Particle-laden turbulent flows are encountered in a wide range of engineering and environmental problems. Understanding the hydrodynamics of such flows is the basis for many applications in engineering design, environmental protection, and weather forecasting.
Large-eddy simulation (LES) has emerged as a promising tool for simulating particle-laden turbulence. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles. However, the accuracy of such a Langevin equation model depends primarily on the prescription of the inertial particle–SGS eddy interaction timescale. Based on the direct numerical simulation (DNS) flow field, Dr. Guodong Jin from LNM, Institute of Mechanics, Chinese Academy of Sciences and his collaborators computed the inertial particle–SGS eddy interaction timescale for a wide range of particle Stokes number and several filter widths. Using the Langevin stochastic equation with the new closure model, they demonstrated that the particle kinetic energy can be much better predicted in LES (Fig.1). This paper has been published in International Journal of Multiphase Flow, 36, 432-437,2010 (http://dx.doi.org/10.1016/j.ijmultiphaseflow.2009.12.005)
Furthermore, the missing small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional LES. As a first step toward addressing this challenge, Dr. Guodong Jin and his collaborators examined the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from DNS are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5(Fig.2 ). The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. The analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers. This paper has been recently published in Physics of Fluids, 22, 055106,2010, http://dx.doi.org/10.1063/1.3425627).
Fig. 1. Comparison of the particle kinetic energy, kp, with different Stokes numbers, , obtained from the DNS, conventional LES and LES with a subgrid Langevin model, where kf is the kinetic energy of fluid field. Also shown is the result of (Fede et al., 2006) obtained from the filtered-DNS and a subgrid Langevin model (1283 DNS and cutoff location). (Picture/LNM)
Fig.2. Effects of filtering operation and spectral eddy viscosity model on collision rate for particles with different Stokes numbers in LES (643), FDNS (), and DNS (2563) flow fields. ST in the legends denotes the Saffman and Turner’s theory for small Stokes number particles. (a) variation with ; (b) relative error of from the LES and FDNS to theDNS results. (Picture/LNM)