Upload
richard-grenville
View
7.501
Download
5
Embed Size (px)
Citation preview
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
โข Hydraulic efficiency (Brown (2010)):
โ Ratio of Fluid Kinetic Energy to Mechanical Energy
Input
โข Flow efficiency (after Foลt et al. (2010)):
โ Mass of Fluid Pumped per Joule of Energy Input
mstarcfd.com Slide 2 of 16
Po
Fl
ฯ
8=ฯ
3
2HYDR
2/3-3/4
3/12FLOW)Tฮต()
T
D(
Po
Fl08.1=
)ND(ฯPo
ฯFl=
P
Qฯ=ฯ
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
๐ฃ๐ฆ ๐ = 0.5๐2 ๐ฃ๐ฆ ๐ = 0.1๐2 + 0.2
๐๐ =2๐ ๐ฃ๐ฆ๐๐๐
๐
๐
๐๐ท3 =๐
4 ๐๐ =
2๐ ๐ฃ๐ฆ๐๐๐๐
๐
๐๐ท3 =๐
4
๐พ =๐ ๐ฃ๐ฆ
3๐๐๐
๐
๐
๐3๐ท5 =57๐
7000= 0.008 ๐พ =
๐ ๐ฃ๐ฆ3๐๐๐
๐
๐
๐3๐ท5 =๐
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
๐๐๐ โ ๐๐๐ข๐ก =๐๐พ
๐๐ก
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
๐๐,๐ป = 0.76
๐๐,๐ = 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
โข Boltzmann is excellent at running numerical experiments
โ No meshing
โ LES turbulence/correct EDR
โ 3D/Fully transient
โ Scales exceptionally well on HPC
โข Impeller efficiency is governed by first law of thermodynamics
โ Power In-Power Out=Total Kinetic Energy
โ Can derive a system-specific Nk
โ Function of impeller/tank competition
โข Np and Nk together combine to score relative efficiency
โข Still should consider implications of energy distribution
mstarcfd.com Slide 16 of 16