## 2 Mechanism of Low-Frequency Pressure Fluctuation
### Resonance Mechanism of Low-Frequency Pressure Fluctuation
#### 2.2.2 Planar Standing Wave in Plenum
For example, at Mach number \(Ma\) = 0.2, Equation (5) suggests that if the size of the plenum in one direction is approximately twice that of the jet (within 20% deviation), resonance can occur between the edgetone and the standing wave in that direction. In the literature [19], [PERSON] et al. reported the existence of standing waves in three directions of the plenum in the IVK 1:4-scale Model Wind Tunnel in Stuttgart (IVK-MWT). To the best of the authors' knowledge, this is the first report of standing waves in the plenum of an open-jet wind tunnel. Due to a lack of confidence in the edgetone feedback model of [PERSON] et al., their paper [19] did not investigate the possibility of planar standing waves resonating with edgetone feedback. Here, we calculated the conditions under which standing waves resonate with edgetone feedback in the three directions of the plenum for the IVK-MWT wind tunnel using Equation (5), as shown in Table 2.  
In Table 2, the discrepancy \(\Delta(L_{i}/L_{j})\) between the actual values of \(L_{i}/L_{j}\) in the three plenum directions and the predicted values from Equation (5) were computed as:  
\[\Delta(L_{i}/L_{j})=\frac{(L_{i}/L_{j})_{real}-(L_{i}/L_{j})_{predict}}{(L_{i} /L_{j})_{real}}\times 100\%. \tag{7}\]  
In Table 2, it can be seen that the discrepancy \(\Delta(L_{i}/L_{j})\) in all three directions is less than 15%. As mentioned above, the resonance of the standing wave with edgetone feedback is likely to occur when the discrepancy falls below 20%. Therefore, it can be inferred that the standing waves in each of the three directions of the plenum of the IVK-MWT wind tunnel (at different wind speed ranges) resonate with edgetone feedback. Additionally, it can also be seen that a smaller discrepancy \(\Delta(L_{i}/L_{j})\) results in larger amplitude oscillations of the standing waves. It should be noted that, in Table 2, the wind speed when the Z-direction standing wave is the strongest is given according to the maximum operating speed of the wind tunnel, which is 77.8 m/s. If the maximum operating wind speed of the wind tunnel can be increased to obtain the real wind speed when the Z-direction standing wave reaches the strongest, the Z-direction discrepancy \(\Delta(L_{i}/L_{j})\) given in Table 2 might be reduced to the same order as that in the X- and Y-directions. Figure 4: Schematic of an open-jet wind tunnel with floor. Another possible example of edgetone feedback resonating with a plenum planar standing wave can be observed in the DNW-LLF wind tunnel. As previously noted, due to the low-frequency pressure fluctuations posing a safety risk to the wind tunnel, DNW-LLF had to impose a maximum wind speed limit of less than 80 m/s for its open test section. According to the literature [4], the open test section of DNW-LLF has a jet length of 18.7 m and a plenum width of 28.2 m. Assuming the speed of sound is 340 m/s, we can calculate the frequency of the standing wave in the width direction utilizing Equation (6) to be \(f_{sw}=6.03\) Hz. Figure 5 displays the relationship between the edgetone frequency and wind speed according to Equation (2) with external feedback, \(\Delta L=0\), and \(n=2\). When the wind speed reaches approximately 80 m/s, the frequency of external edgetone feedback reaches just 0.8\(f_{sw}\), indicating entry into the resonance region. These results are consistent with test runs performed in this wind tunnel, where wind speeds approaching 84 m/s caused roof damage, necessitating wind speeds to be limited to below 80 m/s [4]. Therefore, it is highly probable that significant low-frequency pressure fluctuations in DNW-LLF's open test section are also caused by resonance between edgetone feedback and width-direction planar standing wave in the plenum. In addition, the findings from Figure 5 indicate that low-frequency pressure oscillations in the wind tunnel will likely reach their maximum amplitude at a wind speed of approximately 104 m/s.