Near-Field Acoustical Holography in Cylindrical Spaces

The objective of this investigation is to assess the feasibility of using near-field acoustical holography for the reconstruction of acoustic sources operating in a reverberant cylindrical space, such as that encountered in the test section of wind and water tunnels. As a starting point, two idealized models of an acoustic source operating in the test section of a wind or water tunnel are developed. In both models, the tunnel walls are assumed cylindrical and acoustically rigid, and the source is idealized as a cylinder with a prescribed normal velocity distribution. The acoustic medium is assumed homogeneous, source-free, and at rest. The first model, called the infinite model, assumes that the cylindrical geometry extends to infinity in the axial direction. This is equivalent to an infinite test section with only outward propagating waves. The second model, called the finite model, assumes that the cylindrical geometry extends over the span of the test section. Based on these two models, algorithms for the holographic reconstruction of the velocity distribution on the source cylinder are developed. Both models account for tunnel wall reflections, and both require near-field pressure measurements on a hologram cylinder surrounding the source cylinder. The finite model also requires pressure measurements on fictitious endcaps bounding the finite cylindrical space. Numerical simulations are used to assess the performance of both models in reconstructing known sources, including a baffled ring source, two closely spaced baffled ring sources, and a baffled band source. A range of frequencies, aperture lengths, and spatial sampling frequencies is considered. The effect of spatially incoherent additive noise and the use of wall-mount sensors are also examined. Based on results from these numerical simulations, it seems feasible to use near-field acoustical holography to reconstruct acoustic sources operating in cylindrical spaces, with some restrictions and limitations. The performance of the finite model is generally superior to that of the infinite model, because the finite model is not subject to finite hologram aperture effects, as is the infinite model. Nonetheless, both models are capable of reconstructing a cylindrical source in a cylindrical space.