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A Statistically Conditioned Averaging Formalism for Deriving Two‐Phase Flow Equations
Author(s) -
Aliod Ricardo,
Dopazo C.
Publication year - 1990
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.19900070133
Subject(s) - turbulence , formalism (music) , statistical physics , kinetic energy , dissipation , turbulence kinetic energy , mechanics , closure problem , eulerian path , physics , classical mechanics , momentum (technical analysis) , energy–momentum relation , boltzmann equation , closure (psychology) , two phase flow , particle laden flows , flow (mathematics) , thermodynamics , theoretical physics , lagrangian , market economy , art , musical , finance , economics , visual arts
A statistical formalism overcoming some conceptual and practical difficulties arising in existing two‐phase flow (2 PHF) formulations and modelling techniques is introduced. Basic theorems for the case of dispersed 2 PHF are presented. Phase interaction terms with a clear physical meaning enter the equations and this formalism provides some guidelines to avoid closure assumptions or to close those terms rationally. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations can be rigorously and systematically obtained with this methodology in a single step. These equations display a structure similar to that for single‐phase flows. It is also assumed that the dispersed phase is well described by a "Boltzmann‐type" equation and Eulerian "continuity", momentum and fluctuating kinetic energy equations for the dispersed phase are obtained. A 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. Closure assumptions are proposed for the phase interaction terms. This model is then used to predict the behaviour of an axisymmetric turbulent jet of air laden with solid particles varying in sizes and concentrations. Numerical results compare reasonably well with available experimental data.