Sound generation by turbulent two-phase flow

Abstract

Sound generation by turbulent two-phase flow is considered by the methods of Lighthill's theory of aerodynamic noise. An inhomogeneous wave equation is derived, in which the effects of one phase on the other are represented by monopole, dipole and quadrupole distributions. The resulting power outputs are obtained for the case of a distribution of small air bubbles in water. The monopole radiation resulting from volumetric response of the bubbles to the turbulent pressure field overwhelms that from the quadrupoles equivalent to the turbulent flow, the increase in acoustic power output being about 70 dB for a volume concentration of 10%. The monopole radiation occurs through the forced response of the bubbles at the turbulence frequency; resonant response is shown to be impossible when the excitation is due to turbulence alone. Surface radiation arises from the edge of a cloud of bubbles. This radiation is important when the region containing bubbles is in the form of a sheet with thickness smaller than the length scale of the turbulent motion. Dipole radiation is also considered, and found to be negligible whenever monopole sources are present. In the case of a dusty gas, only dipole and quadrupole sources are present, and here it is shown that the dipole radiation is equivalent to an increase in the usual quadrupole radiation. The increase depends upon the mass concentration of dust, and is significant for mass concentrations in excess of unity.