A multi-objective optimization problem in natural convection for a vertical channel asymmetrically heated

Abstract : This paper deals with a multi-objective topology optimization problem in an asymmetrically heated channel, considering both pressure drop minimization and heat transfer maximization. The problem is modeled under the assumptions of steady-state laminar flow dominated by natural convection forces. The incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation are employed and are solved with the finite volume method. In this paper, we propose two new objective functions: the first one takes into account work of pressure forces and contributes to the loss of mechanical power while the second one is related to thermal power and is linked to the maximization of heat exchanges. In order to obtain a well-defined fluid-solid interface in the optimized design, we use a sigmoid interpolation function for both the design variable field and the effective diffusivity. We also use adjoint sensitivity analysis to compute the gradient of the cost functional. Results are obtained for various Richardson (Ri) number such that 100 < Ri < 400 and for a Reynolds (Re) number set to Re=400. In all considered cases, our algorithm succeeds to enhance one of the phenomenon modeled by our new cost functions without deteriorating the other one. We also show that the reversal flow is suppressed at the exit of the channel, the thermal exchanges are improved by our optimized designs. We also compare the results of standard cost functions from the literature to those of our cost functions. We show that the new objective functions reached stable values in less iteration number and allow best connectivity of solid elements. As a result the new objective functions proposed in this paper are well suited to deal with natural convection optimization problem.
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Pré-publication, Document de travail
2018
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http://hal.univ-reunion.fr/hal-01620054
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Soumis le : mercredi 30 mai 2018 - 10:16:48
Dernière modification le : dimanche 10 juin 2018 - 12:46:48

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  • HAL Id : hal-01620054, version 2

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Delphine Ramalingom, Pierre-Henri Cocquet, Rezah Maleck, Alain Bastide. A multi-objective optimization problem in natural convection for a vertical channel asymmetrically heated. 2018. 〈hal-01620054v2〉

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