The Effect of the Degree of Reaction on the Leakage Loss in Steam Turbines

The degree of reaction selected in designing steam turbines is of paramount importance. There has been competition between 50% reaction and impulse turbines over a century. It is, therefore, important to understand the effect of the degree of reaction on aerodynamic performance. In particular, a change in the degree of reaction affects the leakage flow substantially in both the stationary and rotating blades due to a change in the blade loading. The effect of the degree of reaction on the efficiency loss due to leakage flows is systematically investigated in this paper using analytical models. It is shown that the appropriate way to understand the efficiency loss due to leakage flows is to estimate the kinetic energy dissipation rather than the leakage mass flow rate, as demonstrated by Yoon et al. (Yoon, S., Curtis, E., Denton, J., and Longley, J., 2010, “The Effect of Clearance on Shrouded and Unshrouded Turbine at Two Different Levels of Reaction,” ASME Paper No. GT2010-22541). In order to estimate the efficiency loss due to leakage flows, the well-known Denton model (Denton, J. D., 1993, “Loss Mechanisms in Turbomachinery,” ASME J. Turbomach., 115, pp. 621–656) is extended by considering the velocity triangles in a repeating turbine stage. The extended model is compared with experimental data, at different degrees of reaction, and shows good agreement with measurements. It is shown that a reduction in the degree of reaction, at a fixed flow coefficient and a fixed work coefficient, results in an increase in the efficiency loss across the stationary blade but a decrease in that across the rotating blade. However, the efficiency loss across the stationary blade hub is estimated to be smaller than the efficiency loss across the rotating blade tip. A stationary blade can be better sealed than a rotating blade by applying multiple seals and using a leakage path with a low radius. The efficiency loss due to the tip leakage flow is substantially influenced by the choice of the tip configuration. Shrouded blades show several aerodynamic advantages over unshrouded blades in reducing the tip leakage efficiency loss. Employing multiple seals over the shroud decreases the tip leakage mass flow rate significantly. Moreover, as the degree of reaction approaches zero, the tip leakage mass flow rate over the shroud becomes small since the axial pressure drop across the rotating blade becomes small. In unshrouded blades, a reduction in the degree of reaction is shown to increase the leakage mass flow rate over the tip because the circumferential pressure difference between the blade pressure side and blade suction side generally increases when the pitch-to-chord ratio remains unchanged.