Optimization of a Balance Drum Labyrinth Seal to Minimize Leakage

Annular labyrinth seals are designed as tortuous paths that force a working fluid to expand and contract repeatedly through small clearances between high and low pressure stages of turbomachinery. The resulting expansion and recirculation reduces kinetic energy of the flow and minimizes leakage rate between regions of high and low pressure through the seal. Most current seal geometries are selected based on what has worked in the past, or by incremental improvements on existing designs. In the present research, a balance drum used in a multi-stage centrifugal pump was selected as a starting point, and design of experiments studies were performed to investigate the influence of groove shape and scale on leakage rate across the seal for a fixed pressure differential.
The CFD model of the baseline labyrinth seal has an upstream region leading to 20 evenly spaced semicircular grooves along a 267 mm seal length, with a clearance region of 0.305 mm. For each test parameterization, the definition of the seal geometry was specified by a set of five factors. The first parameterization factors allow for variation in scale of the semicircular grooves within a pattern of five independently scaled grooves repeated four times along the seal length. The second parameterization factors allow for a single repeated groove shape variation between a rectangular, triangular and semi-circular groove.
The seal was constructed with two parameterized CFD models in ANSYS CFX as a 5 degree sector of the full 3D seal. A designed experiment involving a non-central composite design was performed to investigate the effects of 5 parameters, representing seal groove radii, on leakage rate and rotordynamic coefficients of the seal. A second designed experiment was performed as a five-level fractional factorial design to investigate groove shape on seal performance characteristics. This study demonstrates a practical approach for investigating the effects of various geometric factors on leakage rate and rotordynamic coefficients for balance drum seals. The empirical linear regression models fitted to the responses of the experimental designs suggest geometric parameters that could be applied to improve performance of future seals.