# Influence of Blade Wrap Angle on the Hydrodynamic Radial Force of Single Blade Centrifugal Pump
## 3 Results and Discussion
### Influence of Blade Wrap Angle on Radial Force  
The blade wrap angle affects the pressure circular distribution in the impeller. As a result, the wrap angle is an important factor that affects the radial force of the single blade centrifugal pump. In this section, the effect of wrap angle on the radial force of the single blade centrifugal pump is investigated based on unsteady simulation. The unsteady simulation is validated by experiment and the simulation results agree well with the tested  
Figure 8: Turbulence dissipation rate of single blade centrifugal pump with different wrap angle. Figure 9: Energy loss of single blade centrifugal pump with different wrap angles. values [22]. In order to calculate the radial force, the impeller was divided as: FS, the front shroud; BS, back shroud; B, blade [28]. The Cartesian coordinates are used to specify the radial force. It is specified that the radial force in the positive X direction and the positive Y direction is positive; the corresponding forces in the negative X direction and the negative Y direction are negative, as shown in Figure 10.  
Figure 11 shows the time domain diagram of the radial force on the impeller of a single blade centrifugal pump with different blade wrap angles under design flow rate. It can be found from the figure, the radial force fluctuates periodically with the rotation of the impeller, and the periodicity is consistent. The radial force on the back shroud is small, and it does not change significantly with the variation of the wrap angle. The amplitude and direction of the x component of the radial force changes with the change of the blade wrap angle. When the blade wrap angle is 300\({}^{\circ}\), 330\({}^{\circ}\) and 360\({}^{\circ}\), the x component of the radial force is negative and the value decreases with the increase of the blade wrap angle. When the blade angle is larger than 390\({}^{\circ}\), the x component of the radial force turns to positive and the value increases with the increase of the wrap angle. When the wrap angle is 360\({}^{\circ}\) and 390\({}^{\circ}\), the y component of the radial force is the largest. When the wrap angle is 300\({}^{\circ}\) the y component of the radial force is the lowest. Figure 10: Coordinate diagram of force. Figure 12 shows the radial force \(F_{\mathrm{F}}\) curve of the impeller with different blade wrap angles when the impeller rotates. The calculation results are adopted the dimensionless coefficient \(C_{\mathrm{F}}\). \[C_{\mathrm{F}}=\frac{2F}{\rho u_{2}\,^{2}D_{2}b_{2}} \tag{1}\]  
where \(C_{\mathrm{F}}\) is the dimensionless coefficient of the force, \(F\) is the radial force, \(\rho\) is the density, \(u_{2}\) is the circumferential velocity of the impeller outlet, \(D_{2}\) is the impeller outer diameter, \(b_{2}\) is the impeller outlet width. Figure 11: Radial force of a single centrifugal impeller with different wrap angles under the designed flow rate condition. Figure 12: Radial forces of the impellers with different blade wrap angles according to the rotation of the impeller. It can be seen from the figure, when the blade wrap angle is less than 360\({}^{\circ}\), the radial force is significantly greater than that of the impeller with other wrap angles. Under low flow conditions, the radial force of the impeller significantly decreases continuously with the increase of the blade wrap angle. Figures 13 and 14 show the vector and pressure contour of the single blade centrifugal pump with different wrap angles. It can be seen from the vector diagram that the flow field is disturbed when the single blade centrifugal pump is working under part-loading conditions, there is a sudden change in the streamline, and there is an obvious low-speed vortex area in the impeller which means flow separation occurred. When the wrap angle of the impeller blade is increased, the flow field inside the pump is improved. From the pressure contour, it can be found that, with the increase of the wrap angle, the pressure distribution in the circular direction becomes relatively uniform.