Dimensional Analysis of Jet Noise Data

Abstract

*A formula for scaling laboratory model jet noise data to that of a full size jet engine is established. This is done by dimensional analysis and the Buckingham P theorem. It is well known that the noise intensity radiated by a jet varies as a high power of its velocity. This power law dependence is supported by theory and experiment. The most famous power law is the Lighthill U 8 law. In this work, a dimensionless form of the power law is sought and developed. Through the use of this nondimensional form power law, a “hot jet” limit is found at high jet temperature. In the hot jet limit, the velocity exponent and the proportionality constant of the power law are insensitive to further increase in jet temperature. This is a somewhat surprising result. Experimentally, it has been observed that seasonal temperature variation can lead to a 1.5 to 2.0 dB change in jet noise intensity. Here, environmental effects on jet noise such as seasonal and altitude variations are studied through results established by dimensional analysis. Finally, a way to scale jet mixing noise from perfectly expanded jets to shock containing jets is proposed.