A numerical study of compressible flow in labyrinth seals with rub grooves

Abstract

A labyrinth sea] uses a series of knife blades and cavities to create a high frictional flow path that turns a pressure potential into kinetic energy, which is then dissipated as heat. An existing numerical model is extended to include more terms in the pressure-correction equation, and an upwind-differencing scheme is implemented. The presence of rub grooves in labyrinth seals alters the flow pattern and the leakage resistance, and the effect of the rub groove geometry on leakage is determined. The existing pressure-correction equation uses two terms that include a velocity correction, but do not include a density correction. Shyy, et al. (1992) suggests using four terms in the pressure-correction equation for compressible flow calculations to include the density corrections. Karki and Pantakar (1988) use an upwind-differencing scheme to calculate the density at the cell faces. The additional two correction terms and the upwind treatment of density allow for greater numerical stability in calculating compressible flow. Specifically, the new model can solve more complex flow patterns and can give a converged solution for a wider range of initial inlet pressure values. The geometry of the rub groove can determine how much influence the rub groove has on the seal performance. The groove width, groove depth, and seal clearance were varied on the straight-through labyrinth seal to obtain a wide range of seal geometries. The axial position of the teeth with respect to the groove was also varied for the straight-through labyrinth, and the effect of step height was studied for the stepped labyrinth seals. The presence of the rub groove increased the leakage and less of an impact, but the larger rub grooves significantly impaired the seal performance. Shifting the teeth away from the center of the rub groove helped to lessen the detrimental effects, and shifting the teeth downstream