Slopping resulting from gas injection in a peircesmith converter: The period of the standing wave

The periods of the transverse standing waves occurring in the Peirce-Smith converter geometry as a function of bath depth were solved using linear wave theory by formulating an integral equation of the second kind. The eigenvalues of the integral equation gave the wave periods which were calculated to four-figure accuracy. The eigenvalues were approximated using Chebyshev polynomials for the first four wave modes. They include the complete range of eigenvalues for the first two symmetric standing waves, which has not been reported in the literature. The asymptotic eigenvalues for the transverse standing waves are given. Experimental results from a water model agreed with the theoretical predictions over a wide range of bath depths. The first symmetric standing wave was enhanced by the presence of the longitudinal standing wave, which showed that the three-dimensional geometry of the model was important in the modeling of the Peirce-Smith converter. Data from a Peirce-Smith copper converter were in reasonable agreement with the theory. An analysis of the standing wave frequency showed that the presence of standing waves could be minimized by a change in the geometry.