Toward numerical modeling of fine particle suspension using a two-way coupled Euler–Euler model. Part 1: Theoretical formulation and implications

• A two-way coupled EE model to simulate fine particle suspension is formulated.
• We derive various approximations according to the proposed EE model.
• Existing approximations are modified based on the present EE model formulation.
• We examine the influence of the non-equilibrium particle inertia on RT instability.

This paper presents a two-way coupled Euler–Euler model to simulate the dilute suspension of fine particles. The goal is to develop a three-dimensional numerical model that is capable of replicating detailed features of particle-laden turbulent flow. In addition to the terms found in typical two-phase Euler–Euler models, the present formulation also accounts for the effects of added mass and pressure, which are crucial to solid–liquid systems in which densities for each phase are of the same order. This study derives various approximations with which to assess existing model formulations, namely solid–gas equations, equilibrium-state approximation, simplified Euler models, and hindered settling velocity. We then emphasize the deviation of the present simulation results from the equilibrium state, which is simulated by the single-phase approach. We investigate simple examples of the Rayleigh–Taylor instability induced by the suspension of fine particles, the results of which reveals the distribution of non-equilibrium particle inertia. We then examine its influence on the carrier flow. A comparison between the present two-phase model and single-phase approximation demonstrates the importance of the coupled pressure on the evolution of a single bubble induced by the particle-driven Rayleigh Taylor instability.