Shallow Cavity Flow Tone Experiments: Onset of Locked-On States

Fully turbulent inflow past a shallow cavity is investigated for the configuration of an axisymmetric cavity mounted in a pipe. Emphasis is on conditions giving rise to coherent oscillations, which can lead to locked-on states of flow tones in the pipe-cavity system. Unsteady surface pressure measurements are interpreted using three-dimensional representations of amplitude-frequency-inflow velocity; these representations are constructed for a range of cavity depth. Assessment of these data involves a variety of approaches. Evaluation of pressure gradients on plan views of the three-dimensional representations allows extraction of the frequencies of the instability (Strouhal) modes of the cavity oscillation. These frequency components are correlated with traditional models originally formulated for cavities in a free-stream. In addition, they are normalized using two length scales; inflow boundary-layer thickness and pipe diameter. These scales are consistent with those employed for the hydrodynamic instability of the separated shear layer, and are linked to the large-scale mode of the shear layer oscillation, which occurs at relatively long cavity length. In fact, a simple scaling based on pipe diameter can correlate the frequencies of the dominant peaks over a range of cavity depth. The foregoing considerations provide evidence that pronounced flow tones can be generated from a fully-turbulent inflow at very low Mach number, including the limiting case of fully-developed turbulent flow in a pipe. These tones can arise even for the extreme case of a cavity having a length over an order of magnitude longer than its depth. Suppression of tones is generally achieved if the cavity is sufficiently shallow