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.

Three-dimensionality in the wake of a rotating cylinder in a uniform flow

Abstract: The wake of a rotating circular cylinder in a free stream is investigated for Reynolds numbers Re6 400 and non-dimensional rotation rates of 6 2:5. Two aspects are considered. The first is the transition from a steady flow to unsteady flow characterized by periodic vortex shedding. The two-dimensional computations show that the onset of unsteady flow is delayed to higher Reynolds numbers as the rotation rate is increased, and vortex shedding is suppressed for > 2:1 for all Reynolds numbers in the parameter space investigated. The second aspect investigated is the transition from two-dimensional to three-dimensional flow using linear stability analysis. It is shown that at low rotation rates of 6 1, the three-dimensional transition scenario is similar to that of the non-rotating cylinder. However, at higher rotation rates, the threedimensional scenario becomes increasingly complex, with three new modes identified that bifurcate from the unsteady flow, and two modes that bifurcate from the steady flow. Curves of marginal stability for all of the modes are presented in a parameter space map, the defining characteristics for each mode presented, and the physical mechanisms of instability are discussed.

Large-eddy simulations of turbulent flow in a rotating square duct

Abstract: The turbulent flow at low Reynolds numbers in a rotating straight square duct was simulated using the large-eddy simulation technique. The rotation axis is parallel to two opposite walls of the duct, and the pressure-driven flow is assumed to be fully developed, isothermal and incompressible. The Reynolds number based on the friction velocity (Reτ=300) was kept constant in the range of the rotational numbers studied (0⩽Roτ⩽1.5) Computations were carried out using a second-order finite volume code with a localized one-equation dynamic subgrid scale model. Simulations of rotating channel flows were initially carried out and were seen to be in agreement with experiments and direct numerical simulations reported in the literature. The study of the flow in a rotating square duct revealed the influence of the Coriolis force on the spatial distribution of the average velocity fields and Reynolds stresses. At low rotation rates, turbulence-driven secondary flows developed near the corners convect the rotation-generated cross-stream currents. At moderate and high rotation rates, the mean secondary flow structure consists essentially of two large counter-rotating cells convecting low/high momentum fluid from the stable/unstable side to the unstable/stable side. Inspection of the terms of the transport equations of the average axial velocity and vorticity components shows the mechanisms responsible for the changes in the average flow structure. Spatial distributions of the Reynolds stresses are mainly influenced by the changes that rotation induces in the main strain rates. It has been found that, globally, at the low Reynolds number studied, rotation tends to significantly reduce the overall turbulence level of the flow.

Numerical Study of Periodically Fully Developed Flow and Heat Transfer in Cross-Corrugated Triangular Channels in Transitional Flow Regime

Abstract: Cross-corrugated triangular ducts provide high heat transfer capabilities with strong mechanical strength. Flows in such geometries are usually transitional, with typical Reynolds numbers varying from 100 to 6,000. In this study, periodic fully developed fluid flow and heat transfer in a cross-corrugated triangular duct is studied numerically. Periodicity is used to reduce the complexity of the channel geometry and enables the smallest possible segment of the flow channel to be modeled. To model the transitional flow in the topology, a validated low Reynolds number k − ω (LKW) turbulence model is employed to account for the turbulence in the flow. The temperature, velocity, and turbulence contours are obtained in the three-dimensional complex domain. The friction factors and the segment mean Nusselt numbers are calculated and correlated with Reynolds numbers, for both uniform temperature and uniform heat flux boundary conditions. The results are compared with the available experimental data for c...

On Hele–Shaw flow of power-law fluids

Abstract: This paper reviews the governing equations for a plane Hele–Shaw flow of a power-law fluid. We find two closely related partial differential equations, one for the pressure and one for the stream function. Some mathematical results for these equations are presented, in particular some exact solutions and a representation theorem. The results are applied to Hele–Shaw flow. It is then possible to determine the flow near an arbitrary corner for any power-law fluid. Other examples are also given.