## 4 Results
### Molecular Tagging Velocimetry Results  
Figure 10 shows the evolution of the instantaneous velocity profiles measured by MTV at the three locations. The MTV results confirm the findings from the shadowgraphy study (Figures 4 and 7) as the signature of the Mach disk appears in the velocity profiles as early as 0.09 s after the gas pulse starts. The maximum measured velocity at the first MTV measurement station (a few millimeters below the nozzle) is 489 m/s (Mach 1.43); Figure 3 shows the raw MTV image with the deformed tagged line. This maximum speed decreases to 438 m/s (Mach 1.28) and 296 m/s (Mach 0.86) at the two other measurements downstream. The Reynolds number based on the 4 mm nozzle diameter is on the order of \(10^{6}\), as calculated, for the sake of simplicity, using the measured 489 m/s velocity and ideal gas air properties inside the reservoir at 7.7 bar. The temporal evolution of the MTV profiles is divided into the three regimes identified above. Figure 11 highlights the three regimes by stacking multiple velocity profiles on a single plot. The transient leading to the existence of the Mach disk below the nozzle is shorter than 0.09 s after the gas pulse starts. A quasi-steady regime is then observed for \(t=0.12-0.24\) s, and the jet finally decreases after that: the Mach disk retracts laterally, and the peak flow velocity decreases. It should be noted that the first MTV measurement location is very close to the location of the main Mach disk in the quasi-steady regime; the subsonic center part of the velocity profile is characteristic of the subsonic flow in the jet core downstream of the Mach disk. Figure 9: Comparison between shadowgraphy (**left**) and CFD density field (**center, right**) in a vertical slice of the flow domain. The figure highlights similarities and differences between the experimental and numerical fields for the Mach disk structure. Figure 12 displays the validation of CFD versus MTV results in the quasi-steady regime. The quantities compared in that plot are streaklines. Streaklines indicate the destination position of fluid parcels that start along a given line in the domain after a given \(\Delta t\) has elapsed; this is essentially a simulation of the MTV signal. For simplicity, those results are shown in Figure 12 with the dimension of velocity, representing the ratio between the distance from the starting line and \(\Delta t\). For the steady-state CFD results, well-converged streaklines are obtained by post-processing the velocity results using a time-marching Lagrangian algorithm and 100 iterations. The MTV velocity profiles plotted in the figure are the same as in Figure 11 (middle), obtained between 0.12 and 0.14 s. There are seven profiles for the top location (\(x=6.45\) mm), one in the middle (\(x=47.01\) mm), and three at the bottom location (\(x=90.42\) mm). Figure 10: Evolution of the instantaneous velocity profiles and their evolution in time measured by MTV at the three vertical locations, one for each plot. The figure shows the quasi-steady nature of the flow structures. General agreement in terms of trends and approximate magnitudes is observed between the CFD and MTV results at all three locations in which data are available. At the  
Figure 11: Temporal evolution of the MTV profiles at three different heights downstream of the nozzle (top station at \(x=6.45\) mm, middle station at \(x=47.01\) mm, and bottom station at \(x=90.42\) mm). The three plots shown divide the gas pulse history into three regimes. Figure 12: Comparison between MTV (solid lines colored as in Figure 4) and CFD (filled circles) streaklines at three vertical elevations downstream of the nozzle (top station at \(x=6.45\) mm, middle station at \(x=47.01\) mm, and bottom station at \(x=90.42\) mm). The MTV velocity profiles are the same as in Figure 11 in the quasi-steady regime. top line, both CFD and MTV show a dual-peaked streakline profile. MTV data show a low-velocity central feature a few millimeters wide that is not present in CFD results.