Explicit solution of gas film pressure for performance calculation of spiral grooved gas seals

Abstract

The study presents an explicit solution to a narrow groove theory for compressible spiral grooved gas seals. The explicit solution was derived from Muijderman’s narrow groove theory by employing Cauchy’s integral theorem. It expresses the gas film pressure as a function of gas film radius. Using this process, the initial value problem of Muijderman’s equations is avoided, and the gas film pressure can be obtained directly in contrast to the traditional Runge-Kutta method. A complete analytical procedure of the explicit solution is presented. The accuracy of the explicit solution was validated using published results.