Performance Metric for Turbine Stage Under Unsteady Pulsating Flow Environment

In a turbine stage for a vehicular turbocharger or a PDE (Pulse Detonation Engine) system, the power extraction process is inherently unsteady due to a highly pulsating flow delivered from the upstream combustor. Characterizing the operating performance of such a turbine stage would call for defining unsteady efficiency on a physically rigorous basis. Since the instantaneous efficiency can be calculated as the fraction of the actual power to the unsteady ideal power, an expression for the unsteady ideal power from the turbine stage is first derived by applying mass conservation and the First/Second Law of thermodynamics for the turbine stage. The newly derived expression elucidates the distinction from the quasi-steady situation in that the storage effect of mass/energy/entropy over the turbine stage is no longer negligible compared to the flux of mass/energy/entropy at the inlet and outlet. The storage effect resolves the previously reported physical inconsistency that the instantaneous efficiency can be a value of above unity or below zero; an erroneous result associated with defining the efficiency based on a quasi-steady basis. As the reduced frequency of the inlet pulsation of the turbine stage becomes larger than unity, the mass/energy/entropy accumulation rate over the turbine stage becomes significant compared to the mass/energy/entropy influx rate. Then, the definition of the efficiency based on a quasi-steady assumption loses its applicability. In this paper, the role of mass/energy/entropy storage rate in the unsteady ideal power is assessed in order to underpin the inconsistency in the previous quasi-steady approach. The utility of the unsteady efficiency definition is elucidated for the case of a turbocharger turbine stage subjected to high inlet flow pulsation.