The fluid dynamics of symmetry and momentum transfer in microchannels within co-rotating discs with discrete multiple inflows

Abstract

This paper presents a systematic computational study of the flow in a shrouded rotor cavity (with depth of the order of 100 μm) with multiple discrete inflows revealing the physics of how an initially non-axisymmetric flow evolves, both in the Lagrangian and Eulerian frameworks, towards axisymmetry. The approach to axisymmetry happens faster for the tangential velocity as compared to the radial component. The non-uniform inlet condition for the radial and tangential velocities, consisting of high velocity at the inlet openings and zero velocity on the shroud wall in between two consecutive inlets, gives rise to an oscillatory variation in the velocity of a fluid particle, with progressively decreasing amplitude, if one tracks its motion along a surface streamline. The rate of decay of the amplitude increases, i.e., equivalently the approach to the axisymmetric condition happens at a greater radial location, as the number of inlets, Ninlet, is increased. When the rotational speed of the discs, Ω, is increased, the distribution of radial velocity (Ur) is significantly altered, which may result even in a change of the fundamental shape of its z-profile, changing from parabolic to flat to W-shaped. The fluid has to negotiate with two different non-uniformities within a short radial distance (Δrc): one in the θ–direction because of the presence of discrete inlets and the other in the z–direction due to the no-slip condition on the disc surface. An increase in Δrc from zero to a finite value assists in the attainment of the axisymmetric condition for both tangential and radial velocities, i.e., the axisymmetry is obtained at a larger radial location. The subtle and complex fluid dynamics of the approach to axisymmetry is comprehensively analysed by following the progressive development of the z-profiles of Ur along a surface streamline located on the middle-plane of the inter-disc-spacing for an eight-inlet flow-configuration. Two sets of velocity profiles are recorded—the first set at points whose azimuthal positions are directly aligned with the inlets and the second set at points which fall in the middle of two consecutive inlets. Both sets are of W-shape near the disc periphery, then they become flat in the middle, finally becoming parabolic. The velocity profiles of the two sets approach each other and finally become superposed when axisymmetry is attained.