Macrokinetic model of the trapping process in two-phase fluid displacement in a porous medium

A microinhomogeneity-averaged model of the kinetics of the trapping process is proposed for a porous medium in which two fluids are mutually displaced. The traps are treated as a new hydrodynamic phase, and the trapping process as a phase transition. Kinetic relations for the average trapping process are obtained. The structure and quantitative values of the kinetic coefficients are obtained for a model of a porous medium in the form of a system of doublets. The dependence of the characteristic time of the process on the degree of inhomogeneity of the medium is investigated. A variant of the macroscopic model of the process of two-phase flow, in which the kinetic relations obtained are used as the closing relations, is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 92–101, May–June, 1995.     

One-dimensional simulation of viscous fluid displacement from a porous medium with consideration of lateral inflow

A one-dimensional model of fluid displacement in a porous medium is discussed with consideration of lateral inflow. The time period required for the complete displacement of an initially injected fluid from a region is studied. Some numerical results obtained for two formulations of the problem are given; these results are in good agreement with the estimates considered in this paper. The problem under study is of interest in practice for enhancing the oil recovery from oil fields.     

One-dimensional flow of a two-phase medium

Institute of Geotechnical Mechanics, Ukrainian Academy of Sciences, Dnepropetrovsk. Translated from Prikladnaya Mekhanika, Vol. 25, No. 8, pp. 111–118, August, 1989.     

Design of a thin airfoil in a channel with permeable walls

A general solution is obtained for the boundary value problem of designing a thin airfoil in a channel with permeable walls from the given pressure distribution. A suitable choice of permeability coefficients makes it possible to construct a thin airfoil in a channel with impermeable walls, in a jet, etc. The effect of the wall permeability on the shape of the airfoil is studied. Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 28–34, July–August, 1994.     

Acoustics of ducts with plane permeable walls

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 37, No. 5, pp. 82–92, September–October, 1996.     

Turbulent flow in a channel with permeable walls. Direct numerical simulation and results of three-parameter model

Steady turbulent viscous incompressible fluid flow in a plane channel is calculated for the case of uniform blowing and suction through opposite walls. There are no experimental data for flows of this type. The flows were calculated by two methods: a direct numerical simulation method and using a three-parameter turbulence model. Direct numerical simulation was carried out using the same (apart from the boundary conditions) algorithm for numerical solution of the Navier-Stokes equations as that used earlier for calculating flows in pipes and channels with impermeable walls. In the second group of calculations the version of the model published in 1978 was used. The results obtained by the two methods are in good agreement. The difference is within the spread of the experimental data used for determining the parameters of the model. The agreement obtained makes it possible to assert that the turbulence direct numerical simulation algorithm developed can be used for the analysis of flows with quite different boundary conditions, including cases where there are no corresponding experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 18–26, November–December, 1998. The work was financially supported by the Russian Foundation for Basic Research (project Nos. 96-01-00602 and 96-01-00259).     

One-dimensional transonic gas flow in a wind tunnel with perforated walls

Near-sonic inviscid gas flow in the working section of a wind tunnel with perforated walls is investigated in the context of the one-dimensional theory with Darcy's boundary condition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–148, November–December, 1988.     

One-dimensional problem of water-oil displacement in a medium with fracture porosity

We consider the one-dimensional displacement of oil by water in a medium with fracture porosity. A special dependence of saturation on time is assumed, which approximates well the experimental curve. The position of the injected water front in the course of time is found for several flow rate variation laws.The author wishes to thank V. L. Danilov for his scientific guidance.     

Mixed convection boundary layer flow past a wedge with permeable walls

The effects of suction/injection on steady laminar mixed convection boundary layer flow over a permeable horizontal surface of a wedge in a viscous and incompressible fluid is considered in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction/injection parameter f ₀, the constant exponent m of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using an implicit finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are obtained for various values of parameters considered. Dual solutions are found to exist for the case of opposing flow.     

Flows in the initial sections of channels with permeable walls

Calculations of two types of flows in the initial sections of channels with permeable walls are carried out on the basis of semiempirical turbulence theories during fluid injection only through the walls and during interaction of the external flow with the injected fluid. Experimental studies of the first type [1–3] show that at least within the limits of the lengths L/h<30 and L/a< 50 (2h is the distance between permeable walls of a flat channel anda is the tube radius) the velocity distributions in the laminar and turbulent flow regimes differ little and are nearly self-similar for solutions obtained in [4]. For sufficiently large Reynolds numbers, Re₀>100 (Re₀=v₀h/ or Re₀=v₀ a/, where v₀ is the injection velocity), and small fluid compressibility, the axial velocity component is described by the relations for ideal eddying motion: u=(/2)x× cos (y/2) in a flat channel and u=x cos (y²/2) in atube (the characteristic values for the coordinates are, respectively, h anda). Measurements indicate the existence of a segment of laminar flow; its length depends on the Reynolds number of the injection [3]. In the turbulent regime the maximum generation of turbulent energy occurs significantly farther from the wall than in parallel flow. Flows of the second type in tubes were studied in [5–7]. These studies disclosed that for Reynolds numbers of the flow at the entrance to the porous part of the tube Re=u₀ a/<3.10³ fluid injection with v₀/u₀>0.01 leads to suppression of turbu lence in the initial section of the tube. An analogous phenomenon was observed in the boundary layer with v₀/u₀>0.023 [8, 9]. Laminar-turbulent transition in flows with injection was explained in [10, 11] on the basis of hydrodynamic instability theory, taking into account the non-parallel character of these flows. The mechanisms for the development of turbulence and reverse transition in channels with permeable walls are not theoretically explained. Simple semiempirical turbulence theories apparently are insufficient for this purpose. In the present work results are given of calculations with two-parameter turbulence models proposed in [12, 13] for describing complex flows. Due to the sharp changes of turbulent energy along the channel length, a numerical solution of the complete system of equations of motion was carried out by the finite-difference method [14].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 43–48, September–October, 1976.     

Viscous flow in a rotating channel with permeable walls (two-dimensional approximation)

Laminar flow in a rotating rectangular channel with suction through one or more of the permeable walls is studied. The conditions under which a two-dimensional formulation of the flow core calculations is possible are discussed and the corresponding problem is formulated. Calculation results illustrating the combined effect of suction and rotation about the transverse axis are presented for a channel with a stopped end. Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–34, September–October, 1988.     

Viscid fluid motion in a tube with deforming walls

The problem of incompressible fluid flow in a tube with rhythmically deforming walls is of interest in connection with the study of certain physiological processes and has been examined recently in [1] on the basis of the equations of hydrodynamics in the Stokes approximation. This paper solves a more general problem, and the solution is obtained by a considerably simpler method. Along with completely satisfactory agreement of the quantitative results with those of [1], the present method provides simple and convenient computational formulas and apparently admits several useful extensions and improvements.     

Migration of settling particles in a horizontal viscous flow through a vertical slot with porous walls

Particle migration in a horizontal flow of dilute suspension through a vertical slot with porous walls is studied using the two-continua approach. The lateral migration is induced by two opposite effects: an inertial lift force due to particle settling and directed toward the slot centre-line, and a drag due to leak-off entraining particles toward the walls. An expression for the inertial lift on a settling particle in a horizontal channel flow found recently is generalized to the case of a low leak-off velocity. The evolution of an initial uniform particle concentration profile is studied within the full Lagrangian approach. Four migration regimes are found differing by the direction of particle migration and numbers of equilibrium positions. Conditions of the regime change and a critical value of dimensionless leak-off velocity for particle deposition on the walls are obtained analytically. Suspension flows with zones where the particle concentration is zero or increases infinitely, are studied numerically.     

Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.     

Numerical investigation of tube flow with suction through permeable walls

The dependence of turbulent tube flow parameters on the suction intensity and the suction region length is determined by numerical simulation. The comparison of the calculated results with the available experimental data shows mainly their agreement reflecting the main distinctive features of fairly complicated processes of flow rearrangement under suction.     

Mathematical model of two-phase fluid nonlinear flow in low-permeability porous media with applications

IntroductionItisasuccessfulexampleinadevelopmentstoryofscienceandtechnologyformechanicsoffluidsinporousmediatocombinewithengineeringtechnology .Fieldsinfluencedbythemechanicsinvolveddevelopmentofoil_gasandgroundwaterresources,controlonseawaterintrusionandsubsidenceandgeologichazards,geotechnicalengineeringandbioengineering ,andairlineindustry[1～ 7].Aproblemonnonlinearflowinlow_permeabilityporousmediaisbutonlyabasiconeindifferentkindsofengineeringfields,butalsooneoffrontlineresearchfieldsofmod…