## Ideal Cycle Analysis Of A Regenerative Pulse Detonation Engine For Power Production

##### Abstract

Over the last few decades, considerable research has been focused on pulse detonation engines (PDEs) as a promising replacement for existing propulsion systems with potential applications in aircraft ranging from the subsonic to the lower hypersonic regimes. On the other hand, very little attention has been given to applying detonation for electric power production. One method for assessing the performance of a PDE is through thermodynamic cycle analysis. Earlier works have adopted a thermodynamic cycle for the PDE that was based on the assumption that the detonation process could be approximated by a constant volume process, called the Humphrey cycle. The Fickett-Jacob cycle, which uses the one-dimensional Chapman-Jouguet (CJ) theory of detonation, has also been used to model the PDE cycle. However, an ideal PDE cycle must include a detonation based compression and heat release processes with a finite chemical reaction rate that is accounted for in the Zeldovich - von Neumann - Döring model of detonation where the shock is considered a discontinuous jump and is followed by a finite exothermic reaction zone. This work presents a thermodynamic cycle analysis for an ideal PDE cycle for power production. A code has been written that takes only one input value, namely the heat of reaction of a fuel-oxidizer mixture, based on which the program computes all the points on the ZND cycle (both p-v and T-s plots), including the von Neumann spike and the CJ point along with all the non-dimensionalized state properties at each point. In addition, the program computes the points on the Humphrey and Brayton cycles for the same input value. Thus, the thermal efficiencies of the various cycles can be calculated and compared. The heat release of combustion is presented in a generic form to make the program usable with a wide variety of fuels and oxidizers and also allows for its use in a system for the real time monitoring and control of a PDE in which the heat of reaction can be obtained as a function of fuel-oxidizer ratio. The Humphrey and ZND cycles are studied in comparison with the Brayton cycle for different fuel-air mixtures such as methane, propane and hydrogen. The validity and limitations of the ZND and Humphrey cycles related to the detonation process are discussed and the criteria for the selection of the best model for the PDE cycle are explained. It is seen that the ZND cycle is a more appropriate representation of the PDE cycle. Next, the thermal and electrical power generation efficiencies for the PDE are compared with those of the deflagration based Brayton cycle. While the Brayton cycle shows an efficiency of 0 at a compressor pressure ratio of 1, the thermal efficiency for the ZND cycle starts out at 42% for hydrogen-air and then climbs to a peak of 66% at a compression ratio of 7 before falling slowly for higher compression ratios. The Brayton cycle efficiency rises above the PDEs for compression ratios above 23. This finding supports the theoretical advantage of PDEs over the gas turbines because PDEs only require a fan or only a few compressor stages, thereby eliminating the need for heavy compressor machinery, making the PDEs less complex and therefore more cost effective than other engines. Lastly, a regeneration study is presented to analyze how the use of exhaust gases can improve the performance of the system. The thermal efficiencies for the regenerative ZND cycle are compared with the efficiencies for the non-regenerative cycle. For a hydrogen- air mixture the thermal efficiency increases from 52%, for a cycle without regeneration, to 78%, for the regenerative cycle. The efficiency is compared with the Carnot efficiency of 84% which is the maximum possible theoretical efficiency of the cycle. When compared to the Brayton cycle thermal efficiencies, the regenerative cycle shows efficiencies that are always higher for the pressure ratio studied of 5 is less than or equal to πc is less than or equal to 25, where πc the compressor pressure ratio of the cycle. This observation strengthens the idea of using regeneration on PDEs.