The effect of confinement on the stability of viscous planar jets and wakes

This theoretical study examines confined viscous planar jet/wake flows with continuous velocity profiles. These flows are characterized by the shear, confinement, Reynolds number and shear-layer thickness. The primary aim of this paper is to determine the effect of confinement on viscous jets and wakes and to compare these results with corresponding inviscid results. The secondary aim is to consider the effect of viscosity and shear-layer thickness. A spatio-temporal analysis is performed in order to determine absolute/convective instability criteria. This analysis is carried out numerically by solving the Orr–Sommerfeld equation using a Chebyshev collocation method. Results are produced over a large range of parameter space, including both co-flow and counter-flow domains and confinements corresponding to 0.1 < h2/h1 < 10, where the subscripts 1 and 2 refer to the inner and outer streams, respectively. The Reynolds number, which is defined using the channel width, takes values between 10 and 1000. Different velocity profiles are used so that the shear layers occupy between 1/2 and 1/24 of the channel width. Results indicate that confinement has a destabilizing effect on both inviscid and viscous flows. Viscosity is found always to be stabilizing, although its effect can safely be neglected above Re = 1000. Thick shear layers are found to have a stabilizing effect on the flow, but infinitely thin shear layers are not the most unstable; having shear layers of a small, but finite, thickness gives rise to the strongest instability.

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Effect of shear-layer thickness on the Strouhal–Reynolds number relationship for bluff-body wakes

Journal of Fluids and Structures ◽

10.1016/j.jfluidstructs.2006.03.005 ◽

2006 ◽

Vol 22 (8) ◽

pp. 1133-1138 ◽

Cited By ~ 8

Author(s):

F.L. Ponta

Keyword(s):

Reynolds Number ◽

Shear Layer ◽

Layer Thickness ◽

Bluff Body

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1508 Self-Sustained Oscillation Caused by Instability Waves in Planar Jet Shear Layers (2nd report: Relation between Shear Layer Tone and Edge Tone)

The Proceedings of Conference of Hokuriku-Shinetsu Branch ◽

10.1299/jsmehs.2013.50.150801 ◽

2013 ◽

Vol 2013.50 (0) ◽

pp. 150801-150802

Author(s):

Hideo KURASAWA ◽

Yasuhiro KITO ◽

Shouichiro IIO

Keyword(s):

Shear Layer ◽

Shear Layers ◽

Sustained Oscillation ◽

Instability Waves ◽

Planar Jet

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Inviscid axisymmetric absolute instability of swirling jets

Journal of Fluid Mechanics ◽

10.1017/s0022112008003236 ◽

2008 ◽

Vol 613 ◽

pp. 1-33 ◽

Cited By ~ 20

Author(s):

J. J. HEALEY

Keyword(s):

Shear Layer ◽

Axial Velocity ◽

Finite Thickness ◽

Outer Cylinder ◽

Velocity Profiles ◽

Dispersion Relations ◽

Absolute Instability ◽

Pinch Point ◽

Swirling Jets ◽

Codimension Two

The propagation characteristics of inviscid axisymmetric linearized disturbances to swirling jets are investigated for two families of model velocity profiles. Briggs' method is applied to dispersion relations to determine when the basic swirling jets are absolutely or convectively unstable. The method is also applied to the neutral inertial waves used by Benjamin to characterize the subcritical or supercritical nature of the flow. Although these waves are neutral, Briggs' method nonetheless indicates a qualitative change in behaviour at Benjamin's criticality condition. The first model jet has uniform axial velocity, rigid-body rotation and issues into still fluid. A known difficulty in the application of Briggs' method to the analytical dispersion relation for inviscid waves in this flow is resolved. The difficulty is that the pinch point can cross into the left half of the complex-wavenumber plane, where waves grow exponentially with radius and fail to satisfy homogeneous boundary conditions. In this paper the physical consequences of this behaviour are explained. It is shown that if the still fluid is of infinite extent in the radial direction, then the jet is convectively unstable to axisymmetric waves, but if the jet is confined by an outer cylinder concentric with the jet axis, then it becomes absolutely unstable to axisymmetric waves provided that the swirl (ratio of azimuthal to axial velocity) is large enough. This destabilizing effect of confinement occurs however large the radius of the outer cylinder. A second family of model swirling jets with smooth profiles and a finite thickness shear layer at the jet edge is also studied. The inviscid stability equations are solved numerically in this case. The results from the analytical dispersion relations are reproduced as the shear layer thickness tends to zero. However, increasing this thickness acts to destabilize the absolute instability of axisymmetric waves, apparently due to the centrifugal instability present in the shear layer. It is suggested that the transition from convective to absolute instability could be associated with the onset of an unsteady vortex breakdown. The swirl required to produce this transition can be either greater, or less, than the swirl required to produce the transition from supercritical to subcritical flow, depending on the details of the basic velocity profiles. A codimension-two point in parameter space can exist where the unsteady bifurcation associated with the convective–absolute transition coincides with the steady bifurcation associated with the supercritical–subcritical transition. Such codimension-two points can control a rich variety of nonlinear dynamical behaviour.

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A Simplified Model Predicting the Kelvin–Helmholtz Instability Frequency for Laminar Separated Flows

Journal of Turbomachinery ◽

10.1115/1.4032162 ◽

2015 ◽

Vol 138 (4) ◽

Cited By ~ 9

Author(s):

Daniele Simoni ◽

Marina Ubaldi ◽

Pietro Zunino

Keyword(s):

Reynolds Number ◽

Pressure Gradient ◽

Shear Layer ◽

Layer Thickness ◽

Active Flow Control ◽

Linear Stability Theory ◽

Aerodynamic Loading ◽

Gradient Parameter ◽

Semi Empirical ◽

Instability Frequency

A semi-empirical model for the estimation of the Kelvin–Helmholtz (KH) instability frequency, in the case of short laminar separation bubbles over airfoils, has been developed. To this end, the Thwaites's pressure gradient parameter has been adopted to account for the effects induced by the aerodynamic loading distribution as well as by the Reynolds number on the separated shear layer thickness at separation. The most amplified frequency predicted by linear stability theory (LST) for a piecewise linear profile, which can be considered as the KH instability frequency, has been related to the shear layer thickness at separation, hence to the Reynolds number and the aerodynamic loading distribution through the Thwaites's pressure gradient parameter. This procedure allows the formulation of a functional dependency between the Strouhal number of the shedding frequency based on exit conditions and the dimensionless parameters. Experimental results obtained in different test cases, characterized by different Reynolds numbers and aerodynamic loading distributions, have been used to validate the model, as well as to identify the regression curve best fitting the data. The semi-empirical correlation here derived can be useful to set the activation frequency of active flow control devices for the optimization of boundary layer separation control strategies.

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Examining the evolution towards turbulence through spatio-temporal analysis of multi-dimensional structures formed by instability growth along a counter propagating shear layer

10.2172/1148305 ◽

2014 ◽

Author(s):

Elizabeth Merritt ◽

Forrest Doss ◽

Eric Loomis ◽

Kirk Flippo ◽

John Kline

Keyword(s):

Shear Layer ◽

Temporal Analysis ◽

Instability Growth ◽

Spatio Temporal ◽

Propagating Shear

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The effect of counterflow on the development of compressible shear layers

Journal of Fluid Mechanics ◽

10.1017/s0022112096001395 ◽

1996 ◽

Vol 308 ◽

pp. 63-96 ◽

Cited By ~ 47

Author(s):

P. J. Strykowski ◽

A. Krothapalli ◽

S. Jendoubi

Keyword(s):

Shear Layer ◽

High Speed ◽

Reverse Flow ◽

Supersonic Jet ◽

Three Dimensional ◽

Shear Layers ◽

Enhanced Diffusion ◽

Spatio Temporal ◽

Density Ratios ◽

Countercurrent Shear

A compressible countercurrent shear layer was investigated experimentally by establishing reverse flow around the perimeter of a supersonic jet. Measurements demonstrate that spatial growth rates of the countercurrent shear layer significantly exceed those of the classical coflowing layer at comparable density ratios and levels of compressibility. Experiments also reveal the presence of coherent three-dimensional structures in the countercurrent shear layer at convective Mach numbers where similar structures are not present in coflowing layers. It is argued that these kinematic differences are responsible for the enhanced diffusion of the shear layer with counterflow. The spatio-temporal theory is used to examine the connection between the experimental observations and the existence of a transition from convective to absolute instability in high-speed shear layers.

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