scholarly journals Control of the Interfacial Instabilities in a circular Hele-Shaw cell oscillating with a periodic angular velocity

2019 ◽  
Vol 286 ◽  
pp. 07014
Author(s):  
J. Bouchgl ◽  
M. Souhar
Keyword(s):  
Stability Analysis ◽  
Angular Velocity ◽  
Immiscible Fluids ◽  
Interfacial Instability ◽  
Time Dependent ◽  
Interfacial Instabilities ◽  
Periodic Rotation ◽  
The Stability ◽  
Time Periodic ◽  
Hele Shaw Cell

The stability of an interface of two viscous immiscible fluids of different densities and confined in a Hele-Shaw cell which is oscillating with periodic angular velocityis investigated. A linear stability analysis of the viscous and time-dependent basic flows, generated by a periodic rotation, leads to a time periodic oscillator describing the evolution of the interface amplitude. In this study, we examine mainly the effect of the frequency of the periodic rotation on the interfacial instability that occurs at the interface.

scholarly journals Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems

Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Aykut Tamer ◽  
Pierangelo Masarati
Keyword(s):  
Stability Analysis ◽  
Linear Models ◽  
Linear Time ◽  
Flexible Structures ◽  
Time Dependent ◽  
Real Problem ◽  
Actuator Dynamics ◽  
Linear Time Invariant ◽  
The Stability ◽  
Time Periodic

Rotorcraft stability is an inherently multidisciplinary area, including aerodynamics of rotor and fuselage, structural dynamics of flexible structures, actuator dynamics, control, and stability augmentation systems. The related engineering models can be formulated with increasing complexity due to the asymmetric nature of rotorcraft and the airflow on the rotors in forward flight conditions. As a result, linear time-invariant (LTI) models are drastic simplifications of the real problem, which can significantly affect the evaluation of the stability. This usually reveals itself in form of periodic governing equations and is solved using Floquet’s method. However, in more general cases, the resulting models could be non-periodic, as well, which requires a more versatile approach. Lyapunov Characteristic Exponents (LCEs), as a quantitative method, can represent a solution to this problem. LCEs generalize the stability solutions of the linear models, i.e., eigenvalues of LTI systems and Floquet multipliers of linear time-periodic (LTP) systems, to the case of non-linear, time-dependent systems. Motivated by the need for a generic tool for rotorcraft stability analysis, this work investigates the use of LCEs and their sensitivity in the stability analysis of time-dependent, comprehensive rotorcraft models. The stability of a rotorcraft modeled using mid-fidelity tools is considered to illustrate the equivalence of LCEs and Floquet’s characteristic coefficients for linear time-periodic problems.

scholarly journals Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

2019 ◽  
Vol 877 ◽  
pp. 1063-1097 ◽  
Author(s):  
Liam C. Morrow ◽  
Timothy J. Moroney ◽  
Scott W. McCue
Keyword(s):  
Viscous Fluid ◽  
Linear Prediction ◽  
Applied Mathematics ◽  
Viscous Fingering ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Inviscid Fluid ◽  
Interfacial Instabilities ◽  
Hele Shaw Cell ◽  
Injection Rates

Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid–viscous fluid interface. Surprisingly, a converging or diverging taper of the plates leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Our simulations compare well with previous experimental results for various injection rates and geometric configurations. We demonstrate how the number of non-splitting fingers agrees with that predicted from linear stability theory up to some finger number; for larger values of our control parameter, the fully nonlinear dynamics of the problem leads to slightly fewer fingers than this linear prediction.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

Dynamic and Stability Analysis of the Rotating Nanobeam in a Nonuniform Magnetic Field Considering the Surface Energy

2016 ◽  
Vol 08 (04) ◽  
pp. 1650048 ◽  
Author(s):  
M. Baghani ◽  
M. Mohammadi ◽  
A. Farajpour
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Angular Velocity ◽  
Surface Energy ◽  
Axial Load ◽  
Nonuniform Magnetic Field ◽  
Small Scale ◽  
Stability Behavior ◽  
Compressive Axial Load ◽  
The Stability

It is well-known that rotating nanobeams can have different dynamic and stability responses to various types of loadings. In this research, attention is focused on studying the effects of magnetic field, surface energy and compressive axial load on the dynamic and the stability behavior of the nanobeam. For this purpose, it is assumed that the rotating nanobeam is located in the nonuniform magnetic field and subjected to compressive axial load. The nonlocal elasticity theory and the Gurtin–Murdoch model are applied to consider the effects of inter atomic forces and surface energy effect on the vibration behavior of rotating nanobeam. The vibration frequencies and critical buckling loads of the nanobeam are computed by the differential quadrature method (DQM). Then, the numerical results are testified with those results are presented in the published works and a good correlation is obtained. Finally, the effects of angular velocity, magnetic field, boundary conditions, compressive axial load, small scale parameter and surface elastic constants on the dynamic and the stability behavior of the nanobeam are studied. The results show that the magnetic field, surface energy and the angular velocity have important roles in the dynamic and stability analysis of the nanobeams.

scholarly journals ON THIN-SHELL WORMHOLES EVOLVING IN FLAT FRW SPACETIMES

2011 ◽  
Vol 26 (12) ◽  
pp. 857-863 ◽  
Author(s):  
M. LA CAMERA
Keyword(s):  
Stability Analysis ◽  
Equation Of State ◽  
Perfect Fluid ◽  
Dynamic Systems ◽  
Spherical Symmetry ◽  
Thin Shell ◽  
Time Dependent ◽  
State Formula ◽  
Thin Shell Wormholes ◽  
The Stability

We analyze the stability of a class of thin-shell wormholes with spherical symmetry evolving in flat FRW spacetimes. The wormholes considered here are supported at the throat by a perfect fluid with equation of state [Formula: see text] and have a physical radius equal to aR, where a is a time-dependent function describing the dynamics of the throat and R is the background scale factor. The study of wormhole stability is done by means of the stability analysis of dynamic systems.

scholarly journals Interfacial instability in a time-periodic rotating Hele-Shaw Cell

2014 ◽  
Vol 16 ◽  
pp. 09004 ◽  
Author(s):  
J. Bouchgl ◽  
S. Aniss ◽  
M. Souhar ◽  
A. Hifdi
Keyword(s):  
Interfacial Instability ◽  
Time Periodic ◽  
Hele Shaw Cell

scholarly journals Interfacial instability of two inviscid fluid layers under quasi-periodic oscillations

2019 ◽  
Vol 286 ◽  
pp. 07011
Author(s):  
A. Eljaouahiry ◽  
A. Arfaoui ◽  
M. Assoul ◽  
S. Aniss
Keyword(s):  
Numerical Study ◽  
Mathieu Equation ◽  
Immiscible Fluids ◽  
Interfacial Instability ◽  
Periodic Case ◽  
Inviscid Fluid ◽  
Helmholtz Instability ◽  
Periodic Oscillations ◽  
Fluid Layers ◽  
The Stability

We investigate the effect of horizontal quasi-periodic oscillations on the stability of two immiscible fluids of different densities. The two fluid layers are confined in a cavity of infinite extension in the horizontal directions. We show in the inviscid theory that the linear stability analysis leads to the quasi-periodic Mathieu equation, with damping, which describes the evolution of the interfacial amplitude. Thus, we examine the effect of horizontal quasi-periodic vibration, with two incommensurate frequencies, on the stability of the interface. The numerical study shows the existence of two types of instability: the Kelvin-Helmholtz instability and the quasi-periodic resonances. The numerical results show also that an increase of the frequency ratio has a distabilizing effect on the Kelvin-Helmholtz instability and curves converge towards those of the periodic case.

The effect of viscous heating on the stability of Taylor–Couette flow

2002 ◽  
Vol 462 ◽  
pp. 111-132 ◽  
Author(s):  
U. A. AL-MUBAIYEDH ◽  
R. SURESHKUMAR ◽  
B. KHOMAMI
Keyword(s):  
Stability Analysis ◽  
Secondary Flow ◽  
Linear Stability ◽  
Couette Flow ◽  
Temperature Difference ◽  
Time Dependent ◽  
Viscous Heating ◽  
Taylor Couette ◽  
The Stability ◽  
Taylor Couette Flow

The influence of viscous heating on the stability of Taylor–Couette flow is investigated theoretically. Based on a linear stability analysis it is shown that viscous heating leads to significant destabilization of the Taylor–Couette flow. Specifically, it is shown that in the presence of viscous dissipation the most dangerous disturbances are axisymmetric and that the temporal characteristic of the secondary flow is very sensitive to the thermal boundary conditions. If the temperature difference between the two cylinders is small, the secondary flow is stationary as in the case of isothermal Taylor–Couette flow. However, when the temperature difference between the two cylinders is large, time-dependent secondary states are predicted. These linear stability predictions are in agreement with the experimental observations of White & Muller (2000) in terms of onset conditions as well as the spatiotemporal characteristics of the secondary flow. Nonlinear stability analysis has revealed that over a broad range of operating conditions, the bifurcation to the time-dependent secondary state is subcritical, while stationary states result as a consequence of supercritical bifurcation. Moreover, the supercritically bifurcated stationary state undergoes a secondary bifurcation to a time-dependent flow. Overall, the structure of the time-dependent state predicted by the analysis compares very well with the experimental observations of White & Muller (2000) that correspond to slowly moving vortices parallel to the cylinder axis. The significant destabilization observed in the presence of viscous heating arises as the result of the coupling of the perturbation velocity and the base-state temperature gradient that gives rise to fluctuations in the radial temperature distribution. Due to the thermal sensitivity of the fluid these fluctuations greatly modify the fluid viscosity and reduce the dissipation of disturbances provided by the viscous stress terms in the momentum equation.

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