## 1 Introduction  
Liquid launch vehicles usually encounter the pogo phenomenon, recognized by NASA as a threat to spaceflight vehicles and crews as early as the Gemini-Titan II program in the 1960s [1]. Currently, pogo is widely recognized as coupled instability between the vehicle structure and the propulsion system [2]. In typical occurrences, axial periodic vibrations of the entire vehicle have been observed to initiate spontaneously, grow slowly, and then gradually subside in the frequency range of 5 to 120 Hz. Peak vibration amplitudes range from a few tenths of one g to as high as 34 g, with an instability duration of up to 30 s [3]. To mitigate pogo effects, the installation of an accumulator near the pump is crucial and particularly effective [4]. The accumulator, functioning as a soft volumetric spring,contains a volume of gas aimed at shifting hydraulic frequencies to diminish dynamic coupling between the propulsion system and the vehicle's structural vibration modes. The space inside the accumulator is connected to the main propellant pipeline through communication ports, which are some thin-wall holes arranged around the pipe. Typically positioned 1 to 2 feed line diameters upstream of the pump inducer, the accumulator shifts the sensed frequency of the long fluid column segment between the tank and the accumulator by providing compliance [5]. A small maximum accumulator inertance is required to enable the accumulator to promptly react to pogo-induced fluid oscillations and the early stages of pogo pressure pulses. However, it does not adequately absorb energy from the fluid column oscillations in the duct between the accumulator and the pump, and a target design level for resistance is essential for damping the short column oscillations [6]. Stability analyses run for a space shuttle main engine confirmed that the accumulator resistance could be highly effective in eliminating instability [7]. Research indicates that the resistance and inertance of an accumulator primarily depend on the impedance of the communication ports and are kept low over the desired frequency range [6]. However, accurately quantifying the inertance and resistance of communication ports, which are hydraulic parameters, has proven to be challenging, both theoretically and experimentally [8]. Even after the installation of an accumulator, Delta vehicles experienced pogo events due to insufficient resistance in TD-1 flight and due to overestimated resistance in ITOS-E flight, where the accumulator was blocked [9]. Initially, the accumulator is modeled as a side branch, considering the communication port as an orifice. However, [PERSON] found that experimental results demonstrated more flow resistance than predicted by documenting pulse testing to evaluate the flow resistance of a specific accumulator design [10]. [PERSON] reached a similar conclusion, which could be attributed to the classical orifice flow model used for predicting the non-linear flow resistance of the communication ports [11]. Based on the orifice flow model, [PERSON] derived an energy equivalence method to determine the linear flow resistance for pulsating flow through non-linear flow resistance, connecting the communication port's resistance with its structure [2]. [PERSON] further expanded on this model, proving that the resistive nature of the communication port is not solely a function of geometry but also of feedline propellant flow rates and oscillatory flow amplitude in communication ports [2]. However, these two parameters are not considered in the classical orifice flow model, and corrections during the linearization process will not eliminate the limitations of the basic model. [PERSON] established a non-linear communication port flow model considering fluid velocity in the supply pipeline and further derived a quasi-steady assumption-based linear resistance calculation method for communication ports under different oscillatory flow amplitudes [12; 13].