ABSOLUTE INSTABILITY OF A SUPERCRITICAL SHEAR LAYER

2016 ◽  
Vol 26 (8) ◽  
pp. 815-826 ◽  
Author(s):  
Qing-fei Fu ◽  
Li-Jun Yang ◽  
Chao-Jie Mo
Keyword(s):  
Shear Layer ◽  
Absolute Instability

On vortex formation from a cylinder. Part 1. The initial instability

1988 ◽  
Vol 190 ◽  
pp. 491-512 ◽  
Author(s):  
M. F. Unal ◽  
D. Rockwell
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Circular Cylinder ◽  
Shear Layer ◽  
Vortex Shedding ◽  
Vortex Formation ◽  
Absolute Instability ◽  
Near Wake ◽  
Lower Range ◽  
Fluctuation Amplitude

Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

Pulsatile flow in stenotic geometries: flow behaviour and stability

2009 ◽  
Vol 622 ◽  
pp. 291-320 ◽  
Author(s):  
M. D. GRIFFITH ◽  
T. LEWEKE ◽  
M. C. THOMPSON ◽  
K. HOURIGAN
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Base Flow ◽  
Arterial Stenosis ◽  
Working Fluid ◽  
Absolute Instability ◽  
Straight Tube ◽  
Instability Modes

Pulsatile inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted pulsatile flows. The Reynolds number is varied between 50 and 700 and the stenosis degree by area between 0.20 and 0.90. Numerically, a spectral element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. For low Reynolds numbers, the flow is characterized by a vortex ring which forms directly downstream of the stenosis, for which the strength and downstream propagation velocity vary with the stenosis degree. Linear stability analysis is performed on the simulated axisymmetric base flows, revealing a range of absolute instability modes. Comparisons are drawn between the numerical linear stability analysis and the observed instability in the experimental flows. The observed flows are less stable than the numerical analysis predicts, with convective shear layer instability present in the experimental flows. Evidence is found of Kelvin–Helmholtz-type shear layer roll-ups; nonetheless, the possibility of the numerically predicted absolute instability modes acting in the experimental flow is left open.

Stability of inviscid shear flow over a flexible boundary

2001 ◽  
Vol 434 ◽  
pp. 371-378 ◽  
Author(s):  
JOHN MILES
Keyword(s):  
Phase Shift ◽  
Shear Layer ◽  
Inviscid Flow ◽  
Flow Speed ◽  
Critical Layer ◽  
Absolute Instability ◽  
Outer Flow ◽  
Blasius Boundary Layer ◽  
The Stability ◽  
Limiting Value

The stability of an inviscid flow that comprises a thin shear layer and a uniform outer flow over a flexible boundary is investigated. It is shown that the flow is temporally unstable for all wavenumbers. This instability is either Kelvin–Helmholtz-like or induced by the phase shift across the critical layer. The threshold of absolute instability is determined in the form F = F∗(1 + Cεn) for ε [Lt ] 1, where F (a Froude number) and ε are, respectively, dimensionless measures of the flow speed and the shear-layer thickness, F∗ is the limiting value of F for a uniform flow, C < 0 and n = 1 in the absence (as for a broken-line velocity profile) of a phase shift across the critical layer, and C > 0 and n = 2/3 in the presence of such a phase shift. Explicit results are determined for an elastic plate (and, in an Appendix, for a membrane) with a broken-line, parabolic, or Blasius boundary-layer profile. The predicted threshold for the broken-line profile agrees with Lingwood & Peake's (1999) result for ε [Lt ] 1, but that for the Blasius profile contradicts their conclusion that the threshold for ε ↓ 0 is a ‘singular and unattainable limit’.

scholarly journals Stability analysis and breakup length calculations for steady planar liquid jets

2010 ◽  
Vol 668 ◽  
pp. 384-411 ◽  
Author(s):  
M. R. TURNER ◽  
J. J. HEALEY ◽  
S. S. SAZHIN ◽  
R. PIAZZESI
Keyword(s):  
Stability Analysis ◽  
Velocity Profile ◽  
Shear Layer ◽  
Fluid Velocity ◽  
Finite Thickness ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Breakup Length ◽  
The Stability ◽  
Thickness Shear

This study uses spatio-temporal stability analysis to investigate the convective and absolute instability properties of a steady unconfined planar liquid jet. The approach uses a piecewise linear velocity profile with a finite-thickness shear layer at the edge of the jet. This study investigates how properties such as the thickness of the shear layer and the value of the fluid velocity at the interface within the shear layer affect the stability properties of the jet. It is found that the presence of a finite-thickness shear layer can lead to an absolute instability for a range of density ratios, not seen when a simpler plug flow velocity profile is considered. It is also found that the inclusion of surface tension has a stabilizing effect on the convective instability but a destabilizing effect on the absolute instability. The stability results are used to obtain estimates for the breakup length of a planar liquid jet as the jet velocity varies. It is found that reducing the shear layer thickness within the jet causes the breakup length to decrease, while increasing the fluid velocity at the fluid interface within the shear layer causes the breakup length to increase. Combining these two effects into a profile, which evolves realistically with velocity, gives results in which the breakup length increases for small velocities and decreases for larger velocities. This behaviour agrees qualitatively with existing experiments on the breakup length of axisymmetric jets.

Inviscid axisymmetric absolute instability of swirling jets

2008 ◽  
Vol 613 ◽  
pp. 1-33 ◽  
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.

Structural and stability characteristics of jets in crossflow

2014 ◽  
Vol 760 ◽  
pp. 342-367 ◽  
Author(s):  
D. R. Getsinger ◽  
L. Gevorkyan ◽  
O. I. Smith ◽  
A. R. Karagozian
Keyword(s):  
Shear Layer ◽  
Structural Characteristics ◽  
Vortex Pair ◽  
Absolute Instability ◽  
Layer Transition ◽  
Cross Sectional ◽  
Transverse Jet ◽  
Planar Laser ◽  
Density Ratios ◽  
Sectional Shape

AbstractThis experimental study examines the relationship between transverse jet structural characteristics and the shear layer instabilities forming on the upstream side of the jet column. Jets composed of mixtures of helium and nitrogen were introduced perpendicularly into a low-speed wind tunnel using several alternative injectors: convergent circular nozzles mounted either flush with or elevated above the tunnel floor, and a flush-mounted circular pipe. Both non-intrusive optical diagnostics (planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV)) and intrusive probe-based (hot-wire anemometry) measurements were used to explore a range of jet-to-crossflow momentum flux ratios and density ratios for which previous studies have identified upstream shear layer transition from convective to absolute instability. Remarkable correspondences were identified between formation of the well-known counter-rotating vortex pair (CVP) associated with the jet cross-section and conditions producing strong upstream shear layer vorticity rollup, arising typically from absolute instability in the shear layer. In contrast, asymmetries in the jet mean cross-sectional shape and/or lack of a clear CVP were observed to correspond to weaker, convectively unstable jet shear layers.

Absolute Instability in a Supersonic Shear Layer and Mixing Control

1997 ◽  
Vol 13 (6) ◽  
pp. 763-767 ◽  
Author(s):  
Long-Shin Lee ◽  
Philip J. Morris
Keyword(s):  
Shear Layer ◽  
Absolute Instability ◽  
Mixing Control

scholarly journals Spatial-Temporal Instability of an Inviscid Shear Layer

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Qing-fei Fu ◽  
Li-zi Qin ◽  
Li-jun Yang
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Convective Instability ◽  
Velocity Ratio ◽  
Absolute Instability ◽  
Temperature Ratio ◽  
Oblique Angle ◽  
Absolute Growth Rate ◽  
Absolute Growth ◽  
The Absolute

In this work, we explore the transition of absolute instability and convective instability in a compressible inviscid shear layer, through a linear spatial-temporal instability analysis. From linearized governing equations of the shear layer and the ideal-gas equation of state, the dispersion relation for the pressure perturbation was obtained. The eigenvalue problem for the evolution of two-dimensional perturbation was solved by means of shooting method. The zero group velocity is obtained by a saddle point method. The absolute/convective instability characteristics of the flow are determined by the temporal growth rate at the saddle point. The absolute/convective nature of the flow instability has strong dependence on the values of the temperature ratio, the velocity ratio, the oblique angle, and M number. A parametric study indicates that, for a great value of velocity ratio, the inviscid shear layer can transit to absolute instability. The increase of temperature ratio decreases the absolute growth rate when the temperature ratio is large; the effect of temperature ratio is opposite when the temperature ratio is relatively small. The obliquity of the perturbations would cause the increase of the absolute growth rate. The effect of M number is different when the oblique angle is great and small. Besides, the absolute instability boundary is found in the velocity ratio, temperature ratio, and M number space.

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