Reconstruction of turbulence properties for stochastical turbulence modeling

Abstract

The correct modeling of turbulent and transient flow is still a major task for computational fluid dynamics. This is even more a topic concerning the CFD-simulations on wind turbines, which face already highly turbulent in flow conditions. Thus motivated the improvement of stochastic methods of turbulence modeling is the scope of this work. Stochastic turbulence model rely on an estimation of the statistical distribution of the flow properties at a certain point or time. E.g. Bakosi et. al.1 have proposed a model using the probability density functions (PDFs) of the flow properties on an unstructured grid. The method however relies on the knowledge of the PDFs in the flow on the grid. Here we will present a method to gain such PDFs of the flow. We performed a 3D DNS simulation using spectral/hp method on an fx79-w151a airfoil at a Reynolds number of Re=5000. In the wake of the airfoil an inhomogeneous turbulent field evolved. Within this field a time series of the flow properties has been gathered at certain points. As an example the data of the time series at one point has been analyzed using a multi-point correlation method on incremental statistics to gain the Kramers-Moyal coeffcients.2 Using these coeffcients it is possible to reconstruct the time series at the point itself to gain a PDF function artificially. The resulting PDFs did not completely match the statistical properties of the original points. The main reason were to high values of the high order statistical moments and the short time series, that served as a base. However the results were surprisingly good, reproducing the main shapes of the PDFs, even though the underlying function for the reconstruction was a Langevin equation using only Gaussian white noise in the diffusion. Thus further progress is to be expected in the method.