Turbulence in Porous Media

Modeling and Applications

Marcelo J.S. de Lemos

• Publisher: Elsevier
• Year: 2012
• ISBN:
  9780080982632
• Edition: 2
• Topic: Ciencias físicas
• Subtopic: Aerodinámica

Turbulence in Porous Media introduces the reader to the characterisation of turbulent flow, heat and mass transfer in permeable media, including analytical data and a review of available experimental data. Such transport processes occurring a relatively high velocity in permeable media are present in a number of engineering and natural flows. This new edition features a completely updated text including two new chapters exploring Turbulent Combustion and Moving Porous Media. De Lemos has expertly brought together a text that compiles, details, compares and evaluates available methodologies for modelling and simulating flow, providing an essential tour for engineering students working within the field as well as those working in chemistry, physics, applied mathematics, and geological and environmental sciences.

• Brings together groundbreaking and complex research on turbulence in porous media
• Extends the original model to situations including reactive systems
• Now discusses movement of the porous matrix

PART ONE

Modeling

1 Introduction

2 Governing Equations

3 The Double-Decomposition Concept

4 Turbulent Momentum Transport

5 Turbulent Heat Transport

6 Turbulent Mass Transport

7 Turbulent Double Diffusion

8 Turbulent Combustion

9 Moving Porous Media

1

Introduction

Only two things are infinite, the universe and human stupidity, and I’m not sure about the former.

Albert Einstein

1.1 Overview of Porous Media Modeling

Due to its ever-broader range of applications in science and industry, the study of flow through porous media has gained extensive attention lately. Engineering systems based on fluidized bed combustion, enhanced oil reservoir recovery, underground spreading of chemical waste, enhanced natural gas combustion in an inert porous matrix, and chemical catalytic reactors are just a few examples of applications of this interdisciplinary field. In a broader sense, the study of porous media embraces fluid and thermal sciences and materials, and chemical, geothermal, petroleum, and combustion engineering.

Accordingly, applications that are more complex usually require appropriate and, in most cases, more sophisticated mathematical and numerical modeling. Obtaining the final numerical results, however, may require the solution of a set of coupled partial differential equations involving many coupled variables in a complex geometry. This book shall review important aspects of numerical methods, including the treatment of multidimensional flow equations, discretization schemes for accurate solutions, algorithms for pointwise and block-implicit solutions, algorithms for high-performance computing, and turbulence modeling. These subjects shall be grouped into major sections covering numerical formulation and algorithms, geometry, and turbulence.

1.1.1 General Remarks

During the past few decades, a number of textbooks have been written on the subject of porous media. Among them are the works referred to in Muskat (1946), Carman (1956), Houpeurt (1957), Collins (1961), DeWiest (1969), Scheidegger (1974), Dullien (1979), Bear and Bachmat (1990), and Kaviany (1991). Advanced models documented in recent literature try to simulate additional effects such as variable porosity, anisotropy of medium permeability, unconventional boundary conditions, flow dimension, geometry complexity, nonlinear effects, and turbulence. Not all these flow complexities can be analyzed with the early unidimensional Darcy flow model. Recognizing the importance of these applications, the literature has been ingenious in proposing a number of extended theoretical approaches. Below is a short review of basic equations governing fluid flow, followed by a summary of some of the classical models for analyzing transport phenomena in porous media.

1.1.2 Fundamental Conservation Equations

The basic conservation equations describing the flow of a fluid through an infinitesimal volume can be written in a compact form as

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