Using HPC to Advance Water Desalination By Electrodialysis
-
Upload
insidehpc -
Category
Technology
-
view
463 -
download
1
Transcript of Using HPC to Advance Water Desalination By Electrodialysis
![Page 1: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/1.jpg)
Using HPC To Advance Water Desalination By
Electrodialysis
Clara Druzgalski Department of Mechanical Engineering
Stanford University
![Page 2: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/2.jpg)
Water Desalination
Distillation
Reverse Osmosis
Electrodialysis
![Page 3: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/3.jpg)
Electrodialysis: Industrial Electrodialysis water treatment plants in Barcelona, Spain produce 257 million liters of water per day. Abrera (2007) 200 million liters Sant Boi del Llobregat (2009) 57 million liters
Credit: Sant Boi del Llobregat
![Page 4: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/4.jpg)
Electrodialysis: Applications
Gray White Black
Portable water treatment
Salt production
Biomedical analysis: lab-on-a-chip devices
![Page 5: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/5.jpg)
Electrodialysis
![Page 6: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/6.jpg)
Model Problem
Channel Height 10-6 meters
Smallest Feature 10-9 meters
Applied voltage 1-3 Volts
Example Dimensional Values
![Page 7: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/7.jpg)
Model Problem: Experiments
Well-described by 1D theory
Electroconvective chaos: 1D theory
no longer predictive
![Page 8: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/8.jpg)
“ Should we use a commercial
code like Comsol Multiphysics or build a high performance
code from scratch?
?
![Page 9: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/9.jpg)
Commercial Software
Commercial codes often use artificial smoothening for numerical robustness. This dissipates small structures generated by turbulent and chaotic fluid motion.
Commerical codes must be general
enough to handle a wide variety of problems, but this limits the user’s ability to take advantage of crucial time-saving algorithms
![Page 10: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/10.jpg)
Commercial Software
![Page 11: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/11.jpg)
Custom HPC Software
EKaos a high performance direct numerical simulation code that simulates electrokinetic chaos. No artificial smoothening
Over 100 times faster than Comsol on a single node in 2D.
![Page 12: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/12.jpg)
EKaos
![Page 13: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/13.jpg)
2D EKaos Simulation Concentration
Charge Density
![Page 14: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/14.jpg)
Experimental Observation
Joeri C. de Valença, R. Martijn Wagterveld, Rob G. H. Lammertink, and Peichun Amy Tsai Phys. Rev. E 92, 031003(R) – Published 8 September 2015
![Page 15: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/15.jpg)
Simulation vs. Experiment
Experiment: De Valenca, et. al.
Simulation: Davidson, et. al. Submitted to Scientific Reports
![Page 16: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/16.jpg)
2D EKaos: Current-Voltage
16
![Page 17: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/17.jpg)
2D EKaos: Current-Voltage
Qualitative matching with experiment 17
![Page 18: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/18.jpg)
3D EKaos Simulation
![Page 19: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/19.jpg)
165 million mesh points That’s over 1 billion degrees of freedom
11 terabytes of data Per simulation
100,000 time steps To reach converged statistics
Each 3D EKaos simulation…
![Page 20: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/20.jpg)
“ Why is a simulation of just one small section of a desalination channel so
computationally expensive?
?
The computational cost is determined by the range of relevant length and time scales that must be
resolved.
![Page 21: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/21.jpg)
Algorithm
Details The mathematical details behind a high performance code
![Page 22: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/22.jpg)
Governing Equations SpeciesConserva.on:
Navier-Stokes:
Gauss’sLaw:
c+ Concentration of cation c- Concentration of anion ϕ Electric potential u Velocity vector P Pressure 22
yx
![Page 23: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/23.jpg)
Governing Equations SpeciesConserva.on:
Navier-Stokes:
Gauss’sLaw:
23
yx
Reservoir:BoundaryCondi.ons
Membrane:Periodicinxandzdirec.ons
![Page 24: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/24.jpg)
Dimensionless Parameters Parameter Description Range Value
ϵ Screening length, EDL size 10-6 – 10-3 10-3 Δϕ Applied voltage 20-120 120 κ Electrohydrodynamic coupling const. O(1) 0.5 c0
+ Cation concentration at membrane >1 2 Sc Schmidt number 103 103
24
![Page 25: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/25.jpg)
Spatial Discretization
25
EKaos: 2D and 3D Direct numerical simulation (DNS) 3D has over 165 million spatial grid points Staggered mesh configuration Non-uniform mesh is used in the membrane-normal direction to handle sharp gradients Discretization: 2nd order central finite difference scheme
![Page 26: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/26.jpg)
Time Integration SpeciesConserva.on
Navier-Stokes
Gauss’sLaw
26
![Page 27: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/27.jpg)
Time Integration SpeciesConserva.on
2ndOrderImplicitScheme
Semi-Implicit:1storder
27
![Page 28: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/28.jpg)
Time Integration Itera.veAlgorithm
δ-form
Lineariza.on
28
![Page 29: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/29.jpg)
Time Integration Itera.veAlgorithm
δ-form
Lineariza.on
29
![Page 30: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/30.jpg)
Time Integration Equa.oninδ-form
RemoveDirec.onalCoupling
Movenon-s.fftermstoleQhandside
30
![Page 31: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/31.jpg)
Time Integration Equa.oninδ-form
RemoveDirec.onalCoupling
Movenon-s.fftermstoleQhandside
31
![Page 32: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/32.jpg)
Time Integration Equa.oninδ-form
Analy.calsubs.tu.onusingGauss’sLaw
RemoveDirec.onalCoupling
![Page 33: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/33.jpg)
Time Integration FinalEqua.on
• LeQhandsideoperatorislinearandnowonlyinvolveslocalcouplingbetweenδc+andδc-
• Weneedtosolveforu*,v*,w*,P*,andϕ*ateachitera.on
33
![Page 34: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/34.jpg)
Pseudo-spectral Solver Conserva.onofmomentum
Pressureequa.on
Gauss’sLaw
34
![Page 35: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/35.jpg)
By taking advantage of the geometry and using physical insight we were able to: 1. Design operators that reduced the
matrix bandwidth 2. Use fast and robust math libraries
such as LAPACK and FFTW 3. Reduce communication cost across
processors by des ign ing the algorithm with parallelization in mind.
![Page 36: Using HPC to Advance Water Desalination By Electrodialysis](https://reader031.fdocuments.in/reader031/viewer/2022030216/5887d6571a28abfb678b4d3f/html5/thumbnails/36.jpg)
Conclusions Developed EKaos: a parallel 3D DNS code to
simulate electroconvective chaos. Developed a numerical algorithm for efficiently
solving the coupled Poisson-Nernst-Planck and Navier-Stokes equations Improved prediction of mean current density that
has been observed in experiments Comparison of 2D and 3D simulations show
qualitative similarities, but quantitative differences Electroconvective chaos can generate structures
similar to turbulence. 36