Solving industrial design problems by using COMSOL Multiphysics ...

Solving industrial design problems by using COMSOL Multiphysics with MATLAB Benjamin Ivorra MOMAT Research group & Instituto de Matem´ atica Interdisciplinar & Departamento de Matem´ atica Aplicada Universidad Complutense de Madrid

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Outline Outline

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Part I: Industrial examples

- Microfluidic mixer - Toy problem

Part II: COMSOL Multiphysics Part III: MATLAB

Industrial examples

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Conclusions

COMSOL Multiphysics - Creation of the model - Conversion to MATLAB

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MATLAB - Structure of the M-script - Useful commands - Creating a function

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Conclusions

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Outline Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Part I: Industrial examples

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Device: Microfluidic mixer Outline Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics

Application: Microfluidic mixers are used to quickly mix a protein solution with a solvent provoking a rapid change in chemical potential resulting in the unfold of certain proteins. Example of microfluidic mixer: There exist a wide range of techniques to create microfluidic mixers. For instance:

Part III: MATLAB Conclusions

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Industrial problem Outline Part I: Industrial examples Microfluidic mixer Toy problem

Objective: optimize the mixer to reduce the time needed to reach a certain protein concentration. Considered mixer: Knight mixer

Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Parameters Center inlet Outline lc

Part I: Industrial examples Microfluidic mixer Toy problem

Side inlet

uc

px (cx2,cy2) l2 h2

Part III: MATLAB Conclusions

Axial symmetry

Part II: COMSOL Multiphysics

Ω

us

ls

h1 l1 (cx1,cy1)

θ

le

exit

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Mathematical Modeling Outline Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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C90 Steady equations:

C30

Navier−Stokes + Convective−Diffusion

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Design Problem We are interested in minimizing: Outline

x

Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

J(xparam ) = x

Z

c30param x

c90param

dy , uxparam (y) · t

x

where c90param , c30param and uxparam are computed by solving numerically (COMSOL) the following system:  ⊤ )) + ρ(u · ∇)u + ∇p = 0 in Ω, −∇ · (η(∇u + (∇u)    ∇·u=0 in Ω, ∇ · (−D∇c + cu) = 0 in Ω,    + boundary conditions. This optimization problem is solved by using the Global Optimization Platform software (MATLAB): http://www.mat.ucm.es/momat/software.htm

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Some Results Outline Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Experimental implementation Outline Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Bibliography Outline

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Benjamin Ivorra, Juana Redondo, Juan Santiago, Pilar Ortigosa, and Angel Ramos. Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding. Physics of Fluids, 25, 032001, 2013.

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David E. Hertzog, Benjamin Ivorra, Bijan Mohammadi, Olgica Bakajin, Juan G. Santiago. Optimization of a Fast Microfluidic Mixer for Studying Protein Folding Kinetics. Analytical chemistry, 78(13), 4299-4306, 2006.

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Benjamin Ivorra, David E. Hertzog, Bijan Mohammadi, Juan G. Santiago. Semi-deterministic and genetic algorithms for global optimization of microfluidic protein-folding devices. International Journal for Numerical Methods in Engineering , 66(2), 319-333, 2006.

Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Toy problem Outline Part I: Industrial examples Microfluidic mixer Toy problem Part II: COMSOL Multiphysics Part III: MATLAB

We want to optimize the temperature of the left wall (Tl ) of a given rectangular heat chamber such that the mean spatial temperature is 50◦ C: ZZ ZZ
min J(Tl ) = T (x, y, Tl )dxdy/ 1dxdy − 50 Tl ∈[0,100]

Ω

Ω

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Conclusions

Wall

Tl=[0,100]ºC Parameter

Ω

Heat PDE

T=25ºC Fixed

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Wall 12/06/2015

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Outline Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

Part II: COMSOL Multiphysics

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Main steps Outline

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Use the COMSOL GUI to easily create the model.

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Identify and isolate all the parameters to be modified by the MATLAB code.

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Compress history before exporting the model to MATLAB format.

Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Outline Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

Part III: MATLAB

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Useful MATLAB commands Outline Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB

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mphgeom(model,’geom1’)

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mphmesh(model,’mesh1’)

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model.result.table(’tbl1’).getReal

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mphint(model,’u’,’T’,tf,’edim’,2,’selection’,[1])

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mphinterp(model,’u’,’T’,tf,’coord’,[0.2;0.2])

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mphsave(model,’optimum’)

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model=mphload(’optimum’)

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model.variable(’var1’).set(’Tmax’, num2str(x(1)))

Conclusions

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Outline Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

Conclusions

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Extended courses Outline

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etodo de Elementos Finitos: Course (10H): M´ Aplicaciones y Optimizaci´ on con COMSOL MULTIPHYSICS. Doctorado en Ingenier´ıa Matem´atica, Estad´ıstica e Investigaci´ on Operativa. Universidad Complutense de Madrid. February.

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Seminary (2H): Simulaci´ on num´ erica en Ingenier´ıa y Ciencias con MATLAB + COMSOL Multiphysics. Departamento de F´ısica Aplicada II y Vicerrectorado de Investigaci´ on. Universidad de M´ alaga. May.

Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Download files Google keywords: Ivorra Benjamin Researchgate Outline Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB Conclusions

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Thank you Outline

!!! Thank you for your attention!!!

Part I: Industrial examples Part II: COMSOL Multiphysics Part III: MATLAB

Global Optimization Platform http://www.mat.ucm.es/momat/software.htm

Conclusions

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