Eccentric Cylinders Research Articles

Natural Convection from an Eccentric Square Cylinder Using a Novel Flexible Forcing IB-LBM Method

The natural convection process in an annulus of a cold square enclosure with a hot eccentric square cylinder is simulated using a novel flexible forcing immerse boundary (IB)–lattice Boltzmann method (LBM). In the conventional IB–LBM schemes, the explicit force density calculation may not ensure the exact no-slip velocity/no-jump temperature boundary condition, which may produce unphysical streamline/isotherm penetration into the cylinder. Here, we proposed a single Lagrangian velocity/temperature correction that satisfies the boundary conditions accurately. The developed scheme is applied to analyze the flow regime and heat transfer, as functions of Rayleigh number and eccentricity of the cylinder.

Series solution of unsteady peristaltic flow of a Carreau fluid in eccentric cylinders

In the present analysis, the unsteady peristaltic flow of an incompressible Carreau fluid is investigated in eccentric cylinders. The problem is measured in cylindrical coordinates. The governing equations are observed under the conditions of long wavelength and low Reynolds number approximations. The resulting highly nonlinear second order partial differential equations are solved by series solution technique. The relation for pressure rise is evaluated numerically by built-in technique with the help of mathematics software. As a special case, the present results are compared with the existing results given in the literature. The obtained results are then plotted to see the influence of different physical parameters on the velocity, pressure gradient and pressure rise expressions. The velocity profile is drawn for both two and three dimensions. The trapping boluses are also discussed through streamlines.

Experimental investigation of natural convection about drift-emplaced waste canisters

Cylindrical waste canisters placed horizontally in the underground drifts of a nuclear repository will emit decay heat by convection to the surrounding air and by radiation heat transfer. In drifts with no forced air circulation, natural convection about the waste canisters will play an important role in controlling the temperature distribution inside the canisters and on the drift wall. Experiments were conducted to visualize the flow about model canisters and to measure the steady-state temperature distribution about the canister. The results show an enhancement in heat transfer when compared to heat flow between infinitely long eccentric horizontal cylinders. A discussion of the observed flow regimes as a function of Rayleigh number is provided to describe the various experimental results.

Thermal transpiration of a slightly rarefied gas through a horizontal straight pipe in the presence of weak gravitation

Thermal transpiration of a slightly rarefied gas through a horizontal straight pipe in the presence of weak gravitation is studied on the basis of kinetic theory. We consider the situation in which the Knudsen number (the mean free path divided by the characteristic length of the cross section) is small and the dimensionless gravity (the characteristic length divided by the ascent height of the molecules against gravity) is of the order of the square of the Knudsen number. The behavior of the gas is studied analytically on the basis of the fluid-dynamic-type equation and the slip-type boundary condition derived from the Boltzmann equation for small Knudsen numbers. Extending the analysis of the two-dimensional channel problem, the solution for a pipe with an arbitrary cross section is obtained in a semianalytical form. When the temperature gradient is imposed along the pipe, the pressure gradient is produced not only in the vertical direction but also in the horizontal direction due to the effect of gravity. Although this pressure gradient is of the order of the square of the Knudsen number, it induces a flow of the order of the Knudsen number. As a result, the apparently higher order effect of gravity produces a relatively finite effect on thermal transpiration. This phenomenon, first observed in plane thermal transpiration, is clarified for a pipe with a general cross section. The explicit solution is obtained for the pipe with the cross section of an annulus between eccentric circular cylinders. Based on the solution, the effect of weak gravitation on the mass flow rate of the gas, as well as on the flow velocity, is clarified over a wide range of the radii ratio and the eccentricity of the cylinders.

Bounds of cavitation inception in a creeping flow between eccentric cylinders rotating with a small minimum gap

Bounds of cavitation inception are experimentally determined in a creeping flow between eccentric cylinders, the inner one being static and the outer rotating at a constant angular velocity, Ω. The geometric configuration is additionally specified by a small minimum gap between cylinders, H, as compared with the radii of the inner and outer cylinders. For some values H and Ω, cavitation bubbles are observed, which are collected on the surface of the inner cylinder and equally distributed over the line parallel to its axis near the downstream minimum gap position. Cavitation occurs for the parameters {H,Ω} within a region bounded on the right by the cavitation inception curve that passes through the plane origin and cannot exceed the asymptotic threshold value of the minimum gap, Ha, in whose vicinity cavitation may occur at H < Ha only for high angular rotation velocities.

The Dynamic Analyses of the Eccentric Cylinder Moving on the Inclined Plane

The conservation principle of energy and the mass center movement theorem of rigid body and the moment of momentum theorem relative to the center of mass were used to study the dynamic problems of the eccentric cylinder on the inclined plane. The mass center velocity and the acceleration of the cylinder and the normal pressure and the friction force of the cylinder acting on the inclined plane and etc are given. An example is introduced to show the variations of the physical variants, and the numerical results agree with the theoretical analyses.

Hybrid continuum–molecular modelling of multiscale internal gas flows

We develop and apply an efficient multiscale method for simulating a large class of low-speed internal rarefied gas flows. The method is an extension of the hybrid atomistic–continuum approach proposed by Borg et al. (2013) [28] for the simulation of micro/nano flows of high-aspect ratio. The major new extensions are: (1) incorporation of fluid compressibility; (2) implementation using the direct simulation Monte Carlo (DSMC) method for dilute rarefied gas flows, and (3) application to a broader range of geometries, including periodic, non-periodic, pressure-driven, gravity-driven and shear-driven internal flows. The multiscale method is applied to micro-scale gas flows through a periodic converging–diverging channel (driven by an external acceleration) and a non-periodic channel with a bend (driven by a pressure difference), as well as the flow between two eccentric cylinders (with the inner rotating relative to the outer). In all these cases there exists a wide variation of Knudsen number within the geometries, as well as substantial compressibility despite the Mach number being very low. For validation purposes, our multiscale simulation results are compared to those obtained from full-scale DSMC simulations: very close agreement is obtained in all cases for all flow variables considered. Our multiscale simulation is an order of magnitude more computationally efficient than the full-scale DSMC for the first and second test cases, and two orders of magnitude more efficient for the third case.

Series Solutions of Magnetohydrodynamic Peristaltic Flow of a Jeffrey Fluid in Eccentric Cylinders

In this article, the mathematical modelling on magnetohydrodynamic peristaltic flow of Jeffrey fluid in the gap between two eccentric tubes has been discussed in the presence of applied magnetic fi eld. Geometrically, we considered two eccentric tubes in which the inner tube is rigid while the tube at the outer side has a sinusoidal wave pro pagating along the wall. The governing equations for Jeffrey fluid in a cylindrical coordinates for three dimensional flow are given. The approximations of low Reynolds number and long wavelength have been employed to reduce the highly nonlinear partial differential equations. The problem has been solved with the help of homotopy perturbation method alongwith eigen function expansion method. The graphs of pressure rise, pressure gradient and velocity (for two and three dimensional flow) have been drawn. The stre amlines have also been presented to discuss the trapping bolus discipline.

PARTICULATE SUSPENSION FLOW INDUCED BY SINUSOIDAL PERISTALTIC WAVES THROUGH ECCENTRIC CYLINDERS: THREAD ANNULAR

This paper describes a new model for obtaining analytical solutions of peristaltic flow through eccentric annuli. A mathematical model of peristaltic pumping of a fluid mixture (as blood model) in a circular eccentric cylinders is presented and it is motivated due to the fact that thread injection is a promising method for placing medical implants within the human body with minimum surgical trauma. For the eccentric annuli, the inner cylinder is rigid and moving with a constant velocity V, and the outer one is hollow flexible cylinder that has a sinusoidal wave traveling down its wall. The coupled differential equations for both the fluid and the particle phases have been solved by using two methods and the expressions for the velocity distribution of fluid and particle phase, flow rate, pressure drop, friction forces at the inner and outer cylinders have been derived. The results obtained are discussed in brief. The significance of the particle concentration and the eccentricity parameter as well as the nature of the basic flow has been well explained.

A singular perturbation solution of viscous incompressible fluid flow between two eccentric rotating cylinders

The flow inside two concentric cylinders is one dimensional and an exact solution for quantities is easily found. However, when the cylinders axes are displaced by a small distance, two dimensional effects become obvious. In this research, the equations governing an incompressible viscous flow between two rotating cylinders are considered in polar coordinates that can be simplified by introducing vorticity and stream functions. By taking the curl of the vector form of the momentum equation, the pressure term is omitted. Because of the boundary conditions being in terms of perturbation parameter, a modified bi-polar coordinate system is introduced. This transforms the two eccentric cylinders into two concentric ones. By expanding the quantities in terms of the perturbation parameter up to second-order accuracy and by substitution into the vorticity-stream function, sets of differential equations are obtained to be solved for these functions. At the end, the closed-form velocity components are determined.

Exact solution and CFD simulation of magnetorheological fluid purely tangential flow within an eccentric annulus

In this paper, hydrodynamic characteristics of Magnetorheological (MR) fluid flow within an eccentric annulus have been investigated analytically and numerically. The MR fluid obeys the Herschel–Bulkley constitutive relation with a magnetic field dependent on yield stress. While the eccentric ratio or the gap between two cylinders is very small, local flow can be assumed between two parallel plates. With this simplification of motion equation, the effects of the magnetic field, eccentricity ratio and power-law exponent (n=0.25, 0.5 and 1) on the tangential velocity, torque and pressure gradient are analyzed analytically. Then, the results were compared with two-dimensional (2D) simulations for a system of two eccentric cylinders filled with a MR fluid. The Computational Fluid Dynamics (CFD) simulation results show good agreement with analytical solution. A wider range of the various parameters has been studied by the 2-D simulations. The influences of MR effects on flow field are significant and not negligible. The viscosity increases by increasing the magnetic field and eccentricity ratio, consequently providing an enhancement in the yield stresses and total torque required to rotate the inner cylinder.

Effects of heat and mass transfer on peristaltic flow of a nanofluid between eccentric cylinders

In the present investigation, we examined the heat and mass transfer analysis for the peristaltic flow of nanofluid through eccentric cylinders. The complexity of equations describing the flow of nanofluid is reduced through applying the low Reynolds number and long wavelength approximations. The resulting equations are highly nonlinear, coupled and nonhomogeneous partial differential equations. These complicated governing equations are solved analytically by employing the homotopy perturbation method. The obtained expressions for velocity, temperature and nanoparticle phenomenon are sketched through graphs for two as well as three dimensions. The resulting relations for pressure gradient and pressure rise are plotted for various pertinent parameters. The streamlines are drawn for some physical quantities to discuss the trapping phenomenon.

Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case

AbstractSpectral element methods on simplicial meshes, say TSEM, show both the advantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present aTSEM solver of the two-dimensional (2D) incompressible Navier-Stokes equations, with possible extension to the 3D case. It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space. The so-called Fekete-Gauss TSEM is employed,i.e., Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes. Moreover, the algebraic system is never assembled, therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the flow past a cylinder.

Viscous dissipation in plastic pipe extrusion

We study the temperature distribution of a power-law fluid in a pressure-driven axial flow between eccentric cylinders in bipolar cylindrical coordinates. We begin our analysis by writing the equation of energy in bipolar cylindrical coordinates. We then obtain a dimensionless algebraic analytic solution for temperature profiles under a steady, laminar, incompressible, and fully developed flow for an adiabatic core and an isothermal outer cylinder (Eq. (59)). We find that the dimensionless temperature profile depends upon the radius ratio of the inner to outer cylinders, the eccentricity, the angular position, and the power-law exponent n. The temperature is a strong function of the gap between the cylinders. Finally, dimensionless maximum temperatures are plotted to help pipe manufacturing engineers prevent excessive heating during production. POLYM. ENG. SCI., 53:2205–2218, 2013. © 2013 Society of Plastics Engineers

Three dimensional non-axisymmetric transient acoustic radiation from an eccentric hollow cylinder

Theoretical analysis and detailed numerical simulations are presented for three-dimensional non-stationary vibroacoustic response of a doubly fluid-loaded infinitely long eccentric hollow elastic circular cylinder of arbitrary wall thickness, under arbitrary non-axisymmetric time-dependent on-surface mechanical drives. The formulation is based on the Navier equations of linear elasticity for the solid material, the wave equation for the internal and external fluid domains, the classical method of separation of variables, and the translational addition theorem for cylindrical wave functions. Laplace transform with respect to the time coordinate, Fourier transform with respect to the axial coordinate, and Fourier series expansion in the circumferential direction, are employed to obtain the transformed solutions in the form of partial-wave expansions of transcendental functions. A set of equally spaced virtual sources are assumed along the axial direction, and semi-analytical solutions are obtained in the Laplace domain as discrete summations of simple two dimensional solutions with different axial wave numbers. Time domain solutions are subsequently calculated by using Durbin’s numerical inverse Laplace transform scheme. The analytical results are illustrated with numerical examples in which air- or water-filled concentric and eccentric steel cylinders, submerged in water, are driven by a pair of equal and opposite external radial point loads of finite duration described by a Ricker pulse. Some interesting features of the transient fluid–solid interaction problem such as the generation of shell-induced circumnavigating waves, appearance of multiple high/low amplitude pressure spots in the internal fluid, and formation of non-propagating evanescent waves in the external fluid are noted using appropriate 2D images of the three dimensional sound fields. Limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.

Peristaltic Transport through Eccentric Cylinders: Mathematical Model

This paper discusses the effect of peristaltic transport on the fluid flow in the gap between two eccentric tubes eccentric-annulus flows. The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow analysis has been developed for low Reynolds number and long wave length approximation. The velocity and the pressure gradient have been obtained in terms of the dimensionless flow rate $\overline{Q}$, time t, azimuthal coordinate θ and eccentricity parameter e the parameter that controls of the eccentricity of the inner tube position. The results show that there is a significant deference between eccentric and concentric annulus flows.

The Natural Convection in Annular Space Located Between Two Horizontal Eccentric Cylinders: The Grashof Number Effect

The natural convection in an annular space, located between two horizontal eccentric cylinders is studied. This latter is oriented at an arbitrary angle α. The annular space is filled by a Newtonian and incompressible fluid. The number of Prandtl is fixed at 0.702 (case of the air), the eccentricity is fixed at 0.4 but the number of Grashof varies. By using the approximation of Boussinesq and the vorticity-stream function formulation, the flow is modeled by the differential equations with the derivative partial. For the conditions of heating, we suppose the two cylindrical walls of the enclosure isotherms, T1 for the internal wall and T2 for the external wall, with T1>T2.A computer code was developed, the latter uses finite volumes, for the discretization of the equations and in order to show its reliability. We examine the effect of the number of Grashof on the results obtained that it is qualitatively or quantitatively.

Nonhomogeneous Incompressible Herschel–Bulkley Fluid Flows Between Two Eccentric Cylinders

The equations for the nonhomogeneous incompressible Herschel–Bulkley fluid are considered and existence of a weak solution is proved for a boundary-value problem which describes three-dimensional flows between two eccentric cylinders when in each two-dimensional cross-section annulus the flow characteristics are the same. The rheology of such a fluid is defined by a yield stress τ* and a discontinuous stress-strain law. A fluid volume stiffens if its local stresses do not exceed τ*, and a fluid behaves like a nonlinear fluid otherwise. The flow equations are formulated in the stress–velocity–density–pressure setting. Our approach is different from that of Duvaut–Lions developed for the classical Bingham viscoplastic fluids. We do not apply the variational inequality but make use of an approximation of the generalized Bingham fluid by a non-Newtonian fluid with a continuous constitutive law.

Natural Convection Within an Eccentric Annulus at Different Orientations

DOI: 10.2514/1.T3938 The purpose of this study is to predict numerically the natural convection within an annulus formed between two horizontal eccentric circular cylinders. The annulus is isothermally heated from its inner cylinder, and the induced flowandthermal fieldsarepredictedatdifferentorientationsoftheannulussymmetryline.Thegoverningequations for induced laminar natural flow within the annulus are solved using the Fourier spectral method. The heat convection process within the annulus is dependent on the Rayleigh number, Prandtl number, outer-to-inner cylinder radius ratio, eccentricity, and angle of inclination of the annulus symmetry line to the horizontal, � . The Prandtl number and radius ratio are fixed at 0.7 and 2.6, respectively. The Rayleigh number is considered up to 10 5 , while the annulus symmetry line orientation is varied from horizontal position (� 0) to vertical position (� 90). TheresultsforlocalandmeanNussultnumbersareobtainedanddiscussedtogetherwiththedetailsofboth flowand thermal fields. The study has predicted the global flow circulation within the annulus in cases of � ≠ 90 . The study

Mathematical modeling of axial flow between two eccentric cylinders: Application on the injection of eccentric catheter through stenotic arteries

This study is concerned with the surgical technique for the injection of catheter through stenotic arteries. The present theoretical model may be considered as mathematical representation to the movement of physiological fluid representing blood in the gap between two eccentric tubes (eccentric-annulus flows) where the inner tube is uniform rigid representing moving catheter while the other is a tapered cylindrical tube representing artery with overlapping stenosis. The nature of blood is analyzed mathematically by considering it as a Newtonian fluid. The analysis is carried out for an artery with a mild stenosis. The problem is formulated using a perturbation expansion in terms of a variant of the eccentricity parameter (the parameter that controls the eccentricity of the catheter position) to obtain explicit forms for the axial velocity, the stream function, the resistance impedance and the wall shear stress distribution also the results were studied for various values of the physical parameters, such as the eccentricity parameter ϵ, the radius of catheter σ, the velocity of catheter Vo, the angle of circumferential direction θ (azimuthal coordinate), the taper angle ϕ and the maximum height of stenosis δ⁎. The obtained results show that there is a significant deference between eccentric and concentric annulus flows through catheterized stenosed arteries.