3D dimensionally reduced modeling and gradient-based optimization of microchannel cooling networks

This paper presents a dimensionally reduced thermal model and gradient-based shape optimization scheme for the 3D computational design of actively cooled panels. A correction method previously used in wire-based electromagnetics is applied to address convergence issues associated with the singularity of the thermal solution along the microchannels. The numerical solution is obtained with the interface-enriched generalized finite element method (IGFEM), which greatly simplifies mesh generation by allowing for the use of a non-conforming mesh to capture the temperature gradient discontinuity across the microchannels. The temperature distribution calculated with the IGFEM on coarse meshes agrees with that obtained using significantly more complex and costly ANSYS FLUENT simulations. We then combine the IGFEM with a sensitivity analysis and the sequential quadratic programming algorithm in MATLAB to solve two sets of shape optimization problems related to actively cooled microvascular composite panels. These problems demonstrate a key advantage of the IGFEM in avoiding severe mesh distortion during shape optimization. Lastly, we present a semi-analytical model based on the concept of the zone of influence of a channel to estimate the maximum temperature of an actively cooled plate with straight embedded microchannels.