## 4 Conclusions  
The present study describes that thrust, total specific impulse and fuel specific impulse resulted from the experimental campaign of our hydrogen-fueled PDC with different oxidizers and with the same design of the combustor. The choice of freezing the design was to establish the operational map of our combustor, which targets both ground-based or space-based application. Higher time-averaged thrust levels and time-averaged specific impulse values are achieved for the hydrogen/air mixture compared to hydrogen/oxygen operation. This is due to the initial design of the PDC, which targeted air as an oxidizer. For mixture  
Figure 23: Time-averaged specific impulse for a frequency of 350 Hz for \(\mathbf{H_{2}/O_{2}}\). Figure 22: Time-averaged specific impulse for a frequency of 150 Hz (**a–c**) and 233 Hz (**d–f**) for \(\mathbf{H_{2}/O_{2}}\). transition, minimum alteration was considered (fuel injection adapted) to establish a baseline configuration which is capable of achieving high-frequency detonation regimes. The operating frequency of the thruster is primarily influenced by the spark plug, and it is frequently lower than expected due to misfires during the initiation of the detonation cycle. As anticipated, the design frequency of 100 Hz results in rare misfire events. This is an effect of the way the geometry of the PDC has been designed, namely the correlation between the length of the Helmholtz resonators, the premixing and the detonation chamber volume and length, and the length of the exhaust pipe. To approach the performance of a classical gas turbine engine, the PDC operating frequency must be of at least 75 Hz for a near-stoichiometric fuel/air mixture [29]. Further increasing the frequency allows for a reduction in the combustor size, reducing the weight and drag of the engine, and the PDC tested here made use of aerodynamic valves to increase the operating frequency over the above-mentioned performance threshold. The current state-of-the art maximum frequency is around 300 Hz [30; 31], even though significantly higher PDC operating frequencies have been reported more recently [32; 33] (350 Hz [32], and even 800 Hz [33], measured for hydrogen/oxygen mixtures). The design frequency was selected at a conservative 100 Hz for two reasons: to allow the PDC to operate on both air and oxygen with no geometrical changes, and to evaluate the response of the PDC when driven via higher frequency spark plugs. When operating at non-design frequencies, data indicates that using air as an oxidizer allows the PDC system to sometimes replicate a spark plug frequency of 150 Hz. However, in all other scenarios, frequencies higher than the design frequency, driven using the spark plug, are occasionally achieved, but never fully match the spark plug frequency due to misfires. Hydrogen/oxygen performances presented in this paper have lower values, especially for thrust and total specific impulse levels. For this mixture, thrust values are directly impacted by the number of misfires. For hydrogen/air, time-averaged thrust values tend to increase with the ER and oxidizer pressure. The optimal operation of the PDC is for a 400 mm exhaust pipe length, which gives the highest thrust levels across the considered values of the oxidizer pressure, except for the 233 Hz spark plug frequency. The same conclusion can be drawn for the total specific impulse and the fuel specific impulse. The optimum values are also obtained for the 400 mm exhaust pipe, with the same exception. This is due to the decoupling between the aerodynamic system and the ignition frequency. For the hydrogen/oxygen mixture, the optimum values in terms of time-averaged thrust are achieved for a 200 mm exhaust pipe length. This is attributed to the higher energy release of the mixture than for air, which is affected by the heat-transfer with the exhaust pipe walls. Hence, the detonation intensity is less dissipated for shorter exhaust pipe values and thus higher values of thrust are achieved.