<b>Machine-Learning-Aided Development of Surrogate Models for Flexible Design Optimization of Enhanced Heat Transfer Surfaces</b>
Creators: name: Pai, Saeel Shrivallabh
Publisher: name: Purdue University Graduate School
Year: 2025
Subjects: classificationCode: 401204
subject: Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)
classificationCode: 401205
subject: Experimental methods in fluid flow, heat and mass transfer

description: Due to the end of Dennard scaling, electronic devices must consume more electrical power for increased functionality. The increased power consumption, combined with diminishing form factors, results in increased power density within the device, leading to increased heat fluxes at the devices surfaces. Without proper thermal management, the increase in heat fluxes can cause device temperatures to exceed operational limits, ultimately resulting in device failure. However, the dissipation of these high heat fluxes often requires pumping or refrigeration of a coolant, which in turn, increases the total energy usage. Data centers, which form the backbone of the cloud infrastructure and the modern economy, account for ~2% of the total US electricity use, of which up to ~40% is spent on cooling needs alone. Thus, it is necessary to optimize the designs of the cooling systems to be able to dissipate higher heat fluxes, but at lower operating powers.The design optimization of various thermal management components such as cold plates, heat sinks, and heat exchangers relies on accurate prediction of flow heat transfer and pressure drop. During the iterative design process, the heat transfer and pressure drop is typically either computed numerically or obtained using geometry-specific correlations for Nusselt number (<i>Nu</i>) and friction factor (<i>f</i>). Numerical approaches are accurate for evaluation of a single design but become computationally expensive if many design iterations are required (such as during formal optimization processes). Moreover, traditional empirical correlations are highly geometry dependent and assume functional forms that could introduce inaccuracies. To overcome these limitations, this thesis introduces accurate and continuous-valued machine-learning (ML)-based surrogate models for predicting Nusselt number and friction factor on various heat exchange surfaces. These surrogate models, which are applicable to more geometries than traditional correlations, enable flexible and computationally inexpensive design optimization. The utility of these surrogate models is first demonstrated through the optimization of single-phase liquid cold plates under specific boundary conditions. Subsequently, their effectiveness is further showcased in the more practical challenge of designing liquid-to-liquid heat exchangers by integrating the surrogate models with a homogenization-based topology optimization framework. As topology optimization relies heavily on accurate predictions of pressure drop and heat transfer at every point in the domain during each iteration, using ML-based surrogate models greatly reduces the computational cost while enabling the development of high-performance, customized heat exchange surfaces. Thus, this work contributes to the advancement of thermal management by leveraging machine learning techniques for efficient and flexible design optimization processes.First, artificial neural network (ANN)-based surrogate correlations are developed to predict <i>f</i> and <i>Nu</i> for fully developed internal flow in channels of arbitrary cross section. This effectively collapses all known correlations for channels of different cross section shapes into one correlation for <i>f</i> and one for <i>Nu</i>. The predictive performance and generality of the ANN-based surrogate models is verified on various shapes outside the training dataset, and then the models are used in the design optimization of flow cross sections based on performance metrics that weigh both heat transfer and pressure drop. The optimization process leads to novel shapes outside the training data, the performance of which is validated through numerical simulations. Although the ML model predictions lose accuracy outside the training set for these novel shapes, the predictions are shown to follow the correct trends with parametric variations of the shape and therefore successfully direct the search toward optimized shapes.The success of ANN-aided shape optimization of constant cross-section internal flow channels serves as a compelling proof-of-concept, highlighting the potential of ML-aided optimization in thermal-fluid applications. However, to address the complexities of widely used thermal management devices such as cold plates and heat exchangers, known for their intricate surface geometries beyond constant cross-section channels, a strategic shift is imperative. With the goal of crafting ML models specifically tailored for practical design optimization algorithms like topology optimization, the thesis next delves into diverse micro-pin fin arrangements commonly employed in applications like cold plates and heat exchangers. This study on pin fins includes the exploration of hydrodynamic and thermal developing effects, as well as the impact of pin fin cross section shape and orientation. The ML-based predictive models are trained on numerically simulated synthetic data. The large amounts of accurate synthetic data required to train machine learning models are generated using a custom-developed simulation automation framework. With this framework, numerical flow and heat transfer simulations can be run on thousands of geometries and boundary conditions with minimal user intervention. The proposed models provide accurate predictions of <i>f</i> and <i>Nu</i>, with a near exact match to the training data as well as on unseen testing data. Furthermore, the outputs of the ANNs are inspected to propose new analytical correlations to estimate the hydrodynamic and thermal entrance lengths for flow through square pin fin arrays. The ML models are also shown to be useable for fluids other than water, employing physics-based, Prandtl-number-dependent scaling relations.The thesis further demonstrates the utility of the ML surrogate models to facilitate the design optimization of thermal management components through their integration in the topology optimization (TO) framework for heat exchanger design. Topology optimization is a computational design methodology for determining the optimal material distribution within a design space based on given constraints. The use of topology optimization in the design of heat exchangers and other thermal management devices has been gaining significant attention in recent years, particularly with the widespread availability of additive manufacturing techniques that offer geometric design flexibility. Particularly advantageous for heat exchanger design is the homogenization approach to topology optimization, which represents partial densities in the design domain using a physical unit cell structure to achieve sub-grid resolution features. This approach requires geometry-specific, correlations for <i>f</i> and <i>Nu</i> to simulate the performance of designs and evaluate the objective function during the optimization process. Topology optimized pin fin-based component designs rely on additive manufacturing, posing production scalability challenges with current technologies. Furthermore, the demand for flow and thermal anisotropy in several applications adds complexity to the design requirements. To address these challenges, the focus is shifted to traditional heat exchanger surface geometries that can be manufactured using conventional techniques, and which also exhibit pronounced anisotropy in flow and heat transfer characteristics. Traditionally, these geometries are distributed uniformly across heat exchange surfaces. However, incorporating such geometries into the topology optimization framework merges the strengths of both approaches, yielding mathematically optimized heat exchange surfaces with conventionally manufacturable designs. Offset strip fins, one such commonly used geometry, is chosen to be the physical unit cell structure to demonstrate the integration of ML-based surrogate models into the topology optimization framework. The large amount of data required to develop robust machine learning-based surrogate <i>f</i> and <i>Nu</i> models for axial and cross flow of water through offset strip fins are generated through numerical simulations performed for convective flows through these geometries. The data generated are compared against in-house-measured experimental data as well as against data from literature. To facilitate the integration of ML models into topology optimization, a discrete adjoint method was developed to calculate the sensitivities during topology optimization, to circumvent the absence of the analytical gradients.Successful integration of the machine learning-based surrogate models into the topology optimization framework was demonstrated through the design optimization of a counterflow heat exchanger. The topology optimized design outperformed the benchmarks that used uniform, parametrically optimized offset strip fin arrays. The topology optimized design exhibited domain-specific enhancements such as peripheral flow paths for enhanced heat transfer and open channels to minimize pressure drops. This integration showcases the potential of combining ML models with topology optimization, providing a flexible framework that can be extended to a wide range of enhanced surface structure types and geometric configurations for which ML models can be trained. Thus, by enabling spatially localized optimization of enhanced surface structures using ML models, and consequently offering a pathway for expanding the design space to include many more surface structures in the topology optimization framework than previously possible, this thesis lays the foundation for advancing design optimization of thermal-fluid components and systems, using both additively and conventionally manufacturable geometries.