iv Modelling of Turbulence and Combustion in Gas Explosions
4 Turbulence modelling .................................................................................................. 39
4.1 Overview of turbulence models ............................................................................ 39
4.2 k-ε turbulence models as used in FLACS ............................................................. 40
4.2.1 Deficiencies of the k-ε model .................................................................... 41
4.2.2 Initial conditions for k and ε ...................................................................... 41
4.2.3 Turbulent length scales .............................................................................. 42
4.3 Turbulent shear flows ............................................................................................ 42
4.3.1 Free turbulent shear flows ......................................................................... 43
4.4 Turbulent flow experiments .................................................................................. 44
4.4.1 Steady flows from CMR ........................................................................... 44
4.4.2 Steady flows from British Gas .................................................................. 48
4.4.3 Turbulence data for subgrid modelling of turbulence ............................... 48
4.4.4 Turbulence field data from literature ........................................................ 48
4.5 Transient turbulent shear flows ............................................................................. 50
4.5.1 The k-ε model in transient flows ............................................................... 50
4.5.2 Transient turbulence in experiments ......................................................... 51
4.5.3 Modelling of the transient turbulence buildup .......................................... 52
4.5.4 Simulation of transient build up in an ongrid turbulence field ................. 53
4.6 Reactive flows ....................................................................................................... 56
4.6.1 Production of turbulence due to buoyancy ................................................ 59
4.7 Boundary layer flows ............................................................................................ 59
4.7.1 Representation with wall functions ........................................................... 59
4.7.2 Subgrid modelling of boundary layer flows .............................................. 62
4.7.3 Maximum turbulent length scale close to walls ........................................ 64
4.8 Subgrid modelling of turbulence ........................................................................... 65
4.8.1 Turbulence field behind subgrid objects ................................................... 65
4.8.2 Influence of Re and Ma numbers on turbulence production ..................... 66
4.8.3 Analytical analysis .................................................................................... 67
4.8.4 Subgrid turbulence energy generation model ............................................ 67
4.8.5 Subgrid turbulence production with fixed length scale ............................. 69
4.8.6 Subgrid turbulence energy and length generation model .......................... 70
4.8.7 Transient subgrid turbulence build up ....................................................... 73
4.8.8 Turbulence production from subgrid jets .................................................. 73
4.8.9 Flow velocity for subgrid turbulence generation ...................................... 74
4.9 Modelling of transient, reactive sub- and ongrid flows ........................................ 74
4.10 Simulation of turbulent flow experiments ............................................................. 76
4.10.1 One single cylinder .................................................................................... 76
4.10.2 Obstructions used in the EMERGE experiments ...................................... 82
4.11 Summary ............................................................................................................... 88
5 Combustion models, the β flame model ..................................................................... 89
5.1 Analysis of mixing controlled combustion models ............................................... 89
5.1.1 Analysis with cold front quench criteria ................................................... 90
5.1.2 The KPP burning velocity analysis ........................................................... 94
5.2 Analytical determined burning velocities ............................................................. 95
5.2.1 The H-M model in FLACS ........................................................................ 95
5.2.2 The eddy dissipation concept .................................................................... 96
5.2.3 EBU model ................................................................................................ 97
5.2.4 Bray´s model (1990) .................................................................................. 98
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