An estimation method for echo signal energy of pipe inner surface longitudinal crack detection by 2-D energy coefficients integration

The echo signal energy is directly affected by the incident sound beam eccentricity or angle for thick-walled pipes inner longitudinal cracks detection. A method for analyzing the relationship between echo signal energy between the values of incident eccentricity is brought forward, which can be used to estimate echo signal energy when testing inside wall longitudinal crack of pipe, using mode-transformed compression wave adaptation of shear wave with water-immersion method, by making a two-dimension integration of “energy coefficient” in both circumferential and axial directions. The calculation model is founded for cylinder sound beam case, in which the refraction and reflection energy coefficients of different rays in the whole sound beam are considered different. The echo signal energy is calculated for a particular cylinder sound beam testing different pipes: a beam with a diameter of 0.5 inch (12.7mm) testing a φ279.4mm pipe and a φ79.4mm one. As a comparison, both the results of two-dimension integration and one-dimension (circumferential direction) integration are listed, and only the former agrees well with experimental results. The estimation method proves to be valid and shows that the usual method of simplifying the sound beam as a single ray for estimating echo signal energy and choosing optimal incident eccentricity is not so appropriate.