Propagation of Gaussian Beam Through a Curved Interface for Planes of Incidence no Containing a Principle Radius of Curvature

A. Minachi

R.B. Thompson

Volume: 13B Page Numbers: 1415 - 1422

Abstract:

Ultrasonics is one of the preferred methods of inspection for BWR nozzles in nuclear power plants. These nozzles, which connect the piping to the pressure vessel of the nuclear reactors, must be inspected periodically for detection of cracks appearing around the inner wall of the nozzles. Since the curvature of these components can influence the waves propagating through them, there is a need for practical beam models for this geometry. An approximate Gaussian beam model, based on the paraxial approximation, already exists for propagation through curved interfaces with incident angles in planes of symmetry containing one of the principal radii of curvature. However, for practical application to nozzles, there is a need to inject the ultrasonic beams through more general incident angles. Therefore, in this study, the propagation of Gaussian beam with incident angels out of the plane of the symmetry of the nozzles is discussed. It is first shown that the problem can be solved analytically, although the resulting expressions are quite complicated. Then, the effect of the curvature on the amplitude and phase of the Gaussian beam is discussed. It is of particular note that the principal radii of phase and amplitude need not coincide under these conditions. Numerical results are presented to illustrate the key results.---This work is supported by the Electric Power Research Institute.

References:

1. R. B. Thompson and E. F. Lopes. "The effects of focusing and refraction on Gaussian ultrasonic beams." Journal of Nondestructive Evaluation 4 (1984): 107-123.

2. J. W. Goodman. Introduction to Fourier Optics. New York: McGraw-Hill, 1968.