Book contents
- Frontmatter
- Contents
- Figures and Table
- Foreword
- Foreword
- Foreword
- Nomenclature
- Preface
- Acknowledgments
- 1 Introduction
- 2 Averaging relations
- 3 Phasic conservation equations and interfacial balance equations
- 4 Local volume-averaged conservation equations and interfacial balance equations
- 5 Time averaging of local volume-averaged conservation equations or time-volume-averaged conservation equations and interfacial balance equations
- 6 Time averaging in relation to local volume averaging and time-volume averaging versus volume-time averaging
- 7 Novel porous media formulation for single phase and single phase with multicomponent applications
- 8 Discussion and concluding remarks
- Appendix A
- Appendix B
- Appendix C
- Appendix D
- References
- Index
4 - Local volume-averaged conservation equations and interfacial balance equations
Published online by Cambridge University Press: 07 October 2011
- Frontmatter
- Contents
- Figures and Table
- Foreword
- Foreword
- Foreword
- Nomenclature
- Preface
- Acknowledgments
- 1 Introduction
- 2 Averaging relations
- 3 Phasic conservation equations and interfacial balance equations
- 4 Local volume-averaged conservation equations and interfacial balance equations
- 5 Time averaging of local volume-averaged conservation equations or time-volume-averaged conservation equations and interfacial balance equations
- 6 Time averaging in relation to local volume averaging and time-volume averaging versus volume-time averaging
- 7 Novel porous media formulation for single phase and single phase with multicomponent applications
- 8 Discussion and concluding remarks
- Appendix A
- Appendix B
- Appendix C
- Appendix D
- References
- Index
Summary
Application of the local volume-averaging theorems [Eqs. (2.4.1a), (2.4.1b), (2.4.2), and (2.4.7)] to the phasic conservation equations given in leads to the following set of local volume-averaged conservation equations for multiphase flow. These equations are rigorous and subject only to the length-scale restriction, Eq. (2.4.3), which is inherent in the local volume-averaging theorems. Unless otherwise stated, all solid structures are stationary, nonporous, and nonreacting; Uk and Wk vanish in Awk. Both volume porosities (γv) and directional surface porosities ($\gamma _{\hbox{\scriptsize\scitshape a}x} $, $\gamma _{\hbox{\scriptsize\scitshape a}y} $, and $\gamma _{\hbox{\scriptsize\scitshape a}z} $) are invariant in time and in space, and they are functions of their initial structure locations, sizes, and shapes.
Local volume-averaged mass conservation equation of a phase and its interfacial balance equation
The continuity equation is written as
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2011