Acoustic scattering from elastic cylinders has been studied extensively over the last few decades. However, the vast majority of theoretical investigations have focused on idealized plane wave, point receiver solutions, ignoring realistic sonar effects. Acoustic transducers are characterized by spherically spreading waves and often have transmit and receive beams that are directional. Because of the spreading, even during broadside measurements, these sonars excite cylinders obliquely. This investigation involves acoustic scattering by spot-insonified infinitely long elastic cylinders, and studies effects caused by practical sonar constraints both theoretically and experimentally. Calibrated broadside measurements of backscattering are presented for various cylinder and source/receiver geometries including both monostatic and near-monostatic configurations. In all measurements, the ratio of the footprint length of the target relative to the first Fresnel zone diameter is chosen such that the entire first Fresnel zone dominates the scattering. This ensures that the scattering from the cylinder spreads cylindrically and hence the cylinder behaves like an infinite target. A theoretical formulation is developed to account for beam spreading and directivity of practical echo-sounders. Comparisons between theoretical predictions and experimental data are presented. [Work funded by ARPA-E.]

This article presents a two-dimensional steady viscous flow simulation past circular and square cylinders at low Reynolds numbers (based on the diameter) by the finite volume method with a non-orthogonal body-fitted grid. Diffusive fluxes are discretized using central differencing scheme, and for convective fluxes upwind and central differencing schemes are blended using a ‘deferred correction’ approach. A simplified pressure correction equation is derived, and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of variables. The mesh yielding grid-independent solution is then utilized to study, for the very first time, the effect of the Reynolds number on the separation bubble length, separation angle, and drag coefficients for both circular and square cylinders. Finally, functional relationships between the computed quantities and Reynolds number (Re) are proposed up to Re = 40. It is found that circular cylinder separation commences between Re= 6.5-6.6, and the bubble length, separation angle, total drag vary as Re, Re−0.5, Re−0.5 respectively. Extrapolated results obtained from the empirical relations for the circular cylinder show an excellent agreement with established data from the literature. For a square cylinder, the bubble length and total drag are found to vary as Re and Re−0.666, and are greater than these for a circular cylinder at a given Reynolds number. The numerical results substantiate that a square shaped cylinder is more bluff than a circular one.

Acoustic scattering from cylinders has been previously studied extensively for idealized incident plane waves and point receivers. However, the more realistic case of scattering from cylinders insonified by directional sonars has received limited attention. Operational sonars are directional and transmit waves that spread spherically. Due to the spherical spreading, the overall scattered pressure levels are affected and the cylinder is insonified across a continuum of oblique incident angles, even at broadside incidence. The obliqueness in the incident field, in turn, influences the structure of the scattering spectrum by exciting guided wave natural modes. A recently derived theory, accounting for the above realistic effects, is tested against laboratory measurements involving both smooth and rough elastic cylinders, spanning a range of scattering geometries and roughness profiles. The effects of bistatic angle between the source and receiver on overall scattered pressure levels and resonances are investigated and compared with results from the monostatic geometry. The influence of correlation length and root mean square roughness on the scattered field is also studied.

A modal-series-based model for acoustic scattering from smooth and rough elastic cylinders insonified by directional sonars is derived. Sonar directivity, Fresnel zone effects, spherical spreading of the incident field, and axially propagating guided waves excited by this spreading are included while end-effects are assumed to be negligible. The performance of the scattering model is evaluated against laboratory monostatic and bistatic measurements of scattering from both smooth and rough elastic cylinders. Three aspects of scattering — overall scattering levels, resonance frequencies, and resonance shapes — are analyzed both theoretically and experimentally. The roughness on the cylinder has a Gaussian distribution and is characterized by a random variation of the cylinder radius along its length. Effects of various statistical properties of this one-dimensional roughness, such as different rms roughness for a given correlation length and different correlation lengths for fixed rms roughness, are investigated.

Realistic sonars radiate spherically spreading waves and have directivity. Therefore, they insonify a target over a finite number of Fresnel zones and span a continuum of oblique incident angles, even when the center of the beam is at normal incidence. These effects strongly influence both the overall scattered pressure levels and resonances. For example, because of the spreading of the beam and associated oblique insonification within the beam, axially propagating guided waves are generated that would not have otherwise existed for an idealized incident plane wave. This investigation illustrates practical sonar properties and their effects on cylinder scattering both theoretically and experimentally. An approximate theoretical formulation for acoustic scattering by elastic cylinders is proposed in the form of a simple line integral accounting for these properties. Laboratory measurements are also presented to test the range of validity of the formulation for smooth cylinders under both monostatic and bistatic configurations. This study is further extended for the case of rough elastic cylinders.