Small scale localization in turbulent flows. A priori tests applied to a possible Large Eddy Simulation of compressible turbulent flows

摘要

A method for the localization of small scales in turbulent velocity fields is proposed. The method is based on the definition of a function f of the velocity and vorticity fields that reproduces a normalized form of the twisting-stretching term of the Helmholtz equation. By means of this method the equations of motion can be selectively filtered in regions that are rich in small scale motions. The method is applied through a criterion built on a statistical link between the function f and a local property of the turbulence that was derived from the analysis a homogeneous and isotropic high Reynolds number (Reλ=280) turbulence field. The localization criterion is independent of the subgrid scale model used in a possible Large Eddy Simulation carried out after the small scale localization is obtained. This extends the typology of possible applications to the analysis of experimental laboratory data. In case of compressible regimes, a second sensor that depends on the local pressure variation and divergence can be associated to the previous one in order to determine the eventual emergence of shocks. The capture of shocks is made possible by suppressing the subgrid terms where this second sensor indicates the presence of a shock. A priori tests were carried out on the turbulent channel flow, Reλ=180 and 590, to validate the localization procedure in a highly inhomogeneous flow configuration. A second set of a priori test was carried out on a turbulent time decaying jet which initiates its evolution at Mach 5 and which reproduces a few hydrodynamical properties of high Reynolds number hypersonic jets which exist in the Universe.