General formalism for a reduced description and modelling of momentum and energy transfer in turbulence

Based on hierarchies of filter lengths, the large eddy decomposition and the related subgrid stresses are recognized to represent generalized central moments for the study and modelling of the different modes composing turbulence. In particular, the subgrid stresses and the subgrid dissipation are shown to be alternative observables for quantitatively assessing the scale-dependent properties of momentum flux (subgrid stresses) and the energy exchange between the large and small scales (subgrid dissipation). In this work we present a theoretical framework for the study of the subgrid stress and dissipation. Starting from an alternative decomposition of the turbulent stresses, a new formalism for their approximation and understanding is proposed which is based on a tensorial turbulent viscosity. The derived formalism highlights that every decomposition of the turbulent stresses is naturally approximated by a general form of turbulent viscosity tensor based on velocity increments which is then recognized to be a peculiar property of small-scale stresses in turbulence. The analysis in a turbulent channel shows the rich physics of the small-scale stresses which is unveiled by the tensorial formalism and usually missed in scalar approaches. To further exploit the formalism, we also show how it can be used to derive new modelling approaches. The proposed models are based on the second- and third-order inertial properties of the grid element. The basic idea is that the structure of the integration volume for filtering (either implicit or explicit) impacts the anisotropy and inhomogeneity of the filtered-out motions and, hence, this information could be leveraged to improve the prediction of the main unknown features of small-scale turbulence. The formalism provides also a rigorous definition of characteristic lengths for the turbulent stresses, which can be computed in every type of computational elements, thus overcoming the rather elusive definition of filter length commonly employed in more classical models. A preliminary analysis in a turbulent channel shows reasonable results. In order to solve numerical stability issues, a tensorial dynamic procedure for the evolution of the model constants is also developed. The generality of the procedure is such that it can be employed also in more conventional closures.

LES of Normally Impinging Elliptic Air-Jet Heat Transfer at Re=4400

Jet impingement induced heat transfer is an important issue in engineering science. This paper presents results of large eddy simulation (LES) of normally impinging elliptic air-jet heat transfer at a Reynolds number of 4400, with orifice-to-plate distance fixed to be 5 in the unit of jet nozzle effective diameter. The elliptic aspect ratio (a/b) is 3/2. While the target wall is heated under some condition of constant heat flux. The LES are carried out using dynamic subgrid model and Open-FOAM. The distributions ofmean velocity components, velocity fluctuations, and subgrid stresses in vertical and radial directions, and the Nusselt numbers involving heat transfer through the target wall are discussed. The comparison with existing experimental and numerical results shows good agreement.