Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

Fluid Flow and Heat Transfer from Circular and Noncircular Cylinders Submerged in Non-Newtonian Liquids

Abstract: Publisher Summary This chapter discusses the role of non-Newtonian flow characteristics of structured fluids—within the framework of continuum mechanics—on the hydrodynamic and convective heat and mass transport processes for bluff bodies of various shapes immersed in streaming (unconfined or confined) or quiescent fluids in different flow regimes. It focuses on the steady and laminar vortex shedding regimes of the flow over long cylinders of circular, elliptic, semicircular, square, and triangular cross sections. Within this framework, the flow invariably tends to be two-dimensional and laminar. The unconfined or free flow past a circular cylinder exhibits a rich variety of flow regimes depending upon the intrinsic nature of the flow. The simple flow is governed by the Reynolds number that is based upon the diameter of the cylinder, kinematic viscosity of the fluid, and the faraway uniform velocity. Most non-Newtonian fluids tend to be far more viscous than their Newtonian counterparts like air and water and, therefore, laminar flow conditions prevail more often in such fluids than that in Newtonian fluids like air. The chapter describes the flow regimes and fluid mechanical aspects related to circular, elliptical, semicircular, triangular, and square cylinders, together with the critical values of the Reynolds number denoting the transition from one flow regime to another. These values are strongly influenced not only by the rheological characteristics but also by the shape of the bluff body, its orientation with regard to the mean direction of flow, and its extent and type of confinement. The scaling considerations that are used to extract the pertinent dimensionless parameters which influence the detailed and macroscopic momentum and heat transfer characteristics for each shape of the bluff body have also been highlighted.

Particulate suspension effect on peristaltically induced unsteady pulsatile flow in a narrow artery: Blood flow model.

Abstract: This work is concerned with theoretically investigating the pulsatile flow of a fluid with suspended particles in a flow driven by peristaltic waves that deform the wall of a small blood artery in the shape of traveling sinusoidal waves with constant velocity. The problem formulation in the wave frame of reference is presented and the governing equations are developed up to the second-order in terms of the asymptotic expansion of Womersley number which characterizes the unsteady effect in the wave frame. We suppose that the flow rate imposed, in this frame, is a function versus time. The analytical solution of the problem is achieved using the long wavelength approximation where Reynolds number is considered small with reference to the blood flow in the circulatory system. The present study inspects novelties brought about into the classic peristaltic mechanism by the inclusion of Womersley number, and the critical values of concentration and occlusion on the flow characteristics in a small artery with flexible walls. Momentum and mass equations for the fluid and particle phases are solved by means of a perturbation analysis in which the occlusion is a small parameter. Closed form solutions are obtained for the fluid/particle velocity distributions, stream function, pressure rise, friction force, wall shear stress, instantaneous mechanical efficiency, and time-averaged mechanical efficiency. The physical explanation of the Segre–Silberberg effect is introduced and the trapping phenomenon of plasma for haemodilution and haemoconcentration cases is discussed. It has been deduced that the width of the closed plasma streamlines is increased while their number is minimally reduced in case of haemoconcentration. This mathematical problem has numerous applications in various branches in science including blood flow in small blood vessels. Several results of other models can be deduced as limiting cases of our situation.

Turbulent flow between counter-rotating concentric cylinders : a direct numerical simulation study

Abstract: We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

Gas-liquid two-phase flow across a bank of micropillars

Abstract: Adiabatic nitrogen-water two-phase flow across a bank of staggered circular micropillars, 100μm long with a diameter of 100μm and a pitch-to-diameter ratio of 1.5, was investigated experimentally for Reynolds number ranging from 5 to 50. Flow patterns, void fraction, and pressure drop were obtained, discussed, and compared to large scale as well as microchannel results. Two-phase flow patterns were determined by flow visualization, and a flow map was constructed as a function of gas and liquid superficial velocities. Significant deviations from conventional scale systems, with respect to flow patterns and trend lines, were observed. A unique flow pattern, driven by surface tension, was observed and termed bridge flow. The applicability of conventional scale models to predict the void fraction and two-phase frictional pressure drop was also assessed. Comparison with a conventional scale void fraction model revealed good agreement, but was found to be in a physically wrong form. Thus, a modified physically ...