Reconstruction and analysis of a non-stationary sound field in a uniformly flow medium

A multistep time domain plane wave superposition method (M-TPWM) is expanded into a new environment that the medium is fluid, and an M-TPWM with flow medium (FM-TPWM) is proposed to reconstruct the non-stationary sound field in a uniformly flow medium. In the FM-TPWM, two situations that the flow directions of the medium are parallel to and perpendicular to the hologram plane are researched. The time-varying pressures on the hologram plane in these two situations are expressed as a superposition of time convolutions between the pressure time-wavenumber spectra of a virtual source plane and the corresponding new time domain propagation kernel derived in the flow medium. Subsequently, the discrete solving equations in the parallel and perpendicular situations at one time are established. The pressure time-wavenumber spectra at only this time can be solved by once solving inverse calculation. Then, these discrete solving equations in the flow medium at several times are combined for forming the larger solving matrix equations in the parallel and perpendicular situations, and by once multistep calculation, the pressure spectra at these times are acquired concurrently. Consequently, the time-varying pressures on the reconstruction plane in the flow medium are calculated by the corresponding acquired pressure time-wavenumber spectra. Numerical simulations with parallel and perpendicular situations are applied to examine the performance of the proposed FM-TPWM, in which two monopole sources in the flow medium are used to engender the non-stationary sound field. The simulation results prove that the proposed FM-TPWM can reconstruct the non-stationary sound field very well when the flow directions of the medium are parallel to and perpendicular to the hologram plane, respectively. Besides, several meaningful parameters are discussed in detail to prove the adaptability and robustness of the proposed FM-TPWM in the flow medium, and its reconstruction advantages are protruded in comparison to the real-time nearfield acoustic holography with the flow medium.