Incompressible Laminar Boundary Layers on a Parabola at Angle of Attack: A Study of the Separation Point

1972 ◽  
Vol 39 (1) ◽  
pp. 7-12 ◽  
Author(s):  
M. J. Werle ◽  
R. T. Davis
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Angle Of Attack ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Separation Point ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Type Singularity ◽  
Flow Experiences

The laminar boundary-layer equations were solved for incompressible flow past a parabola at angle of attack. Such flow experiences a region of adverse pressure gradient and thus can be employed to study the boundary-layer separation process. The present solutions were obtained numerically using both implicit and Crank-Nicolson-type difference schemes. It was found that in all cases the point of vanishing shear stress (the separation point) displayed a Goldstein-type singularity. Based on this evidence, it is concluded that a singularity is always present at separation independent of the mildness of the pressure gradient at that point.

An Accurate Calculation Method for Two-dimensional Incompressible Laminar Boundary Layers, Including Cases with Regions of Sharp Pressure Gradient

1977 ◽  
Vol 28 (3) ◽  
pp. 149-162 ◽  
Author(s):  
N Curle
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Calculation Method ◽  
Boundary Layer Separation ◽  
Pressure Gradients ◽  
Accurate Calculation ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Type Boundary

SummaryThe paper develops and extends the calculation method of Stratford, for flows in which a Blasius type boundary layer reacts to a sharp unfavourable pressure gradient. Whereas even the more general of Stratford’s two formulae for predicting the position of boundary-layer separation is based primarily upon an interpolation between only three exact solutions of the boundary layer equations, the present proposals are based upon nine solutions covering a much wider range of conditions. Four of the solutions are for extremely sharp pressure gradients of the type studied by Stratford, and five are for more modest gradients. The method predicts the position of separation extremely accurately for each of these cases.The method may also be used to predict the detailed distributions of skin friction, displacement thickness and momentum thickness, and does so both simply and accurately.

Boundary-Layer Separation From Downstream Moving Boundaries

1973 ◽  
Vol 40 (2) ◽  
pp. 369-374 ◽  
Author(s):  
D. P. Telionis ◽  
M. J. Werle
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Adverse Pressure Gradient ◽  
Theoretical Models ◽  
Boundary Layer Separation ◽  
Moving Boundaries ◽  
Unsteady Boundary Layer ◽  
Layer Separation ◽  
Boundary Layer Equations ◽  
Type Singularity

The laminar boundary-layer equations for incompressible flow with a mild adverse pressure gradient were numerically solved for flows over downstream moving boundaries. It was demonstrated that the vanishing of skin friction in this case is not related to separation.2 Indeed the integration proceeds smoothly through a point of vanishing skin friction and further downstream a Goldstein-type singularity appears at a station where all the properties of separation according to the model of Moore, Rott, and Sears are present. It is also numerically demonstrated that the singular behavior is not uniform with n, the distance perpendicular to the wall, but it is initiated at a point away from the wall leaving below a region of nonsingular flow. The foregoing points provide numerical justification of the general theoretical models of unsteady boundary-layer separation suggested by Sears and Telionis.

Effects of Area Ratio and Mean Rise Angle on the Aerodynamics of Interturbine Ducts

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Yanfeng Zhang ◽  
Shuzhen Hu ◽  
Ali Mahallati ◽  
Xue-Feng Zhang ◽  
Edward Vlasic
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Static Pressure ◽  
Computational Study ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Wake Flow ◽  
Height Ratio ◽  
Inlet Swirl

This work, a continuation of a series of investigations on the aerodynamics of aggressive interturbine ducts (ITD), is aimed at providing detailed understanding of the flow physics and loss mechanisms in four different ITD geometries. A systematic experimental and computational study was carried out by varying duct outlet-to-inlet area ratios (ARs) and mean rise angles while keeping the duct length-to-inlet height ratio, Reynolds number, and inlet swirl constant in all four geometries. The flow structures within the ITDs were found to be dominated by the boundary layer separation and counter-rotating vortices in both the casing and hub regions. The duct mean rise angle determined the severity of adverse pressure gradient in the casing's first bend, whereas the duct AR mainly governed the second bend's static pressure rise. The combination of upstream wake flow and the first bend's adverse pressure gradient caused the boundary layer to separate and intensify the strength of counter-rotating vortices. At high mean rise angle, the separation became stronger at the casing's first bend and moved farther upstream. At high ARs, a two-dimensional separation appeared on the casing and resulted in increased loss. Pressure loss penalties increased significantly with increasing duct mean rise angle and AR.

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

Effects of Area Ratio and Mean Rise Angle on the Aerodynamics of Inter-Turbine Ducts

2014 ◽  
Author(s):  
Yanfeng Zhang ◽  
Shuzhen Hu ◽  
Ali Mahallati ◽  
Xue-Feng Zhang ◽  
Edward Vlasic
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Computational Study ◽  
Pressure Rise ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Area Ratio ◽  
Wake Flow ◽  
High Area ◽  
Inlet Swirl

The present work, a continuation of a series of investigations on the aerodynamics of aggressive inter-turbine ducts (ITD), is aimed at providing detailed understanding of the flow physics and loss mechanisms in four different ITD geometries. A systematic experimental and computational study was carried out for varying duct mean rise angles and outlet-to-inlet area ratio while keeping the duct length-to-inlet height ratio, Reynolds number and inlet swirl constant in all four geometries. The flow structures within the ITDs were found to be dominated by the counter-rotating vortices and boundary layer separation in both the casing and hub regions. The duct mean rise angle determined the severity of adverse pressure gradient in the casing’s first bend whereas the duct area ratio mainly governed the second bend’s static pressure rise. The combination of upstream wake flow and the first bend’s adverse pressure gradient caused the boundary layer to separate and intensify the strength of counter-rotating vortices. At high mean rise angle, the separation became stronger at the casing’s first bend and moved farther upstream. At high area ratios, a 2-D separation appeared on the casing. Pressure loss penalties increased significantly with increasing duct mean rise angle and area ratio.

Flow Separation Control in an Annular to Conical Diffuser Using Two-Dimensional and Three-Dimensional Wall Steps

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Kin Pong Lo ◽  
Christopher J. Elkins ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Control ◽  
Separation Bubble ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Core Flow ◽  
Layer Separation ◽  
Wall Boundary Layer ◽  
Wall Boundary

Conical diffusers are often installed downstream of a turbomachine with a central hub. Previous studies showed that nonstreamlined hubs had extended separated wakes that reduced the adverse pressure gradient in the diffuser. Active flow control techniques can rapidly close the central separation bubble, but this restores the adverse pressure gradient, which can cause the outer wall boundary layer to separate. The present study focuses on the use of a step-wall diffuser to stabilize the wall boundary layer separation in the presence of core flow control. Three-component mean velocity data for a set of conical diffusers were acquired using magnetic resonance velocimetry. The results showed the step-wall diffuser stabilized the wall boundary layer separation by fixing its location. An axisymmetric step separation bubble was formed. A step with a periodically varying height reduced the reattachment length of the step separation and allowed the diffuser to be shortened. The step-wall diffuser was found to be robust in a range of core flow velocity profiles. The minimum distance between the core flow control mechanism and the step-wall diffuser as well as the minimum length of the step were determined.

Separation Criterion for Turbulent Boundary Layers Via Similarity Analysis

2004 ◽  
Vol 126 (3) ◽  
pp. 297-304 ◽  
Author(s):  
Luciano Castillo ◽  
Xia Wang ◽  
William K. George
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Boundary Layer Equation ◽  
Outer Part ◽  
Adverse Pressure Gradient ◽  
Gradient Flows ◽  
Boundary Layer Equations ◽  
Gradient Parameter ◽  
Momentum Boundary Layer

By using the RANS boundary layer equations, it will be shown that the outer part of an adverse pressure gradient turbulent boundary layer tends to remain in equilibrium similarity, even near and past separation. Such boundary layers are characterized by a single and constant pressure gradient parameter, Λ, and its value appears to be the same for all adverse pressure gradient flows, including those with eventual separation. Also it appears from the experimental data that the pressure gradient parameter, Λθ, is also approximately constant and given by Λθ=0.21±0.01. Using this and the integral momentum boundary layer equation, it is possible to show that the shape factor at separation also has to within the experimental uncertainty a single value: Hsep≅2.76±0.23. Furthermore, the conditions for equilibrium similarity and the value of Hsep are shown to be in reasonable agreement with a variety of experimental estimates, as well as the predictions from some other investigators.

Micro-Actuated Delta Wings Induced Control of Boundary Layer Separation

2006 ◽  
Author(s):  
Augusto Lori ◽  
Savaas Xanthos ◽  
Mahmoud Ardebili ◽  
Yiannis Andreopoulos
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Separated Flow ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Wall Region ◽  
Delta Wings ◽  
Layer Separation ◽  
Favorable Pressure Gradient ◽  
Dimensional Boundary

Control of boundary layer separation has been investigated employing an array of micro-actuated delta winglets. The flow with the array is simulated computationally in an initially two-dimensional boundary layer, which is subjected to a Favorable Pressure Gradient (FPG) that accelerated the flow substantially, followed by an Adverse Pressure Gradient (APG) where the flow decelerated, the two successive distortions cause a flow separation in the boundary layer developing on the opposite wall of the wind tunnel. The simulations capture vortices formed by the impulsive motion of the delta wings. The vortices are part of recirculating zone in the wake of the actuators, which as they advect downstream, bring high momentum fluid into the near wall region of a separated flow. Preliminary results indicate micro-actuated delta wings array affect boundary layer separation favorably.

Laminar boundary layers

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Momentum Integral ◽  
Aerodynamic Lift

This chapter starts by introducing the concept of a boundary layer and the associated boundary-layer approximations. The laminar boundary-layer equations are then derived from the Navier-Stokes equations. The assumption of velocity-profile similarity is shown to reduce the partial differential boundary-layer equations to ordinary differential equations. The results of numerical solutions to these equations are discussed: Blasius’ equation, for zero-pressure gradient, and the Falkner-Skan equation for wedge flows. Von Kármán’s momentum-integral equation is derived and used to obtain useful results for the zero-pressure-gradient boundary layer. Pohlhausen’s quartic-profile method is then discussed, followed by the approximate method of Thwaites. The chapter concludes with a qualitative account of the way in which aerodynamic lift is generated.

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