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.

Recent developments in scaling of wall-bounded flows

Abstract: Proper scaling of a fluid flow permits convenient, dimensionless representation of experimental data, prediction of one flow based on a similar one, and extrapolation of low-Reynolds-number, laboratory-scale experiments to field conditions. This is a particularly powerful technique for turbulent flows where analytical solutions derived from first principles are not possible. We review in the present paper the topical development in scaling the canonical turbulent boundary layer and pipe and channel flows. Additional to utilizing some of the most comprehensive and high-quality databases available to date, the article focuses on contemporary advances in analytical and asymptotic approaches to determine the mean-velocity profile as well as to scale higher-order statistics. The current debate concerning the mean-velocity profile of turbulent wall-bounded flows has ruled out neither a logarithmic nor power law behavior. Furthermore, a Reynolds number dependence of the mean-velocity profile has not been excluded either. Clearly, a more complex functional form is needed to describe the profile. The present results can be utilized to extrapolate the available low-Reynolds-number physical and numerical data to the more practically important high-Reynolds-number field conditions. Knowledge of the proper scaling of the canonical cases can also be useful to non-canonical wall-bounded flows as well as to calibrate turbulence models and flow sensors in the vicinity of walls.

Multiscale considerations in direct numerical simulations of multiphase flowsa)

Abstract: Direct Numerical Simulations of multiphase flows have progressed rapidly over the last decade and it is now possible to simulate, for example, the motion of hundreds of deformable bubbles in turbulent flows. The availability of results from such simulations should help advance the development of new and improved closure relations and models of the average or large-scale flows. We review recent results for bubbly flow in vertical channels, discuss the difference between upflow and downflow and the effect of the bubble deformability and how the resulting insight allowed us to produce a simple description of the large scale flow, for certain flow conditions. We then discuss the need for the development of numerical methods for more complex situations, such as where the flow creates spontaneous thin films and threads, or where additional physical processes take place at a rate that is very different from the fluid flow. Recent work on capturing localized small-scale processes using embedded analytical models,...

Granular jets and hydraulic jumps on an inclined plane

Abstract: A jet of granular material impinging on an inclined plane produces a diverse range of flows, from steady hydraulic jumps to periodic avalanches, self-channelised flows and pile collapse behaviour. We describe the various flow regimes and study in detail a steady-state flow, in which the jet generates a closed teardrop-shaped hydraulic jump on the plane, enclosing a region of fast-moving radial flow. On shallower slopes, a second steady regime exists in which the shock is not teardrop-shaped, but exhibits a more complex ?blunted? shape with a steadily breaking wave. We explain these regimes by consideration of the supercritical or subcritical nature of the flow surrounding the shock. A model is developed in which the impact of the jet on the inclined plane is treated as an inviscid flow, which is then coupled to a depth-integrated model for the resulting thin granular avalanche on the inclined plane. Numerical simulations produce a flow regime diagram strikingly similar to that obtained in experiments, with the model correctly reproducing the regimes and their dependence on the jet velocity and slope angle. The size and shape of the steady experimental shocks and the location of sub- and supercritical flow regions are also both accurately predicted. We find that the physics underlying the rapid flow inside the shock is dominated by depth-averaged mass and momentum transport, with granular friction, pressure gradients and three-dimensional aspects of the flow having comparatively little effect. Further downstream, the flow is governed by a friction?gravity balance, and some flow features, such as a persistent indentation in the free surface, are not reproduced in the numerical solutions. On planes inclined at a shallow angle, the effect of stationary granular material becomes important in the flow evolution, and oscillatory and more general time-dependent flows are observed. The hysteretic transition between static and dynamic friction leads to two phenomena observed in the flows: unsteady avalanching behaviour, and the feedback from static grains on the flowing region, leading to lev�ed, self-channelised flows.