Influence of a cost–efficient Langevin subgrid-scale model on the dispersed phase of large–eddy simulations of turbulent bubble–laden and particle–laden flows

Abstract

The paper is concerned with the development of a cost-efficient Langevin subgrid-scale model and the analysis of its influence on the dispersed phase of turbulent bubble–laden and particle–laden flows. For this purpose, the Langevin subgrid-scale model of [Pozorski, J., Apte, S. V., 2009. Filtered particle tracking in isotropic turbulence and stochastic modeling of subgrid-scale dispersion. Int. J. Multiphase Flow 35, 118–128.] is chosen as the starting point since it takes the temporal correlations of the subgrid-scale velocity fluctuations, the crossing-trajectory and the continuity effect into account. Based on the idea of [Minier, J.-P., Peirano, E., Chibbaro, S., 2004. PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow. Phys. Fluids 16, 2419–2431.] [Minier, J.-P., Chibbaro, S., Pope, S. B., 2014. Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. Phys. Fluids 26, 113303.] to formulate the drift and diffusion terms in matrix form, the model is extended for an arbitrary direction of the particle motion. Considering turbulent downward channel flows of different setups covering a large range of parameters, the influence of the subgrid-scale model is analyzed. After a detailed validation of the bubble–laden flow the Langevin model and a simple trivial model are applied to investigate the effect of the subgrid-scales. It is found that the Langevin subgrid-scale model only marginally changes the velocity statistics or the volume fraction of the bubbles, which can be attributed to the small magnitude of the subgrid-scale velocities obtained by the Langevin model. The model is able to estimate the correct level of the turbulent kinetic energy of the subgrid-scales. Similar results are found for the second setup consisting of solid particles of Stokes number St+=1.67. In this case the influence of the Langevin subgrid-scale model on the velocity statistics of the particles is found to be more pronounced. Furthermore, it is observed that the model leads to a strongly increased volume fraction of the particles at the walls and thus to a significant increase of particle-wall collisions. To further investigate this behavior and to analyze the impact of the particle inertia, additional simulations containing smaller particles (St+=1 and 0.1) are carried out. The results show that the influence of the Langevin subgrid-scale model on the velocity fluctuations and the volume fraction increases with decreasing Stokes number. Thus, for these cases the extended but nevertheless still cost-efficient Langevin model is a reasonable approach.