Defining the Efficiency of a Cooled Turbine

Despite 40 years development of gas turbine cooling technology, there is no general agreement on the most appropriate definition of cooled turbine efficiency; the critical issue is the choice of a hypothetical “ideal” process. This paper reviews the definitions in use and presents new proposals for overcoming the problems. Attention is first focused on a stationary cooled cascade, and it is shown that the commonly used Hartsel efficiency definition (where the gas and coolant streams expand separately in the ideal process) is unsatisfactory. Three “mixed” efficiencies, referred to as the MP (mainstream-pressure), FR (fully reversible), and WP (weighted-pressure) efficiencies are then discussed. The MP ideal process involves mixing of the coolant and the mainstream to give an unchanged mainstream pressure before expansion. This definition, although sometimes used, is unsatisfactory because the efficiency is independent of the coolant supply pressures. The FR and WP efficiencies have not appeared in the literature previously. The FR efficiency is based on a fully reversible ideal process and has the soundest thermodynamic foundation. It is equivalent to a suitably defined rational efficiency and can be directly related to the various cooling losses. However, as it gives a significantly lower value than the Hartsell and MP definitions, it may not appeal to turbine manufacturers. The WP definition is a pragmatic alternative. In the WP ideal process the entropy increase associated with temperature equilibration of the mainstream and coolant flows is allowed in the mixing before expansion. All three mixed efficiencies can be applied to turbine stages with multiple coolant streams. Turbine manufacturers are urged to reconsider their current procedures with a view to standardizing on a thermodynamically sound definition of efficiency.