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 existence of Taylor vortices and wide-gap instabilities in spherical Couette flow

Abstract: The flow of a viscous incompressible fluid in the gap between two concentric spheres was investigated for the case where only the inner sphere rotates and the outer one is stationary. Flow visualization studies were carried out for a wide range of Reynolds numbers (Re≦2·105) and aspect ratios (0.08≦β≦0.5) to determine the instabilities during the laminar-turbulent transition and the corresponding critical Reynolds numbers as a function of the aspect ratio. It was found that the laminar basic flow loses its stability at the stability threshold in different ways. The instabilities occurring depend strongly on the aspect ratio and the initial conditions. For small and medium aspect ratios (0.08≦β≦0.25), experiments were carried out as a function of the Reynolds number to determine the regions of existence for basic flow, Taylor vortex flow, supercritical basic flow and furthermore, to give the best fit for the maximum number of pairs of Taylor vortices as a function of aspect ratio. For wide gaps (0.33≦β≦0.5), however, Taylor vortices could not be detected. The first instability manifests itself as a break of the spatial symmetry and non-axisymmetric secondary waves with spiral arms appear depending on the Reynolds number. For β=0.33, secondary waves with an azimuthal wave numbern=six, five and four were found, while in the gap with an aspect ratio of β=0.5 secondary waves withn=five, four and three spiral arms exist. Frequencies of these secondary waves were measured, the corresponding critical Reynolds numbers and the transition Reynolds numbers during the transition to turbulence were found. The flow modes occurring at the poles look very similar to those found in the flow between two rotating disks. Effects of non-uniqueness and hysteresis were determined as a function of the acceleration rate.

On the classification of solutions to the zero-surface-tension model for Hele-Shaw free boundary flows

Abstract: We discuss the classification of solutions to the zero-surface-tension model for Hele-Shaw flows in bounded and unbounded regions with suction and injection. We use results from the theory of univalent functions to derive estimates for certain geometric properties of the fluid region in the injection case.

Aerodynamic Interference Induced by Reaction Controls

Abstract: : The literature pertaining to the interaction of a sonic or supersonic gaseous jet with a transverse external flow has been reviewed. The flowfields associated with these interactions are complex, and knowledge of them is based largely on results of experiments. Numerous examples of data from flat-plate experiments are presented. These include static pressure distribution, induced forces, flowfield survey, and flow visualization results. Analyses and correlation techniques for jet interaction flows are discussed. The region upstream of a jet in two-dimensional flow is similar to the flow upstream of a forward-facing step, and the flow associated with a jet from a circular nozzle in a flat plate resembles the flow past a blunt-nosed slender body. The single most important variable in determining the scale of these interactions is the ratio of jet momentum flux to the external-flow dynamic pressure.