Calculations of Cooled Turbine Efficiency

The efficiency of a cooled turbine stage has been discussed in the literature. All proposed definitions compare the actual power output with an ideal output, which has to be determined; but usually, one of two definitions has been used by turbine designers. In the first, the so-called Hartsel efficiency, the mainstream gas flow, and the various coolant flows to rotor and stator are assumed to expand separately and isentropically to the backpressure. In the second, it is assumed that these flows mix at constant (mainstream) gas pressure before expanding isentropically (sometimes, the rotor coolant flow is ignored in this definition). More recently, it has been suggested that a thermodynamically sounder definition is one in which the gas and coolant flows mix reversibly and adiabatically before isentropic expansion to the backpressure. In the current paper, these three efficiencies are compared, for a typical stage—the first cooled stage of a multistage industrial gas turbine. It is shown that all the efficiencies fall more or less linearly with increase of the fractional (total) coolant flow. It is also shown that the new definition of efficiency gives values considerably lower than the other two efficiencies, which are more widely used at present. Finally, the various irreversibilities associated with the flow through a cooled turbine are calculated. Although all these irreversibilities increase with the fractional coolant flow, it is shown that the “thermal” irreversibility associated with film cooling is higher than the other irreversibilities at large fractional coolant flow.