# Study of High-Frequency Pulsating Flow Control Valves
## 1 Introduction  
Pulsating flow signals are crucial in the energy sector, especially in optimizing processes like application of aviation fuel and pipeline transport. They are used to detect flow irregularities, such as leaks or blockages, enhancing safety and efficiency. Pulsating flow valves have evolved significantly since their conceptual development in the mid-20 th century, when early ideas focused on improving fluid system efficiency through controlled flow fluctuations. Introduced in the 1960s, these valves became vital in modulating hydraulic and pneumatic systems, initially for vibration damping and energy recovery. By the 1980s and 1990s, pulsating flow valves saw widespread integration into industries such as automotive and aerospace, with advancements in electronic control further enhancing their precision. In the 2000s, specialized designs and materials improved their performance, making them more compact and efficient [1]. Today, pulsating flow valves are critical in modern fluid power systems, enabling improved energy efficiency, better control, and extended equipment lifespan, while also opening avenues for energy recovery and system optimization with the integration of AI and predictive algorithms in the future. In aviation fuel production, these signals help monitor well production and adjust extraction techniques for better yield [2]. Additionally, pulsating flow improves heat transfer in energy systems, making processes more energy-efficient and reducing operational costs [1]. Hydraulic transmission has the advantages of high power-to-weight ratio and good rapidity, and is widely used in aerospace, engineering machinery, ships, and other fields [3; 4]. A flow meter is an important part of an electro-hydraulic servo system; its static and dynamic performance directly affects the working characteristics of the system, so it is important to realize the accurate measurement of dynamic flow [5]. At present, the measurement methods for dynamic flow are mainly a applying step signal (time domain analysis method) and applying a unidirectional sinusoidal signal (frequency domain analysis method) [6]. Among them, the fluid with zero time-averaged velocity is called oscillating flow, and the non-zero time-averaged velocity is called pulsating flow [7], which can be used for dynamic flow measurement. The sinusoidal signal is typically applied using a proportional or servo valve to achieve a controlled flow signal output. In order toensure that the test results are not distorted, the proportional or servo valve is required to have a bandwidth of at least three times the signal of the dynamic flow being measured [8]. Proportional and servo valves are mainly of two types: direct-acting and pilot-operated [9]. The direct-acting type has a higher frequency response, but its output flow rate is small. The pilot-operated type can output a larger flow rate [10], but its frequency response is smaller than that of the direct-acting type. In order to improve the frequency response of the valve, [PERSON] and [PERSON] designed a permanent magnet synchronous motor-driven electro-hydraulic flow valve; compared with the valve with a proportional solenoid, the valve's step response is faster, with no dead zone [11]. [PERSON] and [PERSON] and [PERSON], and [PERSON] proposed new types of driver for high-frequency voice-coil motors, which effectively improved the frequency response and frequency of the spool valve [12; 13]. [PERSON] et al. put forward a kind of claw-pole torque motor, comparing it with the traditional electro-mechanical converter. It exhibited positive stiffness, small mass, and a good linear relationship between the input current and output angular displacement compared with the traditional electro-mechanical converter [14]. In order to improve the reliability, dynamic characteristics, and digitization of the traditional proportional valves, [PERSON] et al. proposed a two-stage digital proportional flow valve in which the pilot stage is two high-speed switching valves.