# Noise Reduction Using Synthetic Microjet Excitation in Supersonic Rectangular Jets
## 3 Results
### Far-Field Acoustics  
The far-field acoustics were calculated using the FWH methodology described in Section 2.2. The SPL spectrum and OASPL directivity results were compared against experimental data collected at 40 equivalent diameters (\(D_{\rm eff}=0.020665\)) from the nozzle  
Figure 15: First SPOD mode dimensionalized by expansion coefficient \(A_{1}(f)\) at different frequencies. exit. These comparisons aimed to validate the numerical simulations and assess the impact of excitation on the far-field noise characteristics. The SPL spectra for baseline and excited cases at multiple observer angles are shown in Figure 16. While experimental data were only available at \(\theta=0^{\circ}\) and \(\theta=90^{\circ}\)[2], analyzing the \(\theta=45^{\circ}\) case provides additional insight into how excitation alters noise radiation along diagonal planes. This is particularly important as the flow-field results indicate that enhanced mixing primarily occurs along the minor and major planes, with reduced effects in diagonal directions (refer to Figure 9). These comparisons reveal that excitation introduces a distinct tonal component in the far-field noise spectrum while reducing broadband noise across the spectrum. These findings highlight how turbulence intensity and coherent structures are modified by excitation, as observed in the coarse-mesh simulations reported previously [48]. Figure 16: SPL spectrum comparison. The black vertical lines represent the minimum resolved frequency and grid cut-off frequency. The SPL spectrum comparisons also serve to validate the numerical setup. The fine-grid results demonstrate improved agreement with the experimental measurements, addressing discrepancies observed in prior coarse-grid simulations. Proper grid stretching in the fine-grid setup likely contributed to resolving these differences. The OASPL results, shown in Figure 17, compare the baseline and excited cases at three azimuthal angles. This analysis underscores the overall noise reduction achieved through excitation. For example, at \(\theta=0^{\circ}\), the \(St_{F}=0.30\) case reduces the peak OASPL by up to 4 dB compared to the baseline, primarily due to broadband noise reduction. While the excitation introduces a tonal peak, the overall reduction in broadband noise dominates the far-field noise characteristics. The comparisons in Figures 16 and 17 are significant because they provide a comprehensive understanding of how excitation influences noise radiation patterns across a range of observer angles. The SPL spectra highlight the interaction between excitation frequencies and coherent structures, while the OASPL comparisons offer a clear picture of the overall noise reduction. Together, these analyses demonstrate the efficacy of the excitation strategy and validate the simulation methodology against experimental benchmarks. Any discrepancies, such as those observed at upstream angles, may stem from limitations in grid resolution or the placement of the FWH surface. However, the focus on peak noise radiation angles ensures that the findings are meaningful for practical applications. Unlike previous methods relying on pressure fluctuations or plasma-based actuation, this approach employs velocity-based synthetic jets, offering a novel mechanism to influence turbulence dynamics and acoustic fields. While building on the reduced-order modeling methodology utilized in [27], this work adopted a greater energy amplitude for the excitation. The unsteady microjet excitation achieved up to a 4 dB reduction in  
Figure 17: OASPL comparison. OASPL, attributed to the suppression of Kelvin-Helmholtz instabilities and decreased energy of coherent structures across the spectrum. This technique demonstrated effectiveness in both broadband noise reduction and modifying acoustic directivity, presenting a balanced solution for near- and far-field noise control.