Enhancement of a Centrifugal Pump Performance by Simultaneous Use of Splitter Blades and Angular Impeller Diffuser

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1 International Journal of Fluid Machinery and Systems DOI: Vol. 11, No. 2, April-June 2018 ISSN (Online): Original Paper Enhancement of a Centrifugal Pump Performance by Simultaneous Use of Splitter Blades and Angular Impeller Diffuser Davood Khoeini 1, Ebrahim Shirani 2 1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan , Iran, d.khoeeni@me.iut.ac.ir 2 Department of Mechanical Engineering, Foolad Institute of Technology, Fooladshahr, Isfahan, Iran, eshirani@cc.iut.ac.ir Abstract The influences of different configurations of impeller diffusers and splitter blades on performance of a centrifugal pump have been analyzed experimentally and numerically. Each impeller with different configurations including three different splitter blades with lengths of 0, 0.45L and 0.75L (L is the length of impeller blades) and three different cases of impeller with diffuser of α=0o (α is the divergence angle of diffuser walls) and angular diffuser of α=10o and impeller without diffuser have been investigated in this study. Data analyses revealed that there is good compatibility among experimental and numerical results and the highest head discrepancy is only 7 percent. Results showed that simultaneous use of impeller diffuser and splitter blade have profound impact on the centrifugal pump performance. Actually, among all configurations, the maximum performance is achieved for the impeller equipped with angular diffuser of α=10o and splitter blades of 0.75L concurrently. In that case, the head at high flow rate is 1.51 times of the head value of original impeller without impeller diffuser. In addition, at BEP (Best Efficiency Point), efficiency increased by 3.4 percent and its position displaced towards the high flow rate as well. Keywords: Centrifugal pump, performance enhancement, impeller diffuser, splitter blade. 1. Introduction Centrifugal pumps play a significant role in various kinds of industries such as power plants, chemical industries and refinery industries. Hence, improvement of centrifugal pump performance is considered as inevitable part of researches and different approaches has been reached to enhance performance of centrifugal pumps [1-10]. Pei et al. [11] used orthogonal design of experiment to improve cavitation performance of a centrifugal pump. Their results showed that the NPSH (Net Positive Suction Head) decreases by 0.63 m when the main geometric parameters of the impeller are changed. The staggered and fixed cavitation in centrifugal pumps with a gap drainage impeller was investigated by Zhu and Chen [12]. It is found that the formation and development processes are influenced by the attack angle. Moreover, the gap between the main and vice blade causes the formation of this phenomenon. Neuman et al. [13] conducted an experimental study to survey the gas entrainment in centrifugal pumps in two different installation positions of horizontally and vertically. Their results demonstrated that compared the inlet flow conditions, the installation position has negligible impact on the pump performance. Oil cavitating flow in a centrifugal pump was modelled by Li [14]. He presented a new correlation between volume ratio of vapour plus non- condensable gas- to- liquid and the pump head coefficient. The effects of volute throat enhancement and viscous fluids on the centrifugal pump performance were studied by Khoeini et al. [15]. They observed by making appropriate change in the volute throat area, the head can be increased by 6.4%. The impacts of the blades outlet edge profile on the pressure pulsation and performance of centrifugal pumps were presented by Gao et al. [16]. Data analyses indicated that blades outlet edges with ellipse-shaped on pressure side and also with ellipse-shaped on both sides have the best effect on decreasing vortex intensity at trailing edge of blades. Design optimization of a centrifugal pump was performed to enhance the pump performance by Heo et al. [17]. By using surrogate models a considerable efficiency increase was resulted in their studies. Lei et al. [18] investigated the impacts of axial clearances on the pump efficiency. They found that the volumetric efficiency is largely affected by the axial clearance in comparison with the hydraulic and mechanical efficiencies as it is the major factor for the efficiency variations by changing of the axial clearances. The flow characteristics through diffuser passage of a pump were surveyed experimentally by Si et al. [19]. At low flow rate the maximum loss was observed inside the vaneless part of the diffuser due to the rotor- stator interaction. Besides, at flow rates higher than the diffuser design flow rate, large separated region after the diffuser throat on the pressure side was resulted. Unsteady pressure pulsation of a centrifugal pump with slope volute was analysed by Zhang et al. [20]. They accomplished lower Received October ; revised January ; accepted for publication February : Review conducted by Xuelin Tang. (Paper number O17068C) Corresponding author: Davood Khoeini, d.khoeeni@me.iut.ac.ir 191

2 pressure pulsation level by sloped volute pump compared to the conventional spiral volute pump. Influences of volute tongue and impeller geometry on the centrifugal pump performance were studied by Dong et al. [21]. By enhancing the gap between the tongue and impeller to 20% of impeller radius, minimum noise was obtained in their investigations. Zhu et al. [22] performed numerical and experimental studies on the half vane diffusers of a centrifugal pump. They observed that the efficiency rises by 2.5 percent owing to the half vane diffuser on the downstream side of the impeller rather than that of the impeller without it. A deep- well centrifugal pump with different diffusers was examined by Zhou et al. [23]. Their results illustrated that by three- dimensional return diffuser higher performance are obtained in comparison with the cylindrical return diffuser. Performance improvement of diffuser vanes through shape optimization were carried out by Goel et al. [24]. A reduction of total pressure losses of 8 percent by modifying diffuser vane shapes was achieved from their analyses. Sinha et al. [25] surveyed flow field through a vaned diffuser during onset and developed states of rotating stall. In their studies increasing the leakage and reverse flow intense within a stalled diffuser passage by decreasing flow rate were observed. Kergourlay et al. [26] investigated the influences of impeller splitter blades on the centrifugal pump performance. They achieved higher head values and lower pressure fluctuations by using impeller splitter blades rather than that of the impeller without splitter blades. An energy saving of 6.6 percent was resulted from a deep well pump impeller equipped with splitter blades by Golcu et al. [27]. Miyamoto et al. [28] studied splitter blade effects on the performance of a centrifugal pump and they found lower blade loading and higher total pressure and tangential velocity. As mentioned above, however, numerous studies have been conducted to enhance the performance of centrifugal pumps and some research have been performed on the splitter blades effects and impeller diffuser influences on centrifugal pumps separately but the combination effects of splitter blades and impeller diffuser particularly angular ones has not been considered to the knowledge of the authors, yet. Therefore, this study describes the simultaneous influences of splitter blades (Ls=0, Ls=0.45L and Ls=0.75L) and conventional impeller diffuser (α=0 o ) and angular impeller diffuser (α=10 o ) on the performance of centrifugal pump numerically and experimentally. 2. Centrifugal pump main parts Different parts of a centrifugal pump, with specific speed of 18.4 (Eq. 1), containing regions of inlet, impeller and volute casing are demonstrated in Fig. 1. Furthermore, in Table 1 all parameters of the centrifugal pump such as suction and discharge pipes diameters, impeller and diffuser diameters, number of impeller blades and diffuser vanes, inlet and outlet angle of blades, blade thickness and blade height are given. 0.5 N Q N s = 0.75 (1) H where rotational speed (rpm), flow rate (m3 /s) and head (m) are shown with N, Q and H respectively at BEP (Best Efficient Point). Fig. 1 Centrifugal pump main parts Table 1 Main centrifugal pump parameters Cases Suction pipe dia. Discharge pipe dia. Dimension 200 mm 200 mm Impeller dia. 500 mm Rev. Speed 1475 rpm Inlet blade angles Outlet blade angles Number of blades Blade height Blade thickness mm 8 mm Wrap angle 150 o Base Diffuser Diffuser Number Cases circular inner Dia. outer Dia. of vanes width Dimension 504 mm 604 mm 6 42 mm 192

3 3. Experimental Test Set up The test setup scheme utilized in this study is shown in Fig. 2. Based on the [29], water at 25 o C has been regarded as working fluid. By using an electrical AC driver, 1475 rpm, the centrifugal pump is driven. In fact, an electromagnetic flowmeter has been employed at discharge pipe to measure flow rate (Q). In order to control the operation of the pump a globe valve installed at discharge of the tested pump. Pump suction and discharge pressures have been measured and recorded under each test condition. Eventually, all performance curves in different flow rates based on the [29, 30] have been achieved. In addition, according to the [31], the head, flow rate and absorbed power uncertainties have been calculated and they are ±2.8%, ±2.2%, ±2.9% respectively. 4. Geometry 0. Gate valve 6. Pressure gage 1. Flow meter 7. Gate valve 2. Pressure gage 8. Water storage 3. Suction pipe 9. Coupling 4. Tested centrifugal pump 10.Electrical AC driver 5. Discharge pipe 11. Chasis Fig. 2 Experimental test apparatus Schematic view of the impeller and impeller diffuser that was fixed by bolts to the volute is depicted in Fig. 3. As it can be seen the divergence angle (α) of impeller diffuser walls has been considered 0 o and 10 o in the present study. By using computational analyses each impeller and diffuser has been surveyed separately and finally the optimum impeller and diffuser shapes were obtained, built and tested experimentally. Fig. 3 Sectional view of the impeller and angular diffuser for centrifugal pump (α: wall angle of diffuser) 5. Mesh generation and grid study Computational grid is shown in Fig. 4. Grids are refined in the vicinity of acute regions and the structured grid has been used in the proximity of the all walls and unstructured mesh has been used in other regions of computational domain. In order to enhance the accuracy of computation, the optimum numbers of grids have been analyzed, see Table. 2. Eventually minimum error was achieved by different iterations and the last one, 1797*1000 cells, has been considered in this study. 193

4 Fig. 4 Computational grid for flow domain Table 2 Grid study Grid size ( 1000) Torque (N.m) Governing Equations As the working fluid in this steady state study is incompressible, the equations of the Navier-Stokes have the following forms [32]: + ( U ) = 0 t ( U ) +.( UU ) = p +.( ) + g + F t where fluid density, velocity, pressure, stress tensor and source term (centrifugal force) are shown by ρ, U, p, τ and F respectively. For diffusion terms, central difference discretization and for convective terms, high resolution has been reg arded in computations. Total pressure at inlet boundary (approximately 1.2 bar) and mass flow rate (different mass flow rates to generate performance curves) at outlet boundary and the no slip boundary condition at all walls are considered in this research. Also turbulence model of SST has been employed in computations as well. Indeed, the above mention ed equations have been discretized by using a three-dimension Navior-stokes CFD code based on finite volume method and iterations have been done until the converging criteria of 10-6 for all residual figures. 7. Comparison of the numerical and experimental results As shown in Fig. 5, the numerical and experimental results of the original centrifugal pump, without splitter blades and impeller diffuser, have good agreement and the highest deviation between them is 7% at similar operating conditions (working fluid, inlet pressure and uniform flow). (2) (3) Fig. 5 Head as a function of flow rate, numerical and experimental results 194

5 8. Results and Discussion In order to consider various aspects of flow field in the centrifugal pump calculations, the computation domain has been regarded three- dimensional in this study. In fact, three different splitter blade lengths, Ls=0, Ls=0.45L and Ls=0.75L, in three different cases of impeller with impeller diffusers of α=0 o and α=10 o and also with no diffuser studied numerically and finally optimum ones of impeller and diffuser were manufactured and tested thoroughly. The splitter blades have been installed in the center line between two main blades. Also main and splitter blades have exactly similar shapes (the leading and trailing angles, thickness and height) but different lengths. Figure 6 shows changes of differential head of the centrifugal pump versus flow rate for impeller without impeller diffuser. As shown the splitter blades have profound impact on the head values and provide more smooth differential head curves in comparison with the original impeller (without splitter blade). Actually, the maximum head rise of 31 percent was obtained by using splitter blade of 0.75L at high flow rate rather than that of the original impeller. Besides, at all flow rates it is observed that splitter blades of 0.45L and 0.75L deliver the same head values. Moreover, splitter blades broaden operating region of the centrifugal pump as well (Figs. 6-7). The reason is that employed splitter blades contribute to the better flow conduction through the impeller channels and prevent the formation of low velocity regions as well. Therefore transferred energy to the fluid is enhanced and higher head values are accomplished. Variation of overall efficiency against flow rate for mentioned cases is demonstrated in Fig. 7. Numerical results show that the splitter blades of 0.75L improved overall efficiency by 1.5 percent at BEP, Best Efficiency Point, compared to the original impeller and BEP of the impeller with splitter blades of 0.75L shifted approximately by 19.5 percent towards the high flow rate due to the different effects of splitter blades with different lengths. Additionally at low flow rates there are lower overall efficiency values rather than that of the original impeller whereas at high flow rates, the splitter blades not only increase pump operating region but also increase the overall efficiency considerably. The reason why when the splitter blades are used, the efficiency of the pump increases and BEP is moved forward in the head- flow rate performance curves, is that by adding proper number and shape of the splitter blades, the secondary flows generated between the impeller blades are weakened and less energy loss is obtained. Fig. 6 Variation of head with flow rate for impeller without impeller diffuser Fig. 7 Variation of overall efficiency with flow rate for impeller without impeller diffuser 195

6 Concurrent influences of impeller diffuser of α=0 o with impeller splitter blades on the head and overall efficiency of centrifugal pump are indicated in Figs. 8 and 9 respectively. A head enhancement of 8.9 percent has been achieved by merely employing of impeller diffuser of α=0 o which was located on the downstream side of the impeller. At high flow rate, head value of the impeller with splitter blade of 0.75L and vaned diffuser of α=0 o increased by 48 percent compared to the original impeller. Furthermore, in cases of splittered impeller equipped with vaned diffuser of α=0 o, lower slope head curves are resulted. Indeed, vaned diffuser of impeller improves the conduction of flow towards the volute casing and consequently the head values have been increased considerably. As depicted in Fig. 9 the efficiency of BEP rose by 2.5 percent by using impeller diffuser of α=0 o and splitter blade of 0.75L concurrently. Moreover, based on numerical data, BEP moves 27.2 percent toward the maximum flow rate because of differing energy conversion (kinetic to potential) and hydraulic losses of different configurations. Higher overall efficiency values are accomplished at high flow rates while lower overall efficiency values were resulted at low flow rates in comparison with the original impeller without diffuser, see Fig. 9. The main reason is that at high flow rate, the effect of secondary flow is considerable. Moreover, at high flow rate, the velocity of the flow at the impeller exit is very high and the pressure drop is higher when the proper impeller diffuser is not employed. Fig. 8 Variation of head with flow rate for impeller with and without impeller diffuser of α=0 Fig. 9 Variation of overall efficiency with flow rate for impeller with and without impeller diffuser of α=0 Figure 10 illustrates the variation of head with flow rate in different cases of original impeller with and without impeller diffuser. Furthermore, characteristic curves of splittered impellers with diffuser of α=10 o are presented in these figures. Based on the results a head growth of 15 percent is observed by inserting impeller diffuser of α=10 o in the volute casing of investigated centrifugal pump. It is found that the head value of the impeller equipped with a impeller diffuser of α=10 o and splitter blade of 0.75L is 1.51 times the head value of the impeller without them at high flow rate. Experimental tests of the mentioned configuration also reveal that there are reasonable agreement between the numerical and experimental results as highest discrepancy among them is about 6 percent. 196

7 Overall efficiency trends for impeller with and without diffuser α=10 o against flow rate are demonstrated in Fig. 11. Concurrently the use of impeller diffuser α=10 o and splitter blades of 0.75L improve efficiency of BEP by 3.4 percent at high flow rate. Other point is that a movement of 51 percent for BEP position toward the maximum flow rate has been resulted. Also there is a deviation of 3 percent between overall efficiency values of the numerical and experimental results for impeller with diffuser with α=10 o and splitter blades of 0.75L in such conditions. Data analyses showed that increasing the angle of impeller diffuser walls higher than a certain value causes the flow separation and flow blockage and other aspects accordingly resulting in a decrease in the efficiency. Fig. 10 Variation of head with flow rate for impeller with and without impeller diffuser of α=10 Fig. 11 Variation of overall efficiency with flow rate for impeller with and without impeller diffuser of α=10 In Figs. 13 to 21, pressure distributions of all mentioned impellers are depicted at the impeller mid- height plane (Fig. 12) at BEP. In Fig. 13 pressure distribution of original impeller (without diffuser and splitter blade) is shown. As seen it has the lowest pressure gradient of all other cases. By adding splitter blades to the original impeller higher pressure gradient is obtained (Figs ) and by equipping impeller with diffusers of 0 o and 10 o the values of pressure gradient increases profoundly (Figs. 16 and 17, respectively). Moreover, impeller diffuser of 10 o provides a bit lower pressure gradient in comparison with the impeller diffuser of 0 o and it is because of the more passage areas. Furthermore, less value of velocity has been achieved due to the wall diverging angle (α) as well. In fact, angular diffuser of α=10 o creates weaker interaction between impeller blades and diffuser vanes thanks to the enlarged flow passage. Therefore, pressure distribution is become more uniform at impeller with angular diffuser of α=10 o (Figs. 19 and 21). Besides, a pressure drop is caused in the immediate vicinity of the volute tongue of all analyzed cases. The mentioned pressure gradient is the highest in the case of original impeller equipped with vaned diffuser of α=0 o (Fig. 16). By increasing the flow passage through diverging the diffuser walls (α=10 o ), the stated pressure drop has declined and it is minimized in the case of pump without impeller diffuser (Fig. 13). The other point is that splitter blades have beneficial effects on creating more homogeneous pressure fields in the proximity of volute tongue and in all splittered impellers more uniform pressure field in this region can be seen compared with cases without splitter blades. Besides, as shown there is higher pressure drop on the leading edge of volute splitter (at the bottom of volute) of not vaned cases and not splittered impeller cases 197

8 (Figs. 13 to 17) while mentioned deficiency in that region of centrifugal pumps equipped with splitter blades and vaned diffuser concurrently has been minimized (Fig. 18 to 24). Fig. 12 Mid-height plane of the impeller Fig. 13 Impeller without diffuser and splitter blade Fig. 14 Splittered impeller of 0.45L without diffuser Fig. 15 Splittered impeller of 0.75L without diffuser Fig. 16 Non-splittered Impeller with diffuser of α=0 Fig. 17 Non- splittered Impeller with diffuser of α=10 198

9 Fig. 18 Splittered impeller of 0.45L with diffuser of α=0 Fig. 19 Splittered impeller of 0.45L with diffuser of α=10 Fig. 20 Splittered impeller of 0.75L with diffuser of α=0 Fig. 21 Splittered impeller of 0.75L with diffuser of α=10 Velocity streamlines of all investigated impellers are demonstrated in Figs. 22 to 30 at BEP. It is observed that due to the mismatch between the impeller blade angles and flow angles there are some re-circulation on the pressure sides of non-splittered impeller blades (Figs. 22, 25 and 26) and by inserting splitter blades these re- circulations are dying out. Consequently, the higher head values by decreasing the losses related to them are accomplished. Moreover, higher velocity gradient are observed on the circumferences of impeller without impeller diffuser. Actually, by installing impeller diffuser of α=0 o more uniform flow field on the impeller passageways are achieved (Fig. 25). Angular impeller diffuser of α=10 o because of the more flow passagewayes provides lower velocity gradient rather than that of the impeller equipped with diffuser of α=0 o. Additionally, restriction between the volute tongue and diffuser vanes causes some weak wakes in the proximity of volute tongue but their effects are negligible (Figs. 25 to 30). Fig. 22 Impeller without diffuser and splitter blade 199

10 Fig. 23 Splittered impeller of 0.45L without diffuser Fig. 24 Splittered impeller of 0.75L without diffuser Fig. 25 Non-splittered Impeller with diffuser of α=0 Fig. 26 Non- splittered Impeller with diffuser of α=10 Fig. 27 Splittered impeller of 0.45L with diffuser of α=0 Fig. 28 Splittered impeller of 0.45L with diffuser of α=10 Fig. 29 Splittered impeller of 0.75L with diffuser of α=0 Fig. 30 Splittered impeller of 0.75L with diffuser of α=10 200

11 Velocity distributions of all cases are shown in Figs. 31 to 39 at BEP. As illustrated there is minimum velocity uniformity in Fig. 31 as in this configuration no splitter blade and impeller diffuser has been utilized. Positive effects of splitter blades on velocity distribution are seen in Figs. 32 and 33 (splittered impellers) which are more beneficial rather than the role of merely impeller diffuser at meridian of impeller passageways (Figs. 34 and 35) while, at impeller output, more homogeneous velocity fields have been observed in latter ones. Other point is that compared to the velocity field of cases with impeller diffuser of α=0 (Figs. 34, 36, 38), impeller diffuser of α=10 contributes to making more uniform velocity fields thanks to larger passageways of angular diffuser that increases energy transferring that leads to higher performance of centrifugal pump in this case (Fig. 39). Fig. 31 Velocity distribution of impeller without diffuser and splitter blade Fig. 32 Velocity distribution of splittered impeller of 0.45L without diffuser Fig. 33 Velocity distribution of splittered impeller of 0.75L without diffuser Fig. 34 Velocity distribution of non-splittered impeller with Fig. 35 Velocity distribution of non- splittered impeller with 201

12 diffuser of α=0 diffuser of α=10 Fig. 36 Velocity distribution of splittered impeller of 0.45L with diffuser of α=0 Fig. 37 Velocity distribution of splittered impeller of 0.45L with diffuser of α=10 Fig. 38 Velocity distribution of splittered impeller of 0.75L Fig. 39 Velocity distribution of splittered impeller of 0.75L with diffuser of α=0 with diffuser of α=10 In Figs. 40 to 45 velocity streamlines of different cases have been depicted at cross section of volute at BEP. It is observed that secondary flows of original case (without splitter blades and vaned diffuser) are asymmetry (Fig. 40) and by employing impeller splitter blades they become stronger as shown in Fig. 41. While, by equipping the mentioned configuration with impeller diffusers symmetry secondary flows are achieved owing to flow conduction through them. Other point is that installing splitter blades to the equipped impeller with diffuser of α=0 enhances the strength of symmetry secondary flows that is clearly apparent in Fig. 44. Unlike the stated behavior of flow in case of impeller with diffuser of α=0, splitter blades addition to the impeller with diffuser of α=10 positively affects the flow field. In other words, more uniform flow has been resulted owing to the simultaneous role of splitter blades and diffuser of α=10 (Fig. 45) which contributes to higher performance of centrifugal pump by reducing secondary flows. Fig. 40 Volute velocity streamlines- impeller without diffuser Fig. 41 Volute velocity streamlines- splittered impeller of 0.45L 202

13 and splitter blades without diffuser Fig. 42 Volute velocity streamlines- non-splittered impeller Fig. 43 Volute velocity streamlines- non- splittered impeller with diffuser of α=0 with diffuser of α=10 Fig. 44 Volute velocity streamlines- splittered impeller of 0.45L Fig. 45 Volute velocity streamlines- splittered impeller of 0.45L with diffuser of α=0 with diffuser of α=10 9. Conclusions Based on the results the following conclusions of studying simultaneous effects of different splitter blades (Ls=0, Ls=0.45L and Ls=0.75L) and impeller diffusers (α=0o, α=10o) and also impeller with no diffuser on the performance of a centrifugal pump is drawn: 1. Splitter blades have profound impacts on the head values of centrifugal pumps as at high flow rate, head increased by 31 percent for splittered impeller of 0.75L rather than that of the original impeller (without splitter blades). In such conditions the efficiency of BEP rises by 1.5 percent as well. 2. By simultaneous using of impeller diffuser of α=0o and splitter blades of 0.75L head and overall efficiency valuess enhance by 48 and 2.5 percent respectively in comparison with merely using of the original impeller at high flow rate. The results show a head increase of 8.9 percent for the impeller with only diffuser of α=0o. 3. Amongst all surveyed configurations, the impeller with diffuser of α=10o and splitter blades of 0.75L has the best performance as the head and efficiency are 51 and 3.4 percent greater than that of the original impeller (without impeller diffuser and splitter blades) at high flow rate. It seems that more studies are required regarding the impacts of angular impeller diffusers on pressure fluctuations, cavitation performance and other lengths of splitter blades and so forth in future investigations of centrifugal pumps. Nomenclature F L s L P τ Source term Length of splitter blades Length of original impeller blade Pressure Fluid Density Stress tensor scale U Ns N Q H Velocity specific speed, RPM Flow rate Head References [1] Khoeini D., Tavakoli M. R., 2018, The optimum position of impeller splitter blades of a centrifugal pump equipped with 203

14 vaned diffuser, Journal of FME Transactions, Vol. 46. No. 2, pp [2] Yun L., Dezhong W.g, Junlian Y., Youlin C., Chao F., 2017, The Effect of Different Inflows on the Unsteady Hydrodynamic Characteristics of a Mixed Flow Pump, International Journal of Fluid Machinery and Systems, Vol. 10, No. 2, pp [3] Shigemitsu T., Fukutomi J., Matsubara T., Sakaguchi M., 2017, Unsteady Flow Condition of Centrifugal Pump for Low Viscous Fluid Food, International Journal of Fluid Machinery and Systems, Vol. 10, No. 4, pp [4] Liu D., Tang C., Ding S., Fu B., 2017, CFD-DEM Simulation for Distribution and Motion Feature of Crystal Particles in Centrifugal Pump, International Journal of Fluid Machinery and Systems, Vol. 10, No. 4, pp [5] Wu D., Ren Y., Mou J., Gu Y., 2017, Investigation of Pressure Pulsations and Flow Instabilities in a Centrifugal Pump at Partload Conditions, International Journal of Fluid Machinery and Systems, Vol. 10, No. 4, pp [6] Shim H. S., Kim K. 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Computational fluid dynamics analysis of a mixed flow pump impeller

Computational fluid dynamics analysis of a mixed flow pump impeller MultiCraft International Journal of Engineering, Science and Technology Vol. 2, No. 6, 2010, pp. 200-206 INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY www.ijest-ng.com 2010 MultiCraft Limited.

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