## 4 Results and Discussions
### Schlieren Imaging Analysis
Figure 12: Baseline nozzle sample flow in three operating regimes: (**a**,**a**_t_)—35k rpm, (**b**,**b**_t_)—55k rpm and (**c**,**c**_t_)—115k rpm. Figure 13 displays two sets of five consecutive frames, one for the baseline configuration and the other one for the chevron configuration for the first regime (note that both the original and processed pictures are displayed for consistency). The baseline nozzle frames, Figure 13a\({}^{\prime}\)-e\({}^{\prime}\), show a more organized flow structure near the nozzle exit, with large-scale coherent vortical structures developing along the shear layers. These structures persist as they move downstream, gradually transitioning into turbulence. This promotes the formation of prominent low-frequency turbulent regions, a characteristic of flows without additional mixing features. Consequently, the baseline nozzle produces low-frequency noise, which travels farther due to minimal attenuation. Figure 13: Chevron and baseline nozzle—Regime 1: 35k rpm, consecutive frames. (**a–e**)—baseline, (**a\({}^{\prime}\)–e\({}^{\prime}\)**)—chevrons. In contrast, the chevron nozzle disrupts the flow immediately at the nozzle exit, breaking up large-scale coherent structures earlier. This accelerates the transition to smaller-scale turbulence, resulting in a more fragmented and chaotic flow pattern. Smaller eddies form sooner and dominate the flow downstream, leading to a finely distributed turbulence field. By enhancing the mixing, the chevron nozzle shifts the energy spectrum toward higher frequencies, reducing low-frequency noise that propagates over long distances. This high-frequency turbulence is less susceptible to travel forward, as it attenuates more quickly in the atmosphere, making the chevron configuration quieter in the far field. Although this shift may slightly increase high-frequency noise near the source, the overall effect is beneficial in reducing the low-frequency noise that travels farther. Thus, while the baseline nozzle promotes larger, low-frequency structures, the design of the chevron nozzle effectively enhances mixing and reduces noise impact by favoring smaller-scale, high-frequency turbulence. Figure 14: Chevron and baseline nozzle—Regime 2: 55k rpm, consecutive frames. (**a–e**)—baseline, (**a’**-**e**)—chevrons. At a higher rotation speed of 55k RPM, Figure 14 points out differences between the baseline and chevron nozzle configurations. In the baseline nozzle, larger, more prominent vortex structures develop downstream, as highlighted by the red frames in Figure 14b',e'. These structures are larger and more dispersed compared to the 35k RPM case, exhibiting a typical free-jet expansion. In contrast, the chevron nozzle disrupts these large structures immediately at the nozzle exit, fragmenting the flow into smaller vortices and promoting finer-scale turbulence, as seen in the red frames from Figure 14a-e. This enhances mixing and shifts the energy spectrum toward higher frequencies, reducing low-frequency noise. At the highest speed of 115k RPM (Figure 15), the baseline nozzle exhibits even more densely packed large-scale vortices near the cone end, maintaining coherence further downstream. This results in stable, low-frequency turbulence that contributes to significant noise propagation. In the chevron nozzle, however, turbulence is finer and more confined near the nozzle wall. Localized high-shear regions and reverse flow induced by the chevrons generate smaller vortices that remain close to the nozzle, leading to smoother mixing and smaller-scale turbulence. This structure increases high-frequency noise near the source but effectively reduces low-frequency noise that travels farther. Overall, the chevrons enhance mixing and break down large-scale structures, reducing the impact of low-frequency noise compared to the baseline nozzle. This limitation near the wall is key to maintaining smaller vortex scales for a longer distance. When the boundary layer encounters an adverse pressure gradient, it is forced to slow down.