Numerical simulation of turbulent mixing by a hybrid method combining finite-volume and Lagrangian schemes

Predicting the dynamics of mixing of a scalar transported by a turbulent flow is a major challenge. The accurate prediction of mixing is crucial for many environmental or industrial applications in which this scalar may represent the temperature, the concentration of a chemical species or a pollutant. The dynamics of mixing depend on the Schmidt number which corresponds to the ratio between the viscosity of the fluid and the diffusivity of the scalar in the media.

At high Schmidt numbers, in fluids with elevated viscosity, the mixing occurs at two very different levels with regards to space and time: at the micro-scale for the scalar, and at a bigger scale for the fluid’s turbulence. As a result, the grids and time-steps necessary to solve both phenomena are very different, and modelling the whole mixing process therefore meets a dilemma: computing at the fluid’ scale is fast but lacks accuracy, computing at the scalar’ scale is accurate but very costly and time consuming.

We have recently developed an original hybrid approach to counter this problem, allowing to solve the scalar and the fluid dynamics at their own relevant scales with regards to space and time. Our method was set up and validated in rather simple “academic” configurations, and the goal of this project is to move towards more complex and realistic geometries through the implementation of our code based in a “particle method”, in the more generalist YALES2 code, based on a “finite-volume” approach.

This requires specific algorithmic developments to:

• Build up the process enabling to couple the particle method and the finite-volume method, by revisiting the techniques needed to transfer information between particle and finite-volume grids;
• Integrate the “level-set” method in the obtained model to be able to address more complex situations such as two-phase media, in which the interactions between the scalar and the flow occurring at the gas-liquid interface play a key role in the mixing phenomenon;
• Couple our hybrid method with Large Eddy Simulations techniques (LES) enabling to further reduce the computational cost, and make our method suitable for modelling realistic configurations with reasonable processing time and power requirements.