Thermodynamic Cycle Analysis of Pulse Detonation Engines

Abstract

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

Pulse Detonation Assessment for Alternative Fuels

“…This is then followed by Rayleigh type combustion [35]. The whole process satisfies the Chapman-Jouguet (CJ) condition, which requires that the local Mach number at the termination of the heat expansion region be choked [34]. CJ theory requires chemical reactions to be represented by heat discharge in an infinitesimally thin shock front that brings the material from a starting state on the inert Hugoniot line to a subsequent CJ point state [20].…”

“…PDE detonation is modeled as a normal shock wave or Zel'dovich-von Neumann-Doering (ZND) detonation wave, advancing into the undisturbed fuel-air mixture of a uniform cross-sectional area tube, which is almost at rest for combustor entry conditions [34]. This is then followed by Rayleigh type combustion [35].…”

“…Therefore, the exergy can be increased if the heat injection process follows a different thermodynamic cycle path [38]. The thermodynamic cycle of ideal PDE is similar to the ideal Brayton cycle, while the Humphrey cycle is considered a modification to the Brayton cycle in which the constant-pressure heat addition process is replaced by a constant-volume heat addition process [34]. The Humphrey cycle is much more efficient than the Brayton cycle, in which a very rapid burning takes place.…”

Analysis on Thermal Efficiency of Non-Compressor Type Pulse Detonation Turbine Engines

“…A strain gauge attached to the stator vane measured vibrations during PDTE operation and pressure attenuation as shock waves passed through the turbine (Baptista et al, Rasheed et al). 30,31) Based on theoretical PDE analysis, Heiser and Pratt 32) and Zeldovich 33) proposed a thermodynamic detonation combustion cycle (PDE cycle). It is identical to the Brayton cycle except that the combustion process is detonation.…”

Introduction to ?To the Question of Energy Use of Detonation Combustion? By Ya. B. Zel?dovich

“…7,9 The specific numerical values given in the main body are, as Zel'dovich recognized, rough estimates and deviate substantially from detailed computations based on realistic thermodynamic properties. Despite the incorrect values for thermodynamic states, his final results regarding the differences in cycle efficiency are quantitatively correct.…”