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

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.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

Experiments on the Flow Around a Sphere at High Reynolds Numbers

1969 ◽  
Vol 36 (3) ◽  
pp. 598-607 ◽  
Author(s):  
T. Maxworthy
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Distribution ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Recirculation Region ◽  
Layer Separation ◽  
High Reynolds Numbers ◽  
High Reynolds

Flow around a sphere for Reynolds numbers between 2 × 105 and 6 × 104 has been observed by measuring the pressure distribution around a circle of longitude under a variety of conditions. These include the effects of laminar and turbulent boundary layer separation, tunnel blockage, various boundary layer trip arrangements and inserting an object to disrupt the unsteady, recirculation region behind the sphere.

Navier–Stokes solutions of unsteady separation induced by a vortex

2002 ◽  
Vol 465 ◽  
pp. 99-130 ◽  
Author(s):  
A. V. OBABKO ◽  
K. W. CASSEL
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Scale Interaction

Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

Prediction of Confined Flame Flashback Limits Using Boundary Layer Separation Theory

2016 ◽  
Author(s):  
Vera Hoferichter ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer
Keyword(s):  
Boundary Layer ◽  
Burning Velocity ◽  
Pressure Rise ◽  
Boundary Layer Separation ◽  
Burner Surface ◽  
Layer Separation ◽  
Relevant Task ◽  
Flame Flashback ◽  
Turbulent Burning Velocity ◽  
Combustion Processes

Premixed combustion is a common technology applied in modern gas turbine combustors to minimize nitrogen oxide emissions. However, early mixing of fuel and oxidizer opens up the possibility of flame flashback into the premixing section upstream of the combustion chamber. Especially for highly reactive fuels boundary layer flashback is a serious challenge. For high preheating and burner surface temperatures, boundary layer flashback limits for burner stabilized flames converge to those of so-called confined flames, where the flame is stabilized inside the burner duct. Hence, the prediction of confined flashback limits is a highly technically relevant task. In this study, a predictive model for flashback limits of confined flames is developed for premixed hydrogen-air mixtures. As shown in earlier studies, confined flashback is initiated by boundary layer separation upstream of the flame tip. Hence, the flashback limit can be predicted identifying the minimum pressure rise upstream of a confined flame causing boundary layer separation. For this purpose, the criterion of Stratford is chosen which was originally developed for boundary layer separation in mere aerodynamic phenomena. It is shown in this paper that it can also be applied to near wall combustion processes if the pressure rise upstream of the flame tip is modeled correctly. In order to determine the pressure rise, an expression for the turbulent burning velocity is derived including the effects of flame stretch and turbulence. A comparison of the predicted flashback limits and experimental data shows high prediction accuracy and wide applicability of the developed model.

Numerical Simulation of Boundary Layer Separation Flow for Airfoil in a Wind Turbine

2009 ◽  
Author(s):  
Quan Liao ◽  
Wenzhi Cui ◽  
Longjian Li ◽  
Yihua Zhang
Keyword(s):  
Boundary Layer ◽  
Wind Turbine ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Boundary Layer Separation ◽  
Aerodynamic Performance ◽  
Separation Flow ◽  
Layer Separation ◽  
Simulation Results

The characteristic of static stall for an airfoil is very important for the design of wind turbine. As long as the detailed information of boundary layer separation flow around an airfoil is obtained, the static stall characteristics could be predicted appropriately. In this paper, both two dimensional (2D) and three dimensional (3D) mathematical models are implemented to simulate fluid flow around a NREL S809 airfoil. The steady state compressible Reynolds-Averaged Navier-Stokes equations are adopted and solved numerically in this paper. Both one-equation and two-equation turbulence models (i.e., Spalart-Allmaras and k-ω Shear Stress Transport models) are adopted, respectively, to solve the turbulent viscosity in this paper. The simulation results show that more detailed vortex structures are obtained by using 3D Spalart-Allmaras turbulence model at high attack angle as compared to the two-equation k-ω SST turbulence model, and the obtained aerodynamic performance of an airfoil with Spalart-Allmaras model agrees well with the available experimental data. Therefore, it seems that the 3D Spalart-Allmaras turbulence model is more capable to demonstrate the 3D characteristics of boundary layer separation flow than the k-ω SST model, and it is more efficient to predict the characteristics of static stall for the airfoil. Meanwhile, the simulation results also reveal that the 3D characteristics of separation flow play a very important role for the aerodynamic performance of airfoil after the static stall, and then the 2D mathematical model is no longer suitable to simulate the boundary layer separation flow around the airfoil.

Boundary layer separation singularities for an upstream moving wall

1983 ◽  
Vol 49 (3-4) ◽  
pp. 241-254 ◽  
Author(s):  
L. L. van Dommelen ◽  
S. F. Shen
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Separation ◽  
Layer Separation ◽  
Moving Wall
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