## 1 Introduction  
Synchrotron radiation sources are large-scale scientific facilities used to explore microscopic substances widely applied in fields such as chemistry, physics, life sciences, materials science, energy, and environmental science. The synchrotron radiation light source has undergone three iterations of upgrades, and the developmental trend in synchrotron radiation light sources is to provide X-rays with nanoscale spatial resolution. With a significant increase in brightness, a liquid nitrogen cooling system has been adopted to maintain the surface accuracy of DCM (double crystal monochromator) crystals. However, introducing the liquid nitrogen cooling system has induced vibration for the DCM, leading to substantial deterioration in the quality of the emitted light. [PERSON] et al. [1], in their experiments at the PETRA III beamline in Germany, conducted vibration spectrum analysis and identified two sources of vibrations based on a frequency boundary at 150 Hz. They attributed high-frequency vibrations to the Bragg angle feedback control system and low-frequency vibrations to the liquid nitrogen cooling system. However,their analysis did not delve into the specific excitation mechanisms of each component within the liquid nitrogen cooling system, which comprises a pump unit, external transport pipelines, and the cooling circuit. [PERSON] et al. [2; 3], on the BL41 XU beamline in Japan, performed vibration analysis on a needle-pillar cooling structure DCM. They observed vibrations caused by the cooling water machine at frequencies below 5 Hz, pipeline vibrations within the vacuum chamber at 179 Hz, vibrations from the vacuum pump at 207 Hz, and an unidentified vibration at 117 Hz. [PERSON] et al. [4] conducted micro-vibration tests on a DCM at the Bio MAX beamline in Sweden. Their results indicated that operating the DCM under high-pressure and low-flow conditions effectively reduced vibrations, especially at a 9\({}^{\circ}\) Bragg angle. [PERSON] and [PERSON] found a direct correlation between the DCM's stability and the operational mode of the cooling system. However, their research lacked an examination of the coolant flow state. [PERSON] et al. [5] observed significant interference from the coolant circulation system on the DCM. After maintenance of the cooling system, the amplitude of bimorph crystal vibration decreased to 25% of the original system. [PERSON]'s research highlighted that enhancing the DCM's structural stiffness could mitigate the cooling system's negative impact. He emphasized that structural optimization could reduce the vibration effects induced by the cooling system, but did not investigate changes in fluid dynamics before and after optimization. [PERSON] et al. [6] discovered that increasing the liquid nitrogen flow rate from 2.4 L/min to 3.2 L/min to enhance cooling power resulted in a relatively minor increase (only 12%) in the root mean square amplitude of the DCM vibration. Until now, researchers have not conducted in-depth investigations into the specific mechanisms of flow-induced vibrations in the cooling system of a DCM or publicly disclosed relevant findings. This is primarily due to the experimental challenges posed by the method of measuring the crystal angular displacement of the DCM, and subsequently conducting vibration analysis on the synchrotron radiation beamline. It becomes difficult to accurately analyze the specific impacts of various vibration sources within the cooling system. The cooling system of the DCM is complex and consists of various types of pipelines, such as U-shaped, L-shaped, arc-shaped, and straight pipes. These pipes are connected in both series and parallel configurations, making it quite challenging to observe the internal fluid motion of the cooling circuit. When the crystal of the DCM absorbs heat cooled by liquid nitrogen, boiling phenomena occur in the coolant. Boiling inside the pipelines leads to the formation of a two-phase gas-liquid flow, consequently inducing structural vibrations.