Sound field modelling using SimulUS

Abstract

The motivation behind developing the SimulUS beam model was as a tool for the rapid visualisation of ultrasonic fields generated by phased array transducers (both linear and matrix). However, it is possible to model single crystal transducers by defining a 1 by 1 matrix. The present work was carried out using the version released in December of 2005 and was part of a larger validation programme in TWI involving other models. The core of the model is based on Huygen’s discretisation method of evaluating the free field ahead of the sound radiator (Section 2). SimulUS operates principally in the continuous wave (1) mode but a pulse wave expression is incorporated. The model is primarily designed for rapid visualisations of the sound field but it can be used as a pulse wave modelling package. The computing requirements are less intensive when the input waveform is of a single frequency (continuous wave). Hence, in this paper, the evaluation of the performance of SimulUS in its primary continuous wave mode is presented. SimulUS was envisioned for use in applications such as: q Technique development – such that the operator can rapidly evaluate the suitability of a particular setup for the inspection task. q Probe design – confident design of, in particular, phased array probes such that the designer can ensure that the parameters are correctly specified to achieve optimised field properties for the application. q Training – allowing students to understand the basics of phased array ultrasonics and conventional ultrasonics through an interactive learning approach; where the effects of varying the crystal size, pitch, frequency etc on the ultrasonic field generated by the transducer can be understood and even the effects of failed elements modelled. 2. Principles of ultrasonic field models Ultrasonic field models have been developed utilising various different theories. In essence, they are all required to evaluate the sound pressure field ahead of a transducer. As well as SimulUS, two other successful models will be described to illustrate the different approaches that have been taken in the past; both models are well established and have been extensively validated within industry and by research organisations. The models developed in the Non-Destructive Testing Applications Centre (NDTAC) of the Central Electricity Generating Board (CEGB) were based on an analytical approximation to the pressure distribution over the sound radiator. The CIVA model, developed by Commissariat a l’energie Atomique (CEA), is a semi-analytical model using a theory for electromagnetic wave propagation that was adapted for simulating the elastodynamic propagation of sound waves (2) . The sound field ahead of the probe face can be described using Huygen’s principle, which uses elementary waves of the same frequency which originate at discrete points on the radiating surface (3) . These waves then undergo interference effects in front of the radiating surface and their summation, as derived by Fresnel, gives the strength of the field at any point ahead of the probe. The solution depends on noting that at any given point ahead of the radiator, Huygens’ elementary waves from discrete points have taken different paths. Since the sound pressure has an inverse relationship to actual distance travelled from the origin, the path difference dictates actual pressure contributions from each elementary wave at the point of interest. This method of evaluating the resultant pressure contribution is known as zone construction. For each elementary contribution, the path difference is converted to an angular measurement along with the change in pressure at the given distance; vector addition is used to evaluate the pressure and phase at any given point ahead of the radiator. This method can be used effectively for evaluating the pressure values along the beam axis and off axis with modifications to the element configuration. This forms the basis of the SimulUS model where the contribution of wavelets from sources on the transducer is summed on the calculation plane. The NDTAC beam model is an analytical model that was developed to form part of a larger systematic approach to the modelling of ultrasonic inspections. The model was designed to generate the sound fields created by single crystal probes. It is a modified version of the simple piston oscillator model of a single crystal. The Fresnel integral approach to evaluate pressure values at a general point ahead of the probe face is computationally intensive. The NDTAC model was envisaged as a module in a systematic approach to evaluating defect interaction; since the beam model needed to be run several times, it needed to be computationally less intensive while providing sufficient accuracy in the prediction of pressure values ahead of the probe. Hence, the NDTAC model suggests an approximation for the amplitude profile over the radiating face such that the evaluation of the field ahead can be performed analytically as opposed to resorting to numerical methods (4)