An Analytical Model for Over-Shroud Leakage Losses in a Shrouded Turbine Stage

This study presents an analytical model that uses directly measurable flow quantities to predict the effects of leakage on shrouded turbine stage performance. The model displays good predictive ability for the mass leakage fraction, for the tip leakage and for the mixing losses. The model resolves the negative incidence angle induced by mixing the leakage flow with the main stream and predicts the increment in the total mixing loss coefficient at increasing injection angles. The effects of the labyrinth seal geometry, such as the tip gap width and the number of seals, on the associated leakage losses as well as on the turbine stage performance are adequately represented. Overall, the present model exhibits a good qualitative and quantitative agreement with comparative benchmark data. It is concluded that increasing the labyrinth through-flow resistance by increasing the number of fins leads to a decrement in the leakage flow and its adverse effects but the effectiveness of this reduction decreases as the number of fins increases by more than three. The mass leakage fraction, tip leakage loss coefficient and total mixing loss coefficient increase linearly as the sealing gap ratio increases. A conventional injection angle of 90° increases the total mixing loss by about 28% compared to injecting parallel to the main passage flow.