Turbine Efficiency for Unsteady, Periodic Flows

The definition of turbine efficiency for a machine subjected to unsteady periodic inflows is studied. Since mass and energy are conserved quantities over a period, there is no ambiguity in calculating the actual work output of the turbine over a period. The main difficulty lies in calculating the isentropic work output of an ideal turbine operating under the "same" conditions. Two definitions of ideal work output are presented. In the first, the ideal turbine is assumed to operate under the same time traces of inlet and exit total pressures as the actual turbine. The expression for the efficiency that results involves no averages of total pressure. In the second approach, the ideal turbine is assumed to operate under the same average conditions as the actual turbine. Total pressure averages that preserve the isentropic work output are derived and used to calculate an efficiency of the turbine. The two expressions are calculated explicitly for the case of a turbine blade row downstream of a pulse detonation tube. It is found that the definition of efficiency using averages is approximately ten points lower than the first definition. [DOI: 10.1115/1.4003246]