Shape optimization of fluid cooling channel based on Darcy reduced-order isogeometric analysis

There exists the inconsistency among the design model, the analysis model, and the optimization model for the fluid cooling channel, as well as the numerical difficulty and the high computational cost caused by solving the problem of forced convection heat transfer. Our method overcomes these issues by three steps. Firstly, the seamless conversion among the three models is achieved through volume parametric reconstruction. The initial fluid cooling channel model is obtained based on some topological optimization methods, then a suitable model for isogeometric analysis (IGA) is reconstructed. Secondly, the IGA of the heat flux coupling problem is realized. To get a low-cost but sufficiently accurate analysis results, the Darcy reduced-order model is introduced when applying the IGA method, and the method is called DRIGA. After derivation of formulas for DRIGA, and applying the material properties and the boundary conditions, the problem of forced convection heat transfer is solved. With the same Darcy's reduced-order model, the calculation is finished by the finite element method (FEM), and the method is called DRFEM. Solution accuracy is studied by comparing with the solution results from the COMSOL, DRFEM and DRIGA to verify the precision and effectiveness of DRIGA. Finally, the shape optimization is realized by taking the control points on the boundary of the solid and liquid as design variables and the average temperature as objective function. After optimization, not only the average temperature is reduced, but also the boundary is continuous and smooth. The given examples show that high solution accuracy and efficient convergence can be obtained with the condition of fewer computing elements in our method.