Leakage Flow in Staggered Labyrinth Seals: An Analytical Approach for Incompressible Fluids

Staggered labyrinth seals are essential components in the turbine industry. These are crucial in reducing leakage flow through rotating and stationary components. Although numerous models exist to estimate leakage flow in such systems, most studies have focused on compressible fluids. However, fluids are typically incompressible in the context of hydro turbines, requiring a different method to predict the leakage behavior accurately. Existing models for incompressible fluids often depend on several parameters, which can complicate real-world applications. This study presents a unique methodology and analytical formulae for predicting leakage water flow in staggered labyrinth seals. The proposed formula integrates the continuity and energy loss equations to develop a complete framework for analyzing leakage flow in these approaches. Computational Fluid Dynamic (CFD) simulations confirmed the analytical results from the model, revealing a deviation of approximately 2.5% between the CFD and analytical results, thereby demonstrating the accuracy and reliability of the proposed method. Additionally, this study highlights the effect of fin number on the mass flow variation, which is dependent on the governing pressure. According to the results, optimizing the fin geometry and maintaining its height-width ratio around one can significantly affect the flow properties and the minimal leakage volume rates in such a system.