Fluidization of a granular medium in a viscous fluid under vertical vibration

The dynamics of a granular medium in a cavity filled with incompressible viscous fluid under harmonic vertical vibration are studied experimentally. The sand is fluidized in a relatively thin sublayer of the granular layer near the interface between the media. The fluidization is of the threshold type and is accompanied by intense parametric oscillations of the interface. For viscous fluids, the transition of the sand from a quasi-solid to a fluidized state and the reverse transition associated with a decrease in the oscillation rate occur with hysteresis. The nondimensional governing parameters determining the sand dynamics are established. The analysis is focused on the case of low nondimensional frequencies. Perm’, Paris. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–122, May–June, 2000.     

Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid

The scattering of water waves by a flexible porous membrane barrier in a two-layer fluid having a free surface is analysed in two dimensions. The membrane barrier is extended over the entire water depth in a two-layer fluid, each fluid being of finite depth. In the present analysis, linear wave theory and small amplitude membrane response are assumed. The porous membrane barrier is tensioned and pinned at both the free surface and the seabed. The associated mixed boundary value problem is reduced to a linear system of equations by utilizing a general orthogonality relation along with least-squares approximation method. Because of the flow discontinuity at the interface, the eigenfunctions involved have a discontinuity at the interface and the orthogonality relation used is a generalization of the classical one corresponding to a single-layer fluid. The reflection and transmission coefficients for the surface and internal modes, the free surface and interface elevations and the nondimensional membrane deflection are computed for various physical parameters like the nondimensional tension parameter, porous-effect parameter, fluid density ratio, ratio of water depths of the two fluids to analyse the efficiency of a porous membrane as a wave barrier in the two-layer fluid.     

Thermo-Gravitational Convection in a Near-Critical Fluid in a Side-Heated Enclosed Cavity

Convection near a thermodynamic critical point in a square cavity with lateral heating is investigated numerically on the basis of the Navier-Stokes equations for a compressible gas with a Van-der-Waals equation of state. Comparison of a near-critical fluid and a perfect gas with parameters equal to those of the real fluid near the critical point shows that, with the development of convection, the dynamics of these two media are qualitatively different; however, a certain similarity is observed for the steady-state regime. The dependence of the steady-state flow and heat transfer characteristics on the nondimensional governing parameters is investigated.     

Effect of heat transfer on the flow of a second‐grade fluid in divergent/convergent channel

This paper studies the effects of a second‐grade fluid on the flow and heat transfer characteristics in a divergent/convergent channel. The momentum and energy equations are first given in a nondimensional form and then solved analytically using the method of homotopy analysis method. Convergence of derived series solutions is shown. Graphical results for the velocity and the temperatures are presented and discussed for various emerging parameters. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical study of the natural convective cooling of a vertical plate

We study numerically in this paper the natural convective cooling of a vertical plate. The full transient heat conduction equation for the plate, coupled with the natural convection boundary layer equations are solved numerically for a wide range of the parametric space. Assuming a large Rayleigh number for the natural convection flow, the balance equations are reduced to a system of three differential equations with three parameters: the Prandtl number of the fluid, Pr, a non-dimensional plate thermal conductivity α and the aspect ratio of the plate ?. The nondimensional cooling time depends mainly on α/?², obtaining a minimum of this time for values of 1?α??².     

Dynamic structural loading using a light gas gun

A light gas gun was used to dynamically load models of the wall sections typical of those used in the construction of buried structures. Scaling of the loading time history is addressed, and the appropriate nondimensional parameters for the loading and the model structural characteristics are defined. Scaling is simplified by use of structural materials for the models which have a yield strength and material moduli close to those found in prototype structures. Methods for producing the desired loading by using a light gun are investigated, and reasonable accuracy and flexibility in achieving the desired loading time history is demonstrated. Experimental results are given for the loading conditions and the failure mode that occurs when the model wall section is breached. The loading conditions to produce failure in the model are reduced to nondimensional form and compared to results from prototype field tests, also in nondimensional form. The resulting nondimensional data are used to evaluate the suitability of the light gun to dynamically simulate ground shock loading as well as to investigate failure criteria.     

Flow characteristics and mixing performance of electrokinetically driven non-Newtonian fluid in contraction–expansion microchannel

A numerical investigation is performed into the flow characteristics and mixing performance of electrokinetically driven non-Newtonian fluid in a contraction–expansion microchannel. In the study, the rheological behavior of the fluid is characterized using a power-law model. The results show that the volumetric flow rate reduces as the flow behavior index increases, and thus an improved mixing performance is obtained. Furthermore, it is shown that for all considered values of the flow behavior index, the mixing performance can be enhanced by increasing the ratio of the main channel width to the contraction channel width, extending the length of the contraction channel, assigning a smaller value to the nondimensional Debye–Hückel parameter, and applying an appropriate electric field strength. Finally, it is shown that although the mixing efficiency reduces with a reducing flow behavior index, an acceptable mixing performance can still be obtained given an appropriate specification of the flow conditions and geometry parameters.     

Experimental Investigation of Thermo-Oscillatory Convection

The thermal convection in an air column oscillating with a high frequency in a plane channel whose boundaries are isothermal and have different temperatures is investigated. The experiments were performed for various channel orientations and for a wide range of nondimensional governing parameters, i.e. the gravitational Rayleigh number and the thermo-oscillatory parameter. As follows from the experimental results, for relatively large oscillation amplitudes the latter parameter characterizes the average action of high-frequency oscillations on a non-isothermal incompressible fluid. The regions in which either the thermo-oscillatory or gravitational mechanism of thermal convection predominates are determined. The threshold of excitation of thermo-oscillatory convection under weightlessness conditions is found.     

Analysis of three-dimensional effects in oscillating cantilevers immersed in viscous fluids

In this paper, we numerically study the flow physics induced by the flexural vibration of a thin cantilever plate submerged in a viscous and otherwise quiescent fluid. The computational fluid dynamics simulations are based on a finite volume approximation of the incompressible Navier–Stokes equations. We perform a detailed parametric study on relevant nondimensional parameters, including plate aspect ratio, oscillatory Reynolds number, and relative vibration amplitude, to investigate their effects on the hydrodynamic load experienced by the structure and its thrust production. Numerical results are validated with experimental data on underwater vibration of ionic polymer metal composites and used to ascertain the accuracy of theoretical findings from reduced order models available in the literature.     

Finite amplitude oscillations of flanged laminas in viscous flows: Vortex–structure interactions for hydrodynamic damping control

In this paper, we study the problem of harmonic oscillations of a flanged lamina in a quiescent Newtonian incompressible viscous fluid. We conduct a comprehensive fluid–structure interaction investigation with the goal of assessing the effect of the presence of the flanges on the added mass and hydrodynamic damping experienced by the oscillating solid. We determine the complex nonlinear hydrodynamic function incorporating these effects via its real and imaginary parts, respectively, and its dependence on three nondimensional parameters that govern the flow evolution. We further investigate in detail the flow physics and the effects of nonlinearities on vortex shedding, convection, and diffusion in the vicinity of the oscillating structure. We find that the added mass effect is relatively independent of the oscillation amplitude and increases with the flange size. On the other hand, the hydrodynamic damping effect is remarkably affected by the interplay of geometry and dynamic parameters resulting into a peculiar non-monotonic behavior. We show the existence of a minimum in the hydrodynamic damping which can be attained via specific control of vortex–structure interaction dynamics and discuss its properties and significance from a physical perspective through analysis of the relevant flow fields. This novel finding has potential application for damping reduction in elastic systems where reduction of energy losses and increase of oscillation quality factor are desired.     

Droplet formation from a pulsed vibrating micro-nozzle

Micro-droplet formation from a passive vibrating micro-nozzle driven by a pulsed pressure wave is numerically simulated. The micro-nozzle is formed from an orifice in a thin walled plate that is allowed to freely vibrate due to the pressure loading on the plate. The analysis couples the fluid flow from the nozzle and the resultant droplet formation with the nozzle vibration calculated using large deflection theory. The problem is made nondimensional based on the capillary parameters of time, velocity and pressure. The applied pressure and nozzle material properties are varied to alter the vibration characteristics of the orifice plate used to form the nozzle. The initiation of drop formation is found to coincide with a threshold impulse input, defined as the product of the pressure magnitude and the pulse duration. Increasing the impulse can result in multiple satellite droplet formation, but the effect on the primary droplet size is minor. The vibration of the nozzle only weakly influences the droplet break-off time, but is shown to significantly affect the droplet volume, shape, and satellite droplet formation.     

Stability of a Falling Liquid Film with a Non-Equilibrium Adsorbed Sublayer of Soluble Surfactant

The hydrodynamic instability of a falling film of a dilute solution of a volatile surfactant is studied.The flow of the liquid-gas (vapor) two-phase three-component system is accompanied by surfactant mass transfer across the free surface and is described by a system of five evolutionary equations for five functions depending on time and a spatial coordinate. These functions are the thicknesses of the film and the diffusion boundary layer, the concentrations of the free surfactant and the bound surfactant in the adsorbed sublayer, and the fluid velocity on the film surface. The dispersion equation determining the eigenvalues and the corresponding instability modes is solved numerically in the space of ten free nondimensional governing parameters. Main attention is focused on examining the role of the parameters controlling the influence of the surfactant on the Marangoni effect and the film instability at finite adsorption-desorption rates.     

The skidding of an elliptic plate on a wet surface

A viscous fluid separates a massed, sliding, free elliptic plate and a smooth bottom plate. Due to the weight, the gap width between the plates decreases. The increased viscous drag eventually stops the skidding. The Navier-Stokes equations are expanded in terms of a small squeeze number. It is found that the gap width decrease as (time)^–1/2 and the maximum skidding distance depends on five nondimensional groups. An example shows it is easier for the elliptic plate to side longitudinally than laterally.     

Spacetime dimensional analysis and self-similar solutions of linear elastodynamics and cohesive dynamic fracture

We present a dimensional analysis and self-similar solutions for linear elastodynamics with extensions to dynamic fracture models based on cohesive traction–separation relations. We formulate the problem using differential forms in spacetime and show that the scaling rules expressed in terms of forms are simpler and more uniform than those obtained for tensor representations of the solution. In the extension to cohesive elastodynamic fracture, we identify and study the influence of certain intrinsic cohesive scales on dynamic fracture behavior and describe a fundamental set of nondimensional groups that uniquely identifies families of self-similar solutions. We present numerical studies of the influence of selected nondimensional parameters on dynamic fracture response to verify the dimensional analysis, including the identification of the fundamental set for cohesive fracture mechanics. We show that distinct values of a widely-used nondimensional quantity can produce self-similar solutions. Therefore, this quantity is not fundamental, and it cannot parameterize dynamic, cohesive-fracture response.     

Natural convection-radiation interaction on boundary layer flow along a thin vertical cylinder

A free convertion flow of an optically dense viscous incompressible fluid along a vertical thin circular cylinder has been studied with effect of radiation when the surface temperature is uniform. With appropriate transformations, the boundary layer equations governing the flow are reduced to local nonsimilarity equations. Solutions of the governing equations are obtained employing the implicit finite difference methods together with Keller box scheme as well the local nonsimilarity method with second order truncation for all ξ (nondimensional transverse curvature parameter) in the interval [0,10] and are expressed in terms of local Nusselt number for a range of values of the pertinent parameters. Effects of pertinent parameters, such as, the radiation parameter, R _d , the surface temperature parameter, θ _w , taking Prandtl number, Pr, equals 0.7 on the velocity and temperature field are also presented graphically. From the solution it is seen that increase of R _d , or θ _w leads to increase in the local rate of heat transfer coefficients. Results obtained by both the methods are obtained in excellent agreement between each other upto ξ = 10.     

Numerical Modeling of Unsteady Two-Dimensional Convection in a Finite-Length Horizontal Layer Heated from Below

The development of two-dimensional thermo-gravitational convection in an elongated horizontal layer bounded by solid surfaces with the bottom instantaneously heated is investigated. The characteristics of the transition from the heat conduction regime to the convective regime are considered. The flow pattern and the heat transfer properties are described from the initial instant, which corresponds to the isothermal fluid at rest, up to the attainment of the steady-state roll-convection regime. A criterial dependence between the Rayleigh number and the nondimensional time of onset of the influence of thermo-gravitational convection on heat transfer is obtained.     

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

Asymptotic suction profiles for the Blasius and Sakiadis flow with constant and variable fluid properties

A theoretical study of the effect of variable fluid properties on the Blasius and Sakiadis flow with uniform suction at the asymptotic state is presented in this paper. The investigation concerns air and water taking into account the variation of their physical properties with temperature. Velocity and temperature profiles are presented as well as values of the displacement thickness, momentum thickness, shape factor, wall shear stress and Nusselt number for different temperatures of the plate and the ambient fluid. It is found that the nondimensional displacement thickness, momentum thickness, shape factor, absolute wall shear stress and Nusselt number are identical in both Blasius and Sakiadib flow at the asymptotic state for a fluid with constant properties. The same is valid for any fluid with variable properties if the temperature boundary conditions are the same in Blasius and Sakiadis flow.