The modal and flow velocity corrections of microphone turbulence screens

Microphone turbulence screens are used to suppress turbulent pressure fluctuations when measuring the acoustic pressure inside a duct with flow. They consist of a long tube with a slit covered with porous material, and thus are also called sampling tubes. Because they are not omnidirectional, it is necessary to calculate corrections when higher-order modes are propagating in the duct. In order to calculate these corrections it is necessary to know the directivity of the microphone turbulence screen, the propagation direction and energy of the duct modes and the flow velocity of the air in the duct. This paper derives a theoretical formula for the directivity of a microphone turbulence screen. It shows that this theoretical formula agrees better with experimental directivity data than the previously used empirical directivity formula. Because the empirical directivity formula is not a function of the flow velocity, previous research has separated the modal correction from the flow velocity correction. It is shown that it is not theoretically valid to separate the corrections, and that doing so can lead to large errors at high frequencies in the outlet duct. A new method of calculating the modal correction with flow is presented. This method uses a statistical room acoustics approach in contrast to the deterministic numerical approach of the older method. The new method requires much less computing. It is shown that the new method agrees fairly well with the old method for modal corrections without flow. The new method is compared with experimental measurements of the combined modal and flow velocity corrections. Although the trend is the same, the experimental results are higher than the theoretical results in the mid frequency range. The new method agrees reasonably well with the corrections given in ISO 5136:2003.