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Research Papers: Energy Systems Analysis

# Development of Modified Affinity Law for Centrifugal Pump to Predict the Effect of Viscosity

[+] Author and Article Information
Gerald Morrison

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

Wenjie Yin

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

Rahul Agarwal

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

Abhay Patil

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

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received November 28, 2017; final manuscript received March 29, 2018; published online May 7, 2018. Assoc. Editor: Esmail M. A. Mokheimer.

J. Energy Resour. Technol 140(9), 092005 (May 07, 2018) (9 pages) Paper No: JERT-17-1664; doi: 10.1115/1.4039874 History: Received November 28, 2017; Revised March 29, 2018

## Abstract

The purpose of this research is to investigate the flow behavior inside a mixed flow type pump operating with fluids of different viscosities using computational fluid dynamics (CFD) with the goal to establish additional terms for the pump affinity laws to scale pump performance including the effects of viscosity. Several sets of fluids of different viscosities and densities are simulated under various operating conditions. The effect of viscosity on the performance of the impeller and diffuser is discussed. Changes in the pump performance due to fluid viscosity are characterized using the dimensionless flow coefficient, head coefficient, and rotational Reynolds number. The result, which can be regarded as the modified pump affinity laws for viscosity flows, was obtained based on the relationships between dimensionless coefficients. The modified affinity laws agreed well with the CFD results. Further study was conducted to validate the relationships using previously published test data for a semi axial pump design (specific speed, $Ns$: 3869) tested with fluid viscosity ranging from 1 cp to 1020 cp and in-house testing of a split vane impeller pump ($Ns$: 3027) and a helicoaxial pump ($Ns$: 5281) using 1 cp and 5 cp viscosity fluid. The modified affinity laws accurately models the performance dependence upon viscosity. As with the standard affinity laws, a pump's functional relationship varies with each pump design. Yet the modified affinity laws produce a single common curve for all operating conditions and viscosities for a specific pump.

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## References

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## Figures

Fig. 1

Different types of impellers [1]

Fig. 2

An impeller of the pump under consideration

Fig. 3

CAD model of hydraulic flow path and mesh

Fig. 4

Comparison of the head and efficiency between the simulation results and the experimental results for pure water (1 cP)

Fig. 5

Pressure rises for different viscosity oils

Fig. 6

Pressure rise in the (a) impeller and (b) diffuser for different viscosity liquids

Fig. 7

Blade-to-blade views of the streamlines in the impeller and diffuser in (a) pumping water (1 cP) at 583.3 gpm, (b) pumping water (1 cP) at 1312 gpm, (c) pumping 200 cP oil at 533.6 gpm, and (d) pumping 200 cP oil at 1423 gpm

Fig. 8

Head coefficient versus flow rate coefficient for all speeds

Fig. 9

Pump efficiency versus flow rate coefficient

Fig. 10

Head coefficient versus common logarithm of rotational Reynolds number and flow rate coefficient

Fig. 11

Empirical pump head curve by using proposed affinity law for viscosity

Fig. 12

Semi-axial pump (Ns: 3869) [15]

Fig. 13

(a) Pump head curve of semi-axial pump, 3500 rpm and (b) empirical pump head curve using proposed affinity law for viscosity [15]

Fig. 14

(a) Split vane impeller pump and (b) helicoaxial pump

Fig. 15

(a) Pump performance curve of split vane pump and (b) empirical pump head curve using proposed affinity law for viscosity

Fig. 16

(a) Pump performance curve of helicoaxial pump and (b) empirical pump head curve using proposed affinity law for viscosity

Fig. 17

(a) Pump efficiency curve of mixed flow pump and (b) efficiency prediction curve using proposed affinity law for viscosity

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