Exhaust flows from aircraft engines operate at higher temperatures than the free stream. Accurate predictions of the jet noise in heated flows is therefore of considerable interest. In this paper, we develop a self-consistent model for the jet noise in heated flows. The generalized acoustic analogy derived by Goldstein (2003) is used to show that the acoustic spectrum can be written as the sum of three terms: the momentum flux auto-covariance term, the enthalpy flux – momentum flux covariance (or the coupling term) and the enthalpy flux auto-covariance. The axi-symmetric model of the Reynolds stress auto-covariance developed and verified in Afsar et al (2010), is extended to heated jet problem to reduce the number of independent components of the correlation tensor from 63 down to only 11. We focus on the structure of the coupling term, which was not considered in previous work and use recent PIV measurements in heated flows taken at the NASA Glenn Research Center to show that it 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 (OASPL at all observation angles in supersonic jets. We also show how the coupling term provides a fundamental means of jet noise reduction. The final formulas for the acoustic spectrum can be used as the basis for a unified jet noise prediction scheme.
CORE (COnnecting REpositories)
CORE (COnnecting REpositories)