A Dimensional Analysis of Turbo Jet Noise Data

Abstract

Measurements of the total power radiated by turbo jet engines have been analyzed by dimensional techniques. Under the assumption that the noise is created by an aerodynamical mechanism, the acoustic power may be set proportional to the mechanical power in the jet stream. Then the factor of proportionality must be a dimensionless function of the average properties of the jet stream. The dimensionless proportionality function may be shown to be a function of four dimensionless ratios, but physical arguments indicate that at least two of the four ratios may be relatively unimportant. The dimensionless proportionality function may be determined by plotting the acoustic power as a function of the mechanical power. Sixty-eight separate measurements on various types of turbo jet engines under both free-field and reverberant conditions have been examined. In each case the total acoustic power was determined by suitably integrating over space and frequency. The results show that the proportionality function may be written as, 3 × 10−4 [1 + (K/K0)3]; where K is essentially the ratio of the mechanical power in the jet stream to the thermal power conducted through the jet stream, and where K0 is a critical value of K chosen to fit the data. At large values of K/K0, the acoustic power is proportional to the eighth power of the jet velocity for all other variables constant, in agreement with Lighthill's work. At small values of K/K0, however, the acoustic power varies as the square of the velocity.