TAN Minggao, YUAN Shouqi, LIU Houlin, WANG Yong, and WANG Kai

Technology and Research Center of Fluid Machinery Engineering, Jiangsu University, Zhenjiang 212013, China

1 Introduction

Pump performance is decided by inner flow characteristics and inner flow analysis is undoubtedly the best method to improve performance of pump. Therefore,in order to predict performance of pumps exactly on theory,flow field in pump must be obtained correctly[1]. Over the past few years, with the rapid development of the computer technology and computational fluid dynamics(CFD),numerical simulation, like academic analysis and experimental research, has become an important tool to study flow field in pumps and predict pump performance home and abroad. An unsteady simulation of a low specific speed centrifugal pump was done by JOSé, et al[2–3]based on FLUENT to predict the dynamic characteristic between impeller and volute and the pump performance, and the research was validated by the experiment data. Using commercial code FINE/Turbo, BYSKOV, et al[4], did a large eddy simulation of a centrifugal pump at design flow rate and off design flow rates to predict the pump characteristics, and the predicted results agreed well with the data measured by particle image velocimetry(PIV) and laser Doppler velocimetry(LDV)[5]. In China, to forecast performance, ZHAO, et al[6], did a coupled impeller-volute simulation of flow in a centrifugal pump using moving reference frame and FUENT, and CHEN, et al[7], simulated the unsteady flow in a single channel pump, both results above were consistent with pump test data.

The previously mentioned achievements on performance prediction of centrifugal pumps by numerical simulation methods are quite encouraging and these methods are becoming more widely used in hydraulic design of pumps.However, most of the researches were only concerned with one pump and there was no characteristic prediction model in the former study. The more key problems are how to dispose the gap between impeller and volute and how to consider the effect of grid number. So the former research results are not representational and universal. The objective of this paper is to evaluate the precision of numerical prediction method in detail. Hence, six typical centrifugal pumps were chosen as research models and FLUENT was used to do the pumps simulation at the conditions of design,small and large flow rate. The standard k-ε turbulence model and SIMPLEC algorithm were chosen in FLUENT.The simulation was steady and moving reference frame was used to consider rotor-stator interaction. Head and efficiency curves of the models were obtained according to the simulation, and were compared with the experiment data. Also, the flow field was analyzed.

2 Research Models and Prediction Algorithm

Specific speed of the models varies from 34 to 260 and experiment and geometry parameters at design flow rate are shown in Table. The 3D models of impeller, volute and suction were produced by professional software Pro/E and the gap between impeller and volute was appended to impeller (as shown in Fig. 1). The impeller inlet and volute outlet were extended properly to reduce the effect of boundary conditions on inner flow. GAMBIT, the preprocessor of FLUENT, was used to generate grid ofmodels and grid quality was checked. Since the geometry of the pump is very complex, tetrahedron mesh was used for the generation and “EquiAngle Skew” and “EquiSize Skew” of the grid were all less than 0.87, so the grid quality was good. Relativity examination of grid number was done for each model. When the effect of grid number on pump characteristics was less than 2%, the effect is ignored.Convergence precision of residuals was 10–5.

Table. Experiment and geometry parameters of research models

Fig. 1. Computational zones of pump No. 4

2.1 Experiments of research model

All the model pumps were tested in Jiangsu University.The experiments were conducted in an open loop, which consists of a reservoir open to air, a suction valve, a test pump, a discharge pipe and a discharge valve. Each model pump has a single axial suction and a volute casing. In the circuit, water was pumped from and returned to a huge reservoir. The flow rate was regulated by the discharge valve and was measured by electromagnetic flow meter.The rotation speed was detected by plus signals.

Flow rate uncertainties are found to be always less than 0.5%. The head and efficiency uncertainties are kept under 1% and 1.5%, respectively. The experiment data are shown in Table.

2.2 Boundary conditions

Inlet boundary condition: assume that inlet velocity vinis uniform at axis direction and its value equals to ratio of flow rate and inlet area:

where q is the flow rate, Dinis the pump inlet diameter.

Turbulent kinetic energy kinand turbulent dissipation rate εinat inlet can be estimated by the following formula:

where l is the turbulent length scale and l=0.07Din,Cμ=0.09.

Outlet boundary condition: “outflow” is implemented on pump outlet and flow rate weighting is set to be 1.

Wall boundary condition: no slip condition is enforced on wall surface and standard wall function is applied to adjacent region.

2.3 Prediction algorithm

Head H is calculated by the following formula:

where poutis the total pressure at volute outlet, pinis the total pressure at impeller inlet, ρ is the density of liquid, g is the gravity acceleration.

Hydraulic efficiency ηhis calculated as

where M is the impeller torque, ω is the angle velocity.

Volume efficiency ηvis calculated as[8]

Total efficiency η is calculated as

where Peis the water power and Pe=ρgqH, ?Pdis the disk friction loss and its calculation method is in Ref. [9].

3 Prediction Results and Analysis

Fig. 2 shows prediction and experiment performance curves, including flow rate–head curve and flow rate–efficiency curve. According to the data in Fig. 2,prediction discrepancy can be computed as follows:

where ?H is the head discrepancy, ?η is the efficiency discrepancy, Hpis the prediction head, Heis experiment head, ηpis prediction total efficiency, ηeis the experiment total efficiency.

Discrepancy calculation results: for all flow rate points of every model, maximum discrepancy of prediction head is 4.81%, minimum discrepancy is 0.24%, average discrepancy is 2.49% and maximum discrepancy of prediction total efficiency is 4.52%, minimum discrepancy is 0.08%, average discrepancy is 2.02%. At design flow rate, maximum discrepancy of prediction head is 4.81%,minimum discrepancy is 0.65% and average discrepancy is 2.02% and maximum discrepancy of prediction total efficiency is 4.42%, minimum discrepancy is 0.54%,average discrepancy is 2.4%. The calculation indicates that all discrepancies are within 5%.

More information can be obtained from discrepancy computation. Prediction head and prediction efficiency do not show same trends, which means that the former is bigger than experiment data while the latter may be smaller,and so are prediction head discrepancy and prediction efficiency discrepancy. The analysis still shows that precision of performance prediction at design flow rate is not the highest.

4 Analysis of Inner Flow Field at Different Flow Points

4.1 Static pressure distribution

As shown in Fig. 3, at different flow rates, static pressure gradually increases from impeller inlet to outlet, and the static pressure on pressure side is evidently larger than that on suction side at the same impeller radius. According to the density of isobar, it is found that the static pressure increases slowly with the augment of flow rate. At small flow rate, there is an obvious low pressure area at the suction side of blade inlet, especially in flow passages 1, 2 and 3, where cavitations are easy to take place. When the flow increases, the area gets close to the middle of blade suction side, also especially in flow passages 1, 2 and 3.The static pressure on diffusion section of volute outlet increases markedly at small and design flow rates while the static pressure on the same place decreases clearly at big flow rate because of cut-water limitation. As a result of larger offset to design flow rate, the static pressure distribution in the impeller and volute becomes apparently disordered and uniform, particularly near the tongue of volute.

4.2 Relative velocity distribution

As shown in Fig. 4, relative velocity distribution in different flow passages is evidently dissimilar at any flow rate, which indicates that the volute has an important effect on inner flow in the impeller. For different flow rates, the relative velocity distribution in the impeller is obviously different, especially in flow passages 1, 2 and 3. At small flow rate, on blade pressure side, there is a big “dead water” zone where relative velocity is lesser. As the pump flow rate increases, the zone gets smaller gradually,especially in flow passage 2. Meanwhile, from the inlet amplificatory distribution, it is found that the direction of velocity at blade inlet changes obviously at off-design flow rates, which leads to a big impact on the blade. The incident angle at big flow rate is negative and positive at small flow rate, which agrees well with theory analysis[8].

5 Conclusions

With commercial code FLUENT, the coupled simulation of six centrifugal pumps is presented in detail in this paper at different flow rates and characteristic prediction model for centrifugal pumps is established. How to dispose the gap between the impeller and volute is presented and the effect of grid number is considered. The main research conclusions are as below.

(1) The discrepancies of prediction head and prediction total efficiency are less than 5%. For all flow rate points of every model, average discrepancy of head is 2.49% and average discrepancy of prediction total efficiency is 2.02%.Prediction head and prediction efficiency do not show the same trends and precision of performance prediction at design flow rate is not the highest.

(2) There is an obvious low pressure area at the suction side of blade inlet at small flow rate, as the flow increases,the area gets close to the middle of blade suction side. The static pressure on diffusion section of volute outlet increases markedly at small and design flow rate while the static pressure on the same place decreases clearly at big flow rate. As the pump flow rate increases, the “dead water” zone gets smaller gradually. The direction of velocity at blade inlet changes obviously at off-design flow rates. The incident angle at big flow rate is negative and it is positive at small flow rate.

(3) The present study has demonstrated that the proposed numerical method in this paper produces a good prediction of the centrifugal pump performance and can be applied in practice.

Fig. 2. Prediction results of the models

Fig. 3. Static pressure distribution on middle face of pump No. 3 (kPa)

Fig. 4. Relative velocity distribution on impeller middle face of pump No. 3 and its amplificatory distribution at inlet (m/s)

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