# Noise Reduction Using Synthetic Microjet Excitation in Supersonic Rectangular Jets
### Purpose  
Comparative analyses of numerical studies on noise control in rectangular jets reveal distinct approaches and outcomes achieved using various excitation methods. Previous investigations employed techniques such as passive control with flat and wavy plates [26], bi-modal excitation [27], plasma actuation [28], and periodic excitation [29]. Passive control focused on modifying the interaction between the jet and adjacent surfaces to reduce noise, achieving directionally dependent reductions due to shielding effects. However, this approach was constrained by reflections and induced fluctuations, resulting in limited broadband noise mitigation. Bi-modal excitation employed a reduced-order model to identify a frequency that redistributes energy from the dominant frequency to the rest of the spectrum. This method achieved significant noise reductions, with up to a 13 dB reduction at specific far-field angles. While effective in targeting particular modes, it showed limited capability for broadband noise control. Plasma actuation, tested at high Strouhal numbers around 1 and varying duty cycles, achieved its best performance with a 50% duty cycle, leading to approximately 1.5 dB noise reduction. This technique redistributed turbulent kinetic energy, suppressed large coherent structures, and enhanced streamwise vortical elements for localized noise mitigation, although actuator tones were prominent along the sideline direction. Similarly, the use of chevrons [30] and acoustic shielding [26] has elucidated unique features in rectangular jet flow compared to circular jets, attributed to the specific characteristics of the rectangular nozzle-induced free shear flows.  
The present study introduces an active noise control method using synthetic microjet actuation to excite the jet shear layer, tuned to a specific frequency mode identified for its maximal influence on large-scale structures and energy transfer. The time-harmonic microjet velocity injection alters the jet flow structures and far-field acoustic signature. Previous numerical studies proposed various excitation methods and configurations for unsteady jet excitation. For instance, plasma actuation [31] effectively excited the jet at a very high frequency with temperature variation and demonstrated successful jet noise reduction at a Strouhal number of \(St_{D}=1\)[28]. A key aspect of this approach is that the excitation affects the jet's shear layer, requiring the excitation port to be located inside the nozzle, with the excitation wavelength comparable to the size of the boundary layer. Another study [27] employed time-harmonic pressure excitation at the nozzle lip with an amplitude of around 0.4% of the jet exit mean pressure. Similarly to the current study, this noise control approach followed a theoretical analysis [32], showing that nonlinear energy transfer occurs from the most energetic (primary) mode to other modes when the jet is excited with the harmonic of the primary mode. In this case, the excitation frequency at around \(St_{D}=0.3\) was approximately double that of the far-field acoustic peak, targeting the jet's large-scale structure development.  
The present study revisits previous numerical simulations reported in [33] that utilized microjet-based jet shear layer excitation with the harmonic and subharmonic of the near-field pressure peak frequency. In contrast, a finer grid is employed in this study to enhance the accuracy of the results, enabling a more detailed exploration of the jet flow dynamics. The microjet-based excitation is implemented at the nozzle lip where the jet shear layer is most energetic. One of the objectives of this study is to compare the noise control resultswith those in [27], based on jet pressure excitation, while utilizing the same excitation frequency selection strategy proposed in the theoretical analysis of [32].