# Noise Reduction Using Synthetic Microjet Excitation in Supersonic Rectangular Jets
## 2 Methodology
### Excitation Method  
A configuration for active jet noise control is proposed that involves the placement of multiple microjet actuators distributed around the nozzle lip along the major axis. In the numerical setup, this configuration represents a hollow rectangle segment at the nozzle exit, encompassing the nozzle lip surface. The primary concept involves exciting the flow instabilities at a specific frequency by introducing unheated air along the lip line in the downstream direction. Therefore, the approach would be to directly inject the unsteady flow in the shear layer, which is situated downstream from the nozzle lip (see Figure 6). The thickness of the lip measures 0.5 mm, and the injection zone corresponds to the major axis of the nozzle lip, excluding the edges. Hence, the area ratio between the microjet actuator and the nozzle exit obtained using the original geometry is \(A_{t}/A_{e}=0.07722\). The injection velocity is adjusted to achieve the desired amplitude of the sinusoidal microjet velocity profile. The peak injection mass flow rate is determined with an injection-to-jet ratio of 1% (\(m_{i}/m_{j}=0.01\)); this was previously selected for a study on active noise control in axisymmetric jets [43], and provided successful outcomes. Consequently, it serves as a starting point for this current work.  
When analyzing the pressure spectra at the near nozzle lip in the minor and major planes, the spectra in the minor plane of the jet show considerably more fluctuations than those in the major plane, which show very few fluctuations (see Figure 7). This is in accordance with what has been previously observed [27]. Differences in the pressure fluctuations between planes are not entirely unexpected because the expansion in the  
Figure 5: Coordinate system for observer angles \(\Psi\) and azimuth angles \(\theta\).  
Figure 6: Excitation port location.  
nozzle occurs in the minor plane, whereas the nozzle contour in the major plane is flat. For this reason, excitation occurs only along the major axis. Additionally, the peak at around \(St_{D}=0.15\) already provides evidence that the near-field and SPOD analysis might give the Strouhal number range to focus on when attempting to manipulate coherent structures to reduce noise.  
Various excitation frequencies corresponding to different Strouhal numbers can be examined. However, in the current work, the excitation frequencies are selected based on the methodology reported in reference [27], where the authors utilize a reduced-order model that indicates the potential frequencies that would suppress the growth of specific turbulence scales responsible for the most prominent part in the jet noise spectrum. Previously, a Linearized Euler Equation solver (LEE) was used to evaluate this strategy [32], followed by high-fidelity simulations [27], concluding that the harmonic of the near-field peak frequency should be considered. The examination of the baseline case determined that the peak frequency in the near field was at \(St_{D}=0.15\). Thus, it was concluded that the noise sources could be minimized by introducing an excitation at its harmonic, \(St_{F}=0.30\). In the current study, a careful analysis of the baseline case guides the selection of frequencies that may influence the turbulence structures and the acoustic characteristics of the jet.