Universal scaling laws on sound generated aerodinamically

Abstract

In 1952 and 1954, respectively, Sir James Lighthill derived a sound equation by an analogy approach and proposed a well-known U 8 power law for the the power of sound by using magnitude scale analysis. However, the Lighthill U 8 law breaks down at velocities when Mach number M > 1. In order to unify all the scaling laws of sound power, instead of using a Lighthill equation, an alternative way of using dimensional analysis has been proposed and a discovery of the universal power law of the power of sound has been founded as W = ρD2U 3f( c0 U ) = ρ0D2U 3f( 1 M ). As a special scenario, the scaling law for hypersonic flow has been obtained as W = Cρ0D2U 3 , which coincides with the experiments.