IOP Conference Series: Earth and Environmental Science Numerical investigation of solid-liquid two phase flow in a non-clogging centrifugal pump at offdesign conditions To cite this article: B J Zhao et al 2012 IOP Conf. Ser.: Earth Environ. Sci. 15 062020 Related content - Applications of different turbulence models in simulations of a large annular volutetype pump with the diffuser J Y Mao, S Q Yuan, J Pei et al. - Effects of computational grids and turbulence models on numerical simulation of centrifugal pump with CFD H L Liu, M M Liu, L Dong et al. - Numerical simulation of flow in centrifugal pump under cavitation and sediment condition P C Guo, J L Lu, X B Zheng et al. View the article online for updates and enhancements. This content was downloaded from IP address 148.251.232.83 on 13/06/2018 at 18:49
Numerical investigation of solid-liquid two phase flow in a non-clogging centrifugal pump at off-design conditions B J Zhao 1, Z F Huang 2, H L Chen 1 and D H Hou 1 1 School of Energy and Power Engineering, Jiangsu University, Jiangsu, 212013, China 2 School of Science & Technology, Jiangsu University, Jiangsu, 212013, China E-mail: Zhaobinjuan@ujs.edu.cn Abstract. The solid-liquid two-phase flow fields in the non-clogging centrifugal pump with a double-channel impeller have been investigated numerically for the design condition and also off-design conditions, in order to study the solid-liquid two-phase flow pattern and nonclogging mechanism in non-clogging centrifugal pumps. The main conclusions include: The sand volume fraction distribution is extremely inhomogeneous in the whole flow channel of the pump at off-design conditions. In the impeller, particles mainly flow along the pressure surface and hub; In the volute, particles mainly accumulate in the region near to the exit of volute, the largest sand volume fraction is observed at the tongue, and a large number of particles collide with volute wall and exit the volute after circling around the volute for several times. When the particle diameter increases, particles tend to accumulate on the pressure side of the impeller, and more particles crash with the pressure side of the blade. And larger sand volume fraction gratitude is also observed in the whole flow channel of the pump. With the decrease of the inlet sand volume fraction, particles tend to accumulate on the suction side of the blade. Compared with the particle diameter, the inlet sand volume fraction has less influence on the sand volume fraction gratitude in the whole channel of the pump. At the large flow rate, the minimum and maximum sand volume fraction in the whole flow channel of the model pump tends to be smaller than that at the small flow rate. Thus, it is concluded that the water transportation capacity increases with the flow rate. This research will strengthen people s understanding of the multiphase flow pattern in non-clogging centrifugal pumps, thus provides a theoretical basis for the optimal design of non-clogging centrifugal pumps. 1. Introduction Double-channel pump is a new type of solid-liquid centrifugal pump with good non-clogging performance, and widely used in all areas of industrial production, especially in environmental protect area. The flow in a double-channel pump is fully turbulent and highly unsteady, and is characterized by the strong periodic interaction due to the relative motion between the rotating impeller and the stationary volute, known as impeller-volute interaction. This periodic interaction has tow kinds of effects. First there is the downstream effect of the impeller on the volute flow, which is characterized by unsteady effects due to the highly distorted relative impeller flow field and impeller wakes. Second there is the upstream effect of the volute on the impeller flow, which causes unsteady pressure and velocity fluctuations to the relative flow. These two effects of unsteadiness have great influence on the Published under licence by Ltd 1
flow characteristic and energy losses in the double-channel pump. Some studies have been conducted numerically to investigate the flow field in double-channel pumps [1-5]. These research works contribute well to the understanding of the complex multiphase flow in the double-channel pump. However, most simulations were conducted only to study the flow field at design conditions, and few researches were done at the off-design conditions. In the present work, CFD simulations have been conducted to investigate the solid-liquid two-phase flow in a double-channel pump at off-design conditions. The phase-averaged velocity fields, pressure fields, and the sand volume fraction contours are quantitatively examined in detail, which can improve the understanding on particle-fluid interaction in double-channel pumps. Furthermore, the influences of particle diameter, inlet sand volume fraction and flow rate on inner flow field and hydraulic performance of double-channel pumps are comprehensively examined. This research will strengthen people s understanding of the flow pattern in the double-channel pump, thus further improve the optimal design method of double-channel pump, simultaneously might provide references for internal flow research of other multiphase pumps. 2. Nomenclature n s Specific speed m Viscosity of the mixture [Pa s] Q o Design flow rate [m 3 /s] F Volume force [N] H Head [m] n The number of phase n Rotating speed [rpm] Volume fraction of phase k [%] k D j Impeller inlet diameter [m] k Density of phase k [kg/m 3 ] D 2 Impeller outlet diameter [m] v dr, k Floating velocity of phase k [m/s] b 2 Impeller outlet width [m] v qp Sliding velocity of phase k [m/s] D h Diameter of the pump axis [m] C V Sand volume fraction [%] Density of the mixture [kg/m 3 ] d Particle diameter [m] m v Mass averaged velocity [m/s] k Turbulent kinetic energy [m 2 /s 2 ] m 3. Model pump The model pump used in the present study is a double-channel pump. It has a double-channel impeller and a spiral volute, as shown in Fig.1. Table 1 shows specifications of the model pump. (a) Impeller Figure 1. Model pump (b) Volute 2
Table 1. Specifications of the test pump. item value Specific speed n s 110.6 [rpm, m 3 /s, m] Design flow rate Q o 1.4 10-2 m 3 /s head H 10m Rotating speed n 1450rpm Impeller inlet diameter D j 0.08m Impeller outlet diameter D 2 0.2m 4. Numerical model 4.1. Basic assumptions for numerical simulations In this research, the working fluid in the model pump is assumed to be a water and sand mixture. Thus, the flow in the model pump is the complex solid-liquid two-phase flow, and characterized by the strong periodic interaction due to the relative motion between the rotating impeller and the stationary volute. To realize the whole flow channel solid-liquid two-phase flow simulations, some basic assumptions for numerical simulations are made as follows: Liquid phase (water) is assumed to be uncompressible; solid phase (sand) is assumed to be a continuous medium; physical properties for each phase are assumed to be constants. Solid phase (sand) is assumed to be spherical particles with a uniform diameter distribution, and without phase transition. The solid-liquid two-phase flow in the model pump is assumed to be steady. Multi reference frame (MRF) is built to conduct simulations, which includes a synchronized rotating coordinate for the impeller flow field and a stationary coordinate for the volute area. The velocity vectors on the interface are transferred by changing the relative velocity vectors to the absolute velocity vectors. 4.2. Mixture model The solid-liquid two-phase simulations are conducted by using mixture model included in the CFD code Fluent 6.4, which can be used to simulate the multiphase flow with different velocity for each phase. Thus, the strong coupling between the water and sand phases is expected to be revealed by simulations using this model [6-7]. The continuity and momentum equations applied in mixture model are in a form as: The continuity equation ( m ) ( mvm) 0 (1) t The momentum equation n T ( mvm) ( mvmvm) p [ m( vm vm )] mg F ( k kvdr, kvdr, k ) (2) t k 1 The sliding velocity vqp has a relation with the drift velocity vdr, p as: n k k vdr, p vqp vqk (3) k1 m 3
The solid volume fraction equation ( p p ) ( p pvm ) ( p pvdr, p ) (4) t The standard k- turbulence model for the single-phase flow is extended for the multi-phase flow; also the SIMPLE algorithm is extended from the single-phase flow to the multi-phase flow. Computation domain and mesh The solid-liquid two-phase flow in the model double-channel pump was simulated by commercial software FLUENT 6.4 for the off-design conditions. The calculation domain is shown in Fig.2. It includes an extended inlet pipe, impeller, volute and extended outlet pipe. An unstructured tetrahedral mesh was made for the computational grid shown in Fig.2. The grid numbers are 198,685 and 215,579 respectively for the impeller and volute calculation domain. Figure 2. Calculation domain Sliding mesh technology was applied in this unsteady simulation, which introduced an interface with sliding mesh to transfer data between the static and rotating calculation domain [1], as shown in Fig.3. Figure 3. Data transfer between static and rotating calculation domain 4.3. Computational conditions The distribution of all flow variables needs to be specified at the inlet boundary. Due to the mass conversation law and the presumption of no rotation, the inlet velocity of liquid phase is specified by the first boundary condition law, as u j in u j ( x, y, z) ( j 1,2, 3 ) (4) The value of k and at the inlet boundary can be estimated with the following approximate formula, as 4
2 Ckin kin 0. 005u in, in (5) 0.015D At the outlet boundary, it is assumed that the flow reaches a fully developed state where no change occurs in the flow direction. Thus, the gradients of all flow variables are set to be zero in the flow direction, as k u j n out 3 / 2 out out 0, 0, 0 n n ( j 1,2, 3 ) (6) No-slip boundary condition was applied for the surfaces of impeller, hub, shroud and volute. The logarithmic wall function was introduced for near-wall treatment [8-9]. Solid particles are assumed to distribute homogenously at the pump inlet with the same velocity as the liquid phase. The inlet sand volume fraction C V is set to be 1%, 3%,5%, 10% and 15%. The particle diameter d is 0.03mm, 006mm, 0.08mm, 0.12mm and 0.2mm. 5. Results and discussion 5.1. Validation of numerical results Under the condition of d =610-5m and C V =3%, we performed the calculation for a whole flow rate range from the shutoff point (Q/Qo =50%) to the maximum flow (Q/Qo =120%). The simulated results are compared with the tested one, as shown in Table 2. From Table 2, it is observed that the simulated results change tendency correspond well with the tested results, with a maximum deviation of 9%. The reason lies on the machinery and volume losses which haven t been calculated in simulations. Thus, the mixture model proves to be accurate in the internal multiphase flow simulation of double-channel pumps. condition Table 2. Comparison of simulated and tested results Flow rate Head /m Efficiency /% /m3 s-1 simulated tested simulated tested Small flow rate 0.710-2 12.8 11.7 56.3 53.4 Optimum flow rate 1.410-2 10.9 10.5 73.2 68.2 Large flow rate 1.710-2 10.6 9.8 72.4 66.5 5.2. Influence of particle diameter on the flow field Fig.4 shows the sand volume fraction distribution in the whole flow channel of the model pump under the condition of Q=30%Q 0, C V = 5%, d=0.03 mm, 0.08 mm, 0.12 mm and 0.2mm. Fig.5 shows the sand volume fraction distribution in the whole flow channel of the model pump under the condition of Q=150%Q 0, CV = 5%, d=0.03mm, 0.08mm, 0.12mm and 0.2mm. It is found that the sand volume fraction distribution is extremely inhomogeneous in both channels; In the impeller, particles mainly flow along the pressure surface and hub, due to the influence of centrifugal and inertial force; In the volute, particles mainly accumulate in the region near to the exit of volute, and the largest sand volume fraction is observed at the tongue; Entering the volute, few particles can directly flow out, and a large number of particles collide with volute wall and exit the volute after circling around the volute for several times. It is observed that the particle diameter has great influence on the sand volume fraction distribution in the whole flow channel of the model pump. When the particle diameter increases, particles tend to accumulate on the pressure side of the impeller, and more particles crash with the pressure side of the blade. And larger sand volume fraction gratitude is also observed in the whole flow channel of the pump. 5
It is also observed that compared with the small flow rate, the particle diameter has less influence on the sand volume fraction distribution at the large flow rate, resulting in a larger minimum sand volume fraction and a smaller maximum sand volume fraction in the whole flow channel of the model pump. 5.3 Influence of inlet sand volume fraction on the flow field Fig.6 shows the sand volume fraction distribution in the whole flow channel of the model pump under the condition of Q=30%Q 0, d=0.06mm, C V = 1%, 5%, 10% and 15%. Fig.7 shows the sand volume fraction distribution in the whole flow channel of the model pump under the condition of Q=150%Q 0, d=0.06mm, C V = 1%, 5%, 10% and 15%. It is found that with the decrease of the inlet sand volume fraction, particles tend to accumulate on the suction side of the blade. However, compared with the particle diameter, the inlet sand volume fraction has less influence on the sand volume fraction gratitude in the whole channel of the pump. It is also observed that at the large flow rate, the minimum and maximum sand volume fraction in the whole flow channel of the model pump tends to be smaller than that at the small flow rate. Thus it is concluded that the water transportation capacity increases with the flow rate. 4.54 4.86 5.19 5.51 5.84 2.36 3.83 5.31 6.78 8.25 (a) d=0.03mm (b) d=0.08mm 1.39 4.43 7.48 10.5 13.6 0.61 5.28 9.96 14.6 19.3 (c) d=0.12mm (d) d=0.2mm Figure 4. Sand volume fraction contour at the condition of Q=30%Q 0, C V = 5% 6
4.19 4.56 4.93 5.30 5.68 2.26 3.78 5.29 6.81 8.33 (a) d=0.03mm (b) d=0.08mm 1.55 3.72 5.90 8.08 10.3 0.82 4.12 7.42 10.7 14.0 (c) d=0.12mm (d) d=0.2mm Figure 5. Sand volume fraction contour at the condition of Q=150%Q 0, C V = 5% 0.62 0.92 1.22 1.51 1.81 3.53 4.58 5.63 6.68 7.73 (a)cv = 1% (b) CV = 5% 7
7.51 9.11 10.7 12.3 13.9 12.4 14.0 15.6 17.2 18.8 (c) C V = 10% (d) C V = 15% Figure 6. Sand volume fraction contour at the condition of Q=30%Q 0, d=0.06mm 0.60 0.84 1.08 1.31 1.55 3.24 4.18 5.12 6.07 7.01 (a)cv = 1% (b) CV = 5% 6.66 8.25 9.83 11.4 13.0 11.1 12.9 14.6 16.4 18.2 (c) C V = 10% (d) C V = 15% 6. Conclusions Figure 7. Sand volume fraction contour at the condition of Q=150%Q 0, d=0.06mm CFD simulations have been conducted to investigate the solid-liquid two-phase flow in a doublechannel pump at both small flow rate and large flow rate conditions. The phase-averaged velocity 8
fields, pressure fields, and the sand volume fraction contours are quantitatively examined in detail. The main conclusions include: (1) The simulated results corresponds well with the tested results with a maximum deviation of 9%,due to the machinery and volume losses which have not been calculated in simulations. The mixture model proves to be accurate in the internal solid-liquid two-phase flow simulation of doublechannel pumps. (2) The sand volume fraction distribution is extremely inhomogeneous in the whole flow channel of the pump at off-design conditions. In the impeller, particles mainly flow along the pressure surface and hub; In the volute, particles mainly accumulate in the region near to the exit of volute, the largest sand volume fraction is observed at the tongue, and a large number of particles collide with volute wall and exit the volute after circling around the volute for several times. (3) When the particle diameter increases, particles tend to accumulate on the pressure side of the impeller, and more particles crash with the pressure side of the blade. And larger sand volume fraction gratitude is also observed in the whole flow channel of the pump. With the decrease of the inlet sand volume fraction, particles tend to accumulate on the suction side of the blade. Compared with the particle diameter, the inlet sand volume fraction has less influence on the sand volume fraction gratitude in the whole channel of the pump. (4)At the large flow rate, the minimum and maximum sand volume fraction in the whole flow channel of the model pump tends to be smaller than that at the small flow rate. Thus, it is concluded that the water transportation capacity increases with the flow rate. Acknowledgement This work was supported by the National Natural Science Foundation, China, under a young scientist research program Study on Hydraulic Optimization Model for Double-Channel Impeller Based on Multi-Objective Genetic Algorithm (No51109094). References [1] Zhao B J,Yuan S Q,Liu H L,Huang Z F and Tan M G 2008 Transactions of the CSAE 24(1) 7-12 [2] Liu H L, Lu M Z, Lu B B, Tan M G, Wang Y and Wang K Unsteady flow numerical simulation in a double channel pump and measurements of pressure fluctuation at volute outlet Proc. of ASME2009 Fluids Engineering Division Summer Meeting (Colorado, USA,2009) [3] Qi X Y, Yan X W, Ji X and Zhang J 2009 Journal of Jiangsu University 30(2) 156-159 [4] Tan D H, Zhu Z C and Cui B L 2006 Fluid Machinery 34(5) 1-4 [5] Yamade Y, Kato C, Shimize H and Nagahara T Large eddy simulation of internal flow of a mixed-flow pump Proc. of ASME Fluids Engineering Division Summer Meeting (Colorado, USA,2009) [6] Kobayashi K and Chiba Y Numerical simulation of cavitating flow in mixed flow pump with closed type impeller Proc. of ASME Fluids Engineering Division Summer Meeting (Colorado, USA, 2009) [7] Liu S H, Tang X L, Wu Y L and Nishi M Simulation of dense solid-liquid two-phase flow in a pump impeller Proc. of ASME Fluid Engineering Summer Conf. (Charlotte, USA, 2004) [8] Menta M, Kadambi J R and Sastry S Particle velocities in the rotating impeller of a slurry pump Proc. of ASME Fluids Engineering Conf. (San Diego, USA, 2007) [9] Westra R W, Broersma L, Andel K V and Kruyt N P 2010 ASME Journal of Fluid Engineering 132(1) 0611041-0611047 9