| Description |
The purpose of this research is the development of mathematical formalisms for the numerical modeling and simulation of multiphase systems with emphasis in polydisperse flows. The framework for these advancements starts with the William-Boltzmann equation which describes the evolution of joint distributions of particle properties: size, velocity, mass, enthalpy, and other scalars. The amount of statistical information that can be obtained from the direct evolution of particle distribution functions is extensive and detailed, but at a computational cost not yet suitable in usable computational fluid dynamics (CFD) codes. Alternatives to the direct evolution of particle distribution functions have been proposed and we are interested in the family of solutions involving the evolution of the statistical moments from the joint distributions. Rather than tracking every single particle characteristic from the joint distribution, transport equations for their joint moments are formulated; these equations share many of the properties of the regular transport equations formulated in the finite volume framework, making them very attractive for their implementation in current Eulerian CFD codes. The information they produce is general enough to provide the characteristic behavior of many multiphase systems to the point of improvement over the current Eulerian methodologies implemented on standard CFD modeling and simulation approaches. Based on the advantages and limitations of the solutions of the ongoing methodologies and the degree of the information provided by them, we propose formalisms to extend their modeling capabilities focusing on the influence of the size distribution in many of the related multiphase phenomena. The first methodology evolves joint moments based on the evolution of primitive variables (size among them) and conditional moments that are approximants of the joint moments at every time step. The second methodology reconstructs completely the marginal size distribution using the concept of parcel and approximate characteristic behavior of the rest of the conditional moments in each parcel. In both approaches, the representation of size distribution plays a fundamental role and accounts for the polydisperse nature of the system. Also, the numerics of the moment transport equations are to be consistent with the theory of general hyperbolic transport equations but the formulation of the discretization schemes are based on the properties of the underlying distribution. A final contribution is presented in the form of an appendix and it analyzes the role of maximum entropy-based methodologies on the formulation of Eulerian moment-based methods. Attempts to derive new transport equations on the framework of maximum entropy methodologies will be considered and reconstruction of distribution strategies will be presented as preliminary results that might impact future research on Eulerian moment-based methods. |
