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     

Freezing limit of water in a closed circular tube

This paper is concerned with the freezing of water in a closed metal tube by regarding the effect of volumetric change of water which is closely related with solidification. The pressure of unfrozen water in the tube increases gradually with increasing frozen layer, consequently the freezing temperature of the water decreases monotonically. It is found from the present results that the freezing limit of water corresponding to the cease of freezing caused by no temperature difference between environmental temperature and freezing point would exist. This remarkable phenomena are mainly attributed to the combined effect of environmental temperature and inner diameter of the tube.     

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.     

Unsteady motion of a viscous incompressible fluid in a tube with a deformable wall

A flow of a viscous incompressible fluid in a deformable tube is considered. Solutions of unsteady three-dimensional Navier-Stokes equations are obtained for low-Reynolds-number flows in the tube (under the condition of small deformations of the wall): generalized peristaltic flow and flow with elliptical deformations of the vessel walls. At small unsteady deformations of the tube walls, the solutions satisfy the equations and boundary conditions with an error smaller than the tube wall deformation level by an order of magnitude. In the case of elliptical deformations of the vessel, the solution agrees well with experimental data.     

Unsteady motion of viscous fluid in an expanding tube

The problem of unsteady motion of a viscous compressible fluid in a semiinfinite tube with horizontal axis is solved by successive approximation. The circular cross section of the tube depends exponentially on the coordinate measured along the tube axis. At the end of the tube there is a unit such as a sliding valve, compressor, reciprocating pump, or turbine that changes the flow rate. The process is assumed to be barotropic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 79–82, May–June, 1983.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

Unsteady flow around models in an electromagnetic shock tube

Results of experimental studies of the unsteady flow around models of a stream moving behind the front of a very strong shock wave excited in an electromagnetic shock tube are presented. The flow establishment time in the stagnation-point region of blunt bodies is found.     

Stress state in a closed cylindrical shell with a system of cracks

International Applied Mechanics -     

Longitudinal diffusion of solid particle admixture in a flow through a tube

The propagation of solid particle admixture in a flow through a flat channel is studied.The processes of diffusion and convective transfer as well as solid particle deposition due to gravity result in varying admixture concentration both in depth and longtitudinally.The study of admixture longitudinal distribution is of great interest in a lot of applications, therefore this paper gives the derivation of longitudinal diffusion equation for a mean cross-section admixture concentration.The equation contains three effective parameters; i.e. convective tranfer velocity, longitudinal diffusion coefficient and particle deposition time. These parameters integrally reflect local processes of matter transfer as well as momentum.The proposed model is specific and differs from Taylor equation for longitudinal diffusion, since the fact of particle deposition and adhesion is taken into account. As a result of particle deposition a sediment layer is formed on the channel bottom which increases in thickness with time. To describe this process balance conditions for the whole flow mass and admixture mass on sediment sediment surface are formulated and a condition for matter movement towards the channel bottom is derived that is different from zero due to particle adhesion.     

方管内汽油-空气混合气体密闭爆炸和泄爆特性研究

为研究汽油-空气混合气体密闭爆炸和泄爆特性,采用可视化方管进行了两种爆炸模式实验研究,并基于壁面自适应局部涡黏(wall-adapting local eddy-viscosity,WALE)模型和Zimont预混火焰模型进行了数值模拟研究。结果表明：（1）泄爆工况超压-时序曲线峰值数量多于密闭爆炸工况,且泄爆工况超压-时序曲线存在剧烈的类似简谐振动的振荡,而密闭爆炸工况的爆炸超压特征参数显著高于泄爆工况;（2）密闭爆炸工况最大火焰传播速度明显小于泄爆工况,但前者在火焰传播初期即达到最大值,而后者在火焰传播末期才达到最大值;（3）密闭爆炸工况出现郁金香形火焰,而泄爆工况出现蘑菇形火焰,郁金香火焰的形成与管道内火焰锋面、流场和流场动压三者之间耦合效应相关,蘑菇形火焰由外部流场湍流和斜压效应的共同作用引起。

     

Nonlinear gas oscillations in a closed tube driven by the aperiodic motion of a piston

Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation law in place of the entropy conservation laws. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484).     

Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium

The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer.Untersucht wurden kombinierte Effekte der Permeabilität des Mediums, des magnetischen Feldes, der Auftriebskräfte und der Dissipation auf die instationäre Mischkonvektions-Strömung über einen horizontalen Zylinder und eine Kugel, die in einem porösen Medium eingebettet sind. Die nichtlinearen gekoppelten partiellen Differentialgleichungen mit drei unabhängigen Variablen wurden numerisch unter Benutzung eines impliziten Finite-Differenzen-Verfahrens in Verbindung mit der Quasi-Linearisierungstechnik gelöst. Die Oberflächenreibung und die Wärme- und Stoffübertragung steigen mit der Permeabilität des Mediums, dem magnetischen Feld und dem Auftriebsparameter an. Die Wärme- und Stoffübertragung fällt stetig in Strömungsrichtung ab, wohingegen die Oberflächenreibung von Null ansteigt, ein Maximum erreicht und wieder auf Null abfällt. Die Oberflächenreibung und die Wärme- und Stoffübertragung werden signifikant von der Verteilung der Freistromgeschwindigkeit beeinflut. Es wurde festgestellt, das der Dissipations-Parameter stärker die Wärmeübertragung als die Oberflächenreibung und die Stoffübertragung beeinflut.     

Condensation phenomena in capillaries with diffusion of water vapour in air under influence of a constant temperature gradient

A capillary tube filled with water and air is subjected to a temperature varying linearly along its wall. The temperature is highest at the water-filled end. The axis of the capillary may be placed horizontally or vertically. The rate of water transport in the stationary state can be explained by diffusion of water vapour in air. Formation of water droplets on the capillary wall in the air-filled part is observed in a number of cases. The observed position of the boundary between the wet and the dry part of the capillary wall agrees well with the one calculated from diffusion theory. However, the accuracy of the theoretical results is limited because of uncertainties with regard to the true value of the diffusion coefficient of water vapour in air and the unknown influence of diffuso-phoresis.     

Forced convection film condensation of flowing vapour on an inclined circular tube

In this work, an analytical study is made on the process of forced-convection-dominated laminar-film condensation on an inclined circular tube for a pure saturated vapour with vertical downflow. The resultant partial differential equation for the local film thickness has been solved analytically by applying the method of characteristics. Thus, an explicit analytical solution; in closed-form, has been obtained for calculating the local and average Nusselt numbers. The general solution yields, in special cases, the known analytical solutions of vertical and horizontal tubes. The results show that an optimum inclination of the tube, at which the rate of condensation on the whole surface is maximum, is a function of the ratio L/D. Received on 14 April 1999     

Stability of stationary state solution for a reaction density-dependent diffusion equation

In this paper we are interested in the large time behavior of the nonlinear diffusionequationu_1=(φ(u))_xx φ(u), x∈R,t∈R~ =(0, ∞))We consider functionsφ(u)andφ(u)which allow the equation to possess travelingwave solutions.We first present an existence and uniqueness as well as some comparisonprinciple result of generalized solutions to the Cauchy problem.Then we give forφ(u)=u(1-u)(u-a)some threshold results,from which we can see that u=a is stable,while u=0 or u=1 is unstable under some assumptions,etc.