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Despite the closure of the Space Shuttle program, spaceplane remain a promising vehicle, which is being developed in many countries, such as USA, European Union and China. Interest in spaceplane is due to the possibility of their reusability and wider maneuverability in comparison with reentry capsule. However, it’s reusability is directly related to satisfying the temperature limit while descending from orbit. Also, the spaceplane has ricochets in its trajectory due to a high lift-to-drag ratio that decreases landing accuracy. The paper aim is the synthesis of an optimal control program in the problems of gliding descent to the maximizing longitudinal range and lateral range with temperature limitation and the absence of ricochets. The synthesis of the optimal trajectory can be obtained by the control channels of attack angle and bank angle. The approach is to represent the control channels of attack angle and bank angle in the form of Fourier series, and the search for the optimal solution is carried out using the differential evolution algorithm. The paper presents the results of solving problems using a different number of the Fourier series terms.

Despite the application of vortex tubes for cooling, separating gas mixtures, vacuuming, etc., the mechanism of energy separation in vortex tubes remains an object of discussion. This paper studies the effect of secondary swirling in supersonic flows on the energy separation of monatomic and diatomic gases. The approach used is a numerical solution of the Reynolds-averaged Navier-Stokes equations, closed by the Reynolds Stress Model turbulence model. The modelling provided is for a self-vacuuming vortex tube with air, helium, argon, and carbon dioxide. According to the results of the calculations, the effect of secondary swirling is inherent only in viscous gases. A comparison was made between obtained total temperature difference, the level of secondary swirling and power losses on expansion from the nozzle, compression shocks, friction, turbulence, and energy costs to develop cascaded swirl structures. Our results indicate that helium and argon have the highest swirling degree and, consequently, the highest energy separation. Moreover, it can be concluded that the power costs on the development of cascaded vortex structures have a significant role in the efficiency of energy separation.