# Numerical Calculation and Experimental Study of the Axial Force of Aero Fuel Centrifugal Pumps
## 2 Numerical Simulation of Axial Force
### Analysis of Numerical Calculation Results  
Taking the rotational speed of 9000 r/min and fuel flow rate of 54,000 L/h as an example, the steady-state calculating centrifugal blade rotation field is shown in Figure 7. As can be seen from Figure 7, the fuel pressure in the impeller runner increases gradually along the radial direction under the work of the impeller and reaches the maximum static pressure at the volume because part of the kinetic energy is converted into static pressure energy. The flow channel pressure distribution of each blade of the impeller is more uniform and the static pressure is slightly larger near the tongue due to the influence of static and static interference.  
It can be seen from Figure 7 that the fluid velocity distribution has circumferential symmetry. The fluid rotation velocity at the inlet of the centrifugal impeller is low. When it enters the impeller runner, the velocity increases gradually along the direction of the runner outlet and the velocity reaches the maximum near the impeller outlet.  
Keep the inlet pressure unchanged at 0.2 MPa and change the rotational speed of the centrifugal pump. The pressure nephogram of the pump under different rotational speeds is shown in Figure 8. It can be seen from the figure that the fuel pressure increases gradually along the flow direction and reaches its maximum value at the volute. Compared with the centrifugal impeller, the pressurization capacity of the inducer is weaker and the fluid pressure in the inducer gradually increases along the radial direction; the pressurization near the hub is not obvious. The boost value of the centrifugal pump increases with the increase in rotational speed. At the same time, it can be found that the area of the impeller rear pump chamber is larger than the area of the front pump chamber and the pressure of the rear chamber of the following part of the mouth ring is much larger than the inlet pressure of the impeller, which is the main reason for the axial force of the centrifugal blade wheel.  
Figure 8: Y-Z cross-section pressure nephogram centrifugal pump under different speed conditions: (**a**) 2600 r/min; (**b**) 5000 r/min; (**c**) 7000 r/min; and (**d**) 8500 r/min.  
Figure 7: Pressure nephogram and velocity vector of the impeller section: (**a**) pressure nephogram and (**b**) velocity vector.  
Figure 9 shows the pressure nephogram of the front pump chamber of the fuel centrifugal pump. As can be seen from the figure, there is a radial pressure gradient for the liquid in the front and rear pump chambers. The fuel pressure also increases along the direction of the increasing radius. But at the same time, it can be found that the pressure distribution at different circumferential positions with the same radius is different. This is because the volute of the centrifugal pump converts the kinetic energy of the liquid part into static pressure energy, which makes the static pressure in the pump chamber gradually increase along the direction of impeller rotation and the pressure reaches its maximum value near the tongue.  
Select all the force surfaces of the centrifugal impeller and induction wheel and calculate the axial force along the positive direction of the \(Z\) axis. The calculated axial forces on the centrifugal impeller and inducer are shown in Figure 10. It can be seen from the figure that the axial force on the centrifugal impeller and inducer increases with the increase in the centrifugal pump speed and the slope also increases obviously in the process of increasing. The axial force of the centrifugal impeller accounts for the main part of the total axial force.