A New Definition of Impeller Efficiency

John A. Thomas, PhD

&

Richard K. Grenville, PhD

AIChE Annual Meeting

Salt Lake City, UT.

12 November 2015

Efficiency definitions

• Hydraulic efficiency (Brown (2010)):

– Ratio of Fluid Kinetic Energy to Mechanical Energy

Input

• Flow efficiency (after Fořt et al. (2010)):

– Mass of Fluid Pumped per Joule of Energy Input

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Po

Fl

π

8=φ

3

2HYDR

2/3-3/4

3/12FLOW)Tε()

T

D(

Po

Fl08.1=

)ND(ρPo

ρFl=

P

Qρ=φ

Efficiency governed by impeller type and tank morphology

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Flow number does not correctly describe energy flux

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𝑣𝑦 𝑟 = 0.5𝑟2 𝑣𝑦 𝑟 = 0.1𝑟2 + 0.2

𝑁𝑞 =2𝜋 𝑣𝑦𝑟𝑑𝑟

𝑅

𝑜

𝑁𝐷3 =𝜋

4 𝑁𝑞 =

2𝜋 𝑣𝑦𝑟𝑑𝑟𝑅

𝑜

𝑁𝐷3 =𝜋

4

𝐾 =𝜋 𝑣𝑦

3𝑟𝑑𝑟

𝑅

𝑜

𝑁3𝐷5 =57𝜋

7000= 0.008 𝐾 =

𝜋 𝑣𝑦3𝑟𝑑𝑟

𝑅

𝑜

𝑁3𝐷5 =𝜋

56= 0.018

Same pumping number, but 2.2X difference in kinetic energy flux!

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Boltzmann as a numerical experiment: D/T=0.5

https://youtu.be/v82hdKEFB-I https://youtu.be/tTyWIQT-A_c

Power draw output data from the DMT

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Underlying DMT physics are correct

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32334/3

max 08.004.1 sm

w

DNPo

p

Nq

https://youtu.be/x0Zvun5txk8

Power dissipation output data from the DMT

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Net effect is a change in kinetic energy

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𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡 =𝑑𝐾

𝑑𝑡

Non-dimensionalize to create similarity solution

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The kinetic energy number, Ke, for this system

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Same tank: Hydrofoil versus PBT

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𝑁𝑘,𝐻 = 0.76

𝑁𝑘,𝑃 = 2.25

Comparing performance

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Identical Power and Diameter

PBT imparts 12% more KE PBT requires 15% less power

Identical KE and Diameter

-or-

Why is the PBT more efficient (for this tank)?

mstarcfd.com Slide 14 of 16 https://youtu.be/j9hmBA-Hbsw https://youtu.be/tTyWIQT-A_c

But the hydrofoil produces a more homogenous flow

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0.03 0.025 0.015 0.02 0.005 0.01 0

Kinetic Energy (J)

100

101

102

104

105

106

103

Voxels Hydrofoil

Kinetic Energy (J)

0.03 0.025 0.015 0.02 0.005 0.01 0

Voxels

100

101

102

104

105

106

103

Pitched Blade

Conclusions and Key Points

• Boltzmann is excellent at running numerical experiments

– No meshing

– LES turbulence/correct EDR

– 3D/Fully transient

– Scales exceptionally well on HPC

• Impeller efficiency is governed by first law of thermodynamics

– Power In-Power Out=Total Kinetic Energy

– Can derive a system-specific Nk

– Function of impeller/tank competition

• Np and Nk together combine to score relative efficiency

• Still should consider implications of energy distribution

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