scholarly journals Stability analysis of natural convective flows in horizontal annuli: Effects of the axial and radial aspect ratios

2006 ◽  
Vol 18 (10) ◽  
pp. 104107 ◽  
Author(s):  
Giuseppe Petrone ◽  
Eric Chénier ◽  
Guy Lauriat
Keyword(s):  
Stability Analysis ◽  
Convective Flows ◽  
Aspect Ratios ◽  
Horizontal Annuli

Self Organized Array of Quantum Nanostructures Via a Strain Induced Morphological Instability

2001 ◽  
Vol 707 ◽  
Author(s):  
David Montiel ◽  
Judith Müller ◽  
Eugenia Corvera Poiré
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Morphological Instability ◽  
Heteroepitaxial Growth ◽  
Dominant Mechanism ◽  
Quantum Nanostructures ◽  
Spontaneous Formation ◽  
Self Organized ◽  
Aspect Ratios ◽  
Terrace Width

ABSTRACTMotivated by the work of Li et al. [1], we have studied the strain induced morphological instability at the submonolayer coverage stage of heteroepitaxial growth on a vicinal substrate with regularly spaced steps. We have performed a linear stability analysis and determined for which conditions of coverage a flat front is unstable and for which conditions it is stable. For low coverages the instability will cause the front to break in an array of islands. Assuming that the fastest growing mode of the instability determines t he properties of the array, we make an estimation of the islands sizes and aspect ratios as well as an estimation of the separation length between islands of the array formed when the dominant mechanism for transport of matter is diffusion of particles along the growing front. These estimations are given as functions of the terrace width and coverage. Since these ones are experimentally controllable parameters, our results could be used to tailor the spontaneous formation of quantum nanostructures.

scholarly journals Triglobal infinite-wing shock-buffet study

2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Base Flow ◽  
Sweep Angle ◽  
Aspect Ratios ◽  
Spatially Periodic ◽  
Time Marching ◽  
High Reynolds ◽  
Limiting Case ◽  
Base Flows

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

scholarly journals Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

LINEAR STABILITY ANALYSIS GENERALIZED TO A THERMALLY-DRIVEN FLOW

1999 ◽  
Vol 09 (02) ◽  
pp. 415-425
Author(s):  
JEAN-MICHEL CORNET ◽  
CLAUDE-HENRI LAMARQUE
Keyword(s):  
Stability Analysis ◽  
Numerical Methods ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
The Other ◽  
Basic Solution ◽  
Driven Cavity ◽  
Convective Flows ◽  
Other Hand ◽  
Thermally Driven

We intend to establish a methodology suited to the search of the first bifurcations of convective flows using a linear stability analysis so that it permits us to define a relationship between amplitude and frequency of the perturbation. We use a particular combination of various numerical methods to compute on one hand the basic solution. On the other hand the perturbation is applied to the search for the bifurcations in a thermally-driven cavity.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Symmetry breaking and instability mechanisms in medium depth torsionally driven open cylinder flows

2011 ◽  
Vol 672 ◽  
pp. 521-544 ◽  
Author(s):  
STUART J. COGAN ◽  
KRIS RYAN ◽  
GREGORY J. SHEARD
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Symmetry Breaking ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Interfacial Region ◽  
Nonlinear Stability Analysis ◽  
Aspect Ratios ◽  
Instability Modes

A numerical investigation was conducted into the different flow states, and bifurcations leading to changes of state, found in open cylinders of medium to moderate depth driven by a constant rotation of the vessel base. A combination of linear stability analysis, for cylinders of numerous height-to-radius aspect ratios (H/R), and nonlinear stability analysis and three-dimensional simulations for a cylinder of aspect ratio 1.5, has been employed. Attention is focused on the breaking of SO(2) symmetry. A comprehensive map of transition Reynolds numbers as a function of aspect ratio is presented by combining a detailed stability analysis with the limited existing data from the literature. For all aspect ratios considered, the primary instabilities are identified as symmetry-breaking Hopf bifurcations, occurring at Reynolds numbers well below those of the previously reported axisymmetric Hopf transitions. It is revealed that instability modes with azimuthal wavenumbers m = 1, 3 and 4 are the most unstable in the range 1.0 < H/R < 4, and that numerous double Hopf bifurcation points exist. Critical Reynolds numbers generally increase with cylinder aspect ratio, though a decrease in stability occurs between aspect ratios 1.5 and 2.0, where a local minimum in critical Reynolds number occurs. For H/R = 1.5, a detailed characterisation of instability modes is given. It is hypothesized that the primary instability leading to transition from steady axisymmetric flow to unsteady three-dimensional flow is related to deformation of shear layers that are present in the flow, in particular at the interfacial region between the vortex breakdown bubble and the primary recirculation.

scholarly journals Biglobal instabilities of compressible open-cavity flows

2017 ◽  
Vol 826 ◽  
pp. 270-301 ◽  
Author(s):  
Yiyang Sun ◽  
Kunihiko Taira ◽  
Louis N. Cattafesta ◽  
Lawrence S. Ukeiley
Keyword(s):  
Stability Analysis ◽  
Mach Number ◽  
Control Strategies ◽  
Pressure Fluctuations ◽  
Open Cavity ◽  
Nonlinear Flow ◽  
Cavity Flows ◽  
Strong Nonlinearity ◽  
Aspect Ratios ◽  
Subsonic Regime

The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation (DNS) and biglobal stability analysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. This study examines the behaviour of instabilities with respect to stable and unstable steady states in the laminar regime for subsonic as well as transonic conditions where compressibility plays an important role. It is observed that an increase in Mach number destabilizes the flow in the subsonic regime and stabilizes the flow in the transonic regime. Biglobal stability analysis for spanwise-periodic flows over rectangular cavities with large aspect ratio is closely examined in this study due to its importance in aerodynamic applications. Moreover, biglobal stability analysis is conducted to extract two-dimensional (2-D) and 3-D eigenmodes for prescribed spanwise wavelengths $\unicode[STIX]{x1D706}/D$ about the 2-D steady state. The properties of 2-D eigenmodes agree well with those observed in the 2-D nonlinear simulations. In the analysis of 3-D eigenmodes, it is found that an increase of Mach number stabilizes dominant 3-D eigenmodes. For a short cavity with $L/D=2$, the 3-D eigenmodes primarily stem from centrifugal instabilities. For a long cavity with $L/D=6$, other types of eigenmodes appear whose structures extend from the aft-region to the mid-region of the cavity, in addition to the centrifugal instability mode located in the rear part of the cavity. A selected number of 3-D DNS are performed at $M_{\infty }=0.6$ for cavities with $L/D=2$ and 6. For $L/D=2$, the properties of 3-D structures present in the 3-D nonlinear flow correspond closely to those obtained from linear stability analysis. However, for $L/D=6$, the 3-D eigenmodes cannot be clearly observed in the 3-D DNS due to the strong nonlinearity that develops over the length of the cavity. In addition, it is noted that three-dimensionality in the flow helps alleviate violent oscillations for the long cavity. The analysis performed in this paper can provide valuable insights for designing effective flow control strategies to suppress undesirable aerodynamic and pressure fluctuations in compressible open-cavity flows.

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