AICHE 15 - IMPELLER EFFICIENCY
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Transcript of AICHE 15 - IMPELLER EFFICIENCY
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
mstarcfd.com Slide 2 of 16
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
mstarcfd.com Slide 3 of 16
Flow number does not correctly describe energy flux
mstarcfd.com Slide 4 of 16
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!
mstarcfd.com Slide 5 of 16
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
mstarcfd.com Slide 6 of 16
Underlying DMT physics are correct
mstarcfd.com Slide 7 of 16
32334/3
max 08.004.1 sm
w
DNPo
p
Nq
https://youtu.be/x0Zvun5txk8
Power dissipation output data from the DMT
mstarcfd.com Slide 8 of 16
Net effect is a change in kinetic energy
mstarcfd.com Slide 9 of 16
𝑃𝑖𝑛 − 𝑃𝑜𝑢𝑡 =𝑑𝐾
𝑑𝑡
Non-dimensionalize to create similarity solution
mstarcfd.com Slide 10 of 16
The kinetic energy number, Ke, for this system
mstarcfd.com Slide 11 of 16
Same tank: Hydrofoil versus PBT
mstarcfd.com Slide 12 of 16
𝑁𝑘,𝐻 = 0.76
𝑁𝑘,𝑃 = 2.25
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-
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
mstarcfd.com Slide 15 of 16
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
mstarcfd.com Slide 16 of 16