solving industrial design problems by using comsol
TRANSCRIPT
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Solving industrial design problems by using COMSOL
Multiphysics with MATLAB
Benjamin Ivorra
MOMAT Research group &
Instituto de Matematica Interdisciplinar &
Departamento de Matematica Aplicada
Universidad Complutense de Madrid
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Outline
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 2 / 20
• Industrial examples
- Microfluidic mixer- Toy problem
• COMSOL Multiphysics
- Creation of the model- Conversion to MATLAB
• MATLAB
- Structure of the M-script- Useful commands- Creating a function
• Conclusions
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Part I: Industrial examples
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 3 / 20
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Device: Microfluidic mixer
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 4 / 20
Application: Microfluidic mixers are used to quickly mix a proteinsolution with a solvent provoking a rapid change in chemicalpotential resulting in the unfold of certain proteins.
Example of microfluidic mixer: There exist a wide range oftechniques to create microfluidic mixers. For instance:
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Industrial problem
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 5 / 20
Objective: optimize the mixer to reduce the time needed to reacha certain protein concentration.
Considered mixer: Knight mixer
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Parameters
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 6 / 20
px
lc
h2
(cx2,cy2)
l2
ls
(cx1,cy1)
h1l1
le
θ
us
Axi
al s
ymm
etry
exit
Center inlet
Side inlet
Ω
uc
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Mathematical Modeling
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 7 / 20
Steady equations:
C
C30
90
+Convective−Diffusion
Navier−Stokes
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Design Problem
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 8 / 20
We are interested in minimizing:
J(xparam) =
∫ cxparam
30
cxparam
90
dy
uxparam(y) · t
,
where cxparam
90 , cxparam
30 and uxparam are computed by solving
numerically (COMSOL) the following system:
−∇ · (η(∇u+ (∇u)⊤)) + ρ(u · ∇)u+∇p = 0 in Ω,∇ · u = 0 in Ω,∇ · (−D∇c+ cu) = 0 in Ω,+ boundary conditions.
This optimization problem is solved by using the GlobalOptimization Platform software (MATLAB):http://www.mat.ucm.es/momat/software.htm
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Some Results
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 9 / 20
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Experimental implementation
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 10 / 20
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Bibliography
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 11 / 20
Benjamin Ivorra, Juana Redondo, Juan Santiago, PilarOrtigosa, and Angel Ramos. Two- and three-dimensionalmodeling and optimization applied to the design of a fasthydrodynamic focusing microfluidic mixer for protein folding.Physics of Fluids, 25, 032001, 2013.
David E. Hertzog, Benjamin Ivorra, Bijan Mohammadi,Olgica Bakajin, Juan G. Santiago. Optimization of a FastMicrofluidic Mixer for Studying Protein Folding Kinetics.Analytical chemistry, 78(13), 4299-4306, 2006.
Benjamin Ivorra, David E. Hertzog, Bijan Mohammadi, JuanG. Santiago. Semi-deterministic and genetic algorithms forglobal optimization of microfluidic protein-folding devices.International Journal for Numerical Methods in Engineering ,66(2), 319-333, 2006.
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Toy problem
Outline
Part I: Industrialexamples
Microfluidic mixer
Toy problem
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 12 / 20
We want to optimize the temperature of the left wall (Tl) of agiven rectangular heat chamber such that the mean spatialtemperature is 50C:
minTl∈[0,100]
J(Tl) =∣
∣
(
∫
ΩT (Tl)dx/
∫
Ω1dx
)
− 50∣
∣
Parameter
Ω
T =[0,100]ºCl
Wall
Wall
Heat PDEFixed
T=25ºC
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Part II: COMSOL Multiphysics
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 13 / 20
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Main steps
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 14 / 20
Use the COMSOL GUI to easily create the model.
Identify and isolate all the parameters to be modified by theMATLAB code.
Compress history before exporting the model to MATLABformat.
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Part III: MATLAB
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 15 / 20
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Useful MATLAB commands
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 16 / 20
mphgeom(model,’geom1’)
mphmesh(model,’mesh1’)
model.result.table(’tbl1’).getReal
mphint(model,’u’,’T’,tf,’edim’,2,’selection’,[1])
mphinterp(model,’u’,’T’,tf,’coord’,[0.2;0.2])
mphsave(model,’optimum’)
model=mphload(’optimum’)
model.variable(’var1’).set(’Tmax’, num2str(x(1)))
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Conclusions
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 17 / 20
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Extended courses
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 18 / 20
Course (10H): Metodo de Elementos Finitos:
Aplicaciones y Optimizacion con COMSOL
MULTIPHYSICS. Doctorado en Ingenierıa Matematica,Estadıstica e Investigacion Operativa. Universidad
Complutense de Madrid. February.
Seminary (2H): Simulacion numerica en Ingenierıa y
Ciencias con MATLAB + COMSOL Multiphysics.
Departamento de Fısica Aplicada II y Vicerrectorado deInvestigacion. Universidad de Malaga. May.
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Download files
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 19 / 20
Google keywords: Ivorra Benjamin Researchgate
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Thank you
Outline
Part I: Industrialexamples
Part II: COMSOLMultiphysics
Part III: MATLAB
Conclusions
12/06/2015 Iberian COMSOL Multiphysics Conference 2015 – 20 / 20
!!! Thank you for your attention!!!
Global Optimization Platform
http://www.mat.ucm.es/momat/software.htm