Lattice Boltzmann Simulation of a Reacting Micro-mixer

  • Bukreev, Fedor (Lattice Boltzmann Research Group (LBRG))
  • Jeßberger, Julius (Institute of Mechanical Process Engineering and Mechanics (MVM))
  • Kummerlander, Adrian (Institute for Applied and Numerical Mathematics (IANM))
  • J. Krause, Mathias (c Institute for Applied and Numerical Mathematics (IANM))

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Micro-mixers are widely used chemical and pharmaceutical processing apparatuses. They are applied as well for mixing as for reacting flows. Usually, the flow regime in industrial application is turbulent. However, in current state-of-the-art research often reacting multi-component flows are considered in the laminar regime [2, 3, 4]. But even in the fully laminar streaming regime (e.g. Re = 186, static mixer of liquids), there exist micro-structures that enlarge the contact area of the species and enable mixing and reaction processes. For this setup, accurate predictions of that structures are possible with a direct numerical simulation on a sufficient fine meshes resolving the Bachelor microscales, which are about 30 times smaller than the Kolmogorov length scales. Among different computational fluid dynamics discretization approaches the lattice Boltzmann method (LBM) offers a simple and highly efficient option. By using CPU-GPU-clusters, they promise to fully resolve transitional and even turbulent multi-component fluid flow to better understand micro mixing phenomena. With the help of the open-source software OpenLB (, [1]) the reacting micro-mixer was built up and validated based on the previous publications of Bothe et al. [2, 3, 4]. The considered setup consists of a carrier fluid, modelled by the incompressible Navier-Stokes equations, coupled to three transported and reacting species, modelled by three reaction advection diffusion equations (RADEs). The resulting system is discretized by LBM. Due to the small diffusivity coefficients the RADEs become unstable, what requires an artificial addition of diffusion at the critical locations, similarly to the famous Smagorinsky-Lilly approach in the framework of large eddies simulations. This method has been already applied in the context of LBM to heat flux simulations and showed good stability as well as good accuracy [5, 6]. Due to the locality of the whole simulation ansatz (especially the local computation of the shear stresses), it can also takes advantage of modern CPU-GPU-cluster which enables highly resolved simulations. The results show good agreement with simulation results using an FVM discretization and experiments, both done by Bothe et al. [3, 4]. A convergence study is also part of the presented approach which is also a novelty. The computation was performed on the CPU/GPU-cluster HoreKa on up to 7,600 cores (100 nodes with 2 CPUs and 38 cores). Finally, the RADE-LBM stabilization method is applied to micro-mixing in a turbulent flow regime. The preliminary results show its usability for this regime. It is found stable and shows very promising performance especially on CPU-GPU-clusters.