Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

Abstract

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation ͑LES͒ of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale ͑SGS͒ 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 direct numerical simulation ͑DNS͒ 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. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS ͑FDNS͒ 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 Ͼ 3. Our analysis suggests that, for St K Ͻ 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.

Space-Time Correlations and Dynamic Coupling in Turbulent Flows

“…The FDNS result is in between those of the DNS and LES. The peak from the LES is located to the left of the one from the DNS, and the variances (area integrations) from the LES and FDNS are smaller than that from the DNS ( Jin et al 2010). These results indicate that the particles in the LES and FDNS are located at larger scales and are more uniform than those in DNS at small Stokes numbers.…”

“…In contrast, the collision-related statistics of inertial particles can be significantly affected by SGS motions: For small Stokes numbers, FDNS underpredicts the radial distribution function and radial relative velocity at contact; for intermediate Stokes numbers, FDNS results are larger than those from DNS; and for larger Stokes numbers, the collision rate can be well predicted by FDNS ( Jin et al 2010, Ray & Collins 2011. For practical LES, the errors due to neglecting the SGS motions are combined with those caused by the SGS model, which lead to profound effects on the collisionrelated statistics of inertial particles ( Jin et al 2010, Chibbaro et al 2014, Cernick et al 2015.…”

“…Evidently, the particles accumulate in regions of low vorticity and high strain rates (Squires & Eaton 1991, Wang & Maxey 1993, Balachandar & Eaton 2010. However, the opposite effects of the SGS motions on particle clustering are found at different Stokes numbers: The particle clustering is greater in DNS than in LES at small Stokes numbers; in contrast, the particle distribution is less uniform in DNS compared to LES at large Stokes numbers (not shown in figure) (Pozorski & Apte 2009, Jin et al 2010, Ray & Collins 2011. Figure 2c plots the particle density spectra obtained from DNS, FDNS, and LES.…”

Lagrangian statistics in isotropic turbulent flows with deterministic and stochastic forcing schemes

“…He and his coworkers developed a series of elliptic models for two-point, two-time correlation of Eulerian [6,7] and Lagrangian [8] velocities, respectively, which have been powerful tools for turbulence measure [9]. In recent years, direct numerical simulation (DNS) and largeeddy simulation (LES) have been taken as main tools to explore the fundamental features of turbulence and its interaction with other physical process [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In order to obtain turbulence statistics under stationary conditions in isotropic turbulent flows, energy is fed into the flow at large scales to balance the energy dissipation at small scales by molecular viscosity in DNS or by both molecular viscosity and subgrid scale (SGS) eddy viscosity in LES.…”

Turbulent Clustering of Point Particles and Finite-Size Particles in Isotropic Turbulent Flows

“…When particle response time τ p is comparable to the turbulent Kolmogorov time scale τ K , that is, the particle Stokes number St K = τ p /τ K is about 1.0, the particle cluster is most favorable. 2 Under gravity, particles have a mean relative velocity to the surrounding flows. The relative velocity reduces the interaction time scale between the turbulent structures and particles, thus it could suppress the level of particle clustering in turbulence.…”