Analysis of Compressible Fluid Flow in Gas Turbine Mainshaft Seals

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Abstract
Determination of leakage flow and separation force of gas turbine engine mainshaft seals and similar devices represents a unique application of the quasi-one-dimensional compressible flow equation (6), (10). This nonlinear equation has been solved numerically by various authors, for nozzle, diffuser, duct, seal, and similar applications. It has been found, however, that the solution methods reported in the literature may be inoperative for seals with small clearance-to-length ratio, or when the seal is appreciably distorted. This difficulty is caused by a boundary layer type behavior (12) resulting from a singularity in the vicinity of sonic flow, i.e., when the flow Mach number approaches unity. In this new analysis, an alternative numerical integration technique is introduced. The governing compressible flow differential equation has been solved by using nonuniform meshes and integrating from the vicinity of the singularity towards the entrance leading edge. This procedure not only avoids some of the convergence problems associated with other solution techniques, as reported elsewhere in the literature, but also results in more accurate solutions and a substantial computer time savings of from 2 to 10 times, depending on whether the flow is sonic or subsonic. This new analysis considers the combined effects of entrance losses, fluid inertia, fluid friction, area change, and fluid turbulence and is applicable to steady, one dimensional gas flow in general. The computer program calculates the distribution of pressure, temperature, velocity, Mach number, and Reynolds number along the flow path.

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