Abstract: A statistical formalism overcoming some conceptual and practical difficulties arising in
existing two- phase flow (2PHF) mathematical modelling has been applied to propose a model
for dilute 2PHF turbulent flows. Phase interaction terms with a clear physical meaning
enter the equations and the formalism provides some guidelines for the avoidance of closure
assumptions or the rational approximation of these terms. Continuous phase averaged
continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations
have been rigorously and systematically obtained in a single step. These equations display
a structure similar to that for single-phase flows. It is also assumed that dispersed phase
dynamics is well described by a probability density function (pdf) equation and Eulerian
continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are
deduced. An extension of the standard k-ε turbulence model for the continuous phase is
used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of
momentum and kinetic energy at the non-colliding, large inertia limit. This model is then
used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid
particles varying in size and concentration. Qualitative and quantitative numerical
predictions compare reasonably well with the three different sets of experimental results,
studying the influence of particle size, loading ratio and flow confinement velocity.

Key words: two-phase flow, turbulence, phase indicator function, pdf ensemble average, jet

摘要： A statistical formalism overcoming some conceptual and practical difficulties arising in
existing two- phase flow (2PHF) mathematical modelling has been applied to propose a model
for dilute 2PHF turbulent flows. Phase interaction terms with a clear physical meaning
enter the equations and the formalism provides some guidelines for the avoidance of closure
assumptions or the rational approximation of these terms. Continuous phase averaged
continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations
have been rigorously and systematically obtained in a single step. These equations display
a structure similar to that for single-phase flows. It is also assumed that dispersed phase
dynamics is well described by a probability density function (pdf) equation and Eulerian
continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are
deduced. An extension of the standard k-ε turbulence model for the continuous phase is
used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of
momentum and kinetic energy at the non-colliding, large inertia limit. This model is then
used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid
particles varying in size and concentration. Qualitative and quantitative numerical
predictions compare reasonably well with the three different sets of experimental results,
studying the influence of particle size, loading ratio and flow confinement velocity.

关键词: two-phase flow;turbulence;phase indicator function;pdf ensemble average;jet