## 2 Mechanism of Low-Frequency Pressure Fluctuation
### Excitation Source of Low-Frequency Pressure Fluctuation  
The primary source of excitation for low-frequency pressure fluctuations in open-jet wind tunnels is the feedback loop resulting from the interaction between the jet and the collector [5; 8; 16; 26; 30; 31], commonly referred to in the literature as edgetone. As the jet shear layer progresses downstream, large-scale vortex structures are generated as a result of the Kelvin-Helmholtz instability [33]. These vortex structures interact with the collector, resulting in outward-radiating pressure waves. The upstream propagation of these pressure waves induces further effects on the shear layer, leading to the formation of a self-sustaining oscillation loop known as edgetone feedback. Once established, this edgetone feedback becomes the dominant mode of low-frequency oscillations in the shear layer. The phenomenon of edgetone feedback is commonly observed in open-jet wind tunnels. When intrinsic modes in the wind tunnel structure have frequencies close to it, edgetone feedback can produce significant low-frequency pressure fluctuations by resonance, as it directly harnesses energy from the jet. In the edgetone loop of an open-jet wind tunnel, the pressure wave can propagate upwards, either through the interior of the jet at a velocity of \((a-U)\), where \(a\) is the speed of sound and \(U\) is the jet velocity, or through its exterior at a velocity of \(a\)[20]. The edgetone loop formed by the inner path can be called internal feedback, while the edgetone loop formed by the outer path can be called external feedback. There is a certain difference in the frequency of these two feedback loops, and which one plays a dominant role depends on the configuration and flow conditions of the specific wind tunnel. The edgetone phenomenon is not unique to the jet impingement problem. In fact, edgetone feedback is commonly observed in various scenarios involving the interaction between shear layers and solid structures [28; 29], such as subsonic and supersonic flows with open cavities [34], adjacent tall buildings, and hydraulic system valves. The edgetone phenomenon was first documented by [PERSON] in 1854 [28]. In 1979, [PERSON] provided a comprehensive review of contemporary research on shear-layer impingement configurations [28]. He identified two key conditions for the self-sustaining oscillation phenomenon in shear-layer impingement systems: instability of the shear-layer and feedback formed by upstream disturbance propagation. [PERSON] believed that the primary cause of edgetone feedback was shear-layer instability. The majority of experimental investigations on edgetone have used flow-field visualization in conjunction with velocity and pressure measurements [28; 35; 36; 37; 38; 39; 40; 41]. Researchers generally characterize the propagation of upstream disturbances as either an acoustic or a hydrodynamic phenomenon [28; 35; 36; 37; 38; 39]. [PERSON] [36], [PERSON] [42; 43], [PERSON] [44], and others have proposed formulas for predicting the frequency of edgetone in terms of the jet length, jet velocity, etc. [PERSON] [6], based on the above works, developed the following formula for predicting the frequency of edgetone in open-jet wind tunnels:  
\[f=\frac{1}{\frac{1}{n}\frac{L_{j}+AL}{V_{c}}+\frac{L_{j}+AL}{V_{a}}}. \tag{1}\]  
where \(V_{c}=0.65U\) represents the velocity of the downstream vortex transfer and \(V_{a}\) is the velocity of the feedback pressure wave propagating upstream. For external feedback, \(V_{a}=a\), while for internal feedback, \(V_{a}=a-U\), where \(U\) is the jet velocity and \(a\) is the speed of sound. \(L_{j}\) is defined as the distance from the nozzle to the collector with an uncertainty measure, \(\Delta L\), and the number of large-scale vortex pairs contained between the nozzle and the collector is denoted by \(n\). [PERSON] et al.