“Basic” jet noise patterns after deletion of convection and refraction effects: Experiments vs. Theory

In earlier work of Grande experimental jet-noise polar plots were corrected for refraction (by experiment) and for convection (by theory) to yield the relatively small experimental basic directivity in narrow frequency bands. The experimental correction for refraction at each frequency was obtained from the difference in the directional patterns of a point source placed in the air jet with jet off and jet on. In the present work, with new measurements, the procedure has been updated and extended. There is a minor change in the convection correction dictated by theory, and a substantial change in the refraction correction, owing to a shortcoming of the injected point source technique, (i) The results have been presented in the equivalent forms of spectra and narrow-band directivities at jet Mach numbers of 0'5 and 0'9. (ii) Theory has been fitted in two-parameter form at each frequency to generate spectral curves of basic self-noise a(CfDJU) and shear-noise b(CfD/U). The peaks occur at the theoretical 2/1 in frequency, and the Doppler-corrected Strouhal numbers CfD/U are invariant with Mach number, (iii) The semi-empirical theory, with convection and refraction re-introduced, has been used to predict the overall directivity in narrow frequency bands. The agreement with the direct measurements is quite good for what is essentially a two-point fit. (iv) The broadband convection factor C−5, with α = 0·55 and Mc = 0·5 Uj/C0 (supported by theoretical arguments), is found to correlate well with experimental results—these and others—for Uj up to turbojet speeds (e.g., 1·64 C0). (The factor C−3 with α = 0 and Mc = 0·63 Uj/C0 that has been proposed for shear noise fails badly at these high speeds ; but if Mc is reduced to correct this, the factor fails at low speeds.) (v) A critique is given of analytical factors for Doppler shift and convective amplification, including the effect of the general flow enveloping the moving eddies.