Application of the polynomial chaos expansion to multiphase CFD : a study of rising bubbles and slug flow

Abstract

Part I of this thesis considers subcooled nucleate boiling on the microscale, focusing on the analysis of heat transfer near the Three-Phase (solid, liquid, and vapor) contact Line (TPL) region. A detailed derivation of one representative TPL model is presented. From this work, it was ultimately concluded that heat transfer in the vicinity of the TPL is rather unimportant in the overall quantification of nucleate boiling heat transfer; despite the extremely high heat fluxes that are attainable, it is limited to a very small region so the net heat transfer from this region is comparatively small. It was further concluded that many of the so-called microlayer heat transfer models appearing in the literature are actually models for TPL heat transfer; these models do not model the experimentally observed microlayer. This portion of the project was terminated early, however, in order to focus on the application of advanced computational uncertainty quantification methods to computational multiphase fluid dynamics (Part II). Part II discusses advanced uncertainty quantification (UQ) methods for long-running numerical models, namely computational multiphase fluid dynamics (CMFD) simulations. We consider the problem of how to efficiently propagate uncertainties in the model inputs (e.g., fluid properties, such as density, viscosity, etc.) through a computationally demanding model. The challenge is chiefly a matter of economics-the long run-time of these simulations limits the number of samples that one can reasonably obtain (i.e., the number of times the simulation can be run). Chapter 2 introduces the generalized Polynomial Chaos (gPC) expansion, which has shown promise for reducing the computational cost of performing UQ for a large class of problems, including heat transfer and single phase, incompressible flow simulations; example applications are demonstrated in Chapter 2. One of main objectives of this research was to ascertain whether this promise extends to realm of CMFD applications, and this is the topic of Chapters 3 and 4; Chapter 3 covers the numerical simulation of a single bubble rising in a quiescent liquid bath. The pertinent quantities from these simulations are the terminal velocity of the bubble and terminal bubble shape. the simulations were performed using the open source gerris flow solver. A handful of test cases were performed to validate the simulation results against available experimental data and numerical results from other authors; the results from gerris were found to compare favorably. Following the validation, we considered two uncertainty quantifications problems. In the first problem, the viscosity of the surrounding liquid is modeled as a uniform random variable and we quantify the resultant uncertainty in the bubbles terminal velocity. The second example is similar, except the bubble's size (diameter) is modeled as a log-normal random variable. In this case, the Hermite expansion is seen to converge almost immediately; a first-order Hermite expansion computed using 3 model evaluations is found to capture the terminal velocity distribution almost exactly. Both examples demonstrate that NISP can be successfully used to efficiently propagate uncertainties through CMFD models. Finally, we describe a simple technique to implement a moving reference frame in gerris. Chapter 4 presents an extensive study of the numerical simulation of capillary slug flow. We review existing correlations for the thickness of the liquid film surrounding a Taylor bubble and the pressure drop across the bubble. Bretherton's lubrication analysis, which yields analytical predictions for these quantities when inertial effects are negligible and Ca[beta] --> o, is considered in detail. In addition, a review is provided of film thickness correlations that are applicable for high Cab or when inertial effects are non-negligible. An extensive computational study was undertaken with gerris to simulate capillary slug flow under a variety of flow conditions; in total, more than two hundred simulations were carried out. The simulations were found to compare favorably with simulations performed previously by other authors using finite elements. The data from our simulations have been used to develop a new correlation for the film thickness and bubble velocity that is generally applicable. While similar in structure to existing film thickness correlations, the present correlation does not require the bubble velocity to be known a priori. We conclude with an application of the gPC expansion to quantify the uncertainty in the pressure drop in a channel in slug flow when the bubble size is described by a probability distribution. It is found that, although the gPC expansion fails to adequately quantify the uncertainty in field quantities (pressure and velocity) near the liquid-vapor interface, it is nevertheless capable of representing the uncertainty in other quantities (e.g., channel pressure drop) that do not depend sensitively on the precise location of the interface.