An approach for topology optimization of heat sinks for two-phase flow boiling: Part 2 – Model calibration and experimental validation

Abstract

Flow boiling offers increased heat transfer coefficients and effective heat capacity rates that can be leveraged by topology optimization (TO) to generate high-performance microchannel heat sinks. Topology optimization of heat sinks having two-phase flows can be accomplished using the homogenization approach wherein designs are represented as spatially varying distributions of microstructures, as demonstrated in Part 1 of this two-part study. Flow and heat transfer within the microstructures are captured using a two-phase mixture model featuring an effective porous medium formulation. However, closure of these governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, geometry, and surface finish. Therefore, it must be demonstrated these available correlations can be successfully calibrated over a range of microstructural variations present within the homogenization framework, so as to attain the required prediction generality and accuracy needed to ensure the resulting designs achieve Pareto-optimality. This Part 2 of our study successfully demonstrates a comprehensive end-to-end process for two-phase flow model calibration, topology optimized design generation, and experimental validation of optimized performance for flow boiling heat sinks. To this end, a TO algorithm with the homogenization approach and a two-phase mixture model is implemented using available flow boiling correlations for microchannels. A set of uniform pin fin calibration samples are additively manufactured and experimentally tested under flow boiling at various flow rates and heat inputs for model calibration. All of the unknown/free coefficients in the adopted correlations are determined by minimizing the error between the model predictions and the experimental measurements using gradient-based optimization. The calibrated topology optimization algorithm is then used to generate a Pareto-optimal set of heat sinks optimized for minimum pressure drop and thermal resistance during flow boiling. Experimental characterization of these additively manufactured heat sinks, unseen during the model coefficient calibration process, reveals that the measured Pareto optimality curve matches that predicted by the topology optimization algorithm. Lastly, a heat sink design is generated for a design space involving multiple hot spots and background heating to showcase the capability of the experimentally calibrated two-phase topology optimization algorithm at handling complex boundary conditions. The optimized heat sink intelligently distributes an adequate amount of coolant flow to each of the heated regions to avoid local dry-out. This work demonstrates a complete framework for two-phase topology optimization of heat sinks through experimental calibration of flow boiling correlations to the porous medium used by the homogenization approach.