Estimating the high frequency in-duct sound power using sound pressures at the duct wall

When studying the acoustic wave propagation in a channel, the frequency range can be divided to the low frequency plane wave range and to the high frequency range with non-plane waves. In the low frequency range the wave propagation is one-dimensional and the governing equations are rather simple. The larger the duct the lower the frequency limit of the non-plane waves. Therefore taking into account also the three-dimensional acoustic wave propagation is important especially when considering the duct systems used in large structures, e.g., medium speed internal combustion engines (IC-engines), fans, or compressors. Harsh environment and unmovable structures restrict the use of standardized noise measuring methods. To characterize the medium speed IC-engine exhaust noise in situ, the in-duct sound pressures are measured using wall mounted transducers. Then the source sound power is estimated from the propagating sound pressures, which is the power based approach. The power based approach is only valid in frequency averaged sense and therefore the source power must be defined in one-third octave frequency bands, for example. One way to estimate the source sound power in the high frequency range, is to extend the classical plane wave formulation by defining the one-third octave frequency band weighting factors for different excitation types. The aim of this study is to define these weighting factors using finite element method (FEM) simulations of a test duct with non-reflecting terminations. The sound pressures at the duct wall were compared to the sound pressures at the duct end for randomized multi-modal excitations. From statistics, the one-third octave band weighting factors and their reliability were estimated.