Filtration model of longitudinal flow in a finned cylindrical channel

The problem of laminar flow of a viscous incompressible fluid in a finned circular tube is considered. A solution is obtained in the form of series in eigenfunctions of the Laplace operator; the coefficients in the series are found numerically. For the same problem, a simpler filtration approximation is proposed in which the system of fins is modeled by a radially inhomogeneous porous layer, and fluid flow in it is described by the Brinkman equation. A formula for the effective permeability of the porous medium is obtained by varying the number and height of fins. The formula provides an accurate evaluation of the mean flow velocity and viscous drag coefficient in finned channels.     

A numerical study of the longitudinal thermoconvective rolls in a mixed convection flow in a horizontal channel with a free surface

This paper presents a numerical study of three-dimensional laminar mixed convection within a liquid flowing on a horizontal channel heated uniformly from below. The upper surface is free and assumed to be flat. The coupled Navier–Stokes and energy equations are solved numerically by the finite volume method taking into account the thermocapillary effects (Marangoni effect). When the strength of the buoyancy, thermocapillary effects and forced convective currents are comparable (Ri ⋍ O(1) and Bd = Ra/Ma ⋍ O(1)), the results show that the development of instabilities in the form of steady longitudinal convective rolls is similar to those encountered in the Poiseuille–Rayleigh–Bénard flow. The number and spatial distribution of these rolls along the channel depend on the flow conditions. The objective of this work is to study the influence of parameters, such as the Reynolds, Rayleigh and Biot numbers, on the flow patterns and heat transfer characteristics. The effects of variations in the surface tension with temperature gradients (Marangoni effect) are also considered.     

Hydromagnetic flow in a rotating channel

The steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains two parameters: the Hartmann number, M ², and K ² which is the reciprocal of the Ekman number. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values of the parameters, there arise thin boundary layers on the walls of the channel.     

Magnetohydrodynamic entrance flow in a channel

A MHD entrance flow in a channel is studied in the Prandtl approximation. It is shown that consistency with the approximation requires an appropriate change in the boundary conditions which hold for the original, unsimplified equations. The correct boundary conditions are established and used to repete the numerical calculations in a few cases studied by other authors with the unmodified boundary conditions. In the cases here considered the numerical differences do not amount in practice to more than 10%, though they grow with increasing Hartmann number. Gabinete de Aplicaciones Nucleares de O.P. and Centro Coordinado de Fisica (C.S.I.C.-U.A.M.). Present address: Departamento de Física, Facultad de Ciencias, Universidad Autónoma de Madrid.     

Density-stratified Sadovskii flow in a channel

Stably density-stratified and nonstratified flows in a channel past a pair of symmetrical closed-streamline vortices on the channel axis are considered. The numerical results obtained cover the whole range of subcritical stratification and eddy lengths. An asymptotic solution for a very long closed-streamline region is found. The results can be used directly in the asymptotic theory of separated flows at high Reynolds number. Sadovskii flows are plane potential inviscid flows past a pair of closed-streamline regions of uniform vorticity. The flow velocity may be discontinuous at the boundary of the closed-streamline region. The analysis below is restricted to the specific case of continuous velocity distribution, so that the Bernoulli constant jump at the eddy boundary is zero. Unbounded nonstratified flows of this kind were studied in [1, 2]. Calculations of the corresponding channel flow were restricted to relatively wide channels. Closely related problems were also considered in [3, 4].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 118–123, May–June, 1993.     

Gas flow in a bent channel

The results are given of experimental investigations of flow of gas (air) in a curvilinear cylindrical channel. Patterns of the streamlines near the wall and the separation region were obtained by blowing cold air through a transparent model. In an investigation of the flow of hightemperature gas, in which an electric arc heater was used to supply the thermal energy, the profiles of the total pressure and the stagnation temperature were measured at different sections of the channel. It was found that the deformation of the profiles after the bend ends earlier for the hot gas than for the cold. The heat flux increases sharply after the bend.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–157, September–October, 1981.I thank A. B. Vatazhin for helpful discussions.     

Two-fluid oscillatory flow in a channel

The validity of Navier's partial slip condition is investigated by studying the oscillatory flow in a coated channel. The two-fluid model is used to solve the unsteady viscous equations exactly. Partial slip is experienced by the core fluid. It is found that Naviers condition does not hold for an unsteady core fluid.     

Asymptotic form of the admixture transport equation for a channel flow with an anisotropic diffusion tensor

The problem of the asymptotically correct reduction of a 3-D mass (heat) transfer equation to a 1-D equation in a flow with anisotropic diffusion properties is considered. The convective mass (heat) transfer domain is a cylindrical channel of arbitrary cross section. The diffusion coefficient matrix is assumed to be independent of the spatial coordinates. In the equivalent diffusion equation constructed, a certain effective diffusion (dispersion [1]) coefficient is introduced. Formulas for this coefficient are obtained. A relation between the effective diffusion coefficient calculations and the problem of minimization of a certain functional is established, i. e. the possibility of calculations based on variational methods is noted. An example of an exact calculation of the effective diffusion coefficient is considered. The possibility of a generalization of the problem, in which the effective diffusion (heat conduction) equation is essentially a nonlinear equation of general form for the one-dimensional case, is indicated. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 110–123, March–April, 2000.     

Calculation of the flow within the channel of an axisymmetric entrance diffuser

One of the possible flow schemes within the channel of a supersonic axisymmetric entrance diffuser is considered. The channel is formed by the surfaces of the central body of the diffuser and its outer surface and has an annular section. Axisymmetric flow in the channel of such a diffuser is calculated in the presence of an oblique shock in front of the separation region formed at the corner of the central body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 164–168, January–February, 1981.We thank É. A. Ashratov for valuable comments and assistance in preparing the program and discussing the results of the computer calculations.     

Longitudinal diffusion in a flow through a tube

The results of research concerned with a fluid mixing during the movement in a tube, are given. A method of definining the one-dimension theory of matter transfer, accounting for the difference of mixture component velocities is presented. The longitudinal transfer in a zone of “passive” fluids contact is discussed in detail. It has been possible to formulate the theory, which generalises the well-known Taylor and Aris models. The theory presented is based on the integro-differential equation, accounting for the delay effects. It has been possible to describe the experimental facts, which had no explanation so far, in bounds of the given theory.     

Turbulent mixing and diffusion combustion of a jet in a channel

An attempt is made to study in some detail the turbulent mixing of reacting (propane) and inert jets (air and carbon dioxide) in a channel. The results are given of an experimental investigation into diffusion combustion in a channel, and these are compared with calculated data obtained using a semiempirical theory of turbulence. Such a comparison makes it possible to estimate the applicability of this theory for calculating the characteristics of diffusion combustion in a channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 25–33, July–August, 1980.We thank V. R. Kuznsatsov and A. N. Sekundov for great interest in the work and for discussing the results and V. I. Rasshchupkin for assisting in the experiments.     

Unsteady convective diffusion in a rotating parallel plate channel

The paper presents an exact analysis of the dispersion of a passive contaminant in a viscous fluid flowing in a parallel plate channel driven by a uniform pressure gradient. The channel rotates about an axis perpendicular to its walls with a uniform angular velocity resulting in a secondary flow. Using a generalized dispersion model which is valid for all time, we evaluate the longitudinal dispersion coefficientsK _i (i=1, 2, ...) as functions of time. It is shown thatK ₁=0 andK ₃,K ₄, ... decay rapidly in comparison withK ₂. ButK ₂ decreases with increasing (the dimensionless rotation parameter) for values of upto approximately =2.2. ThereafterK ₂ increases with further increase in and its value gets saturated for large values of (say, 500) and does not change any further with increase in . A physical explanation of this anomalous behaviour ofK ₂ is given.

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Instationäre konvektive Diffusion in einem rotierenden Parallelplattenkanal

Zusammenfassung In dieser Untersuchung wird eine exakte Analyse der Ausbreitung eines passiven Kontaminierungsstoffes in einer zähen Flüssigkeit gegeben, die, befördert durch einen gleichförmigen Druckgradienten, in einem Parallelplattenkanal strömt. Der Kanal rotiert mit gleichförmiger Winkelgeschwindigkeit um eine zu seinen Wänden senkrechte Achse, wodurch sich eine Sekundärströmung ausbildet. Unter Verwendung eines generalisierten, für alle Zeiten gültigen Dispersionsmodells werden die longitudinalen DispersionskoeffizientenK _i (i=1, 2, ...) als Funktionen der Zeit ermittelt. Es wird gezeigt, daßK ₁=0 gilt und dieK ₃,K ₄, ... gegenüberK ₂ schnell abnehmen.K ₂ nimmt ab, wenn , der dimensionslose Rotationsparameter, bis etwa zum Wert 2,2 ansteigt. Danach wächstK ₂ mit bis auf einem Endwert an, der etwa ab =500 erreicht wird. Dieses anomale Verhalten vonK ₂ findet eine physikalische Erklärung.

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List of symbols C solute concentration - D molecular diffusivity - K _i longitudinal dispersion coefficients - 2L depth of the channel - P ₀ dimensionless pressure gradient along main flow - Pe Péclet number - q velocity vector - Q _x,Q _y mass flux along the main flow and the secondary flow directions - dimensionless average velocity along the main flow direction - (x, y, z) Cartesian co-ordinates Greek symbols dimensionless rotation parameter - the inclination of side walls withx-axis - kinematic viscosity - fluid density - dimensionless time - angular velocity of the channel - dimensionless distance along the main flow direction - dimensionless distance along the vertical direction - dimensionless solute concentration - integral of the dispersion coefficientK ₂() over a time interval     

Time-dependent viscous flow in a straight channel

An infinite straight channel, filled with an incompressible viscous fluid, is closed at one end by a piston. This is set in motion with finite acceleration and then maintained at constant velocity until the flow pattern in the fluid reaches a steady state. The development of velocity profiles, stream lines, and streak lines is investigated by direct numerical solution of the complete Navier Stokes equations. It is found that the nonconvex velocity profiles found in previous work on steady-state problems appear from the beginning, and their development is studied. In the downstream region alternative methods can be used which serve as a check on the accuracy of the numerical procedures. The asymptotic behaviour downstream is studied in some detail.Nomenclature a acceleration of piston - f(t) nondimensional distance travelled by piston up to time t - 2l width of channel - p pressure (in units of u ₀ ² ) - R Reynolds number, lu ₀/ - t ₀ time during which piston is accelerated - u ₀ final velocity of piston - (u, v) (x, y) components of fluid velocity (relative to piston, in units of u ₀) - x distance measured downstream from piston (in units of l) - y distance from central axis of channel (in units of l) - vorticity - density of fluid - kinematic viscosity - stream function     

Convective magnetohydrodynamic flow in a vertical channel

An analysis is presented for the combined forced and free convective magnetohydrodynamic flow in a vertical, finite rectangular channel that is subjected simultaneously to a pressure gradient and a temperature gradient. Exact solutions are found for electrically nonconducting channel walls and perfectly conducting walls. In particular, the case of heating from below is examined and discussed.     

Oscillatory channel flow in a rotating system

Oscillatory channel flow in a rotating system is considered. The Navier–Stokes equations reduce to the Ekman equations that are solved exactly. The results show the interaction between oscillation frequency and rotation rate. Resonance occurs when the oscillation frequency is twice the rotation rate.     

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.     

Peristaltic flow of a Bingham fluid in a channel

We study the peristaltic transport of a Bingham fluid in a channel with small aspect ratio whose walls behave as a periodic traveling wave. The governing equations in the unyielded phase are obtained writing the integral formulation for the momentum balance. As shown in Fusi et al. (2015), this approach allows to overcome the so-called “lubrication paradox” which may arise in the thin film approximation. We consider the case in which the inlet flux is prescribed and the one in which the flow is driven by a given pressure drop. In both cases the solution of the problem is determined solving a nonlinear integral equation for the yield surface. We perform some numerical simulations to illustrate the behavior of the yield surface, assuming that the traveling wave describing the peristaltic motion has a sinusoidal shape.     

Viscoelastic flow in a two-dimensional collapsible channel

We compute the flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens blood model) in a two-dimensional channel partly bounded by a tensioned membrane, a benchmark geometry for fluid–structure interactions. The predicted flow patterns are compared to those of a Newtonian liquid. We find that computations fail beyond a limiting Weissenberg number. Flow fields and membrane shape differ significantly because of the different degree of shear thinning and molecular extensibility underlying the three different microstructural models.