An integrated two-step strategy for an optimal design of liquid-cooled channel layout based on the MMC–density approach

This paper proposes an integrated two-step strategy for an optimal design of liquid-cooled channel layout based on the moving morphable component (MMC)-density approach. The proposed strategy intends to take the advantage of both the MMC approach for its high flexibility in searching a physically reasonable layout and the density approach for its better capacity of topology description. On the basis of the above-mentioned strategy, an intermediate layout is obtained through MMC approach and further optimized as initial solution of density approach step. Through density approach step, the final layout shows smoother boundary while retaining reasonable feature size. The original contributions of this paper are as follows: (i) An assembled quadratic Bézier curves component is proposed to describe the largely curved channel with limited numbers of optimization variables and computation order. (ii) Benefited from explicit geometric description, adaptive mesh refinement (AMR) is applied in MMC approach step for the first time. The application of AMR, from the numerical point of view, has two key ingredients to be highlighted: (i) the accuracy of solution in fluid–solid boundary region can be ensured with relatively limited computational cost. (ii) The contradiction that the difference step of MMC updating needs to be both as small as possible and integer multiple of the mesh size can be avoided. The performance of our methodology is demonstrated by numerical examples aiming for maximal heat exchange with power dissipation constraint. The main finding reveals that the proposed strategy can offer reasonable channel layout with better thermal performance, compared with conventional density approach. The whole numerical implementation relies on OpenFOAM and PETSc open-source software packages.