The discipline of acoustics is intimately related to fluid dynamics.Many sounds that are technologically important in industrial applications are generated by and propagated in fluid flows. The phenomena associated with sounds can therefore be understood and analyzed in the general framework of fluid dynamics. (The governing equations for acoustics are indeed the same as the ones governing fluid flows.)
The main challenge in numerically predicting sound waves stems from the well-recognized fact that sounds have much lower energy than fluid flows, typically by several orders of magnitude. This poses a great challenge to the computation of sounds in terms of difficulty of numerically resolving sound waves, especially when one is interested in predicting sound propagation to the far field. Another challenge comes from the difficulty of predicting the very flow phenomena (for example, turbulence) in the near field that are responsible for generating sounds.
Broadband Noise Source Models
In many practical applications involving turbulent flows, noise does not have any distinct tones, and the sound energy is continuously distributed over a broad range of frequencies. In those situations involving broadband noise, statistical turbulence quantities readily computable from RANS equations can be utilized, in conjunction with semi-empirical correlations and Lighthill’s acoustic analogy, to shed some light on the source of broadband noise.
ANSYS Fluent offers several such source models that enable you to quantify the local contribution (per unit surface area or volume) to the total acoustic power generated by the flow. They include the following:
Proudman’s formula
jet noise source model
boundary layer noise source model
source terms in the linearized Euler equations
source terms in Lilley’s equation
Considering that one would ultimately want to come up with some measures to mitigate the noise generated by the flow in question, the source models can be employed to extract useful diagnostics on the noise source to determine which portion of the flow is primarily responsible for the noise generation. Note, however, that these source models do not predict the sound at receivers.
Unlike the direct method and the FW-H integral method, the broadband noise source models do not require transient solutions to any governing fluid dynamics equations. All source models require what typical RANS models would provide, such as the mean velocity field, turbulent kinetic energy and the dissipation rate. Therefore, the use of broadband noise source models requires the least computational resources.
Proudman’s Formula
Proudman(I. Proudman. "The Generation of Noise by Isotropic Turbulence". Proc. Roy. Soc. A214. 119. 1952), using Lighthill’s acoustic analogy, derived a formula for acoustic power generated by isotropic turbulence without mean flow. More recently, Lilley (G. M. Lilley. "The radiated noise from isotropic turbulence revisited". NASA Contract Report 93-75. NASA Langley Research Center, Hampton, VA. 1993.) re-derived the formula by accounting for the retarded time difference that was neglected in Proudman’s original derivation.