## 3 Results and Discussions
### Hydrogen/Oxygen Mixture
#### 3.2.1 Time-Averaged Thrust  
The time-averaged thrust variation with the ER, for different oxygen pressures, exhaust pipe lengths and spark plug frequencies, is presented in Figures 15-17. For oxidizer pressures of 4.5 bar and 9 bar, few stable detonation regimes were found. Overall, the time-averaged thrust levels for hydrogen/oxygen operation are lower compared to the ones for hydrogen/air.  
From an energetic point of view, this is explained by the low ER values where stable detonation was achieved. The stable regimes for hydrogen/oxygen mixture operation are shifted to low ER values compared to hydrogen/air operation. The tests yielding sustained pulsed detonation were recorded only for ERs ranging between 0.05 and 0.25. The engine design is defined as such that both oxidizers' operations could be achieved; however, air operations were targeted in the beginning for detonation achievement, as hydrogen/air is safer than hydrogen/oxygen.  
The oxidizer switch, although keeping the same combustor configuration and high frequency DDT achievement, comes at the price of a non-optimal injection for oxygen. Hence, mixing is the main influence for downgraded performances for oxygen operation, as the number of misfires is higher. However, for this experimental campaign, there is a shift in the operation map to higher oxidant pressure values. Detonation achievement is possible for 9 bar oxidant pressure, due to the mixture having an increased proneness to detonation. Hence, there is a trade-off between optimal fuel injection and oxidizer high-frequency oscillations in the aerodynamic system (detonation achievement at high oxidizer pressures).  
Figure 15: Time-averaged thrust for a frequency of 100 Hz for \(\mathbf{H_{2}/O_{2}}\).  
The theoretical trend of increasing thrust with increasing equivalence ratio, which is to be expected, is slightly visible for the hydrogen/oxygen campaign and in most cases, it is not monotonic over the entire range of ERs. This is a direct result of the higher number of misfires across the hydrogen/oxygen operational map, which impact the time-average values. For all the frequencies, the increase in oxidizer supply pressure from 6 bar to 7.5 bar results in a slight increase in thrust level for some operating points. The additional possible influence of the pipe length is little to almost none. Moreover, the 9 bar oxidizer pressure introduces penalties in thrust, as the vortex system inside the mixer operates off-design, thus leading to poor mixing.  
For the 100 Hz (Figure 15) spark plug frequency operation, the 6 bar oxidizer supply pressure with a 300 mm configuration leads to a plateau in thrust close to 0.1 ER of about 6N and reduced gradients on the sides. The maximum thrust of 10N is reached for the 7.5 oxidizer supply pressure for the minimum length configuration of 200 mm at 150 Hz (Figure 16) spark plug frequency. This performance is achieved through 350 Hz operation  
Figure 16: Time-averaged thrust for a frequency of 150 Hz (**a**–**c**) and 233 Hz (**d**–**f**) for **H2**/**O2**.  
as well (Figure 17) for 200 mm at 9 bar oxidizer supply pressure and for 400 mm at 7.5 bar oxidizer supply pressure.