Direct simulation of transport through stochastic porous media

Karthik Kumar Bodla, Purdue University

Abstract

Porous sintered microstructures are critical to the functioning of heat transport devices such as heat pipes and vapor chambers that are employed in a variety of thermal management applications. Accurate understanding of the pore-scale transport phenomena is important for enhancing the thermal performance of such devices. In the first part of the thesis, a direct simulation methodology based on the actual, detailed microstructure of the porous media obtained via X-ray microtomography is developed for predicting fundamental transport characteristics. Open-celled aluminum foams are first considered for validating the procedure. The approach is then employed for predicting single- and two-phase transport properties of commercial sintered copper wicks. In the later part of the thesis, two different approaches useful for designing optimized wick structures are presented. X-ray microtomography is a novel, non-destructive 3D imaging technique suitable for analyzing intricate porous media. Three commercial metal foam samples of similar volumetric porosity (in the range ∼ 91–93%), but with different pore sizes (10, 20 and 40 pores per inch), are first considered for validating the direct simulation approach developed here. Effective transport properties such as thermal conductivity and interfacial heat transfer coefficient are computed and successfully compared against data and models from the literature. A network model for the estimation of effective thermal conductivity of open-celled metal foams, constructed out of 3D image skeletons is then presented, and significant computational cost savings relative to detailed numerical analysis are demonstrated. A thorough microstructural characterization of foam features—pore size, ligament thickness, ligament length and pore shapes—is also performed. All the three foam samples are observed to have similar pore shapes and volumetric porosity, while the other features scale with pore size. The validated direct simulation approach is then employed for a detailed characterization of single-phase transport properties of commercially available sintered copper wick microstructures, in the second part of the thesis. A scan resolution of 5.5 µm is employed, and the current computations are compared with correlations and other experimental data available in the literature. Based on the computational results, new correlations for predicting convective heat transfer through porous sintered beds are also proposed. Pore-scale analysis of thin-film evaporation through sintered copper wicks is subsequently performed, again employing real microstructures. For improving convergence, modifications are introduced into the Volume of Fluid (VOF) model available in a commercial software package. Important two-phase characteristics, such as capillary pressure, effective pore radius, and evaporative mass and heat fluxes, are estimated. Based on the analysis, the best performing sample (particle size range) is identified along with the optimum contact angle. The final part of the thesis focuses on reverse-engineering and design of sintered wick structures with two approaches. In the first approach, a cellular automaton model is developed for predicting microstructural evolution during sintering. After thorough validation, the developed model is employed to predict the sintering dynamics of randomly packed multi-particle configurations in two and three dimensions. The effect of sintering parameters, particle size, and porosity on fundamental transport properties, viz., effective thermal conductivity and permeability, is quantified. The second approach employs 2D image data which are readily obtainable via techniques such as SEM. Firstly, based on the two-point autocorrelation function, a detailed microstructural characterization of sintered beds is performed. Further, a reconstruction technique is implemented for reconstructing a three-dimensional stochastic equivalent structure of the considered thin-sections. These reconstructed domains are employed for predicting single-phase fluid-thermal characteristics, and a detailed comparison with the actual 3D XMT data is also performed. Finally, based on the nature of two-point autocorrelation functions, a new parametrized model is proposed for the design of porous materials. The utility of this model in reconstructing three-dimensional porous microstructures with controllable fluid-thermal properties of interest is demonstrated. With advances in additive manufacturing techniques, such an approach may eventually be employed to design intricate porous structures with properties tailored to specific applications.

Degree

Ph.D.

Advisors

Murthy, Purdue University.

Subject Area

Mechanical engineering

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