Frequency-domain acoustic pressure formulation for rotating source in uniform subsonic inflow with arbitrary direction

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

“…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]:…”

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

“…As a first step, we consider the case of uniform mean flow in this paper, and earlier investigations in this area can be found in [24][25][26][27][28] [30,31] and frequencydomain [32] acoustic pressure integral formulations for the monopole and dipole sources in uniform mean flow have been deduced. The above-mentioned formulations explicitly account for the effect of the uniform mean flow on both the sound sources and sound propagation.…”

“…On the other hand, the Lorentz or Prandtl-Glauert transformation [33,34] is an alternative method to analyze sound propagation in uniform mean flow. Investigations have indicated that a moving background flow with high Mach numbers has a significant effect on sound generation and propagation [28,[30][31][32]35], implying that the classic exponent law of radiated acoustic power [1][2][3] is only valid approximately for low-Mach-number flows and should be corrected at high Mach numbers. In a quiescent acoustic medium, acoustic power can be computed once the distribution of the acoustic pressure is known on a closed far-field surface with an enough distance between sources and observers.…”