Linear and rotatory oscillations of a sphere in infinite expanse of elastico-viscous fluids

Summary A number of rotatory oscillating systems have been used in literature in the study of elastico-viscous fluids.Frater suggested another type of oscillating system for the same. In this system a sphere is suspended in an infinite expanse of fluid and is made to perform small linear oscillations about a mean position. In the present paper, we have considered the rotatory and linear oscillations of a sphere in an infinite mass of elasticoviscous fluids. The general solutions obtained cover almost all types of elastico-viscous models, includingWalters liquidB, Oldroyd type fluids and the Second order fluids. Considering two different representations of the same dilute polymer solution, we arrive at such results which make us to suspect whether the experimental values of the material constants obtained for a certain polymer solution through rotatory oscillating experiments can be used to assess or predict correct results for linear oscillatory flow situations.     

Secondary flow in the neighborhood of a cylinder oscillating in a viscoelastic fluid

Measurements were made of the steady secondary flow which is caused by a cylinder executing small-amplitude oscillations perpendicular to the cylinder generators. Test fluids were a water-glycerine mixture and two non-Newtonian fluids: aqueous solutions of Separan AP-30 and PolyHall 295 polyacrylamide polymers. The fluids were contained in a cylinder whose center coincides with the rest position of the oscillating cylinder. Experimental results are consistent with a theoretical analysis for a three-constant Oldroyd fluid model in its simplified convected-Maxwell form. Both experiment and theory show that at an oscillation frequency of 40 Hz the secondary flow of the dilute polymer solutions is, essentially, in a sense opposite from that of a Newtonian fluid.     

The squeeze flow of a bi-viscosity fluid between two rigid spheres with wall slip

In this paper, the squeeze flow between two rigid spheres with a bi-viscosity fluid is examined. Based on lubrication theory, the squeeze force is calculated by deriving the pressure and velocity expressions. The results of the normal squeeze force are discussed, and fitting functions of the squeeze and correction coefficients are given. The squeeze force between the rigid spheres increases linearly or logarithmically with the velocity when most or part of the boundary fluid reaches the yield state, respectively. Furthermore, the slip correction coefficient decreases with the increase in the velocity. The investigation may contribute to the further study of bi-viscosity fluids between rigid spheres with wall slip.     

Finite element analysis of the axially symmetric motion of an incompressible viscous fluid in a spherical annulus

This paper presents results obtained by employing a modified Galerkin finite element method to analyse the steady state flow of a fluid contained between two concentric, rotating spheres. The spheres are assumed to be rigid and the cavity region between the spheres is filled with an incompressible, viscous, Newtonian fluid. The inner sphere is constrained to rotate about a vertical axis with a prescribed angular velocity, while the outer sphere is fixed. Results for the circumferential function Ω, streamfunction ψ, vorticity function ζ and inner boundary torque T₁ are presented for Reynolds numbers Re ? 2000 and radius ratios 0.1 ? α ? 0.9. The method proved effective for obtaining results for a wide range of radius ratios (0.1 ? α ? 0.9) and Reynolds numbers (0 ? Re ? 2000). Previous investigators who employed the finite difference method experienced difficulties in obtaining results for cases with radius ratios α ? 0.2, except for small Reynolds numbers (Re ? 100). Results for Ω, Ψ, ζ and T₁ obtained in this study for radius ratios 0.8 ≤ α ≤ 0.9 verified the development of Taylor vortices reported by other investigators. The research indicates that the method may be useful for analysing other non-linear fluid flow problems.     

Thermal effects of the micropolar fluid parameters on the laminar free convection in spherical annuli with mixed boundary conditions

The effects of micro-rotation and vortex viscosity in micropolar fluids have been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with specified mixed boundary conditions. Calculations were carried out systematically for several different eccentricities and a range of modified Rayleigh numbers to determine the average Nusslet numbers which are affected by the micropolar parameters (F) of the flow and temperature fields. The skin friction stress on the walls has also been studied and discussed. The governing equations, in terms of vorticity, stream function, temperature and angular momentum are expressed in a spherical polar coordinate system. Results were obtained for steady heat-transfer in spherical annuli at a Prandtl number of 0.7, with the modified Rayleigh number ranging from 10³ to 5 × 10⁵, for a radius ratio of 2.0 and eccentricities varying from −0.625 to +0.625. Comparisons are attempted between the Newtonian fluid and micropolar fluid.     

Secondary flow induced by the rotation of two concentric spheres about their common diameter in micropolar fluids

Summary In this paper, we have studied the secondary flow induced in a micropolar fluid by the rotation of two concentric spheres about a fixed diameter. The secondary flow exhibits behaviour commonly observed in visco-elastic fluids. In particular we have obtained the expressions for microrotation vector. Numerical results have been obtained for a number of values of relative rotations of the two spheres for a chosen set of values of fluid parameters. The results are presented graphically and compared with the previous investigations.     

Flow measurement on an oscillating pipe flow near the entrance using the UVP method

 The authors have carried out a study to investigate and clarify the characteristics of purely oscillating pipe flows over the developing region. The main objective of this study is to establish the method of time-dependent velocity profiles obtained by the ultrasonic velocity profile (UVP) measurement method. First, the relationship between the test fluids and the microparticles, as reflectors of ultrasonic pulses, was investigated. In addition, the relationship between the sound speeds of the test fluids and the wall materials was studied. Second, the UVP was used to obtain the instantaneous velocity profiles in oscillating pipe flows, and the developing characteristics of the flows were analyzed. Finally, the “entrance length” (by analogy with a unidirectional pipe flow) required for oscillating pipe flows was analyzed by examining the amplitude of the harmonic spectral components of the oscillating frequency. A fast Fourier transform (FFT) is proposed as the applicable method to estimate the “entrance length”. From the Fourier transform of the velocity on the centerline, nonlinear oscillation of fluid occurs in the “entrance length” of the oscillating flows, and the viscous dissipation of the higher-order velocity harmoncis determines the entrance region. The “entrance length” can be obtained from the dissipation length of the third-order harmonic. These results prove that the UVP method is highly applicable to carry out the flow measurement in the “entrance length” of oscillating pipe flow. Received: 20 March 2000 / Accepted: 10 August 2001     

On the unsteady rotational flow of a generalized Maxwell fluid through a circular cylinder

In this paper, the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized Maxwell fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. Initially, the fluid is at rest, and the motion is produced by the rotation of the cylinder about its axis with a unsteady angular velocity. The solutions that have been obtained are presented under series form in terms of the generalized G _a,b,c (, t)-functions. The similar solutions for the ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases, when β → 1, respectively β → 1 and λ → 0, from general solutions. Finally, the solutions that have been obtained are compared by graphical illustrations, and the influence of the pertinent parameters on the fluid motion is also underlined by graphical illustrations.     

Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates

Analytical solutions are presented using method of separation of variables for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson–Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of half channel width to Debye length, the periodic EOF electric oscillating Reynolds number Re and normalized relaxation time λ₁ω on velocity profiles and volumetric flow rates are presented. Results show that for prescribed electrokinetic width K, lower oscillating Reynolds number Re and shorter relaxation time λ₁ω reduces the plug-like EOF velocity profile of Newtonian fluids. For given Reynolds number Re and electrokinetic width K, longer relaxation time λ₁ω leads to rapid oscillating EOF velocity profiles with increased amplitude. With the increase of the K, the velocity variations are restricted to a very narrow region close to the EDL for small relaxation time. However, with the increase of the relaxation time, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. As far as volume flow rates are concerned, for given electrodynamic width K, larger oscillating Reynolds number Re results in a smaller volume flow rates. For prescribed oscillating Reynolds number Re, with the changes of relaxation time λ₁ω, volume flow rates will produce some peaks no matter how the electrodynamic width K varies. Moreover, the time periodic evolution of the velocity profiles provides a detail insight of the flow characteristic of this flow configuration.     

Fluids with microstretch

Summary In this paper fluids with stretch are introduced as a subclass of simple microfluids. In these fluids the local fluid elements are allowed to undergo only a uniform stretch, or contraction without microrotation. These fluids might find applications especially inNewtonian fluids with bar-like polymeric additives. The field equations are obtained, initial and boundary conditions discussed and the thermodynamics of such fluids is studied. The solution of the problem ofPoiseuille flow between two parallel plates is given. Microstretch fluids with constrained microrotation are also discussed briefly as another subclass of simple microfluids.     

On unsteady flow of an elastico-viscous fluid past an infinite plate with variable suction

Approximate solutions of the Navier-Stokes equations are derived through the Laplace transform for two dimensional, incompressible, elastico-viscous flow past a flat porous plate. The flow is assumed to be independent of the distance parallel to the plate. General formulae for the velocity distribution, skin friction and displacement thickness as functions of the given free stream velocity and suction velocity are obtained. The response of skin friction to the impulsive perturbations in the stream and suction velocities is studied. It is found that the order of singularity in the skin friction at t=0 increases due to the elastic property of the fluid in the impulsive case. When the stream is accelerated the skin friction still anticipates the velocity but the time of anticipation is reduced from 1/4 to (1/4) (1—k), where k is the elastic parameter of the fluid. It is found that in general the resistance of the elastico-viscous fluids to an impulsive increase in the stream velocity is greater than the viscous fluids, the elasticoviscous fluids also reach the steady state earlier than the viscous fluids.     

Rotationally symmetric flow over a rotating disk

The rotationally symmetric flow over a rotating disk in an incompressible viscous fluid is analyzed by a new method when the fluid at infinity is in a state of rigid rotation (in the same or in the opposite sense) about the same axis as that of the disk. Asymptotic expansions for the velocity field over the entire flow field are obtained for the general class of one-parameter rotationally symmetric flows. This method is further extended to the case when a uniform suction or injection is assumed at the rotating disk. Fluid motion induced by oscillatory suction of small amplitude at the rotating disk is also discussed.An initial-value analysis reveals that resonance is possible only when the angular velocity of the rotating fluid is greater than that of the rotating disk.     

The stokes flow of the rotating double spheres and multiple spheres

In this paper the expressions for a kind of new rotlets in Stokes flow are derived. By means of superposition of this new rotlets, the drag moment for rotating double spheres and multiple spheres along the smae axis are presented. It has been demonstrated that drag moment for each sphere is the linear function of its angular velocity.     

Transient oscillatory and constantly accelerated non-Newtonian flow in a porous medium

This paper looks at the magnetohydrodynamic (MHD) analysis for transient flow of an Oldroyd-B fluid in a porous medium. The presented analysis takes into account the modified Darcy's law. The flow is induced due to constantly accelerated and oscillating plate. Expressions for the corresponding velocity field and the adequate tangential stress are determined by means of the Fourier sine transform. The influence of various parameters of interest on the velocity and tangential stress has been shown and discussed. A comparison for different kinds of fluids is also provided.     

A boundary element analysis of multiply connected three‐dimensional cavity mixing flow of polymer solutions

The emergence of non‐linear dynamics in cavity mixing is examined using the boundary element method (BEM). The method is implemented for the simulation of three‐dimensional transient creeping flow of Newtonian or linear viscoelastic fluids of the Jeffreys type. A boundary only formulation in the time domain is proposed for viscoelastic flow. Special emphasis is placed on cavity flow involving multiply connected moving domains. The BEM becomes particularly suited for this case, when part of the boundary (stirrer or rotor) is moving, and the remaining outer part (cavity) is at rest. In contrast to conventional volume methods, the BEM is shown to be much easier to implement since the kinematics of the elements bounding the fluid is known (imposed). It is found that, for a simple cavity flow induced by a rotating vane at constant angular velocity, the tractions at the vane tip and cavity face exhibit non‐linear periodic dynamical behaviour with time for fluids obeying linear constitutive equations. Copyright © 1999 John Wiley & Sons, Ltd.     

A THEORETICAL ANALYSIS OF THE FLOW DISTURBANCE INDUCED BY A SPHERE OSCILLATING IN INCOMPRESSIBLE FLUID

为了改进基于不可压缩流场的声类比法的气动声数值预测方法,首先要明确扰动在可压缩和不可压缩流体媒介中的传播特性. 推导了震荡小球在不可压缩流体中产生的小扰动的理论解,分析其速度场与压力场的特点,并与可压缩情况的解进行比较. 结果显示,速度场中包含传播速度为无穷大和有限值的分量;而压力场只有传播速度为无穷大的分量. 当流体黏性趋于零或小球震荡频率趋于无穷大时,其流场与经典声学中震荡小球声辐射问题的近场声一致,这表明震荡小球产生的近场扰动为不可压缩流场,即伪声.     

Dynamics of the flow around colliding spheres

An investigation of the flow resulting from the collision of two spheres at low Reynolds numbers is presented. Each sphere starts from rest and traverses a distance of 5 sphere diameters to the point of contact. Experimental and numerical results are compared for a symmetric collision; that is, a collision between two spheres of the same diameter and travelling with the same velocity. The flow consists of two axisymmetric recirculation zones which become a pair of colliding vortex rings, expanding radially from the collision point. Several examples of unbalanced collisions are also presented numerically, with one or both of the velocity and diameter of the spheres altered. These collisions break the symmetry, altering the post-collision expansion of the vortex rings.     

Marangoni Mixed Convection Boundary Layer Flow

The paper deals with a steady coupled dissipative layer, called Marangoni mixed convection boundary layer, which can be formed along the interface of two immiscible fluids, in surface driven flows. The mixed convection boundary layer is generated when besides the Marangoni effects there are also buoyancy effects due to gravity and external pressure gradient effects. We shall use a model proposed by Golia and Viviani (L’ Aerotecnica missili e Spazio 64 (1985) 29–35, Meccanica 21 (1986) 200–204) wherein the Marangoni coupling condition has been included into the boundary conditions at the interface. The similarity equations are first determined, and the pertinent equations are solved numerically for some values of the governing parameters and the features of the flow and temperature fields as well as the interface velocity and heat transfer at the interface are analysed and discussed.     

Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane

An exact solution of the Navier–Stokes equations is obtained for the flow between two eccentric disks rotating with the same angular velocity and one of them executing non-torsional oscillations. An analytical solution describing the flow at large and small times after the start is given. The solutions depend on the ratio of the frequency of oscillation to the angular velocity of the disks and the ratio of the amplitude of oscillation to the angular velocity of the disks and to the distance between the axes of rotation, and the Reynolds number based on the distance between the disks and the angular velocity of the disks. The solutions for three cases when the angular velocity is greater than the frequency of oscillation or it is smaller than the frequency or it is equal to the frequency are discussed.     

A NUMERICAL STUDY OF FLOW PAST A ROTATIONALLY OSCILLATING CIRCULAR CYLINDER

Vortex shedding from a rotationally oscillating circular cylinder in a uniform flow is studied by numerical solutions of the two-dimensional incompressible Navier-Stokes equations using primitive variables. To demonstrate the viability and accuracy of the method, we calculate the approach flow past a rotating cylinder with constant angular velocity. For approach flow past a rotationally oscillating cylinder, the object of the study is to examine the effect of oscillating rotation on the flow structure. In the present study, some basic patterns of vortex shedding can be identified according to our calculated results and are in good agreement with available experiments. In addition, the influence of the oscillating frequency and amplitude on the forces acting on the cylinder is also investigated.