Servicenavigation

Project Details

Back

Projekt Print View

High-Schmidt number turbulent mixing as an aggregation process

Subject Area Fluid Mechanics
Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Term from 2014 to 2018
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 258767971
 
Final Report Year 2019

Final Report Abstract

In this project, we studied the mixing of a passive scalar field in a three-dimensional turbulent flow at Schmidt numbers Sc ≥ 1. The project addressed general and fundamental aspects of scalar mixing which is the reason of why this study was restricted to simple flow configurations and geometries. We showed that different spatio-temporal correlations of the flow affect the statistics of passive scalar turbulence at the small scales in the flows with Sc ≥ 1. These correlations were for example varied by an increase of the simulation box size and thus of the flow Reynolds number. In contrast to the original plan, we did not study many different driving mechanisms. It was however shown that for a strongly anisotropic driving by a constant mean scalar gradient in a very high Reynolds number flow, the passive scalar builds up a pronounced ramp-cliff structure that dominates the statistical properties, in particular the highest-order statistical moments. The major focus of the project was on the development, test and subsequent analysis of our Lagrangian mixing model and its comparison with the standard Eulerian model of passive scalar turbulence. The direct comparison of freely decaying Lagrangian and Eulerian passive scalars gives a good agreement of the scalar variance for times t ≲ 10(ts) and for the probability density functions P (Θ, t) taken with respect to the whole simulation domain. We also showed how the multi-layer aggregations of scalar filaments and sheets in the Lagrangian frame are increasingly influenced by the noise due to discreteness with progressing dilution of the initially high tracer particle concentration. This limits the Lagrangian approach in its present form and for the obtainable Schmidt numbers to studies of shorter time periods. A simple one-dimensional advection-diffusion model of a solitary strip is finally applied to the problem at hand to derive the probability density function of the scalar concentration, P (Θ, t), from the one of the compressive local finite-time Lyapunov exponent, p(λ3, t). Model prediction with and without self-convolution and numerical data of the scalar distributions agree qualitatively, however with quantitative differences particularly for small scalar concentrations. The present Lagrangian approach to passive scalar mixing in turbulence opens the application of new and more flexible passive scalar injection and boundary conditions and allows to relax the resolution constraints for high-Schmidt number mixing studies. Although we were facing several numerical difficulties in our Lagrangian approach, we can finally state that the project could be finished successfully. Also, we would like to underline that the DFG-ANR support has contributed to the progress of the field of Mixing in a broader sense beyond, and in parallel to this precise project. We have been able to contribute to several other closely related topics such as mixing in disordered porous media, or to the physics of dense sprays evaporation, for example. Our collaboration will be hopefully successfully continued by the participation in an ITN Network on Scalar Mixing.

Publications

 
 

Additional Information

© 2024 DFG Disclaimer / Copyright / Privacy Policy

Textvergrößerung und Kontrastanpassung