Oscillations of a viscous fluid in a thin layer between two coaxial disks rotating together

A study is made of the problem of the motion of an incompressible viscous fluid in the space between two coaxial disks rotating together with constant angular velocity under the assumption that the pressure changes in time in accordance with a harmonic law. The problem is solved using the equations of unsteady motion of an incompressible viscous fluid in a thin layer. It is shown that the velocity field in this case is a superposition on a steady field of damped oscillations with cyclic frequency equal to twice the angular velocity of the disks and forced oscillations with cyclic frequency equal to the cyclic frequency of the oscillations of the pressure field. It is shown that the amplitude of the forced oscillations of the velocity field depends strongly on the ratio of the cyclic frequency of the oscillations of the pressure field to the angular velocity of the disks. It is shown that there is a certain value of the ratio at which the amplitude of the forced oscillations has a maximal value (resonance). It is shown that even for very small amplitudes of the pressure oscillations the amplitude of the oscillations of the relative velocity at resonance may reach values comparable with the mean velocity of the main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–169, January–February, 1984.     

黏弹性饱和多孔介质中圆柱孔洞的频域响应

研究了无限黏弹性饱和多孔介质中圆柱孔洞(有衬砌)表面受轴对称简谐荷载和流体压力 作用下的频域响应问题. 引入Carcione提出的本构模型来描述介质的流变和松弛性质. 考 虑衬砌和介质的相对渗透性，孔洞处于半封闭状态，边界半透水. 引入两个势函数，在频域 中得到了应力、位移和超孔隙水压力响应解答. 并进行了算例分析，讨论了反映介质黏弹 性性质的最小质量因子，反映孔洞边界半透水性质的渗透性参数及衬砌和介质的相对刚度对 问题的影响. 分析结果表明：以上参数对圆柱孔洞的频域响应有很大影响.     

VORTEX SHEDDING RESONANCE FROM A ROTATIONALLY OSCILLATING CYLINDER

Vortex shedding resonance of a circular cylinder wake to a forced rotational oscillation has been investigated experimentally by measuring the velocity fluctuations in the wake, pressure distributions over the cylinder surface, and visualizing the flow field with respect to cylinder oscillations. The vortex shedding resonance occurs near the natural shedding frequency at small amplitude of cylinder oscillations, while the peak resonance frequency shifts to a lower value with an increase in oscillation amplitude. The drag and lift forces acting on the cylinder at fixed forcing Strouhal number indicate that the phase lag of fluid forces to the cylinder oscillations increases with an increase in oscillation amplitude, supporting the variation of resonance frequency with oscillation amplitude. The comparative study of the measured pressure distributions and the simultaneous flow visualizations with respect to cylinder rotation shows the mechanisms of phase lag, which is due to the strengthened vortex formation and the modification of the surface pressure distributions.     

Mechanical seals with oscillating stator

This paper presents theoretical analyses and experimental investigations of a mechanical seal subjected to axial impulses of one of its mating rings (stator). The amplitude of oscillations of stator depends on the pressure of sealed fluid. The frequency of oscillations is influenced by the geometry of frontal faces of the seal rings and depends on the rotational speed of rotor. The analytical models include the analyses of the static equilibrium of the investigated mechanical seal and the dynamic response of stator. The experimental analysis implies the conception of the testing system, the experimental estimation of the leakage and the measurements of amplitude and frequency of oscillations. During operating time, the experimental variations of leakage of a mechanical seal with oscillating stator are monitored for different rotational speed of rotor. Finite element analysis is used to visualize the stress distribution of stator as a function of the applied forces.     

Oscillatory Motion of a Viscous Fluid in Contact with a Flat Layer of a Porous Medium

Analytical solutions are obtained for two problems of transverse internal waves in a viscous fluid contacting with a flat layer of a fixed porous medium. In the first problem, the waves are considered which are caused by the motion of an infinite flat plate located on the fluid surface and performing harmonic oscillations in its plane. In the second problem, the waves are caused by periodic shear stresses applied to the free surface of the fluid. To describe the fluid motion in the porous medium, the unsteady Brinkman equation is used, and the motion of the fluid outside the porous medium is described by the Navier–Stokes equation. Examples of numerical calculations of the fluid velocity and filtration velocity profiles are presented. The existence of fluid layers with counter-directed velocities is revealed.     

Forced oscillations of pressure in tubes of active material

A study is made in the quasione-dimensional inertialess approximation of the axisymmetric flow of a Newtonian fluid in a tube of finite length made of a nonlinear active material with the capability of reducing deformations in response to an increase in tensile stresses [1, 2]. A study is made of the influence of the frequency and amplitude of forced oscillations of pressure at the entrance of the tube on its flow rate characteristics and on the behavior of the tube, depending on its length and certain rheological parameters. The first attempts at a study within the framework of this model of flow for unsteady conditions at the ends of the tube and in the ambient medium are described in [3, 4]. A general solution of this problem for external periodic disturbances of low amplitude is constructed in [5]. The present study gives an analysis of certain results of the numerical solution of an analogous problem for a wide range of variations in the frequency and amplitude of the pressure oscillations at the entrance to the tube.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 88–90, March–April, 1985.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

An analytical poroelastic model for laboratorial mechanical testing of the articular cartilage (AC)

The articular cartilage (AC) can be seen as a biphasic poroelastic material. The cartilage deformation under compression mainly leads to an interstitial fluid flow in the porous solid phase. In this paper, an analytical poroelastic model for the AC under laboratorial mechanical testing is developed. The solutions of interstitial fluid pressure and velocity are obtained. The results show the following facts. (i) Both the pressure and fluid velocity amplitudes are proportional to the strain loading amplitude. (ii) Both the amplitudes of pore fluid pressure and velocity in the AC depend more on the loading amplitude than on the frequency. Thus, in order to obtain the considerable fluid stimulus for the AC cell responses, the most effective way is to increase the loading amplitude rather than the frequency. (iii) Both the interstitial fluid pressure and velocity are strongly affected by permeability variations. This model can be used in experimental tests of the parameters of AC or other poroelastic materials, and in research of mechanotransduction and injury mechanism involved interstitial fluid flow.     

Linear dynamic model for porous media saturated by two immiscible fluids

A linear isothermal dynamic model for a porous medium saturated by two immiscible fluids is developed in the paper. In contrast to the mixture theory, phase separation is avoided by introducing one energy for the porous medium. It is an important advantage of the model based on one energy approach that it can account for the couplings between the phases. The volume fraction of each phase is characterized by the porosity of the porous medium and the saturation of the wetting phase. The mass and momentum balance equations are constructed according to the generalized mixture theory. Constitutive relations for the stress, pore pressure are derived from the free energy function. A capillary pressure relaxation model characterizing one attenuation mechanism of the two-fluid saturated porous medium is introduced under the constraint of the entropy inequality. In order to describe the momentum interaction between the fluids and the solid, a frequency independent drag force model is introduced. The details of parameter estimation are discussed in the paper. It is demonstrated that all the material parameters in our model can be calculated by the phenomenological parameters, which are measurable. The equations of motion in the frequency domain are obtained in terms of the Fourier transformation. In terms of the equations of motion in the frequency domain, the wave velocities and the attenuations for three P waves and one S wave are calculated. The influences of the capillary pressure relaxation coefficient and the saturation of the wetting phase on the velocities and attenuation coefficients for the four wave modes are discussed in the numerical examples.     

Primary and Secondary Infiltration of Wetting Liquid Sessile Droplet into Porous Medium

The infiltration of a wetting droplet into the porous medium is a two-step process referred to as primary and secondary infiltration. In the primary infiltration there is a free liquid present at the porous medium surface, and when no fluid is left on the surface, the secondary infiltration is initiated. In both situations the driving force is the capillary pressure that is influenced by the local medium heterogeneities. A capillary network model based on the micro-force balance is developed with the same formulation applied to both infiltrations. The only difference between the two is that the net liquid flow into the porous medium in the secondary infiltration is equal to zero. The primary infiltration starts as a single-phase (fully saturated) flow and may proceed as a multiphase flow. The multiphase flow emerges as the interface (flow front) becomes irregular in shape. The immobile clusters of the originally present phase can be locally formed due to entrapment. Throughout the infiltration, it was found that portions of the liquid phase can be detached from the main body of the liquid phase forming some isolated liquid ganglia that increase in number and decrease in size. The termination of the secondary infiltration occurs once the ganglia become immobile due to their reduction in size. From the transient solution, the changes in the liquid saturation and capillary pressure during the droplet infiltration are determined. The solution developed in this study is used to investigate the droplet infiltration dynamics. However, the solution can be used to study the flow in fuel cell, nano-arrays, composites, and printing.     

Two-Phase Flow in Heterogeneous Porous Media with Non-Wetting Phase Trapping

This article presents a mathematical model describing flow of two fluid phases in a heterogeneous porous medium. The medium contains disconnected inclusions embedded in the background material. The background material is characterized by higher value of the non-wetting-phase entry pressure than the inclusions, which causes non-standard behavior of the medium at the macroscopic scale. During the displacement of the non-wetting fluid by the wetting one, some portions of the non-wetting fluid become trapped in the inclusions. On the other hand, if the medium is initially saturated with the wetting phase, it starts to drain only after the capillary pressure exceeds the entry pressure of the background material. These effects cannot be represented by standard upscaling approaches based on the assumption of local equilibrium of the capillary pressure. We propose a relevant modification of the upscaled model obtained by asymptotic homogenization. The modification concerns the form of flow equations and the calculation of the effective hydraulic functions. This approach is illustrated with two numerical examples concerning oil–water and CO₂–brine flow, respectively.     

Thermodynamic approach to effective stress in partially saturated porous media

The form of the equilibrium effective stress acting on the solid phase of a porous medium containing two immiscible fluid phases is derived. The derivation makes use of the postulation of the thermodynamics of the system at the macroscale, a scale on the order of tens of pore diameters. The postulation at this scale facilitates the identification of the fraction of the solid surface in contact with each fluid phase as being the appropriate coefficient weighting each of the fluid phase pressures analogous to the Bishop parameter. In addition, the curvature of the surface of the solid phases is shown to impact the pressure exerted on the solid phase by the fluid. For the special case of low saturations when the wetting phase may be considered to be present only as a film on the solid phase, the macroscale disjoining pressure is found to modify the equilibrium form of the effective stress. In addition to the equilibrium effective stress, which is related to the forces acting on the interface between the solid phase and the fluids, the appropriate relation between the fluid pressures at the fluid–fluid interface is obtained. This analysis leads to the expression for the capillary pressure as a function of the phase pressures and the disjoining pressure.     

Calculation of the decay rate of oscillations of a low-viscosity fluid rotating in a cylindrical vessel

A study is made of the problem of small oscillations of a low-viscosity fluid rotating under conditions of weightlessness in a cylindrical vessel. For fixed volume of the fluid and different values of the angular velocity and the wetting angle the decay rate and frequency of the characteristic oscillations are calculated. For an ideal fluid, the shapes of the characteristic oscillations of the free surface of the fluid are also calculated.     

Transient response of fluid pressure in a poroelastic material under uniaxial cyclic loading

Poroelasticity is a theory that quantifies the time-dependent mechanical behavior of a fluid-saturated porous medium induced by the interaction between matrix deformation and interstitial fluid flow. Based on this theory, we present an analytical solution of interstitial fluid pressure in poroelastic materials under uniaxial cyclic loading. The solution contains transient and steady-state responses. Both responses depend on two dimensionless parameters: the dimensionless frequency Ω that stands for the ratio of the characteristic time of the fluid pressure relaxation to that of applied forces, and the dimensionless stress coefficient H governing the solid-fluid coupling behavior in poroelastic materials. When the phase shift between the applied cyclic loading and the corresponding fluid pressure evolution in steady-state is pronounced, the transient response is comparable in magnitude to the steady-state one and an increase in the rate of change of fluid pressure is observed immediately after loading. The transient response of fluid pressure may have a significant effect on the mechanical behavior of poroelastic materials in various fields.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。     

Fluid convection in a rotating porous layer under modulated temperature on the boundaries

The linear stability of thermal convection in a rotating horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation, using Brinkman’s model. In addition to a steady temperature difference between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The combined effect of rotation, permeability and modulation of walls’ temperature on the stability of flow through porous medium has been investigated using Galerkin method and Floquet theory. The critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Taylor number, porous parameter and Prandtl number. It is found that both, rotation and permeability are having stabilizing influence on the onset of thermal instability. Further it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls’ temperature.     

Seismic Reflection from an Interface Between an Elastic Solid and a Fractured Porous Medium with Partial Saturation

The theory of Tuncay and Corapcioglu (Transp Porous Media 23:237–258, 1996a) has been employed to investigate the possibility of plane wave propagation in a fractured porous medium containing two immiscible fluids. Solid phase of the porous medium is assumed to be linearly elastic, isotropic and the fractures are assumed to be distributed isotropically throughout the medium. It has been shown that there can exist four compressional waves and one rotational wave. The phase speeds of these waves are found to be affected by the presence of fractures, in general. Of the four compressional waves, one arises due to the presence of fractures in the medium and the remaining three are those encountered by Tuncay and Corapcioglu (J Appl Mech 64:313–319, 1997). Reflection and transmission phenomena at a plane interface between a uniform elastic half-space and a fractured porous half-space containing two immiscible fluids, are analyzed due to incidence of plane longitudinal/transverse wave from uniform elastic half-space. Variation of modulus of amplitude and energy ratios with the angle of incidence are computed numerically by taking the elastic half-space as granite and the fractured porous half-space as sandstone material containing non-viscous wetting and non-wetting fluid phases. The results obtained in case of porous half-space with fractures, are compared graphically with those in case of porous half-space without fractures. It is found that the presence of fractures in the porous half-space do affect the reflection/transmission of waves, which is responsible for raising the reflection and lowering the transmission coefficients.     

Flow-induced vibrations of a tethered circular cylinder

One of the most basic examples of fluid-structure interaction is provided by a tethered body in a fluid flow. The tendency of a tethered buoy to oscillate when excited by waves is a well-known phenomenon; however, it has only recently been found that a submerged buoy will act in a similar fashion when exposed to a uniform flow at moderate Reynolds numbers, with a transverse peak-to-peak amplitude of approximately two diameters over a wide range of velocities. This paper presents results for the related problem of two-dimensional simulations of the flow past a tethered cylinder. The coupled Navier–Stokes equations and the equations of motion of the cylinder are solved using a spectral-element method. The response of the tethered cylinder system was found to be strongly influenced by the mean layover angle as this parameter determined if the oscillations would be dominated by in-line oscillations, transverse oscillations or a combination of the two. Three branches of oscillation are noted, an in-line branch, a transition branch and a transverse branch. Within the transition branch, the cylinder oscillates at the shedding frequency and modulates the drag force such that the drag signal is dominated by the lift frequency. It is found that the mean amplitude response is greatest at high reduced velocities, i.e., when the cylinder is oscillating predominantly transverse to the fluid flow. Furthermore, the oscillation frequency is synchronized to the vortex shedding frequency of a stationary cylinder, except at very high reduced velocities. Visualizations of the pressure and vorticity in the wake reveal the mechanisms behind the motion of the cylinder.     

Effect of a periodic action on average flow in an inhomogeneous liquid-saturated porous medium

The problem of the average flow of a viscous incompressible fluid saturating a stationary porous incompressible matrix under a periodic action is considered. It is shown that a spatial inhomogeneity of the medium porosity leads to an average fluid flow, quadratically dependent on the action amplitude, in the direction of increase in porosity. In particular, this means that wave action on an oil reservoir could lead to fluid flow on the interfaces from low-porosity,weakly permeable collector regions into high-porosity regions, for example, to flow from blocks to fractures in fractured porous reservoirs, which makes it possible to enhance oil production. It is shown that in the presence of a constant pressure gradient the flow component generated by a periodic action can provide a substantial proportion of the total flow, especially on the boundaries with low-porosity strata or blocks. With increase in amplitude this may significantly exceed the component associated with the constant pressure gradient.