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.

The separating flow through a severely constricted symmetric tube

Abstract: The axisymmetric flow of an incompressible fluid through a pipe (of radius a) suffering a severe constriction is studied for large Reynolds numbers R, the features of symmetric channel flows being virtually the same. Here ‘severe’ refers to a constriction whose typical dimensions are finite, and the oncoming velocity profile is taken to be of a realistic type, i.e. with no slip at the wall. The study adopts (Kirchhoff) free-streamline theory, which, for the mostly inviscid description, affords a rational basis consistent with viscous separation. The major (triple-deck) separation takes place on the constriction surface and is followed by a downstream eddy of length O(aR). Another, less familiar, separation is predicted to occur at a distance 0.087a In R + O(a) ahead of the finite obstacle. Free-streamline solutions are found in the two main extremes of moderately severe and very severe constriction. In both extremes, and in any slowly varying constriction, the major separation is sited near the maximum constriction point. The upstream separation point is also derived, to O(a) accuracy in each case. The upstream separation can be suppressed, however, if the constriction has no definite starting point and decaysslowly upstream, but then the upstream flow response extends over a much increased distance. Comparisons with Navier-Stokes solutions and with experiments tend to favour the predictions of the free-streamline theory.

Two-Phase Flow Analysis of Concentration Profiles

Abstract: Two-phase flow analysis is used to analyze sediment concentration profiles in uniform open-channel flows over flat, sediment-starved beds that have high concentrations of single-sized sediment. Two-phase flow analysis can explicitly incorporate the effects of particle-particle interactions and particle inertia. Conventional convection-diffusion modeling cannot directly represent these phenomena and are thus limited. Both the two-phase flow formulation and the convection-diffusion modeling are compared against experimental data collected in sediment-starved sediment-laden flows. The two-phase flow model is shown to simulate the effect of both particle-particle interactions and particle inertia in these experimental flows. Simple criteria are given to determine when particle-particle interactions and particle inertia are important in sediment-laden open-channel flows over a flat bed. The current two-phase approach requires empirical formulas of the turbulence quantities and further experimental and analytical work is necessary to develop improved models for the velocity distribution and turbulence quantities.

Assessment of the validity of Stokes and Reynolds equations for fluid flow through a rough-walled fracture with flow imaging

Abstract: Understanding fluid flow through a rough-walled fracture is important in many problems such as petroleum and geothermal reservoir exploitation, geological storage of CO2, and sitting of radioactive waste repositories. In order to advance the understanding of fracture flow, we conducted the first direct measurement of flow velocity across rough-walled fractures at Reynolds number (Re) of 0.014 to 0.086. The results were used for an order of magnitude analysis to evaluate assumptions underlying the Stokes and the Reynolds equations, which are derived from simplifying the Navier–Stokes equations. Even at very rough subregions, viscous forces were at least 2 orders of magnitude greater than inertial forces, indicating that the Stokes equations are valid for Re < 0.1. However, the assumption made in the derivation of the Reynolds equation that ∂2ux/∂z2 is dominant over other viscous terms was not satisfied even at moderate roughness for Re < 0.1. The Reynolds equation overestimated flow rate.

Miscible quarter five-spot displacements in a Hele-Shaw cell and the role of flow-induced dispersion

Abstract: Miscible quarter five-spot displacements in a Hele-Shaw cell are investigated by means of experimental measurements and numerical simulations. The experiments record both the volumetric as well as the surface efficiency at breakthrough as a function of the dimensionless flow rate in the form of a Peclet number and the viscosity contrast. For small flow rates, both of these efficiency measures decrease uniformly with increasing Peclet numbers. At large flow rates, an asymptotic state is reached where the efficiencies no longer depend on the Peclet number. Up to Atwood numbers of approximately 0.5, the less viscous fluid occupies close to 23 of the gap width, which indicates a near-parabolic velocity profile across the gap. Consequently, in this parameter range a Taylor dispersion approach should be well suited to account for flow-induced dispersion effects. For larger viscosity contrasts, accompanying two-dimensional numerical simulations based on Taylor dispersion predict an increased stabilization for hi...