Enthalpy flux/momentum flux coupling in the acoustic spectrum of heated jets

Exhaust flows from aircraft engines operate at higher temperatures than those of the freestream. Accurate predictions of jet noise in heated flows is therefore of considerable interest. In this paper, a self-consistent jet noise model in heated flows is developed using the generalized acoustic analogy. To begin with, it is demonstrated that the exact acoustic spectrum can be written as the sum of three terms: the momentum-flux autocovariance term, the enthalpy-flux/momentum-flux covariance (or the coupling term), and the enthalpy-flux autocovariance. By extending an axisymmetric turbulence model to heated-jet flows, it is shown that the number of independent components in the acoustic spectrum can be reduced to 11 terms. The paper then focuses on the structure of the coupling term using recent Rayleigh scattering measurements in heated flows taken at NASA John H. Glenn Research Center at Lewis Field. It is shown that the coupling term becomes increasingly important as the acoustic Mach number increases. That is, it can provide either enhancement or cancellation to the acoustic spectrum, depending on the acoustic Mach number and the position of the observation point. This behavior can help explain why heating reduces the overall sound pressure level at all observation angles in supersonic jets.