A two-dimensional model of the edge tone is studied by a highly accurate and reliable method of direct numerical simulation of the compressible Navier-Stokes equations, and used to verify key features observed in previous experimental and numerical studies, and to discover new features related to the jet motion and the edge tone generation mechanism. The first and second modes of the edge tone that are numerically reproduced agree well with Brown’s equation. In the mode transition region, dynamical mode transition is observed at a fixed jet velocity. For both first and second modes, the pressure distributions are antisymmetric with respect to the edge plate, and the sound intensity is proportional to the fifth power of the jet velocity. These results are consistent with the edge tone being radiated from a dipole-like source. Spatial profiles of the velocity and the velocity variance of the oscillating jet are also investigated for each mode over a range of the jet velocity including the mode transition regime. The amplitude of the velocity oscillation becomes constant with increasing jet velocity, while a measure of the amplitude of the velocity variance profile, which is introduced to characterize the strength of the jet fluctuation and named the ’fluctuation strength’, is proportional to the third power of the jet velocity. Some properties of the fluctuation strength correspond to properties of the sound intensity, including the first mode having larger amplitude than the second mode, and the way of deviating from the power law at smaller values of jet velocity and in the mode transition region. It is proposed that the third-power law exhibited by behavior of the fluctuation strength could be related to the increase of the skewness observed in the velocity profile with increase of jet velocity, and a model calculation is used to support this proposal.
Direct numerical simulation of primary breakup for power-law biodiesel sprays
