Showing papers on "Second-order fluid published in 2001"

Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

Abstract: The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.

Local linear stability characteristics of viscoelastic periodic channel flow

Abstract: Linear stability of periodic channel (PC) flow of an upper convected Maxwell (UCM) liquid is investigated in inertial (Reynolds number Re ⪢0, Weissenberg number We ∼O(1)) and in purely elastic ( Re ≡0, We ∼O(1)) flow regimes. Base state solution is evaluated using O( e 2 ) domain perturbation analysis where e denotes the channel wall amplitude. Significant destabilization, i.e. reduction in critical Reynolds number Re c , with increasing e is predicted for the Newtonian flow, especially in the diverging section of the channel. Introduction of elasticity E ≡ We / Re , representing the ratio of fluid relaxation time to a time scale of viscous diffusion based on channel half height, leads to further destabilization. However, the minimum in the Re c – E curve reported for plane channel flow is not observed. Analysis of the budget of perturbation kinetic energy shows that this minimum in the plane channel flow results from two competing contributions to kinetic energy: a normal stress contribution that increases with increasing E and a shear stress contribution that decreases monotonically with increasing E with the two curves intersecting for E ≈0.002. This value is approximately equal to the value of E for which the plane shear layer is maximally destabilized. When this happens, the critical Deborah number, defined as the ratio of the fluid relaxation time to time scale of the perturbation, is O(1). Comparison of results obtained for the UCM and second order fluid (SOF) models shows that the latter model does not predict a minimum Re c for E ≤0.003. Moreover, eigenspectrum for the SOF contains a set of eigenvalues with positive real parts equal to 1/ We . Results obtained for the eigenspectrum in the purely elastic limit indicate that the PC flow is linearly stable for O(1) axial wavenumbers for We ≤10, e ≤0.1 and n ≤0.1, although the decay rates of the perturbation are smaller than that of the plane channel flow. The local eigenspectrum could contain spurious eigenvalues with positive real parts that could lead to erroneous predictions of flow instability. Using a contour mapping technique, it is shown that deformation of the flow domain can lead to spurious eigenvalues.

Rheology of a suspension of particles in viscoelastic fluids

Abstract: In this paper we study the bulk stress of a suspension of rigid particles in viscoelastic fluids. We first apply the theoretical framework provided by Batchelor [J. Fluid Mech. 41 (1970) 545] to derive an analytical expression for the bulk stress of a suspension of rigid particles in a second-order fluid under the limit of dilute and creeping flow conditions. The application of the suspension balance model using this analytical expression leads to the prediction of the migration of particles towards the centerline of the channel in pressure-driven flows. This is in agreement with experimental observations. We next examine the effects of inertia (or flow Reynolds number) on the rheology of dilute suspensions in Oldroyd-B fluids by two-dimensional direct numerical simulations. Simulation results are verified by comparing them with the analytical expression in the creeping flow limit. It is seen that the particle contribution to the first normal stress difference is positive and increases with the elasticity of the fluid and the Reynolds number. The ratio of the first normal stress coefficient of the suspension and the suspending fluid decreases as the Reynolds number is increased. The effective viscosity of the suspension shows a shear-thinning behavior (in spite of a non-shear-thinning suspending fluid) which becomes more pronounced as the fluid elasticity increases.

Unsteady MHD flow of a non-Newtonian fluid due to eccentric rotations of a porous disk and a fluid at infinity

Abstract: An exact solution of the unsteady flow of a second-order fluid due to non-coaxial rotations of a porous disk and a fluid at infinity in the presence of a uniform transverse magnetic field is investigated. It is once again shown that for uniform suction or uniform injection at the disk an asymptotic profile exists for the velocity distribution. The effects of the magnetic field, the material parameters of the second-order fluid, suction and injection on the velocity distribution are studied. Further, from the solution of a rigid disk, it is found that for parameter β>.01, a non-Newtonian effect is present in the velocity field. However, for β<.01 the velocity field becomes a Newtonian one.

Injection of a non-Newtonian fluid through one side of a long vertical channel

Abstract: The problem considered here is the injection of a non-Newtonian fluid with elastic properties through one side of a long vertical channel. Using the transformations proposed by Wang and Skalak [14] for the velocity components, the basic equations governing the flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions. The effect of the non-Newtonian parameter,S, on the velocity field and heat transfer on the walls is examined carefully.

Algorithmic solution to second-order fluid flow

Abstract: We develop a numerically stable algorithm for the solution of a general fluid-flow model in steady-state. The fluid dynamics is modulated by a semi-Markov process, with phase-type distributions for the sojourn times. We use an algorithmic solution to examine the impact of variance in the case of homogeneous on-off sources, and differences between the infinite and finite buffer case. The need for the complete distribution of the buffer is demonstrated through analysis of two existing approximations, which perform unsatisfactorily. Our numerical results demonstrate the robustness of the numerical algorithm; we compute both the cumulative distribution functions (CDF) and the moments of the process, over a wide range of time-scales and system parameters.

Analysis of axisymmetric flow of a second order fluid near a stagnation point

Abstract: The steady, laminar axisymmetric flow of a second order viscoelastic fluid near a stagnation point is considered. The viscoelasticity of the fluid gives rise to a boundary value problem in which th...

Existence and uniqueness of steady, fully developed flows of second order fluids in curved pipes

Abstract: Steady, fully developed flows of second order fluids in curved pipes of circular cross-section have previously been studied using regular perturbation methods.2,3,12,20 These perturbation solutions are applicable for pipes with small curvature ratio: The cross sectional radius of the pipe divided by the radius of curvature of the pipe centerline. It was shown by Jitchote and Robertson12 that perturbation equations could be ill-posed when the second normal stress coefficient is nonzero. Motivated by the singular nature of the perturbation equations, here, we study the full governing equations without introducing assumptions inherent in perturbation methods. In particular, we examine the existence and uniqueness of solutions to the full governing equations for second order fluids. We show rigorously that a solution to the full problem exists and is locally unique for small non-dimensional pressure drop, in agreement with earlier results obtained using a formal expansion in the curvature ratio.12 The results obtained here are valid for arbitrarily shaped cross-section (sufficiently smooth) and for all curvature ratios. An operator splitting method has been employed which may be useful for numerical studies of steady and unsteady flows of second order fluids in curved pipes.

Anisotropic Second-Order Fluid

Abstract: A classification of fluids is presented in accordance with the terminology of the school of rational mechanics. Rheological equations of state are formulated for an anisotropic second-order fluid. A qualitative assumption is made in regard to the rheological behavior of a dilute suspension of rigid ellipsoids of revolution whose dispersion medium is modeled by a second-order fluid.

Study on hydrodynamic lubrication with second-order fluid (II)——Numerical Analysis

Abstract: The basic lubrication equations are used to calculate two kinds of lubrications examples, a plane inclined slider and a journal bearing respectively. In the calculation of the journal bearing, the Reynolds' boundary conditions are used. In the calculation, it is found that the load carrying capacities of the slider and the journal are of different tendencies with increase in Deborah number. Furthermore, the results show that with decrease in the film thickness the increase in the normal stress of second-order fluid is greater than that of Newtonian fluid. Finally, it is found that the dis- tribution of the normal stress changes significantly at a certain thickness.