Fluid Mechanics for Chemical Engineering

Chapter 12

Micromixing Models

12.1. Introduction

We discuss in this chapter the numerical modeling of mixing and chemical reaction(s). For a turbulent flow, we have seen in the previous chapters that mixing at the molecular scale, which is necessary to perform the chemical reaction, involves very fine scale motions in the flow. These are so minute that currently it is hardly possible to carry out direct numerical simulations of reacting flows for Reynolds numbers typical of situations of practical interest. In order to treat industrial situations, coarser models have been developed. In this chapter, we focus on two such models, which, by implementing the concepts described in the previous chapters, model the mixing and chemical reaction of constituents in a fluid:

– the interaction by exchange with the mean (IEM) model, and

– the coalescence-dispersion (CD) model.

These classical models are nowadays embedded in certain numerical codes, and they are most commonly used in engineering processes. It is useful to know them, as well as the k-ε model summarized in Chapter 8.

The set of problems to be modeled is illustrated in Figure 12.1. Let us consider a reactor into which two volumes respectively containing chemicals A and B are injected. In a turbulent flow, the introduced fluid volumes split up to form elementary fluid particles (EFP). Their size is such that the concentrations of products are homogeneous in each EFP. It is through interactions between EFPs that mixing is modeled. ...