Vortex formation in front of a piston moving through a cylinder

Abstract

This paper contains the details of an experimental study of the vortex formed in front of a piston as it moves through a cylinder. The mechanism for the formation of this vortex is the removal of the boundary layer forming on the cylinder wall in front of the advancing piston. The trajectory of the vortex core and the vorticity distribution on the developing vortex have been measured for a range of piston velocities. Velocity field measurements indicate that the vortex is essentially an inviscid structure at the Reynolds numbers considered, with viscous effects limited to the immediate corner region. Inviscid flow is defined in this paper as being a region of the flow where inertial forces are significantly larger than viscous forces. Flow visualization and vorticity measurements show that the vortex is composed mainly of material from the boundary layer forming over the cylinder wall. The characteristic dimension of the vortex appears to scale in a self-similar fashion, while it is small in relation to the apparatus length scale. This scaling rate of t 0.85+0.7m , where the piston speed is described as a power law At m , is somewhat faster than the t 3/4 scaling predicted by Tabaczynski et al. (1970) and considerably faster than a viscous scaling rate of t 1/2 . The reason for the structure scaling more rapidly than predicted is the selfinduced effect of the secondary vorticity that is generated on the piston face. The vorticity distribution shows a distinct spiral structure that is smoothed by the action of viscosity. The strength of the separated vortex also appears to scale in a self-similar fashion as t 2m+1 . This rate is the same as suggested from a simple model of the flow that approximates the vorticity being ejected from the corner as being equivalent to the flux of vorticity over a flat plate started from rest. However, the strength of the vorticity on the separated structure is 25% of that suggested by this model, sometimes referred to as the 'slug' model. Results show that significant secondary vorticity is generated on the piston face, forming in response to the separating primary vortex. This secondary vorticity grows at the same rate as the primary vorticity and is wrapped around the outside of the primary structure and causes it to advect away from the piston surface.

Vortex formation in a cavity with oscillating walls

“…The second vortex generation mechanism (labeled M 2) is the sharp change in the flow direction as the fluid set in motion by the moving walls meets the fixed wall. The main physical process in this case consists on roll up of cast off vortex sheets and has been discuscussed by Tabaczynski et al [4] and Allen and Chong [7] for large Reynolds numbers. Vortices generated by M 1 are noticeable along the whole cycle, they change their vorticity sign along the cycle and are located in the regions near the moving walls.…”

“…It has been found that as a vortex approaches a wall perpendicular to its direction of motion, a region with opposite vorticity is formed between its core and the wall. See for instance Walker et al [28] and Allen and Chong [7] for experimental observations and Peace and Riley [30] for numerical calculations. In our simulations, this effect is present at the lower fixed wall for φ = 0 as can be seen from figure (16) where the vorticity field is plotted as a function of position for Re = 500, Y = 0.8.…”

“…Also, close to the corner, viscous forces are much larger than inertial ones. Using an order of magnitude argument Batchelor [6] indicates that the distance r from the corner to where a steady viscous solution is applicable is of the order of r ≪ ν/U w , but experiments of Allen and Chong [7] have shown that the validity of the viscous solution is significantly larger than ν/U w .…”

“…Tabaczynski et al [4] and Allen and Chong [7] studied the dimension of the vortex generated when the lateral wall moves towards the piston. The first authors considered constant and sinusoidal wall speed while Allen and Chong [7] observed the phenomenon for constant or power law wall speed.…”

“…The first authors considered constant and sinusoidal wall speed while Allen and Chong [7] observed the phenomenon for constant or power law wall speed. Analysis and numerical studies on incompressible flows are done considering isothermal conditions.…”