###### Abstract  
This paper investigates the transient flow rate performance of small piezoelectric-hydraulic pumps. In a previous study, a small piezoelectric hydraulic pump was designed and developed to be applicable to the braking systems of small- and medium-sized UAVs (unmanned aerial vehicles). To this end, a thin plate spring check valve was designed in order to effectively discharge the flow in a single direction. The flow rate of the piezoelectric-hydraulic pump is an important criterion for evaluating pump efficiency. Therefore, a study on the parameters affecting such a flow rate is necessary to enhance the efficiency of piezoelectric hydraulic pumps used in brake systems. This study on small piezoelectric-hydraulic pumps is performed to accurately predict the flow rate using a CFD (Computational Fluid Dynamics) tool. In other words, an unsteady CFD method is applied to model the transient flow rate characteristics and the internal flow field of the fluid. The visualization of the internal flow field is evaluated for a better understanding of the flow fields inside the pump. Moreover, this work also illustrates the detailed motion of both the inlet and outlet check valves during the pump operation that fully reflects the phase shift between the check valves and the piston motion, all of which affect the flow rate performance of the pump. An experiment of flow rate characteristics was conducted on a designed piezoelectric-hydraulic pump, which verifies the validity of the CFD results. piezoelectric actuator; check valve; phase shift; CFD; flow field Article  
Performance of a Small Piezoelectric-hydraulic Pump  
10 April 2021 25 May 2021 26 May 2021  
-valve pumps [9; 10; 11], and peristaltic pumps [12; 13; 14] with its benefits of compact structure and volume. Besides, some scholars have approached the problem differently by utilizing piezostack actuators [15; 16] called piezoelectric-hydraulic pumps, or piezostack pumps. For high-power applications, the piezoelectric-hydraulic pumps are more relevant and possess the ability to obtain higher backpressure, especially for the piezoelectric-hydraulic linear actuators compared to the piezo membrane pumps. The design and fabrication of a small piezo-electric hydraulic pump with a PZT actuator applied to UAV brake systems have been proposed to demonstrate superior performances, i.e., low power consumption, high reliability, and precise pressure control in comparison with its conventional counterparts. To satisfy the brake system requirements of small- and medium-sized UAVs, e.g., the delivered flow rate, fast response speed, high pressure, and stability during its operation, a small piezoelectric-hydraulic pump was proposed [17]. Piezoelectric ceramic actuators have the potential to generate greater force and work at high speeds with small deflection compared to other smart materials. It is, therefore, necessary to design a relevant check valve that can release the small flow rate of the piezoelectric-hydraulic pump to ensure a single-direction flow. In this study, a thin-plate spring check valve was proposed to transmit the small flow rate in the output direction, which allows the check valve to open more easily whenever there is a pressure variation on its two sides. Also, the valve has the capability of operating well under the high-speed vibration of the piezo-ceramic actuator. Furthermore, being a passive type, the check valve can lessen the complexity of the system to satisfy the lightweight and miniaturization standards. Despite the delivered flow rate being relatively small [18; 19; 20], the piezoelectric-hydraulic pump can increase the driving frequency to reach the required flow rate. A formula to calculate flow rate performance has been developed [21]. The results obtained from the calculated formula are quite accurate and consistent with the experimental results. However, evaluating the flow velocity as well as the pressure inside the pump during operation is impossible, so a complete simulation of the pump is essential.