Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Abstract

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

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“…Обычно используются осредненные по Рейнольдсу [5][6][7][8] уравнения Навье-Стокса (Reynoldsaveraged Navier-Stokes, RANS) модели турбулентности (МТ), для замыкания которых используется совокупность дифференциальных уравнений, эмпирических и полуэмпирических соотношений. Также существуют модели, позволяющие непосредственно исследовать крупные вихревые структуры -метод крупных вихрей (LES), или же сразу все вихревые структуры -прямое численное моделирование (DNS).…”