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.

Drag reduction and improvement of material transport in creeping films

Abstract: It is widely accepted that for bodies in turbulent flows a reduction of skin friction can be reached if the surface of the body is provided with small ridges aligned in the local flow direction. This surprising and counterintuitive phenomenon is called the shark-skin effect, motivated from the dermal surface morphology of sharks. In the present article we examine the possibility of resistance reduction due to a rippled surface topography in Stokes flow. We especially analyse the influence of wall riblets perpendicular to the flow direction on the mean transport velocity in gravity-driven creeping film flows following the idea that eddies generated in the valleys of the riblets act like fluid roller bearings and hence may reduce drag. Using a theoretical treatment of the Stokes equations with complex function theory, parameter studies with varying flow rate, bottom amplitude and bottom shape are presented. For the given bottom shapes the maximum enhancement of transport velocity is found by optimising the film thickness.

Supersonic and hypersonic flow with attached shock waves over delta wings

Abstract: A unified theory is developed for supersonic and hypersonic flow with attached shock waves over the lower surface of a delta wing at an angle of attack. The flow field on the lower surface of a delta wing consists of uniform flow regions near the leading edges, where the cross flow is supersonic and a nonuniform flow region near the central part, where the cross flow is subsonic. In the nonuniform flow region, the theory is based on the assumption that the flow differs slightly from the corresponding two-dimensional flow over a flat plate. Thus a linearized perturbation on a nonlinear flow field is first calculated and then strained and corrected so that the flow is matched continuously to the uniform flow which is obtained exactly. When compared with available exact numerical solutions the theory gives, in all cases, almost identical results, except near the crossflow sonic line where existing numerical methods fail to produce a discontinuous slope in the pressure curve, whereas the present theory predicts such a discontinuity and shows that the slope has a square root singularity at the crossflow sonic line similar to that in the supersonic linear theory.

Radial displacement of a fluid annulus in a rotating Hele-Shaw cell

Abstract: The radial displacement of a fluid annulus in a rotating circular Hele–Shaw cell has been investigated experimentally. It has been found that the flow depends sensitively on the wetting conditions at the outer interface. Displacements in a prewet cell are well described by Darcy’s law in a wide range of experimental parameters, with little influence of capillary effects. In a dry cell, however, a more careful analysis of the interface motion is required; the interplay between a gradual loss of fluid at the inner interface, and the dependence of capillary forces at the outer interface on interfacial velocity and dynamic contact angle, result in a constant velocity for the interfaces. The experimental results in this case correlate in the form of an empirical scaling relation between the capillary number Ca and a dimensionless group, related to the ratio of centrifugal to capillary forces, which spans about three orders of magnitude in both quantities. Finally, the relative thickness of the coating film lef...

Clustering in high Re monodispersed bubbly flows

Abstract: Experiments were conducted to determine the amount of clustering that occurs in bubbly flows for which the liquid motion can be described, with a certain degree of accuracy, using potential flow theory. A Hele-Shaw-type channel was used in which bubble overlap was avoided. Direct video image analysis was performed to calculate bubbles properties and identify cluster formation. Despite the significant wall influence of this configuration, it was found that the bubbles do form aggregates with a statistical horizontal tendency. The flow structure was also analyzed using the radial probability distribution, giving indications that support the clustering hypothesis.

Calculation of laminar separated flow in symmetric two-dimensional diffusers

Abstract: This study is concerned with numerical analysis of laminar separated flow in symmetric, two-dimensional, straight-walled diffusers. With Reynolds numbers Re=56 and 114 and expansion ratios ER=3 and 4, totally, there are four cases considered. At the low Reynolds number and the low expansion ratio the flow in the diffuser is nearly symmetric to the center line, irrespective of the diffusion angle. As Reynolds number or expansion ratio increases, a large recirculation region forms at one side wall and a small one at the other side. For the case with Re=114 and ER=4 the small recirculating flow disappears at small main recirculation region for large diffusion angles. The pressure recovery reaches its peak value somewhere downstream of the reattachment point of the large recirculating flow. The effectiveness of the diffuser deteriorates as the diffusion angle increases, aprt from that at Re=56 the effectiveness increases from θ=15 to 30 deg. Symmetric flow solutions can be obtained by incorporating a symmetric relaxation method. The pressure recovery is higher for the symmetric flow than that for the asymmetric flow owing to the weaker recirculating strength in the former.