Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.     

Slow Viscous Flow through Arbitrary Triangular Tubes and Its Application in Modelling Porous Media Flows

In this article we extend the analytical solution for viscous flow in an equilateral triangular tube to irregular triangular tubes. The validity of the solution is examined and proved by comparison with the numerical simulation results. With the new extension of the equations, the average velocity of viscous flow through an arbitrary triangular tube can be readily calculated as a function of inscribed radius of the triangular cross-section of the tube, and the volumetric flow rate is computed as a function of inscribed radius and the cross- sectional area. To illustrate the advantages in using an arbitrary triangular tube for modelling a porous medium, we present examples of tube bundle models, which give a wide range of variation in porosity and permeability with a fixed pore size distribution, by using various combinations of three types of triangular tubes.     

Frictional resistance to accelerated flow in a tube

A study is made of the development of the flow of a viscous incompressible fluid from the state of rest in a circular cylindrical tube with constant pressure gradient. The tangential frictional stress at an arbitrary point of the flow is found as a function of the pressure gradient and the ratio of the values, averaged over the flow, of the accelerations corresponding to the considered time and the initial time. An analysis is made of the exact solution of the linear equation [1], which shows that the development of the drag forces in the case of viscous flow is determined by a characteristic time which depends on the kinematic viscosity and the tube radius. The value of the hydraulic friction drag coefficient for the unsteady flow is determined more accurately by introducing a correction that takes into account the velocity profile of the flow. The equations of motion are analyzed, and six different cases of development of the flow are described for the characteristic values of the dimensionless numbers. These cases determine the methods of calculation of one-dimensional problems. This question has not been fully clarified in earlier work [2, 3].     

Axial buckling of perforated plates reinforced with strips and middle tubes

Global buckling of perforated plates reinforced with circumferential strip or short tube is investigated. Effects of the hole radius, width of the strip, thickness and radius of the tube and boundary conditions are studied numerically and experimentally. Axial buckling loads of the holed plates decrease versus the hole radius. By using the strip or tube, the buckling strength increases significantly. In some cases, the stiffened plate has buckling load greater than the perfect plate. Numerical studies showed that the increasing restraints at the boundaries increase the buckling strength in any case and geometry of the plate.     

Thermal analysis of an infinite tube during quenching

 This paper deals with a numerical solution of the two-dimensional convection–diffusion equation in an infinite domain, arising out of quenching of an infinite tube. On the wetted side, upstream of the quench front, a constant heat transfer coefficient is assumed. The downstream of the quench front as well as the inside surface of the tube are assumed to be adiabatic. The solution gives the quench front temperature as a function of various model parameters such as Peclet number, Biot number and the radius ratio. The solution has been found to be in good agreement with the available analytical solutions and thus validates the numerical procedure suggested. Received on 10 July 2000     

Wave propagation in a fluid flowing through a curved thin-walled elastic tube

The pulsatile flow in a curved elastic pipe of circular cross section is investigated. The unsteady flow of a viscous fluid and the wall motion equations are written in a toroidal coordinate system, superimposed and linearized over a steady state solution. Being the main application relative to the vascular system, the radius of the pipe is assumed small compared with the radius of curvature. This allows an asymptotic analysis over the curvature parameter. The model results an extension of the Womersley's model for the straight elastic tube. A numerical solution is found for the first order approximation and computational results are finally presented, demonstrating the role of curvature in the wave propagation and in the development of a secondary flow.     

Incompressible low-speed-ratio flow in non-uniform distensible tubes

The fluid flow in distensible tubes is analysed by a finite element method based on an uncoupled solution of the equations of wall motion and fluid flow. Special attention is paid to the choice of proper boundary conditions. Computations were made for sinusoidal flow in a distensible uniform tube with the Womersley parameter α = 5, and a ratio between tube radius and wavelenth from 0·0001 to 0·5. The agreement between the numerical results and Womersley's analytic solution depends on the speed ratio between fluid and wave velocity, and is fair for speed ratios up to 0·05. The analysis of the flow field in a distensible tube with a local inhomogeneity revealed a marked influence of wave phenomena and wall motion on the velocity profiles.     

Charged droplets evaporation and motion in an electric field

Monodisperse spray evaporation is investigated theoretically when a pure liquid or an electrolyte solution spray is charged and moves through an electric field. The solution of the equations in the case of electrolyte solutions gives the droplet size evolution down to the “equilibrium radius” when the relative humidity is high and down to the saline kernel when the humidity is lower. This solution also gives the dynamic behaviour in an electric field when the droplets are charged and are moving in a gas stream. A non dimensional curve is obtained for a given humidity, molality and temperature, independently of the electric field. With this curve it is possible to predict the droplet evolution only knowing a “middle time” of evaporation, calculated for a given electric force and a given initial radius.     

Non-linear waves in a fluid-filled inhomogeneous elastic tube with variable radius

In the present work, by employing the non-linear equations of motion of an incompressible, inhomogeneous, isotropic and prestressed thin elastic tube with variable radius and the approximate equations of an inviscid fluid, which is assumed to be a model for blood, we studied the propagation of non-linear waves in such a medium, in the longwave approximation. Utilizing the reductive perturbation method we obtained the variable coefficient Korteweg–de Vries (KdV) equation as the evolution equation. By seeking a progressive wave type of solution to this evolution equation, we observed that the wave speed decreases for increasing radius and shear modulus, while it increases for decreasing inner radius and the shear modulus.     

Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube

The effect of yield stress on the flow characteristics of a Casson fluid in a homogeneous porous medium bounded by a circular tube is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. The non-linear coupled implicit system of differential equations governing the flow is first transformed into suitable integral equations and are solved numerically. Analytical solution is obtained for a Newtonian fluid in the case of constant permeability, and the numerical solution is verified with that of the analytic solution. The effect of yield stress of the fluid and permeability of the porous medium on shear stress and velocity distributions, plug flow radius and flow rate are examined. The minimum pressure gradient required to start the flow is found to be independent of the permeability of the porous medium and is equal to the yield stress of the fluid.     

The influence of rotation on turbulent flow and heat transfer in an annulus between independently rotating tubes

Experimental and numerical investigations of turbulent flow and heat transfer have been performed in a concentric annulus between independently rotating tubes. Numerical predictions, applying a Reynolds stress turbulence model, are compared with experimental fluid flow and heat transfer results for the case of a heated outer tube and an adiabatic inner tube. Compared to the above mentioned boundary conditions for the conservation equation of energy, differences in heat transfer in case of a heated inner tube and an adiabatic outer one, are examined by analysis, applying a mixing length turbulence model. Numerical investigations with both kinds of models about the influence of annulus radius ratio make evident that due to different superimpositions of centrifugal force and additional shear stress there is a wide variation of effects on fluid flow and heat transfer caused by the rotation of the inner and the outer tube.     

On the motion of thin vortex tubes

The motion of a tube of vorticity with a cross sectional radius that is everywhere small compared to local radius of curvature of the tube is considered. In particular, we determine the inviscid motion of the 3D space curve that traces the centerline of the tube for an arbitrary distribution of axial vorticity within the core.     

The stokes flow from half-space into semi-infinite circular cylinder

The infinite-series solutions for the creeping motion of a viscous incompressible fluid from half-space into semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%. The inlet length in this case is comparable to that computed for a finite circular cylinder pore by Dagan et al.^[1]. In the half-space outside the cylinder pore region, the flow is strongly affected by the wall. Beyond one radius of the tube from the orifice, the solutions match almost exactly the flow through an orifice of zero thickness given by Sampson^[2]. The relationship between the pressure drop and the volumetric flow rate is also computed in the present paper for the semi-infinite tube.     

Motion of a spherical solid particle in a nonuniform flow of a viscous incompressible liquid

The effect of a particle on the basic flow is studied, and the equations of motion of the particle are formulated. The problem is solved in the Stokes approximation with an accuracy up to the cube of the ratio of the radius of the sphere to the distance from the center of the sphere to peculiarities in the basic flow. An analogous problem concerning the motion of a sphere in a nonuniform flow of an ideal liquid has been discussed in [1]. We note that the solution is known in the case of flow around two spheres by a uniform flow of a viscous incompressible liquid [2], and we also note the papers [3, 4] on the motion of a small particle in a cylindrical tube.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 71–74, July–August, 1976.     

Laminar compressible flow in a tube

A two-dimensional solution for the velocity and pressure distributions in steady, laminar, isothermal flow of an ideal gas in a long tube is obtained as a double perturbation expension in β, the radius to length ratio, and ε, the relative pressure drop. It is found that simple approximations estimate the exact flow rate-pressure drop relationship accurately.     

Wave propagation in an elastic tube: a numerical study

In this paper, a fluid–wall interaction model, called the elastic tube model, is introduced to investigate wave propagation in an elastic tube and the effects of different parameters. The unsteady flow was assumed to be laminar, Newtonian and incompressible, and the vessel wall to be linear-elastic, isotropic and incompressible. A fluid–wall interaction scheme is constructed using a finite element method. The results demonstrate that the elastic tube plays an important role in wave propagation. It is shown that there is a time delay between the velocity waveforms at two different locations and that the peak velocity increases while the low velocity decreases in the elastic tube model, contrary to the rigid tube model where velocity waveforms overlap each other. Compared with the elastic tube model, the increase of the wall thickness makes wave propagation faster and the time delay cannot be observed clearly, however, the velocity amplitude is reduced slightly due to the decrease of the internal radius. The fluid–wall interaction model simulates wave propagation successfully and can be extended to study other mechanical properties considering complicated geometrical and material factors.     

Computational study of reacting flow establishment in expansion tube facilities

We study the temporal evolution of the combustion flowfield established by the interaction of ram accelerator-type projectiles with an explosive gas mixture accelerated to hypersonic speeds in an expansion tube. The Navier-Stokes equations for a chemically reacting gas mixture are solved in a fully coupled manner using an implicit, time accurate algorithm. The solution procedure is based on a spatially second order, total variation diminishing scheme and a temporally second order, variable-step, backward differentiation formula method. The hydrogen-oxygen-argon chemistry is modeled with a 9-species, 19-step mechanism. The accuracy of the solution method is first demonstrated by several benchmark calculations. Numerical simulations of expansion tube flowfields are then presented for two different geometries: an axisymmetric projectile and a ram accelerator configuration. The development of the shock-induced combustion process is followed. The temporal variations of the calculated thrust and drag forces on the ram accelerator projectile are also presented. In the axisymmetric projectile case, which was designed to ensure combustion only in the boundary layer, the radial extent of the flame front during the initial transient phase was surprisingly large. In the ram accelerator configuration the flame propagated upstream along both the projectile and tube wall boundary layers, resulting in unstart. Received 25 September 1996 / Accepted 15 January 1997     

颗粒毛细效应影响因素的离散元分析

颗粒毛细效应是指将一根细管插入填充有颗粒物质的容器中并对管施加竖直振动时颗粒在管内上升并最终达到一个稳定的高度的现象,该现象为颗粒物料的逆重力输运提供了一种潜在的技术途径.为探究颗粒毛细效应的影响因素,采用离散元方法,模拟再现了颗粒毛细效应过程,展示了不同管径下颗粒竖直方向速度演变特性,考察了不同容器宽度和振动条件下颗粒最终毛细上升高度随管径的演变规律.结果表明,在容器宽度与粒径比为40、管振幅与粒径比为14.33、管振动频率为12 Hz情况下,管径与粒径比D/d=3.33时,管内颗粒堵塞严重,使得颗粒上升缓慢,并造成颗粒柱中断; D/d=8.33时,起初毛细上升高度增加迅速,随后毛细上升高度的增大逐渐减缓,管内颗粒在管径方向几乎不存在速度梯度; D/d=15时,随着颗粒毛细上升高度的增大,管内颗粒柱分离为速度截然不同的两层,上层颗粒在管径方向几乎不存在速度梯度,而下层颗粒存在明显的速度梯度.研究还发现,在毛细效应能够发生的管径范围内,存在一个对应于颗粒最终毛细上升高度最大值的临界管径,当管径小于临界管径时,颗粒最终毛细上升高度随管径的增大而增大,当管径大于临界管径时,颗粒最终毛细上升...     

Three-dimensional motion of a viscous incompressible fluid in a narrow tube

An approximate solution of the problem of unsteady motion of a viscous incompressible fluid in a long narrow deformable tube at low Reynolds numbers is obtained. Pressure oscillations and tube deformation are shown to be related by an integrodifferential equation. The solution obtained extends the Poiseuille solution in elliptic tubes to the case of comparatively arbitrary small deformations in terms of the tube length and angle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 28–32, July–August, 2009.     

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.