Transition in oscillating boundary layer flows

Abstract

An experimental investigation of transition phenomena in non-steady boundary layers of sinusoidally oscillating flows was conducted, and the effect of various parameters on the transition process was observed.The manner in which transition occurs appears to be related to a dimensionless grouping designated as the non-steady Reynolds number, (Re)NS= LΔU/2πvν. When this number exceeds a certain critical value, transition begins with turbulent bursts appearing periodically at the frequency of the free stream oscillation; these are preceded by instability waves having the appearance of a Tollmien-Schlichting instability. The transition Reynolds number depends, in this case, only on the amplitude of the free stream oscillations and not on their frequency, at least to the first order. Below a critical value of this parameter, transition occurs at a relatively constant Reynolds number which appears independent of the amplitude and frequency of the oscillation, at least over the range tested.When the bursts appear periodically, their development appears to occur in two succeeding phases: an initial or ‘creative’ phase marked by a sequential appearance of turbulence upstream and rapid development and a latter or ‘convective’ phase marked by turbulent spots having relatively constant leading and trailing edge velocities.The dimensionless amplitude, ΔU/U∞, of the imposed oscillations was varied from 0.014 to 0.29 while the oscillation frequencies extended from 4.5 to 62c/s.Pressure gradients imposed on the flat plate model during the course of the study are given bydCp/dx = − 0.004/ft., −0.081/ft. and 0.045/ft. whereCp= 2p/ρU2∞and x is the distance (ft.) along the plate.