Connecting the Convective Mach Number to Full-scale Supersonic Jet Noise Directivity

Abstract

This paper describes investigations into convective Mach number and its relationship to maximum radiation angle for an installed afterburner-capable military jet engine. The convective Mach number describes the velocity of coherent structures in the turbulent mixing layer of a jet. For supersonic jets, this parameter should be useful in predicting the maximum noise radiation angle. However, of the several definitions of the convective Mach number, none have been successful in predicting the peak radiation angle of all jets. In this paper, physicsbased and empirically derived convective Mach numbers are calculated from data collected from a T-7A-installed GE F404 engine and are compared against measured maximum noise directivity angles. Of the physics-based definitions, the T-7A data how the convective Mach number associated with Oertel’s first family of instability waves predicts the maximum radiation angle within 6° over a range of engine conditions. Additionally, the so-called “Oertel convective Mach number,” which has successfully predicted peak directivity angles in rocket noise studies, is a relatively poor predictor of the T-7A maximum directivity angle. An empirical formulation of the convective Mach number suggests that, for the T-7A, the “convective velocity” of coherent structures in the shear layer is about 60% of the fullyexpanded centerline velocity for supersonic engine conditions. Evaluating this empirical definition of the convective Mach number using data from other jet noise studies shows that the acoustic Mach number appears to be the best predictor of the convective velocity. Finally, a frequency-dependent study of the convective Mach number at afterburner shows the peak directivity angle is roughly constant at low and high frequencies, while the frequencies associated with the transition from the potential core to the supersonic core show the greatest change in directivity.