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.

scholarly journals Shear instability of an axisymmetric air–water coaxial jet

2018 ◽  
Vol 843 ◽  
pp. 575-600 ◽  
Author(s):  
Jean-Philippe Matas ◽  
Antoine Delon ◽  
Alain Cartellier
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Scaling Laws ◽  
Shear Instability ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Instability Waves

We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to predict the boundaries between these three regimes.

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 The effect of a lifted flame on the stability of round fuel jets

2008 ◽  
Vol 609 ◽  
pp. 275-284 ◽  
Author(s):  
JOSEPH W. NICHOLS ◽  
PETER J. SCHMID
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Local Stability ◽  
Premixed Flame ◽  
Absolute Instability ◽  
Low Mach Number ◽  
Lifted Flame ◽  
Local Stability Analysis ◽  
The Stability ◽  
Globally Stable

The stability and dynamics of an axisymmetric lifted flame are studied by means of direct numerical simulation (DNS) and linear stability analysis of the reacting low-Mach-number equations. For light fuels (such as non-premixed methane/air flames), the non-reacting premixing zone upstream of the lifted flame base contains a pocket of absolute instability supporting self-sustaining oscillations, causing flame flicker even in the absence of gravity. The liftoff heights of the unsteady flames are lower than their steady counterparts (obtained by the method of selective frequency damping (SFD)), owing to premixed flame propagation during a portion of each cycle. From local stability analysis, the lifted flame is found to have a significant stabilizing influence at and just upstream of the flame base, which can truncate the pocket of absolute instability. For sufficiently low liftoff heights, the truncated pocket of absolute instability can no longer support self-sustaining oscillations, and the flow is rendered globally stable.

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.

Spatial stability and the onset of absolute instability of Batchelor's vortex for high swirl numbers

2007 ◽  
Vol 583 ◽  
pp. 27-43 ◽  
Author(s):  
L. PARRAS ◽  
R. FERNANDEZ-FERIA
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Absolute Instability ◽  
Spatial Stability ◽  
The Past ◽  
Trailing Vortices ◽  
The Stability ◽  
Large Aircraft

Batchelor's vortex has been commonly used in the past as a model for aircraft trailing vortices. Using a temporal stability analysis, new viscous unstable modes have been found for the high swirl numbers of interest in actual large-aircraft vortices. We look here for these unstable viscous modes occurring at large swirl numbers (q > 1.5), and large Reynolds numbers (Re >103), using a spatial stability analysis, thus characterizing the frequencies at which these modes become convectively unstable for different values of q, Re, and for different intensities of the uniform axial flow. We consider both jet-like and wake-like Batchelor's vortices, and are able to analyse the stability for Re as high as 108. We also characterize the frequencies and the swirl numbers for the onset of absolute instabilities of these unstable viscous modes for large q.

Stability of a Stationary Flexible Cantilevered Plate in an Axial Flow

2014 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Keiji Matsumoto
Keyword(s):  
Stability Analysis ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Axial Flow ◽  
Complex Eigenvalue ◽  
Flexible Plate ◽  
Moving Plate ◽  
Cantilevered Plate ◽  
The Stability

As the flexible plates, the papers in printing machines, the thin plastic and metal films, and the fluttering flag are enumerated. In this paper, the flexible plate is assumed to be stationary in an axial flow although both the stationary plate and the axially moving plate can be thought. The fluid is assumed to be treated as an ideal fluid in a subsonic domain, and the fluid pressure is calculated using the velocity potential theory. The coupled equation of motion of a flexible cantilevered plate is derived in consideration of the added mass, added damping and added stiffness, respectively. The velocity potential is obtained by assuming the unsteady axial fluid velocity to be zero at the trailing edge of a flexible cantilevered plate, neglecting the effect of a circulation. The complex eigenvalue analysis is performed for the stability analysis. In order to investigate the validity of the proposed analysis, another stability analysis is also performed by using the non-circulatory aerodynamic theory. The comparison between both solutions is investigated and discussed. Changing the velocities of a fluid and the specifications of a plate as parametric studies, the effects of these parameters on the stability of a flexible cantilevered plate are investigated.

The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory

2002 ◽  
Vol 459 ◽  
pp. 43-65 ◽  
Author(s):  
I. M. WALLWORK ◽  
S. P. DECENT ◽  
A. C. KING ◽  
R. M. S. M. SCHULKES
Keyword(s):  
Weber Number ◽  
Multiple Scales ◽  
Asymptotic Methods ◽  
Travelling Wave ◽  
Liquid Jet ◽  
Inviscid Liquid ◽  
Breakup Length ◽  
The Stability ◽  
Good Agreement ◽  
Wave Modes

We examine a spiralling slender inviscid liquid jet which emerges from a rapidly rotating orifice. The trajectory of this jet is determined using asymptotic methods, and the stability using a multiple scales approach. It is found that the trajectory of the jet becomes more tightly coiled as the Weber number is decreased. Unstable travelling wave modes are found to grow along the jet. The breakup length of the jet is calculated, showing good agreement with experiments.

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