## 1 Introduction
### Low-Frequency Pressure Fluctuation in Open-Jet Wind Tunnel  
Low-frequency pressure fluctuation is a common phenomenon in open-jet wind tunnels, characterized by periodic low-frequency pressure oscillations within a certain range of test wind speeds [5; 8; 13; 14; 15; 16]. The acoustic wavelength corresponding to the pulsating frequency is usually close to one order of magnitude of the plenum scale. Sound-absorbing wedges mounted on the plenum walls are unable to effectively eliminate pressure pulsations at this scale. Researchers commonly refer to this phenomenon as \"low-frequency pressure fluctuation\" [7; 17], \"low-frequency pressure oscillation\" [9], \"low-frequency pressure pulsation\" [6; 9; 11; 16; 17; 18], or \"low-frequency pressure surging\" [16; 17]. The literature often employs terms such as \"wind tunnel buffeting\" [9], \"wind tunnel pumping\" [19], \"wind tunnel swaying\" [11], \"vibration of the test hall\" [4], \"wind tunnel is breathing\" [20], or \"wind tunnel is undergoing a canning effect\" [20] to describe the structural characteristics caused by this phenomenon. Many large open-jet wind tunnels suffer from low-frequency fluctuations [4; 9; 16; 21; 22; 23; 24; 25]. The Langley 4 m \(\times\) 7 m wind tunnel developed flow pulsations in the open test section configuration that produced static pressure fluctuations, increasing turbulence, and velocity non-uniformity [16; 21]. Extensive research has been conducted by researchers at this institution to mitigate these low-frequency pressure fluctuations [16; 21]. The low-frequency pressure fluctuations in the large German-Dutch low-speed wind tunnel DNW-LLF with an open test section (8 m \(\times\) 6 m) directly jeopardized the structural safety of the plenum, and therefore its maximum operating wind speed had to be limited to below 80 m/s [4]. The 3.25 m \(\times\) 2.8 m low-speed wind tunnel DNW-NWB in Braunschweig, Germany, experienced strong low-frequency pulsations over a wide range of wind speeds, with sound pressure levels as high as 120 dB [9]. The wind tunnel was equipped with Seiferth-wing spoilers on the jet nozzle to reduce the low-frequency pressure fluctuations, but this only reduced the sound pressure level to 93 dB and generated significant high-frequency noise [9]. Significant low-frequency pressure fluctuations were also observed in the open test section of the Large Acoustic Wind Tunnel (LAWT) in China [22; 23; 24; 25]. The specific performance was as follows: once the wind speed exceeded 40 m/s, the pulsation gradually became  
Figure 1: Schematic of a wind tunnel with an open-jet section. perceptible to the human ear and there was a discernible vibration in the collector and the control building; at 65 m/s, the vibration intensified and a distinct vibration frequency appeared in the whole test hall and the control building; beyond 75 m/s, the vibration basically disappeared. Low-frequency pressure fluctuations are also prevalent in automotive wind tunnels, which usually use 3/4-opening jet wind tunnels (square jets, and one side of the jet is at ground level, while the other three sides are free jet surfaces) [5; 7; 8; 13; 14; 15; 26; 27]. The S2A automotive wind tunnel located in Montigny-le-Bretonne, France, identified four distinct oscillation zones within the wind speed range of 10 m/s to 60 m/s. At a wind speed of 16.7 m/s, the pressure pulsation frequency outside the jet was close to 1.6 Hz, with an amplitude of nearly 100 dB, accompanied by a velocity pulsation of nearly 3% in the core of the jet [8]. The initial operation of the Hyundai Motor Aeroacoustic Wind Tunnel (HAWT) in South Korea revealed significant static pressure fluctuations over most wind speed ranges [7]. The use of vortex generators effectively mitigated pressure pulsations, but inadvertently resulted in an increased background noise level within the test section and an excessive static pressure gradient ahead of the collector, exceeding the design specifications of the wind tunnel.