Effects of Distributed Surface Roughness on the Linear Stability of Laminar Boundary Layers

摘要

This paper presents an original procedure for the evaluation of models describing the laminar mean flow over rough surfaces. The evaluation and validation of such models is a crucial aspect to consider before studying the transition over rough surfaces since most transition analysis are based on the stability characteristics of the laminar mean flow. The proposed evaluation procedure is based on comparisons between the stability caracteristics of the computed laminar mean flow and those measured experimentally. Since the stability characteristics of a boundary layer are directly related to the details of the mean flow, agreement between predicted and measured amplification ratio of disturbances should imply accurate predicted velocity profiles. A modified-viscosity model and a discrete element model for describing the manner in which distributed surface roughness affects the laminar mean flow characteristics of boundary layers are considered in this work. Once a rough-wall boundary layer solution is obtained using the models, a stability analysis is undertaken using the linear stability theory. The stability analyses have shown that the modified-viscosity and discrete-element models alter the mean velocity profile of the boundary layer in a way that amplifies the Tollmien-Schlichting waves, and that the presence of distributed roughness increases both the range of unstable frequencies and the spatial growth rate. The two models predicted amplification of low frequency disturbances in good agreement with experimental data.