Numerical Optimization of Leakage by Multifactor Regression of Trapezoidal Groove Geometries for a Balance Drum Labyrinth Seal

Grove configuration has a direct influence on the performance of the labyrinth seal. In this study, the geometry of the groove cavities in a water balance drum labyrinth seal was varied to investigate the effects on fluid leakage. A design of experiments (DOE) study varied the groove cavity cross-section through various trapezoidal shapes with one or both internal base angles obtuse. The grooves are parameterized by the groove width connected to the jet-flow region, the internal entrance and exit angles, the flat width inside the groove, and the depth. The corners inside the groove cavity are filleted with equal radii. As with the baseline model the grooves are evenly spaced along the seal length and identical copies of each other. The flow path starting at the rear of the pump impeller and proceeding through the seal was created as a 5 degree sector CFD model in ANSYS CFX. Three five-level factorial designs were selected for the cases where the entrance angle is obtuse and the exit angle acute, the exit angle obtuse and entrance angle acute, and both angles were obtuse. The feasible geometries from each factorial design were selected based on the nonlinear geometric constraints and CFD simulation experiments were performed in ANSYS CFX. The leakage results from these simulation experiments were then analyzed by multifactor linear regression to create prediction equations relating the geometric design variables to leakage and enable geometric optimization for minimum leakage. Streamline plots along the seal cross-section were then used to visualize the flow and understand regression trends. This study investigates the effect of groove cavities with obtuse internal entrance and exit angles on vortex size and position and subsequent seal leakage.