Entropy Generation Analysis During Adjoint Variable-based Topology Optimization of Porous Reaction-Diffusion Systems under Various Design Dimensionalities  

Several studies attempted to enhance the performance of various reaction-diffusion systems, such as electrodes of electrochemical devices, by modifying the spatial distribution of porosity throughout the porous reactor. However, research is proceeding without knowing the theoretical limitation of the improvement. To connect optimization techniques with a well-established theoretical approach, this paper presents topology optimization for the design of diffusion field in reaction-diffusion systems together with entropy generation analysis using nonequilibrium thermodynamics. Topology optimization of porosity distribution in reaction-diffusion systems was carried out using the adjoint variable methods. The optimization problem was formulated to maximize the reaction in the design domain. The results obtained from the investigation under various dimensionalities were compared and discussed. A formula for the local entropy generation of reaction-diffusion systems was derived and used to assess the topology optimization results. While the findings showed the insignificant difference between the overall reaction rate of 0D and 1D cases, optimization of higher dimensionalities (2D and 3D) enhanced the overall reaction rate considerably. The results revealed that the optimum porosity distribution corresponds to the most uniform and minimum entropy generation.