# Influence of Blade Wrap Angle on the Hydrodynamic Radial Force of Single Blade Centrifugal Pump
## 1 Introduction  
A single blade centrifugal pump has a good non-clogging performance, which is widely used in the process of wastewater treatment [1]. To improve the ability of the flow channel to pass particles and strip impurities, the impeller is designed with only one blade that has a very large wrap angle. Such a kind of non-axisymmetric structure brings different kinds of problems to the single blade centrifugal pump, such as larger radial force, shock, and vibrations than the traditional centrifugal pumps. With the development of high-speed and high-capacity pumps, the safety and reliability of the centrifugal pump have attracted attention from engineers and researchers [2]. Unstable problems like shock and vibrations are usually caused by the unsteady flow characteristics in the pump, which is extensively investigated till now. [PERSON] and [PERSON] [3; 4] first proposed the radial force empirical formula, which estimates the radial force experienced by the impeller based on the impeller geometric parameters, flow rate and head, but the empirical coefficient has certain limitations. [PERSON] [5; 6; 7; 8] comprehensively and systematically tested the radial force of NASA high-speed liquid oxygen and liquid hydrogen turbo pumps in the United States. The effect of impeller eccentricity, front and rear pump cavity leakage, and vortex frequency on the radial force were analyzed to establish the mathematical model of the radial force. [PERSON] [9] summarized the reasons for the radial force of the pump in his review: the uneven distribution of the circumferential pressure of the impeller, the radial force generated by the labyrinth seal, the dynamic and static interference effect of the impeller guide vane (volute), the steady radial force, thespecific speed of the pump, the type of impeller or guide vane, the geometric parameters of the impeller and the operating conditions are related. [PERSON] [10] compared the effects of single volute, annular volute, and double volute on the radial force of the blood pump using a combination of numerical simulation and experiment. At the designed flow conditions, the radial forces are equivalent in the case of single volute and annular volute, and all have large radial forces, while the double volutes have almost no radial forces. [PERSON] [11] analyzed the influence of different volute structures on the radial force based on numerical simulation. The results showed that when the volute diaphragm was at 270\({}^{\circ}\), the radial force was the smallest in all flow rate conditions. Due to the asymmetric structure of the impeller, the radial force problem of single blade centrifugal pumps is particularly prominent, which makes the pumps less stable and the vibration-induced noise is stronger. [PERSON] [12; 13; 14; 15] has carried out a lot of research on the flow characteristics and hydraulic induced vibration in single-channel centrifugal pumps. [PERSON] [16] measured the transient pressure distribution of an open single-blade centrifugal impeller and obtained the dynamic and static radial forces of the impeller. [PERSON] [17; 18; 19] conducted a lot of research on the radial force of the single blade centrifugal pump by combining numerical simulation and experiment. The radial force on the single blade impeller was measured by installing a force measuring ring at the bearing. The influence of the blade outlet angle and blade outlet width on the radial force was investigated. It was found that to increase the blade outlet width can reduce the averaged value of the radial force at part-loading conditions. The radial force is divided into the inertial term, momentum term, and pressure term. The calculation results are basically consistent with the numerical calculation pressure integral results. Since the single blade centrifugal pump has only one blade, to select reasonable parameters for the impeller during the design process is of great importance. [PERSON] analyzed the influence of blade wrap angle on a single-channel pump performance [20].