## 4 Discussion
This proves the possibility of using moderately low values of swirl numbers in order to boost the efficiency considerably without an excessive increase in the regression rate, although this finding was not replicated as equally well in the subsequent tests with the F5 paraffin formulation, probably again due to shorter grain and combustion chamber lengths. Adding a post-chamber increased the performance by few percent, as expected from the CFD analyses. A benefit has been also observed in operating at lower oxidizer fluxes, i.e., larger port volumes. It is again expected that larger (and more useful from an application perspective) scales should provide better results. The use of low swirl numbers with a conventional fuel is optimal on the other side of the spectrum compared with the previously mentioned case, i.e., this time at lower scales and long burning times, where high efficiency values remain paramount but the regression rate is kept at moderate levels. In the intermediate range of scales and burning times, more solutions overlap, like higher regressing fuels with lower swirl numbers and lower regressing fuels with higher swirl numbers. The final choice will be thus dictated by other affected aspects like nozzle erosion and blocking, injector size and pressure drop, fuel thermo-mechanical properties and so on. In any case, the combination of all test campaigns proved the third stated goal of the work, the possibility of playing with two different design variables in order to properly optimize the grain and chamber geometries for a wide range of possible different mission requirements, spanning large variations in size, burning times and motor envelopes, always keeping high performance levels. A relation that was not specifically studied but was inferred from the data is the one between the regression rate and the average \(G_{ox}\) value of the tests. In particular, for identical fuel type and \(SN_{g}\), experiments with lower average \(G_{ox}\), that is, with larger average fuel port diameters, measure a comparably higher regression value, as shown in Figure 15. The effect is related to the progression of the port diameter during firing, or, more specifically, the time-varying ratio of \(\Phi_{port}/\Phi_{injection}\), and this was confirmed for all three types of fuel used. The inferred \(a\) constant calculated with the procedure shown earlier shifts slightly upward as \(\Phi_{port}/\Phi_{injection}\) increases. This occurrence may explain why pressure graphs (especially those with longer durations) indicate slightly growing pressure in the chamber, which correlates with an \(n\) exponent <0.5 and should be examined further in future investigations. Thus, this phenomenon must be considered when designing hybrid motors with long burning times, where the diameter of the grain port may vary greatly between the ignition and the tail off, while the injection diameter remains constant. During the design phase of the PHAEDRA program, Avio established the requirements for the DEMO test-bed, including a minimum efficiency threshold, a target regression rate level, and the number and timing of the re-ignitions. These parameters are fulfilled by a proper combination between the tested paraffin blends and swirl numbers. The target \(O/F\) is then achieved by adjusting the length of the fuel grain accordingly. The next step of the PHAEDRA program will be the testing of the 7.5 kN DEMO test-bed with the selected configuration to validate all predictions and confirm the fulfillment of the target performance goals. Figure 16 provides a qualitative summary of the main outcomes reported in this article. Figure 15: Plotting the values of the \(a_{exp}\) constant versus the associated \(SN_{g}\). Experimental points with an average \(G_{ox}\) value greater than 80 kg/m\({}^{2}\)s are highlighted in violet.