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.

Experimental and Theoretical Investigations of Edge Tones in High Speed Jets

“…Most of the reported experimental results of impinging tones are for axisymmetric jets and flat plat (1), (5), (11) . On the other side, most of the reported experimental results of edgetones are for two-dimensional jets and wedge-shaped edge (10), (12) .…”

“…Investigations of discrete tone generation mechanism of impinging jets by Marsh (14) , Wagner, (15) , Neuwerth, (16) , Umeda et al (17) , and Tam and Ahuja (1) revealed that in order to produce stable impinging tones, the Strouhal number of the instability frequency must match the Strouhal number of the Kelvin-Helmholtz instability in an axisymmetric free jet which is usually less than 0.7. Their studies also reveal that for subsonic jets the stability waves and the flow field associated with the feedback loop possess axial symmetry.…”

“…Semi-empirical frequency formula for the dominant tone is proposed based on the present experimental data for small edge angles. The theoretical results based on the vortex-sheet model proposed by Tam and Ahuja (1) showed that both helical and axisymmetric stability modes exist during jet impingement. The dominant tone usually has helical stability mode which is the well known edge-tone.…”

“…It has experimentally shown that as the distance between the wall and the jet is increased, the impingement tone frequency does not change continuously rather it changes discontinuously. The impingement tone frequency, f n , is determined by the phase-lock principle which state that the sum of the time taken for the instability waves to propagate from the nozzle exit to the wall and the time taken for the feedback acoustic waves to propagate from the wall upstream inside or outside the jet to the nozzle exit must be equal to an integer multiple of the period of oscillation (1), (9), (10) . Using this principle, an expression for the impingement tone frequency, f n , can be derived as follows…”

Computation of Tone Noise from Supersonic Jet Impinging on Flat Plates

“…For example, after careful observations over the experimental data, Powell [1] pointed out that the small instability waves (vortices) around the jet shear layers and the consequent radial wall jet are responsible for the noise as they interact with the flat plate and produce sound waves. Ho and Nosseir [2] explained the feedback loop in the impinging jets; while Tam and Ahuja [3] put forward another theoretical model for the acoustic feedback loop. In the meantime, experimentalists are conducting various physical experiments in search for the feedback mechanism in different impinging jet situations.…”