CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 26, No. 3, 2013

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DOI: 10.3901/CJME.2013.03.469, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn

Effects of Meridional Flow Passage Shape on Hydraulic Performance of Mixed-flow Pump Impellers BING Hao1, *, CAO Shuliang1, TAN Lei2, and ZHU Baoshan1 1 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China 2 State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China Received January 18, 2012; January 7, 2013; accepted February 25, 2013

Abstract: During the process of designing the mixed-flow pump impeller, the meridional flow passage shape directly affects the obtained meridional flow field, which then has an influence on the three-dimensional impeller shape. However, the meridional flow passage shape is too complicated to be described by a simple formula for now. Therefore, reasonable parameter selection for the meridional flow passage is essential to the investigation. In order to explore the effects of the meridional flow passage shape on the impeller design and the hydraulic performance of the mixed-flow pump, the hub and shroud radius ratio (HSRR) of impeller and the outlet diffusion angle (ODA) of outlet zone are selected as the meridional flow passage parameters. 25 mixed-flow pump impellers, with specific speed of 496 under the design condition, are designed with various parameter combinations. Among these impellers, one with HSRR of 1.94 and ODA of 90° is selected to carry out the model test and the obtained experimental results are used to verify accuracies of the head and the hydraulic efficiency predicted by numerical simulation. Based on SIMPLE algorithm and standard k-ε two-equation turbulence model, the three-dimensional steady incompressible Reynolds averaged Navier-Stokes equations are solved and the effects of different parameters on hydraulic performance of mixed-flow pump impellers are analyzed. The analysis results demonstrate that there are optimal values of HSRR and ODA available, so the hydraulic performance and the internal flow of mixed-flow pumps can be improved by selecting appropriate values for the meridional flow passage parameters. The research on these two parameters, HSRR and ODA, has further illustrated influences of the meridional flow passage shape on the hydraulic performance of the mixed-flow pump, and is beneficial to improving the design of the mixed-flow pump impeller. Key words: mixed-flow pump, meridional flow passage, numerical simulation, hydraulic performance

1

Introduction ∗

Mixed-flow pumps, which are widely used in drainage, irrigation, flood control, water treatment and other fields, have various advantages, such as wide application scope, wide high efficiency range and a low probability of cavitation[1]. Compared with centrifugal pumps and axial flow pumps, the development of mixed-flow pump hydraulic model relatively lagged behind[2]. Therefore, in recent years, domestic and foreign scholars have concentrated on the researches of three-dimensional design[3–4], optimization design[5–6], flow analysis[7] and performance prediction[8–10] of mixed-flow pump impellers. KIM, et al[11], optimized mixed-flow pump impellers and diffusers and improved the internal flow in a fixed meridional flow passage shape. BONAIUTI, et al[12], analyzed the effects of the leading edge location, the velocity moment distribution and the meridional flow passage shape on the hydraulic and the cavitation * Corresponding author. E-mail: [email protected] This project is supported by National Natural Science Foundation of China (Grant No. 51176088) © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2013

performances of the mixed-flow pump by inverse design, CFD calculations and experiments. OH, et al[13], predicted the hydraulic and the cavitation performances of the mixed-flow pump based on numerical simulation, and compared the simulation predictions with the experimental results. KIM, et al[14], analyzed the effects of straight vane length radio and diffusion area radio on the hydraulic efficiency of the mixed-flow pump by numerical simulation. Based on the simultaneous solution of direct problem and inverse problem, BING, et al[15], achieved the mutual feedback between meridional flow field calculation results and inverse design results in the impeller design process, which improved the impeller hydraulic efficiency. XIE, et al[16], adopted a multi-parameter optimal method to optimize the blade profile, and their research demonstrated that the vortex and the flow separation at impeller inlet and near the blade surface could be reduced effectively by controlling the blade curvature. In this paper, the hub and shroud radius ratio (HSRR) of impeller and the outlet diffusion angle (ODA) of outlet zone were selected as the meridional flow passage parameters, effects of which on the mixed-flow pump

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BING Hao, et al: Effects of Meridional Flow Passage Shape on Hydraulic Performance of Mixed-flow Pump Impellers

impellers were analyzed by numerical simulation.

2

Meridional Flow Passage Parameters

and the hub and the shroud radius are set as Rh and Rs, respectively (Fig. 3). Thus, HSRR of the mixed-flow pump impeller R can be defined as follows:

Table 1 reveals main parameters of the mixed-flow pump model designed in this paper, with specific speed of 496 under the design flow rate. Table 1.

Main parameters of mixed-flow pump model

Parameter Design volume flow rate Q(m3 • h–1) Head Hm Rotational speed n(r • min–1) Specific speed ns

Value 2 127.6 16.53 1 450 496

The meridional flow passage, significantly influencing the flow capacity, the hydraulic and the cavitation performances of mixed-flow pump impellers, is generally required to have a smooth shape and determined by the hub shape, the shroud shape and the leading and the trailing edge locations. The hub and the shroud shapes in impeller zone are both hemispherical and arcs are employed to create smooth transitions for the inlet and the outlet zones. The meridional flow passage shape of the mixed-flow pump model designed in this paper (Fig. 1) is completed by referring to the superior performance mixed-flow pump model with specific speed of close to 500. The 3D mixed-flow pump model is demonstrated in Fig. 2.

R

Rs . Rh

(1)

After fixing the hub shape, the different shroud shapes can be determined by selecting different R values, which are illustrated in Fig. 3.

Fig. 3. Meridional flow passage shape under different R

The diffusion flow passage is generally employed in the outlet zone of mixed-flow pumps, and the hub streamline is gradually getting closer to the rotation axis along the flow direction. ODA (α) of the mixed-flow pump can be defined as the angle between the shroud streamline and the straight line perpendicular to the impeller rotation axis, which is shown in Fig. 4.

Fig. 1. Meridional flow passage of mixed-flow pump model

Fig. 4. Meridional flow passage shape under different ODA

Due to the impact of HSRR R on the flow capacity of the mixed-flow pump and the impact of α on diffusion characteristics of the mixed-flow pump outlet zone, R and α are selected as the meridional flow passage parameters of the mixed-flow pump. Therefore, the effects of the mixed-flow pump meridional flow passage shape on the impeller design and the hydraulic performance can be studied by changing the parameters R and α. Fig. 2. 3D modeling of mixed-flow pump model

In the process to determine the meridional flow passage, the hemispherical flow passage is used in impeller zone,

3

Model Test and Numerical Simulation

3.1 Model test With R of 1.94 and α of 90°, the structural design (Fig. 5) of the mixed-flow pump is determined according to the

CHINESE JOURNAL OF MECHANICAL ENGINEERING parameter values given in Table 1 and the test apparatus is built to carry out the hydraulic performance test. The hydraulic performance curves of mixed-flow pump model under different blade angles are demonstrated in Fig. 6.

Fig. 5. Structural design diagram of mixed-flow pump model

3.2

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Numerical simulation

3.2.1 Governing equations and algorithm The governing equations of the fluid flow are three-dimensional steady incompressible Reynolds averaged Navier-Stokes equations and employ standard k-ε model for closing. The steady flow governing equations are numerically solved by the widely used SIMPLE algorithm. The convection term is discretized by the first-order upwind scheme, and the other terms are discretized by central difference scheme. The boundary conditions are given as follows. The flow velocity is set to be constant and uniform at the inlet and its value is determined according to the design flow rate and the inlet section area. The free outflow condition is set at the outlet. In addition, the no-slip condition with a logarithmic law for the boundary layers has been imposed over impeller blades, sidewalls, and inlet and outlet pipe walls. Based on the internal flow field of the mixed-flow pump impeller obtained by numerical simulation, the hydraulic efficiency can be calculated with the following formula:

η

ρ gQH 100%, Mω

(4)

where ρ is the density of water, Q is the flow rate, M is the torque of water to the impeller rotation axis, ω is the angular velocity of the impeller rotation, H is the actual head of the mixed-flow pump impeller. 3.2.2 Prediction results Validation Fig. 7 compares the head and the hydraulic efficiency of the mixed-flow pump, obtained by three-dimensional flow field calculation, with the test results. It can be found that the head and the hydraulic efficiency of the mixed-flow pump obtained by numerical simulation have a good agreement with the test results. Thus, the accuracy of the numerical simulation has been verified. Therefore, it can be concluded that three-dimensional flow field calculation results are reliable for analyzing the hydraulic performance of the mixed-flow pump impeller.

Fig. 6.

Hydraulic performance of mixed-flow pump model

In Fig. 6, the flow rate coefficient Φ and the head coefficient Ψ are defined as follows:

Φ

Q , nD 3

(2)

Ψ 

H , n2 D 2

(3)

where D is the diameter of blade rotation axis at the shroud.

Fig. 7. Validation of numerical simulation prediction results

BING Hao, et al: Effects of Meridional Flow Passage Shape on Hydraulic Performance of Mixed-flow Pump Impellers

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4

Results Analysis and Discussion

25 kinds of meridional flow passage schemes are developed with different combinations of five different R values selected from Fig. 3 and five different α values selected from Fig. 4. Thus, 25 mixed-flow pump impellers are designed accordingly and the hydraulic performances with different meridional flow passages are all predicted by numerical simulation. 4.1 Hydraulic performance analysis The blade wrap angles of mixed-flow pumps under different meridional flow passages are revealed in Table 2. For the same HSRR R, the blade wrap angle of the mixed-flow pump is reduced as α increases, but the variation range is quite small. For the same α, the blade wrap angle of the mixed-flow pump increases significantly as HSRR R grows up. The rise of R means enlarged flow area of the mixed-flow pump flow passage, reduced velocity of fluid movement and increased residence time of fluid in the impeller. When the mixed-flow pump rotation speed is constant, the angle of fluid movement in impeller, relative to the impeller rotation axis, increases inevitably. Therefore, the blade wrap angle needs to be enlarged in order to fit the decrease of fluid velocity and satisfy the requirement of the pump impeller on working capability of the fluid. Table 2. Blade wrap angles (°) of mixed-flow pumps under different meridional flow passage parameters

Fig. 8.

Hydraulic efficiency prediction results of impellers

For further analysis of the blade surface pressure distribution, a pressure coefficient is defined as

Cp 

2( p  p0 ) , ρV02

(5)

Outlet diffusion angle α(°)

Parameter

Radius ratio R

efficiency increment decreases continuously with the increase of R. The reason is that, as the blade wrap angle increases, the blade surface area gets enlarged accordingly and then the hydraulic friction loss in the flow passage between blades grows up sharply, which leads to the decrease of the hydraulic efficiency increment. Thus, the further increase of R may lead to reduction of the hydraulic efficiency. Based on the numerical simulation results, selecting R2 is generally considered to be beneficial to obtaining the impeller with superior hydraulic performance.

87.5

90.0

92.5

95.0

100.0

1.75

64.54

64.42

64.37

64.33

64.25

1.84

72.59

72.46

72.38

72.31

72.19

1.94

79.19

79.05

78.95

78.87

78.73

2.03

85.86

85.68

85.56

85.45

85.31

2.12

97.33

97.11

96.87

96.70

96.54

The hydraulic efficiency curves of mixed-flow pumps under different meridional flow passage parameters are demonstrated in Fig. 8. For the same HSRR R, the hydraulic efficiency of the mixed-flow pump increases gradually to reach the peak at the point of 92.5° and then decreases, as ODA α grows up. Thus, it can be found that there is an optimal value of ODA available in the outlet zone. In other words, whether too large or too small ODA value can lead to the increase of internal flow losses, and then affect the hydraulic performance. For the same α, the hydraulic efficiency of the mixed-flow pump increases monotonically as HSRR R increases. The reason is that, as the HSRR R grows up, the flow area of impeller rises, the velocity of fluid decreases and the blade wrap angle increases significantly, which leads to significant improvement of working capability of the mixed-flow pump impeller. However, the hydraulic

where p is the static pressure of any point, p0 is the static pressure of the selected reference point, V0 is the absolute velocity of the selected reference point. The blade surface pressure coefficient distributions at mid-span under different meridional flow passage parameters (R1.94 or α90°) are illustrated in Fig. 9. When R is equal to 1.94, whether too large or too small α value leads to bending deformations of suction surface pressure coefficient curves near the leading edge. Within the range of α (90°–95°), the curves are smooth and the impellers have relatively superior hydraulic performances. When α is equal to 90°, for the different R values, the pressure surface pressure coefficient distributions at mid-span are quite similar to each other, but the suction surface pressure coefficient distributions under different parameters have significant differences. As the value of R increases, the suction surface pressure coefficient curves get increasingly smoother, and the suction surface pressure distributions become more and more uniform, which can contribute to improvement of the hydraulic performance of the impeller. In the meanwhile, the minimum value of suction surface pressure coefficient increases gently, which means that the suction performance at the inlet of the impeller gets improved.

CHINESE JOURNAL OF MECHANICAL ENGINEERING

Fig. 9.

Blade surface pressure coefficient distributions at mid-span

Fig. 10.

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4.2 Internal flow analysis Based on the hydraulic performance analysis of mixed-flow pump impellers, mixed-flow pump impellers with different meridional flow passage parameters are selected and employed to analyze their internal flow fields. The relative velocity distributions on the meridional section of x0, with R of 1.94, are exhibited in Fig. 10. Within the range of α from 87.5° to 95°, the relative velocity distributions are uniform, the streamlines are smooth and the predicted hydraulic efficiencies are all beyond 87% (Fig. 8). This means that a properly designed outlet diffusion flow passage shape can lead to uniform and stable flow in the flow passage. However, as α is raised to 100°, the uniformity of the relative velocity distribution gets reduced in the outlet diffusion flow passage, and the streamlines in the outlet zone have significant bending deformations near the hub, which is marked with a red rectangle in Fig. 10. After processing local amplification and increasing streamline denseness (Fig. 11), a vortex can be obviously found near the hub in the outlet extension zone. This vortex can result in energy dissipation and loss, thus, the hydraulic efficiency of the impeller decreases significantly to less than 86% (Fig. 8). Appropriate selection of α of outlet diffusion flow passage is beneficial to slowing down the fluid and transferring kinetic energy into pressure energy. However, an excessive large α will cause flow separations in the mixed-flow pump and rapid decline of the hydraulic efficiency. Therefore, it is significantly important to select an appropriate value of α for improving the internal flow.

Relative velocity distribution on meridional section x0 (ms)

Fig. 11. Local amplification of relative velocity distribution

The static pressure distributions on section A (Fig. 3) in the impeller zone under different HSRR are displayed in Fig. 12. The static pressure increases gradually from the suction surface to the pressure surface of the blade. As HSRR R increases, the pressure isolines in the flow passage between blades become smoother and smoother, especially significant near the blade suction surface. This means that an appropriate increase in HSRR of the impeller can not only enhance the flow capacity of the impeller, but also improve the internal pressure distribution and the efficiency of the impeller. The total pressure distributions on section B (Fig. 3) of the outlet zone under different HSRR are illustrated in Fig. 13. As HSRR R is raised, the total

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BING Hao, et al: Effects of Meridional Flow Passage Shape on Hydraulic Performance of Mixed-flow Pump Impellers

pressure increases gradually and the uniformity of total pressure distribution on section B is also getting improved at the same time. This demonstrates that an appropriate increase in HSRR of the impeller contributes to a more

5

uniform energy distribution at the outlet of impeller and a significantly enhanced energy conversion capacity of the impeller. Thus, the hydraulic efficiency gets improved under such circumstance.

Fig. 12.

Static pressure distribution in section A when α90° (kPa)

Fig. 13.

Total pressure distribution in section B when α90° (kPa)

Conclusions

(1) As HSRR of the mixed-flow pump impeller R was raised, the blade wrap angle of the mixed-flow pump increased sharply, the working capability of impeller was enhanced and the hydraulic efficiency got improved significantly as well. However, as the blade wrap angle increased, the hydraulic friction loss in the flow passage between blades grew up rapidly, so that the increment of the hydraulic efficiency decreased accordingly. With consideration of both the working capability of the impeller and the hydraulic friction loss, the designed impeller with R of 2 has been approved to have better hydraulic performance. The internal flow field analysis of these mixed flow pumps demonstrates that the static pressure distributions and the total energy distributions can be more uniform with an appropriate selection of HSRR. (2) As ODA of the mixed-flow pump outlet zone α was enlarged, the blade wrap angle of the mixed-flow pump decreased gradually, but the variation range was quite small.

However, the hydraulic efficiency firstly increased to reach the peak at ODA of 92.5°, and then decreased steadily. This means that there is an optimal value of ODA in the outlet zone available, so that whether too large or too small value can result in an increase of internal flow losses, and then affect the hydraulic performances of mixed-flow pumps. From the internal flow field analysis, it can be seen that the flow separation near the hub in the outlet zone can be effectively avoided by selecting an appropriate ODA. References [1] GUAN Xingfan, YANG Jingjiang, YUAN Jianping, et al. Experimental research of high specific speed mixed-flow pump[J]. Pump Technology, 2002(4): 3–8. (in Chinese) [2] PAN Zhongyong, NI Yongyan, YUAN Shouqi, et al. Overview for research on mixed flow pumps with vaned diffuser[J]. Fluid Machinery, 2009, 37(9): 37–41. (in Chinese) [3] GOTO A, NOHMI M, SAKURAI T, et al. Hydrodynamic design system for pumps based on 3-D CAD, CFD, and inverse design method[J]. Journal of Fluids Engineering, Trans. of the ASME, 2002, 124(2): 329–335. [4] GOTO A, ZANGENEH M. Hydrodynamic design of pump diffuser using inverse design method and CFD[J]. Journal of Fluids

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Biographical notes

BING Hao, born in 1984, is currently an assistant professor at State Key Laboratory of Hydroscience and Engineering, Tsinghua University, China. His research interests include fluid machinery optimization design, performance prediction and flow analysis. Tel: +86-10-62773212; E-mail: [email protected] CAO Shuliang, born in 1955, is currently a professor at State Key Laboratory of Hydroscience and Engineering, Tsinghua University, China. His research interest is fluid machinery. TAN Lei, born in 1984, is currently an assistant professor at State Key Laboratory of Tribology, Tsinghua University, China. His research interest is fluid machinery. ZHU Baoshan, born in 1967, is currently an associate professor at State Key Laboratory of Hydroscience and Engineering, Tsinghua University, China. His research interest is fluid machinery.