Purdue University Graduate School


Reason: Some of the chapters/papers in the thesis are not published yet. I need the papers to be published before the thesis is published.





until file(s) become available

Topology Optimization of Microchannel Heat  Sinks under Single- and Two-Phase Flows

posted on 2023-08-04, 17:30 authored by Serdar OzgucSerdar Ozguc

Advancements in future technologies such as artificial intelligence, electric vehicles, and renewable energy create a consistent need for more powerful and smaller electronic devices and systems. As a result, thermal management components such as heat sinks need to remove higher heat loads from more compact spaces to keep electronics within their operational temperature limits. Constraints imposed by conventional manufacturing processes restrict the design of heat sinks to simple geometries with limited cooling performance. Recent widespread commercialization of metal additive manufacturing (AM) tools offers new potential for leveraging the design freedom of these manufacturing technologies to design and fabricate heat sinks with improved performance. 

In AM, three dimensional parts are created through layer-by-layer depositing of materials, which allows fabrication of complex geometries that would be impossible or too costly using conventional subtractive methods. Many novel heat sink geometries have been proposed in literature which incorporate features such as manifolds, flow mixers, and curved channels using engineering intuition to reduce pressure drop or enhance heat transfer. Although such designs have been shown to offer improved performance, mathematical design algorithms such as topology optimization (TO) have been shown to outperform engineering intuition. Topology optimization optimizes the material distribution within a given design space, guided by physics-based simulations, to achieve a user-defined objective such as minimization of thermal resistance. Previous TO approaches have used penalization methods to ensure the final designs are composed of macroscopic and non-porous features due to the past precedent of fabrication capabilities. This traditional penalization approach is well-suited to the constraints of conventional manufacturing methods; however, microstructures and porous features are easily fabricable with additive manufacturing. There is a need to develop TO approaches that are better suited for leveraging AM for the design of heat sinks. In this thesis, a homogenization approach to topology optimization is proposed wherein the material distribution is represented as parametrized microstructures. This formulation allows design of thermal management components that have sub-grid features and leverages AM for fabrication. The focus of this thesis is the development of the homogenization approach for TO of heat sinks, as well as the exploration of the design problems it can address, the performance benefits made available, and the two-phase flow physics that it uniquely allows to be incorporated into the topology optimization process.

A topology optimization algorithm using the homogenization approach is developed by representing the material distribution as arrays of pin fins with varying gap sizes. To this end, the pin fins are modeled as a porous medium with volume-averaged effective properties. Height-averaged two-dimensional flow and non-equilibrium thermal models for porous media are developed for transport in the pin fin array. Through multi-objective optimization, TO designs are generated for an example case involving a hotspot over a uniform background heat input. The resulting topologies have porous-membrane-like designs where the liquid is transported through a fractal network of open, low-hydraulic-resistance manifold pathways and then forced across tightly spaced arrays of pin fins for effective heat transfer. The TO designs are revealed to offer significant performance improvements relative to the benchmark straight microchannel (SMC) heat sink with features optimized under the same multi-objective cost function. A series of microchannel heat sinks are fabricated using direct metal laser sintering to investigate the printing capabilities and to experimentally demonstrate the performance of topology optimized designs. Advantages of the homogenization approach over the penalization approach can be summarized as follows: (1) reduced computational costs due to its ability to create sub-resolution features, (2) intrinsically fabricable parts using available metal AM tools, and (3) easier to use due to significantly reduced number of hyperparameters (e.g., penalization factors) that are controlled by the user. 

Topology optimization has been applied to thermal management methods involving single-phase flows such as natural convection, forced air cooling, and pumped liquid cooling. Compared to these conventional heat sink technologies, flow boiling offers very high heat transfer coefficients and effective heat capacities, making it a promising candidate for future cooling electronics applications. The final goal of this thesis is to enable topology optimization of flow boiling heat sinks. However, TO of flow boiling heat sinks has been avoided due to difficulties in modeling the boiling phenomena; of note, there are no examples of TO being applied to the design of heat sink under flow boiling throughout the literature. Multi-dimensional two-phase flow models require prior knowledge of friction factor and heat transfer coefficients. Correlations are available in literature but are not universal and depend significantly on channel/fin geometries, surface roughness, and operating conditions. Given that traditional penalization-based TO approach results in fin and channel geometries with unknown shapes, dimensions, and alignment before the optimization is completed, this prohibits their use for optimization of flow boiling heat sinks. However, the homogenization approach to topology optimization developed in this thesis enables the optimization of flow boiling heat sinks. As it relies on user-defined microstructures with known shapes, alignments, and ranges of geometric dimensions, a universal correlation for flow boiling in microchannels is not needed. Instead, correlations for the user-defined microstructures are sufficient to simulate flow boiling in TO designs generated using the homogenization approach. To this end, a predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. Topology optimized heat sink designs under flow-boiling are generated and investigated at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared.  There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.

The flow and heat transfer of the TO algorithm for microchannel heat sinks under flow boiling use a two-phase mixture model featuring an effective porous medium formulation. However, closure of the governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, microstructure 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. To this end, 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. 

The major contribution of this thesis is the development of a homogenization approach for TO of additively manufactured microchannel heat sinks under single- and two-phase flows. Not only does the homogenization approach provide several advantages over the traditional penalization approaches such as reduced computational costs, intrinsic fabricability using AM, and ease of use, but it also enables TO of heat sinks under flow boiling and potentially TO of other two-phase thermal management components. The work discussed in this thesis serves a comprehensive end-to-end guide on TO of microchannel heat sinks using the homogenization approach with experimental demonstrations for validation.


Degree Type

  • Doctor of Philosophy


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Justin A. Weibel

Advisor/Supervisor/Committee co-chair

Liang Pan

Additional Committee Member 2

Partha P. Mukherjee

Additional Committee Member 3

John Howarter