Calculation and verification of balance force of multistage pump balance drum

The axial force balancing capacity of a balance drum is a key factor affecting the life of multi-stage centrifugal pumps. At present, the traditional calculation formula of the balance force of a balance drum is mainly obtained by modifying the relationship between the last-stage impeller head and the total head through empirical coefficient, and the calculation result is less sensitive to the change of the balance drum clearance. However, many studies have shown that the increase of clearance is the main factor affecting the balance force of a balance drum. In addition, the cost of measuring the balance force of a balance drum is relatively high. Therefore, it is particularly necessary to derive the mathematical expression and to propose a simple method for measuring the balance force of a balance drum. According to the resistance equation of clearance fluid and the N-S equation under cylindrical coordinate system, the variation laws of the pressure difference along axial and radial directions in the two sides of the balance drum clearance were derived. And the mathematical formula of the balance force of a balance drum, the balance drum clearance leakage and the balance tube flow was established. The new derived formula calculation results were compared with the traditional formula calculation results and the numerical calculation results. The results show that: at nominal flow rate, the mean value of the pressure difference of a balance drum increases in a parabolic shape along the radial direction. When the clearance increases from 0.1 to 0.35 mm, the relative error of the balance force between the traditional formula calculation and the numerical calculation is 71.1%, 58.5%, 19.6%, 8.1%, −18.6% and −32.31%, while that between the new formula calculation and the numerical calculation is 3.08%, 6.21%, 4.82%, 1.17%, 3.42% and 6.58%, indicating that the new derived formula can accurately calculate the balance force of a balance drum. In addition, according to the new derived formula, the balance force of a balance drum can be measured directly by the flow rate of the balance tube, which provides a theoretical support for dynamic monitoring of the balance force of a balance drum in engineering.