Multiphase Flow Dynamics 1

Cover -- Introduction -- Summary -- Nomenclature -- Table of Contents -- 1 Mass conservation -- 1.1 Introduction -- 1.2 Basic definitions -- 1.3 Non-structured and structured fields -- 1.4 Slattery and Whitaker's local spatial averaging theorem -- 1.5 General transport equation (Leibnitz rule) -- 1.6 Local volume-averaged mass conservation equation -- 1.7 Time average -- 1.8 Local volume-averaged component conservation equations -- 1.9 Local volume- and time-averaged conservation equations -- 1.10 Conservation equations for the number density of particles -- 1.11 Implication of the assumption of mono-dispersity in a cell -- 1.12 Stratified structure -- References -- 2 Momentums conservation -- 2.1. Introduction -- 2.2. Local volume-averaged momentum equations -- 2.3 Rearrangement of the surface integrals -- 2.4 Local volume average and time average -- 2.5 Viscous and Reynolds stresses -- 2.6 Non-equal bulk and boundary layer pressures -- 2.7 Working form for dispersed and continuous phase -- 2.8 General working form for dispersed and continuous phases -- 2.9 Some practical simplifications -- 2.10 Conclusion -- Appendix 2.1 -- Appendix 2.2 -- Appendix 2.3 -- References -- 3 Derivatives for the equations of state -- 3.1 Introduction -- 3.2 Multi-component mixtures of miscible and non-miscible components -- 3.3 Mixture of liquid and microscopic solid particles of different chemical substances -- 3.4 Single-component equilibrium fluid -- Appendix 3.1 Application of the theory to steam-air mixtures -- Appendix 3.2 Useful references for computing properties of single constituents -- References -- 4 On the variety of notations of the energy conservation for single-phase flow -- 4.1 Introduction -- 4.2 Mass and momentum conservation, energy conservation -- 4.3 Simple notation of the energy conservation equation -- 4.4 The entropy -- 4.5 Equation of state -- 4.6 Variety of notation of the energy conservation principle -- 4.7 Summary of different notations -- 4.8 The equivalence of the canonical forms -- 4.9 Equivalence of the analytical solutions -- 4.10 Equivalence of the numerical solutions? -- 4.11 Interpenetrating fluids -- 4.12 Summary of different notations for interpenetrating fluids -- Appendix 4.1 Analytical solution of the shock tube problem -- Appendix 4.2 Achievable accuracy of the donor-cell method for single-phase flows -- References -- 5 First and second laws of the thermodynamics -- 5.1 Introduction -- 5.2 Instantaneous local volume average energy equations -- 5.3 Dalton and Fick's laws, center of mass mixture velocity, caloric mixture properties -- 5.4 Enthalpy equation -- 5.5 Internal energy equation -- 5.6 Entropy equation -- 5.7 Local volume- and time-averaged entropy equation -- 5.8 Local volume- and time-averaged internal energy equation -- 5.9 Local volume- and time-averaged specific enthalpy equation -- 5.10 Non-conservative and semi-conservative forms of the entropy equation -- 5.11 Comments on the source terms in the mixture entropy equation -- 5.12 Viscous dissipation -- 5.13 Temperature equation -- 5.14 Second law of the thermodynamics -- 5.15 Mixture volume conservation equation -- 5.16 Lineari.