effect and drag the angle of attack, at which the maximum increment is obtained, from the up stroke to the down stroke. The large lift coefficient increments of two airfoils and their difference also have a similar change trend with the reduced frequency. Compared to that of NACA0012 airfoil, the increments of S809 airfoil are obviously greater at three mean angles of attack, especially at 8°, which is the commonly used operating angle. In addition, the angle of attack, at which the maximum lift coefficient is obtained, can be significantly changed by particles in two regions: one is under the effect of deep stall, the other is under the effect of light stall at a low, reduced frequency.