Three-dimensional fluid topology optimization for heat transfer

Abstract

In this work, an in house topology optimization (TO) solver is developed to optimize a conjugate heat transfer problem: realizing more complex and efficient coolant systems by minimizing pressure losses and maximizing the heat transfer. The TO method consists in an idealized sedimentation process in which a design variable, in this case impermeability, is iteratively updated across the domain. The optimal solution is the solidified region uniquely defined by the final distribution of impermeability. Due to the geometrical complexity of the optimal solutions obtained, this design method is not always suitable for classic manufacturing methods (molding, stamping....) On the contrary, it can be thought as an approach to better and fully exploit the flexibility offered by additive manufacturing (AM), still often used on old and less efficient design techniques. In the present article, the proposed method is developed using a Lagrangian optimization approach to minimize stagnation pressure dissipation while maximizing heat transfer between fluid and solid region. An impermeability dependent thermal conductivity is included and a smoother operator is adopted to bound thermal diffusivity gradients across solid and fluid. Simulations are performed on a straight squared duct domain. The variability of the results is shown on the basis of different weights of the objective functions. The solver builds automatically three-dimensional structures enhancing the heat transfer level between the walls and the flow through the generation of pairs of counter rotating vortices. This is consistent to solution proposed in literature like v-shaped ribs, even if the geometry generated is more complex and more efficient. It is possible to define the desired level of heat transfer and losses and obtain the closest optimal solution. It is the first time that a conjugate heat transfer optimization problem, with these constraints, has been tackled with this approach for three-dimensional geometries.

A Review of Topology Optimisation for Fluid-Based Problems

“…In 2019, Pietropaoli et al [135] extended their previous work to three-dimensional internal coolant systems. Makhija and Beran [136] presented a concurrent optimisation method using a shape parametrisation for the external shape and a density-based parametrisation for the internal geometry.…”

“…For species transport, there are four papers [93,98,105,107]. For conjugate heat transfer, there are eight in forced convection [110,117,119,122,126,129,132,135] and six in natural convection [150,151,[153][154][155]160]. The fluid-structure interaction category counts four papers [164,168,172,173], but it must be noted that, common for all, the three-dimensional design freedom is severely limited, as the design domain is restricted in the third dimension.…”

Topology optimization of thermal fluid–structure systems using body-fitted meshes and parallel computing

“…Fairly many works have proposed topology optimization methods for situations where several of the aforementioned physical effects arise: convective heat transfer problems (involving coupled fluid and thermal equations, where the elastic response of the underlying structure is neglected) have been addressed using density methods [73,34,38,109,97,37,36,86,91], or variants of the level-set method [4,29,107]. Systems featuring interactions between a fluid and a solid phase, without taking thermal effects into account, have been studied in slightly fewer works, and in two space dimensions only [108,80,14,57,72,66].…”

Deep Neural Network and Monte Carlo Tree Search applied to Fluid-Structure Topology Optimization

“…The structure design is optimized according to the fluid path which drives the solution and performance. The objective of a FSTO is to build for example channels with low pressure losses and high heat transfer [3][4][5] .…”

“…Some examples can be found by the recent work of 10 , who minimized the pressure losses. Other examples using LSM include 11,12 while an adjoint formulation has been used by [3][4][5] .…”