Planar nearfield acoustical holography in moving fluid medium at subsonic and uniform velocity

Abstract

Nearfield acoustical holography (NAH) data measured by using a microphone array attached to a high-speed aircraft or ground vehicle include significant airflow effects. For the purpose of processing the measured NAH data, an improved nearfield acoustical holography procedure is introduced that includes the effects of a fluid medium moving at a subsonic and uniform velocity. The convective wave equation along with the convective Euler's equation is used to develop the proposed NAH procedure. A mapping function between static and moving fluid medium cases is derived from the convective wave equation. Then, a conventional wave number filter designed for static fluid media is modified to be applicable to the moving fluid cases by applying the mapping function to the static wave number filter. In order to validate the proposed NAH procedure, a monopole simulation at the airflow speed of Mach=-0.6 is conducted. The reconstructed acoustic fields obtained by applying the proposed NAH procedure to the simulation data agree well with directly-calculated acoustic fields. Through an experiment with two loudspeakers performed in a wind tunnel operating at Mach=-0.12, it is shown that the proposed NAH procedure can be also used to reconstruct the sound fields radiated from the two loudspeakers.

Non-intrusive planar velocity-based nearfield acoustic holography in moving fluid medium

“…These propagators allow the assessment of acoustic fields from measured acoustic pressure or normal acoustic velocity, when the mean flow is either parallel or perpendicular to the hologram plane. Thus, the proposed approach is based on a realspace formulation contrary to the Kwon et al 13 one which is based on a wave number-frequency-domain formulation. A parallel between these two approaches is proposed to assess the interest of using real-space or wave number-frequencydomain convective velocity-to-pressure propagators.…”

“…These conclusions were then confirmed by Zhang et al 20 in the case of NAH based on the Equivalent Source Method, which confirms the interest of using velocity-based NAH. First convective velocity-based propagators were more recently proposed by Kwon et al,13 but no application from acoustic velocity measurements was presented.…”

“…For this purpose, Kwon et al 13 have presented an NAH procedure for sources radiating in high subsonic Mach number flows. The convective wave equation is used to derive a mapping function which links wave number-frequencydomain in the static medium case to the moving one, giving convective Green's functions and wave number filter.…”

“…The expressions of wave number-frequency-domain convective pressure-to-pressure and pressure-to-velocity propagators were derived by Kwon et al 13 from the study of plane wave propagation in the case of a uniform and subsonic flow parallel to the hologram plane. For a hologram plane ðx; y; z ¼ z h Þ and a uniform subsonic flow along x, these propagators are…”

“…As for the static case, the convective Euler's equation can be used to link normal acoustic pressure gradient to normal acoustic velocity u n : @pðr 0 ; xÞ=@n ¼ Àq ðÀix þ U@=@x Þ u n ðr 0 ; xÞ: (13) Note that in the case of a uniform flow, convective Euler's equation is dependent on normal acoustic velocity and normal acoustic velocity gradient along the flow direction. Thus using integral Eqs.…”