Instability and transient growth for two trailing-vortex pairs

1997 ◽  
Vol 350 ◽  
pp. 311-330 ◽  
Author(s):  
J. D. CROUCH
Keyword(s):  
Transient Growth ◽  
Vortex System ◽  
Long Wavelength ◽  
Vortex Pairs ◽  
Temporal Differentiation ◽  
Trailing Vortices ◽  
The Stability ◽  
Time Required ◽  
Crow Instability ◽  
Time Periodic

The stability of two vortex pairs is analysed as a model for the vortex system generated by an aircraft in flaps-down configuration. The co-rotating vortices on the starboard and port sides tumble about one another as they propagate downward. This results in a time-periodic basic state for the stability analysis. The dynamics and instability of the trailing vortices are modelled using thin vortex filaments. Stability equations are derived by matching the induced velocities from Biot–Savart integrals with kinematic equations obtained by temporal differentiation of the vortex position vectors. The stability equations are solved analytically as an eigenvalue problem, using Floquet theory, and numerically as an initial value problem. The instabilities are periodic along the axes of the vortices with wavelengths that are large compared to the size of the vortex cores. The results show symmetric instabilities that are linked to the long-wavelength Crow instability. In addition, new symmetric and antisymmetric instabilities are observed at shorter wavelengths. These instabilities have growth rates 60–100% greater than the Crow instability. The system of two vortex pairs also exhibits transient growth which can lead to growth factors of 10 or 15 in one-fifth of the time required for the same growth due to instability.

scholarly journals Entrapment of the Fastest Known Carbonic Anhydrase with Biomimetic Silica and Its Application for CO2 Sequestration

Polymers ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2452
Author(s):  
Chia-Jung Hsieh ◽  
Ju-Chuan Cheng ◽  
Chia-Jung Hu ◽  
Chi-Yang Yu
Keyword(s):  
Carbonic Anhydrase ◽  
High Activity ◽  
Co2 Sequestration ◽  
Residual Activity ◽  
Entrapment Efficiency ◽  
Free Form ◽  
Uncatalyzed Reaction ◽  
The Stability ◽  
Time Required

Capturing and storing CO2 is of prime importance. The rate of CO2 sequestration is often limited by the hydration of CO2, which can be greatly accelerated by using carbonic anhydrase (CA, EC 4.2.1.1) as a catalyst. In order to improve the stability and reusability of CA, a silica-condensing peptide (R5) was fused with the fastest known CA from Sulfurihydrogenibium azorense (SazCA) to form R5-SazCA; the fusion protein successfully performed in vitro silicification. The entrapment efficiency reached 100% and the silicified form (R5-SazCA-SP) showed a high activity recovery of 91%. The residual activity of R5-SazCA-SP was two-fold higher than that of the free form when stored at 25 °C for 35 days; R5-SazCA-SP still retained 86% of its activity after 10 cycles of reuse. Comparing with an uncatalyzed reaction, the time required for the onset of CaCO3 formation was shortened by 43% and 33% with the addition of R5-SazCA and R5-SazCA-SP, respectively. R5-SazCA-SP shows great potential as a robust and efficient biocatalyst for CO2 sequestration because of its high activity, high stability, and reusability.

scholarly journals The Application of an Impedance-Passivity Controller in Haptic Stability Analysis

2021 ◽  
Vol 11 (4) ◽  
pp. 1618
Author(s):  
Ping-Nan Chen ◽  
Yung-Te Chen ◽  
Hsin Hsiu ◽  
Ruei-Jia Chen
Keyword(s):  
Control Systems ◽  
Force Feedback ◽  
Training System ◽  
Considerable Time ◽  
Virtual Training ◽  
Control Gain ◽  
Negative Damping ◽  
The Stability ◽  
Time Required ◽  
Stable Control

This paper proposes a passivity theorem on the basis of energy concepts to study the stability of force feedback in a virtual haptic system. An impedance-passivity controller (IPC) was designed from the two-port network perspective to improve the chief drawback of haptic systems, namely the considerable time required to reach stability if the equipment consumes energy slowly. The proposed IPC can be used to achieve stability through model parameter selection and to obtain control gain. In particular, haptic performance can be improved for extreme cases of high stiffness and negative damping. Furthermore, a virtual training system for one-degree-of-freedom sticking was developed to validate the experimental platform of our IPC. To ensure consistency in the experiment, we designed a specialized mechanical robot to replace human operation. Finally, compared with basic passivity control systems, our IPC could achieve stable control rapidly.

Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

Simple Leg Placement Strategy for a One Legged Running Model

2012 ◽  
Author(s):  
Timothy Sullivan ◽  
Justin Seipel
Keyword(s):  
Stance Phase ◽  
Energy State ◽  
Center Of Mass ◽  
Mass Movement ◽  
Legged Locomotion ◽  
Energy Conserving ◽  
Lower Torque ◽  
The Stability ◽  
Time Required ◽  
Torque Values

The Spring Loaded Inverted Pendulum (SLIP) model was developed to describe center of mass movement patterns observed in animals, using only a springy leg and a point mass. However, SLIP is energy conserving and does not accurately represent any biological or robotic system. Still, this model is often used as a foundation for the investigation of improved legged locomotion models. One such model called Torque Damped SLIP (TD-SLIP) utilizes two additional parameters, a time dependent torque and dampening to drastically increase the stability. Forced Damped SLIP (FD-SLIP), a predecessor of TD-SLIP, has shown that this model can be further simplified by using a constant torque, instead of a time varying torque, while still maintaining stability. Using FD-SLIP as a base, this paper explores a leg placement strategy using a simple PI controller. The controller takes advantage of the fact that the energy state of FD-SLIP is symmetric entering and leaving the stance phase during steady state conditions. During the flight phase, the touch down leg angle is adjusted so that the energy dissipation due to dampening, during the stance phase, compensates for any imbalance of energy. This controller approximately doubles the region of stability when subjected to velocity perturbations at touchdown, enables the model to operate at considerably lower torque values, and drastically reduces the time required to recover from a perturbation, while using less energy. Finally, the leg placement strategy used effectively imitates the natural human response to velocity perturbations while running.

scholarly journals Demulsification of Liquid Membrane Emulsion using High Voltage Glass Coated Electrode in Batch System

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
N. Othman ◽  
A. Ahmad ◽  
M. A. Piramali
Keyword(s):  
High Voltage ◽  
Liquid Membrane ◽  
Alternate Current ◽  
Cost Effective ◽  
Electrical Field ◽  
Electrical Field Strength ◽  
Oil Emulsion ◽  
Internal Phase ◽  
The Stability ◽  
Time Required

Demulsification is one of the key processes in emulsion liquid membrane application. This study involved the effect of electrical field on demulsification of water in oil using batch high voltage demulsifier system. This technique widely used because of its advantages of easy manipulation of applied field direction and strength, offers cost–effective separation and minimal environmental impact combined with mechanical simplicity. Influence of various values of frequency (400–1500 Hz) and voltage was studied experimentally using Alternate Current (AC) High Voltage Demulsifier with insulated electrode. The emulsion consists of kerosene as organic phase, sulfuric acid as internal phase and span 80 (3 and 5 w/v %) as a surfactant. The effect of emulsion preparation such as homogenizer speed, internal phase and surfactant concentrations on the stability of water–in–oil emulsion was also investigated. The results showed that the attractive forces between the water droplets under an electrical field increase by raising the applied electrical field strength. Meanwhile, the time required for the emulsion to separate and coalescence under electrical field increased when the stability of emulsion increased.

scholarly journals Modified Kawahara equation within a fractional derivative with non-singular kernel

2018 ◽  
Vol 22 (2) ◽  
pp. 789-796 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Water Waves ◽  
Iterative Scheme ◽  
Singular Kernel ◽  
Kawahara Equation ◽  
Long Wavelength ◽  
Exponential Kernel ◽  
The Stability ◽  
Linear Water Waves

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

scholarly journals The Lyapunov Stability for the Linear and Nonlinear Damped Oscillator with Time-Periodic Parameters

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Jifeng Chu ◽  
Ting Xia
Keyword(s):  
Periodic Function ◽  
Lyapunov Stability ◽  
Stability Criterion ◽  
Normal Forms ◽  
Sufficient Condition ◽  
Periodic Functions ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Time Periodic ◽  
Damped Oscillator

Leta(t),b(t)be continuousT-periodic functions with∫0Tb(t)dt=0. We establish one stability criterion for the linear damped oscillatorx′′+b(t)x′+a(t)x=0. Moreover, based on the computation of the corresponding Birkhoff normal forms, we present a sufficient condition for the stability of the equilibrium of the nonlinear damped oscillatorx′′+b(t)x′+a(t)x+c(t)x2n-1+e(t,x)=0, wheren≥2,c(t)is a continuousT-periodic function,e(t,x)is continuousT-periodic intand dominated by the powerx2nin a neighborhood ofx=0.

An Improved Lifting Line Model for the Design of Marine Propellers

2006 ◽  
Vol 43 (02) ◽  
pp. 100-113
Author(s):  
Fahri Celik ◽  
Mesut Guner
Keyword(s):  
Autonomous Underwater Vehicle ◽  
Cfd Analysis ◽  
Vortex System ◽  
Marine Propellers ◽  
Propeller Design ◽  
Trailing Vortices ◽  
Realistic Representation ◽  
Computational Fluid Dynamics Cfd ◽  
Volume Method ◽  
Lifting Line

This paper describes a procedure for the design of marine propellers where more realistic representation of the slipstream shape by the trailing vortex system is taken into account. The slipstream shape behind the propeller is allowed to deform and to align with the direction of local velocity, which is obtained by the sum of the inflow velocity and induced velocities due to the trailing vortices. In classical lifting line approaches, that deformation is neglected. Applications for an autonomous underwater vehicle (AUV) and a fishing vessel are carried out to demonstrate propeller design and the effect of the slipstream contraction. Furthermore, a computational fluid dynamics (CFD) analysis based on the finite volume method and experimental validation of the method are carried out for the propellers. CFD analysis and experimental results are compared with the results obtained from present method.

On the collective instability of salt fingers

1981 ◽  
Vol 110 ◽  
pp. 195-207 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Prandtl Number ◽  
Internal Wave ◽  
Stability Criterion ◽  
Long Wavelength ◽  
Salt Fingers ◽  
The Stability

In this paper we consider the stability of salt fingers to long wavelength internal wave perturbations. The Prandtl number of the fluid is assumed to be large, but the ratio of the two diffusivities (KS/KT) is allowed to be any size provided that KS < KT. This problem was first considered by Stern (1969), where several untested assumptions were made about the motion. Here we use a two-scale approach to separate the salt finger motions from the long-scale internal wave perturbations and to obtain the stability criterion. This collective instability of salt fingers succeeds in transferring energy from the small salt finger scales to the long internal wave scales.

Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

Sign in / Sign up

Export Citation Format

Share Document