Aeroacoustics of Low Mach Number Flows

5

The Ffowcs Williams and Hawkings equation

Abstract

Lighthills acoustic analogy gives the general solution to the wave equation for a medium that includes turbulence and stationary scattering objects. In many important applications, such as for propellers and helicopter rotor noise, the surfaces are moving and so we need to modify the analysis to take full account of surface motion. Very powerful techniques to address this problem have been pioneered by Ffowcs Williams and Farassat, and the objective of this chapter is to introduce these techniques. We will start by reviewing the concept of a generalized derivative and then show how these may be used to give solutions to Lighthill's equation for a medium that includes moving surfaces and ...