Cylinder aeroacoustics: experimental study of the influence of cross-section shape on spanwise coherence length

Abstract

New data and review of the spanwise coherence length is provided for flows over cylinders of different cross-sections: circular of diameter d, and rectangular of sectional aspect ratios (breadth (b) to height (d) ratio AR = b/d) of 1, 2 and 3. In the present measurements, the body has both d and spanwise length of 70d fixed, and the Reynolds number (based on d) range 6000–27,000 is covered. Two-point data are obtained from two hot-wire probes, one fixed in the symmetry plane and the other moving on the corresponding spanwise axis. Their position in a cross plane are deduced from preliminary measurement of the mean flow with a single probe, allowing fair comparisons between the different geometries and the introduction of uncertainty bars on coherence length values. At all tested regimes, a very good agreement is noticed between velocity-based and pressure-based coherence experimental data. Coherence length definitions are revisited, and the aeroacoustically consistent, integral length definition is selected, allowing fair synthesis of literature data into a single chart and empirical functions. Definitions for coherence decay models (e.g. Gaussian or Laplacian) are also adapted so that coherence length and coherence integral shall be equivalent. This preliminary work on coherence data and its spanwise integration enables transparent regressions and model selection. Generally, the Gaussian model is relevant for the lift peak, while the coherence exhibits a Laplacian decay at harmonics. On average, at peak Strouhal number, the coherence length for the circular and square cylinders is of 5d while it is of the order of 15d for the rectangular sections. It is concluded that the flow over those latter geometries is still a two-dimensional dynamics at the tone frequency. These values are almost preserved over the tested Reynolds number range. Coherence length value at harmonics is extensively documented. Spanwise coherence length is also discussed as an ingredient of acoustic efficiency.