Interdependence of Discharge Behavior, Swirl Development and Total Temperature Increase in Rotating Labyrinth Seals

Leakage flows between stationary and rotating components are one of the main sources for losses in turbo machines. Therefore, their reduction is a main goal in the design of modern aircraft engines. Contactless seals, mainly labyrinth seals are key elements either to seal rotating parts or to control the amount of leakage flow for internal use in the secondary air system. Even though new seal types like, brush seals, carbon seals etc. will be seen more often in advanced gas turbines, labyrinth seals will continue to play an important role in the primary and secondary air system and thus improved design tools are a necessity for more efficient and reliable engines. In the design process but also during the life time of the engine the characterization of contactless seals e.g. their discharge behavior, the development of the circumferential velocity (swirl) and the loss induced total temperature increase (windage heating) are of special interest for designers and operators. Despite of today’s efficient CFD methods, analytical models remain a valuable tool as they provide for reasonably estimates fast with small computational effort. Additionally, analytical models are especially suited to improve the understanding of the complex interdependency of the aforementioned parameters. As one limit of the swirl in rotating seals, the equilibrium swirl is defined in this paper and a simple method to determine its value is presented. In this context, the influences of the rotor-stator area ratio and the stator roughness on the equilibrium swirl are taken into account. In the case the inlet swirl is known or can be estimated with reasonable confidence an analytical approach to determine the swirl development from chamber to chamber is proposed. Given this swirl development along the seal axis, the overall total temperature increase can be calculated. Based on the final dimensionless equation for the total temperature change the interdependent influences of discharge behavior, swirl development and the total temperature increase on each other are discussed.