Lattice Boltzmann simulation of the laminar-turbulent transition in a constricted tube

Lattice Boltzmann method (LBM) is a mesoscale numerical method suitable for incompressible fluid flow simulations and its popularity has increased in recent years. It is applicable for many engineering applications dealing with fluid flow and the method can be fully parallelised which is beneficial for calculation on CPU clusters or GPUs. In this paper, the LBM is tested on the benchmark geometry of a constricted tube to verify the laminar-turbulent transition, which can appear in many engineering and biological systems (lungs, arteries). The motivation for this study is to identify suitable models for simulation of human airways which consists of several bifurcations and constricted channels. For this research, the CPU cluster Salomon from IT4Innovations was used. The flow regime through a cosine-curved constriction given by Reynolds number 2000 was simulated with the Lattice Boltzmann Smagorinsky subgrid model. To reveal the unsteady flow character, a period of 5 seconds was simulated. The results of the time-averaged (last 2 seconds) axial velocities on the tube axes and at 6 determined cross sections in the post-stenotic part were compared with already published CFD simulations using the conventional finite volume method FVM (several LES and RANS turbulence models) and experimental data. To reduce numerical errors caused by discretization, the grid independent test for different three types of geometries was done. The LBM predicts the velocities in the wall vicinity well, but in the constriction the velocities are higher and it underestimates the velocities in the core flow behind the constriction compared to the remaining models and experimental data. At the moment, the results from this benchmark simulation will be used for education purposes. However, it is also the initial step for the application of the LBM to solve the flow through the human airways and the deposition of aerosols there.