Stability of Flow in a Corrugated Channel

摘要

Understanding how surface roughness affects the laminar-turbulent transition process is one of questions of fundamental importance in fluid dynamics that has so far eluded rational resolution. This question is also of considerable practical importance, particularly for the design of laminar airfoils in aeronautical applications. Generally speaking, the presence of the roughness favors transition in the sense that under otherwise identical conditions, transition occurs at a lower Reynolds number on a rough wall that on a smooth wall. If the roughness height is sufficiently small, it has no effects on the transition process and the corresponding wall is considered to be hydraulically smooth. Various experiments indicate that when the roughness is operative the departure from the laminar state is explosive with the underlying cause not being known. The objective of this analysis is to elucidate the character of this very process. Difficulties preventing successful solution of the above problem stem from the fact that various physical processes may initiate the transition process, depending on the distribution, amplitude and geometry of the roughness. The existing experimental investigations provide a phenomenological description of transition in the form of correlations between the height of the roughness, the flow conditions and the critical Reynolds number for certain classes of geometrical forms of the roughness. The range of applicability of these correlations is not certain because they are based on a limited experimental data and have been determined for, in essence, artificially created roughness forms.