Sinuous instability of a planar air jet: Propagation parameters and acoustic excitation

Abstract

The sinuous instability wave of a planar air jet is excited by localized acoustic flow across the nozzle. Phase velocity and the growth exponent are found from synchronous hot-wire measurements made beyond the excited region, where the profile is approximately sech-squared. In the observed range of scaled radian frequency, 0.02-1.33 (the stability limit), results agree with real-frequency (spatially growing) analysis but not with complex-frequency (temporally growing) analysis. The latter predicts smaller phase velocity at low frequencies and has been questioned in edgetone analysis. In further tests, the acoustic driving signal is made independent of downstream distance, as in an organ pipe. The jet deflection is then the sum of acoustic convection and of the instability wave, summing to zero at the nozzle, as proposed by Fletcher, Elder, and others. The instability-wave theory applies to linear behavior in the inviscid limit and therefore to a hypothetical nonspreading jet. The local velocity profile width must be considered in relating to a physical jet. In a flue organ pipe oscillating at equilibrium amplitude the stability-wave theory is not applicable near the lip, where the laminar flow assumed in the theory disappears and the jet deflection exceeds the range of linear behavior. Direct sound generation by the jet is investigated briefly.

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“…Many of these questions can be settled only by detailed experiments such as those of Thwaites and Fletcher. The most recent studies by Nolle [29] sugupon the jet, the phase delay for propagation along the jet, and phase shift involved in the interaction of the jet flow with internal acoustic waves in the pipe. In total these must sum to 2π for the feedback loop to close.…”