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DISSIPATION ELEMENT ANALYSIS OF SCALAR FIELDS IN WALL-BOUNDED TURBULENT FLOW

Fettah Aldudak
Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Petersenstr. 30, 64287 Darmstadt, Germany

Martin Oberlack
Chair of Fluid Dynamics, Dept. Mech. Eng., TU Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany; Center of Smart Interfaces, TU Darmstadt, Germany; GS Computational Engineering, TU Darmstadt, Germany

要約

The scalar fields obtained by Direct Numerical Simulations (DNS) are decomposed into numerous finite size regions using the dissipation element analysis proposed by Wang & Peters (2006) providing detailed information about the geometry of turbulent structures - presently for the turbulent channel flow. Therefore local pairs of minimal and maximal points in the scalar field φ(x;y;z;t) are detected where ∇φ = 0. Gradient trajectories of finite length starting from every point in the scalar field in the directions of ascending and descending scalar gradients will reach a minimum and a maximum point with ∇φ = 0. The set of all points belonging to the same pair of extremal points defines a dissipation element (DE). Hence, the decomposition of the domain into dissipation elements is not arbitrary but follows from the structures of the flow itself and further is completely space filling. The components of the velocity, the vorticity vector, the kinetic energy and its dissipation could be chosen as such a scalar field &phi. The Euclidian distance l between the extremal points and the absolute value of the scalar difference Δφ at these two points mark the key parameters to parameterize the geometry and the field variable structure of the dissipation elements. Although these spatial structures are irregularly shaped the parameters mentioned give a deep insight into the length scale and scalar increment distribution (Wang & Peters (2006)). For the case of homogeneous shear turbulence the authors in Wang & Peters (2006) report that the mean DE length is in the order of the Taylor scale defined as λ = (10νk/ε)1/2. This can be confirmed presently for the turbulent channel flow though it is a statistically inhomogeneous flow in the wall-normal direction y.