Stability of a supersonic boundary layer over a surface with sublimation
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DOI: 10.1134/S0869864320020043
Stability of a supersonic boundary layer over a surface with sublimation* S.A. Gaponov and B.V. Smorodsky Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia E-mail: [email protected] (Received May 28, 2019; revised May 28, 2019; accepted for publication November 6, 2019) The paper presents a theoretical study for a supersonic boundary layer over a flat plate in a stream of air at Mach number M = 2 under the conditions of surface sublimation. The sublimation-prone material is naphthalene (C10 H8 ). Calculations demonstrated that at a higher surface temperature the mass flowrate of naphthalene evaporation is increasing. This reduces the wall temperature in comparison with a similar flow without sublimation. The high molecular mass of naphthalene (vs. air) and reduction of wall temperature due to the wall material evaporation creates a higher density of the binary gas mixture (air and naphthalene vapor) near the wall. This modification of the boundary layer profiles induces a significant reduction of instability growth rate. This fact was confirmed by calculations based on the linear stability theory. It was found that boundary layer stabilization occurs for growing sublimation surface temperature; it becomes a maximum near the triple point temperature of the coating material. The eN method gives the estimates of the Reynolds number for laminar-turbulent transition. This shows a theoretical possibility of extension of the laminar boundary layer above a model with sublimation coating. Keywords: supersonic boundary layer, laminar-turbulent transition, hydrodynamic stability, binary gas mixture, sublimation.
Introduction Today, a need for studying at a boundary layer under conditions of surface ablation remains a topical problem. This is dictated by practical applications aimed at flight vehicle thermal protection (e.g., for a reentry space probe) by using air-thermo-chemically decaying protection coatings. The monograph [1] was focused on this subject: authors wrote that this kind of thermal protection for the pioneering series of space vehicles had been overestimated at those years because of insufficient knowledge about the thermal aspects of fluid dynamics. Onset of turbulence in a boundary layer is a significant factor for those aspects. The problems related to a laminar-turbulent transition have been studied intensively worldwide in recent years. It is a common knowledge that for a situation of low external noise, this laminar-turbulent transition is caused by instability of the boundary layer. The foundations of the stability theory for a compressible boundary layer were formulated in 1950s. [2]. Further *
Research was performed in the framework of the Program for fundamental research for state academies of sciences in 2013-2020 (Project АААА-А17-117030610125-7, No. 0323-2018-0009) and was also supported by Russian Foundation for Basic Research (Project No.18-01-00070-а) and by Russian Science Foundation (Project No. 17-19-01289). S.A. Ga
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