Viscous dissipation with fluid inertia in oscillatory shear flow

For liquids with high viscosity and low thermal conductivity, viscous dissipation can cause appreciable errors in rheological property measurements. Here, the influences of both viscous dissipation and fluid inertia on the property measurements in oscillatory sliding plate rheometry are investigated. For Newtonian fluids, Bird (1965) solved the combined problem analytically, but only for high frequencies. Here his solution is extended to any frequencies. Also, the equations of motion and energy are solved for linear viscoelastic fluids, and new analytical solutions for the velocity and temperature profiles are given. In both Newtonian and linear viscoelastic fluids, the temperature rise in the gap increases with frequency. The location of the maximum temperature shifts from the mid-plane at low frequency towards the moving wall at high frequency. The fluid inertia increases the viscous dissipation in both fluids. By solving the combined problem, this paper simplifies rheometer design by providing one unified criterion for avoiding measurement errors. Operating limits are presented graphically for minimizing the effects of both fluid inertia and viscous dissipation in oscillatory sliding plate rheometry.     

Convective Instability of Oldroyd-B Fluid Saturated Porous Layer Heated from Below using a Thermal Non-equilibrium Model

The linear stability of a viscoelastic fluid saturated densely packed horizontal porous layer heated from below and cooled from above is investigated by considering the Oldroyd-B type fluid. A generalized Darcy model, which takes into account the viscoelastic properties, is employed as momentum equation and a two-field model is used for energy equation each representing solid and fluid phases separately. Linear stability analysis suggests that, there is a competition between the processes of viscous relaxation and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. Analytical expression for the occurrence of oscillatory onset is obtained, and it is found that the necessary condition for the existence of the same is Λ < 1. Besides, the effect of viscoelastic parameters and the thermal non-equilibrium on the stability of the system is analyzed.     

Equivalent linearizations for practical hysteretic systems

Experimental testing of a friction damped base isolation system has indicated a need for a new model of friction damping and for an appropriate equivalent linearization technique. The model for the damping adopted is a combination of viscous damping, constant Coulomb friction and linear Coulomb friction.This model is incorporated into the equation of motion for a single-degree-of-freedom system and the exact solutions are given for free vibrations and for steady-state vibrations excited by a harmonic force. The exact solution is taken as a basis for an equivalent linearization technique that can be used in conjunction with conventional design spectra for a practical design of such a system.     

The viscous curtain: General formulation and finite-element solution for the stability of flowing viscous sheets

The stability of thin viscous sheets has been studied so far in the special case where the base flow possesses a direction of invariance: the linear stability is then governed by an ordinary differential equation. We propose a mathematical formulation and a numerical method of solution that are applicable to the linear stability analysis of viscous sheets possessing no particular symmetry. The linear stability problem is formulated as a non-Hermitian eigenvalue problem in a 2D domain and is solved numerically using the finite-element method. Specifically, we consider the case of a viscous sheet in an open flow, which falls in a bath of fluid; the sheet is mildly stretched by gravity and the flow can become unstable by ‘curtain’ modes. The growth rates of these modes are calculated as a function of the fluid parameters and of the geometry, and a phase diagram is obtained. A transition is reported between a buckling mode (static bifurcation) and an oscillatory mode (Hopf bifurcation). The effect of surface tension is discussed.     

An analytical study of linear and non-linear double diffusive convection with Soret and Dufour effects in couple stress fluid

The onset of double diffusive convection in a two component couple stress fluid layer with Soret and Dufour effects has been studied using both linear and non-linear stability analysis. The linear theory depends on normal mode technique and non-linear analysis depends on a minimal representation of double Fourier series. The effect of couple stress parameter, the Soret and Dufour parameters, and the Prandtl number on the stationary and oscillatory convection are presented graphically. The Dufour parameter enhances the stability of the couple stress fluid system in case of both stationary and oscillatory mode. The effect of positive Soret parameter is to destabilize the system in case of stationary mode while it stabilizes the system in case of oscillatory mode. The negative Soret parameter enhances the stability in both stationary and oscillatory mode. The couple stress parameter enhances the stability of the system in both stationary and oscillatory modes. The Dufour parameter increases the heat transfer while the couple stress parameter has reverse effect. The Soret parameter has negligible influence on heat transfer. Both Dufour and Soret parameters increases the mass transfer while the couple stress parameter has dual effect depending on the value of the Rayleigh number.     

A model for the viscous attenuation of waves on the common boundary of two superposed fluids

We study the formation and propagation of waves on the interface between two superposed fluids in relative horizontal motion, and the resulting attenuation of the oscillatory component of the motion caused by viscous dissipation in laminar boundary layer attached to the bottom wall and in a shear layer at the interface.     

Magneto-convection in an anisotropic porous layer with Soret effect

Thermal instability in an electrically conducting two component Boussinesq fluid-saturated-porous medium has been investigated, in the presence of Soret coefficient. The porous medium is confined between two horizontal surfaces, and subjected to a constant vertical magnetic field. Flow in the porous medium is characterized by generalized Darcy model, which includes the time derivative term. Performing linear and non-linear stability analysis, the effect of magnetic field on the stability of flow through porous medium has been investigated. The normal mode method is used in linear stability analysis, while a weak non-linear analysis based on a minimal representation of double Fourier series method is used in non-linear analysis. The critical Rayleigh number, wave number for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. Effects of various parameters on stationary, oscillatory and finite amplitude convection, rate of heat and mass transfer have been obtained analytically and presented graphically.     

Two-fluid oscillatory flow in a channel

The validity of Navier's partial slip condition is investigated by studying the oscillatory flow in a coated channel. The two-fluid model is used to solve the unsteady viscous equations exactly. Partial slip is experienced by the core fluid. It is found that Naviers condition does not hold for an unsteady core fluid.     

Non-linear Damping and Frequency Identification in a Progressively Damaged R.C. Element

This paper describes the non-linear identification of a progressively damaged reinforced concrete beam-column node. The aims are the detection and identification of the different sources of damping and their dependence from the damage level. To this end a specially formulated non-linear identification method is proposed, based on a time-varying polynomial approximation of the system dynamics, suitable for use in the presence of excitations of any form. A minimum condition imposed to the identified dissipated energy leads to the distinction of the linear viscous component from the other damping mechanisms. The estimated values obtained from the experimental tests show a significant influence of the damage level on the linear viscous damping coefficient. This suggests that, in a non-linear dynamic time-history analysis, the use of Rayleigh damping model with proportionality to the initial stiffness is basically in contrast with experimental evidence and more refined viscous damping models are needed for prediction purposes.     

Research on linear/nonlinear viscous damping and hysteretic damping in nonlinear vibration isolation systems

A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance. In this paper, a generalized vibration isolation system is established with nonlinear stiffness, nonlinear viscous damping, and Bouc-Wen(BW)hysteretic damping. An approximate analytical analysis is performed based on a harmonic balance method(HBM) and an alternating frequency/time(AFT) domain technique.To evaluate the damping effect, a generalized equivalent damping ratio is defined with the stiffness-varying characteristics. A comprehensive comparison of different kinds of damping is made through numerical simulations. It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes. The linear damping, hysteretic damping, and nonlinear viscous damping are suitable for the small-amplitude, medium-amplitude, and large-amplitude conditions, respectively. The hysteretic damping has an extra advantage of broadband isolation.     

Damping in a parametric pendulum with a view on energy harvesting

The present article addresses the quantification of damping in a parametric pendulum, with a view on further applications in the design of energy harvesting devices. Detailed new experimental data is obtained for such purpose, and a novel mathematical model is presented. Linear and quadratic viscous damping and also dry friction are taken into account. To introduce the dry friction component, the pendulum axis is mounted on ball bearings. This is considered as a very realistic situation of a harvester. Damping parameters are determined by minimizing the difference between numerical and experimental time histories. It is shown that the damping model here presented is more adequate to replicate experiments than commonly used linear models, which consider only a linear viscous damping term characterized by means of free decay tests. It is also pointed that linear models are not adequate for refined studies, since they can lead to erroneous predictions of rotation zones, and consequently to wrong considerations in the design of pendulum harvesters.     

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink(NES)are investigated.The linear system is excited by a harmonic and random base excitation,consisting of a mass block,a linear spring,and a linear viscous damper.The NES is composed of a mass block,a linear viscous damper,and a spring with ideal cubic nonlinear stiffness.Based on the generalized harmonic function method,the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system.The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions.The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities,the transmissibility transition probability density,and the percentage of the energy absorption transition probability density of the linear oscillator.The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio.The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters,which will affect the stability of the system.     

Slip effects and heat transfer analysis in a viscous fluid over an oscillatory stretching surface

In this study, we investigate the heat transfer problem in a viscous fluid over an oscillatory infinite sheet with slip condition. The sheet is moved back and forth in its own plane. The derived problem involves a dimensionless parameter indicating the relative magnitude of frequency to sheet stretching rate. A system of non‐linear partial differential equations is solved numerically using the finite‐difference scheme, in which a coordinate transformation is employed to transform the semi‐infinite physical space to a bounded computational domain. The physical features of interesting parameters on the velocity and temperature distributions are shown graphically and discussed. The values of the skin‐friction coefficient and the local Nusselt number are given in tabular form. Copyright © 2008 John Wiley & Sons, Ltd.     

Heat transfer performance for batch oscillatory flow mixing

Experimental heat transfer data is presented for two batch operations of oscillatory flow mixing. In one case fluid is oscillated within a baffled tube and in the second case baffles are oscillated within a process fluid. For both situations the heat transfer coefficient depends on the intensity of oscillation, and the energy performance of each configuration corresponds to that of an equivalent net turbulent flow in a pipe or a batch stirred vessel. The results indicate that oscillatory flow batch mixing is as energy efficient as other conventional mixing configurations and the heat transfer performance indicates that each oscillatory flow mixing configuration could be satisfactorily used as a batch reactor system.     

粘滞和粘弹性阻尼器减震结构的等效阻尼

利用积分型本构关系,建立了带支撑的一般粘滞和粘弹性阻尼器单自由度耗能结构的微分-积分混合地震响应方程;基于与随机平均分析完全相同的等效准则,推导了可直接应用反应谱的阻尼器的等效刚度和等效阻尼的解析公式;得到了带支撑广义Maxwell阻尼器和广义微分模型阻尼器的等效刚度和等效阻尼的一般结果。通过与一些典型问题的数值计算结果比较,表明了所提方法的有效性。     

Identification of discrete-time bilinear systems through equivalent linear models

This paper presents a novel method for identification of discrete-time, time-invariant state-space models of bilinear dynamical systems using the steady-state portion of a single input/multiple output time-history measurements. These measurements are recorded by exciting the system with a linear combination of sine and cosine functions of user-selected frequencies enriched by a subtle amount of random component. The proposed method relies on conversion of the bilinear system into an equivalent linear model (ELM) by an accurate approximation of the state in the bilinear term using a set of sine and cosine basis functions whose frequencies are obtained as combinations of the input frequencies. Observer/Kalman Filter Identification (OKID), a?linear time invariant (LTI) system identification algorithm, is used to identify the aforementioned ELM from which the original bilinear model is recovered. A?numerical example is also provided.     

The simulation of oscillatory pipe flow on an analogue computer

Summary A formulation of equations governing oscillatory flow of a fluid in a circular pipe is given. The equations are then cast in a form suitable for analogue computation and a corresponding programming diagram suitable for use with an EAI 680 Analogue Computer is provided. Results have been obtained forNewtonian flow for a range ofReynolds numbers and for combinations of the realReynolds number, and the ratio of elastic to viscous forces in the case of linear viscoelastic fluids.The displacement profiles given in this work do not depend upon specific rheological models and are therefore of universal validity for linear fluids.     

Velocity measurements in the oscillatory boundary layer produced by acoustic waves

Simultaneous amplitude and phase velocity measurements in the oscillatory viscous boundary layer (OVBL) produced by acoustic waves are reported. The structure of the OVBL of acoustic standing waves in air with frequencies of 35, 46, and 130 Hz is determined using hot-wire anemometry. The experimental results in amplitude are close to theoretical results of linear theories; small differences are pointed out. The phase results are in good agreement for 130 Hz, the agreement decreases for 35 and 46 Hz. A discussion on the possible causes of these discrepancies is made. Received: 25 May 2001/Accepted: 31 July 2001     

Présentation d'une méthode d'étude de la stabilité linéaire d'écoulements instationnairesPresentation of a method for linear stability analysis of unsteady flow

We propose a linear stability analysis of unsteady viscous flow. We apply this method to an oscillatory pipe flow with an axisymetric 2D perturbation which has received considerable attention. The numerical results are relevant. To cite this article: M. Siouffi et al., C. R. Mecanique 330 (2002) 641–645.     

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible,hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat transfer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two-and three-dimensional flow phenomena are also shown through graphical results.