The linear stability of high-frequency flow in a torsionally oscillating cylinder

2007 ◽  
Vol 576 ◽  
pp. 491-505 ◽  
Author(s):  
P. J. BLENNERHASSETT ◽  
ANDREW P. BASSOM
Keyword(s):  
Linear Stability ◽  
High Frequency ◽  
Longitudinal Axis ◽  
Critical Conditions ◽  
Neutral Stability ◽  
Entry Length ◽  
Stokes Layer ◽  
Shear Modes ◽  
The Stability ◽  
Pseudo Spectral

The linear stability of the Stokes layer induced in a fluid contained within a long cylinder oscillating at high frequency about its longitudinal axis is investigated. The disturbance equations are derived using Floquet theory and the resulting system solved using pseudo-spectral methods. Both shear modes and axially periodic centripetal disturbance modes are examined and neutral stability curves and corresponding critical conditions for instability identified. For sufficiently small cylinder radius it is verified that the centripetal perturbations limit the stability of the motion but that in larger-radius configurations the shear modes associated with the Stokes layer take over this role. These results suggest a possible design, free of entry-length effects, for experiments intended to examine the breakdown of oscillatory boundary layers.

scholarly journals The linear stability of a Stokes layer subjected to high-frequency perturbations

2014 ◽  
Vol 764 ◽  
pp. 193-218 ◽  
Author(s):  
Christian Thomas ◽  
P. J. Blennerhassett ◽  
Andrew P. Bassom ◽  
Christopher Davies
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
High Frequency ◽  
Wall Motion ◽  
Critical Reynolds Number ◽  
Narrow Channel ◽  
Critical Conditions ◽  
Stokes Layer ◽  
Quantitative Results ◽  
Sinusoidal Wall

AbstractQuantitative results for the linear stability of planar Stokes layers subject to small, high-frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a 1 % perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60 %, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.

An extended car-following model considering the low visibility in fog on a highway with slopes

2019 ◽  
Vol 30 (11) ◽  
pp. 1950090
Author(s):  
Jinhua Tan ◽  
Li Gong ◽  
Xuqian Qin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Car Following ◽  
Low Visibility ◽  
Car Following Model ◽  
The Stability

To depict the effect of low-visibility foggy weather upon traffic flow on a highway with slopes, this paper proposes an extended car-following model taking into consideration the drivers’ misjudgment of the following distance and their active reduction of the velocity. By linear stability analysis, the neutral stability curves are obtained. It is shown that under all the three road conditions: uphill, flat road and downhill, drivers’ misjudgment of the following distance will change the stable regions, while having little effect on the sizes of the stable regions. Correspondingly, drivers’ active reduction of the velocity will increase the stability. The numerical simulations agree well with the analytical results. It indicates that drivers’ misjudgment contributes to a higher velocity. Meanwhile, their active reduction of the velocity helps mitigate the influences of small perturbation. Furthermore, drivers’ misjudgment of the following distance has the greatest effect on downhill and the smallest effect on uphill, so does drivers’ active reduction of the velocity.

On the linear stability of Stokes layers

2008 ◽  
Vol 366 (1876) ◽  
pp. 2685-2697 ◽  
Author(s):  
P.J Blennerhassett ◽  
Andrew P Bassom
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Practical Interest ◽  
Transition To Turbulence ◽  
Large Reynolds Number ◽  
Poor Agreement ◽  
Oscillatory Flows ◽  
Stokes Layer ◽  
The Stability ◽  
Time Periodic

Oscillatory flows occur naturally, with applications ranging across many disciplines from engineering to physiology. Transition to turbulence in such flows is a topic of practical interest and this article discusses some recent work that has furthered our understanding of the stability of a class of time-periodic fluid motions. Our study starts with an examination of the linear stability of a classical flat Stokes layer. Although experiments conducted over many years have demonstrated conclusively that this layer is unstable at a sufficiently large Reynolds number, it has only been relatively recently that rigorous theoretical confirmation of this behaviour has been obtained. The analysis and numerical calculations for the planar Stokes layer were subsequently extended to flows in channels and pipes and for the flow within a torsionally oscillating circular cylinder. We discuss why our predictions for the onset of instability in these geometries are in disappointingly poor agreement with experimental results. Finally, some suggestions for future experimental work are given and some areas for future theoretical analysis outlined.

scholarly journals The linear stability of oscillatory Poiseuille flow in channels and pipes

2011 ◽  
Vol 467 (2133) ◽  
pp. 2643-2662 ◽  
Author(s):  
Christian Thomas ◽  
Andrew P. Bassom ◽  
P. J. Blennerhassett ◽  
Christopher Davies
Keyword(s):  
Pressure Gradient ◽  
Linear Stability ◽  
Plane Channel ◽  
Fluid Flows ◽  
Critical Conditions ◽  
Neutral Stability ◽  
Parallel Flows ◽  
Comprehensive Information ◽  
Flow Components ◽  
Bounding Surfaces

The linear stability of confined, periodic, parallel fluid flows is examined. The flow fields considered consist of a steady pressure gradient-driven velocity field combined with a purely oscillatory component generated by either an oscillatory pressure gradient or by harmonically oscillating bounding surfaces. Plane channel and circular pipe geometries are studied and all possible combinations of the steady and oscillatory flow components investigated. Neutral stability curves and critical conditions for instability are computed for a selection of steady–unsteady velocity ratios, channel half-widths and pipe radii. The results obtained confirm previous investigations into the effects of small amounts of periodic modulation on the linear stability of the underlying steady flow, but provide much more comprehensive information on the linear stability regions of unsteady parallel flows in channels and pipes.

scholarly journals Instability of a binary liquid film flowing down a slippery inclined heated plate

2021 ◽  
Author(s):  
Eglal Ellaban
Keyword(s):  
Liquid Film ◽  
Numerical Solutions ◽  
Soret Effect ◽  
Critical Conditions ◽  
Heated Plate ◽  
Neutral Stability ◽  
Inclined Plate ◽  
Binary Liquid ◽  
Chebyshev Spectral Collocation ◽  
The Stability

In this thesis we studied the stability of a binary liquid film flowing down a heated porous inclined plate. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier- tokes equations governing the flow with equations for the concentration and temperature. The effect of substrate permeability is incorporated by applying a specific slip condition at the bottom of the liquid layer. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We used a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld type equations. We also obtained an asymptotic solution which yielded an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. We present our findings by illustrating and interpreting our results for the critical Reynolds number for instability.

scholarly journals The linear stability of a Stokes layer with an imposed axial magnetic field

2010 ◽  
Vol 662 ◽  
pp. 320-328 ◽  
Author(s):  
CHRISTIAN THOMAS ◽  
ANDREW P. BASSOM ◽  
CHRISTOPHER DAVIES
Keyword(s):  
Magnetic Field ◽  
Linear Stability ◽  
Floquet Theory ◽  
Axial Magnetic Field ◽  
Direct Numerical Simulations ◽  
Critical Parameters ◽  
Neutral Stability ◽  
Steady Flows ◽  
Stokes Layer ◽  
Boundary Wall

The effects of a uniform axial magnetic field directed towards an oscillating wall in a semi-infinite viscous fluid (or Stokes layer) is investigated. The linear stability and disturbance characteristics are determined using both Floquet theory and via direct numerical simulations. Neutral stability curves and critical parameters for instability are presented for a range of magnetic field strengths. Results indicate that a magnetic field directed towards the boundary wall is stabilizing, which is consistent with that found in many steady flows.

scholarly journals Instability of a binary liquid film flowing down a slippery inclined heated plate

2021 ◽  
Author(s):  
Eglal Ellaban
Keyword(s):  
Liquid Film ◽  
Numerical Solutions ◽  
Soret Effect ◽  
Critical Conditions ◽  
Heated Plate ◽  
Neutral Stability ◽  
Inclined Plate ◽  
Binary Liquid ◽  
Chebyshev Spectral Collocation ◽  
The Stability

In this thesis we studied the stability of a binary liquid film flowing down a heated porous inclined plate. It is assumed that the heating induces concentration differences in the liquid mixture (Soret effect), which together with the differences in temperature affects the surface tension. A mathematical model is constructed by coupling the Navier- tokes equations governing the flow with equations for the concentration and temperature. The effect of substrate permeability is incorporated by applying a specific slip condition at the bottom of the liquid layer. We carry out a linear stability analysis in order to obtain the critical conditions for the onset of instability. We used a Chebyshev spectral collocation method to obtain numerical solutions to the resulting Orr-Sommerfeld type equations. We also obtained an asymptotic solution which yielded an expression for the state of neutral stability of long perturbations as a function of the parameters controlling the problem. We present our findings by illustrating and interpreting our results for the critical Reynolds number for instability.

scholarly journals Delay compensation based controller for rotary electrohydraulic servo system

2021 ◽  
Author(s):  
Zakarya Omar ◽  
Xingsong Wang ◽  
Khalid Hussain ◽  
Mingxing Yang
Keyword(s):  
High Frequency ◽  
Dead Time ◽  
Sliding Mode ◽  
Servo System ◽  
Smith Predictor ◽  
Delay Compensation ◽  
Mechanical Parts ◽  
System Output ◽  
Electrohydraulic Servo System ◽  
The Stability

AbstractThe typical power-assisted hip exoskeleton utilizes rotary electrohydraulic actuator to carry out strength augmentation required by many tasks such as running, lifting loads and climbing up. Nevertheless, it is difficult to precisely control it due to the inherent nonlinearity and the large dead time occurring in the output. The presence of large dead time fires undesired fluctuation in the system output. Furthermore, the risk of damaging the mechanical parts of the actuator increases as these high-frequency underdamped oscillations surpass the natural frequency of the system. In addition, system closed-loop performance is degraded and the stability of the system is unenviably affected. In this work, a Sliding Mode Controller enhanced by a Smith predictor (SMC-SP) scheme that counts for the output delay and the inherent parameter nonlinearities is presented. SMC is utilized for its robustness against the uncertainty and nonlinearity of the servo system parameters whereas the Smith predictor alleviates the dead time of the system’s states. Experimental results show smoother response of the proposed scheme regardless of the amount of the existing dead time. The response trajectories of the proposed SMC-SP versus other control methods were compared for a different predefined dead time.

An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Mario Durán ◽  
Jean-Claude Nédélec ◽  
Sebastián Ossandón
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
High Frequency ◽  
High Accuracy ◽  
Integral Representations ◽  
Stability And Convergence ◽  
Symmetric Matrices ◽  
Frequency Interval ◽  
Numerical Treatment ◽  
The Stability

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

SiGe Heteroepitaxy for High Frequency Circuits

1998 ◽  
Vol 525 ◽  
Author(s):  
B. Tillack ◽  
D. Bolze ◽  
G. Fischer ◽  
G. Kissinger ◽  
D. Knoll ◽  
...  
Keyword(s):  
Heterojunction Bipolar Transistors ◽  
High Frequency ◽  
Defect Density ◽  
Process Capability ◽  
Chemical Vapor ◽  
Bipolar Transistors ◽  
Capability Indices ◽  
Data Points ◽  
B Doping ◽  
The Stability

ABSTRACTWe have determined the process capability of Low Pressure (Rapid Thermal) Chemical Vapor Deposition (LP(RT)CVD) of epitaxial Si/SiGe/Si stacks for heterojunction bipolar transistors (HIBTs). The transistor parameters primarily influenced by the epitaxial characteristics were measured for 600 identically processed 4” wafers. The results demonstrate that it is possible to control accurately the epitaxial process for a 25 nm thick graded SiGe base profile with 20 % Ge and very narrow B doping (5 nm). The pipe limited device yield of about 90 % for an emitter area of 104 μm2 indicates a very low defect density in the epitaxial layer stack. The process capability indices determined from about 40,000 data points demonstrate the stability and capability of the LP(RT)CVD epitaxy with regard to manufacturing requirements.

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