On the Aerodynamic Noise of a Turbulent Jet

Abstract

Summary A new model is advanced for analyzing the broad-spectrum noise of a turbulent jet. The shear layer bounding the turbulent jet is assumed to play an important role in modifying the quadrupole sound radiation from the interior. To the sound-emit­ ting, small-scale turbulent eddies (with frequencies much higher than those of large-scale eddies), the laminar shear layer has an irregular contour, as if the large-scale turbulent motions were frozen. The linearized analysis is then applied to the laminar shear layer to relate the acoustic oscillations across it. The concept of geometrical acoustics is generalized to represent the passage of an acoustic ray through a laminar shear layer. Acoustic rays may be traced across the shear layer as transmis­ sion and refraction, but they may also be apparently absorbed or generated by the laminar layer. This generation is visual­ ized as the schematic representation, within the framework of geometrical acoustics, of the action of the Reynolds stress in transferring energy from the shearing mean flow to the acoustic waves. Such action of the Reynolds stress can be neglected in ordinary acoustics when the acoustic medium is not moving at speeds comparable to the speed of sound in the medium. How­ ever, this action is of crucial importance in the aerodynamic noise of high-speed turbulent jets where the Reynolds stress is the fun­ damental element of the radiating quadrupoles, according to Lighthill. Those acoustic waves that become stationary with respect to the local mean flow somewhere in the interior of the shear layer are significantly modified by the viscous action through the critical layer. The shear layer therefore serves as a selective amplifier of the acoustic waves passing through it. Kinematically, the shear layer brings about the preferred downstream emission. Dynamically, the shear-layer augmentation signifi­ cantly increases the polar peak noise level. The acoustic power output per unit solid angle for such downstream emissions aug­ mented by the shear layer (including the polar peak) varies as Uj8, as predicted by Lighthill, but without Lighthill's convective corrections. On the other hand, the acoustic power output per unit solid angle nearly normal to the jet, due to the transmitted downstream-propagating waves, varies roughly as £//. Heating the jet gas increases the shear-layer augmentation and may in­ crease the polar peak noise level by several db. The silencing action of the edge notches and edge teeth may also be inter­ preted as due apparently to the result of possible distortion of the shear-layer profiles.