The effect of coolant addition or “mixing loss” on aerodynamic performance is formulated for the turbine, where mixing takes place between gas streams of different compositions as well as static temperatures. To do this, a second law efficiency measure is applied to a generalization of the one-dimensional mixing problem between a main gas stream and a single coolant feed, first introduced and studied by Hartsel  for the turbine application. Hartsel’s 1972 model for mass-transfer cooling loss still remains the standard for estimating mixing loss in today’s turbines. The present generalization includes losses due to the additional contributions of “compositional mixing” (mixing between unlike compositions of the main and coolant streams) as well as the effect of chemical reaction between the two streams. Scaling of the present dissipation function-based loss model to the mainstream Mach number and relative cooling massflow and static temperature is given. Limitations of the constant specific heats assumptions and the impact of fuel-to-air ratio are also quantified.
The Dissipation Function-Based Efficiency for Turbomachinery: Part 1 — The Efficiency of a Cooled Turbine Row
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Cha, CM. "The Dissipation Function-Based Efficiency for Turbomachinery: Part 1 — The Efficiency of a Cooled Turbine Row." Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. Volume 2C: Turbomachinery. Düsseldorf, Germany. June 16–20, 2014. V02CT38A043. ASME. https://doi.org/10.1115/GT2014-26656
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