Abstract:The current paper studies the influence of annular seal flow on the transient response of centrifugal pump rotors during the start-up period. A single rotor system and three states of annular seal flow were modeled. These models were solved using numerical integration and finite difference methods. A fluid-structure interaction method was developed. In each time step one of the three annular seal models was chosen to simulate the annular seal flow according to the state of rotor systems. The objective was to o… Show more
“…The outlet boundary condition is set as free outflow, the flow is considered to be absolutely developed, the fixed wall boundary condition is selected as no slip wall. [37][38][39][40][41][42][43]…”
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.
“…The outlet boundary condition is set as free outflow, the flow is considered to be absolutely developed, the fixed wall boundary condition is selected as no slip wall. [37][38][39][40][41][42][43]…”
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.
“…Jiang analyzed the fluid-structure interaction of annular seals with transient turbulent methods. However, the effect of groove on the seal performance was ignored [4,12]. These scholars did not analyze the specific compliant structures.…”
Compliant foil gas seal is a non-contact and high-efficiency sealing technology. The dynamic performance of compliant foil gas seal with different structure parameters was analyzed in this paper. These parameters include the seal diameter, gas film thickness and the ratio of groove. Compared with the rigid film, the advantage of compliant film is analyzed. The stability performance and dynamic performance with the different structures are obtained. The results show that the larger diameter is a disadvantage for the stability performance. However, the increase of seal length can decrease the leakage. Otherwise, the increase of gas thickness improves the dynamic characteristics with the leakage rising and gas force dramatically decreasing. While the groove length ratio is around 0.6, the seal performance and dynamic characteristics are best. The compliant structure benefits the improvement of the sealing performance.
“…2 During the past few decades, there have been several studies on the transient characteristics of turbo-machine systems. 3 Tanaka and Tsukamoto 4 explored the transient phenomena at pump startup/shutdown processes of a centrifugal pump. A Dazin et al 5 used angular momentum equations and energy equations to predict the torque, power, and head of the impeller under transient operating conditions.…”
Axial-flow pumps with siphon outlet are widely used in South-to-North Water Transfer Project of China for the excellent characteristics and good performance in stopping period. The reverse rotational speed and the head of impeller are the key parameters for the system's safety in stoppage. In this article, the computational fluid dynamics method was used for three-dimensional unsteady numerical simulations. The method based on volume of fluid model was executed on geometrical model of the whole flow system to get the variation laws of internal and external characteristic parameters. Through numerical calculation, the variation laws of the parameters were got in the pump operating condition, braking condition, and turbine condition, and the maximum reverse speed of the impeller was 203.0 r/min (20.947 times the rated speed). Compared with the designed mode, when the air valve was opened in advance, the pump system would go through the weir flow state first, and a higher head of impeller would be got as a result. When the air valve refused to open, the pump system would get into runaway state. Comparisons of the calculated and measured results indicate the proposed computational fluid dynamics method is reliable in the simulation of the transient flow in axial-flow pump system.
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