Bragg scattering of ultrasound by a regular array of rigid cylinders

This paper discusses the use of narrow band ultrasonic waves to inspect closely packed arrays of regularly spaced cylinders contained within a thin-walled metal channel, or ''box'', for the purpose of detecting defective, missing, or misplaced fuel rods. In particular, the method described utilizes the properties of coherently scattered ultrasonic waves to inspect reconstituted fuel bundles. When one considers inspection of a staggered array of uniform, rigid rods completely immersed in water, Bragg scattering comes to mind as a possible means, provided there is nothing preventing or impeding the scattering process. Such an impediment might consist of gas bubbles that locally perturb the acoustic impedance, thereby disrupting at least part of the coherent process. Alternatively, if a given rod is swollen or bowed, then it breaks the required symmetry and its contribution to the coherent wave is reduced. Therefore, analysis of the interference pattern detected at the opposite face of the array might offer information concerning rod integrity. The question is one of sensitivity of the coherent scattering to symptoms of defective rods and whether such a technique is technically sufficient for inspection purposes. In this paper, conditions for coherent scattering in a rod array are derived and the intensity calculated for a specific geometry. Effects of symmetry-breaking on coherence are modeled and assessed mathematically. It is concluded that the technique is feasible, but will require extensive experimental and theoretical work to reduce it to practice