A thermodynamical formulation for chemically active multiphase turbulent flows

A general thermodynamic theory for chemically active multiphase solid–fluid mixtures in turbulent state of motion is formulated. The global equations of balance for each phase are ensemble averaged and the local conservation laws for the mean motions are derived. As a classical treatment, the averaged form of the Clausius–Duhem inequality is used and the thermodynamics of the chemically active mixtures in turbulent state of motion is studied. Particular attention is given to the species concentration of the miscible fluid constituents and chemical reaction effects, in addition to the transport of the phasic fluctuation energies between phases. Based on the averaged entropy inequality, constitutive equations for the stresses, energy, heat and mass fluxes of various species are developed. Explicit governing equations of motion, along with the equation of the dissipation rate of the turbulent kinetic energy are also derived and discussed. A particular emphasis is on the thermodynamically consistent formulation of different solid–fluid interaction terms in these equations.