## 2 Materials and Methods
### Test Matrix  
To better understand the fluidodynamic behavior at low values of the \(SN_{g}\), a preliminary numerical analysis was carried out prior to define the experimental test matrix. CFD numerical simulations were performed by Sapienza University of Rome, a PHAEDRA project partner, to examine the combustion chamber internal flowfield with low swirl numbers, two fuel formulations (including the F5) and various post chamber lengths (Figures 7 and 8 from [50]). The results were encouraging for the proceeding of the work. The length of the grains in the initial tests and the length of the post chambers were two examples of the parameters that were defined using the results. The F8 blend was the first fuel type tested. This formulation was chosen as the reference paraffin-based fuel for the PHAEDRA project. This paraffin combines a relatively high regression rate and good mechanical properties. Thus, it was decided to test F8 paraffin throughout an extensive spectrum of the \(SN_{g}\). The geometrical swirl number of the tests extended from zero, or axial flow, up to the value of 3.33. During the course of the investigation, the grain length was adjusted to be closer to the ideal \(O/F\) value based on the findings of earlier trials. A total of ten fire tests were executed. Only one F8 paraffin grain was tested with a different initial port diameter (F8_008), while two other configurations included the post chamber (F8_001-F8_002). Most of the tests performed had durations of 10 s and 15 s, which allowed us to perform regression assessments and performance calculations for two distinct average oxidizer mass flux values. Since the initial test main goal was to confirm that the fuel would ignite, it was scheduled for a shorter period. Figure 8: Temperature flowfield with varying post chamber configurations. Adapted, with permission, from [50]. Figure 7: Temperature flowfield with varying swirl intensities (F2 formulation). Adapted, with permission, from [50]. The second phase of the test campaign focused on vortex injectors with low swirl number values. Along with evaluating the regression rate, the goal was to confirm how efficiency changes when the vortex intensity inside the chamber decreases. It has been possible to compare the collected data with those found in the literature thanks to the utilization of a standard polyethylene fuel. Furthermore, HDPE is less susceptible to post-burn effects (such as grain port surface melting and thermal deformations), which makes it possible to quantify and observe the fuel consumption rate more accurately. A total of six tests were performed: each of the three vortex injectors, with the \(SN_{g}\) equal to 0.50, 0.75 and 1.00, were tested twice, varying the oxidizer mass flow running time, 15 s and 20 s, respectively. Throughout the experiments, the fuel initial port diameter, which was set at 20 mm, did not change. Otherwise, to reach the desired \(O/F\) value, the grain length was varied. The final leg of testing was carried out using formulation F5. This paraffin blend has a composition different from F8, and produces a comparatively lower regression rate. In addition to investigating a different blend, this campaign completed the results gained in prior tests, and, indeed, it examined the low swirl numbers coupled to a paraffin-based fuel. At this point, it was also possible to focus on the variation in combustion efficiency as the chamber volume changed. There were nine tests run, three of which (F5_002, F5_003 and F5_004) had a \(SN_{g}\) equal to 1, and the remaining six had a value of 0.75. The grain length of 95.1 mm varied only in the first and last sample of this series (F5_001 and F5_009). The F5_003 test was the only one with a varied experimental duration with respect to 15 s; it fired indeed for 20 s. The post chamber was added to F5_005 and to the last three tests. Initial fuel port diameters of 15 mm, 50 mm and 65 mm were examined. In Table 2, the entire test matrix is displayed together with the key data from each test individually.