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A 2D model for hydrodynamics and biology coupling applied toalgae growth simulations

Published online by Cambridge University Press:  30 July 2013

Olivier Bernard ,
Anne-Céline Boulanger ,
Marie-Odile Bristeau  and
Jacques Sainte-Marie
Olivier Bernard
Affiliation:
Inria, team BioCore, BP93, 06902 Sophia-Antipolis Cedex, France.. [email protected]
Anne-Céline Boulanger
Affiliation:
Inria, team ANGE, B.P. 105, 78153 Le Chesnay Cedex, France.; [email protected] UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.; [email protected]
Marie-Odile Bristeau
Affiliation:
Inria, team ANGE, B.P. 105, 78153 Le Chesnay Cedex, France.; [email protected] UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.; [email protected]
Jacques Sainte-Marie
Affiliation:
Inria, team ANGE, B.P. 105, 78153 Le Chesnay Cedex, France.; [email protected] UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 75005, Paris, France.; [email protected] CETMEF, 2 boulevard Gambetta, 60200 Compiègne, France.; [email protected]
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Abstract

Cultivating oleaginous microalgae in specific culturing devices such as raceways is seenas a future way to produce biofuel. The complexity of this process coupling non linearbiological activity to hydrodynamics makes the optimization problem very delicate. Thelarge amount of parameters to be taken into account paves the way for a usefulmathematical modeling. Due to the heterogeneity of raceways along the depth dimensionregarding temperature, light intensity or nutrients availability, we adopt a multilayerapproach for hydrodynamics and biology. For free surface hydrodynamics, we use amultilayer Saint–Venant model that allows mass exchanges, forced by a simplifiedrepresentation of the paddlewheel. Then, starting from an improved Droop model thatincludes light effect on algae growth, we derive a similar multilayer system for thebiological part. A kinetic interpretation of the whole system results in an efficientnumerical scheme. We show through numerical simulations in two dimensions that ourapproach is capable of discriminating between situations of mixed water or calm andheterogeneous pond. Moreover, we exhibit that a posteriori treatment ofour velocity fields can provide lagrangian trajectories which are of great interest toassess the actual light pattern perceived by the algal cells and therefore understand itsimpact on the photosynthesis process.

Keywords

Hydrostatic Navier–Stokes equationsSaint–Venant equationsfree surface stratified flowsmultilayer systemkinetic schemedroop modelracewayhydrodynamics and biology couplingalgae growth
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1387 - 1412
Copyright
© EDP Sciences, SMAI, 2013

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