Improved jet noise modeling using a new acoustic time scale

To calculate the noise emanating from a turbulent flow (such as a jet flow) using Lighthill's analogy, knowledge concerning the unsteady characteristics of the turbulence is required. Specifically, the form of the turbulent correlation tensor together with various time and length-scales and convection velocities are needed. However, if we are using a RANS calculation then we obtain only steady characteristics of the flow and it is then necessary to model the unsteady behaviour in some way. While there has been considerable attention given to the correct way to model the form of the correlation tensor (or equivalently the spectral density), less attention has been given to underlying physics that dictate the proper choice of timescale. In early studies various authors tended to assume that the acoustic timescale was proportional to the turbulent dissipation rate but later studies have revealed that a frequency dependent relationship gives better results. In this paper we recognise that there are several time dependent processes occurring within a turbulent flow and propose a new way of defining an acoustic timescale. An isothermal single-flow M0.75 jet has been chosen for the present study and essential fluid dynamic information and turbulent parameters have been obtained using a modified k-ε method. The jet noise prediction at 90 deg is found using Lighthill's analogy and directivity is estimated using an asymptotic solution of Lilley's formulation. Predictions reveal good agreement between the noise predictions and observations. Furthermore, the new time-scale has an inherent frequency dependency that arises naturally from the underlying physics thus avoiding supplementary mathematical enhancements to the model.