Cross-Flow Instability with Periodic Distributed Roughness

Abstract

This work involves the study of the sensitivity of the Type 1 cross-flow instability to patterned distributed roughness, and the evolution of these modes to turbulence. The basic flow consists of the 3-D boundary layer over a rotating disk. The roughness is made up of ink dots which were applied to the surface of the disk. The pattern of dots consisted of an equally spaced array in the azimuthal direction, at a fixed radius. Logarithmic spiral patterns of dots were also used to enhance azimuthal wave angles. Both subcritical and supercritical radii were explored. The dots were accurately placed using the computer controlled traversing mechanism which was equipped with an inking pen. The diameter and heights of the dots are 1.6mm and 0.06mm \(\left( {h\sqrt {{w \mathord{\left/ {\vphantom {w v}} \right. \kern-\nulldelimiterspace} v}} = 0.16} \right)\) respectively. The azimuthal number of dots was intended to excite a particular azimuthal mode number of cross-flow modes. By this, uniform stationary modes could be excited so that we could more accurately separate fluctuations in velocity time series due to these, from modes which were travelling with respect to the disk rotation frame. The velocity time series were simultaneously measured at two radial positions. The instability azimuthal wave number, β, was found to change in response to the azimuthal dot number, α. The result was that the local angles of the cross-flow waves changed to keep the most amplified radial wave number, a. We documented the linear growth stage for stationary and travelling modes. We also documented a triad coupling between pairs of travelling modes and a stationary mode. The strongest of these was a difference interaction which lead to the growth of low azimuthal number stationary mode. This mode had the largest amplitude and appeared to dominate transition.KeywordsRadial PositionFlow DistortionVelocity Time SeriesAzimuthal NumberAzimuthal Wave NumberThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.