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Pulse detonation engines (PDEs) are currently attracting considerable research and development attention because they promise performance improvements over existing airbreathing propulsion devices. Because of their inherently unsteady behavior, it has been dif cult to conveniently classify and evaluate them relative to their steadystate counterparts. Consequently, most PDE studies employ unsteady gasdynamic calculations to determine the instantaneous pressures and forces acting on the surfaces of the device and integrate them over a cycle to determine thrust performance. A classical, closed thermodynamic cycle analysis of the PDE that is independent of time is presented. The most important result is the thermal ef ciency of the PDE cycle, or the fraction of the heating value of the fuel that is converted to work that can be used to produce thrust. The cycle thermal ef ciency is then used to nd all of the traditional propulsion performance measures. The bene ts of this approach are 1) that the fundamentalprocesses incorporated in PDEs are clari ed; 2) that direct, quantitativecomparisonswith other cycles (e.g., Brayton or Humphrey) are easily made; 3) that the in uence of the entire ranges of the main parameters that in uence PDE performance are easily explored; 4) that the ideal or upper limit of PDE performance capability is quantitativelyestablished; and 5) that this analysis provides a basic building block for more complex PDE cycles. A comparison of cycle performance is made for ideal and real PDE, Brayton, and Humphrey cycles, utilizing realistic component loss models. The results show that the real PDE cycle has better performance than the real Brayton cycle only for ight Mach numbers less than about 3, or cycle static temperature ratios less than about 3. For ight Mach numbers greater than 3, the real Brayton cycle has better performance, and the real Humphrey cycle is an overoptimistic (and unnecessary) surrogate for the real PDE cycle.Nomenclature C p = constant-pressurespeci c heat capacity, Btu/lbm ¢ ± R (kJ/kg-K) F = thrust, lbf (N) f = mass fuel-air ratio g c = gravitational constant, 32.174 lbm ¢ ft/lbf ¢ s 2 (1 kg-m/N ¢ s 2 ) g 0 = standard acceleration of gravity, 32.174 ft/s 2 (9.8067 m/s 2 ) h PR = lower heating value of fuel, Btu/lbm (kJ/kg) I sp = speci c impulse, s M = Mach number P m = mass-ow rate, lbm/s (kg/s) p = static pressure, lbf/ft 2 (N/m 2 ) q = heat added or rejected, Btu/lbm (kJ/kg) Q q = nondimensional heat added, q=C p T S = speci c fuel consumption, lbm/s ¢ lbf (mg/N ¢ s) s = speci c entropy, Btu/lbm ¢ ± R (kJ/kg-K) T = static temperature, ± R (K) V = velocity, ft/s (m/s)°= ratio of speci c heatś = ef ciency ¼ c = compression static pressure-rise ratio, p 3 =p 0 Ã = compression static temperature-rise ratio, T 3 =T 0 Subscripts b = burner (combustion) process CJ = Chapman-Jouguet state c = compression process e = expansion process tc = thermodynamic cycle th = thermal X = isentropic end state in Fig. 11 Y = isentropic end state in Fig. 11 0 = freestream

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This paper reviews important advances in understanding and predicting the behavior of scramjet combustion systems since the classic article published in this series by Antonio F e d (1973). The review focuses on basic fluid phenomena and is divided into three distinct sections. The first briefly describes progress that has been made in the design and demonstration of practical scramjets around the world, especially in the US, the FSU, France, and Germany. The second provides a contemporary exposition of the aerothermodynamics of the dual-mode ramjetkcramjet combustion system, accounting for the role of the isolator in preventing unstart from either thermal choking or flow separation due to heat release. The third part summarizes the current state of knowledge regarding fuelair mixing in dual-mode ramjetkcramjet combustors, especially the potential of axial vorticity to increase mixing effectiveness over that of lateral vorticity. 'The US Government has the right to retain a nonexclusive, royalty-free license in and to any 323 copyright covering this paper.