Value Of Critical Velocity Research Articles

Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation

We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011).

Study on Kelvin–Helmholtz Instability With Heat and Mass Transfer

The effect of heat and mass transfer on the Kelvin–Helmholtz instability between liquid and vapor phases of a fluid has been studied using three different theories: a purely irrotational theory based on the dissipation method, a hybrid irrotational-rotational theory, and an inviscid potential flow theory. These new results are compared with previous results from viscous irrotational theory. The stability criterion is given in terms of the critical value of relative velocity. The system is shown to be unstable when the relative velocity is greater than the critical value of relative velocity; otherwise, it is stable. It is observed that heat and mass transfer has a destabilizing effect on the stability of the system while vapor fraction has a stabilizing effect.

Viscous correction for the viscous potential flow analysis of Kelvin–Helmholtz instability of cylindrical flow with heat and mass transfer

We study the linear Kelvin–Helmholtz instability of the interface between two viscous and incompressible fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface in presence of mass and heat transfer across the interface. Here we use an irrotational theory known as viscous correction for the viscous potential flow theory; in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. Both asymmetric and axisymmetric disturbances have been studied and stability criterion is given in terms of a critical value of relative velocity. It has been shown that the irrotational viscous flow with viscous correction gives rise to exactly the same dispersion relation as obtained by the dissipation method in which the viscous effect is accounted for by evaluating viscous dissipation using the irrotational flow. It has been observed that heat and mass transfer has destabilizing effect while irrotational shearing stresses stabilize the system.

The influence of touchdown conditions and contact phase technique on post-flight height in the straight handspring somersault vault

In vaulting the gymnast must generate sufficient linear and angular momentum during the approach and table contact in order to complete the rotational requirements in the post-flight phase. This study investigated the effects of touchdown conditions and contact technique on peak post-flight height of a straight handspring somersault vault. A planar seven-segment torque-driven computer simulation model of the contact phase in vaulting was evaluated by varying joint torque activation time histories to match three performances of a straight handspring somersault vault by an elite gymnast. The closest matching simulation was used as a starting point to optimise peak post-flight height of the mass centre for a straight handspring somersault. It was found that optimising either the touchdown conditions or the contact technique increased post-flight height by 0.1m whereas optimising both together increased post-flight height by 0.4m above that of a simulation matching the recorded performance. Thus touchdown technique and contact technique make similar contributions to post-flight height in the straight handspring somersault vault. Increasing touchdown velocity and angular momentum lead to additional post-flight height although there was a critical value of vertical touchdown velocity beyond which post-flight height decreased.

Finite Element Analysis of Fluid-Elastic Instability of Heat Exchanger Array

From the viewpoint of primary theory of Finite Element Analysis, as well as practical application, the present paper sets up a model for the use of analyzing the fluid-elastic instability of heat exchanger array. In accordance with related compared velocity and mass damping parameter, the author obtains the stability diagram and analyzes the diagram of the array displacement when it reaches the critical value of flow velocity. Accordingly, the instability of heat exchanger array in critical value if flow velocity was verified.

Magnetoviscous potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer

A linear analysis of the Kelvin–Helmholtz instability of interface between two viscous and magnetic fluids has been carried out where there was heat and mass transfer across the interface while the fluids have been subjected to a constant magnetic field parallel to the streaming direction. The viscous potential flow theory has been used for the investigation. A dispersion relation has been obtained and a stability criterion is given by a critical value of relative velocity as well as the critical value of magnetic field. The resulting plots show the effect of various physical parameters such as wave number, viscosity ratio, ratio of magnetic permeabilities and heat transfer coefficient. It has been observed that heat and mass transfer has a destabilizing effect whereas the horizontal magnetic field stabilizes the system.

Stochastic analysis of the critical velocity of an axially moving cracked elastic plate

In this study, a probabilistic analysis of the critical velocity for an axially moving cracked elastic and isotropic plate is presented. Axially moving materials are commonly used in modelling of manufacturing processes, like paper making and plastic forming. In such systems, the most serious threats to runnability are instability and material fracture, and finding the critical value of velocity is essential for efficiency. In this paper, a formula for the critical velocity is derived under constraints for the probabilities of instability and fracture. The significance of randomness in different model parameters is investigated for parameter ranges typical of paper material and paper machines. The results suggest that the most significant factors are variations in the crack length and tension magnitude.

Water Effects on the First-Order Transition in a Model of Earthquakes

The study of 1D spring-block model of earthquake dynamics with consideration of water effects in preexisting fault deals with new forms of frictional force. An analytical study of the equation of motion enables us to establish that motion of geological fault is accelerated by water pressure. In the same setting the critical value of frictional velocity for which appears the discontinuous (first-order) transition from a stick-slip behavior to a creep motion strongly depends on water pressure. The investigation also displays the magnitude and probability of events as a function of water pressure; these two quantities decrease and increase, respectively, with the variation of water pressure.

Stroking Parameters Patterns in A Training Set Performed at the Critical Velocity

Swimming critical velocity is defined as the maximum velocity that could be maintained during a long period of time without exhaustion, being accepted as a valid parameter to assess aerobic capacity. Our purpose was to observe the patterns of the stroking parameters during a typical aerobic capacity training set conducted at critical velocity. Thirtysix juvenile swimmers performed front crawl 200 and 800 m tests at maximum intensity. Critical velocity and critical stroke rate were assessed as the slope of the regression line obtained between the test distances, and between the total number of stroke cycles in each test distance, and the respective times, respectively. Twenty-four hours after, swimmers performed a typical aerobic capacity training set (8x200 m front crawl, 20s rest). It were observed moderate to high correlation coefficients between critical velocity values and mean velocity of the aerobic training set (r=0.84 and r=0.66, respectively for female and male groups). The same phenomenon was observed when considering the relationship between critical stroke rate and the mean stroke rate obtained in the training set (r=0.93 for both gender groups). Velocity decreased from the 1st to 2nd repetitions, becoming stable in the middle of the set and increasing during the last repetition. Stroke rate was stable during the first seven repetitions and increased from the 7th to the 8th repetition. Stroke length was stable in the female group and, in the male group, increased from the 2nd to the 3rd repetition, followed by a decrease in the final of the training set.

Three-dimensional magnetohydrodynamic Kelvin–Helmholtz instability of cylindrical flow with permeable boundaries

We study the linear magnetohydrodynamic Kelvin–Helmholtz instability of the interface between two viscous, incompressible, and electrically conducting fluids. The phases are enclosed between two coaxial cylindrical porous layers with the interface through which mass and heat transfer takes place. The fluids are subjected to a constant magnetic field parallel to the streaming direction, and the suction/injection velocities for the fluids at the permeable boundaries are also taken into account. Here, we use an irrotational theory in which the motion and pressure are irrotational, and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. We consider both asymmetric and axisymmetric disturbances in our analysis. A quadratic dispersion relation is deduced and stability criterion is given in terms of a critical value of relative velocity, as well as, magnetic field. It has been observed that in the case of permeable boundaries, heat and mass transfer phenomena play a dual in the stability analysis. The flow through porous medium is more stable than the pure flow.

Electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer: Effect of perpendicular electric field

In this paper, we investigate the effect of perpendicular electric field on the linear analysis of Kelvin–Helmholtz instability of a plane interface between two viscous and dielectric fluids, when the fluids are subjected to constant normal electric field and, when there is heat and mass transfer across the interface. We use viscous correction for the viscous potential flow theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. A quadratic dispersion relation that accounts for the growth of disturbance waves is obtained and stability criterion is given in terms of a critical value of relative velocity as well as applied electric field. It is observed that heat transfer and perpendicular electric field both have destabilizing effect while vapor fraction stabilizes the interface.

Tip-splitting instability and transition to seaweed growth during alloy solidification in anisotropically preferred growth direction

The evolution of the solid–liquid interface morphology during the initial transient of directional solidification is investigated by quantitative phase-field numerical simulation during cooling down of an Al–4wt.% Cu alloy growing in the preferred 〈100〉-direction. Simulations show that the shape of the non-planar solid–liquid interface varies with the instantaneous growth parameters; in particular, above a critical value of tip velocity, cell/dendrite tips undergo Mullins–Sekerka morphological instability resulting in tip splitting and transition from cells or dendrites to seaweeds. The numerical simulations demonstrate that, despite the 〈100〉-direction corresponding to high solid–liquid interface energy, seaweed formation is predicted when noise, either inherent to the numerical mesh and/or intentionally added to the phase field, is strong enough to blur the solid anisotropy at the cell/dendrite tip, which confirms the analytical predictions of Brener et al. (1996). Both the tip-splitting mechanism responsible for the seaweed morphological transition as well as the seaweed growth dynamics are characterized. The numerical predictions are then compared to the seaweed transition evidenced on an Al–4wt.% Cu alloy by in situ and real-time synchrotron X-ray radiography in the initial transient of directional solidification, and good agreement is found.

Численное исследование профильной задачи внутренней эрозии в межмерзлотном водоносном слое

In this paper, a numerical solution of a profile problem of suffusion in an intrapermafrost water bearing layer is investigated. Underground water filtration occurs in the water bearing layer being in contact with frozen sandy soil. During a process of soil thawing at a certain magnitude of filtration velocity the removal of soil particles from the flow has been found to occur. A mathematical model is developed with the mass conservation equations for water, moving solids, and stationary porous skeleton along with Darcy’s law for water and moving solid particles and the equation for the intensity of suffusion flow. The setting of the problem is provided in Paragraph 1 with the following: predetermined impermeability conditions are set on a part of the boundary, and predetermined pressure conditions are set at inlet and outlet. Also, an overview of suffusion models is presented. A numerical solution of the profile problem of water and solid particles movement without porous medium deformation is elaborated in Paragraph 2. The problem is reduced to a system of three equations for the porosity, pressure of the aqueous phase and concentration of solid particles. The initial boundary value problem is considered for the model problem, and the finite difference scheme based on the alternating directions method is developed. Test calculations and validations are preformed, and pressure and velocity of the aqueous phase are evaluated. Suffusion area is estimated by the comparison of the found velocity with the critical velocity value.

Numerical Simulation and Analysis of Critical Velocity in Tunnel Fires Based on FDS

Critical velocity is a very important parameter in smoke control of tunnel fires and the variation of critical velocity against fire heat release rate is also one of the most important issues in tunnel fire researches. In this paper, a simplified physical model of a tunnel was established and the predictions of critical velocity for fire sizes in the 5-100MW range were carried out by FDS simulations. The FDS-predicted dimensionless critical velocities were compared with the values calculated by Wu and Bakar’s model. The result indicated that when the heat release rate was relatively small, Q≤30MW, the critical velocity increased with the increasing of heat release rate and varied as the one-third power of the heat release rate; when Q≥40MW, the growth rate of critical velocity became very small; after Q reach to 60MW, the critical velocity was almost unchanged with the increasing of heat release rate. In addition, the values of critical velocity calculated by Wu and Bakar’model which was derived from small-scale gas fire tests were underestimated. Therefore, the model suggested by Wu and Bakar is not suitable for critical velocity prediction in tunnel fires.

Viscous Potential Flow Analysis of Kelvin–Helmholtz Instability of a Cylindrical Flow with Heat and Mass Transfer

A linear analysis of Kelvin–Helmholtz instability of a cylindrical interface has been carried out when there is heat and mass transfer across the interface, using viscous potential flow theory. Both fluids are considered as incompressible, viscous, and thermally conducting with different kinematic viscosities. Both axisymmetric as well as asymmetric disturbances are considered. Stability criterion is given by a critical value of relative velocity and stability is discussed theoretically as well as numerically. Various graphs with respect to physical parameters such as wave number, viscosity ratio, heat transfer coefficients, Reynolds number, etc., have been drawn and the effect of various parameters have been described. A comparison with the linear stability analysis of inviscid fluids (Lee [10]) has been made and it is observed that viscosity has a stabilizing effect on the stability of the system. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 489–503, 2014; Published online 3 October 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21092

Experimental and theoretical study of counter-current oil–water separation in wells with in-situ water injection

Abstract The study investigates a counter-current gravity separation in a downwards-flowing mixture of (up to 3%) oil in water. At much higher oil fraction, the separation is a basis for the conventional downhole oil–water separation (DOWS) where the whole oil and water separate in the well. In contrast, the counter-current separation of a very small oil content is needed in the new “downhole water loop” technique (DWL) prior to injecting the oil-free water in-situ. In the DWL triple-completed wells, the top completion produces oil and only trace of the oil contaminates the water drained by the lower “water sink” completion and is re-injected in-situ using the (third) bottom completion. A drift-flux concept was used to develop an empirical model for predicting the oil droplets raise velocity at different water flow velocities. The model was derived from experiments using seven different oils with a wide range of density, viscosity and interfacial tension values. The experiments monitored oil droplets ejected from a single perforation into the stream of water flowing downwards at various velocities. The results show that the oil–water interfacial tension is the most important factor in the separation process, as it controls the oil droplet size. This observation significantly simplifies the model by replacing the droplet size (most difficult to measure) with a correlation based on interfacial tension developed using the experimental results. The new model also considers the effect of oil viscosity that has been ignored in the co-current separation studies. (Our results reveal over 10% contribution of the viscosity effect to the counter-current separation process.) A practical finding in this study is the 0.33 ft/s (0.1 m/s) value of critical maximum water velocity for counter-current oil separation. In a real DWL well, this value corresponds to a point in the perforated well section above which separation takes place. It is also shown how oil separation could be predicted from a given water sink completion length and drainage–injection rate.

Study on magnetohydrodynamic Kelvin-Helmholtz instability with mass transfer through porous media

We study the linear analysis of Kelvin-Helmholtz instability of the interface between two viscous and magnetic fluids in a fully saturated porous medium using viscous potential flow theory, when the fluids are subjected to a constant tangential magnetic field, and when there is heat and mass transfer across the interface. The Darcy-Brinkman model has been used for the investigation. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. The stability criterion is given in terms of a critical value of relative velocity as well as the critical value of applied magnetic field. It has been observed that both tangential magnetic field and vapor fraction have stabilizing effect on the stability of the system while heat and mass transfer destabilizes the interface. Porosity stabilizes the interface while the porous medium has destabilizing effect.

Anaerobic running capacity determined from the critical velocity model is not significantly associated with maximal accumulated oxygen deficit in army runners

The aim of this study was to verify whether there is an association between anaerobic running capacity (ARC) values, estimated from two-parameter models, and maximal accumulated oxygen deficit (MAOD) in army runners. Eleven, trained, middle distance runners who are members of the armed forces were recruited for the study (20 ± 1 years). They performed a critical velocity test (CV) for ARC estimation using three mathematical models and an MAOD test, both tests were applied on a motorized treadmill. The MAOD was 61.6 ± 5.2 mL/kg (4.1 ± 0.3 L). The ARC values were 240.4 ± 18.6 m from the linear velocity–inverse time model, 254.0 ± 13.0 m from the linear distance–time model, and 275.2 ± 9.1 m from the hyperbolic time–velocity relationship (nonlinear 2-parameter model), whereas critical velocity values were 3.91 ± 0.07 m/s, 3.86 ± 0.08 m/s and 3.80 ± 0.09 m/s, respectively. There were differences ( P < 0.05) for both the ARC and the CV values when compared between velocity–inverse time linear and nonlinear 2-parameter mathematical models. The different values of ARC did not significantly correlate with MAOD. In conclusion, estimated ARC did not correlate with MAOD, and should not be considered as an anaerobic measure of capacity for treadmill running. Le but de cette étude est de vérifier s’il existe une relation entre les valeurs de la capacité anaérobie en course à pied (CACP) estimées à partir de modèles à deux paramètres et le déficit maximal d’oxygène accumulé (DMOA) chez les coureurs de l’armée. Onze coureurs de demi-fond des forces armées ont été recrutés pour cette étude (20 ± 1 ans). Un test de vitesse critique (VC) a été réalisé afin d’estimer la CACP à l’aide de trois modèles mathématiques et d’un test DMOA, réalisé sur un tapis roulant motorisé. Les valeurs du DMOA test ont été de 61,6 ± 5,2 mL/kg (4,1 ± 0,3 L). Les valeurs de CDA estimées à partir du modèle linéaire vitesse-temps inverse ont été de 240,4 ± 18,6 m, pour le modèle linéaire distance-temps les valeurs ont été de 254,0 ± 13,0 m et pour la relation hyperbolique temps-vitesse (modèle non linéaire à deux paramètres) la valeur a été de 275,2 ± 9,1 m, tandis que les valeurs de vitesse critique étaient respectivement de 3,91 ± 0,07 m/s, 3,86 ± 0,08 m/s et 3,80 ± 0,09 m/s. Des différences ( p < 0,05) ont été constatées pour les valeurs de CACP et VC comparées entre le modèle linéaire vitesse-temps inverse et les modèles mathématiques non linéaires à deux paramètres. Aucune corrélation significative n’a été notée entre les différentes valeurs de la CACP et le DMOA.

Magnetic Kelvin–Helmholtz instability in the solar atmosphere

Main aim of this paper is to twofold: firstly, to investigate the formation mechanism and secondly to search the effects of fundamental parameters like magnetic field, shear velocity and wave number on the growth rate of the magnetic Kelvin–Helmholtz instability occured in the solar atmosphere. In this investigation, occurrence and unoccurrence of instability are determined for the different values of magnetic field, shear velocity and wave number in the solar atmosphere. We have obtained the critical values of shear velocity and magnetic field.

Verification of equations for incipient motion studies for a rigid rectangular channel

The current study aims to verify the existing equations for incipient motion for a rigid rectangular channel. Data from experimental work on incipient motion from a rectangular flume with two different widths, namely 0.3 and 0.6 m, were compared with the critical velocity value predicted by the equations of Novak & Nalluri and El-Zaemey. The equation by El-Zaemey performed better with an average discrepancy ratio value of 1.06 compared with the equation by Novak & Nalluri with an average discrepancy ratio value of 0.87. However, as the sediment deposit thickness increased, the equation by El-Zaemey became less accurate. A plot on the Shields Diagram using the experimental data had shown the significant effect of the sediment deposit thickness where, as the deposit becomes thicker, the dimensionless shear stress θ value also increased. A new equation had been proposed by incorporating the sediment deposit thickness. The new equation gave improved prediction with an average discrepancy ratio value of 1.02.