THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

386 14. Machinery Noise ControlPrior to Lighthill’s pioneering work, there have been even earlier studies madeon aerodynamic noise in conjunction with efforts to reduce noise in axial fans. Wecan go back even further to find that the effect of jet streaming was mentioned in theearliest recorded references to sound. When the wind blew past the pillars of theancient Greek temples, eerie discrete tones were produced. The Greeks adjudgedthese tones to be the voice of Aeolus, the god of the wind, and hence these tonesare called Aeolian tones.The mechanism of the Aeolian sound can be explained by visualizing the flowof air over a cylinder. At a given velocity, the downsteam flow behind the cylinderexhibits an oscillatory pattern, as vortices are shed alternatively on one side of thecylinder and then the other. The ensuing trail of eddies form what is referred to as avon Kàrmàn vortex street, which contains strong periodic components, resulting ina sound of nearly pure tonal quality. On the basis of empirical data, the frequencyof the Aeolian tone can be predicted fromf Aeolian = αvdwherev = velocity of air, m/sd = diameter of cylinder, mα = Strouhal number, approximately 0.2Figure 14.11 displays the simplest example of a gas jet, in which the highvelocity airflow is emanating from a reservoir through a nozzle. The gas acceleratesfrom virtually zero velocity in the reservoir to a peak velocity in the core at theexit of the nozzle. The peak velocity of the jet depends greatly on the pressuredifference between the reservoir pressure p r and external (ambient) pressure p a .As the pressure ratio increases, the velocity of the gas at the discharge increasesup to a point when the pressure ratio of 1.89 (for the case of the gas being air) isreached. Once the flow velocity reaches the velocity of sound, any further increaseof the reservoir pressure will not result in an increase of the velocity at the end ofthe straight duct. When the critical pressure ratio of 1.89 is reached, the nozzle isFigure 14.11. A simple gas jet.