Model of Effect of Hot Gas Ingress on Temperatures of Turbine Disks

Ingress is the leakage of hot mainstream gas through the rim-seal clearance into the wheel-space between the rotating turbine disk (the rotor) and the adjacent stationary casing (the stator). The high-pressure rotor is purged by a radial outflow of air from the high-pressure compressor, and this cooling air is also used to reduce the ingress. The engine designer needs to predict the stator and rotor temperatures as a function of cooling-flow rate. The sealing effectiveness determines how much air is needed to reduce or prevent ingress; although there are numerous theoretical and experimental papers on the effectiveness of different seal geometries, there are few papers on the effect of ingress on the temperature of the rotating disk. This is an unsolved problem of great practical importance: under high stress, a small increase in metal temperature can significantly reduce operating life. In this paper, conservation equations and control volumes are used to develop theoretical equations for the exchange of mass, concentration and enthalpy in an adiabatic rotor–stator system when ingress occurs. It is assumed that there are boundary layers on the rotor and stator, separated by an inviscid rotating core, and the fluid entrained from the core into the boundary layer on the rotor is recirculated into that on the stator. The superposed cooling flow protects the rotor surface from the adverse effects of hot-gas ingress, which increases the temperature of the fluid entrained into the rotor boundary layer. A theoretical model has been developed to predict the relationship between the sealing effectiveness on the stator and the adiabatic effectiveness on the rotor, including the effects of both ingress and frictional heating. The model involves the use of a nondimensional buffer parameter, $Ψ$⁠, which is related to the relative amount of fluid entrained into the rotor boundary layer. The analysis shows that the cooling flow acts as a buffer, which attenuates the effect of hot gas ingress on the rotor, but frictional heating reduces the buffer effect. The theoretical effectiveness curves are in good agreement with experimental data obtained from a rotor–stator heat-transfer rig, and the results confirm that the buffer effect increases as the sealing effectiveness of the rim seals decreases. The analysis quantifies the increase in the adiabatic rotor temperature due to direct frictional heating, which is separate from the increase due to the combined effects of the ingress and the indirect frictional heating of the entrained fluid. These combined effects are reduced as $Ψ$ increases, and $Ψ$ = 1 at a critical flow rate above which there is no entrained fluid and consequently no indirect heating of the rotor. The model also challenges the conventional physical interpretation of ingress as, in general, not all the hot gas that enters the rim-seal clearance can penetrate into the wheel-space. The ingress manifests itself through a mixing of enthalpy, which can be exchanged even if no ingested fluid enters the wheel-space.