Research Papers: Fundamental Issues and Canonical Flows

Affinity Law Modified to Predict the Pump Head Performance for Different Viscosities Using the Morrison Number

[+] Author and Article Information
Abhay Patil

Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: abhyapatil@gmail.com

Gerald Morrison

Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: gmorrison@tamu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 22, 2017; final manuscript received July 29, 2018; published online September 21, 2018. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 141(2), 021203 (Sep 21, 2018) (11 pages) Paper No: FE-17-1748; doi: 10.1115/1.4041066 History: Received November 22, 2017; Revised July 29, 2018

The goal of this study is to provide pump users a simple means to predict a pump's performance change due to changing fluid viscosity. During the initial investigation, it has been demonstrated that pump performance can be represented in terms of the head coefficient, flow coefficient, and rotational Reynolds number with the head coefficient data for all viscosities falling on the same curve when presented as a function of ф*Rewa. Further evaluation of the pump using computational fluid dynamics (CFD) simulations for wider range of viscosities demonstrated that the value of a (Morrison number) changes as the rotational Reynolds number increases. There is a sharp change in Morrison number in the range of 104<Rew<3*104 indicating a possible flow regime change between laminar and turbulent flow. The experimental data from previously published literature were utilized to determine the variation in the Morrison number as the function of rotational Reynolds number and specific speed. The Morrison number obtained from the CFD study was utilized to predict the head performance for the pump with known design parameters and performance from published literature. The results agree well with experimental data. The method presented in this paper can be used to establish a procedure to predict any pump's performance for different viscosities; however, more data are required to completely build the Morrison number plot.

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Weisbach, J. , 1848, Principles of the Mechanics of Machinery and Engineering, Lea and Blanchard, Philadelphia, PA.
Darcy, H. , 1856, Les Fontaines Publiques De La Ville De Dijon, Dalmont, Paris, France.
Reynolds, O. , 1883, “ An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous and of the Law of Resistance in Parallel Channels,” Philos. Trans. R. Soc. London, 174, pp. 935–982. https://www.jstor.org/stable/109431?seq=1#page_scan_tab_contents
Moody, L. F. , 1944, “ Friction Factors for Pipe Flow,” Trans. ASME, 66, pp. 671–684.
Colebrook, C. , 1939, “ Turbulent Flow in Pipes, With Particular Reference to Transition Region Between Smooth and Rough Pipe Laws,” J. Inst. Civ. Eng. London, 11, pp. 133–156.
LaViolette, M. , 2017, “ On the History, Science, and Technology in the Moody Diagram,” ASME J. Fluids Eng., 139(3), p. 030801. [CrossRef]
White, F. M. , 2010, Fluid Mechanics, 7th ed., McGraw-Hill, New York.
Pirouzpanah, S. , Gudigopuram, S. R. , and Morrison, G. L. , 2017, “ Two-Phase Flow Characterization in a Split Vane Impeller Electrical Submersible Pump,” J. Pet. Sci. Eng., 148, pp. 82–93. [CrossRef]
Liu, P. , Patil, A. , and Morrison, G. L. , 2017, “ Multiphase Flow Performance Prediction Model for Twin-Screw Pump,” ASME J. Fluids Eng., 140(3), p. 031103. [CrossRef]
Patil, A. , and Morrison, G. L. , 2018, “ Performance of Multiphase Twin-Screw Pump During the Period of Wet-Gas Compression,” SPE Prod. Oper., 33(1), p. 186099.
Buckingham, E. , 1914, “ On Physically Similar Systems: Illustrations of the Use of Dimensional Equations,” Phys. Rev., 4, pp. 345–376. [CrossRef]
Morrison, G. , and Patil, A. , 2017, “ Pump Affinity Laws Modified to Include Viscosity and Gas Effects,” 46th Turbomachinery and 33rd Pump Symposia, Houston, TX. https://oaktrust.library.tamu.edu/handle/1969.1/166770
Morrison, G. , Yin, W. , Agarwal, R. , and Patil, A. , 2018, “ Development of Modified Affinity Law for Centrifugal Pump to Predict the Effect of Viscosity,” ASME J. Energy Resour. Technol., 140(9), p. 092005. [CrossRef]
Yu, W. S. , Lakshrninarayana, B. , and Thompson, D. E. , 1996, “ Computation of Three Dimensional Viscous Flow in High Reynolds Number Pump Guide Vane,” ASME J. Fluids Eng., 118(4), pp. 698–705. [CrossRef]
Blanchard, D. , Ligrani, P. , and Gale, B. , 2006, “ Miniature Single-Disk Viscous Pump (Single-DVP) Performance Characterization,” ASME J. Fluids Eng., 128(3), pp. 602–610. [CrossRef]
Cheng, H.-P. , and Chen, C.-J. , 2003, “ Computational Fluid Dynamics Performance Estimation of Turbo Booster Vacuum Pump,” ASME J. Fluids Eng., 125(3), pp. 586–589. [CrossRef]
Gülich, J. F. , 1999, “ Pumping Highly Viscous Fluids With Centrifugal Pumps—Part 1,” World Pumps, 1999(395), pp. 30–34. [CrossRef]
Gülich, J. F. , 1999, “ Pumping Highly Viscous Fluids With Centrifugal Pumps—Part 2,” World Pumps, 1999(396), pp. 39–42. [CrossRef]
Timar, P. , 2005, “ Dimensionless Characteristics of Centrifugal Pump,” Chem. Papers- Slovak Acad. Sci., 59, pp. 500–503. https://www.chempap.org/file_access.php?file=596ba500.pdf
Martelli, F. , and Michelassi, V. , 1990, “ Using Viscous Calculations in Pump Design,” ASME J. Fluids Eng., 112(3), pp. 272–280. [CrossRef]
Wen-Guang, L. , 2004, “ A Method for Analyzing the Performance of Centrifugal Oil Pumps,” ASME J. Fluids Eng., 126, pp. 482–485. [CrossRef]
Gülich, J. F. , 2003, “ Effect of Reynolds Number and Surface Roughness on the Efficiency of Centrifugal Pump,” ASME J. Fluids Eng., 125(4), pp. 670–679. [CrossRef]
Li, W.-G. , 2012, “ An Experimental Study on the Effect of Oil Viscosity and Wear-Ring Clearance on the Performance of an Industrial Centrifugal Pump,” ASME J. Fluids Eng., 134(1), p. 014501. [CrossRef]
Li, W.-G. , 2013, “ Model of Flow in the Side Chambers of an Industrial Centrifugal Pump for Delivering Viscous Oil,” ASME J. Fluids Eng., 135 (5), p. 051201. [CrossRef]
Hydraulic Institute, 2010, “ Effects of Liquid Viscosity on Rotordynamic (Centrifugal and Vertical) Pump Performance,” Hydraulic Institute, Parsippany, NJ, Standard No. ANSI/HI 9.6.7-2010.
Muggli, F.-A. , Holbein, P. , and Dupont, P. , 2002, “ CFD Calculation of a Mixed Flow Pump Characteristic From Shutoff to Maximum Flow,” ASME J. Fluids Eng., 124(3), pp. 798–802. [CrossRef]
He, L. , and Sato, K. , 2001, “ Numerical Solution of Incompressible Unsteady Flows in Turbomachinery,” ASME J. Fluids Eng., 123(3), pp. 680–685.
Anagnostopoulos, J. S. , 2006, “ Numerical Calculation of the Flow in a Centrifugal Pump Impeller using Cartesian Grid,” Second WSEAS International Conference on Applied and Theoretical Mechanics, Venice, Italy, pp. 124–129.
Ippen, A. T. , 1945, “ The Influence of Viscosity on Centrifugal Pump Performance,” Issue 199 of Fritz Engineering Laboratory Report, American Society of Mechanical Engineers, New York, pp. 45–57.
Le Fur, B. , Moe, C. K. , and Cerru, F. , 2015, “ High Viscosity Test of a Crude Oil Pump,” 44th Turbomachinery and 31st Pump Symposium, Houston, TX, Sept. 14–17.
Beall, R. , Sheth, K. K. , Pessoa, R. F. , and Olsen, H. , 2011, “ Peregrino: An Integrated Solution for Heavy Oil Production and Allocation,” SPE Brazil Offshore Conference, Macaé, Brazil, June 14–17, SPE Paper No. SPE 142944.


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Fig. 1

(a) Head coefficient—flow coefficient relationship for a pump and (b) modified affinity law relationship [13]

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Fig. 2

Morrison number as a function of specific speed

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Fig. 3

(a) Typical electrical submersible pump configuration and (b) hexahedral structural gridding scheme utilized for the pump stage under consideration

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Fig. 4

Computational fluid dynamics performance of mixed flow pump for the speeds 3000 rpm, 3600 rpm, 4200 rpm at viscosities varying from 1 mPa·s to 2000 mPa·s

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Fig. 5

Modified affinity law applied based on constant value of Morrison number

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Fig. 6

Modified affinity law applied based on varying values of Morrison number

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Fig. 7

Variation in Morrison number with dynamic viscosity at 3600 rpm

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Fig. 8

Variation in Morrison number with Rotational Reynolds Number

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Fig. 9

Hydraulic Reynolds number at the pump outlet

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Fig. 10

Performance data of typical low specific speed pump (Ns: 1163) extracted from Ref. [30]

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Fig. 11

Modified affinity law applied to data from Ref. [30]

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Fig. 12

Variation in Morrison number with viscosity for the data extracted from Ref. [30]

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Fig. 13

Variation in Morrison number for the data from Ref. [30]

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Fig. 14

Variation in Morrison number as a function of flow regime and specific speed

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Fig. 15

Morrison number using proposed equation (16) compared with Ippen's data (Ns: 1163) and Beall (Ns: 3200)

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Fig. 16

Prediction of head and comparison with the measured data extracted from Ref. [31]



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