A robust momentum closure approach for multiphase computational fluid dynamics applications

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages [183]-190).Multiphase computational fluid dynamics (M-CFD) modeling approaches allow for the prediction of critical three-dimensional thermal-hydraulics phenomena in nuclear reactor applications. The advancement and consistent adoption of such tools could transform the industry's approach to the design of reliable systems, and the efficient operation of systems existing, which in the past have been dependent upon correlation-based sub-channel analysis codes. The success of these M-CFD methods in simulating two-phase flow and boiling heat transfer depends on their demonstrated accuracy and robustness, which signals a dual need for the comprehensive analysis of existing data and a reevaluation of the underlying physics. By virtue of the Eulerian-Eulerian two-fluid approach, additional terms manifest in the M-CFD phase momentum equations, which represent information that has been lost, and require closure through prescription of interfacial force models. These momentum "closures" are vital to M-CFD prediction of mean flow profiles, including void fraction and phase velocity distributions, and require high-resolution, robust models to perform accurately throughout a diverse array of flow conditions. While an overwhelming number of models have been developed with a wide range of varying performance, no consensus exists about how to assemble these models successfully in a CFD framework, suggesting that their predictive power is still limited. The lift force, responsible for lateral void fraction redistribution, is particularly refractory to the development of a consistent modeling strategy for these closures. Historically, CFD approaches have been forced to inconsistently leverage existing models derived for single bubbles in laminar flow, which disregard the complex dynamics and interactions of bubbles with turbulence and bubble wakes. Current understanding of the lift force in turbulent flow has been limited to qualitative evidences that small spherical bubbles experience a positive lift, resulting in a wall-peaked void fraction distribution, while larger deformed bubbles experience a negative lift and corresponding center-peaked profile. The present work brings forward a new physical interpretation of the lift force in turbulent bubbly flow through a synthesis of information from DNS studies, fine and coarse scale experiments, and analytical investigations. To overcome the limitations of previous models, a simple dimensionless quantity, the Wobble number, a number which systematically describes the unsteady behavior of bubbles in turbulent flow conditions, is proposed. Introducing this dependency into the lift formulation allows for precise identification of lift inversion, which alone exceeds capabilities of existing models. Additionally, the model is extended to account for group behavior with the introduction of a swarm-like function based on void fraction. Its formulation is built on the conceptual understandings of drift phenomena, bubble interaction probability, and the maximum packing factor for dispersed bubbly flow. These two key mechanisms are assembled into a lift model for turbulent bubbly flow, which is implemented in CFD and validated on several experimental databases spanning an extensive range of flow conditions. Error analyses demonstrate the new formulation's robustness and predictive abilities, allowing for a more comprehensive representation of the two-phase phenomena particularly significant in nuclear reactor applications; moreover, it avoids the introduction of case-specific adjustments to unphysical coefficients and tunable parameters which are characteristic and typical limitations of previous models, indicating another valuable improvement. Finally, the new model's performance in a prototypical rod bundle is evaluated and a qualitative assessment of its applicability in a nuclear reactor geometry context is demonstrated.by Rosemary M. Sugrue.Ph. D