(74g) Verification of Euler-Lagrange and Euler-Euler Simulations of Meso-Scale Gas-Solid Flows

Simulations of gas-solid flows will aid the modeling effort for many chemical engineering technologies, such as fluidized bed reactors. However, fully resolved simulations of gas-solid flows are too expensive to capture emerging dynamics involving clusters of particles. Reactor-scale modeling requires data from “meso-scale” simulations that resolve these emerging dynamics, but model smaller scales. These simulations are challenging to perform, particularly in flows with a range of particle Knudsen numbers. Two classes of techniques are commonly used: Euler-Lagrange (EL) and Euler-Euler (EE). However, standard EL and EE simulations are incapable of converging under mesh refinement. Previous work has introduced methods that can, in principal, converge: Euler-Euler Anisotropic Gaussian (EE-AG) and volume-filtered Euler-Lagrange (VF-EL).

In this work, we study the convergence properties of three gas-solid simulation techniques: VF-EL, EE-AG, and Euler-Euler Two-fluid model (EE-TFM), a method that has been shown to yield unphysical shocks in dilute regions of flow. Using these three techniques, we perform simulations of two idealized problems: particles in frozen homogeneous isotropic turbulence (HIT), and cluster-induced turbulence (CIT). Statistical quantities from these simulations, such as the volume fraction distribution and the granular temperature, will inform macro-scale models of gas-solid flows.

We find, for HIT, that flow statistics from only the VF-EL simulations converge. In contrast, for CIT, both EE-AG and VF-EL simulations converge and approach similar values, while statistics from EE-TFM show no such convergence. We explore the mechanisms behind convergence in these simulation techniques. In VF-EL we also study the recovery of the particle density function and associated statistics. Here, we use kernel density estimation for reconstructing the particle density function and show the estimated statistics depend strongly on the kernel bandwidth. This work demonstrates the need for further verification of meso-scale simulation techniques.