Multiscale Simulations of Heterogeneous Particulate Flows

University Of Houston, Houston TX

Investigators

Abstract

The proposed research is on development and simulation of a multiscale model for heterogeneous particulate flows, in which the motion of a very large number of small solid particles is coupled with a Newtonian incompressible fluid. The problem derives from particle transport, sedimentation, fluidization and separation processes that are common in many applications. Currently, there are two major approaches to simulate such flows: one of them is based on averaged equations, the other one - on direct numerical simulations. The first approach requires homogeneity in the flow which is often violated in applications, while the second one is currently limited to a relatively small number (compared to applications) of particles. However, practical applications involve millions and billions of particles whose small size leads the problem of interest to span two length scales: fine scale - the scale of particles, and coarse scale - the scale of the application. In developing the proposed approach the variational multiscale framework is employed, in which the problem is split into two problems corresponding to the coarse and fine scales. It is assumed that in each coarse grid the particle distribution can be of three different regimes depending on their concentrations: dilute, moderate and dense. The main goal of the proposed study is to design a multiscale method that can handle heterogeneous flows in all three regimes in a unified way. The key idea of the proposed approach is, after separating the two scales, to use properly chosen subgrid models adaptively to represent micro-scale flow and particle dynamics on a coarse grid. In the dilute limit, a modified viscosity is used to represent averaged effects. In the dense limit, the discrete network approximation method to approximate the subgrid effects is utilized. Network models allow avoiding detailed fine-scale simulations in the dense regimes and provide substantial CPU savings. In the intermediate regime, fine-scale features within a target coarse-grid block are resolved. The issues to be focused on are (1) coarse coupling, (2) boundary conditions for local problems, (3) approximation of subgrid effects, (4) effective solution strategies. The proposed project provides tools to simulate heterogeneous particulate flows of small rigid particles in an incompressible fluid which have been of great interest for the last decade and are commonly encountered in many applications and fundamental fluid mechanics. The complexity of this problem due to the presence of two different length scales is enormous and only very recently the development of numerical techniques for direct numerical simulations and computing power allowed for some attempts to numerically resolving flows containing a relatively large number of particles. However, existing direct numerical simulations methods have been developed for flows where the maximal number of particles to be handled does not exceed a couple dozens of thousands while for practical applications much larger amount is of primary importance. This dictates a need in developing a state-of-the-art predictive multiscale model for heterogeneous particulate flows which allows one to obtain a detailed and accurate representation of the flow, and which is the main focus of the proposed research.