This document summarizes a presentation given at an AIChE conference that proposed a new definition of impeller efficiency based on the kinetic energy imparted to the fluid rather than traditional definitions. It discussed two common efficiency definitions and introduced a new "kinetic energy number" metric. The presentation used computational fluid dynamics simulations to compare the efficiency of different impeller types in an experimental tank, finding that a pitched blade turbine imparted 12% more kinetic energy while requiring 15% less power than a hydrofoil impeller, demonstrating its higher efficiency for that system based on the first law of thermodynamics. However, the hydrofoil produced a more homogeneous flow distribution.

1. A New Definition of Impeller Efficiency
John A. Thomas, PhD
&
Richard K. Grenville, PhD
AIChE Annual Meeting
Salt Lake City, UT.
12 November 2015

2. 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
mstarcfd.com Slide 2 of 16
Po
Fl
π
8
=φ
3
2HYDR
2/3-3/4
3/12FLOW
)Tε()
T
D
(
Po
Fl
08.1=
)ND(ρPo
ρFl
=
P
Qρ
=φ

3. Efficiency governed by impeller type and tank morphology
mstarcfd.com Slide 3 of 16

4. Flow number does not correctly describe energy flux
mstarcfd.com Slide 4 of 16
𝑣 𝑦 𝑟 = 0.5𝑟2
𝑣 𝑦 𝑟 = 0.1𝑟2
+ 0.2
𝑁𝑞 =
2𝜋 𝑣 𝑦 𝑟𝑑𝑟
𝑅
𝑜
𝑁𝐷3
=
𝜋
4
𝑁𝑞 =
2𝜋 𝑣 𝑦 𝑟𝑑𝑟
𝑅
𝑜
𝑁𝐷3
=
𝜋
4
𝐾 =
𝜋 𝑣 𝑦
3
𝑟𝑑𝑟
𝑅
𝑜
𝑁3 𝐷5 =
57𝜋
7000
= 0.008 𝐾 =
𝜋 𝑣 𝑦
3
𝑟𝑑𝑟
𝑅
𝑜
𝑁3 𝐷5 =
𝜋
56
= 0.018
Same pumping number, but 2.2X difference in kinetic energy flux!

5. mstarcfd.com Slide 5 of 16
Boltzmann as a numerical experiment: D/T=0.5
https://youtu.be/v82hdKEFB-Ihttps://youtu.be/tTyWIQT-A_c

6. Power draw output data from the DMT
mstarcfd.com Slide 6 of 16

7. Underlying DMT physics are correct
mstarcfd.com Slide 7 of 16
32
334/3
max 08.0
04.1 
 sm
w
DNPo
p

Nq
https://youtu.be/x0Zvun5txk8

8. Power dissipation output data from the DMT
mstarcfd.com Slide 8 of 16

9. Net effect is a change in kinetic energy
mstarcfd.com Slide 9 of 16
𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡 =
𝑑𝐾
𝑑𝑡

10. Non-dimensionalize to create similarity solution
mstarcfd.com Slide 10 of 16

11. The kinetic energy number, Ke, for this system
mstarcfd.com Slide 11 of 16

12. Same tank: Hydrofoil versus PBT
mstarcfd.com Slide 12 of 16
𝑁𝑘,𝐻 = 0.76
𝑁𝑘,𝑃 = 2.25

13. Comparing performance
mstarcfd.com Slide 13 of 16
Identical Power and Diameter
PBT imparts 12% more KE PBT requires 15% less power
Identical KE and Diameter
-or-

14. 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

15. But the hydrofoil produces a more homogenous flow
mstarcfd.com Slide 15 of 16
0.030.0250.015 0.020.005 0.010
Kinetic Energy (J)
100
101
102
104
105
106
103
Voxels
Hydrofoil
Kinetic Energy (J)
0.030.0250.015 0.020.005 0.010
Voxels
100
101
102
104
105
106
103
Pitched Blade

16. 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
mstarcfd.com Slide 16 of 16