Turbulent Flow Characteristics in an Axial-flow Pump at Direct and Reverse Modes

Transcription

1 Journal of Applied Science and Engineering, Vol. 19, No. 4, pp (2016) DOI: /jase Turbulent Flow Characteristics in an Axial-flow Pump at Direct and Reverse Modes Can Kang 1 *, Ning Mao 1, Chen Pan 1 and Ya Zhou 2 1 School of Energy and Power Engineering, Jiangsu University, Zhenjiang , P.R. China 2 Faculty of Process and Systems Engineering, Otto-Von-Guericke-University Magdeburg, Magdeburg, Germany Abstract A reversible axial-flow pump equipped with S-shaped blades is investigated. Numerical simulation is employed as the major instrument to virtually visualize complex turbulent flows in the pump at direct and reverse operation modes. Cavitation is taken into account as well. Pressure fluctuations near the inlet and outlet of the impeller are obtained with unsteady simulation. At nominal flow rate, a relative difference of pump head of 15% is manifested between direct and reverse operation modes. At direct mode merely, cavitation zones are aggregated near the leading edge of the blade and assume a small volume fraction. The contribution of pump shaft is remarkable in terms of affecting pressure fluctuation characteristics upstream of the impeller. Characteristic frequencies immediately downstream of the impeller are analogous for the two operation modes and pressure fluctuation magnitudes are large relative to their counterparts upstream of the impeller. Key Words: Reversible Pump, S Blade, Pump Head, Flow Structure, Cavitation, Pressure Fluctuation 1. Introduction Since its debut, the reversible impeller pump has proved its suitability in many industrial applications. The most distinct advantage of the reversible impeller pump is that fluid transportations in two opposite directions are realized by one single pump instead of two pumps. With the switch of the operation direction of the electric motor, the pump impeller will rotate in desired direction. For hydraulic machinery, the idea of reversible delivery is known in the pump-turbine [1,2]. Even the centrifugal pump has been used reversely as a turbine [3]. For the purpose of delivering fluid solely, the miniature pump has adopted the bi-directional configuration [4]. However, the literature about the reversible pump has been scarcely found [5]. *Corresponding author. kangcan@mail.ujs.edu.cn The performance of the reversible impeller pump depends essentially on flows in the pump. In practice, numerous efforts have been devoted to the exploration of inner flow characteristics of the reversible impeller pump. However, generalizable conclusions have rarely been reported hitherto. On one hand, current flow measurement techniques are deficient in the presence of the flows shielded by the curved duct. On the other hand, the most critical pump component, the impeller blades are highly curved, even if the flow parameters can be measured, the association between flow structures and blade geometry is difficult to establish. The rapid development of computational fluid dynamics (CFD) technique enables a detailed description of complex turbulent flows in the pump. For flows confined in highly curved blade passages, diverse flow structures can be accurately shaped with CFD technique. In the present study, a reversible axial-flow pump is

2 448 Can Kang et al. numerically investigated. The highlight of this pump lies in the difference between its direct and reverse modes. In this context, the emphasis of present study is placed on the relationship between flow characteristics and pump performance. Averaged flow parameters are used to represent pump performance. And cavitation is examined in terms of cavitation zone position and cavitation severity. As a further step, unsteady simulation is carried out in order to seek pressure fluctuation features upstream and downstream of the impeller. It is anticipated to provide an in-depth insight into the flow factors underlying the performance of the reversible impeller pump and the influence of solid boundary on flow characteristics. The configuration of the pump is illustrated in Figure 1(a), where direct and reverse operation modes are denoted respectively. Figure 1(b) displays the impeller model manufactured using the 3D printing technique. 3. Numerical Scheme 3.1 Governing Equations In consideration of the attainable velocity magnitude, the medium delivered by the pump is assumed to be incompressible. Therefore, flows in the pump abide by the fundamental flow governing equations, which are expressed as: 2. Geometrical Model (1) For both direct and reverse modes, the pump studied is designed with the nominal flow rate of 650 m 3 /h, pump head 6.0 m and impeller rotational speed 1750 rpm. An axial-flow impeller with five blades is designed and the blades are featured by S-shaped cross-sections. A large hub-to-tip ratio of 0.5 is adopted. The employment of this blade geometry is to balance the work capability of the impeller at direct and reverse operation modes. In [6], the optimization of the geometrical parameters of the cascade composed of S-shaped blades was provided. Similarly, a design study considering simultaneously multiple influential geometrical parameters was presented in [7]. With the fulfillment of both direct and reverse operation requirements, the chord length of the crosssectional foil is intentionally enlarged relative to the common one-way impeller design and the blade angle is associated with a large value. The pump is installed between two coaxial horizontal pipe with the same inner diameter of 250 mm. Both the configuration and the parameter setup are in agreement with practical applications. There is no guide vane upstream and downstream of the impeller, as reduces both the pump weight and dimensions. Certainly, the contribution of the guide vane to energy transformation cannot be neglected [8]. In addition, the match between the impeller and the guide vane is another issue that influences pump performance [9,10]. (2) Figure 1. Schematic view of the reversible axial-flow pump and the impeller manufactured with the 3D printing technique.

3 Turbulent Flow Characteristics in an Axial-flow Pump at Direct and Reverse Modes 449 u i is the velocity in the coordinate direction x i and p is the static pressure. t is the time and and are the density and dynamic viscosity of the medium. S is the source term related to body force. 3.2 Turbulence Model The renormalization group (RNG) k- turbulence model is employed here. This model was first developed by Yakhot and Orszag and later reformulated by Yakhot and Smith [11,12]. Relative to other turbulence models, this model proves to be desirable in the presence of highly curved blade surfaces. In particular, the solution of turbulent kinetic energy as well as turbulent kinetic energy dissipation rate facilitates the identification of local flow structures and the elucidation of the energy consumption due to turbulent fluctuations. The transport equations for turbulent kinetic energy k and turbulent kinetic energy dissipation rate are: (3) model inter-phase transfer. This model is remarkably feasible in assessing the cavitation rate. Taking bubble generation and collapse into account, this model reflects the most fundamental mechanism of cavitation inception and evolution. Volume content of the initial volume fraction of cavitation nuclei was set to and the nucleus diameter is set to 10-3 mm. The growth of a gas bubble in a liquid is given by: (6) where R denotes the bubble radius, is the surface tension coefficient, l is the liquid density and p v is the vapor pressure. The above nonlinear ordinary differential equation is difficult to solve within an Eulerian-Eulerian framework for multiphase flows, therefore a first order approximation is used where: (7) (4) Therefore, the vapor source term S v is given by where eff is the effective dynamic viscosity equal to the sum of the molecular and turbulent viscosities. The model coefficients: C 1 =1.42andC * 2 is given by: (5) (8) The number of bubbles per unit volume of the mixture, N,isgivenby: where C 2 =1.68, 0 =4.38, = 0.012, =Sk/, S is the skewness factor of turbulent velocity fluctuations. The term G denotes the generation of turbulent kinetic energy with mean velocity gradients. The RNG k- turbulence model furnishes an option of depicting swirl effects through modifying the turbulent viscosity. Therefore, the RNG k- model can well accommodate sharp strain and large streamline curvature. (9) where d is the volume fraction of non-condensable gas and v is the volume fraction of vapor. It is assumed that the bubble growth is not sensitive to thermal effects. 3.3 Cavitation Model The Rayleigh-Plesset cavitation model is adopted to 3.4 Boundary Conditions The commercial code ANSYS CFX served as the

4 450 Can Kang et al. numerical solver in current simulation [13]. Non-slip boundary condition was set at the solid walls wetted by the medium. The surface roughness of all solid walls was set as 0.02 mm. Near-wall zones were treated with scalable wall functions. For the direct mode, a constant static pressure of 0.1 MPa was maintained at the inlet of the pump, and at the outlet of the computational domain, the flow rate was set according to its relationship with area-averaged velocity. Similar boundary conditions were adopted for the reverse mode and the outlet at the direct mode acted as the inlet for the reverse mode. Since that the pump and the linked ducts were installed horizontally, gravity was not taken into account. The entire computational domain was divided into five subdomains which were discretized individually. The tip clearance between the impeller rim and the pump casing was not considered [14]. For the interfaces between adjacent subdomains, the fidelity of data communication was ensured through adjusting the grid density near the interface. The relative angular speed of the impeller was set for the impeller subdomain. After grid independence examination, totally 4,138,606 meshes were devoted to the discretization of the whole computational zone. The equiangle skewness is and the y+ ranges from 27 to 50. The grid quality is favorable. The computational domain discretized by the employed grids is shown in Figure 2. from not only industrial but also academic aspects. Here, pump head is calculated from area-averaged total pressures at the inlet and outlet of the whole domain. The head is the energy increment through the pump unit rather than the impeller merely. For comparison, the pump was tested in the test rig displayed in Figure 3. The experimental loop was specifically designed for impeller pump performance test and data of inlet and outlet pressure, flow rate, rotational speed, liquid level in the tank were automatically acquired through an integrated control system. The flow rate could be adjusted accurately. In consideration of all possible factors, the overall uncertainty in the case of pump head measurement is less than 2.0%. And the overall uncertainty with respect to pump efficiency measurement is less than 3.5%. The flow rate and pump head are denoted by flow coefficient and head coefficient, respectively. And the results are plotted in Figure 4. On the whole, numerical and test results are in good accordance. In particular, at flow rate coefficient about 0.118, which are about 1.2Q, the difference between nu- 4. Results and Discussion 4.1 Pump Performance Pump performance bears the most important concern Figure 2. Computational zone and locally refined grids. Figure 3. Schematic of the test rig.

5 Turbulent Flow Characteristics in an Axial-flow Pump at Direct and Reverse Modes 451 Figure 4. Comparison between numerical and test data. merically obtained pump head and the test data is even slight. The validity of the numerical scheme is approved. As for the numerical results, the two pump head curves share the point that positive slope appears at small flow rates. This is one of the distinct features of the axial-flow pump. The reason lies in the secondary flows occurring at the blade edge near impeller inlet and at the impeller hub at impeller outlet. Pumps operating with such a flow rate range is susceptible to operation unsteadiness. Meanwhile, the difference between the two pump head curves is minimized at 0.4 q v and 1.3 q v as well. Although the pump head at reverse operation mode is 15% larger than its counterpart at nominal flow rate, the overall variations of pump head with flow rate are consistent. For pump efficiency, similar variation tendency is shared by the numerical and experimental results. The reverse mode is associated with the highest efficiency, which is obtained at flow rates slightly larger than the nominal flow rate. In this context, the largest efficiency gap between the two modes reaches as high as 5%. Although the impeller can be deemed as symmetrical with respect to positive and reverse rotations, the inflow conditions are apparently different, as leads to the disagreement shown in Figure 4. It has been reported that hydraulic losses in the curved outlet flow passage at direct mode increase with flow rate, and this argument can be substantiated only in an absolute fashion [15]. The comparison between the two modes is based upon the same flow rate range, there is also a practice that makes use of different flow rate ranges to evaluate the pump performance with direct and reverse modes [16]. 4.2 Flow Characteristics Flow characteristics in the pump determine to a large extent the pump performance. In Figure 5, azimuthal ve- Figure 5. Distributions of absolute velocity: (a) direct mode; (b) reverse mode.

6 452 Can Kang et al. locity distributions in the whole pump passage at direct and reverse operation modes are displayed. For both modes, the impetus behind the medium comes solely from the rotating impeller [17]. In terms of overall velocity magnitude, large value is associated with the reverse operation mode instead of the direct operation mode. Regarding the direct mode, although the inlet pipe axis is not parallel to the impeller shaft, the local flows are fairly smooth, as is in agreement with the visualized results in [18]. The bended inlet pipe has been studied and it has been testified that it can arouse the emergence of irregular suction vortices [19]. For the reverse mode, the intrusion of the shaft helps regulate azimuthal velocity distributions before the medium enters the impeller passage, as can be reasonably extrapolated. In another perspective, at direct operation condition, the unevenness of velocity distribution immediately upstream of the impeller is developed without being restricted by the impeller shaft. Then two cross sections immediately upstream and downstream of the impeller are extracted. Absolute velocity distributions over these two cross sections are shown in Figure 6. As seen in Figure 6(a), upstream of the impeller, there are five subzones which correspond to the five blades. Furthermore, such a match is well remained downstream of the impeller. In contrast, in Figure 6(b), for the impeller inlet, the effect of blade number is apparently limited. In this connection, the intrusion of the shaft changes the profiles of flow structures. At both impeller inlet and outlet shown in Figure 6(b), sparsely distributed elements dominate the two cross sections, as is considerably different from that at direct operation mode. Relative velocity distributions over three lines located in the azimuthal plane are extracted. Both the lines and velocity distributions are displayed in Figure 7. Near the hub and the blade tip, with x/(r d r h ) approaching 1.0 and 0.0 respectively, high velocity gradients are shared by the direct and reverse modes. For the direct mode, the Figure 6. Cross-sectional velocity distributions upstream and downstream of the impeller.

7 Turbulent Flow Characteristics in an Axial-flow Pump at Direct and Reverse Modes 453 development of relative velocity along the streamwise direction is fairly regular and the velocity profiles do not fluctuate along the x direction. In contrast, the reverse mode is associated with complex flow patterns, as are indicated by the R m and R o lines. Near the blade tip, velocity magnitudes over the R m and R o lines drop obviously, as enhances the possibility of secondary flow formation. With respect to overall velocity magnitude, the reverse mode is more desirable. As a further step, static pressure distributions over the impeller blades are shown in Figure 8. The direct and reverse operation modes show considerably different distribution patterns. For the direct mode, the distribution is in good accordance with the general viewpoints. For the reverse mode, low-pressure speckle forms near the blade leading edge, although this does not apply explicitly for every blade, it changes essentially pressure distributions in radial direction. In addition, the downstream pressure distributions over the blades are affected as well. Based upon pressure distributions shown in Figure 8, hydraulic forces acting upon the impeller blades can be derived. It can be inferred that at direct mode, the resultant forces exerted upon the blades conform to the principles of energy transfer in the axial-flow pump. Figure 7. Relative velocity distributions over lines in the azimuthal plane. r d and r h denote the radii of the impeller and the hub, respectively. 4.3 Cavitation Cavitation should be avoided or lessened in the reversible pump. Cavitation phenomenon is accompanied with pump vibration and noise, the entire system will be endangered. In Figures 9(a) and (b), cavitation zones, denoted by identical cavitation volume fractions of 0.1, are depicted at the two operation conditions. The two conditions share the phenomenon that except those near blade leading edges, no cavitation zones are identified. Experimentally visualized cavitation zones near an axialflow impeller are shown in Figure 9(c). It is seen in Figure 9 that cavitation zone appears at blade leading edge, as is shared by each blade. From the impeller hub to impeller blade outer edge, cavity zone spreads in circumferential direction. Such a profile is in Figure 8. Static pressure distributions over impeller blades.

8 454 Can Kang et al. agreement with general conclusions of cavitation occurring in the axial-flow pump [20]. Since that the background pressure prevents the inception of cavitation, the only drive for cavitation comes from the impeller rotational speed. Circumferential velocity increases with radial distance from the impeller hub, as contributes greatly to the cavity profile displayed in Figure 9(a). Furthermore, with the rotation of the impeller, the overall cavity profile remains nearly stable. Both the effects of blade angle and its variation along the blade height cannot be neglected [21]. In contrast, for the reverse operation, no clear cavity is detected except the small cavity zones at the hub and near the blade leading edges. The overall velocity magnitude is high for the reverse mode, as in turn intensifies the streamwise transportation of the medium. Therefore, even near the blade leading edge, cavitation cannot take into shape in the presence of the powerful bulk flow. With respect to the emergence of cavitation zones near the impeller hub, it is ascribed to the seemingly suppressed flows, as can be perceived from Figure Unsteady Pressure Fluctuations For the pump considered, its dimensions are rather limited. The medium is confined in a limited space with the periodic disturbance of the impeller. Therefore, the Figure 9. Cavitation zone near blade leading edge (volume fraction = 0.1).

9 Turbulent Flow Characteristics in an Axial-flow Pump at Direct and Reverse Modes 455 flow-induced pump vibration must be paid more attention. The startup and shutdown transient processes are not considered here. Two cross sections, immediately upstream and downstream of the impeller, are monitored. And the employment of monitored points is schematically shown in Figure 10. The pressure fluctuation frequency spectra at direction operation mode are plotted in Figure 11 where f 0 denotes shaft frequency and 5f 0 is the blade passing frequency. At direct operation mode, the overall pressure fluctuation amplitude at outlet section is considerably larger than its counterpart at inlet section. Apparently, at the outlet section, the most prominent frequency is the blade passing frequency 5f 0. And the harmonics of blade passing frequency dominate the entire spectrum of pressure fluctuations. This well explains the effects of blade rotation. In addition, the two points monitored on the outlet section bear almost identical pressure fluctuation tendencies. In contrast, pressure fluctuations at impeller inlet are complicated, as is substantiated by the disparity between Point A and Point B. It is reasonable that the shaft frequency is the most predominant frequency since that the direct impact of impeller blades on the medium does not start yet. At Point A, the influence of blade passing frequency excels that of the shaft frequency, while for Point B, the shaft frequency is dominant. As shown in Figure 12, pressure fluctuations at reverse operation mode are rather similar to those at direct mode, in particular for the monitored points downstream of the impeller. Nevertheless, the pressure fluctuation magnitudes in Figure 12(b) are small relative to those shown in Figure 11(b). As for the inlet section, Point B, upstream of the impeller, which is near the impeller hub, exhibits distinctly different characteristics. Moreover, the frequency of 3f 0 is also noticeable. Such a frequency is associated with the flow patterns shown in Figure 6(b). In this context, it is appreciable that the intrusion of the shaft at impeller inlet contributes to the occurrence of such an influential frequency. At Point A, pressure fluctuations at both shaft frequency and blade passing frequency are insignificant compared with those at Point B. Relative to pressure fluctuation spectra obtained with outlet guide vane, the spectra shown in Figures 11 and 12 Figure 10. Monitored points in the azimuthal plane. Figure 11. Pressure fluctuations at direct operation mode.

10 456 Can Kang et al. Figure 12. Pressure fluctuations at reverse operation mode. are fairly clear-cut and no apparent peaks of pressure fluctuations between the harmonics of blade passing frequencies are witnessed. In this connection, the absence of inlet and outlet guide vanes for the impeller is the most essential reason for such a difference [22]. 5. Conclusions The present study treats numerically the flows in a reversible axial-flow pump. Both steady and unsteady simulations are performed. And cavitation is explored as well. Conclusions obtained in the present study are as follows: (1) A relative difference of pump head of 15% exists between the direct and reverse modes of the pump considered. Such a difference is inherently related to the hydraulic losses in the inlet and outlet pipes. With the reverse mode, overall velocity magnitude is high and the velocity development in the impeller passages is remarkable compared with the direct mode. (2) The direct mode is associated with cavitation zones near blade leading edges. And cavitation zone extends from the hub to the blade tip, as conforms to the general knowledge of cavitation phenomenon in the axial-flow impeller. With the reverse mode, small cavities appear near the hub and at blade leading edges as well. This is inseparable from potential secondary flows near the impeller hub. (3) As for the inlet section with the direct mode, near the impeller hub, shaft frequency is most salient, while near the blade tip, blade passing frequency is dominant. However, this does not apply to the reverse mode, which is featured by complex flow patterns even on the inlet section. Regarding the pressure fluctuations at outlet sections, the two modes are similar except the difference in pressure fluctuation magnitude. Acknowledgements The authors gratefully acknowledge the support of the Six Talent Peaks Project in Jiangsu Province (Grant No. ZBZZ-018) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). References [1] Jain, S. V. and Patel, R. N., Investigations on Pump Running in Turbine Mode: A Review of the State-ofthe-art, Renewable and Sustainable Energy Reviews, Vol. 30, pp (2014). doi: /j.rser [2] Bozorgi, A., Javidpour, E., Riasi, A. and Nourbakhsh, A., Numerical and Experimental Study of Using Axial Pump as Turbine in Pico Hydropower Plants, Renewable Energy, Vol. 53, pp (2013). doi: /j.renene

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12 458 Can Kang et al. for Pump Gate, Proceedings of the 8th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows, Lyon, France, Jul. 2 6 (2007). [20] Johann Friedrich Gülich, Centrifugal Pumps, 2nd ed., Springer-Verlag, Berlin, Heidelberg (2010). [21] Premkumar, T. M., Kumar, P. and Chatterjee, D., Cavitation Characteristics of S-blade Used in Fully Reversible Pump-turbine, Journal of Fluids Engineering, Vol. 136, No (2014). doi: / [22] Kang, C., Yu, X., Gong, W., Li, C. and Huang, Q., Influence of Stator Vane Number on Performance of the Axial-flow Pump, Journal of Mechanical Science and Technology, Vol. 29, No. 5, pp (2015). doi: /s Manuscript Received: Jan. 18, 2016 Accepted: Aug. 4, 2016