## 1 Introduction
The second employs dynamic CFD simulations with deforming mesh technology, providing a high-fidelity resolution of valve response and transient fluid-structure interactions. Comparing results from both approaches validates the use of reduced-order models for stability predictions. The scientific work [14] focused on the design and modeling of a buffer relief valve using ANSYS 2021 R1 software, in order to achieve an optimized design for this valve. The findings revealed a high level of agreement between the results obtained from ANSYS simulations and the actual experimental results, affirming that the valve is suitable and safe for operation at a pressure rating of 0.14 MpPa. [PERSON] et al. (2014) [15] conducted a study that both summarized and expanded upon recent scientific investigations into the causes of instability in pressure relief valves. The primary objective was to obtain a deeper and more comprehensive understanding of the factors influencing the stability of pressure relief valves during their operation. The authors specifically focused on direct spring-loaded pressure relief valves used in gas applications, with a particular emphasis on how valve dynamics interact with acoustic pressure waves in the inlet pipe, considering their combined effect on valve stability. The paper [16] offers a comprehensive analysis of experimental findings concerning the static and dynamic behavior of a hydraulic pressure relief valve, specifically focusing on the factors that influence valve instability. The study reveals that both signals exhibit similar frequency content, and the frequency of chatter remains relatively constant over various parameter ranges, such as fluid velocity and set pressure. The paper also delineates different motion patterns, including stable operation, free motion, impacting oscillations, and chaotic behavior, as they relate to the interplay between fluid velocity and set pressure. A model that captures the dynamic response of a pressure relief valve in gas or vapor service is introduced by [PERSON] [17], taking into account a range of influencing factors. The model allows the prediction of the valve disk's position over time, considering specific valve characteristics, operational conditions, and installation parameters. The model also incorporates the impact of these various parameters on the stability or instability of the valve disk's response. Part II of the investigation program [18] presents an experimental testing program designed to investigate the opening stability of direct-acting pressure relief valves used in gas/vapor service, testing three different valve sizes from three manufacturers at two set pressures to assess their opening characteristics, specifically the relationship between disk lift and time. The tests varied the length of inlet piping and considered the presence or absence of discharge piping to identify conditions leading to unstable valve operation. Part III [19] includes a comparative analysis between the model's predictions and the actual dynamic response data and also examines the details necessary for putting the model into practical use. The article [10] aims to expand the understanding of self-excited oscillations in pressure relief valves through a combination of time history analysis, spectrogram post-processing, and experimental testing under various conditions. The study reveals the presence of low-frequency and high-frequency self-excited oscillations, identifying their potential causes, which include external vibrations and acoustic resonance in the vessel-pipe system, shedding light on the factors contributing to valve damage. The scientific paper [20] gives important details regarding the utilization of Computational Fluid Dynamics (CFD) simulation techniques to analyze hydrodynamic phenomena within pipes, exploring various aspects related to the hydraulic efficiency of the pipe system. On the other hand, external mechanical vibrations can disrupt the stability of valves when applied to their bodies.