**Can Luo 1,2,\*, Hao Liu 1, Li Cheng 1,\*, Chuan Wang 1, Weixuan Jiao <sup>1</sup> and Di Zhang <sup>1</sup>**


Received: 20 October 2019; Accepted: 27 November 2019; Published: 3 December 2019

**Abstract:** The unsteady flow process of waterjet pumps is related to the comprehensive performance and phenomenon of rotating stall and cavitation. To analyze the unsteady flow process on the unsteady condition, a computational domain containing nozzle, impeller, outlet guide vane (OGV), and shaft is established. The surface vortex of the blade is unstable at the valley point of the hydraulic unstable zone. The vortex core and morphological characteristics of the vortex will change in a small range with time. The flow of the best efficiency point and the start point of the hydraulic unstable zone on each turbo surface is relatively stable. At the valley point of the hydraulic unstable zone, the flow and pressure fields are unstable, which causes the flow on each turbo surface to change with time. The hydraulic performance parameters are measured by establishing the double cycle test loop of a waterjet propulsion device compared with numerical simulated data. The verification results show that the numerical simulation method is credible. In this paper, the outcome is helpful to comprehend the unsteady flow mechanism in the pump of waterjet propulsion devices, and improve and benefit their design and comprehensive performance.

**Keywords:** waterjet propulsion pump; unsteady flow process; test; computational fluid dynamics

#### **1. Introduction**

Unlike a propeller device, the waterjet propulsion device enables the ship to obtain navigational power by utilizing the reaction force of the water flow ejected by the propulsion pump. The waterjet propulsion device has the advantages of flexible operation, excellent maneuverability, high speed, outstanding anti-cavitation performance, and high efficiency [1]. The propulsion pump is well-protected for being arranged inside. When the ship speed exceeds 25 knots, the total efficiency of the waterjet propulsion device can reach more than 60%. Based on these advantages, the waterjet propulsion device has been widely used in high-speed performance vessels [2,3]. As the core component of the waterjet propulsion device, the performance of the propulsion pump is related to the performance of the entire device, and the nozzle is also an important part. Considering the thrust and layout requirements, the guide vane mixed-flow pump and axial flow pump are generally adopted in current waterjet propulsion vessels. In addition, other types of pump such as screw pump and permanent maglev (shaft less) pump utilized in the waterjet propulsion device are in the experimental research stage [4,5]. The pump employed in the waterjet propulsion device of this research is the guide vane mixed-flow pump. Moreover, pumps are essential for all animals. The heart tube of the embryonic vertebrate has been described as a peristaltic pump before the development of discernable chambers and valves at

these early stages [6]. Then the bioinspired valveless pump is designed related to the pumping process of the heart tube and applied in the fields, such as microfluidics, drug delivery, biomedical devices, and cardiovascular pumping systems, becoming an important topic nowadays [7].

In recent years, simulation methods, such as CFD (Computational Fluid Dynamics) and control system simulation, combined with experiment technology, has been applied in numerous fields such as noise [8], vibration [9–13], turbo machinery [14–20], valve [21,22], jet flow [23,24], heat transfer [25], and hydraulic systems [26]. The researchers not only carried out research on waterjet propulsion devices from both theoretical and experimental aspects, but also conducted research works on waterjet propulsion devices by means of CFD technology. By using CFD technology, Ahn predicted the performance of the designed mixed-flow pump. The results are well agreed with the measured data in the cavitation tunnel test [27]. Wu et al. compared and analyzed the cavitation in the tip clearance of propulsion pump at different revolutions utilizing LDV (Laser Doppler Velocimetry) test technology and high-speed photography technology [28]. Tang analyzed the influence of the guide vane on the performance of the axial flow pump, adopting a numerical simulation and model test. A fixed axial clearance value between the impeller and the vane was concluded. When the value was exceeded, the influence on the performance of impeller was negligible [29]. Duerr analyzed the characteristics of the waterjet propulsion device, applying the non-uniform inflow condition [30]. Verbeek and Bulten focused on the uniformity of the flow field in front of the impeller, and analyzed the effects of boundary laminar flow and turbulence intensity on the uniformity of the flow field [31,32]. Brandner and Walker used pressure probes and visual test methods to conduct quantitative and qualitative experimental studies on the waterjet propulsion flush inlet. It was found that cavitation occurred in the lips in a wide range of operating conditions [33,34]. Park conducted a model test on the influent runner model at the wind tunnel laboratory [35,36]. Gong et al. simulated the flow in the entire waterjet propulsion device with unsteady methods and obtained the changes of the free surface in the waterjet propulsion device at different times [37]. Cao et al. compared the effects of uniform inflow and non-uniform inflow on the performance of the waterjet propulsion pump [38]. Zhang et al. analyzed the effect of cavitation on the thrust performance of the nozzle with CFD technology [39]. Cheng and Xia et al. studied the rotation stall existing in the propulsion pump and proposed corresponding suppression measures [40,41]. Recently, works have mainly focused on the property of the waterjet propulsion device, but research on the unsteady flow process between the nozzle and the propulsion pump has not been seen yet. In this study, the hydraulic performance and unsteady flow process of the propulsion pump with nozzle will be analyzed by using CFD technology, and the numerical simulation results are verified compared with the experiment result on the model test.

#### **2. Numerical Simulation Method**

#### *2.1. Geometry Model*

A computational domain geometric model including the nozzle is established to obtain stable flow field data of the mixed-flow waterjet propulsion device. Along the flow direction, subdomains are the prolonged inlet section, the inlet transition section, the impeller, the guide vane (GV), the nozzle, and the prolonged outlet section, as shown in Figure 1.

**Figure 1.** Computational domain of mixed waterjet pump.
