Heat Mass Transfer (2013) 49:197–206 DOI 10.1007/s00231-012-1074-y

ORIGINAL

A parametric study for improving the centrifugal pump impeller for use in viscous fluid pumping M. H. Shojaeefard • M. Tahani • A. Khalkhali M. B. Ehghaghi • H. Fallah • M. Beglari

•

Received: 16 April 2012 / Accepted: 3 September 2012 / Published online: 12 October 2012 Ó Springer-Verlag 2012

Abstract Essentially, performance of centrifugal pumps is affected when pumping viscous fluids. In this paper a new idea is proposed to overcome the undesirable effects of viscosity on the pump performance parameters. This idea based on this matter that one specific impeller can be designed, made and installed on the pump for pumping of one fluid with specific viscosity. Therefore a specific pump can be used for pumping of different fluids with different viscosity, by replacement of pump impeller. Replacement of the impeller is more cost effective in comparison to the replacement of the whole of the pump. Passage width and outlet angle of impeller are considered as design variables and the effects of such variables investigated using experimentally validated numerical model. The H–Q, P–Q and g–Q graphs are extracted experimentally for the improved impeller, which show good improvement in comparison with original impeller. List of symbols A Area (m2) b2 Passage width of impeller (mm) BEP Best efficiency point CFD Computational fluid dynamics d Pipe diameter (m) M. H. Shojaeefard  M. Tahani (&)  H. Fallah  M. Beglari School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran e-mail: [email protected]

g H imp K k MRF OL P PL Q RMSE SST V Z

Gravity acceleration Head (m) Impeller Turbulent kinetic energy (m2/s2) Friction loss factor Multi reference frames Over load performance Pressure (Pa) Part load performance Flow rate (m3/h) Root mean square error (%) Shear stress transport model Velocity (m/s) Altitude (m)

Greek symbols g Efficiency (%) b2 Outlet angle of blade (°) q Density of the fluid (kg/m3) l Viscosity (Pa s) m Kinematic viscosity (mm2/s) c Specific weight (kg/m2 s2) Subscripts and superscripts d Discharge elect Electrical in Inlet out Outlet s Suction t Total

M. Tahani  A. Khalkhali School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran

1 Introduction

M. B. Ehghaghi Department of Mechanical Engineering, Tabriz University, Tabriz, Iran

Centrifugal pumps are one of the substantial devices which are used for transferring viscous fluids in the different

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industries such as power plants and refineries. In utilizing centrifugal pumps for transferring fluids with various viscosities, the important point is that the flow rate and the performance of the pumps are affected significantly by the fluid viscosity as a main factor of frictional losses. Head and efficiency of the pumps decrease with increasing in the fluids viscosity and the pumps will require more power in this situation. On the other hand, pumping the high viscose fluids make some troubles for mechanical seals and cause more loads on bearings [1, 2]. Therefore, the performance of centrifugal pumps is weakened when they services high viscosity fluids due to increase in losses. Performed tests in the previous works have shown that the performance of centrifugal oil pumps is a function of oil viscosity [3, 4]. Some correction factors are proposed for determining pump performance when it handles viscous fluid. There are great insights into the effects of oil viscosity on the performance of centrifugal oil pumps, which have been applied in the important guidelines used today for the design of these pumps. Within the last few years, analyzing the effects of the viscosity and boundary layers on turbo machinery performance have been carried out, experimentally and numerically [5–11]. Li et al. [9–11] investigated the effects of fluids viscosity on the performance of centrifugal oil pumps. All of these researches show that the high viscosity results in rapid increases in the disc friction losses over outside of the impeller shroud and hub. The viscosity of fluid affects the slip coefficient and also causes the reduction of flow in the impeller and volute. Furthermore, increasing in the fluid viscosity causes the wide wake near the blade suction side of impeller. Many studies have been performed to reduce the undesirable effects of viscosity on the pump efficiency [11–15]. Shojaeefard et al. [12–14] performed experimental and numerical investigations to obtain the effects of the impeller’s outlet angle on the pump performance considering oil as working fluid. As a result of these researches, when the blade outlet angle increases the width of wake at the outlet of impeller decreases. Thus, improvement of centrifugal pump performance can be done with increase in blade outlet angle for use in viscose fluid pumping. Grapsas et al. [15] carried out a parametric study to examine the influence of the blade length, the inlet height and the leading edge inclination on the performance and the efficiency of the impeller. They extracted the optimum values of the above parameters which maximize the hydraulic efficiency. There are many other valuable references covering the ongoing research and review of the computational fluid dynamics (CFD) to study the viscous flow in the impeller of a centrifugal pump [16–18]. The aim of this study is to offer an improved impeller to overcome the undesirable effects of viscosity in viscous

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fluid pumping. In this way, geometrical characteristics of pump impellers are considered as effective parameters in design of impellers for use in viscous fluid pumping instead of water pumping. The effects of blade outlet angle and passage width on the pump performance are investigated numerically and experimentally. Based on experimentally verified numerical model, an improved impeller is offered for KWP K-Bloc 65-200 centrifugal pumps. The improved impeller is made and installed on the pump and tested experimentally. Performance graphs extracted experimentally show good improvement in pumping of oil using improved impeller. The results also represent this matter that specially designed impellers can be replaced with original impellers for pumping of viscous fluids to prevent weakening of pump performance.

2 Experimental setup and original centrifugal pump specifications In this section, efficiency and performance of KWP K-Bloc 65-200 centrifugal pump was studied under steady condition, experimentally. Geometrical characteristics of the original impeller of the centrifugal pump are shown in Fig. 1a. Specifications of this pump with single axial suction and vane less volute casing are depicted in Table 1. The pump is driven by a three-phase AC electric motor. The input power and rotational speed of the electric motor were 5.5 kW, 1,450 rpm, respectively. Test setup shown in Fig. 2 was used to measure the performance parameters of the centrifugal pump. The pipe of the rig was made of stainless steel with inner diameter of 80 mm. The tank net volume was 2,400 l. The operation condition was controlled by a gate valve on the discharge pipe. Also, two digital pressure transmitter gages were used at the pump inlet and outlet pipes. Baffle plates were used for damping the disturbance of discharged fluid. The pump head at all stages was measured using Bernoulli equation which can be written in the following from:   pd  ps m2  m2s kf ;d :m2d  kf ;s :m2s H¼ þ þ ðZd  Zs Þ þ d q:g 2g 2g ð1Þ where p is the fluid static pressure that measured by digital pressure transmitter gages, m is the flow velocity, kf is the friction loss factor between the measurement points and the corresponding pump flange, and Z is the vertical distance of the pressure sensor from the reference point. The subscripts d and s denote the discharge side and the suction side of the pump, respectively. Volumetric flow rate of pump can be calculated by division of fluid volume difference in discharge tank by time.

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199

Fig. 1 Geometrical characteristics and meridian plane of impellers: a original impeller, b improved impeller

Re ¼

Table 1 Specifications of original centrifugal pump Specification

Dimensions

Suction pipe diameter (d1)

103 mm

Outlet pipe diameter (d2)

103 mm

Impeller outside diameter

209 mm

Specific speed (ns)

26

Number of backward blades (N)

6

Roughness of the impeller and volute

100 lm

Twist angle (u)

10°

Outlet angle (b2)

27.5°

Wrapping angle

140°

Outlet passage width (b2)

17 mm

Q ¼ 3600 

A  Dh t

Vd :dd v

ð4Þ

The friction loss factor for different Reynolds values is obtained from the Moody diagram. The centrifugal pump efficiency at all stages was defined as the ratio between the output power and the input electrical power of the pump. Pout;pump cQH ¼ ; Pin;pump ¼ Pout;elect Pin;pump Pin;pump ¼ gelect  Pin;elct

g¼

ð2Þ

That A is the area of discharge tank and t is the time of increasing the height of fluid in discharge tank equal to Dh. The discharge velocity of fluid is calculated by Eq. 3. Q m Vd ¼ ð3Þ Ad s That Ad is the area of outlet pipe. Therefore Reynolds number (Re) can be obtained as follow:

ð5Þ

where c, Q, H and P are specific weight, volume flow rate, head and power respectively, and the efficiency of the electromotor was almost constant ðgelect  83 %Þ. In order to investigate the effects of viscosity on the pump performance, two type of working fluids, water (q = 998 kg/m3 and m = 1 CSt) and fuel oil (q = 875 kg/m3 and m = 43 CSt) are used in the experiments. Such fluids are Newtonian verified by using the rotary viscosity meter at 25 °C. H–Q, P–Q and g–Q curves of the pump with original impeller for water and fuel oil are shown in Fig. 3a–c, respectively. In these figures part load performance (PL), best efficiency point (BEP), and overload performance (OL) [1] are depicted. The uncertainty percentage [19] of

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Heat Mass Transfer (2013) 49:197–206

Fig. 2 Test setup of centrifugal pump

head, power consumption, and efficiency at BEP were 3.1, 1.2, and 2.4 %, respectively. The maximum uncertainty percentage of head, power consumption, and efficiency at OL were 1.5, 1.3, and 2.2 %, respectively. It is clear from Fig. 3 that head and efficiency are decreased and the power consumption is increased when the pump handles the fuel oil. This is because of increasing in impeller hydraulic losses. Based on these results, around the BEP the efficiency and head values decrease about 20.5 % and 1.9 m respectively, and the power consumption increases about 1.03 kW when the fuel oil was used as working fluid. The mentioned quantities result in a remarkable reduction in the performance. Improving of the original impeller and the testing of the improved impeller will be discussed in the Sect. 4.

3 Numerical scheme The discipline of CFD has fostered a unified approach to turbomachinery analysis and design. For present numerical simulation, the finite volume method has been used for the discretization of equations, but the analysis of the geometry has been based on the finite element approach. So, the geometrical flexibility of the finite element method can be used; however, the equations are dealt with in the form of finite volume [22]. In the discrete finite volume equations, high precision algorithm has been used. This technique allows different advection schemes to be applied to each class of equation. This is particularly useful if the fluid flow physics is more correlated with specific aspects of the flow model. In this numerical solution, the high precision algorithm was used to solve the governing equations of incompressible viscous/turbulent flows passing through the pump at different operating conditions, which based on the

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average Reynolds values or the time-averaging approach. In this case, the advection terms of the momentum and continuity equations are high resolution with second order accurate and a first order accurate of upwind differencing scheme is used for turbulence equations. In this section, the definition of geometry covers the pump sections of volute, impeller, and outlet pipe, which are connected together for the analysis of the whole pump (see Fig. 4a). In the mesh generation part, mesh configuration is produced based on the type of physics that is considered for the problem. For better conformity of the geometry with the computational domain, at the near-wall regions, the structured mesh is used for the boundary layer, and at regions away from the wall, the unstructured mesh configuration is employed to correctly cover the complex geometry (see Fig. 4b). For producing the unstructured mesh configuration, six-sided, pyramid, and wedge-shaped elements are used in appropriate situations, which are shown in Fig. 4c. In this approach, the computational space is divided into small elements and the surfaces of the control volume are defined on the mid plane of each of those elements. The numerical scheme employed in this case, involves generating finite control volumes from the mesh. In order to take advantage of mesh compaction near the rigid walls, the wall rule function is applied to the turbulence model equations. ‘‘k–x SST’’ has been adopted as the turbulence model in the simulation. The use of a k–x formulation in the inner parts of the boundary layer makes the model directly usable all the way down to the wall through the viscous sub-layer; hence the SST k–x model can be used as a low Reynolds turbulence model without any extra damping functions. The SST formulation also switches to a k–e behavior in the free-stream and thereby avoids the standard k–x problem that the model is too sensitive to the inlet free-stream turbulence properties [20, 21]. Since the inflow to the pump

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201

Fig. 3 Centrifugal pump performance graphs for original impeller: a H–Q, b P–Q, c g–Q

Fig. 4 a General view of the centrifugal pump model, b the mesh configuration used for flow analysis, c typical mesh element with nodes (n1, n2 and n3) and integration points (ip1, ip2 and ip3)

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from the suction reservoir occurs at a high volume, and this flow has already been smoothed by baffle plates, the average turbulence intensity is considered as 5 %, which, in light of the existing system and the flow at the entrance to the pump, is a totally empirical value [17, 22]. This simulation is defined by means of the multi-reference frame (MRF) technique, in which the impeller is situated in the rotating reference frame, and the volute is in the fixed reference frame, and they are related to each other through the ‘‘frozen rotor’’. The frozen rotor method employs a quasisteady algorithm where the rotor and stator are modeled at a fixed (frozen) position relative to each other [23]. The ‘‘coupled solver’’ has been used to calculate the pressure and velocity field in this simulation. Pressure is given indirectly by the continuity equation in that when the correct pressure is substituted into the momentum equations, the resulting velocity field satisfied mass continuity. Therefore, an algorithm coupling velocity and pressure is employed in this numerical simulation. If the central differencing is used to calculate velocities at cell faces, a chequerboard velocity field could result [24]. These phenomena are clearly unrealistic and must be avoided. Many commercial codes, such as FLUENT, deal with this problem, but this computer code uses a co-located grid in which all variables are calculated at cell center, and avoid velocity–pressure decoupling by using the Rhie Chow algorithm to interpolate the velocities calculated at the cell center to the cell faces [25]. The complete iteration process can be summarized as follows. 1. 2. 3. 4. 5. 6. 7.

Set (guess) the initial values for all variables at grid nodes Calculate the convection and diffusion coefficients Use the guessed pressure field to calculate values for the velocity components Solve pressure correction equation Set the new guess for pressure Calculate update values for the velocity components Solve all scalar transport equations (e.g. k and x)

Use the last pressure as anew pressure field, return to step 2 until a converged solution is obtained. For the boundary conditions definition, the static pressure of the reservoir is used at the entrance boundary of the pump, and the mass flow rate is defined at the exit plane of the pipe attached to the volute. Since the whole pump is modeled in this analysis, at the solid boundaries, no-slip condition with relative roughness of 100 lm is applied. Other boundary condition parameters and physical properties of working fluids are demonstrated in Table 2. Figure 5 shows the study of the dependency of results from mesh configuration and summary of CPU run time for the original impeller of centrifugal pump during pumping fuel oil. According to Fig. 5a the output pressure and mean

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Table 2 Boundary conditions and physical properties of working fluids Region

Parameter

Description

Inlet

Frame type

Stationary

Stationary total pressure

97.58 (kPa)

Flow regime Turbulence intensity

Subsonic 5%

Wall Outlet

Roughness

100 lm

Condition

No slip

Mass flow rate

Different for each case

Flow regime

Subsonic

Other

Steady state time scale

0.0007 s

Reference pressure

89 (kPa)

Working fluids

Water

q = 998 kg/m3 m = 1 CSt

Fuel oil

q = 875 kg/m3 m = 43 CSt

differences of circumferential velocities values doesn’t change much at 3,277,226 elements. The number of mesh elements includes the sum of elements in the whole pump. To determine the accuracy of boundary layer predictions, the average y? around the impeller blades has been calculated for different impeller type at different working conditions [20]. The mentioned y? is calculated equal to 0.869. In this case, the SST model will switch to a low-Re formulation near the wall rather than the wall function formulation. The results of developed numerical simulation are compared with the results obtained using commercial software FLUENT 6.3. Comparisons of such results with experimental results are performed in Table 3. It is clear from this table that numerical simulation is more capable than FLUENT for simulation of the fluid flow in the centrifugal pump as a radial turbomachine.

4 Improving centrifugal pump impeller In this section, original impeller of KWP K-Bloc 65-200 centrifugal pump which was investigated experimentally and numerically in Sects. 2 and 3 has been improved for use in oil pumping. In this way, blade outlet angle (b2) and the passage width (b2) which was recognized as significant parameters in the previous works [11–13] are considered as design variables. According to the results of previous experimental and numerical researches, for minimizing the effects of wakes and hydraulic losses, the best ranges of the blade outlet angle and passage width are considered between 27.5°–32.5° and 17–21 mm, respectively [12, 13]. Three values for b2 and two values for b2 are considered and six various design of impeller are generated

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203

Fig. 5 Evaluation of a the dependency of mesh and b summary of CPU run time of numerical simulation for original impeller

Table 3 Comparisons of numerical simulation and FLUENT results with experimental results for original impeller during pumping fuel oil (m = 43 CSt) Flow rate Q (m3/h)

Experimental head, H (m)

Numerical head, H (m)

FLUENT head, H (m)

Numerical error (%)

FLUENT error (%)

38.76 (PL)

12.79

12.22

12.18

4.46

4.77

47.56 (BEP)

12.05

11.61

11.34

3.65

5.89

49.15 (OL)

11.54

11.46

10.82

0.69

6.24

56.9

10.15

10.45

9.48

2.96

6.60

60.27

9.3

9.9

8.63

6.45

7.20

4.10

6.19

Root mean square errors: RMSE

Table 4 Experimental and numerical results for different impeller specifications and working fluids Working fluid

Water

Fuel oil

Imp. type

Impeller specifications

Numerical head (m)

b2 (°)

b2 (mm)

PL

BEP

OL

PL

BEP

OL

A

27.5

17

14.21

13.51

11.70

14.31

13.82

11.50

3.07

B

30

21

13.93

13.01

12.21

14.07

12.87

11.89

3.12

C

32.5

17

14.02

13.12

12.43

14.15

13.33

12.11

4.07

A

27.5

17

12.22

11.61

10.45

12.79

12.05

10.15

4.10

B

30

21

13.79

13.58

13.27

13.84

13.53

13.00

3.94

C

32.5

17

13.29

12.59

12.09

13.20

12.15

11.44

6.42

D

27.5

21

12.91

12.37

12.02

–

–

–

–

E

30

17

13.18

12.63

12.11

–

–

–

–

F

32.5

21

13.42

12.89

12.21

–

–

–

–

(see Table 4) and the pump performance parameters are calculated numerically. Using developed numerical simulation for obtaining the H–Q curves of centrifugal pumps, the amounts of total pressure at the entrance and exit of the simulated geometry (similar to the experimental test points) are determined and then using following equation the pump head is calculated.

H¼

Experimental head (m)

Pt;d  Pt;s qg

RMSE (%)

ð6Þ

Considering a fuel oil with viscosity of 43 Cst as a working fluid, all of six various models are numerically simulated and the results of head at PL, BEP and OL versus flow rate are depicted in Table 4.

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Fig. 6 Comparison of the numerical simulation and FLUENT with experimental results

Fig. 7 Variations of power consumption and efficiency versus flow rate for different fluids and impellers

Evidently, numerical results indicate that the Imp.B with b2 = 30° and b2 = 21 mm (see Fig. 1b) has highest pressure head in oil pumping and therefore is a best design in comparison with other impellers. The results show that the improved impeller (Imp.B) is better than original impeller (Imp.A). This reveals that the Imp.B is also better than the Imp.C which was proposed previously by the authors [13]. It should be noted that the Imp.C was resulted when the authors considered b2 as a design parameter despite in this work b2 and b2 are considered as design parameters, simultaneously.

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In the next step, for more investigation and validation of the numerical simulation, two impellers Imp.B and Imp.C were made and installed on the centrifugal pump and the head was measured experimentally for various flow rates. The head-flow curves for the original impeller (Imp.A), improved impeller (Imp.B) and Imp.C are shown in Fig. 6. In this figure, numerical results for mentioned impellers have been superimposed with the corresponding experimental results. The root mean square error (RMSE) between the experimental and numerical values of head for three impellers (Imp.A, Imp.B and Imp.C) during pumping

Heat Mass Transfer (2013) 49:197–206

water and oil is presented in Table 4. The agreement between the numerical and experimental results seems to be quite satisfactory. 5 The power consumption and efficiency of the improved impeller

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2.

3. 4.

Figure 7 shows the variations of power consumption and efficiency versus flow rate for the improved and two other impellers (Imp.A, Imp.B and Imp.C). The working fluid was fuel oil and results have been derived experimentally. It is clear from Fig. 7 that centrifugal pump with improved impeller requiring more power. It is because of increasing in passage width and fluids inertial influence. Moreover, Fig. 7 confirms that increasing in blade outlet angle cause decrease in the power consumption [11, 13]. However this figure shows that the modified impeller improved the efficiency of the centrifugal pump significantly. The Results shown in this figure reveal that by improving the impeller geometry the improvement of efficiency at BEP and OL operating are about 7.93 %. 6 Conclusion

5.

6.

7.

8.

9.

10.

11. 12.

Improving the centrifugal pump impeller for use in oil pumping is investigated in the present study experimentally and numerically. The numerical simulation of the steady state flow using the URANS and k–x SST model has been carried out and investigating the fluid flow characteristics in a single axial suction and vane less volute casing centrifugal pump has been performed. The methodology was checked by means of grid dependence tests and comparison of the numerical predictions with experimental data which shows acceptable agreement. According to the results of this study, the friction on the discs decreases the efficiency and increases the power consumption when pumping oil instead of water. This weakening is overcome by altering the original impeller with an improved one. Experimental and numerical results offered an improved impeller to increase the head and efficiency values when using oil. Finally, results show that change in blade outlet angle and impeller passage width simultaneously is more effective than each one and this improvement cause to move BEP at higher flow rate with head and efficiency increment. Also, these changes are more effective in BEP and OL performances in comparison to PL performance. References 1. U.S. Department of Energy’s Industrial Technologies Program (ITP) and the Hydraulic Institute (HI) (2006) Improving pumping system performance: a sourcebook for industry, 2nd edn. The

13.

14.

15.

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22.

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