Fluid Mechanics for Chemical Engineering

Chapter 8

Large Scales in Turbulence: Turbulent Diffusion – Dispersion

8.1. Introduction

All the five chapters in Part II are devoted to the phenomenon of turbulence and its applications to mixing and chemical reactions. We have already familiarized ourselves to some extent, in the first part, with the notion of turbulence, and discussed two of its characteristics:

1. Turbulence increases dissipation of kinetic energy in a fluid flow. We have observed this in pipe flows (Chapter 4); the regular head loss of the flow inside a pipe is larger when the flow is turbulent than when it is laminar. It was also shown (Chapter 2, section 2.8) that the rate of kinetic energy dissipation per unit volume depends on the square of its velocity gradients. The strengthening of velocity gradients in a turbulent flow is, therefore, directly responsible for this increase in dissipation.

2. Turbulence spatially homogenizes a quantity that is dispersed within a fluid. This mixing property also impacts the structure of velocity fields. For the turbulent flow in a pipe (Chapter 4, section 4.3), the average profile (of a turbulent flow) is more uniform than that of a laminar flow (Poiseuille solution). Conversely, the mean velocity gradient in the vicinity of the walls is larger in a turbulent flow than in a laminar flow. The increase in friction forces of the wall is correlated with that of head loss, in accordance with the momentum theorem (Chapter 2).

The aim of Part II is to introduce the elementary ...