Exit loss model for plain axial seals in multi-stage centrifugal pumps

Plain axial seals are often used in centrifugal pumps as a means to achieve acceptable sealing against leakage flow without the much higher friction losses that are associated with mechanical seals. Examples of their application are the front seals in shrouded radial and mixed-flow pumps and the inter-stage seals in multi-stage pumps. Knowledge about the relation between leakage flow rate and pressure drop over the seal is vital, not only for estimating the volumetric losses, but also for calculating the axial thrust and shaft power of a pump. Investigations up till now have mainly concentrated on the frictional pressure drop in the seal (e.g. Yamada [1], Weber [2]), and hardly on the expansion losses at the exit of the seal. These exit losses are commonly modelled by a kinetic loss coefficient equal to or close to 1, but recent measurements by Storteig [3] have shown that exit loss coefficients can have values well above 1. This paper presents an analytical method to compute the exit loss coefficient of a plain axial seal. It is derived from energy and momentum balances and assumes power-law profiles for the velocity distribution in the seal. The power-law coefficients are computed using CFD and are found to only depend on the Reynolds numbers based on axial flow, Reax, and Couette flow in circumferential direction, ReW. The resulting exit loss coefficients are shown to range between 1 and 2, depending on the ratio of Reax and ReΩ. Results of the analytical model are compared with measurements and CFD calculations. This new analytical model can help improve the prediction of rotor dynamic stability, efficiency and axial thrust of turbomachinery without the need for dedicated CFD calculations in these tight clearances

Part load instability and rotating stall in a multistage low specific speed pump

A new diffuser design is developed for a low specific speed, multistage pump. In this design the diffuser and the de-swirl vanes are integrated into single vanes. This creates diffuser channels that extend from behind the impeller exit through the cross-over, up to the eye of the next stage impeller. Experiments show the occurrence of a saddle type instability in the head curve. At a critical flow rate of close to 50% of the flow rate at Best Efficiency Point (BEP), the head drops by 7% of the head at BEP. In this study Computational Fluid Dynamics (CFD) are used in an effort to understand the underlying flow phenomena. The head curve that is obtained with the transient CFD simulations contains a saddle type instability at a flow rate that is approximately the same as in the experiments, but with a lower magnitude. At flow rates higher than the critical flow rate, the predicted head and power are in very good agreement with the experimental data. At flow rates lower than the critical flow rate, the head and power are slightly over-predicted. An analysis of the pressure distribution in the pump reveals that the head loss at different flow rates in the diffuser shows a discontinuity at the critical flow rate. Since both the impeller head and the head loss in the vaneless gap increase continuously for decreasing flow rate, this is an indication that the cause of the head instability lies in the diffuser. Moreover, a strong increase in the variability of head and power at flow rates below the critical flow suggests that the phenomenon is unsteady. Flow patterns in the impeller and in the diffuser, as calculated by CFD, show a high degree of periodicity and are very similar for flow rates down to the critical flow rate. However, for lower flow rates the flow pattern changes completely. A single rotating stall cell is observed that causes two or three neighboring diffuser channels to stall, leading to a significantly lower flow rate or even a reversed flow. This stall pattern rotates in the direction of impeller rotation at a very low frequency of approximately 3.3% of the impeller rotation frequency

Design of a new type of balance drum to reduce axial loading in centrifugal pumps

In centrifugal pumps, axial thrust bearings are required to compensate for the axial loading on the pump impeller(s). These forces are mainly the result of unequal distributions of pressure on projected areas at both sides of the impeller(s). Axial loading tends to be highest in multistage pumps in which all impellers face the same direction. Balancing devices are often used to reduce the loading of the axial bearings. Common types of balancing devices are the balance drum and the balance disc. Both of them have their advantages and disadvantages. A stepped balance drum is a new concept for a balancing device that can be used in any type of turbomachinery. It combines the benefits of the balance drum and the balance disk without the drawbacks of both. In this paper, the new concept is presented along with a semi-empirical model of its performance. A CFD analysis is also presented which serves to verify the analytical model. An optimization procedure of a stepped balance drum is given using a multistage centrifugal pump as an example

Axial thrust prediction for a multi-stage centrifugal pump

The prediction of axial thrust for centrifugal pumps has been an important topic for many years. This is especially the case for multi-stage pumps with opposed or inline impellers, as the correct selection of balancing device(s) and bearings depends highly on the accuracy of the calculated thrust. Up till now, many investigations regarding axial thrust have focused on fully analytical or (semi-)empirical relations while others have tried to predict the axial thrust using CFD simulations. Full analytical or empirical methods tend to give poor results or need tuning for each specific pump, while the full CFD methods are costly in both setup time and computer resources. This paper presents a hybrid method to calculate the axial thrust of a multi-stage pump with an inline impeller design. The hybrid method combines analytical methods and CFD to reduce the required setup time and computation costs. The CFD calculation of the main flow is used as a boundary condition for the semi-empirical models for the side chambers and the inter-stage seals, such that these tight regions can be excluded from the CFD calculation. To verify and validate the hybrid method, results are compared with measurements and with full CFD calculations that include the side chambers and seals. These results show that the hybrid method and the full CFD method give comparable results, but there is still some difference with the measurements