Theoretical model of discrete tone generation by impinging jets

Abstract

It is well known that when a high subsonic (Mach number > 0.7) high Reynolds number (Re > 2 × 105) jet is directed normal to a wall intense discrete frequency sound waves called impingement tones are emitted. This phenomenon has been studied by a number of investigators in the past. It is generally accepted that the tones are generated by a feedback loop. Despite this general agreement critical difference in opinion as to how the feedback is achieved remains unresolved. Early investigators (e.g. Wagner 1971; Neuwerth 1973, 1974) proposed that the feedback loop is closed by acoustic disturbances which propagate from the wall to the nozzle exit inside the jet. Recent investigators (e.g. Ho & Nosseir 1981; Umeda et al. 1987), However, believed that the feedback is achieved by sound waves propagating outside the jet. In this paper a new feedback mechanism is proposed. It is suggested that the feedback is achieved by upstream-propagating waves associated with the lowest-order intrinsic neutral wave modes of the jet flow. These wave modes have well-defined radial and azimuthal pressure and velocity distributions. These distributions are dictated by the mean flow of the jet exactly as in the case of the well-known Kelvin-Helmholtz instability waves. The characteristics of these waves are calculated and studied. These characteristics provide a natural explanation of why the unsteady flow fields of subsonic impinging jets must be axisymmetric, whereas those for supersonic jets may be either axisymmetric or helical (flapping). In addition they also offer, for the first time, an explanation as to why no stable impingement tones have been observed for (cold) subsonic jets with Mach number less than 0.6. Furthermore, the new model allows the prediction of the average Strouhal number of impingement tones as a function of jet Mach number. The predicted results compare very favourably with measurements. For subsonic jets the pressure and velocity field of these upstream-propagating neutral waves are found to be confined primarily inside the jet. This is in agreement with the observations of Wagner (1971) and Neuwerth (1973, 1974) and their contention that the feedback disturbances actually propagate upstream inside the jet.