Quantitative analysis of flow visualizations in an unsteady channel flow

Abstract

Quantitative results concerning the modulation of the ejection and bursting frequency in an unsteady channel flow obtained by flow visualizations are presented and compared with probe measurements. The frequency of the imposed velocity oscillations f covers a large range going from the quasi steady limit to the time mean bursting frequency in the corresponding steady flow. The imposed amplitudes of the velocity oscillations are 13% and 20% of the centerline velocity. The bursting process is identified by the intermittent lift up of the dye injected at the wall. Qualitative analysis of the flow visualizations show that the ejection activity at a given phase of the oscillation cycle is repetitive from one cycle to the other. The modulation amplitude of the ejection frequency 〈f _e 〉 is sensitive to the imposed frequency. At low imposed frequency 〈f _e 〉 is modulated as the wall shear stress, but the inner scaling does not hold when f ⁺ is high. Here, (+) corresponds to the quantities normalized with the inner variables, i.e. the friction velocity u _τ and the viscosity ν. The grouping of the ejections into bursts show the coexistence of two categories of events which react differently to the forcing. The groups of ejections (Multiple Ejection Bursts) are governed by the modulation of the wall shear stress 〈τ〉 in the whole imposed frequency range. The solitary ejections (or the Single Ejection Bursts) have modulation amplitudes and phases which differ significantly from those of 〈τ〉 in the intermediate and high imposed frequency range. There is a good agreement between the flow visualization data and the probe measurements.