Radial Mode Analysis of Ducted Sound Fields with Sensor Rakes and Wall Flush Sensor Arrays under Consideration of a Radial Flow Profile

The radial mode analysis of ducted sound fields enables the detailed examination of the noise generation in turbomachinery. The standard approach bases on the convective Helmholtz-equation including a uniform mean flow profile and has the advantage that the associated mode eigenfunctions can be derived analytically. Several theoretical studies indicate a significant impact of the flow boundary layer profile on specific mode orders, but for the related enhanced analysis approach the mode eigenfunctions have to be derived by the use of complex numerical methods. The objective of the current study is to reveal the differences that result between the standard and the enhanced method in an application to experimental data. Two test cases are considered: The sound field measured in the bypass duct of a turbo-fan test rig by means of sensor rakes and alternatively by a wall flush sensor array. In the analysis of a dominant rotor-stator-interaction mode with sensor rakes a substantial shift of energy between modes of low radial order is found, although the overall sound power of the azimuthal order results almost identical for both flow profiles. In contrast to this, for the wall-flush sensor array much larger sound power level are evaluated for the low radial order in the case of the uniform flow profile. A thorough analysis of the reconstructed sound fields and an accompanying study using synthetic data suggests that the deviation is mainly caused by a mismatch of the axial wave numbers.