Silke Guenther

Consistent Invariant Modelling of Axially Rotating Pipe Flow

In rans modelling it is common practice to use classical canonical flow cases such as the isotropic decay, the logarithmic law of the wall or homogeneous shear flows for calibrating the model constants. With the help of Lie group analysis a broad variety of invariant solutions (scaling laws) can be derived comprising the latter classical solutions as well as a broad variety of new solutions which have so far not been used for model calibration or development. The symmetry methods provide therefore a very useful tool for the improvement of existing turbulence models or may be a guideline for the development of new models. In the following we will exemplary investigate linear and nonlinear eddy viscosity models as well as Reynolds stress transport models for their capability to reproduce the scaling laws derived from symmetry methods for the fully developed turbulent rotating pipe flow.

Incompatibility of the exponential scaling law for a zero pressure gradient boundary layer flow with Reynolds averaged turbulence models

Analyzing the multipoint-correlation equations for parallel turbulent shear flows and zero pressure gradient turbulent boundary layer flows with the help of Lie symmetry methods, a new exponential scaling law has been derived in the work by Oberlack [“A unified approach for symmetries in plane parallel turbulent shear flows,” J. Fluid Mech. 427, 299 (2001)]. In the frame work of Lie group methods these solutions are called invariant solutions. From experiments [B. Lindgren, J. M. Osterlund, and A. Johansson, “Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressuere-gradient turbulent boundary layers,” J. Fluid Mech. 502, 127 (2004)] and direct numerical simulations [G. Khujadze and M. Oberlack, “DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow,” Theor. Comput. Fluid Dyn. 18, 5 (2004)] the exponential velocity profile was clearly validated in the mid-wake region of high Reynolds number flat-plate boundary layers. It was identified as an explicit...

New Scaling Laws of Shear-Free Turbulent Diffusion and Diffusion-Waves

We consider the problem of turbulence generation at a vibrating grid in the x 2-x 3 plane. Turbulence diffuses in the x 1 direction. Analyzing the multi-point correlation equation using Lie-group analysis we find three different solutions (scaling laws): classical diffusion-like solution (heat equation like), decelerating diffusion-wave solution and finite domain diffusion due to rotation. All solution have been obtained using Lie- group (symmetry) methods. It is shown that models based on Reynolds averaging are only capable to model either the diffusion-like solution or the decelerating diffusion-wave solution. The latter solution is only admitted under certain algebraic constraints on the model constants. Turbulent diffusion on a finite domain induced by rotation is not admitted by any of the classical models.