Tube Of Elliptic Cross-section Research Articles

Capillary driven flow in oval tubes under microgravity

The capillary driven flow of a liquid in a tube of elliptical cross section under microgravity is studied in this paper. All the factors including the dynamic contact angle between the liquid and the tube wall, the pressure loss caused by convection, the viscous resistance in the tube and the reservoir, and the curved liquid surface in the reservoir are considered. The equation of capillary driven flow in the tube of elliptical cross section is derived. The flow equation can be transformed into an equation that combines external forces on the control body in the tube. In the case of low Ohnesorge (Oh) numbers, the flow behavior is divided into three time domains by using the capillary force as the driving force that balances with the inertial force in the reservoir, the convective pressure loss in the reservoir, and the viscous resistance in the tube in the three domains, respectively. The liquid climbing height in these three sections is proportional to t2, t, and t, respectively. However, in the case of high Oh numbers, the flow is divided into two regions, something which has not been proposed in previous work about capillary driven flow in cylinder tubes. This study is verified by drop tower experiments and numerical simulation with the volume of fluid method.

UNSTEADY POISEUILLE FLOW OF SECOND-ORDER FLUID IN A TUBE OF ELLIPTICAL CROSS SECTION ON A POROUS BOUNDARY

The exact solution of an unsteady flow of elastico-viscous fluid through a porous media in a tube of elliptical cross section under the influence of a constant pressure gradient has been obtained in this paper. Initially, the flow is generated by a constant pressure gradient. After attaining steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in the tube of elliptical cross section is investigated by taking into account the porosity factor of the bounding surface. The problem is solved in two stages. The first stage is the steady motion in the tube under the influence of the constant pressure gradient and the second stage is concerned with unsteady motion. The problem is solved by employing the separation of variables technique. The results are expressed in terms of the non-dimensional porosity (K) and elastico-viscosity (β) parameters, which depend on the non-Newtonian coefficient. The flow parameters are found to be identical with that of the Newtonian case as β → 0 and K →∞. It is seen that the effects of elastico-viscosity (β) and porosity (K) parameters of the bounding surface have a significant effect on the velocity parameter.

Viscous flow in a curved tube filled with a porous medium

Viscous flow in a tube is basic in fluid mechanics. However, there are cases where the tube is filled with a porous medium, such as those in filters, catalytic reactors or matrix-filled biological pores. In these cases the appropriate governing equation is the DarcyBrinkman equation, where both the resistance of the matrix and the bounding walls are taken into account [1, 2]. There are many articles on the flow in a straight tube filled with a porous medium, notably Refs. [3– 10]. This paper considers the flow in a curved tube filled with a porous medium. Previous literature include the works of Avramenko and Kuznetsov [11, 12] who solved analytically for the flow in a curved channel and a curved rectangular tube. Full numerical solution was also done for a helically coiled tube [13]. We shall introduce a Ritz method to treat the flow through a porous medium in a general curved tube, then apply the method to a curved tube of elliptic cross section. The Ritz method and its convergence have been known in elasticity (e.g. [14]), but its applications

Solution of the Reynolds Equation for Viscous-Fluid Flow in the Clearance between a Rotating Ellipsoid and a Surface

Slow viscous-fluid flows in the narrow clearance (i) between a moving ellipsoid and a straight tube of elliptic cross section and (ii) between a rotating ellipsoid and a toroidal tube, including the case of an ellipsoid near a plane, are considered. A solution of the boundary-value problem for the Reynolds equation describing the flow in the clearance is found. The similarity of the pressure profiles in the “ellipsoid-plane” and “ cylinder-plane” systems is indicated.

Pulsatile flow in tubes of elliptic cross sections.

The compression of blood vessels by surrounding tissue is an important problem in hemodynamics, most prominently in studies relating to the heart. In this study we consider a long tube of elliptic cross section as an idealization of the geometry of a compressed blood vessel. An exact solution of the governing equations for pulsatile flow in a tube of elliptic cross section involves Mathieu functions which are considerably more difficult to evaluate than the Bessel functions in the case of a circular cross section. Results for the velocity field, flow rate and wall shear stress are obtained for different values of the pulsation frequency and ellipticity, with emphasis on how the effects of frequency and ellipticity combine to determine the flow characteristics. It is found that in general the effects of ellipticity are minor when frequency is low but become highly significant as the frequency increases. More specifically, the velocity profile along the major axis of the elliptic cross section develops sharp double peaks; the flow rate is reduced in approximately the same proportion as in the case of circular cross section; and the point of maximum shear on the tube wall migrates away from the minor axis where it is located in steady flow.

Laminar Natural Convection From an Elliptic Tube With Different Orientations

The problem of two-dimensional natural convection heat transfer from a straight tube of elliptic cross section is investigated. The tube, which has an isothermal surface, is placed with its axis horizontal in an initially quiescent fluid of infinite extent. The velocity and thermal fields are obtained by studying the time development of these fields following a sudden increase of the tube surface temperature until reaching steady state. The study is based on the solution of the full conservation equations of mass, momentum, and energy with no boundary layer simplifications. The paper focuses on the effects of the tube orientation, axis ratio, and Rayleigh number while keeping the Prandtl number unchanged (Pr = 0.7). The study revealed that the maximum average Nusselt number is obtained when the tube major axis is vertical. Within the range of axis ratios considered (Ar = 0.4 to 0.98), smaller Ar resulted in higher heat transfer rate in most cases. Higher Rayleigh number leads to higher velocities and also higher local and average Nusselt numbers in all cases considered. The details of the steady flow and thermal fields are presented in the form of local Nusselt number and surface vorticity distributions as well as streamline and isotherm patterns for some selected cases.

The steady laminar flow of an elastico-viscous liquid in a curved pipe of varying elliptic cross section

The fully developed steady laminar flow of an idealized elastico-viscous liquid through a curved tube with elliptic cross section is studied. The axes of the ellipse are placed in an arbitrary position with respect to the radius of curvature, and the cross-sectional area varies slowly with the longitudinal distance. A perturbation scheme in terms of Dean number [1, 2] and a nonuniform curvature parameter is applied to determine the effects of 1. (i) the nonuniformity of the curvature 2. (ii) the shape of the cross section of the curved pipe 3. (iii) the arbitrary positioning of the elliptic cross section relative to the radius of curvature of the curved pipe. It is shown that in a tube of increasing curvature, there will be delay in setting up a secondary motion. The point of maximum shear stress varies with the cross section under consideration. The flow of Newtonian fluid in a curved tube of elliptic cross section is discussed, as a particular case.

Stenotic effects in a tube of elliptic cross-section at low reynolds numbers

With an objective to understanding arteriosclerosis, the blood flow in a cylindrical tube with local constriction is analysed. The cross-section of the tube is an ellipse, the axes of which are in an arbitrary position with respect to the axis of the tube. Blood is taken to be a Newtonian and homogeneous fluid. The cross-sectional area varies slowly with the longitudinal distance and the area change is so adjusted to take account of stenosis. The transverse velocity field and the effects of inertia on the primary velocity and pressure distribution are calculated to a first order in the relevant small parameter and effects of asymmetry on the wall shear stress and impedance are presented.

Effect of Tube Ovalling on Pressure Wave Propagation Speed

For physiological and other flows it is often assumed that the pressure pulse wave speed is given by the classic Moens-Korteweg expression and this may be used, for example, to assist in the determination of in vivo blood vessel wall incremental Young's modulus. A number of physical factors affecting the value of this wave speed have been reviewed in the literature, but the effect of slight ovalling of the tube cross-section is rarely mentioned. The analysis for a tube of elliptic cross-section shows that even a very small degree of ovalling can cause quite substantial reductions in Young mode wave propagation velocities compared with the classic Moens-Korteweg expression. Bending-induced changes in cross-section shape with internal pressure increase the apparent elasticity of the tube wall. Experimental confirmation is provided by waterhammer wave speed measurements in a copper tube that has been ovalled by coiling. Even though the Young mode is not dominant in this case, as it would be for a physiological case, the measured wave speed is quite clearly less than the Moens-Korteweg theory and it can be shown that the small degree of measured tube ovality explains this.

On a pulsatile flow of a two‐phase viscous fluid in a tube of elliptic cross‐section

A study is made of an unsteady flow of an incompressible viscous fluid with embedded small inert spherical particles contained in a tube of elliptic cross‐section due to a periodic pressure gradient acting along the length of the tube. The solutions for the fluid velocity and the particle velocity are obtained for large and small times. It is shown that the effect of particles on the flow is significant in the small‐time solution while the large‐tlme solution shows no effect of the particles on the flow.

Rotation driven plasma transport: The coupling of macroscopic motion and microdiffusion

The model of Pontius et al. (1986) for plasma transport in a corotation‐dominated magnetosphere is modified to satisfy observational constraints introduced by Richardson and McNutt (1987). As in the earlier model, small discrete flux tubes whose plasma content differs significantly from the longitudinally averaged value (transient flux tubes) move steadily under the influence of the centrifugal force. We consider the electric fields surrounding a transient flux tube of elliptical cross section and derive expressions for the translational velocity and cross‐sectional distortion of such flux tubes. To account for the observed radial decrease of flux shell content at Jupiter, we assume that plasma can pass between transient flux tubes and the background by means of single‐particle microdiffusion. The background plasma distribution is affected by the passage of a transient in two ways: direct mass loading through microdiffusion, and radial displacement to conserve magnetic flux. Upon adopting a simple form to describe the microdiffusion process, we find that there exists a particular slope of flux shell plasma content for which these effects cancel and the background maintains a steady state distribution.

The Effect of Heat Generation on the Convective Heat Transfer in a Tube of Elliptical Cross Section Maintained Under Constant Wall Temperature

The analysis of convective heat transfer within a pipe of elliptical cross section from Ebadian et al. is extended to the case of a heat-generating fluid. Using the method of successive approximations, the temperature distribution in any section of the pipe is obtained. On the basis of this temperature field, the Nusselt number is obtained as a function of the ellipticity m of the cross section of the pipe, and the dimensionaless heat generation number {gamma}. For the dimensionless heat generation number {gamma} = 3.01 the variation of Nusselt number with the ellipticity of the cross section is plotted and compared with the case of no heat generation. A further comparison is made between the ratio of Nusselt number for the case of no heat generation ({gamma} = 0.0).

On the Convective Heat Transfer in a Tube of Elliptic Cross Section Maintained Under Constant Wall Temperature

The convective heat transfer problem along the portion of a tube of elliptic cross section maintained under a constant wall temperature where hydrodynamically and thermally fully developed flow conditions prevail is solved in this paper. The successive approximation method is used for the solution utilizing elliptic coordinates. Analytical expressions for temperature distribution and Nusselt number corresponding to the first cycle of approximation are obtained in terms of the ellipticity of the cross section. In the case of a circular section, the first cycle approximation of the Nusselt number is obtained as 3.7288 compared to the exact value of 3.6568. Representative temperature distribution curves are plotted and compared to those corresponding with constant wall heat flux conditions.

The Effects of Geometry, Wettability, Viscosity And Interfacial Tension On Trapping In Single Pore-throat Pairs

Abstract Multiple displacement experiments in the same pore-throat pair show that the amount of trapped, residual oil is a function of pore-throat geometry and wettability and is not affected much by differences of viscosity or interfacial tension within the limits studied. Displacement efficiency was least where the displacing phase was strongly wetting (contact angles <30 degrees) and greatest for conditions of intermediate wettability (contact angles – 90 degrees) in systems with large pore-to-throat size ratios. In extending these conclusions to multi-pore media with branching networks of pores and throats, it must be understood that trapping by capillary instability (snap-off) is only one of several mechanisms of trapping which may occur. However, in strongly water-wet rocks with large aspect ratios, it may be the most important mechanism of trapping. Semi-rigid films formed by a contaminant at the interface of an aqueous solution with decane inhibited snap-off and could favour higher displacement efficiency by maintaining continuity of decane during imbibition. Introduction Trapping of oil and gas on a microscopic scale in a petroleum reservoir rock is affected by the geometric and topologic properties of the pores, by the properties of the fluids and by properties related to fluid-rock interaction such as wettability. Trapping also is affected by gravity, capillary and viscous forces which prevail during the displacement of one fluid by another. In a system with two fluid phases, one fluid can be referred to as the displacing phase and the other as the displaced phase. The amount of residual displaced phase is very variable in different fluid-rock systems. Many artificial and natural porous media consist of branching networks of elements which, individually, have irregular, converging and diverging portions. The restrictions in such elements are called throats and the bulges pores. Several distinct mechanisms of trapping may occur during the displacement of one fluid by another in porous media (Stegemeier, 1977; Mohanty et al., 1980). This paper deals only with trapping in individual pores caused by associated restricting throats. However, in strongly water-wet rocks with large aspect ratios, this may be the most important mechanism of trapping. The objective is to define the effects of geometry, wettability, interfacial tension and viscosity on trapping in individual pore-throat pairs. The results show that pore-throat geometry and wettability are the most important factors affecting this type of trapping. Numerous authors have cited wettability as an important variable affecting recovery during a water flood (Moore and Slobod, 1956; Coley et al., 1956; Donaldson et al., 1969; McCaffery and Bennion, 1974). Pore-Throat Ratio, Wettability and Trapping Figure 1 illustrates a glass micromodel with elements of differing pore-throat size ratio. At the bottom of the figure there is a simple tube of elliptical cross section with principal radii of 250 and 125 µm. (Figure in full paper) Similar tubes above act as throats connecting pores of various sizes. The pores have circular outlines of 600 µm, 700 µm. 1560 µm and 1940 µm radii and are confined between parallel plates with 250-µm separation. The model was prepared by etching images into two glass surfaces which were then fused together.

Calculation of nonsteady convective heat transfer for turbulent viscous incompressible flow in a tube of elliptical cross section

An approximate analytical expression is obtained for the temperature field. The variations of the dimensionless mass-average temperature of the fluid and the dimensionless integral-average heat flux at the tube wall are determined for various values of the Reynolds and Prandtl numbers.

Steady flow of a viscous liquid in a porous elliptic tube

Flow of a viscous-liquid in a porous tube of elliptic cross-section is studied using the generalized momentum equation. As a particular case, flow of the liquid in a tube of a circular cross-section is obtained. It is observed that the classical Darcian effect is realized only in a core very near to the axis of the tube while the non-Darcian phenomenon is felt predominantly near the boundary of the tube.

Asymptotic theory for peristaltic transport in a tube of arbitrary cross section

An asymptotic theory within the framework of long wave approximation is proposed for the study of peristaltic transport in a flexible tube of arbitrary cross section. The nonlinear problem of the three-dimensional Navier–Stokes equations is reduced to a sequence of linear boundary-value problems of the two-dimensional Laplace and biharmonic operators. Explicit expressions for the velocity profiles are obtained in terms of the solutions of the boundary value problems. Results for a tube of elliptical cross section are given.

The tube effect in sound-velocity measurements

The modifications of Kirchhoff's formula required to take account of the finite thermal conductivity of the tube, slip between the gas and the walls, temperature-discontinuity between the gas and the walls, and absorption of energy by the walls are calculated and are found to be negligible. The effect of roughness of the walls is discussed, and the conclusion is drawn that the large tube-effects often found in practice are due to irregular motion of the gas. It is argued that the methods of correcting for the tube-effect used hitherto are unreliable. The effects of oscillation of the piston and of the gas behind the piston are investigated and it is shown that these may become appreciable in some forms of apparatus. The yielding of a tube of elliptical cross-section is calculated and is shown to have a negligible effect.