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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

## Abstract

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 $ф*Rew−a$. 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 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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## Figures

Fig. 1

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

Fig. 2

Morrison number as a function of specific speed

Fig. 3

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

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

Fig. 5

Modified affinity law applied based on constant value of Morrison number

Fig. 6

Modified affinity law applied based on varying values of Morrison number

Fig. 7

Variation in Morrison number with dynamic viscosity at 3600 rpm

Fig. 8

Variation in Morrison number with Rotational Reynolds Number

Fig. 9

Hydraulic Reynolds number at the pump outlet

Fig. 10

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

Fig. 11

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

Fig. 12

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

Fig. 13

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

Fig. 14

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

Fig. 15

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

Fig. 16

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

## Errata

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