Vector Aeroacoustics for Uniform Mean Flow: Acoustic Velocity and Vortical Velocity

Vector Aeroacoustics for a Uniform Mean Flow: Acoustic Intensity and Acoustic Power

“…(15). The result also indicates that, at a lowMach-number flow, the contribution from the last three terms in Eq.…”

“…By using the assumption of In order to properly visualize the distribution of the acoustic field around sources, the acoustic velocity and acoustic intensity levels are used to illustrate contours shown in this paper, which are defined as follows: Frequency-domain acoustic pressure and acoustic velocity are computed numerically by using the following equations [15,16]:…”

“…(see detailed expressions in [15,16]). Note that the first term on the right-hand side (RHS) of the above equations is named far-field term which will be used to deduce the analytical acoustic power formulation in Section IV.…”

“…For the rotating monopole and dipole sources either in the quiescent acoustic medium or in the uniform mean flow, frequency-domain acoustic pressure and acoustic velocity are computed with the following integral formulations [15,16]:…”

“…The dipole source only radiates acoustic waves in the quiescent acoustic medium, thus the acoustic power is always conservative during the propagation without considering the effect of fluid viscosity. However, in the uniform mean flow, the dipole source simultaneously stimulates acoustic and vortical waves [15], Eq. (14) clearly indicates that there is an energy conversion between the acoustic wave and the vortical wave, thus the acoustic power output from the dipole source is non-conservative in the uniform mean flow, as shown in Fig.…”