Nonlinear analyses of the PVT crystal growth, the free-surface flow and the two-phase flow

Abstract

Engineering practices, e.g. physical or chemical processes, often encounter nonlinear factors, which result in complex issues, such as nonlinear distribution, multi-solution or instability. Those issues can undermine engineering efficiency or even cause failure in production. Consequently, the nonlinear analyses by theoretical (or analytical) studies, numerical simulations and experimental researches are implemented to determine the underlying nonlinearity and to further improve the performance of the nonlinear systems. The physical-vapor-transport (PVT) crystal-growth method is popular in the semiconductor industry. It involves precise control on high temperature, around 3,000 K, and relies on the phase change of the target crystal material. Thus, the thermal radiation in the small reaction chamber is one of the main nonlinear factors to affect the output quality. By numerical modeling, the energy balance criteria between the thermal radiation and the heat conduction is formulated to improve the uniformity of the temperature distribution on the crystal ingot. Moreover, based on the Finite-Volume Method (FVM) discretization, it is analytically proved that the reaction chamber with the strong thermal radiation still has unique and stable temperature field with respect to either the external disturbance or the initial condition. The free-surface flow is strongly affected by the interfacial tension, which can be described by the Young-Laplace Equation. However, the Young-Laplace Equation is highly nonlinear and leads to great challenge in terms of either analytical or numerical solutions. Thus, an overlapped grid is developed to enhance FVM’s numerical accuracy by two orders of magnitude. Moreover, the overlapped grid is applied to model the two-dimensional (2D) free-surface flow, which breeds several wave modes due to the interaction among the interfacial tension, the flow momentum and the fluid viscosity. The capillary advective mode is one of them and can propagate upstream to cause the steady standing wave. The numerical results are compared with those traditional one-dimensional (1D) approximations, and justify the properties of the capillary advective mode at the viscid limit. Likewise, the two-phase flow in the microchannel is also strongly influenced by the interfacial tension, and is essentially unstable due to the Rayleigh-Plateau instability. By imposing suitable changes in the boundary condition, the convective instability and even the absolute instability on the two-phase flow can be attenuated and postponed. Specifically, the expansion-contraction unit in the microchannel can attenuate the downstream-propagating modes and can transfer the upstream-propagating modes into stable oscillation. A qualitative energy model is proposed to unveil the functionality of the expansion-contraction unit. Thus, the jet length of the micro two-phase flow can be greatly extended to even a decimeter with periodically-connected expansion-contraction units. In summary, this thesis details three nonlinear analyses, e.g. analytical, numerical and experimental, to deal with three nonlinear engineering systems. By implementing suitable nonlinear analyses, more insights can be obtained to determine the optimal performance, to improve the prediction accuracy, and even to relieve the intrinsic instability. Ultimately, human being can achieve higher effectiveness and efficiency in various engineering practices.