Self-destabilising loop of a low-speed water jet emanating from an orifice in microgravity

2016 ◽  
Vol 797 ◽  
pp. 146-180 ◽  
Author(s):  
Akira Umemura
Keyword(s):  
Mode Analysis ◽  
Unstable Wave ◽  
Complex Conjugate ◽  
Transfer Energy ◽  
Global Mode ◽  
Weakly Nonlinear ◽  
Low Speed ◽  
Nonlinear Growth ◽  
Breakup Length ◽  
The Stability

A one-dimensional global mode analysis is conducted for low-speed water jets emanating from a circular orifice in microgravity, in which the observed spontaneous convective instability causes almost periodic jet disintegrations at a fixed location for each jet-issue speed that exceeds a certain threshold. The inviscid spatial linear stability analysis identifies four wave modes excitable at the frequency: the Plateau–Rayleigh (PR) unstable wave, its complex conjugate and two neutral waves which may transfer energy upstream. Their linear combination satisfying the orifice exit condition may describe the synchronised reproduction of a PR unstable wave from each neutral wave at the orifice exit. On the other hand, a weakly nonlinear analysis shows that the growth of the nonlinear PR unstable wave produces the two neutral waves near the orifice. Thus, the same PR unstable wave can be reproduced on a newly issued liquid surface owing to the neutral waves produced by its own nonlinear growth. This self-destabilising loop, dominantly operating for the most unstable PR wave, determines the initial PR unstable wave amplitude and, consequently, the breakup length as a function of jet-issue speed. The predicted initial amplitude of the PR unstable wave is in reasonably good agreement with the value calculated from the average breakup length measured in our microgravity experiments. It is found that that the loop consists mainly of the downstream- and upstream-moving neutral waves at relatively high and low jet speeds, respectively. The stability of the self-destabilising loop is also discussed.

Boussinesq global modes and stability sensitivity, with applications to stratified wakes

2017 ◽  
Vol 812 ◽  
pp. 1146-1188
Author(s):  
Kevin K. Chen ◽  
Geoffrey R. Spedding
Keyword(s):  
Bluff Body ◽  
Boussinesq Equations ◽  
Base Flow ◽  
Mode Analysis ◽  
Flow Density ◽  
Global Mode ◽  
Multiple Production ◽  
Small Density ◽  
Global Modes ◽  
The Stability

For the Boussinesq equations, we present a theory of linear stability sensitivity to base flow density and velocity modifications. Given a steady-state flow with small density variations, the sensitivity of the stability eigenvalues is computed from the direct and adjoint global modes of the linearised Boussinesq equations, similarly to Marquetet al.(J. Fluid Mech., vol. 615, 2008, pp. 221–252). Combinations of the density and velocity components of these modes reveal multiple production and transport mechanisms that contribute to the eigenvalue sensitivity. We present an application of the sensitivity theory to a stably linearly density-stratified flow around a thin plate at a$90^{\circ }$angle of attack, a Reynolds number of 30 and Froude numbers of 1, 8 and$\infty$. The global mode analysis reveals lightly damped undulations pervading through the entire domain, which are predicted by both inviscid uniform base flow theory and Orr–Sommerfeld theory. The sensitivity to base flow velocity modifications is primarily concentrated just downstream of the bluff body. On the other hand, the sensitivity to base flow density modifications is concentrated in regions both immediately upstream and immediately downstream of the plate. Both sensitivities have a greater upstream presence for lower Froude numbers.

scholarly journals Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities

2009 ◽  
Vol 622 ◽  
pp. 1-21 ◽  
Author(s):  
OLIVIER MARQUET ◽  
MATTEO LOMBARDI ◽  
JEAN-MARC CHOMAZ ◽  
DENIS SIPP ◽  
LAURENT JACQUIN
Keyword(s):  
High Speed ◽  
Passive Control ◽  
Three Dimensional ◽  
Adjoint Problem ◽  
Base Flow ◽  
Mode Analysis ◽  
Global Mode ◽  
Recirculation Bubble ◽  
Global Modes ◽  
The Stability

The stability of the recirculation bubble behind a smoothed backward-facing step is numerically computed. Destabilization occurs first through a stationary three-dimensional mode. Analysis of the direct global mode shows that the instability corresponds to a deformation of the recirculation bubble in which streamwise vortices induce low- and high-speed streaks as in the classical lift-up mechanism. Formulation of the adjoint problem and computation of the adjoint global mode show that both the lift-up mechanism associated with the transport of the base flow by the perturbation and the convective non-normality associated with the transport of the perturbation by the base flow explain the properties of the flow. The lift-up non-normality differentiates the direct and adjoint modes by their component: the direct is dominated by the streamwise component and the adjoint by the cross-stream component. The convective non-normality results in a different localization of the direct and adjoint global modes, respectively downstream and upstream. The implications of these properties for the control problem are considered. Passive control, to be most efficient, should modify the flow inside the recirculation bubble where direct and adjoint global modes overlap, whereas active control, by for example blowing and suction at the wall, should be placed just upstream of the separation point where the pressure of the adjoint global mode is maximum.

Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows

2007 ◽  
Vol 593 ◽  
pp. 333-358 ◽  
Author(s):  
DENIS SIPP ◽  
ANTON LEBEDEV
Keyword(s):  
Reynolds Numbers ◽  
Cavity Flow ◽  
Open Cavity ◽  
Mode Analysis ◽  
Mean Flow ◽  
Global Mode ◽  
Weakly Nonlinear ◽  
Experimental Function ◽  
The Mean ◽  
Cylinder Flow

This article deals with the first Hopf bifurcation of a cylinder flow, and more particularly with the properties of the unsteady periodic Kármán vortex street regime that sets in for supercritical Reynolds numbers Re > 46. Barkley (Europhys. Lett. vol.75, 2006, p. 750) has recently studied the linear properties of the associated mean flow, i.e. the flow which is obtained by a time average of this unsteady periodic flow. He observed, thanks to a global mode analysis, that the mean flow is marginally stable and that the eigenfrequencies associated with the global modes of the mean flow fit the Strouhal to Reynolds experimental function well in the range 46 < Re < 180. The aim of this article is to give a theoretical proof of this result near the bifurcation. For this, we do a global weakly nonlinear analysis valid in the vicinity of the critical Reynolds number Rec based on the small parameter ε = Rec−1 − Re−1 ≪ 1. We compute numerically the complex constants λ and μ′ which appear in the Stuart-Landau amplitude equation: dA/dt = ε λA − εμ′ A|A|2. Here A is the scalar complex amplitude of the critical global mode. By analysing carefully the nonlinear interactions yielding the term μ′, we show for the cylinder flow that the mean flow is approximately marginally stable and that the linear dynamics of the mean flow yields the frequency of the saturated Stuart-Landau limit cycle. We will finally show that these results are not general, by studying the case of the bifurcation of an open cavity flow. In particular, we show that the mean flow in this case remains strongly unstable and that the frequencies associated with the eigenmodes do not exactly match those of the nonlinear unsteady periodic cavity flow. It will be demonstrated that two precise conditions must hold for a linear stability analysis of a mean flow to be relevant and useful.

scholarly journals The nonlinear evolution of the inviscid secondary instability of streamwise vortex structures

1995 ◽  
Vol 352 (1700) ◽  
pp. 483-502 ◽  
Keyword(s):  
Nonlinear Evolution ◽  
Streamwise Vortex ◽  
Unstable Wave ◽  
Neutral Stability ◽  
Weakly Nonlinear ◽  
Nonlinear Growth ◽  
History Of ◽  
Finite Distance ◽  
The Mean ◽  
Mean State

The weakly nonlinear evolution of an inviscid marginally unstable wave growing on a boundary layer supporting a streamwise vortex structure is investigated. The nonlinear growth of the wave is found to be controlled by the diffusion layer located at the edge of the critical layer associated with the wave. The evolution equation is found to depend on the upstream history of the wave and the solution of the equation suggests th at the wave either restructures the mean state so as to make it stable or develops a singularity at a finite distance downstream of the point of neutral stability.

Numerical Investigation of the Solidity Effect on Linear Compressor Cascades

2014 ◽  
Author(s):  
J. Sans ◽  
M. Resmini ◽  
J.-F. Brouckaert ◽  
S. Hiernaux
Keyword(s):  
Numerical Investigation ◽  
State Of The Art ◽  
Leading Edge ◽  
Operating Conditions ◽  
Compressor Cascade ◽  
Minimum Loss ◽  
Low Speed ◽  
High Mach ◽  
The Stability ◽  
The Impact

Solidity in compressors is defined as the ratio of the aerodynamic chord over the peripheral distance between two adjacent blades, the pitch. This parameter is simply the inverse of the pitch-to-chord ratio generally used in turbines. Solidity must be selected at the earliest design phase, i.e. at the level of the meridional design and represents a crucial step in the whole design process. Most of the existing studies on this topic rely on low-speed compressor cascade correlations from Carter or Lieblein. The aim of this work is to update those correlations for state-of-the-art controlled diffusion blades, and extend their application to high Mach number flow regimes more typical of modern compressors. Another objective is also to improve the physical understanding of the solidity effect on compressor performance and stability. A numerical investigation has been performed using the commercial software FINE/Turbo. Two different blade profiles were selected and investigated in the compressible flow regime as an extension to the low-speed data on which the correlations are based. The first cascade uses a standard double circular arc profile, extensively referenced in the literature, while the second configuration uses a state-of-the-art CDB, representative of low pressure compressor stator mid-span profile. Both profiles have been designed with the same inlet and outlet metal angles and the same maximum thickness but the camber and thickness distributions, the stagger angle and the leading edge geometry of the CDB have been optimized. The determination of minimum loss, optimum incidence and deviation is addressed and compared with existing correlations for both configurations and various Mach numbers that have been selected in order to match typical booster stall and choke operating conditions. The emphasis is set on the minimum loss performance at mid-span. The impact of the solidity on the operating range and the stability of the cascade are also studied.

Investigation of the stability of AC repulsive-force levitation systems for low-speed maglev

1992 ◽  
Vol 28 (5) ◽  
pp. 3315-3317 ◽  
Author(s):  
J.L. He ◽  
Z. Wang ◽  
D.M. Rote ◽  
S. Winkelman
Keyword(s):  
Repulsive Force ◽  
Low Speed ◽  
The Stability

Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown

1999 ◽  
Vol 396 ◽  
pp. 73-108 ◽  
Author(s):  
D. M. MASON ◽  
R. R. KERSWELL
Keyword(s):  
Finite Amplitude ◽  
Complex Conjugate ◽  
Small Scale ◽  
Conjugate Pair ◽  
Weakly Nonlinear ◽  
Elliptical Instability ◽  
Elliptical Flow ◽  
Complex Conjugate Pair ◽  
Generic Instability ◽  
Secondary Instabilities

A direct numerical simulation is presented of an elliptical instability observed in the laboratory within an elliptically distorted, rapidly rotating, fluid-filled cylinder (Malkus 1989). Generically, the instability manifests itself as the pairwise resonance of two different inertial modes with the underlying elliptical flow. We study in detail the simplest ‘subharmonic’ form of the instability where the waves are a complex conjugate pair and which at weakly supercritical elliptical distortion should ultimately saturate at some finite amplitude (Waleffe 1989; Kerswell 1992). Such states have yet to be experimentally identified since the flow invariably breaks down to small-scale disorder. Evidence is presented here to support the argument that such weakly nonlinear states are never seen because they are either unstable to secondary instabilities at observable amplitudes or neighbouring competitor elliptical instabilities grow to ultimately disrupt them. The former scenario confirms earlier work (Kerswell 1999) which highlights the generic instability of inertial waves even at very small amplitudes. The latter represents a first numerical demonstration of two competing elliptical instabilities co-existing in a bounded system.

An adaptive sliding mode controller for the lateral control of articulated long vehicles

2018 ◽  
Vol 233 (3) ◽  
pp. 487-515 ◽  
Author(s):  
Naser Esmaeili ◽  
Reza Kazemi ◽  
S Hamed Tabatabaei Oreh
Keyword(s):  
High Speed ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Lane Change ◽  
Lateral Velocity ◽  
Low Speed ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller ◽  
Articulated Vehicle ◽  
The Stability

Today, use of articulated long vehicles is surging. The advantages of using large articulated vehicles are that fewer drivers are used and fuel consumption decreases significantly. The major problem of these vehicles is inappropriate lateral performance at high speed. The articulated long vehicle discussed in this article consists of tractor and two semi-trailer units that widely used to carry goods. The main purpose of this article is to design an adaptive sliding mode controller that is resistant to changing the load of trailers and measuring the noise of the sensors. Control variables are considered as yaw rate and lateral velocity of tractor and also first and second articulation angles. These four variables are regulated by steering the axles of the articulated vehicle. In this article after developing and verifying the dynamic model, a new adaptive sliding mode controller is designed on the basis of a nonlinear model. This new adaptive sliding mode controller steers the axles of the tractor and trailers through estimation of mass and moment of inertia of the trailers to maintain the stability of the vehicle. An articulated vehicle has been exposed to a lane change maneuver based on the trailer load in three different modes (low, medium and high load) and on a dry and wet road. Simulation results demonstrate the efficiency of this controller to maintain the stability of this articulated vehicle in a low-speed steep steer and high-speed lane change maneuvers. Finally, the robustness of this controller has been shown in the presence of measurement noise of the sensors. In fact, the main innovation of this article is in the designing of an adaptive sliding mode controller, which by changing the load of the trailers, in high-speed and low-speed maneuvers and in dry and wet roads, has the best performance compared to conventional sliding mode and linear controllers.

scholarly journals Thermosolutal Instability in Compressible Viscoelastic Dusty Fluid through Porous Medium

2013 ◽  
Vol 18 (1) ◽  
pp. 99-112 ◽  
Author(s):  
P. Kumar ◽  
H. Mohan
Keyword(s):  
Porous Medium ◽  
Viscoelastic Fluid ◽  
Normal Mode Analysis ◽  
Suspended Particles ◽  
Mode Analysis ◽  
Stationary Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
The Stability ◽  
Solute Gradient

Thermosolutal instability in a compressible Walters B’ viscoelastic fluid with suspended particles through a porous medium is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the Walters B’ viscoelastic fluid behaves like a Newtonian fluid and it is found that suspended particles and medium permeability have a destabilizing effect whereas the stable solute gradient and compressibility have a stabilizing effect on the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and viscoelasticity are found to introduce oscillatory modes in the system which are non-existent in their absence.

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