A LES-Langevin model for turbulence

We propose a new model of turbulence for use in large-eddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddy-viscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advection and stretching by the resolved scale. The stochastic noise is derived as the sum of a contribution from the energy cascade and a contribution from the pressure. The LES model is thus made of an equation for the resolved scale, including the turbulent force, and a generalized Langevin equation integrated on a twice-finer grid. The model is validated by comparison to DNS and is tested against classical LES models for isotropic homogeneous turbulence, based on eddy viscosity. We show that even in this situation, where no walls are present, our inclusion of backscatter through the Langevin equation results in a better description of the flow.Comment: 18 pages, 14 figures, to appear in Eur. Phys. J.

On the use of the Peak Stress Method for the calculation of Residual Notch Stress Intensity Factors: a preliminary investigation

Residual stresses induced by welding processes significantly affect the engineering properties of structural components. If the toe region of a butt-welded joint is modeled as a sharp V-notch, the distribution of the residual stresses in that zone is asymptotic with a singularity degree which follows either the linear-elastic or the elastic-plastic solution, depending on aspects such as clamping conditions, welding parameters, material and dimension of plates. The intensity of the local residual stress fields is quantified by the Residual Notch Stress Intensity Factors (R-NSIFs), which can be used in principle to include the residual stress effect in the fatigue assessment of welded joints. Due to the need of extremely refined meshes and to the high computational resources required by non-linear transient analyses, the R-NSIFs have been calculated in literature only by means of 2D models. It is of interest to propose new coarse-mesh-based approaches which allow residual stresses to be calculated with less computational effort. This work is aimed to investigate the level of accuracy of the Peak Stress Method in the R-NSIFs evaluation