On existence and regularity of solutions for 2‐D micropolar fluid equations with periodic boundary conditions

In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.     

Homogenization of two-phase flow: high contrast of phase permeabilityHomogénéisation d'écoulement diphasique : grand contraste de perméabilité d'une phase

The steady-state two-phase flow non-linear equation is considered in the case when one of phases has low effective permeability in some periodic set, while on the complementary set it is high; the second phase has no contrast of permeabilities in different zones. A homogenization procedure gives the homogenized model with macroscopic effective permeability of the second phase depending on the gradient and on the second order derivatives of the macroscopic pressure of the first phase. This effect cannot be obtained by classical (one small parameter) homogenization. To cite this article: G.P. Panasenko, G. Virnovsky, C. R. Mecanique 331 (2003).     

Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel

The effect of a third-order fluid on the peristaltic transport in an asymmetric channel is studied. The wavelength of the peristaltic waves is assumed to be large compared to the varying channel width, whereas the wave amplitudes need not be small compared to the varying channel width. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with velocity of the wave. The effects of Deborah number, phase difference, varying channel width and wave amplitudes on the pumping characteristics, streamline pattern and trapping phenomena are investigated. It is observed that the trapping regions increase as the channel becomes more and more symmetric and the trapped bolus volume decreases for increasing Deborah number, phase difference and varying channel width whereas it increases for increasing flow rate and wave amplitudes. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.     

A simple formula for mean multiplexing delay for independent regenerative sources

Simple expressions are given for the mean delay, mean waiting time, and mean busy period length in a multiplexer. Data streams with active periods having a general distribution are permitted, and the data rate during the active periods can be random. Data can also arrive in batches. The key restrictions of the model are that the sources are independent, idle periods are exponentially distributed, and a source generates at least enough data during an active period to keep the server busy throughout the period. The exact formulas allow evaluation of the error in approximations such as a heavy traffic diffusion approximation.Both continuous and discrete time models are considered. The discrete-time model includes that studied by Viterbi and subsequently generalized by Neuts. The Pollaczek-Khinchine formula for the mean amount of work in anM/GI/1 queue is retrieved as a limiting case.Preliminary version presented at IEEE INFOCOM, San Francisco, April 1993.     

The Properties of Voronoi Tessellations for 2D Ising Fluid Near the Second-Order Magnetic Phase Transition

The topological and geometrical properties of Voronoi cells generated for 2D fluid of hard disks with Ising-like spins near the second-order phase transition from the paramagnetic to ferromagnetic phase are described for different disk densities. The comparison with Voronoi cells generated for the random hard disk system is given.     

The effects of flow split ratio and flow rate in manifolds

This paper reports a combined experimental and numerical investigation of three-dimensional steady turbulent flows in inlet manifolds of square cross-section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches. The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.     

Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

潜热型热功能流体强化换热分析

本文建立了分析带有相变微胶囊的潜热型热功能流体的流动和换热过程数理模型,应用有限差分法和移动热源法进行联合求解。计算结果表明,相变微胶囊的加入:较好地提高了流体的换热性能。获得了相变颗粒大小和体积分数对强化换热影响等结果。计算结果对该类流体的设计和应用提供了理论依据。     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.