Subgrid-scale modeling and wavelet analysis for preferential concentration of inertial point particles in turbulent flows

A striking feature of particle-laden turbulent flows is the presence of particle clouds that result from the tendency of inertial particles to preferentially sample specific regions of the flow field. This phenomenon is central to a number of important physical processes. However, computational predictions of preferential concentration at high Reynolds numbers are challenging, since the numerical resolution of the participating scales is typically unaffordable. This dissertation contributes both to the analysis of the preferential concentration phenomenon and the development of subgrid-scale models for the prediction of preferential concentration in large-eddy simulations of particle-laden turbulence. First, direct numerical simulations of incompressible homogeneous-isotropic turbulence laden with a dilute suspension of inertial point particles are performed in conjunction with a wavelet multi-resolution analysis of the results. The use of spatially localized wavelet basis functions enables the simultaneous consideration of physical and scale spaces in the spectral characterization of the flow field of the carrier phase and the concentration field of the disperse phase. The multi-resolution analysis of the disperse phase provides statistical information about the spatial variability of a scale-dependent coarse-grained number density field and the local energy spectra of its fluctuations, characterizing the sensitivities of those quantities to variations in scale and Stokes number. In particular, the spatial variabilities of the wavelet energy spectrum of the particle concentration fluctuations are observed to be maximum in regimes where the particles preferentially concentrate. The results highlight the scale-dependent inhomogeneities of the structures in the concentration field generated by preferential concentration, and the existence of characteristic scales of interaction between the disperse and carrier phases. Additionally, an inter-phase multi-resolution analysis is performed that indicates the occurrence of a spatial anti-correlation between the enstrophy and kinetic-energy spectra of the carrier phase and the particle concentration at small scales in regimes where preferential concentration is important. This anti-correlation vanishes as the scale is increased, and is largely suppressed when the preferential-concentration effect is negligible. Secondly, a wavelet-based method for extraction of clusters of inertial particles in turbulent flows is presented that is based on decomposing Eulerian particle number-density fields into the sum of a coherent (organized) and an incoherent (disorganized) components. The coherent component is associated with the clusters and is extracted by filtering the wavelet-transformed particle number-density field based on an energy threshold. The analysis shows that in regimes where the preferential concentration is important, the coherent component representing the clusters can be described by just 1.6% of the total number of wavelet coefficients, thereby illustrating the sparsity of the particle number-density field. On the other hand, the incoherent portion is visually structureless and much less correlated that the coherent one. An application of the method is illustrated in the form of a grid-adaptation algorithm that results in non-uniform meshes with fine and coarse elements near and away from particle clusters, respectively. In regimes where preferential concentration in clusters is important, the grid adaptation leads to a reduction of the number of control volumes by one to two orders of magnitude. Thirdly, two dynamic models for turbulent velocity fluctuations are proposed for large-eddy simulations of dispersed multiphase flows. The first model is simple, involves no significant computational overhead, contains no adjustable parameters, and is flexible enough to be deployed in any type of flow solvers and grids, including unstructured setups. The approach is based on the use of elliptic differential filters to model the subgrid-scale velocity. The only model parameter, which is related to the nominal filter width, is determined dynamically by imposing consistency constraints on the estimated subgrid energetics. The second model constructs a velocity that contains scales smaller than the coarse-grid resolution, thereby enabling the prediction of small-scale phenomena such as the preferential concentration of particles in high-strain regions. The construction of the spectrally enriched velocity field in physical space is made dynamically, and is based on 1) modeling the smallest resolved eddies of sizes comparable to the grid size via approximate deconvolution, and 2) reconstructing the subgrid-scale fluctuations via non-linear generation of small-scale turbulence. The model does not contain tunable parameters, can be deployed in non-uniform grids, and is applicable to inhomogeneous flows subject to arbitrary boundary conditions. The performance of both models is tested in large-eddy simulations of homogeneous-isotropic turbulence laden with particles, where improved agreement with direct numerical simulation results is obtained for the statistics of preferential concentration. Lastly, application to wall-modeled large-eddy simulations of particle-laden channel flow is presented. Results of the application of existing wall models to particle-laden turbulent channel flows are described, and prospective pathways for improving their performance are suggested. The focus is on the prediction of the spatial distribution statistics of the disperse phase. It is observed that wall-modeled large-eddy simulations without particular treatment for the particles in the wall-adjacent cells overpredict the near-wall accumulation of particles. The choice of the continuous representation of the velocity field between the first grid point and the wall is shown to be of primary importance. A wall-modeling strategy is explored that performs well at large Stokes numbers. It relies on using interpolation kernels near the wall that mimic the law of the wall for the wall-parallel velocity, and direct numerical simulation profiles of the fluctuations for the wall-perpendicular velocity. Applications of the two developed subgrid-scale models are shown to improve the prediction of preferential concentration, but have no effect on the mean concentration profile.

Keywords: Mechanical Engineering.
Advisor: Moin Parviz 
Mani Ali (Professor of mechanical engineering) 
Urzay Lobo Javier