Experimental verification of a mathematical model for internal ultrasonic inspection of pipes

Abstract

The present paper experimentally verifies the accuracy of a quasi-three-dimensional (3-D) numerical code [C. Randall and F. E. Stanke, ‘‘Mathematical model for ultrasonic, internal inspection of cylindrically layered structures,’’ J. Acoust. Soc. Am. 83, 1295–1305 (1988)] that models a finite-sized, broadband ultrasonic transducer inspecting a cylindrically layered structure from its interior. All verifications employ one of a collection of steel pipes, which have a variety of thicknesses and diameters. In all cases, a fluid fills the pipe and envelops the transducer. This fluid is either water or a dispersive, attenuative, water-based suspension. The exterior surface of the pipe is loaded by a homogeneous layer that is either water, the suspension previously mentioned, or a loaded epoxy. The transducer is operated in pulse/echo mode at a distance of between 10 and 20 wavelengths in water from the pipe. Multiple reflections between the pipe and the transducer itself are excluded by time gating. The transducer has a flat, rectangular active region that is roughly three wavelengths wide (in water) and ten wavelengths high. Consequently, diffraction significantly affects the received waveforms. The transducer, its excitation, and receiving electronics have a broad bandwidth that encompasses several of the low-order thickness resonances of the pipe that can interfere to produce very complex waveforms and spectra. The transducer is aligned with its length parallel to the axis of the pipe, with a radius of the pipe passing either through the center of its width or to one side. Comparisons are presented as overlayed waveforms (in the time domain) and overlayed spectra (in the frequency domain) of the experimental and calculated results, so that emphasis is placed on the ability of the model to accurately predict even subtle details, as opposed to integrated or other more global measures. Comparisons between the experiments and calculated predictions show that, for all cases examined, the model predicts virtually all visually distinguishable features of waveforms and spectra with at least qualitative accuracy, even when the levels of these features are on the order of 5% of the maximum level of the echo. For many cases, the model is in error by less than 10% on a point-by-point basis even for such fine features. In cases where the model does not perform as well quantitatively, it is a good qualitative guide, and, even for these worst cases, it is still considerably more accurate than a 2-D model would be for any of the cases examined and is computationally nearly as fast.