Sha W.T. Novel porous media formulation for multiphase flow conservation equations. - Cambridge; New York: Cambridge University Press, 2011. - xliii, 214 p.: ill. - Ref.: p.193-200. - Ind.: p.201-214. - ISBN 978-1-107-01295-0  Место хранения:   014 | Институт теоретической и прикладной механики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Figures and Table .............................................. xv Foreword by Alan Schriesheim ........................................... xix Foreword by Wm. Howard Arnold .......................................... xxi Foreword by Charles Kelber ........................................... xxiii Nomenclature ................................................ xxvii Preface ...................................................... xxxv Acknowledgments ............................................. xliii 1 Introduction ................................................. 1 1.1 Background information about multiphase flow ............ 2 1.2 Significance of phase configurations in multiphase flow .................................................... 6 1.3 Need for universally accepted formulation for multiphase flow conservation equations .................. 8 2 Averaging relations ......................................... 12 2.1 Preliminaries .......................................... 13 2.2 Local volume average and intrinsic volume average ...... 14 2.3 Local area average and intrinsic area average .......... 15 2.4 Local volume averaging theorems and their length- scale restrictions ..................................... 17 2.5 Conservative criterion of minimum size of characteristic length of local averaging volume ........ 21 3 Phasic conservation equations and interfacial balance equations ................................................... 23 3.1 Phasic conservation equations .......................... 23 3.2 Interfacial balance equations .......................... 25 4 Local volume-averaged conservation equations and interfacial balance equations ............................... 27 4.1 Local volume-averaged mass conservation equation of a phase and its interfacial balance equation ........... 27 4.2 Local volume-averaged linear momentum equation and its interfacial balance equation ....................... 29 4.3 Local volume-averaged total energy equation and its interfacial balance equation ........................... 33 4.4 Local volume-averaged internal energy equation and its interfacial balance equation ....................... 36 4.5 Local volume-averaged enthalpy equation and its interfacial balance equation ........................... 38 4.6 Summary of local volume-averaged conservation equations .............................................. 41 4.6.1 Local volume-averaged mass conservation equation ........................................ 41 4.6.2 Local volume-averaged linear momentum conservation equation ........................... 42 4.6.3 Local volume-averaged energy conservation equations ....................................... 43 4.6.3.1 In terms of total energy Ek, Ek = uk + ½Uk• Uk ...................... 43 4.6.3.2 In terms of internal energy uk ......... 44 4.6.3.3 In terms of enthalpy hk ................ 45 4.7 Summary of local volume-averaged interfacial balance equations ...................................... 45 4.7.1 Local volume-averaged interfacial mass balance equation ........................................ 45 4.7.2 Local volume-averaged interfacial linear momentum balance equation ....................... 46 4.7.3 Local volume-averaged interfacial energy balance equation ................................ 46 4.7.3.1 Total energy balance (capillary energy ignored) ........................ 47 4.7.3.2 Internal energy balance (dissipation and reversible work ignored) ........... 47 4.7.3.3 Enthalpy balance (capillary energy ignored) ............................... 47 5 Time averaging of local volume-averaged conservation equations or time-volume-averaged conservation equations and interfacial balance equations ........................... 48 5.1 Basic postulates ....................................... 48 5.2 Useful observation without assuming υ'k = 0 ............ 53 5.3 Time-volume-averaged mass conservation equation ........ 54 5.4 Time-volume-averaged interfacial mass balance equation ............................................... 59 5.5 Time-volume-averaged linear momentum conservation equation ............................................... 60 5.6 Time-volume-averaged interfacial linear momentum balance equation ....................................... 73 5.7 Time-volume-averaged total energy conservation equation ............................................... 75 5.8 Time-volume-averaged interfacial total energy balance equation (capillary energy ignored) .................... 88 5.9 Time-volume-averaged internal energy conservation equation ............................................... 90 5.10 Time-volume-averaged interfacial internal energy balance equation ...................................... 100 5.11 Time-volume-averaged enthalpy conservation equation ... 101 5.12 Time-volume-averaged interfacial enthalpy balance equation (capillary energy ignored) ................... 109 5.13 Summary of time-volume-averaged conservation equations ............................................. 110 5.13.1 Time-volume-averaged conservation of mass equation ....................................... 110 5.13.2 Time-volume-averaged linear momentum conservation equation .......................... 111 5.13.3 Time-volume-averaged total energy conservation equation .......................... 112 5.13.4 Time-volume-averaged internal energy conservation equation .......................... 113 5.13.5 Time-volume-averaged enthalpy conservation equation ....................................... 113 5.14 Summary of time-volume-averaged interfacial balance equations ............................................. 114 5.14.1 Time-volume-averaged interfacial mass balance equation ....................................... 114 5.14.2 Time-volume-averaged interfacial linear momentum balance equation ...................... 115 5.14.3 Time-volume-averaged interfacial total energy balance equation ............................... 115 5.14.4 Time-volume-averaged interfacial internal energy balance equation ........................ 115 5.14.5 Time-volume-averaged interfacial enthalpy balance equation ............................... 116 6 Time averaging in relation to local volume averaging and time-volume averaging versus volume-time averaging ......... 117 6.1 Time averaging in relation to local volume averaging ............................................. 117 6.2 Time-volume averaging versus volume-time averaging .... 121 7 Novel porous media formulation for single phase and single phase with multicomponent applications .............. 125 7.1 COMMIX code capable of computing detailed microflow fields with fine computational mesh and high-order differencing scheme ................................... 128 7.1.1 Case (1): Von Karmann vortex shedding analysis ....................................... 128 7.1.2 Case (2): Shear-driven cavity flow analysis .... 134 7.1.3 Some observations about higher-order differencing schemes ........................... 138 7.2 COMMIX code capable of capturing essential both macroflow field and macrotemperature distribution with a coarse computational mesh ......... 140 7.2.1 Case (6): Natural convection phenomena in a prototypical pressurized water reactor during a postulated degraded core accident ............ 140 7.2.1.1 Heat transfer ......................... 144 7.2.1.2 Natural convection patterns ........... 145 7.2.1.3 Temperature distribution .............. 145 7.2.2 Case (7): Analysis of large-scale tests for AP-600 passive containment cooling system ...... 149 7.2.2.1 Circumferential temperature distribution .......................... 152 7.2.2.2 Condensation and evaporation rate ..... 154 7.2.2.3 Air partial pressure and containment pressure .............................. 155 7.2.2.4 Condensation and evaporating film thickness ............................. 156 7.2.2.5 Temperature distributions at various locations ............................. 156 7.3 Conclusion ............................................ 158 8 Discussion and concluding remarks .......................... 160 8.1 Time averaging of local volume-averaged phasic conservation equations ................................ 161 8.1.1 Length-scale restriction for the local volume average ........................................ 162 8.1.2 Time scale restriction in the time averaging ... 163 8.1.3 Time-volume-averaged conservation equations are in differential-integral form .............. 165 8.1.4 Unique features of time-volume-averaged conservation equations ......................... 166 8.2 Novel porous media formulation ........................ 168 8.2.1 Single-phase implementation .................... 169 8.2.2 Multiphase flow ................................ 171 8.3 Future research ....................................... 172 8.4 Summary ............................................... 176 APPENDIX A Staggered-grid computational system ............... 179 APPENDIX B Physical interpretation of αk = -υ-1∫Ak nk dA with γυ = l ....................................... 184 APPENDIX C Evaluation of t for non-Newtonian fluids with γυ = 0 ....................................... 188 APPENDIX D Evaluation of t for isotropic conduction with variable conductivity and with γυ = 1 ........ 191 References .................................................... 193 Index ......................................................... 201