Spectra and directivity of a Hartmann whistle

Experimental and theoretical studies of the spectral and directivity characteristics of a Hartmann whistle are presented for pressure ratios in the range of 4.92–6.88. Cavity resonance is observed for the range of pressure ratios studied and the sound pressure amplitudes are larger than those of free jets. Distinct spectra with high sound pressure levels are observed at the fundamental frequency as well as the higher harmonics. Based on dimensional analysis, an expression for the fundamental frequency is derived in terms of the stagnation sound speed, cavity length, and stand-off distance. The analogy between Hartmann whistle and a classical Helmholtz resonator is discussed. Numerical simulations of the flow field, carried out to supplement the experimental findings, show that the jet regurgitance is significant at smaller values of cavity-stand-off distances. The correspondence between flow pattern seen from numerical simulations and the maximum directivity observed from acoustical measurements is highlighted. The flow diversion around the cavity explains the observed shift in directivity towards higher angles for the whistle, as compared to the free jet flow. The acoustic power and efficiency are high for small values of stand-off distances and larger cavity lengths.