Filtration convection in a high-frequency vibration field

Abstract

Convection in a porous medium under nonisothermal conditions occurs widely in nature and engineering and is of interest, for example, for studies of the operation of thermal insulators made of porous materials, which are used in modern equipment both under earth conditions and in space studies. In this connection, it makes sense to study the effect of various factors on filtration convection from the viewpoint of controlling the stability of convective flows in a porous medium. One of these factors is the vibration effect.Zen'kovskaya [1] studied the effect of high-frequency vertical vibrations on the occurrence of filtration convection in a plane horizontal layer of a liquid saturating a porous medium. It is established that vertical vibrations prevent the occurrence of filtration convection and can even completely suppress it.The present work is a continuation of [1], where the influence of the vibration direction and velocity on the convective instability in a layer of a viscous incompressible liquid saturating a porous medium at a given transverse temperature gradient is studied. The present investigation is based on an analysis of the averaged equations that are a generalization of the equations obtained in [1]. These equations are derived for an arbitrary region and analyzed in the particular case of a horizontal layer. It is established that for any vibration direction different from the vertical one, destabilizing effects are possible: filtration convection under conditions of zero gravity and occurrence of convective regimes under heating from above in gravity.Critical values of the thermal and vibration Rayleigh-Darcy numbers are calculated for different directions and velocity of vibration in zero gravity and gravity. In the case of reduced gravity, values for the vibration parameter are obtained for which transition to zero gravity occurs. These results can be used in modeling zero gravity under earth conditions and in controlling convection in a porous medium.1. Formulation of the Problem and Derivation of the Averaged Equations. Let a vessel D containing a porous medium saturated with a viscous incompressible liquid perform plane simple harmonic oscillations in a specified direction s ---(cos ~, 0, sin~2) by the law a/w cos(wt). The equations of thermal convection in a porous medium in the Darcy-Oberbeck-Boussinesq approximation, written in a moving coordinate system, have the form [1, 2] "This work was presented at the joint X European and VI Russian Symposium on Physical Sciences in Microgravity (St. Petersburg, June 15-20, 1997).Rostov State university, Rostov-on-Don 344090. 1Rostov State Academy of Building, Rostov-on-Don 344022.

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: The effect of vertical vibrations

“…However, in our problem, high-frequency vibrations cause very large accelerations, making it necessary to consider this non-stationary term [6].…”

“…In the case of a horizontal porous layer saturated by a pure fluid, heated from below or from above Zenkovskaya et al [6] and Bardan et al [7] used the Darcy model including the non-stationary term and adopted the timeaveraged equations formulation to study the influence of high-frequency and small-amplitude vibrations on the onset of convection. They found that vertical vibrations stabilize the rest solution.…”

Effect of Vertical Modulation on the Onset of Filtration Convection

“…The onset of convection in a region of fluid saturating a porous medium subjected to high-frequency vibration of arbitrary direction has been examined by Zenkovskaya [12,13] using the averaging method. Malashetty and Padmavathi [14] asymptotically analyzed the linear stability of a horizontal fluid-saturated porous layer heated from below for the case of small-amplitude gravity modulation.…”

Onset of Vibrational Convection in a Binary Fluid Saturated Non-Darcy Porous Layer Heated from Above

“…Zenkovskaya and Rogovenko [6] and Govender [7] have investigated the effect of vertical vibration on the onset of convection in a Darcian porous layer subject to high frequency and low-amplitude vibrations respectively. Recently, Strong [8] reported the results of this problem for arbitrary range of modulation parameters by the use of continued fraction method.…”