A 3D ALE Finite Element Method for Two-Phase Flows with Phase Change

A new numerical method is proposed to study two-phase flow and heat transfer for interlayer cooling of the new generation of multi-stacked computer chips. The fluid flow equations are developed in 3-dimensions based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a new two-phase method with an improved model for the liquid-gas interface. A new adaptive mesh update procedure is also proposed for effective management of the mesh at the two-phase interface to remove, add and repair surface elements, since the computational mesh nodes move according to the flow. The Lagrangian description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The new methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost. Static and dynamic tests have been carried out to validate the method and so far all the obtained results have compared well to analytical solutions and experimental results found in the literature, demonstrating that the new proposed methodology to simulate two-phase flows provides good accuracy to describe the interfacial forces and bubble dynamics. The new code was then used to simulate elengated bubble flows in square microchannels, being considered for two-phase interlayer cooling in future 3D-IC compute chips.

Numerical Modeling of Annular Laminar Film Condensation in Circular and Non-Circular Micro-Channels under Normal and Micro-Gravity

Stefano Nebuloni

A theoretical and numerical model to predict film condensation heat transfer in mini, micro and ultra micro-channels of different internal shapes is presented in this thesis. The model is based on a finite volume formulation of the Navier-Stokes and energy equations and it includes the contributions of the unsteady terms, surface tension, axial shear stresses, gravitational forces and wall thermal conduction. Notably, interphase mass transfer and near-to-wall effects (disjoining pressure) are also included. This model has been validated versus various benchmark cases and versus published experimental results from three different laboratories, predicting micro-channel heat transfer data with an average error of 20 % or better. The conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid and the heat conduction in the channel wall has been studied and analyzed. The work has focused on the effects of three external wall boundary conditions: a uniform wall temperature, a non uniform wall heat flux and single-phase convective cooling. The thermal axial and peripheral conduction occurring in the wall of the channel can affect the behavior of the condensate film, not only because it redistributes the heat, but also because the annular laminar film condensation process is dependent on the local saturation to wall temperature difference. When moving from mini to micro and ultra-micro channels, the results shows that the axial conduction effects can become very important in the prediction of the wall temperature profile and they can not be ignored. Under these conditions, the overall performances of the heat exchanger become dependent not only on the fluid properties and the operative conditions but also on the geometry and wall material. Results obtained for steady state conditions are presented for circular, elliptical and flattened shape cross sections for R-134a and ammonia, for hydraulic diameters between 10 µm and 3 mm. Microscale condensation finds applications in heat pipes and compact heat exchangers for electronic equipment or spacecraft thermal control, in automotive condensers, in residential air conditioning and in refrigeration applications: the influence of the steady or unsteady gravitational field and of the inertia forces on the flow field and consequently on the heat transfer performances is investigated allowing the model to be applied as a design and optimization tool for enhanced heat exchangers.

EPFL2010

Numerical investigation of the influence of leading and sequential bubbles on slug flow boiling within a microchannel

Mirco Magnini, John Richard Thome

Multiphase CFD simulations are presently employed to investigate the flow boiling of multiple sequential elongated bubbles in a horizontal microchannel. Most of the computational studies published so far explored the features of boiling flows within microchannels by simulating the fluid-dynamics of a single evaporating bubble, but the present work shows that multiple bubble simulations are necessary to capture the essential features of the heat transfer process of a slug flow. In particular, it is shown that leading and sequential bubbles interact thermally and hydrodynamically due to the evaporation process, thus possessing different growth rates, velocities and thicknesses of the thin liquid films trapped between the bubbles interfaces and the channel wall. The evaporation of this thin liquid film is the dominant heat transfer mechanism in the vapor bubble region and the transit of trailing bubbles strongly enhances the time-averaged heat transfer coefficient of the bubble-liquid slug unit, by as much as 60% higher relative to the leading bubble under the operating conditions presently set. Furthermore, the presence of a recirculating vortex just after the tail of the bubble in the liquid slug trapped between the bubbles was found in the simulations, significantly improving the heat transfer between the wall and the bulk liquid, thus maintaining the heat transfer coefficient much higher than otherwise expected in the liquid slug region as well. Finally, a new multiple bubble heat transfer model is proposed to predict the local variation of the heat transfer coefficient, which might prove to be useful to improve the current boiling heat transfer methods, such as the three-zone model of Thome et al. [1,2]. The numerical framework employed to perform this study was the commercial CFD solver ANSYS Fluent 12 with a Volume Of Fluid interface capturing method, which was improved here by implementing external functions, in particular a Height Function method to better estimate the surface tension force and an evaporation model to compute the phase change. (C) 2013 Elsevier Masson SAS. All rights reserved.

Elsevier2013

3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

Navid Borhani, Gustavo Rabello Dos Anjos, John Richard Thome

We seek to study numerically two-phase flow phenomena with phase change through the finite-element method (FEM) and the arbitrary Lagrangian-Eulerian (ALE) framework. This method is based on the so-called one-fluid formulation; thus, only one set of equations is used to describe the flow field at the vapor and liquid phases. The equations are discretized on an unstructured tetrahedron mesh and the interface between the phases is defined by a triangular surface, which is a subset of the three-dimensional mesh. The Navier-Stokes equation is used to model the fluid flow with the inclusion of a source term to compute the interfacial forces that arise from two-phase flows. The continuity and energy equations are slightly modified to take into account the heat and mass transport between the different phases. Such a methodology can be employed to study accurately many problems, such as oil extraction and refinement in the petroleum area, design of refrigeration systems, modeling of biological systems, and efficient cooling of electronics for computational purposes, which is the aim of this research. A comparison of the obtained numerical results to the classical literature is performed and presented in this paper, thus proving the capability of the proposed new methodology as a platform for the study of diabatic two-phase flows.