The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous ows is obtained by exact integration of the modeled di erential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy e ects...

The dynamics of the Reynolds stress tensor is given by an evolution equation coupling geometrical effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected. In this case, the Reynolds stress tensor is expressed as the sum of three tensor products of vector fields only associated with the mean flow. The vector fields are governed b...

For developing a reliable data-driven Reynold stress tensor (RST) model, successful reconstruction of the mean velocity field based on high-fidelity information (i.e., direct numerical simulations or large-eddy simulations) is crucial and challenging, considering ill-conditioning problem Reynolds-averaged Navier–Stokes (RANS) equations. It shown that frozen treatment Reynolds force vector (RFV)...

A formulation to include the e ects of wall proximity in a second moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented The wall proximity e ects are modeled through an elliptic relaxation process of the tensor expansion coef cients that properly accounts for both correlation length and time scales as the wall is ap...

The flow and turbulence in an IC engine cylinder were studied using the SSG variant of the Reynolds stress turbulence closure model. In-cylinder turbulence is characterized by strong turbulence anisotropy and flow rotation, which aid in air-fuel mixing. It is argued that solving the differential transport equations for each turbulent stress tensor component, as implied by second-moment closures...

The derivation of the space averaged Navier–Stokes equations for the large eddy simulation (LES) of turbulent incompressible ows introduces two groups of terms which do not depend only on the space averaged ow eld variables: the divergence of the Reynolds stress tensor and commutation errors. Whereas the former is studied intensively in the literature, the latter terms are usually neglected. Th...

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the ...

In this paper, an investigation into the effect of explicit non-linear turbulence modelling on anisotropic flows is presented. Such are typified in corner separations turbomachinery. The commonly used Reynolds-Averaged Navier-Stokes (RANS) closures, which Reynolds stress tensor modelled by Boussinesq (linear) constitutive relation with mean strain-rate tensor, often struggle to predict separati...

We re-examine the Boussinesq hypothesis of an effective turbulent viscosity within the context of simple closure considerations for models of strong magnetohydrodynamic turbulence. Reynolds-stress and turbulent Maxwell-stress closure models will necessarily introduce a suite of transport coefficients, all of which are to some degree model-dependent. One of the most important coefficients is the...