# Simulation Analysis and Experiment of Piezoelectric Pump with Tapered Cross-Section Vibrator
## 1 Introduction  
Piezoelectric pumps utilize the inverse piezoelectric effect of piezoelectric components to convert electrical energy into mechanical energy and then transfer it to fluid through a specific structure to pump the fluid [1; 2; 3]. Piezoelectric pumps not only have simple control, fast response, and high displacement resolution but also have a linear relationship between displacement response and voltage in a large range [4; 5; 6]. Therefore, piezoelectric pumps can be used in fluid delivery applications that require precise control of flow [7; 8]. For example, they have broad application prospects in the fields of microfluidic delivery and microfluidic circulation such as aerospace, robots, automobiles, medical devices, biological genetic engineering, micro-electromechanical, agricultural drip irrigation, and spraying of agricultural blossom thinning chemicals [9; 10; 11; 12]. At present, piezoelectric pumps are mostly volumetric pumps, which can be divided into two categories according to whether there is a check valve in the pump. One is piezoelectric pumps with check valves and the other does not have check valves. The valved piezoelectric pumps usually have check valves at the inlet and outlet of the pump. This kind of pump has limited applications due to wear of moving parts in the valve and its poor followability. Although the valve-less ones do not have valves and moving parts, they need to have an asymmetric flow path or a certain flow barrier that can form a resistancedifference so as to result in a one-way flow, such as the valve-less piezoelectric pump with a multi-stage \"Y-shaped\" flow tube [13], flat valveless piezoelectric pump [14], and valveless piezoelectric pump with a spiral flow tube [15; 16]. Due to the complex structure of this type of piezoelectric pump and other problems such as low flow rate, however, their operability could be affected in specific applications. Therefore, it is imperative to seek a breakthrough through the working principles of the pump. With the development of science and technology, the performance of piezoelectric pumps has been greatly improved, and the application field has been expanding, mainly in the following areas: (1) the cooling of micro-circuit systems: because of the advantages of the micro-piezoelectric pump, such as easy miniaturization and strong anti-interference ability, the micro-piezoelectric pump shows good application prospects in the integration with micro-circuit. (2) The micro-transport of liquids in the field of aeronautics and astronautics: the miniaturization of the piezoelectric pump plays an important role in promoting the miniaturization of aerospace equipment because of the high precision demand of aeronautics and astronautics consistent with the characteristics of the miniature piezoelectric pump pump. (3) The liquid delivery of bio-medicine field: the miniature piezoelectric pump can realize the accurate delivery of medicament liquid in bio-medicine and make up for the defect of the traditional pump, which is too large and cannot be controlled accurately. (4) The application in the field of agricultural production: there is some need for accurate fluid transportation in agricultural production such as irrigation and chemical thinning flower and so on. In the process of application, there are also some deficiencies: (1) the pumping capacity is poor and cannot withstand back pressure and small flow; (2) the valve-less piezoelectric pump with the fish-tail-like vibrator has better pumping capacity and smaller flow pulsation, but the welded vibrator easily falls off and fatigue fractures; (3) there are few studies on the fluid-solid two-way coupling of the piezoelectric pump flow field, and the driving mechanism is complex. Because the multi-field coupling analysis of a piezoelectric pump involves many subjects (such as electricity, solid mechanics, and fluid mechanics), the fluid-solid two-way coupling analysis of the piezoelectric pump flow field is difficult.