Study on cavitation performance improvement of high-power centrifugal pump impeller

High power centrifugal pump is frequently used in large project for water resources allocation. Cavitation phenomenon causes noise and vibration and affects the centrifugal pump unit stability. The impeller model was used an initial impeller to be developed, and the impeller geometry, the blade profile, blade inlet edge were optimized by design method based on numerical simulation technique to improve cavitation performances. The 3D model with the initial and optimized impeller were simulated to obtain cavitation characteristic. The results of optimization impeller are compared and verified by model test. The numerical simulation results show that the pressure distribution is distributed on the blade surface is uniform and the location of lowest pressure is reasonable. The test results show that the optimized design significantly increases the ratio of plant cavitation coefficient σp to incipient cavitation coefficient σi and critical cavitation coefficient σ1 of the impeller under normal operation conditions, the safety margin of cavitation is increased. It was confirmed from numerical simulation and model test results that the impeller blade optimization is a reasonable and effective method for cavitation performance improvement. The study results provides design reference for the cavitation performance improvement and safe operation of high power centrifugal pump.


Introduction
A centrifugal pump uses liquid as the working medium to convert mechanical energy into liquid energy, which plays a critical role in long-distance water transfer project and large-scale irrigation and drainage system [1].Cavitation is a common unsteady flow phenomenon, it is well known to occur in a variety of fluid machinery, including pumps, turbines and pump-turbines.Cavitation phenomenon is the main reason for energy loss, head drop and affects the operation safety of high-power pump unit.Vibration and noise caused by cavitation seriously affect the normal operation of the pump unit and shorten the pump operating life.In some pump stations, cavitation erosion brings safety risks to normal operation of the pump unit.Cavitation has become one of the most important indicators to measure the comprehensive performance of high-power hydraulic units.
When the centrifugal pump impeller rotates at a high speed, various unsteady phenomena may appear in the water inside the impeller, rotating stall, divorced flow and backflow [2], which cause the change of velocity and pressure remarkably, when the local pressure of the liquid near the blade reaches or is lower than the vapour pressure, cavitation appears.The flow rate and head of the centrifugal pump changes according to its operating condition, the cavitation bubbles expand rapidly with decreasing pressure until collapse.The generation and collapse of cavitation destroys the continuity of flow, reduces hydraulic efficiency, and seriously impacts the operation safety and stability of the centrifugal pump.
Cavitation performance improvement of centrifugal pump impeller is one of the research highlights in pump field [3][4] [5].The cavitation problem of centrifugal pumps has been studied a lot by many scholars [6] [7].The cavitation erosion in centrifugal pumps is commonly found in the impeller leading edge, which is complicated and random.It is difficult to obtain the distribution characteristics of the flow parameters only through theoretical analysis.CFD numerical simulation is widely used to obtain the cavitation characteristics of large centrifugal pump [8][9][10] [11], analysis the cavitation and hydraulic performance of the centrifugal pump.At the same time, the cavitation performance of the centrifugal pump is verified by model test [12] [13].Because the cavitation performance is closely related to the impeller design, especially the key parameters of blade design, impeller design and optimization is the main method to improve the cavitation and hydraulic performance of centrifugal pump.
Cavitation phenomenon generally appears in the non-design condition of centrifugal pump, such as the low flow rate zone and the large flow rate conditions.The occurrence and collapse of cavitation causes turbulence and strong pressure pulsation in the internal flow field of centrifugal pump.Unit stability requirements are even higher for high power, high head, low specific speed centrifugal pumps.Therefore, the cavitation performance analysis of centrifugal pump can provide a strong basis for hydraulic performance and cavitation characteristics improvement of centrifugal pump.In this paper, the technical measures to improve the cavitation characteristics of centrifugal pump from theoretical explanation, numerical simulation and model test was introduced, which provided technical reference for the engineering application.

3D model
This paper relies on a high-power centrifugal pump project with the specific speed of ns=100 to find the hydraulic design direction to improve the impeller cavitation performance through CFD numerical simulation and model test.In order to simplify the meshing process, the flow domain was divided into 3 main parts, namely, volute and guide vane domain, impeller domain, draft tube domain.The 3D model of centrifugal pump used in this paper is shown in Figure 1.The impeller has 7 blades and guide domain contains 11 guide vanes.

Computational grid
The computational grid of three calculation domains were generated respectively.To improve the calculation speed and accuracy of iterative calculation in the simulation, grid-independent validation is carried to determine number of grids for final calculation.According to the numerical calculation results of centrifugal pump efficiency and head, when the grid elements' number is more than 8.5×10 6 , the head and efficiency of pump tends to be stable.The number of grid elements for volute and guide vanes domain, impeller domain and draft tube domain were 3.5 million, 3.5 million and 1.5 million respectively.The grids for each part are shown in Figure 2. The influence of elements number on the model is shown in Figure 3.

Numerical methods
To obtain the flow characteristics and cavitation performance in the internal flow field of centrifugal pump, this paper adopts steady numerical simulation with SST (Shear Stress Transport) turbulence model.The inlet boundary condition adopts mass flow rate and the outlet boundary uses static pressure of 0 Pa.Simulations were performed using the stage (Mixing-plane) interface transfer model, other solid walls were adopted non-slip wall boundary conditions.To keep the boundary conditions similar to the real conditions, the reference pressure was set as 101.325kPa.The rotational speed of the model impeller was 1000 rpm in CFD simulation.

Cavitation performance improvement measures
The cavitation of pump can be reduced by reasonably determining setting elevation of the unit for small pumps.In the operation of centrifugal pump, the cavitation can also be reduced by selecting of cavitation free operation conditions.But for high-power pumps, the elevation was set before installation, and the pump operation condition was restricted by the pipeline characteristics and pump input power.The cavitation characteristics shall be considered at the pump design stage.Cavitation margin and the cavitation performance of centrifugal pump can be improved by optimizing the blade profile design and reducing the hydraulic loss of fluid around the inlet edge.The inlet diameter, shape of meridional plane, blade airfoil and other parameters are mainly considered in the optimization of impeller cavitation performance.In most centrifugal pump model tests, cavitation firstly appears near the leading edge of the impeller, so cavitation performance mainly depends on the flow condition at the leading edge.The cavitation performance is closely related to the inlet area of the impeller and the relative inlet angle.Based on CFD optimization design method, this paper completed the hydraulic optimization aiming at improving the cavitation characteristics of a high-power centrifugal pump.The cavitation characteristics were optimized to improve cavitation performances, while the energy characteristics kept unchanged.To reduce variables, the draft tube, the guide vanes and the volute were not changed, only the shape of the impeller was modified.
In this paper, based on the pump station requirements, parametric design of pump was developed based on CFD optimization method.The optimized plan A of the pump, at the first stage, was numerically calculated and model-tested.The model test results were shown in Figure 4 and Figure 5.The horizontal axis was the relative flow Q/Qd, Qd means the design flow, while the vertical axis was the relative cavitation coefficient of the pump P/σi and σP/σ1 , σP means plant cavitation coefficient, σi means incipient cavitation coefficient, σ1 means critical cavitation coefficient.It can be seen from Figure 4 and Figure 5 that, in the pump operating zone, the incipient and critical cavitation margin are insufficient at large mass flow rate working conditions.The impeller of Plan B increased the blade wrap angle, reduced the inlet setting angle and outlet setting angle.As shown in Figure 6, the impeller meridional plane of the flow passage remains unchanged, while the inlet diameter of Plan B is reduced.The model impeller 3D shape was shown in Figure 7 and Figure 8.

Numerical simulation of centrifugal pump
Plan A and Plan B model were simulated with same computational method for comparison of cavitation performance.Figure 9 shows the pressure side of blade pressure distribution of Plan A and Plan B at the same mass flow rate of Qd.The pressure distribution on Plan B blade became smoother when compared with Plan A, the pressure distribution near the trailing edge became more uniform.The suction side of blade pressure distribution was shown in Figure 10.It was obvious that after optimization, the minimum pressure distribution is reasonable, the pressure distribution on the inlet section was more uniform, and the pressure gradient on the inlet section was higher.The minimum pressure is moderate and the distribution position is reasonable, which indicates that the impeller has excellent cavitation performance.The CFD estimated pump cavitation performance curve is shown in Figure 11.

Cavitation test analysis of centrifugal pump
According to the CFD numerical calculation results, the cavitation margin was improved in Plan B compared to Plan A. To confirm the reasonable and accuracy of numerical simulation results, model test was carried out on IWHR hydraulic machinery laboratory.Figure 12 shows the centrifugal pump model test bench.

Figure 12.
Centrifugal pump model test bench.The energy performance test results of the centrifugal pump is shown in Figure 13 and Figure 14.In Figure 13, the horizontal axis was the relative flow Q/Qd, while the vertical axis was the relative head of the pump H/Hd and the relative hydraulic efficiency of the pump η/ηopt, Hd means the design head, ηopt means maximum hydraulic efficiency.In Figure 14, the vertical axis was the relative input power of the pump P/Pmax, Pmax means the maximum input power.Model test results show that the centrifugal pump energy characteristics, pump efficiency and hump margin of Plan B are significantly improved compared with the initial impeller Plan A. As a result, the pump input power was reduced.1, and the comparison of primary cavitation performance under normal operating conditions is shown in Figure 15.
Table 1.Incipient cavitation results of the centrifugal pump.According to the results of centrifugal pump cavitation test, the optimized impeller has sufficient safety margin for cavitation under normal operation conditions of the pump station, and the cavitation performance is greatly improved.In the normal operation range of the pumping station, the ratio of cavitation coefficient σp to initial cavitation coefficient σi is greater than 1.1.theratio of the cavitation coefficient σp to the critical cavitation coefficient σ1 is greater than 1.5.The excellent cavitation performance can ensure the safe operation of the pump unit in the state of no-cavitation, and fully achieve the requirements of safe and stable operation.The test results are consistent with the trend of the CFD numerical calculation results, the cavitation performance estimate was consistent with the test results, and the cavitation margin of Plan B was significantly improved.

Conclusions
In this paper, pump cavitation mechanism and the cavitation performance improvement was introduced.The optimization method and results of cavitation on a high-power pump was carefully introduced.Based on the numerical simulation technique.Through the optimization of the inlet edge inlet setting angle and blade airfoil of impeller, the pressure distribution on the blade surface is uniform and the location of lowest pressure is reasonable in the pump operating zone.The numerical simulation result shows that the cavitation margin was obviously improved.The model test was carried out to verify the optimization results.The test results are consistent with the CFD numerical calculation results, the accuracy of numerical simulations is verified.The analysis proved that the cavitation margin can be enlarged by impeller optimization.This research provides a design reference for the stability operation of high-power centrifugal pump unit.

Figure 1 .
Figure 1.3D model for the whole centrifugal pump.

Figure 14 .
Figure 14.Centrifugal pump maximum input power curve.The centerline of the guide vane is used as the reference plane of the cavitation coefficient in the model test.The cavitation test covered the entire operating range of the centrifugal pump.The results of the primary cavitation test of the centrifugal pump model test are shown in Table1, and the comparison of primary cavitation performance under normal operating conditions is shown in Figure15.Table1.Incipient cavitation results of the centrifugal pump.
Centrifugal pump energy performance curve.

Table 2 .
Comparison of test results of incipient cavitation performance curve.The critical cavitation test results of the centrifugal pump model test are shown in Table2, and the comparison of critical cavitation performance of the centrifugal pump under normal operating conditions is shown in Figure16.Critical cavitation results of the centrifugal pump.
Figure 16.Comparison of test results of critical cavitation performance curve.