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International Journal of Fluid Machinery and Systems DOI: http://dx.doi.org/10.5293/IJFMS.2017.10.4.378 Vol. 10, No. 4, October-December 2017 ISSN (Online): 1882-9554

Original Paper

CFD-DEM Simulation for Distribution and Motion Feature of Crystal Particles in Centrifugal Pump

Dong Liu1, Cheng Tang1, Shicheng Ding1, Binhao Fu1

1School of Energy and Power Engineering Jiangsu University, Zhenjiang, 212013, China liudong@ujs.edu.cn, tangcheng@ujs.edu.cn

Abstract

In consideration of the particle features and behaviors, the Computational Fluid Dynamics (CFD)-Discrete Element Method (DEM) coupled method has been applied to simulate the liquid-solid flows in the centrifugal pump with crystallization phenomenon. The crystal particles tend to distribute more uniformly in the inlet section and enter the impeller along the pressure sides of the blades with a moderate rise in velocity. Particle number density is different at different regions in the impeller passages with the characteristics of small density near suction sides and large density near pressure sides. In addition, large crystal particles are mainly located near the pressure sides and small crystal particles predominantly appear in the region near suction sides. The relative velocity magnitude of flow near the impeller inlet tends to be higher than that of crystal particles, while the velocities of the solid particles are substantially higher than liquid phase at the outlet.

Keywords: Centrifugal pump, crystallization phenomenon, CFD-DEM, particle feature and behavior.

1. Introduction

During the transportation process of salt aqueous solution, the crystal particles crystallizing from the solution can cause negative effects on the relevant equipment operations and even severe economic losses, since the solid particles would be absorbed on the inner wall of pipelines and pumps [1]. At present, centrifugal pump has a wide application in chemical industry, transporting a variety of brine, which leads to common crystallization problems. From the beginning to end of crystallization phenomenon, the pump efficiency declines gradually and then drops abruptly due to the particle behaviors. The liquid-solid flows with crystallization phenomenon in the centrifugal pump have been studied and some experiments have been made by several scholars [2-4]. Liu Dong et al. [2, 3] used Particle Image Velocimetry (PIV) combined with developed image processing method to analyze the two-phase velocity fields in a centrifugal pump. Investigation proved that the crystal particles changed the relative liquid velocity distribution, and had a tendency of moving towards the pressure side in the middle channel of impeller. Yang Minguan et al. [4] measured the diameter distribution of crystal particles in a centrifugal pump impeller at different operating conditions. Experimental results showed that the particle number density was different at different axial direction with the characteristics of small density near shroud and large density near hub. In addition, there were some large crystal particles along radial direction, which were mainly located near the pressure side with even distribution at the outlet．

Attentions also have been focused on the numerical study of liquid-solid flows in the centrifugal pump with crystallization phenomenon. Sakr [5] used finite element method to make a primary analysis on the flows in impeller inlet and outlet when pumping seawater. In the work by Yang Minguan et al. [6], the commercial computational fluid dynamics software Fluent, containing the Eulerian model, was used for the simulation of flows in a centrifugal pump with crystallization phenomenon. For the further research, in consideration of the particle nucleation and growth, a population balance model was incorporated with the mixture model based on Fluent by Liu Dong [7]. Generally, these CFD methods [8, 9] prefer to treat the solid particles in the mixed flow as a kind of pseudo-liquid medium. By this means, they can obtain the particles motion by governing equations of multiphase flow models, with global accuracy in two-phase flow prediction, applicability to a wide range of solid volume fractions and relatively low computational demand. However, the influences of various particle features, the material properties, shape and size, can not get an accurate assessment in this way. Moreover, these CFD methods can not provide a reliable estimate for the behaviors of particle-particle and particle-wall, such as the collision, agglomeration and separation, which have a significant effect on the pump performance.

Received March 8 2016; revised March 2 2017; accepted for publication August 29 2017: Review conducted by Dohyung Lee. (Paper number O16007K) Corresponding author: Dong Liu, Professor, liudong@ujs.edu.cn

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Alternatively, the discrete element method (DEM), first proposed by Cundall and Strack [10], is a new numerical method for analyzing the movement and mechanical problems of complex discrete systems, which can contribute to a precision analysis of solid particle motion in two-phase flow through considering the essential solid particle features. Dealing with solid phase of the two-phase flow, DEM has incomparable superiority of the other methods, providing an accurate description of the particle dynamic motions in accordance with Newton’s second law of motion. For further research, the study on DEM coupled with the CFD method has also been proposed to improve the computational efficiency and numerical accuracy in two-phase flow by Tsuji et al. [11] and Kafui et al. [12].

Based on the above, this work used CFD-DEM method to study the distribution and motion feature of crystal particles in a centrifugal pump. The simulation was performed by using the commercial CFD tool STAR-CCM+, with a DEM-code inside. Therefore, the calculation factored in the shape, size, material properties of the crystal particles and the interactions of particle-particle, particle-wall and particle-liquid. The results would present some guiding advice to prevent the negative behaviors of crystal particles in centrifugal pump through obtaining the characteristics of two-phase flow.

2. Numerical Model and Methods

2.1 Computational domain

A single stage centrifugal pump consisting of the inlet pipe, impeller, and volute was selected in this work to study the two-phase flow and the basic parameters of centrifugal pump are as follows: design discharge Q=20m3/h, head H=10m, rotational speed n=1450rpm, blade number Z=5, inlet diameter D0=75mm, outlet width b2=10mm. The polyhedron meshes were generated in the entire computational domain as shown in the Fig. 1(a). In addition, for the turbulent flow simulation, an appropriate resolution of the near wall region was needed and 5 prism layers are created next to all the wall surfaces (Fig. 1(b)) to improve the accuracy of the flow solution. Table 1 shows the results of mesh dependency test for the head of pump. From the results, 535,665 is determined as optimal number of mesh cells. The acceleration of gravity (g=9.81 m/s2) was also taken into consideration with its direction in accordance with the x-axis.

(a) (b)

Fig. 1 Computational domains and cells

Table 1 Mesh dependency test Grid number Head/m Deviation

250,493 10.291 331,976 10.367 0.73% 427,510 10.395 0.27% 535,665 10.413 0.17% 689,142 10.421 0.08%

2.2 Particles

The DEM phase interaction model, determining how particles behave when they come into contact with each other or solid boundaries, is used for describing the particle-particle and particle-wall interactions. In this model, particles were seemed as a discrete phase, the so-called soft sphere model was adopted to estimate the effects of contact on particle collision. The density of the crystal particles (sodium sulfate) were taken as 2680kg/m3, while the size of the particles was selected in diameter of 82.5μm according to Gao Bo’s research [13]. The volume fraction of the solid particles was set to 4.5×10-4 at the pump inlet. Meanwhile, the DEM phase interaction model provides access to other models, Hertz Mindlin model and linear cohesion model. The Hertz Mindlin non-slip contact model is the standard model that is used for describing the particle-particle and particle-wall interactions and the linear cohesion modeling facilitates the simulation of inter-molecular attraction forces between particle surfaces, which are proportional to adhesion energy density and contribute to the progress of aggregating smaller particles into bigger particles. Remarkably, all the pump walls used in the experiments by several scholars [2, 3, 4] were made of special material and possessed high surface accuracy, causing the fact that the crystal particles have not been absorbed on the inner walls. Given this, the simulation of behavior between particle and wall would not take the linear cohesion model. The collision parameters used in the models are summarized in Table 2.

Table 2 Collision parameters Collision Particle-particle Particle-wall Coefficient of restitution 0.5 0.5 Coefficient of static friction 0.61 0.8

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Coefficient of rolling friction 0.01 0.01 Adhesion energy density/(J/m3) 5×104

2.3 Fluids

The transient fluid phase flow was analyzed, using CFD simulations through solutions of the transient Reynolds averaged Navier-Stokes (RANS) equation. The standard k-epsilon turbulence model and ‘high-y+ wall treatment’ were employed in the STAR-CCM+ platform for turbulence modeling. This wall treatment assumes that the near-wall cell lies within the region of boundary layer. In the present simulations, the values of y+ range from 1.97 to 111.11 and average y+ values for the impeller and volute surfaces were 32.02 and 40.84 respectively. The flow was assumed to be isothermal and incompressible with the physical properties of sodium sulfate solution (μ=3.096×10-3Pa·s, ρ=1356kg/m3). The pump walls were defined as no-slip wall and the outlet was defined as pressure-outlet with p=1.0bar. At the velocity-inlet, a constant profile was specified.

2.4 CFD-DEM coupling

The modeling of the particle by DEM code is at the individual particle level, while the liquid flow by CFD solver is at the computational cell level [14]. The two-coupling is adopted in this study. The transient fluid phase flow is initially analyzed using CFD simulations and the flow simulation is iterated until convergence is achieved for a given time step. The DEM simulations are subsequently initiated to compute the instantaneous drag force acting on each DEM particle from the transient fluid conditions of the mesh cell containing the particular particle. The simulations are continued using the DEM to determine the instantaneous position, velocity and forces of particles, subsequently updated and transferred to CFD solver, together with the inertia forces. For this purpose a momentum source is introduced to each mesh cell to represent the effect of energy transfer from each DEM particle, taking into account the volume fraction of the CFD mesh cell occupied by the solid particle [15].

3. Results and Discussions

3.1 Particle tracks

Figure 2 presents the tracks of crystal particles in the pump at various moments during the simulation of design discharge. To get a better observation of the solid particles distribution inside the impeller and volute, the computational domains of the inlet pipe is hidden in the current vision. It can be clearly seen that the particle volume experience a gradual increase over time in the figures. As regards the details on motion feature of particles, the crystal particles tend to distribute more uniformly in the inlet section (Fig. 2(a)), and enter the impeller along the pressure sides of the blades (Fig. 2(b-f)) with a moderate rise in velocity however. Generally, the majority of particles tend to maintain spiral tracks during flowing towards the volute, which corresponds with the shape of the impeller blades, as shown in Fig. 2(c). Acquiring a significant speed from the impeller, the particles, especially the ones in contact with blades, tend to cluster along the volute outside wall and move downstream towards the outlet (Fig. 2(d)), while some of them would bounce back to the volute inside wall after impacting on the outside wall and then hover there with a considerable low speed (Fig. 2(e-f)). Furthermore, when one blade rotates over the casing tongue, because of the narrow volute passage here, the particles bouncing back tend to return into impeller and scatter near the impeller outlet as shown in Fig. 2(e-f).

(a) t=0.035s (b) t=0.045s (c) t=0.060s

(d) t=0.080s (e) t=0.120s (f) t=0.200s

Fig. 2 Particle tracks in the pump of different moments

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3.2 Particles distribution

Figure 3 shows the distribution of crystal particles in the impeller of the centrifugal pump at three different operating conditions (0.8Q=16m3/h, 1.0Q=20m3/h, 1.2Q=24m3/h). Focusing on the design condition (Fig. 3(b)), it can be obtained that the particle number density is different at different regions in the impeller passages with the characteristics of small density near suction sides and large density near pressure sides. In addition, as shown in Fig. 3(d), large numbers of small crystal particles are evenly distributed in the inlet section, while there are some large crystal particles along radial direction, which are mainly located near the pressure sides with even distribution at the outlet. On the contrary, small crystal particles predominantly appear in the region near suction sides of impeller passages. The reason for this kind of distribution characteristics is the density of solid phase bigger than liquid. Due to the effect of inertia force and centrifugal force, entering the impeller passage, the large particles gradually get closer to the pressure sides. On the other hand, the crystal particle distribution at different operating conditions has different characteristics (Fig. 3(a-c)). Along with the discharge increasing, the trend of large particles move to the pressure sides gets more distinct. Meanwhile, the number of particles bouncing back to impeller outlet experiences a rapid decline from 0.8Q condition to 1.2Q condition on account of the increasing fluid drag forces in opposite direction. These numerical calculation results are generally consistent with the experimental observations of Yang Minguan et al. [4], indicating that CFD-DEM can be applied to study particle motion in the centrifugal pump, and this method is feasible in this paper.

(a)0.8Q (b)1.0Q (c)1.2Q

(d)

Fig. 3 Particles distribution in the pump impeller at different conditions (t=0.400s)

3.3 Velocity field of liquid and influence

Figure 4 presents the relative velocity distribution of the liquid in the impeller. It can be obtained that, in radial direction of the impeller, the velocity near pressure side increases gradually, but decreases gradually near the suction side and relative velocity of liquid phases on pressure side is less than that on suction side because of the rotational action of impeller. These conclusions of liquid velocity field in this kind of two-phase flow are highly consistent with those in single-phase flow calculated by Yang Minguan et al. [16]. Preliminary analysis suggests that particle size is at micron-scale leading to the crystal particles having little influence on liquid flow field.

(a)0.8Q (b)1.0Q (c)1.2Q

Fig. 4 Velocity fields of liquid in the pump impeller at different conditions (t=0.400s)

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Comparing Fig. 3 with Fig. 4, observation that the velocity magnitude and distribution of solid phase in the middle region of impeller is similar to that of liquid phase reveals the dominant influence on the crystal particles exerted by the liquid, but there are some differences between liquid and crystal particles at impeller inlet and outlet, especially the area near the pressure side of blades. By the comparison with Fig. 3(b), Fig. 4(b) illustrates that the relative velocity magnitude of flow near the impeller inlet tends to be relatively higher than that of crystal particles, while the maximum is obtained near 5.7m/s. In contrast, the velocities of the solid particles are substantially higher than liquid phase at the outlet. Although the particle velocity is only approximate 2.2m/s at the inlet section, while they tend to accelerate in the impeller passages and discharge from the impeller outlet at a speed of about 6m/s. This can be explained by the fact that the inertia of particles impedes their acceleration from the fluid drag forces, causing their velocities are lower at the impeller inlet. However, at the outlet, the liquid velocities have a considerable decrease due to the increase in the cross-sectional area of the impeller passages, while the solid particles retain their inertia from the impeller, keeping a higher speed. These results of interaction between the two phases are basically similar to the experimental one by Liu Dong et al. [3]. Near the pressure side of blades, boundary layer creates a low-speed region (Fig. 4). As a result, the velocities of particles get a decline with the consequent drag force getting smaller, leading to a bigger probability of small particles aggregating into larger particles. Consequently, the large particles contact with the blades because of bigger inertia and then gradually acquire speed (Fig. 3). From 0.8Q condition to 1.2Q condition, the crystal particles distribution tends to be more even as shown in Fig. 3(a-c). Analysis suggests that with the rate of flow increasing, the flow velocities get a climb (Fig. 4(a-c)), resulting in more powerful fluid drag forces to carry particles to wider region in the impeller passages.

3.4 Particles agglomeration

As shown in the Fig. 5, a considerable number of crystal particles begin to agglomerate apparently near the every inlet edge of the five blades at the pump design condition, with the characteristic of more particle clusters generating close to the suction side and the shroud side. It can be reasoned that particles agglomeration is located near these two regions because of the wall structure and dramatic changes in velocity field of liquid here. It is the fact that narrow cross-sectional area of impeller passages at the inlet of blades causes the high number density of crystal particles. Simultaneously, the dramatic changes in both magnitude and direction of velocities there (Fig. 4(b)) cause a big probability in particle collision with each other. This result and further research may present some guiding advice to prevent the crystal agglomeration.

(a) (b) (c)

(d) (e) (f)

Fig. 5 The crystal particle agglomeration near inlet edges

3.5 Pump performance curves

The head and efficiency of centrifugal pump as a function of the liquid flow rate are presented in Fig. 6. The experimental curves for the pump by Dong Xiang [17] was also included for comparison purposes. The curves obtained from numerical simulation follow the tendency of experimental result with an acceptable accuracy. However, the heads predicted by means of CFD-DEM is greater for all conditions. This discrepancy could be due to the neglect of mechanical and volume losses caused by

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bearings and seals in the numerical simulation. Moreover, the head of centrifugal pump was calculated through the flow simulation of single phase without crystal particles. From this comparison between CFD-DEM simulation and single-phase simulation, it can be also concluded that the effect of the crystal particles on the liquid flow is little, as the pump head calculated by single-phase simulation is slightly higher than that by CFD-DEM simulation.

Fig. 6 Comparison between experimental head and simulation

4. Conclusion

In this paper, the CFD-DEM method was applied to study the distribution and motion feature of crystal particles in a centrifugal pump with crystallization phenomenon. The results were compared with the experimental ones, which proves that the CFD-DEM method used in this paper is reliable. The following conclusions can be obtained from this research:

(1) The crystal particles tend to distribute more uniformly in the inlet section and enter the impeller along the pressure sides of the blades with a moderate rise in velocity. Acquiring a significant speed from the impeller, the particles tend to cluster along the volute outside wall and move downstream, while some of them would bounce back to the volute inside wall or impeller outlet after impacting on the outside wall.

(2) The particle number density is different at different regions in the impeller passages with the characteristics of small density near suction sides and large density near pressure sides. In addition, large crystal particles are mainly located near the pressure sides and small crystal particles predominantly appear in the region near suction sides of impeller passages. Along with the discharge increasing, the trend of large particles move to the pressure sides gets more distinct. Meanwhile, the number of particles bouncing back to impeller outlet experiences a rapid decline.

(3) The particle size is at micron-scale leading to the crystal particles having little influence on liquid flow field, but liquid phase exert dominant influence on the crystal particles. The relative velocity magnitude of flow near the impeller inlet tends to be relatively higher than that of crystal particles, while the velocities of the solid particles are substantially higher than liquid phase at the outlet. A low velocity region near area of pressure side contributes to the crystal growth there.

(4) A number of crystal particles begin to get agglomeration apparently near the inlet edges of blades, forming the larger particles.

Acknowledgments

This work was supported by Six talent peaks project in Jiangsu Province (2014-ZBZZ-016), National Natural Science Foundations of China (51676086), Natural Science Foundation of Jiangsu Province (BK20161351), China Postdoctoral Science Foundation (2017M610305).

References

[1] Jia, W. D., Yang, M. G., Gao, B., and Zhou, H. B., 2005, “Crystal mechanism in pipelines while conveying green liquid,” Journal of Jiangsu University, Vol. 26, No. 6, pp. 514-516. [2] Liu, D., Yang, M. G., and Gao B., 2008, “PIV measurement of flow with salt-out in centrifugal pump,” Transactions of the Chinese Society for Agricultural Machinery, Vol. 39, No. 11, pp. 55-58. [3] Liu, D., Wang, Y. Y., Wang, Y. Z., Wang, C. L. and Yang, M. G., 2014, “Research of liquid-solid two phase flow in centrifugal pump with crystallization phenomenon,” International Journal of Fluid Machinery and Systems, Vol. 7, No. 2, pp. 54-59. [4] Yang, M. G., Wu, C. F., Gao, B., Kang, C., and Feng, L., 2011, “Distribution feature experiment of salt-out crystal particles in a centrifugal pump impeller,” Journal of Jiangsu University, Vol. 32, No. 5, pp. 528-532. [5] Sakr, S. A., 2010, “Type curves for pumping test analysis in coastal aquifer,” Ground Water, Vol. 39, No. 1, pp. 5-9. [6] Yang, M. G., Liu, D., Kang, C., and Wang, C. L., 2006, “Analysis of flow with salt's separation and accumulation in centrifugal pump impeller,” Transactions of the Chinese Society of Agricultural Machinery, Vol. 37, No. 12, pp. 83-86. [7] Liu, D., Tang, C., Yan, J. H., Teng, G. R., and Zhang, P., 2015, “Numerical simulation of salt-out flow in centrifugal pump based on population balance model,” China Rural Water and Hydropower, No. 5, pp. 160-163. [8] Wang, J., Ye, Q., Yan, K., Feng, Y. and Yu, X., 2014, “Effects of particle diameter on erosion wear performance of slurry pump,” Journal of Drainage and Irrigation Machinery Engineering, Vol. 32, No. 10, pp. 840-844.

384

[9] Cheng, X., Zhang, N. and Zhao, W., 2015, “Pressure fluctuation features of sand particle-laden water flow in volute of double-suction centrifugal pump,” Journal of Drainage and Irrigation Machinery Engineering, Vol. 33, No. 1, pp. 37-42. [10] Cundall, P. A., and Strack, O. D. L., 1979, “A discrete numerical model for granular assemblies,” Géotechnique, Vol. 30, No. 30. pp. 331-336. [11] Tsuji, Y., Kawaguchi, T., and Tanaka, T., 1993, “Discrete particle simulation of two-dimensional fluidized bed,” Powder Technology, Vol. 77, No. 1, pp. 79-87. [12] Kafui, K. D., Thornton, C., and Adams, M. J., 2002, “Discrete particle-continuum fluid modelling of gas-solid fluidized beds,” Chemical Engineering Science, Vol. 57, No. 13, pp. 2395-2410. [13] Gao, B., 2009, “Salt-out two-phase flow theory and investigation on internal flow in a vortex pump,” Ph.D. Thesis, School of Energy and Power Engineering, Jiangsu University, Zhenjiang, China. [14] Chu, K. W., and Yu, A. B., 2008, “Numerical simulation of complex particle–fluid flows,” Powder Technology, Vol. 179, No. 3, pp. 104-114. [15] Huang, S., Su, X. H., and Qiu, G. Q., 2015, “Transient numerical simulation for solid-liquid flow in a centrifugal pump by DEM-CFD coupling,” Engineering Applications of Computational Fluid Mechanics, Vol. 9, No. 1, pp. 411-418. [16] Yang, M. G., Liu, D., Jia W. D., Kang, C., and Gu, H. F., 2006, “Analysis on turbulent flow in impeller of centrifugal pump,” JournaI of Jiangsu University, Vol. 27, No. 6, pp. 524-527. [17] Dong, X., 2008, “Study on the influence of outlet angle on salt-out flow in centrifugal pump,” M.S. Thesis, School of Energy and Power Engineering, Jiangsu University, Zhenjiang, China.