- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 512523, 11 pages

http://dx.doi.org/10.1155/2013/512523

## Analysis on Energy Conversion of Screw Centrifugal Pump in Impeller Domain Based on Profile Lines

^{1}School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China^{2}Gansu Lanpec Technologies Co. Ltd., Lanzhou 730070, China^{3}Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Received 31 October 2013; Accepted 6 November 2013

Academic Editor: Shi Wei-dong

Copyright © 2013 Hui Quan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to study the power capability of impeller and energy conversion mechanism of screw centrifugal pump, the methods of theoretical analysis and numerical simulation by computational fluid dynamics theory (CFD) were adopted, specifically discussing the conditions of internal flow such as velocity, pressure, and concentration. When the medium is sand-water two-phase flow and dividing the rim of the lines and wheel lines of screw centrifugal pump to segments to analyze energy conversion capabilities which along the impeller profile lines with the dynamic head and hydrostatic head changer, the results show that the energy of fluid of the screw centrifugal pump is provided by helical segment, and the helical segment of the front of the impeller has played the role of multilevel increasing energy; the sand-water two phases move at different speeds because the different force field and the impeller propeller and centrifugal effect. As liquid phase is the primary phase, the energy conversion is mainly up to the change of liquid energy, the solid phase flows under the wrapped action of liquid, and solid energy is carried out through liquid indirectly.

#### 1. Introduction

As a new kind of impurity pump, screw centrifugal pump combines the advantages of screw pump and centrifugal pump, and the special structure can bring into play their advantages, sufficiently (Figure 1). Comparing with the traditional impurity pump, screw centrifugal pump has a series of strong advantages, such as without clogging, suction performance, adjustment of the performance, and cavitation resistance, and with no load, high efficiency, and high efficiency zone width [1, 2].

Screw centrifugal pump internal flow apparently shows mixed spiral movement because of the unique structure of impeller, comparing with ordinary centrifugal pumps; there is still much room for efficiency improvement for screw centrifugal pump. Screw centrifugal pump is a typical sand-water two-phase flow pump, due to the different density of the solid and liquid phases, resulting in the slip velocity, which does not only affect the hydraulic performance of the pump, but also makes it easy for the solid particles and over-current surface conflicts caused by the wear of the pump flow parts and other problems [3–5]. Therefore, the study of mechanism of energy conversion and the analysis of factors that impact the conversion have a great significance for the improvement of efficiency. It is also the primary problem that optimizes the design methods of established impurity pump and advanced design concept.

#### 2. Performance Testing

##### 2.1. Parameters of 150X100LN-32 Type in Screw Centrifugal Pump

The 150X100LN-32 type screw centrifugal pump is used as a model pump. The main parameters are summarized in Table 1.

##### 2.2. The Establishment of Test System

Under different working conditions and with different media, the pump test method is a method that uses the test device to make a direct measurement of the performance of the pump. It is the most direct, most effective, and most reliable research method of the pump.

The performance test of the screw centrifugal pump is in order to measure the relationship between the flow rate and the pump’s head, shaft power, and efficiency and get the complete performance curve.

With the advantages of the open test rig, such as simple structure, easy to use, good cooling conditions, and good stability, in order to operate easily and save the cost, under the test’s requirements, this test rig uses an open loop operation and horizontal arrangement, as shown in Figure 2.

##### 2.3. The Drawing of Flow Performance Curve and Analysis

Through the performance test of the 150X100LN-32 type screw centrifugal pump on the test rig, the outlet pressure, flow rate, torque, and speed are measured, and then the performance curves are drawn and shown in Figure 3.

As can be seen from Figure 3, is greatly affected by . It is reflected on the characteristic curve that is like a steep drop of a straight line. Corresponding to the smaller flow rate change, the head should have a greater change. So, the pump of this characteristic curve is very suitable for sewage treatment occasions.

As can be seen from the efficiency-flow curve, the optimal condition of 150X100LN-32 screw centrifugal pump is beside the point of m^{3}/h. It is a tendency to the working condition of large flow rate. The maximum efficiency of the pump is 63%. It is close to the design efficiency of 65%. In the flow rate range from m^{3}/h to m^{3}/h, the pump efficiency is higher than 50%. Compared with the general water pump, the screw centrifugal pump shows a low overall efficiency. This is because that the screw centrifugal pump is designed for a two-phase flow pumping. In pumping sand-water two-phase flow, the efficiency of the screw centrifugal pump is higher than that of the other sewage pumps. With a large range, the shaft power curve of the test pump is close to a straight line and rises slightly. When the flow rate reaches m^{3}/h, the shaft power begins to fall. So, the motor will not overload if we select the pump’s motor according to the shaft power value of the maximum power point.

#### 3. Theoretical Basis and Modeling

##### 3.1. Theoretical Basis

From the point of view of energy conversion, pump converted mechanical energy into liquid energy by the impeller; so that the liquid state of motion has changed. This paper intended to analyze energy conversion and transfer of mechanical fluid through the Euler equation [6–10].

Euler equation is expressed as

As a result, the theoretical energy has the following two parts, the first item is called the dynamic head which is mainly due to the rotation of the impeller. It partially converts into the hydrostatic head after the impeller guide vanes or volutes; the second item and the third item are called the hydrostatic head which is the added value of hydrostatic head when the fluid through the impeller. We divided the obtained by the fluid at the impeller energy into the dynamic pressure and static pressure head, which provides a theoretical basis for numerical simulation to study the acting ability of the impeller.

##### 3.2. Modeling and Meshing

Machine model is shown in Figure 4 according to the parameters in Table 1.

For computational domain, mesh type is unstructured grid, the grid node number of flow channel is 89 403 and the unit number is 507 886, and grid-independent inspection [11].

#### 4. Numerical Simulation and Analysis

##### 4.1. Instantaneous Efficiency Head and Pump Instantaneous Efficiency in a Cycle Water under the Rated Conditions

(1)According to the numerical simulation of the whole flow passage complex turbulent flow field of the screw centrifugal pump under different conditions, the following formula can be applied to predict the head and efficiency [12–15].

The calculation method of instantaneous head (see formula (2)) is as follows: is calculated as follows:

The calculation method of instantaneous efficiency is as follows: (2)In order to facilitate the analysis of research, the pump’s instantaneous head and efficiency of a cycle can be obtained by means of unsteady numerical simulation. The result is shown in Figures 5, 6, and 7.

Figures 5 and 6, respectively, are the wave curves of pump instantaneous efficiency head and pump instantaneous efficiency in cycle water under the rated conditions.

As can be seen from the graph, with the rotating of the impeller, instantaneous efficiency and instantaneous head of pump display a periodic variation that is close to a sine curve, and change trends are almost the same. There are a maximum and a minimum value in a period, and its two extreme value points correspond to the maximum radius around a specific position.

Figure 7(a) is the position of the impeller corresponding to the maximum of the instant head; Figure 7(b) is the position of the impeller corresponding to the minimum of the instant head. Figure 7 shows the location of impeller when instantaneous efficiency and instantaneous head achieve the maximum and minimum values. Figure 7(a) shows the impeller position when instantaneous efficiency and instantaneous head achieve maximum value; we can see that the maximum radius place of the impeller has just turned to the VI section; this is because, with the rotating of the impeller, the volume becomes smaller and compression quantity increases gradually between the maximum radius place and the volute export, which is equivalent to the impeller working within the medium in volute, at the same time, with reflux at the casing tongue. The backflow strengthens and the energy loss increases when the impeller maximum radius place is gradually close to casing tongue. So pump instantaneous head is the largest when impeller turned to as shown in Figure 7(a) shows position, and the change of torque is very small in the pump running, at the moment, the pump efficiency reached a maximum in a period. Figure 7(b) shows that instantaneous efficiency and instantaneous head minimum value correspond to the location of the impeller, which the impeller just turned casing tongue in maximum radius the position; this is because the working principle of the screw centrifugal pump is similar to the rotor type volume pump, which is the use of content product changes of pump cylinder to transfer energy and transport liquid. And the screw centrifugal pump between the maximum radius place and volute export volume with the rotation of the impeller change, when the maximum radius place is just after the casing tongue and the volume is the biggest in pump cylinder inside, equivalent to impeller of volute medium power capability of the most weak, so the pump instantaneous head is at its minimum.

##### 4.2. Determining the Test Program

We take piecewise monitoring points of impeller (profile lines shown in Figure 8), analyze their work capacity, and complete the following processes [16–18]. Taking monitoring points along the impeller, their acting ability is analyzed following processes: Establish monitoring points—Numerical simulation—get the monitoring—point parameters (velocity, pressure)—the change of dynamic pressure and static pressure head along the rim and hub.

The impeller axis as the axis in Pro/E software, the application of projection method make rim line and wheel line projected on the impeller, the impeller shaft plane projection rotated 36° with the upper and lower flange and the intersection of the wheel to take the monitoring points in order to get the uniform monitoring points and well reflect the flow field changes along the various parts of the impeller. Monitoring points shown in Figure 9.

##### 4.3. Numerical Method

Screw centrifugal pump flow consists of impeller and volute; the surface of the impeller rotating coordinate system is seen as the relative coordinate system, so the flow within the impeller can be regarded as the steady flow, but the internal flow field of the entire flow channel can be regarded as the 3d incompressible stable state turbulent flow field. Boundary conditions of velocity inlet are adopted at the entrance and the boundary conditions of natural outflow are adopted at the exit, at the same time, the boundary condition of the no-slip is adopted at the wall, such as the inlet section, impeller cone section, or volute wall. The region near the wall uses standard wall functions [19].

To establish continuous equations, N-S equations, and other control equations at the relative coordinate system, we used a standard turbulence model to close the equations [20]. In this Paper, we adopt the Euler multiphase model since it contains a sand water specific case of the sand-water two-phase flow. In order to save computing time under the premise of ensuring the accuracy as much as possible, the convection terms of discrete first-order up wind scheme, dissipation of the iterative solution of central difference scheme, set the convergence accuracy 10^{−5}, pressure—the velocity of iterative solution of the equation use the SIMPLE algorithm.

##### 4.4. The Results of Numerical Simulation

Transportation of sand-water two-phase flow of screw centrifugal pump of simulation is sandy water that it is common in the test. Water in liquid is the first phase, sand in solid phase is the second phase, the Euler multiphase flow model is chosen; velocity imports conditions of unsteady state along the axial are adopted in computational domain. In the definition of solids volume concentration (vof) assume inlet concentration distribution is uniform and conduct numerical simulation, obtaining the pressure distribution, velocity distribution, the solid concentration distribution, and correlation curve of interior flow of screw centrifugal pump, in which the two-phase flow properties are shown in Table 2.

###### 4.4.1. Results and Analysis of Flow Field

Through analysis of Figure 10, the pressure range of the water is broader than the solid liquid two phase flow; this effect is related to the volute. Volute is mainly used for collecting the liquid, guide to discharge pipe, and will eventually convert liquid kinetic energy into static pressure energy. Therefore, when the medium is replaced with sand water of two-phase flow, the pressure on the volute increases.

Analysis of Figure 11 shows that, for sand-water two-phase flow in the liquid phase and solid phase, the speed range is different at the work surface of impeller, the maxima of liquid phase velocity is significantly larger than that of solid phase, the minimum is smaller than that of the solid phase, the speed range of liquid phase is wider than that of the solid. This is because on one hand the liquid phase is the main phase, while on the other hand sand density is heavy and inertia is larger, so the velocity slip emerges, which also shows that the slip velocity will appear when the impeller works for water sand of two-phase flow.

##### 4.5. Energy Conversion Analysis of Impeller

For the Euler equations, water sand medium of two phases is divided into water and sand (sand diameter mm, volume concentration vof = 20%); then the Euler equations of the two-phase flow are as follows.

Figure 12 analyzes that the changes of liquid phase and solid phase pressure head and static pressure head except at the exit centrifugal section where the overall change is basically consistent under the action of impeller and the changes are similar to the single-phase water medium.

This is because the solid phase volume concentration and particle diameter are relatively smaller in the simulated condition; solid phase will not generate great impact on flow of the liquid phase. Dynamic pressure head and static pressure head are significantly different in the two phases: the dynamic pressure head of solid phase is higher than that of the liquid phase and the static pressure head of liquid phase is higher than that of the solid phase. This is because, in the work process, due to the different stress field, velocity of solid phase is lower than that of the liquid phase and solid has “relative blocking" effect on channel of liquid flow, so that the liquid flow passage area is relatively narrow and liquid flow distortion velocity increases. In the impeller centrifugal paragraph exit, fluid phase not only by the flow velocity distortion, but also by the volute flow area distortion in the working face and back of either the rim or hub so that the dynamic pressure head and static pressure head get to complicate at the outlet. Among them, the common characteristic is that because the solid particles specific gravity is greater than its pressure value in the liquid flow, the static pressure head changes of liquid flow are significantly faster than those of solids. Except impeller centrifugal section outlet flange back, the pressure static head of work face and back has a sharp decline in the impeller hub exit section. On one hand it is because the pressure of the centrifugal section is maximum in a maximum radius and then as the angle increases the pressure first decreases and then increases, but still less than the pressure of the maximum radius; the main reason is that the working surface of the centrifugal section radial distance becomes short and blade outlet angle is relatively smaller, so that the centrifugal force is less than the maximum radius, so the working is less for fluid; on the other hand centrifugal axial distance is shorter, impeller play the important function on velocity from the axial change to radial at the some time, it generates the energy loss in the maximum radius of back face when solid and fluid into impeller domain. At different degree, the dynamic pressure head and the pressure head are reduced at the outlet of impeller.

##### 4.6. The Influences of the Two-Phase Flow Medium on Energy Conversion

Under the design conditions, in addition to simulated two-phase flow volume concentration vof = 20%, mm, simulated volume concentrations were 40% and 60%, and diameters were 0.5 mm and 1 mm two-phase flow, in order to analyze the effects of media on energy conversion.

###### 4.6.1. The Influences of the Particle Diameter of Solid Phase in Two-Phase Flow Medium on Energy Conversion

Compare the particle diameters of 0.076 mm and 1 mm and the changes of the dynamic pressure head and the static pressure head of liquid phase and solid phase with angle changes. It can be seen from Figure 10, no matter liquid or solid phase, solid particles are greater; the proportion is the greater, therefore, the changes of dynamic pressure is more slower; small proportion of the particle size is easy to change, and the spiral section of the centrifugal transition after dynamic head decreased at first and then increased. There are larger changes. Hydrostatic head changes of the liquid and solid is the same trend. When the medium is large particles, the hydrostatic head of the pump changes is slower than the small particles. The same speed gives the big size obtained a higher energy. Therefore, the increased value of diameter of 1 mm is larger than the diameter of 0.076 mm (Figure 13).

###### 4.6.2. The Influences of the Concentration of Solid Phase in Two-Phase Flow Medium on Energy Conversion

From Figures 14(a) and 14(c) it can be seen, concentration in centrifugal section of spiral centrifugal pump is higher, and the dynamic pressure head of liquid is larger. The dynamic head change of liquid phase in elsewhere is similar. Due to the increasing concentration, solid phase proportion increases, the dynamic pressure head has bigger change, small volume concentration speed changes easily, and so the changes of dynamic pressure head are obvious under the action of the impeller.

From Figures 14(b) and 14(d) it can be seen that, on the liquid hydrostatic head, in a helical section, the coupling of the liquid of small solid volume concentration and solid phase is better. In the centrifugal section, due to the sudden change of velocity direction, the inertia of the large volume concentration of solid phase is large, static pressure heads are not easy to change, and the small volume concentration of solid phase is just the opposite; due to the axial velocity shift to the radial velocity in the transition section, there has been large energy loss and static pressure head has dropped suddenly. The changes of the small volume concentration of solid phase are similar to the changes of water; the inertia of the large volume concentration of solid phase is large; when volume concentration of solid phase is 60% in simulation, the state changes is smaller, static head only weak increasing.

#### 5. Conclusions

(1)In the process of screw centrifugal pump impeller power, the spiral section hydrostatic head and the dynamic pressure head increase the overall trend positively, whereas the centrifugal section has larger fluctuation. At the maximum radius, static head reaches the maximum, which explains that the pressure of screw centrifugal pump is mainly generated by the spiral segment; spiral segment of impeller front plays a role of multilevel increasing energy, which explains that the work of impeller is mainly provided by spiral section.(2)When the particle size is relatively small, at the same time, volume concentration is enough big, the two flow coupling of solid phase (secondary phase) and liquid (host phase) is very good, velocity slip phenomenon is not obvious.(3)Allow one line off space between the table or figure and the adjacent text.(4)The coupling of the solid phase (secondary phase) and liquid phase (main phase) of two-phase flow is very good, and the phenomenon of velocity slip is not obvious. When the convey medium is the sand-water two-phase flow, the solid-phase particle size is relatively small, and a volume concentration is large enough.

#### Nomenclature

: | Peripheral speed (m^{3}/s) |

: | Absolute speed (m^{3}/s) |

: | Relative velocity (m^{3}/s) |

: | Head (m) |

: | Volume flow (m^{3}/h) |

: | Blade height (mm) |

: | Diameter (mm) |

: | Shaft power (kw) |

: | Area weight average pressure |

: | Efficiency (%) |

: | Vane angle (°) |

: | Wrap angle (°) |

: | Density (kg/m^{3}) |

: | Radius (mm) |

: | Volume concentration (%) |

: | The rotation angular velocity. |

*Abbreviations*

CFD: | Computational fluid dynamics |

150X100LN-32: | The type of screw centrifugal pump. |

*Subscripts*

: | Liquid |

: | Sand |

1: | Inlet |

2: | Outlet |

: | Theory |

: | Volume |

: | Lift |

: | Centrifugal force |

: | Infinity |

: | Instant. |

#### Conflict of Interests

All the authors declare that there is no conflict of interests regarding the publication of this paper. They do not have a direct financial relation with the commercial identities mentioned in their paper that might lead to a conflict of interests for any of them.

#### Acknowledgment

This project was supported by National Natural Science Foundation of China (Grant no. 51079066).

#### References

- M. Stahle and D. Jackson, “The development of a Screw centrifugal pump for handling delicate solids,”
*World Pumps*, no. 2, pp. 53–55, 1982. View at Scopus - A. A. Zhirnov, L. A. Pavlovich, and S. L. Aleksandrov, “Effect of constructional and technological factors on the cavitational characteristics of screw-centrifugal pump assemblies,”
*Chemical and Petroleum Engineering*, vol. 15, no. 2, pp. 99–103, 1979. View at Publisher · View at Google Scholar · View at Scopus - M. Dular, R. Bachert, B. Stoffel, and B. Širok, “Influence of the velocity distribution at the inlet boundary on the CFD prediction of local velocity and pressure fields around a hydrofoil,”
*Experimental Thermal and Fluid Science*, vol. 32, no. 3, pp. 882–891, 2008. View at Publisher · View at Google Scholar · View at Scopus - L. I. Renian, Q. Hui, H. Wei, et al., “Influences of variable-pitch blade on the Screw centrifugal pump axial force Chinese,”
*Journal of Mechanical Engineering*, vol. 47, no. 14, pp. 158–163, 2011. - D. Wadnerkar, R. P. Utikar, M. O. Tade, et al., “CFD simulation of solid-liquid stirred tanks,”
*Advanced Powder Technology*, vol. 23, pp. 445–453, 2012. - I. V. Scherbatenko and V. I. Surikov, “Distribution of the absolute flow velocity behind the screw impeller of a centrifugal pump,”
*Khimicheskoe I Neftegazovoe Mashinostroenie*, no. 4, pp. 21–25, 2005. View at Scopus - F. C. Visser, R. J. H. Dijkers, and J. G. H. op de Woerd, “Numerical flow-field analysis and design optimization of a high-energy first-stage centrifugal pump impeller,”
*Computing and Visualization in Science*, vol. 3, pp. 103–108, 2000. - Y. Li, Z. Zhu, W. He, and Z. He, “Numerical simulation and experimental research on the influence of solid-phase characteristics on centrifugal pump performance,”
*Chinese Journal of Mechanical Engineering*, vol. 6, no. 25, pp. 1184–1189, 2012. - S. Yuan, Y. Li, and Z. He, “3-D calculation of solid-liquid two-phase turbulent flow within a non-clogging centrifugal pump,”
*Chinese Journal of Mechanical Engineering*, vol. 39, no. 7, pp. 18–22, 2003. View at Scopus - R. Li, B. Li, and W. Han, “Analysis on working characteristics of screw centrifugal pump,”
*Transactions of the Chinese Society of Agricultural Machinery*, vol. 36, no. 6, pp. 51–53, 2005. View at Scopus - S. Yuan, J. Zhou, J. Yuan, J. Zhang, Y. Xu, and T. Li, “Characteristic analysis of pressure fluctuation of unsteady flow in screw-type centrifugal pump with small blade,”
*Transactions of the Chinese Society of Agricultural Machinery*, vol. 43, no. 3, pp. 83–92, 2012. View at Publisher · View at Google Scholar · View at Scopus - B. K. Gandhi, S. N. Singh, and V. Seshadri, “Effect of speed on the performance characteristics of a centrifugal slurry pump,”
*Journal of Hydraulic Engineering*, vol. 128, no. 2, pp. 225–233, 2002. View at Publisher · View at Google Scholar · View at Scopus - R. Li, Q. Wang, J. Shen, et al., “Numerical simulation of solid-liquid two phase flow in the screw centrifugal pump,”
*Fluid Machinery*, vol. 12, no. 36, pp. 24–27, 2008. - S. Bross and G. Addie, “Prediction of impeller nose wear behaviour in centrifugal slurry pumps,”
*Experimental Thermal and Fluid Science*, vol. 26, no. 6-7, pp. 841–849, 2002. View at Publisher · View at Google Scholar · View at Scopus - K. V. Pagalthivarthi and R. J. Visintainer, “Solid-liquid flow-induced erosion prediction in three-dimensional pump casing,” in
*Proceedings of the ASME Fluids Engineering Division Summer Conference (FEDSM '09)*, pp. 611–617, Vail, Colo, USA, August 2009. View at Scopus - X. Guan,
*Modern Pumps Theory and Design*, China Astronautic Publishing House, 2011. - Y. Tateaayashi, K. Tanaka, T. Kobayashi, et al., “Pump perfermance prediction in screw-type centrifugal pump,”
*Journal of Turbomachiner*, vol. 1, no. 10, pp. 582–589, 2003. - M. Asuaje, F. Bakir, S. Kouidri, F. Kenyery, and R. Rey, “Numerical modelization of the flow in centrifugal pump: volute influence in velocity and pressure fields,”
*International Journal of Rotating Machinery*, vol. 2005, no. 3, pp. 244–255, 2005. View at Publisher · View at Google Scholar - S. Duplaa, O. Coutier-Delgosha, A. Dazin, O. Roussette, G. Bois, and G. Caignaert, “Experimental study of a cavitating centrifugal pump during fast startups,”
*Journal of Fluids Engineering*, vol. 132, no. 2, Article ID 021301, 2010. View at Publisher · View at Google Scholar · View at Scopus - Z. Driss, S. Karray, and H. Kchaou, “CFD simulation of the laminar flow in stirred tanks generated by double helical ribbons and double helical screw ribbons impellers,”
*Central European Journal of Engineering*, vol. 1, no. 4, pp. 413–422, 2011.