Topology Optimization of Heat and Mass Transfer Problems: Laminar Flow

Abstract

International audienceThe design of efficient structures for heat and mass transfer problems involves the implementation of an appropriate topology optimization strategy in order to fully take into account the bi-objective nature of the problem. This article couples the finite-volume method (FVM), for the direct solver, with the discrete adjoint approach, for the sensitivity analysis, in order to tackle both fluid dynamic and heat transfer optimization in the frame of laminar flows. Details are provided about the sparsity pattern of the discrete adjoint system, which requires special attention to select a suitable matrix iterative solver. Several examples underline the adequacy of topology optimization in conjunction with the FVM for the minimization of the power dissipated by the fluid. Then, a bi-objective problem aiming at minimizing the pressure drop while maximizing the recoverable thermal power is solved by the identification of its Pareto frontier, thanks to an aggregate objective function (AOF) method. The main conclusion deals with the possibility of finding an acceptable trade-off between both objectives and the potential of topology optimization for heat and mass transfer optimization

A design approach for integrating thermoelectric devices using topology optimization

“…Prior studies on heat transfer using topology optimization have mainly focused on pure 2D heat conduction problems [22,26,27] as well as heat conduction with convective heat transfer to an ambient fluid [28][29][30][31][32]. Later works have included the explicit modeling of the fluid flow within the optimization domain in thermo-fluid models with forced convection in 2D [33][34][35][36][37][38] and 3D [39]. More recent applications of the approach have extended models to consider 2D topology optimization of natural convection [40] and radiation as the dominant heat transfer mechanism [41].…”

Topology optimization of inertia driven dosing units

“…passive transport (Andreasen et al, 2009), reacting flows (Okkels and Bruus, 2007), buoyancy problems (Alexandersen et al, 2014), active transport e.g. heat (Yoon, 2010a;Marck et al, 2013;Alexandersen et al, 2016). Models for including the fluid structure interaction have been developed as demonstrated in Yoon (2010b) and Kreissl et al (2010).…”

Topology optimization of convective laminar heat transfer

“…Let denote dJ(η), h , the differential of J with respect to η in direction h. This derivative is determined thanks to an adjoint state built from the discrete form of Problem (1): the corresponding numerical strategy is detailed in [23] and is beyond the scope of this proceeding. However, before being used in the optimization process, the shape derivative is filtered with a convolution product involving the discrete field η as follows (see [7]),…”

“…This set of equations is discretized with the finite volume method and the so-called SIMPLER algorithm is used to solve the pressure-velocity coupling [22]. Furthermore, an additional correction is included to properly take into account the viscous dissipation caused by the wall shear stress along the solid domain (see [23] for details).…”