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.

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.

Sensitivity analysis and passive control of cylinder flow

2008 ◽  
Vol 615 ◽  
pp. 221-252 ◽  
Author(s):  
OLIVIER MARQUET ◽  
DENIS SIPP ◽  
LAURENT JACQUIN
Keyword(s):  
Sensitivity Analysis ◽  
Vortex Shedding ◽  
Passive Control ◽  
Control Device ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Sensitivity Analyses ◽  
Global Modes ◽  
The Stability ◽  
Steady Force

A general theoretical formalism is developed to assess how base-flow modifications may alter the stability properties of flows studied in a global approach of linear stability theory. It also comprises a systematic approach to the passive control of globally unstable flows by the use of small control devices. This formalism is based on a sensitivity analysis of any global eigenvalue to base-flow modifications. The base-flow modifications investigated are either arbitrary or specific ones induced by a steady force. This leads to a definition of the so-called sensitivity to base-flow modifications and sensitivity to a steady force. These sensitivity analyses are applied to the unstable global modes responsible for the onset of vortex shedding in the wake of a cylinder for Reynolds numbers in the range 47≤Re≤80. First, it is demonstrated how the sensitivity to arbitrary base-flow modifications may be used to identify regions and properties of the base flow that contribute to the onset of vortex shedding. Secondly, the sensitivity to a steady force determines the regions of the flow where a steady force acting on the base flow stabilizes the unstable global modes. Upon modelling the presence of a control device by a steady force acting on the base flow, these predictions are then extensively compared with the experimental results of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, p. 71). A physical interpretation of the suppression of vortex shedding by use of a control cylinder is proposed in the light of the sensitivity analysis.

Experiments on the stability of sinusoidal flow over a circular cylinder

2002 ◽  
Vol 457 ◽  
pp. 157-180 ◽  
Author(s):  
TURGUT SARPKAYA
Keyword(s):  
Stokes Flow ◽  
Coherent Structures ◽  
High Speed ◽  
Three Dimensional ◽  
Separated Flow ◽  
Circular Cylinders ◽  
Centrifugal Forces ◽  
Complex Interactions ◽  
Sinusoidal Flow ◽  
The Stability

The instabilities in a sinusoidally oscillating non-separated flow over smooth circular cylinders in the range of Keulegan–Carpenter numbers, K, from about 0.02 to 1 and Stokes numbers, β, from about 103 to 1.4 × 106 have been observed from inception to chaos using several high-speed imagers and laser-induced fluorescence. The instabilities ranged from small quasi-coherent structures, as in Stokes flow over a flat wall (Sarpkaya 1993), to three-dimensional spanwise perturbations because of the centrifugal forces induced by the curvature of the boundary layer (Taylor–Görtler instability). These gave rise to streamwise-oriented counter-rotating vortices or mushroom-shaped coherent structures as K approached the Kh values theoretically predicted by Hall (1984). Further increases in K for a given β led first to complex interactions between the coherent structures and then to chaotic motion. The mapping of the observations led to the delineation of four states of flow in the (K, β)-plane: stable, marginal, unstable, and chaotic.

scholarly journals A Study on the Relationship between the Design of Aerotrain and Its Stability Based on a Three-Dimensional Dynamic Model

Robotics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 96
Author(s):  
Quang Huan Luong ◽  
Jeremy Jong ◽  
Yusuke Sugahara ◽  
Daisuke Matsuura ◽  
Yukio Takeda
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Three Dimensional ◽  
Vehicle Body ◽  
Directional Stability ◽  
Rigid Body Model ◽  
Body Design ◽  
The Stability ◽  
New Generation ◽  
The Relationship

A new generation electric high-speed train called Aerotrain has levitation wings and levitates under Wing-in-Ground (WIG) effect along a U-shaped guideway. The previous study found that lacking knowledge of the design makes the prototype unable to regain stability when losing control. In this paper, the nonlinear three-dimensional dynamic model of the Aerotrain based on the rigid body model has been developed to investigate the relationship between the vehicle body design and its stability. Based on the dynamic model, this paper considered an Aerotrain with a horizontal tail and a vertical tail. To evaluate the stability, the location and area of these tails were parameterized. The effects of these parameters on the longitudinal and directional stability have been investigated to show that: the horizontal tail gives its best performance if the tail area is a function of the tail location; the larger vertical tail area and (or) the farther vertical tail location will give better directional stability. As for the lateral stability, a dihedral front levitation wing design was investigated. This design did not show its effectiveness, therefore a control system is needed. The obtained results are useful for the optimization studies on Aerotrain design as well as developing experimental prototypes.

scholarly journals Global linear stability of the non-parallel Batchelor vortex

2009 ◽  
Vol 629 ◽  
pp. 139-160 ◽  
Author(s):  
C. J. HEATON ◽  
J. W. NICHOLS ◽  
P. J. SCHMID
Keyword(s):  
Numerical Simulation ◽  
Linear Stability ◽  
Stokes Equations ◽  
General Structure ◽  
Base Flow ◽  
Illustrative Case ◽  
Arnoldi Method ◽  
Unstable Flow ◽  
Global Mode ◽  
Global Modes

Linear stability of the non-parallel Batchelor vortex is studied using global modes. This family of swirling wakes and jets has been extensively studied under the parallel-flow approximation, and in this paper we extend to more realistic non-parallel base flows. Our base flow is obtained as an exact steady solution of the Navier–Stokes equations by direct numerical simulation (with imposed axisymmetry to damp all instabilities). Global stability modes are computed by numerical simulation of the linearized equations, using the implicitly restarted Arnoldi method, and we discuss fully the numerical and convergence issues encountered. Emphasis is placed on exploring the general structure of the global spectrum, and in particular the correspondence between global modes and local absolute modes which is anticipated by weakly non-parallel asymptotic theory. We believe that our computed global modes for a weakly non-parallel vortex are the first to display this correspondence with local absolute modes. Superpositions of global modes are also studied, allowing an investigation of the amplifier dynamics of this unstable flow. For an illustrative case we find global non-modal transient growth via a convective mechanism. Generally amplifier dynamics, via convective growth, are prevalent over short time intervals, and resonator dynamics, via global mode growth, become prevalent at later times.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

1997 Best Paper Award—Turbomachinery Committee: A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1998 ◽  
Vol 120 (3) ◽  
pp. 393-401 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Short Length ◽  
Operating Conditions ◽  
Length Scale ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms in a low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short length-scale disturbance known as a “spike,” and the second with a longer length-scale disturbance known as a “modal oscillation.” In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented that relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: Long length-scale disturbances are related to a two-dimensional instability of the whole compression system, while short length-scale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed that explains the type of stall inception pattern observed in a particular compressor. Measurements from a single-stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1997 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Stability Criteria ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms a in low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short lengthscale disturbance known as a ‘spike’, and the second with a longer lengthscale disturbance known as a ‘modal oscillation’. In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented which relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: long lengthscale disturbances are related to a two-dimensional instability of the whole compression system, while short lengthscale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed which explains the type of stall inception pattern observed in a particular compressor. Measurements from a single stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer

2002 ◽  
Vol 456 ◽  
pp. 49-84 ◽  
Author(s):  
PETER WASSERMANN ◽  
MARKUS KLOKER
Keyword(s):  
Boundary Layer ◽  
Passive Control ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Secondary Instability ◽  
Base Flow ◽  
Transition Control ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Underlying Mechanisms

Crossflow-vortex-induced laminar breakdown in a three-dimensional flat-plate boundary-layer flow is investigated in detail by means of spatial direct numerical simulations. The base flow is generic for an infinite swept wing, with decreasing favourable chordwise pressure gradient. First, the downstream growth and nonlinear saturation states initiated by a crossflow-vortex-mode packet as well as by single crossflow-vortex modes with various spanwise wavenumbers are simulated. Second, the secondary instability of the flow induced by the saturated crossflow vortices is scrutinized, clearly indicating the convective nature of the secondary instability and strengthening knowledge of the conditions for its onset. Emphasis is on the effect of crossflow-vortex-mode packets and of the spanwise vortex spacing on the secondary stability properties of the saturation states. Saturated uniform crossflow vortices initiated by single crossflow-vortex modes turn out to be less unstable than vortices initiated by a packet of vortex modes, and closely spaced saturated vortices are even stable. Third, we investigate the transition control strategy of upstream flow deformation by appropriate steady nonlinear vortex modes as applied in wind tunnel experiments at the Arizona State University. A significant transition delay is shown in the base flow considered here, and the underlying mechanisms are specified.

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

2015 ◽  
Vol 768 ◽  
pp. 113-140 ◽  
Author(s):  
Vincenzo Citro ◽  
Flavio Giannetti ◽  
Luca Brandt ◽  
Paolo Luchini
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Closed Orbit ◽  
Three Dimensional ◽  
Base Flow ◽  
Open Cavity ◽  
Critical Conditions ◽  
Global Mode ◽  
Structural Sensitivity

The viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results.

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