The Rayleigh Efficiency of Pressure Gain Combustors

This paper describes a new method for calculating the performance of pressure gain combustors for gas turbine applications. The method judges the value of a combustor based on the flow’s increased potential to do shaft work from combustor inlet to exit. This potential is defined as the work that could be extracted from the flow by a reversible adiabatic turbine exhausting to the combustor supply pressure. A new performance metric, the Rayleigh efficiency, is defined as the increased potential of the flow to do shaft work divided by the heat input. A novel control volume analysis is used, which directly links this performance metric to source terms within the combustor. Two primary source terms are shown: The first is a thermal creation term, which occurs in regions of the flow where combustion heat release occurs at pressures above that of the environment and acts to raise the flow’s potential to do shaft work. The term is a nonlinear analog of Lord Rayleigh’s acoustic energy creation term, from his 1878 thermoacoustic criterion. The second term is a viscous destruction term that always acts to reduce the flow’s potential to do shaft work. In the final part of the paper, the utility of the method is demonstrated using experimental measurements and computational predictions from a SNECMA (Société nationale d'études et de construction de moteurs d'aviation)/Lockwood-type valveless pulse combustor. The analysis enables a number of previously unanswered questions about pulse combustors to be answered.