On quasi-steady boundary-layer separation in supersonic flow. Part 2. Downstream moving separation point

2020 ◽  
Vol 900 ◽  
Author(s):  
A. I. Ruban ◽  
A. Djehizian ◽  
J. Kirsten ◽  
M. A. Kravtsova
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Boundary Layer Separation ◽  
Separation Point ◽  
Layer Separation ◽  
Flow Part ◽  
Image Position

Abstract

scholarly journals On unsteady boundary-layer separation in supersonic flow. Part 1. Upstream moving separation point

2011 ◽  
Vol 678 ◽  
pp. 124-155 ◽  
Author(s):  
A. I. RUBAN ◽  
D. ARAKI ◽  
R. YAPALPARVI ◽  
J. S. B. GAJJAR
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Supersonic Flow ◽  
Body Surface ◽  
Boundary Layer Separation ◽  
The Body ◽  
Separation Point ◽  
Coordinate Frame ◽  
Characteristic Time Scale ◽  
Layer Separation

This study is concerned with the boundary-layer separation from a rigid body surface in unsteady two-dimensional laminar supersonic flow. The separation is assumed to be provoked by a shock wave impinging upon the boundary layer at a point that moves with speed Vsh along the body surface. The strength of the shock and its speed Vsh are allowed to vary with time t, but not too fast, namely, we assume that the characteristic time scale t ≪ Re−1/2/Vw2. Here Re denotes the Reynolds number, and Vw = −Vsh is wall velocity referred to the gas velocity V∞ in the free stream. We show that under this assumption the flow in the region of interaction between the shock and boundary layer may be treated as quasi-steady if it is considered in the coordinate frame moving with the shock. We start with the flow regime when Vw = O(Re−1/8). In this case, the interaction between the shock and boundary layer is described by classical triple-deck theory. The main modification to the usual triple-deck formulation is that in the moving frame the body surface is no longer stationary; it moves with the speed Vw = −Vsh. The corresponding solutions of the triple-deck equations have been constructed numerically. For this purpose, we use a numerical technique based on finite differencing along the streamwise direction and Chebyshev collocation in the direction normal to the body surface. In the second part of the paper, we assume that 1 ≫ Vw ≫ O(Re−1/8), and concentrate our attention on the self-induced separation of the boundary layer. Assuming, as before, that the Reynolds number, Re, is large, the method of matched asymptotic expansions is used to construct the corresponding solutions of the Navier–Stokes equations in a vicinity of the separation point.

Detecting boundary-layer separation point with a micro shear stress sensor array

2007 ◽  
Vol 139 (1-2) ◽  
pp. 31-35 ◽  
Author(s):  
Kui Liu ◽  
Weizheng Yuan ◽  
Jinjun Deng ◽  
Binghe Ma ◽  
Chengyu Jiang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Sensor Array ◽  
Boundary Layer Separation ◽  
Separation Point ◽  
Stress Sensor ◽  
Layer Separation ◽  
Shear Stress Sensor

Numerical solution of unsteady boundary-layer separation in supersonic flow: upstream moving wall

2012 ◽  
Vol 706 ◽  
pp. 413-430 ◽  
Author(s):  
R. Yapalparvi ◽  
L. L. Van Dommelen
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Pressure Rise ◽  
Boundary Layer Separation ◽  
Recirculation Region ◽  
Characteristic Time Scale ◽  
Layer Separation ◽  
Moving Wall

AbstractThis paper is an extension of work on separation from a downstream moving wall by Ruban et al. (J. Fluid. Mech., vol. 678, 2011, pp. 124–155) and is in particular concerned with the boundary-layer separation in unsteady two-dimensional laminar supersonic flow. In a frame attached to the wall, the separation is assumed to be provoked by a shock wave impinging upon the boundary layer at a point that moves downstream with a non-dimensional speed which is assumed to be of order ${\mathit{Re}}^{\ensuremath{-} 1/ 8} $ where $\mathit{Re}$ is the Reynolds number. In the coordinate system of the shock however, the wall moves upstream. The strength of the shock and its speed are allowed to vary with time on a characteristic time scale that is large compared to ${\mathit{Re}}^{\ensuremath{-} 1/ 4} $. The ‘triple-deck’ model is used to describe the interaction process. The governing equations of the interaction problem can be derived from the Navier–Stokes equations in the limit $\mathit{Re}\ensuremath{\rightarrow} \infty $. The numerical solutions are obtained using a combination of finite differences along the streamwise direction and Chebyshev collocation along the normal direction in conjunction with Newton linearization. In the present study with the wall moving upstream, the evidence is inconclusive regarding the so-called ‘Moore–Rott–Sears’ criterion being satisfied. Instead it is observed that the pressure rise from its initial value is very slow and that a recirculation region forms, the upstream part of which is wedge-shaped, as also observed in turbulent marginal separation for large values of angle of attack.

Boundary-Layer Separation Due to Combustion-Induced Pressure Rise in a Supersonic Flow

AIAA Journal ◽  
2009 ◽  
Vol 47 (4) ◽  
pp. 1050-1053 ◽  
Author(s):  
Myles A. Frost ◽  
Dhananjay Y. Gangurde ◽  
Allan Paull ◽  
David J. Mee
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Pressure Rise ◽  
Boundary Layer Separation ◽  
Layer Separation
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