Direct Correlation of Noise and Flow of a Jet Using Laser Doppler

Abstract

Ribner's self and shear noise theory has successfully described many features of jet noise. However, earlier attempts to cross-correlate postulated source terms and jet noise have been only partially successful owing to hot wire-flow interaction. Thus a nonintrusive laser Doppler velocimeter (LDV) has replaced the hot wire. Source strength distributions and far-field self and shear noise spectra are inferred from jet flow (measured with LDV) correlations with jet noise for a model air jet operating at Mach 0.3. Source distributions over slices of jet are unexpectedly somewhat pearshaped. Spectra computed from LDV-jet noise correlations are compatible with corresponding spectra extracted from farfield intensities and with theory. HE generation of noise by turbulent flow is described by a variety of theories. The governing equations differ primarily in the interpretation of certain terms as either source or propagation mechanisms. Measurable properties of the sound field are predicted by summation over all sources, typically a volume integral. These sources are described by an approximate model of the underlying process. Integration over the source region is a smoothing operation; thus pre- dictions tend to be somewhat insensitive to variations of parameters of the assumed model. It is therefore desirable to eliminate the empiricism of source modeling and to demonstrate a one-to-one correspondence between the postulated source mechanism and the radiated sound. Such relationships are readily measured in terms of cross-correla tions in the time domain and cross-spectral densities in the frequency domain. These functions are indicators of the measure of coherence between two signals. Statistically independent functions possess no coherence; input and output of a linear system, on the other hand, are well correlated. The source terms measured herein may be thought of as inputs and the jet noise as the output. The existence of coherence is not sufficient proof of a definite causal relationship between the assumed source terms and the radiated sound. Both may be the result of an unidentified forcing function. One must also demonstrate that the measured cross-correlations are consistent with the postulated source mechanism. Consider a collection of independent radiators as a rather heuristic model of jet nosie. The cross-correlation (cross- spectrum) of a single source and the far-field pressure is a measure of the contribution to the far-field pressure autocorrelation (power spectrum). The latter can be con- structed by adding the contributions of all sources. Closure occurs only if the source model is a valid description of the physical process. Jet noise diagnostics combine the measurement of cross- correlations between the postulated source terms and the