Basic Flow Analyses Used in the Study of Broad-Band Noise in Compressors

The propagation of sound in a moving compressible fluid displays interesting features which are important in the problem of noise generation in compressors. Without considering the discrete frequency noise generated by interacting rotating blades and stationary parts, a perturbation method applied to the equations of flow motion in an idealized continuous medium leads to an equation of density waves propagation in a nonhomogeneous moving fluid. The right-hand side is considered as describing distributed noise sources which involve velocity fluctuations. On the left-hand side there appears a negative diffusive effect due to a negative divergence of the velocity field, which downstream entails a streamwise amplification of the intensity of the sound generated upstream. Further, there is a dispersive effect entailing, for a given wave number, a group velocity which in a simple example is shown to be larger than the phase velocity and to become imaginary for a velocity divergence sufficiently high in absolute value. This, together with the amplification effect, may explain the relative importance of the high frequency band in the actual noise spectra of compressors. An attempt at determining the coefficients of the acoustical equation for compressors is made in the schematic Beltrami-Gromeka case of a helicoidal axisymmetrical flow. With simplified assumptions on the behavior of density, depending either solely on the axial coordinate or only on the radial one, both types of axial and radial compressors are considered simultaneously and the method of analytical solution applied. It is emphasized that this treatment is restricted to the mechanical aspect of the broad-band noise generation.