Convective Mach Number and Full-Scale Supersonic Jet Noise Directivity

This paper examines the connection of convective Mach number definitions to maximum noise radiation angle for a T-7A-installed GE F404 jet engine. Definitions include those corresponding to Kelvin-Helmholtz (K-H) and supersonic instability (SI) Mach waves, and an empirical formulation. Under convectively supersonic conditions without an afterburner (AB), only K-H waves are present. At AB, SI Mach waves may exist, but at shallow angles outside the main radiation lobe. Evidence suggests that Mach wave radiation from faster-than-ordinary K-H waves could stem from shock-cell velocity fluctuations. The empirical convective Mach number indicates decreasing effective convective velocity from similar to 80 to similar to 60% of fully expanded velocity as engine power increases to AB. This convective velocity decreases with frequency, especially for those whose maximum source locations occur between the potential and supersonic core tips. Additionally, a new definition of supersonic-jet convective Mach number, dependent solely on the jet acoustic Mach number, similar to Mac, has been derived from wide-ranging jet data. This definition describes the F404 maximum noise radiation angle from intermediate thrust through AB within 2 degrees. Relating this expression to K-H Mach waves for an isothermal jet indicates the relative unimportance of temperature in determining maximum radiation angle for heated supersonic jets, including military jet aircraft and rockets.