Occurrence of Taylor vortices in the flow between two rotating conical cylinders

The behavior of the flow between two coaxial conical cylinders with the inner one rotating and the outer one stationary is studied numerically. Special attention is paid to the occurrence of Taylor vortices in basic flow and unsteady helical vortices. It is found that, in basic flow, the vortices occur in the direction toward smaller radius, while toward bigger radius in unsteady helical vortices; moreover, the unsteady helical vortices can coexist with unstable steady Taylor vortices. The results suggest that the behavior of conical flow is dominated by a competition between the meridional flow and radial flow. The effect of meridional flow is most significant at small apex angle or in basic flow and helical vortices, while the radial flow dominates the structure at larger apex angle or in steady vortical flow. In order to get better understanding the competition and the transition of Taylor–Couette flow to conical flow, a velocity angle related to velocity components is defined, and the pattern evolution of velocity, streamlines and the velocity angle are examined with respect to apex angle, as well as Reynolds number. Finally, the statistical properties of turbulent conical flow are investigated.     

The wall jet flow of a conducting gas over a permeable surface in the presence of a variable transverse magnetic field

The effects of the magnetic field, Mach number and the permeability parameter on the wall jet flow (radial or plane) of an electrically conducting gas spreading over a permeable surface have been investigated. Taking the Prandtl number of the fluid as unity and assuming a linear relationship between viscosity and temperature, it is found that similar solutions for the velocity distribution exist for a specified distribution of the normal velocity along the wall and the corresponding distribution of the transverse magnetic field. Previous non-magnetic flow results have been improved by adopting a new and simple transformation of variables.     

Fluid flow in an inhomogeneous granular medium

The seepage of a compressible fluid in an inhomogeneous undeformable granular medium is investigated. It is assumed that the fluid flow in a porous space is described by the Navier–Stokes equations. It is shown that, in the case of an inhomogeneous velocity field, a tensor of additional effective stresses occurs in connection with the transfer of fluid particles in a transverse direction when flow occurs around the granules of the medium in a longitudinal direction. Using the fundamental propositions of Reynolds’ averaging theory and Prandtl's mixing path, the structure of the effective viscosity coefficient is determined and hypotheses are formulated which enable it to be assumed to be independent of the flow velocity. It is established by comparison with experimental data that the effective viscosity coefficient can exceed the viscosity coefficient of the flowing fluid by an order of magnitude. The equations of average motion are obtained, which in the case of an incompressible fluid have the form of the Navier–Stokes equations with body forces proportional to the velocity. It is established that, in addition to the well-known dimensionless flow numbers, there is a new number which characterizes the ratio of the Darcy porous drag forces to the effective viscosity forces. The proposed equations are extended to the case of the flow of an aerated fluid. The components of the angular momentum vector are used as the required functions instead of the components of the velocity vector. This enables a solving system of equations to be obtained, which, apart from the notation, is identical with the similar equations for the case of an incompressible fluid. The solution of a new problem of the fluid flow in a plane channel with permeable walls is presented using three models: Darcy's law for an incompressible and aerated fluid, and also of an aerated fluid taking the effective viscosity into account. It is established that, for the same pressure drop, the maximum flow rate corresponds to Darcy's law. Compressibility leads to its reduction, but by simultaneously taking into account the compressibility and the effective viscosity one obtains minimum values of the flow rate. The effective viscosity and aeration of the fluid has a considerable effect on the flow parameters.     

Effect of wall compliance on compressible fluid transport induced by a surface acoustic wave in a microchannel

Effects of complaint wall properties on the flow of a Newtonian viscous compressible fluid has been studied when the wave propagating (surface acoustic wave, SAW) along the walls in a confined parallel‐plane microchannel is conducted by considering the slip velocity. A perturbation technique has been employed to analyze the problem where the amplitude ratio (wave amplitude/half width of channel) is chosen as a parameter. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters and wall parameters. The phenomenon of the “mean flow reversal” is found to exist both at the center and at the boundaries of the channel. The effect of damping force, wall tension, and compressibility parameter on the mean axial velocity and reversal flow has been investigated, also the critical values of the tension are calculated for the pertinent flow parameters. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 621–636, 2011 Keywords:     

The Evolution of Linearized Perturbations of Parallel Flows

The equations of an incompressible fluid are linearized for small perturbations of a basic parallel flow. The initial-value problem is then posed by use of Fourier transforms in space. Previous results are systematized in a general framework and used to solve a series of problems for prototypical examples of basic shear flow and of initial disturbance. The prototypes of shear flow are (a) plane Couette flow bounded by rigid parallel walls, (b) plane Couette flow bounded by rigid walls at constant pressure, (c) unbounded two-layer flow with linear velocity profile in each layer, (d) a piecewise linear profile of a boundary layer on a rigid wall. The prototypes of initial perturbation are the fundamental ones: (i) a point source of the field of the transverse velocity (represented by delta functions), (ii) an unbounded sinusoidal field of the transverse velocity, (iii) a point source of the lateral component of vorticity, (iv) a sinusoidal field of the lateral vorticity. Detailed solutions for an inviscid fluid are presented, but the problem for a viscous fluid is only broached.     

Meshless solution of two-dimensional incompressible flow problems using the radial basis integral equation method

The two-dimensional incompressible fluid flow problems governed by the velocity–vorticity formulation of the Navier–Stokes equations were solved using the radial basis integral (RBIE) equation method. The RBIE is a meshless method based on the multi-domain boundary element method with overlapping subdomains. It solves at each node for the potential and its spatial derivatives. This feature of the RBIE is advantageous in solving the velocity–vorticity formulation of the Navier–Stokes equations since the calculated velocity gradients can be used to compute the vorticity that is prescribed as a boundary condition to the vorticity transport equation. The accuracy of the numerical solution was examined by solving the test problem with known analytical solution. Two benchmark problems, i.e. the lid driven cavity flow and the thermally driven cavity flow were also solved. The numerical results obtained using the RBIE showed very good agreement with the benchmark solutions.     

Analytic solution for MHD Transient rotating flow of a second grade fluid in a porous space

This article looks into the unsteady rotating magnetohydrodynamic (MHD) flow of an incompressible second grade fluid in a porous half space. The flow is induced by a suddenly moved plate in its own plane. Both the fluid and plate rotate in unison with the same angular velocity. Analytic solution of the governing flow problem is obtained by using Fourier sine transform. Based on the modified Darcy's law, expression for velocity is obtained. The influence of pertinent parameters on the flow is delineated and appropriate conclusions are drawn. Several existing solutions of Newtonian fluid have been also deduced as limiting cases.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.     

Numerical evaluation of the suppression effect of a free-to-rotate triangular fairing on the vortex-induced vibration of a circular cylinder

The suppression of vortex-induced vibration (VIV) of a circular cylinder with a free-to-rotate triangular fairing in the Reynolds number range of Re = 1100–6100 is numerically investigated using computational fluid dynamics. The unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transport k–ω turbulence model coupled with an improved fourth-order Runge–Kutta method are used to solve the wake flow, the structure's vibration, and the fairing's rotation. The computational model is validated with the available experimental results for a cylinder with an attached short-tail fairing. The numerical results indicate that the triangular fairing has a positive role in suppressing vibration when it achieves a stable position deflected from the flow direction. The suppression effect is sensitive to the incoming flow velocity. The fairing shifts from a stable state to an unstable one when the flow velocity varies. Therefore, maintaining the hydrodynamic stability of the fairing is the key to achieving success in vibration suppression, and the stability is dependent on the characteristic length and the rotational friction. Although the strong flapping of the 70° triangular fairing excites a more vigorous vibration, it may be used as an amplifier of VIV for energy harvesting.     

Pulsatile flow of Herschel–Bulkley fluid through catheterized arteries – A mathematical model

The pulsatile flow of blood through catheterized artery has been studied in this paper by modeling blood as Herschel–Bulkley fluid and the catheter and artery as rigid coaxial circular cylinders. The Herschel–Bulkley fluid has two parameters, the yield stress θ and the power index n. Perturbation method is used to solve the resulting quasi-steady nonlinear coupled implicit system of differential equations. The effects of catheterization and non-Newtonian nature of blood on yield plane locations, velocity, flow rate, wall shear stress and longitudinal impedance of the artery are discussed. The existence of two yield plane locations is investigated and their dependence on yield stress θ, amplitude A, and time t are analyzed. The width of the plug core region increases with increasing value of yield stress at any time. The velocity and flow rate decrease, whereas wall shear stress and longitudinal impedance increase for increasing value of yield stress with other parameters held fixed. On the other hand, the velocity, flow rate and wall shear stress decrease but resistance to flow increases as the catheter radius ratio (ratio of catheter radius to vessel radius) increases with other parameters fixed. The results for power law fluid, Newtonian fluid and Bingham fluid are obtained as special cases from this model.     

Some Self-Similar Two-Phase Flows of Non-Newtonian Fluids Through a Porous Medium

Pascal This paper addresses the question of the rheological effects of non-Newtonian fluids in a flow system, in which a two-phase flow zone is coupled to a single-phase flow zone by a moving fluid interface. This flow system is involved in a technique for oil displacement in a porous medium, where a non-Newtonian displacing fluid (a polymer solution) is used to displace a non-Newtonian heavy oil. The self-similar solutions of the equations governing the dynamics of the moving interface, separating the displacing and displaced fluids, are obtained for the one-dimensional and plane radial flows. The effects associated with the presence of a two-phase flow zone, behind the moving interface, on the interface movement are analyzed. The existence of a pressure front ahead of the moving interface, moving with a finite velocity, is also shown. The relevance of this result to the propagation of pressure disturbances in a non-Newtonian fluid flowing through a porous medium is discussed with regard to interpretation of the transient pressure response in an injection well for polymer-solution floods.     

On the unsteady flow and temperature distribution of a viscous incompressible fluid between two parallel flat plates

The unsteady flow and temperature distribution of a viscous incompressible fluid between two parallel flat plates has been investigated. The pressure gradient is varying linearly with time. The velocity and temperature profiles for various values oft have been shown graphically. Fort = 0, the velocity and temperature profiles correspond to the plane Poiseuille flow. The velocity and temperature both increase with time and they are maximum on the central plane of the channel.     

Effects of partial slip,viscous dissipation and Joule heating on Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid

The steady Von Kármán flow and heat transfer of an electrically conducting non-Newtonian fluid is extended to the case where the disk surface admits partial slip. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The constitutive equation of the non-Newtonian fluid is modeled by that for a Reiner–Rivlin fluid. The momentum equations give rise to highly non-linear boundary value problem. Numerical solutions for the governing non-linear equations are obtained over the entire range of the physical parameters. The effects of slip, magnetic parameter and non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. It is interesting to find that the non-Newtonian cross-viscous parameter has an opposite effect to that of the slip and the magnetic parameter on the velocity and the temperature fields.     

Retracted: Unsteady flow and heat transfer on a rotating disk in a porous medium

This article has been retracted. See retraction notice DOI: 10.1002/mma.850 . An unsteady flow and heat transfer in a porous medium of a viscous incompressible fluid over a rotating disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The new self‐similar solution of the Navier–Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier–Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation‐point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large porosity or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also, the surface shear stress in the radial direction and the surface heat transfer decrease with increasing porosity, but the surface shear stress in the tangential direction increases. Copyright © 2006 John Wiley & Sons, Ltd.     

An assessment of streamline curvature effects on the mixing region of a turbulent plane jet in crossflow

The flow field of a turbulent plane jet in a weak or moderate crossflow, which is characterised by mild streamline curvature, has been investigated computationally. The values of the jet-to-crossflow velocity ratios chosen are 6, 9 and 10. The time-averaged Navier–Stokes equations are solved on a staggered Cartesian grid using the standard k–ϵ model and the k–ϵ model with streamline curvature modification. The predictions using both the models are compared with available experimental data. It has been shown that by accounting for the effect of streamline curvature in the k–ϵ model results in good prediction of this flow configuration.     

Couette flow of a non-homogeneous fluid

The two dimensional Couette flow of a non-homogeneous viscous fluid is studied. The plane boundaries of the channel are maintained at different temperatures. The upper plane moves with a uniform horizontal velocity and the lower plane is at rest. The fluid is subjected to suction and injection at the boundaries. Thesteady equations are solved by introducing similarity variables which are expanded in series of powers of a small stratification parameter. The non-linear theory predicts that the temperature depends on the distancex from the throat section, an observation which is not predicted by the linear theory. The non-linear effects on velocity and temperature are studied. The rate of heat transfer is discussed.     

Slip at the surface of a sphere translating perpendicular to a plane wall in micropolar fluid

The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems. Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid and micropolar fluid.      

Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface

A new kind of analytic technique, namely the homotopy analysis method (HAM), is employed to give an explicit analytical solution of the steady two-dimensional stagnation-point flow of an electrically conducting power-law fluid over a stretching surface when the surface is stretched in its own plane with a velocity proportional to the distance from the stagnation-point. A uniform transverse magnetic field is applied normal to the surface. An explicit analytical solution is given by recursive formulae for the first-order power-law (Newtonian) fluid when the ratio of free stream velocity and stretching velocity is not equal to unity. For second and real order power-law fluids, an analytical approach is proposed for magnetic field parameter in a quite large range. All of our analytical results agree well with numerical results. The results obtained by HAM suggest that the solution of the problem under consideration converges.     

Elastico-viscous flow engendered due to an impulsively started porous plane wall

Approximate solution for the flow past an impulsively started infinite porous plane wall in an elastico-viscous fluid is obtained for the velocity and shearing stress. The roles of elasticity of the liquid and the suction on the velocity and the shearing stress have been studied.     

Modeling of local particle accumulation in disperse flows with kinematic singularities

The aim of the study is to model the formation of local particle accumulation zones near several typical kinematic singularities. The flows considered are: (i) a steady two–dimensional flow with localized vorticity of the Kelvin cat's eye type (vortex in a mixing layer), (ii) a steady axisymmetric flow formed by a vortex filament normal to a plane in viscous fluid (simple model of tornado), (iii) a neighbourhood of a zero acceleration point in two–dimensional unsteady (harmonic) flow. From parametric numerical calculations, we investigated the inertial mechanisms of forming local particle accumulation zones and found the threshold values of governing parameters separating qualitatively different particle velocity and density patterns. In particular, it is shown that the zero–acceleration point can either “attract” or “scatter” the particles. Zones of concentrated vorticity are typically devoid of particles. In the tornado–like flow, an axisymmetric “cup-shaped” particle accumulation region is formed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)