Fiber suspension flow in a tapered channel: The effect of flow/fiber coupling

A numerical model for predicting the flow and orientation state of semi-dilute, rigid fiber suspensions in a tapered channel is presented. The effect of the two-way flow/fiber coupling is investigated for low Reynolds number flow using the constitutive model of Shaqfeh and Fredrickson. An orientation distribution function is used to describe the local orientation state of the suspension and evolves according to a Fokker–Plank type equation. The planar orientation distribution function is determined along streamlines of the flow and is coupled with the fluid momentum equations through a fourth-order orientation tensor. The coupling term accounts for the two-way interaction and momentum exchange between the fluid and fiber phases. The fibers are free to interact through long range hydrodynamic fiber–fiber interactions which are modeled using a rotary diffusion coefficient, an approach outlined by Folgar and Tucker. Numerical predictions are made for two different orientation states at the inlet to the contraction, namely a fully random and a partially aligned fiber orientation state. Results from these numerical predictions show that the streamlines of the flow are altered and that velocity profiles change from Jeffery–Hamel, to something resembling a plug flow when the fiber phase is considered in the fluid momentum equations. This phenomenon was found when the suspension enters the channel in either a pre-aligned, or in a fully random orientation state. When the suspension enters the channel in an aligned orientation state, fiber orientation is shown to be only marginally changed when the two-way coupling is included. However, significant differences between coupled and uncoupled predictions of fiber orientation were found when the suspension enters the channel in a random orientation state. In this case, the suspension was shown to align much more quickly when the mutual coupling was accounted for and profiles of the orientation anisotropy were considerably different both qualitatively and quantitatively.     

Steady Natural Convection Flow of a Particulate Suspension Through a Parallel-Plate Channel

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long channel. The walls of the channel are maintained at constant but different temperatures. The two-phase model accounts for particle-phase viscous effects. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Various closed-form solutions for different special cases are obtained. A parametric study of the physical parameters involved in the problem are performed to illustrate the influence of these parameters on the flow and heat transfer aspects of the problem.     

Entropy maximum principle for a steady gas flow in a channel

An expression is derived for the maximum admissible increment of entropy in a steady gas flow in a variable-section channel with energy supply and with dissipation of kinetic energy. A condition of the transition through the velocity of sound is obtained for a quasi-one-dimensional flow. Examples of flows are considered.     

Evaporation from a surface and vapor flow through a plane channel into a vacuum

Two-dimensional steady rarefied-gas channel flow between two parallel walls, from an evaporating face to a perfectly absorbing plane end face, is studied. The vapor is considered to be a monatomic gas. The corresponding problem for the kinetic equation with collision integral in BGK form is formulated and solved numerically by two different finite-difference methods. Attention is focused on the calculation of the total gas flow rate through the channel cross-section. The structure of the gas channel flow as a function of the flow rarefaction, the channel length, and the ratio of the evaporation temperature to the wall temperature is studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–158, January–February, 1996.     

Lifting of Disperse Particles from a Cavity Behind the Front of an Unsteady Shock Wave with a Triangular Velocity Profile

The gas flow in plane shock waves slipping along an impermeable surface with a rectangular cavity where solid disperse particles are suspended is considered numerically. The motion of the gas and particles (gas suspension) is modeled by equations of mechanics of multiphase media. Some laws of the behavior of the dusty cloud in the cavity are established for the case of wave interaction with the cavity.     

A Kinetic Approach to the Plane Poiseuille Flow Over a Porous Matrix

The Poiseuille–Couette gas flow in a channel and the gas flow through an adjacent porous medium are considered when the governing equations are obtained via a molecular kinetic approach based on the Boltzmann equation. The mass continuity, momentum balance and energy conservation are written for the gas in the contiguous regions, whereas the behavior of the solid matrix obeys to the heat diffusion equation. Two different space scalings lead to different forms of the equations for the steady flow through the fully saturated matrix. The boundary conditions at the interface between the two domains are investigated via a matching procedure.     

Numerical study of particulate suspension flow through wavy‐walled channels

The particulate suspension flow in a channel whose walls describe a travelling wave motion is examined numerically. A perturbation method is employed and the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first‐order perturbation quantities are numerically determined by solving the governing system of ordinary differential equations by shooting technique. The present approach does not impose any restriction on the Reynolds number of the flow and the wave number and frequency of the wavy‐walled channel, although it is limited by the linear analysis. The wall shear stress and the positions of flow separation and reattachment points are computed and the influence of the volume fraction density of the particles is examined. The variations of velocity and pressure of the particulate suspension flow with frequency of excitation are also presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Two-dimensional subcritical and supercritical open channel flow calculation using a time-marching method

A time-marching method is presented for the calculation of two-dimensional, high-speed channel flow, including the usually neglected terms of slope and bottom friction. Time-marching methods are potentially the most flexible means of calculating flow through geometrically complex channel passages, since they can readily deal with subcritical and supercritical flows. The adopted numerical scheme comes straight from gas flow computations in turbomachines. The flow is assumed to be fully mixed in the vertical direction, so that vertical variations may be neglected. Comparisons with other numerical solutions for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique. It can be utilized for open channel designs.     

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.     

Dusty-gas flow in a channel with horizontalwalls

An unsteady motion of a dilute gas-particle mixture in a plane channel under the action of a constant longitudinal pressure gradient and the transverse gravity force is studied theoretically. Within the Euler approach, a combined problem of finding the velocity components of the gas and the dust phase is formulated. The flow similarity parameters are found. The solution of the problem formulated is calculated using a finite-difference method. Asymptotic formulas are obtained, which describe the two-phase flow parameters for limiting values of the similarity parameters. The cases of both monodisperse and polydisperse particles are considered.     

A steady laminar flow of a suspension in a channel

A two dimensional model of a steady flow of a suspension in an inclined channel is developed and studied with the aid of an integral method. The model explains the existence of two operational modes in such a channel, predicted earlier by Probstein et al. (1977).     

Investigation of the stability of a plane-channel suspension flow with account for finite particle volume fraction

Within the framework of the two-fluid approach, a variant of a heterogeneous-medium model which takes into account a finite volume fraction of the inclusions and a small but finite phase velocity slip is proposed. The interphase momentum exchange is described by the Stokes force with the Brinkman correction for the finite particle volume fraction. The suspension viscosity depends on the particle volume fraction in accordance with the Einstein formula. Within the framework of the model constructed, a formulation of the problem of linear stability of plane-parallel two-phase flows is proposed. As an example, the stability of a channel suspension flow is considered. The system of equations for small disturbances with the boundary conditions is reduced to an eigenvalue problem for a fourth-order ordinary differential equation. Using the orthogonalization method, the dependence of the critical Reynolds number on the governing nondimensional parameters of the problem is studied numerically. It is shown that taking a finite volume fraction of the inclusions into account significantly affects the laminar-turbulent transition limit.     

On the orientation probability distribution of flexible fibres in a contracting channel flow

The development of fibre orientation distribution in a plane contracting channel flow is investigated with combining experiments and modelling. A dilute suspension of flexible wood fibres is used in the experiments. The salient feature of the suspension is the flexibility of the fibres. To model the fibre orientation probability distribution (FOPD) a diffusion–convection equation is used. The effect of random motion, in this case turbulence, is considered with translational and rotational diffusion coefficients. In addition to providing the inlet conditions, experiments are used to determine the rotational diffusion coefficient for the model. The work addresses the problems related to the above mentioned modelling method and combines the experiments and modelling in order to understand the mechanisms affecting the development of fibre orientation.     

Rarefied gas flow into a vacuum from a plane long channel closed at one end

The time-dependent problem of rarefied gas flow into a vacuum from a plane long channel closed at one end is solved on the basis of the kinetic S-model. The effect of diffuse molecular reflection from the channel walls on the flow velocity and the process of channel cavity vacuumization is studied as a function of the channel length and the extent of gas rarefaction under the condition that the wall temperature is maintained to be constant. The kinetic equation is solved numerically using a conservative finite-difference method of the second order of accuracy in spatial coordinates. The possibility of simplification of the problem for long times by means of reduction to the diffusion process is considered.     

Multi-fluid model of suspension filtration in a porous medium

In the framework of a three-fluid approach, a new model of suspension filtration in a porous medium is constructed with account for the formation of a dense packing of trapped particles with finite permeability and porosity. The following three continua are considered: the carrier fluid, the suspended particles, and the deposited particles. For a one-dimensional transient flow of suspension, a system of equations for the concentrations of the suspended and deposited particles, the suspension velocity, and the pressure is constructed. Two cases of the flow in a porous medium are considered: plane and radial. Numerical solution is found using a finite-difference method. Numerical calculations are shown to be in agreement with an analytical solution for the simplest case of filtration with a constant velocity and constant porosity and permeability. A comparison is performed with the classic filtration models for five sets of experimental data on the contamination of a porous sample. It is shown that near the inlet boundary, where an intense deposition of particles takes place, the new model describes the concentration profile of the deposited particles more accurately than the classical model.     

Numerical simulation of effects of flow maldistribution on heat and mass transfer in a PEM fuel cell stack

A 3D numerical study was carried out to analyze flow, heat and mass transfer first in a single half-cell cathode channel of proton exchange membrane (PEM) fuel cell. From practical point of view, it is necessary to put the appropriate number of cells in a stack. Hence, the above study on a single half-cell is extended to a stack of channels. Due to stacking, the assumption of uniform flow distribution would no longer hold true. Therefore, the channel flow-maldistribution is considered. The water formed at the active surface due to the electrochemical reaction diffuses through the porous layer and eventually enters the gas flow duct. The higher gas velocities in the duct result in faster water vapour removal which leads to a lower value of water vapour into the duct and hence a lower Nusselt number.     

Acceleration of a conducting gas in a strong nonstationary electromagnetic field

The problem of nonstationary acceleration of a conducting gas in a channel is solved, together with the problem of a discharge in an electric-circuit. As distinct from other papers, in which the typical solution assumed a thin cluster subject to acceleration, we examine the case in which the gas flow fills the entire channel. The motion of the gas in the channel is examined in one-dimensional formulation, under the assumption that the particle transit time in the channel is small compared to the discharge time and that the electromagnetic force is large compared to the pressure gradient.For impulsive acceleration of the conducting gas, use is made of a discharge with a certain capacitance. Since the (time-variable) resistance of the channel and, consequently, the behavior of the discharge depend upon the channel flow of the conducting gas, the correct solution of the problem of gas acceleration in the induced electromagnetic field can be obtained only by analyzing simultaneously the magnetogasdynamic channel flow and the discharge process in the entire electric circuit. On the other hand, the acceleration of the gas itself is a function of the instantaneous potential difference at the electrodes. Hitherto, such simultaneous solutions were obtained by many investigators under the assumption, proposed in [1], that a channel gas flow may be treated as the motion of a unique narrow cluster, whose length is negligible as compared to the channel length. Experiments and theoretical estimates show, however, that in many cases the conducting gas fills the entire channel length during the acceleration process, so that the assumption of a narrow cluster is not even approximately fulfilled [4, 5].     

Effect of the form of the electrodes on the current distribution in a magnetogasdynamic channel

A solution is given to the plane problem of the flow of a conducting gas across a homogeneous magnetic field in a magnetogasdynamic channel taking account of the Hall effect at small magnetic Reynolds numbers. The channel is formed by two long electrodes, and the cross section of the channel varies slightly and periodically along the gas flow. It is assumed that the electromagnetic forces are small. It is shown that the current distribution in the channel is nonuniform to a consider able degree and that inverse currents can form at the electrodes, with both subsonic and supersonic flows of the conducting gas. Transverse motion of the gas, due to a change in the cross section of the channel, leads to an increase of Joule energy losses. In [1] the current distribution was obtained in a flat channel formed by infinite dielectric walls, with the flow of a steady-state stream of plasma through the channel across a homogeneous magnetic field. With interaction between the flow and the magnetic field, closed current loops develop in the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 26–33, November–December, 1970.     

Numerical simulation of the flow in a variable-section channel with pulsed-periodic energy supply

Results of numerical simulations of a quasi-one-dimensional unsteady flow in a channel considered as an element of an air-breathing engine are presented. The influence of parameters of energy supplied in the pulsed-periodic mode (power, pulse frequency, and distribution of energy sources along the channel) on the characteristics of the flow with Mach numbers M ₀ = 2.4–4.0 at the channel entrance is determined. A channel configuration that allows the energy supply distribution to be found from the condition of restriction of the maximum value of the gas temperature is proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 3–11, January–February, 2009.