Modeling the Ultrasonic Radiation of a Planar Transducer Through a Plane Fluid—Solid Interface

Abstract

Three types of transducer beam models are developed for obtaining the bulk waves generated by a plane piston transducer radiating through a planar fluid-solid interface. The first type, called the surface integral model, is based on a Rayleigh-Sommerfeld-like integral that requires a two-dimensional surface integral to be evaluated. The second model, called the boundary diffraction wave (BDW) paraxial model, simplifies the two-dimensional integration of the surface integral model to a one-dimensional line integration. The third type of model, called the edge element model, is shown to be a novel way of efficiently evaluating the two-dimensional surface integration of the surface integral model. The limitations of these models for simulating inspections near critical refracted angles and near the interface are discussed.It is shown that the introduction of the paraxial approximation in the BDW model allows that model to be computed with a very large (300-1) speed advantage over the surface integral while retaining the same accuracy in most cases. The edge element model, while having a smaller (5-1) advantage over the direct numerical integration of the surface integral model, retains the accuracy of the surface integral model in cases where the paraxial approximation fails and can be easily generalized to more complex testing situations (focused probes, curved interfaces, etc.).

Improvement of SAFT by Implementation of Approximate Wave Solution in Fluid-Solid Two-Phase Media: A Case Study on Imaging of Aluminum Rod with Side-Drilled Holes

“…The approximate displacement field can be used to predict ultrasonic beam radiation from a planar transducer. A good review of various methods in modelling ultrasonic radiation from a planar transducer through fluid-solid interface problem was written by Lerch et al [17]. We use a surface integral model derived by Schmerr et al [14], which will be called the Approximate Wave Solution abbreviated as AWS, to improve the quality of flaw images by SAFT.…”

“…Constants used in MSSIM calculation throughout this paper are K 1 = 0.01, K 2 = 0.03 and L = 1. μ x and μ y in Eq. (17) are mean intensities of images and can be calculated from Eq. (20)…”