Numerical analysis of flow characteristics and heat transfer performance in straight-through labyrinth seals with teeth of different numbers uniformly distributed

The labyrinth seal is one of the most cost-effective solutions for controlling leakage flow in turbomachinery, and its performance has a significant impact on the aerodynamic efficiency of turbines. This paper proposes a tooth pitch-to-height ratio for evaluating the sealing performance of straight-through labyrinth seals. The relationship between the discharge coefficient and the number of teeth is investigated using ANSYS CFX. The SST k-ω turbulence model was employed to capture the details of the flow field, and the sealing mechanism was revealed through shear stress analysis. Three-dimensional steady-state numerical results show that the minimum discharge coefficient of each group occurs when the tooth pitch-to-height ratio is close to 3, and this regularity is not affected by the pressure ratio or inlet angle. For the test group with the most significant optimization effect, the discharge coefficient decreases from 0.5364 to 0.4420 (with a change rate of 21.4 %). The location of the vortex core in the downstream side of the cavity is a significant feature of improved sealing performance; at this point, the average vortex-induced shear stress is the highest among all test groups, effectively reducing the velocity of the main flow. In addition, the relationship between the average vortex-induced shear stress and the tooth pitch-to-height ratio exhibits convex and concave patterns, corresponding to the confinement of the high-velocity main flow to single or multiple cavities. The Nusselt numbers of the rotating walls (ranging from 104.28 to 411.35) are all higher than those of the stationary walls (ranging from 16.13 to 117.11). The increase in the temperature gradient within the labyrinth teeth is another characteristic of improved sealing performance. This study extracts the characteristics of flow fields with high-efficiency sealing performance based on extensive numerical results, which provides certain guiding significance for the design and optimization of labyrinth seals.