Large eddy simulation and the filtered equation of a contaminant

A new model of LES is proposed together with a new methodology for the simulation of concentration fields of contaminant coherent with the LES methodology. In this paper a new LES model is proposed. The closure relation for the generalised SGS turbulent stress tensor: a) complies with the principle of turbulent frame indifference; b) takes into account both the anisotropy of the turbulence velocity scales and turbulence length scales; c) removes any balance assumption between the production and dissipation of SGS turbulent kinetic energy. In the proposed model: a) the closure coefficient which appears in the closure relation for the generalised SGS turbulent stress tensor is theoretically and uniquely determined without adopting Germano's dynamic procedure; b) the generalised SGS turbulent stress tensor is related exclusively to the generalised SGS turbulent kinetic energy (which is calculated by means of its balance equation) and the modified Leonard tensor. The calculation of the viscous dissipation is carried out by integrating its exact balance equation. In this paper the form invariance and frame dependence of the above mentioned equation of the viscous dissipation transport is shown. The concentration field is simulated by the spatially filtered equation of the concentration. In this equation the first-order tensor (produced by the correlation between the velocity and the concentration) is related to the gradient of the resolved concentration according to an original dynamic Germano procedure.