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Pore-resolved direct numerical simulations (DNS) are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, $Re_K$, of 2.56, 5.17, and 8.94, representative of natural stream or river systems. Time-space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment-water interface (SWI). The mean flow and shear penetration depths increase with $Re_K$ and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (PDFs) of normalized local bed stress are found to collapse for all Reynolds numbers and their root mean-squared fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer, their PDFs are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI can potentially be used in providing better boundary conditions in modeling of incipient motion and reach-scale transport in the hyporheic zone., Comment: 34 pages, 15 figures, 9 tables. arXiv admin note: text overlap with arXiv:2204.13875

The predictive capability of two way--coupled point-particle Euler-Lagrange model in accurately capturing particle-flow interactions under grid refinement, wherein the particle size can be comparable to the grid size, is systematically evaluated. Two situations are considered, (i) uniform flow over a stationary particle, and (ii) decaying isotropic turbulence laden with Kolmogorov-scale particles. Particle-fluid interactions are modeled using only the standard drag law, typical of large density-ratio systems. A zonal, advection-diffusion-reaction (Zonal-ADR) model is used to obtain the undisturbed fluid velocity needed in the drag closure. Two main types of interpolation kernels, grid-based and particle size--based, are employed. The effect of interpolation kernels on capturing the particle-fluid interactions, kinetic energy, dissipation rate, and particle acceleration statistics are evaluated in detail. It is shown that the interpolation kernels whose width scales with the particle size perform significantly better under grid refinement than kernels whose width scales with the grid size. Convergence with respect to spatial resolution is obtained with the particle size--based kernels with and without correcting for the self-disturbance effect. While the use of particle size--based interpolation kernels provide spatial convergence and perform better than kernels that scale based on grid size, small differences can still be seen in the converged results with and without correcting for the particle self-disturbance. Such differences indicate the need for self-disturbance correction to obtain the best results, especially when the particles are larger than the grid size., Comment: Submitted to International Journal of Multiphase Flow

Pore-resolved direct numerical simulations of turbulent open channel flow are performed comparing the structure and dynamics of turbulence over impermeable rough and smooth walls to a porous sediment bed at permeability Reynolds number ($Re_K$) of 2.6, representative of aquatic beds. Four configurations are investigated; namely, (i) permeable bed with randomly packed sediment grains, (ii) an impermeable-wall with full layer of roughness elements matching the top layer of the sediment bed, (iii) an impermeable-wall with half layer of roughness elements , and (iv) a smooth wall. A double-averaging methodology is used to compute the mean velocity, Reynolds stresses, form-induced stresses, and turbulent kinetic energy budget. It is observed that the mean velocity, Reynolds stresses, and form-induced pressure-velocity correlations representing upwelling and downwelling fluxes are similar in magnitude for the permeable-bed and impermeable-full layer wall cases. However, for the impermeable-half layer case, the wall blocking effect results in higher streamwise and lower wall-normal stresses compared to the permeable-bed case. Bed roughness increases Reynolds shear stress whereas permeability has minimal influence. Bed permeability, in contrast to Reynolds stresses, significantly influences form-induced shear stress. Bed shear stress statistics show that probability of extreme events increases in permeable bed and rough wall cases as compared to the smooth wall. Findings suggest that bed permeability can have significant impact on modeling of hyporheic exchange and its effect on bed shear and pressure fluctuations are better captured by considering at least the top layer of sediment., Comment: 31 pages, 18 figures, journal paper

Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centered cubic porous unit cell on the transport, clustering, and deposition of fine particles at different Stokes numbers ($St = 0.01, 0.1, 0.5, 1, 2$) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and collision of particles with pore walls is modeled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyze the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with Stokes number. However, unlike homogeneous, isotropic turbulence, formation of large number of very small volumes was observed at all Stokes numbers and is attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density showed peak of clustering shifts towards larger scales with increase in Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers.

A general, two-way coupled, point-particle formulation that accounts for the disturbance created by the dispersed particles in obtaining the undisturbed fluid flow field needed for accurate computation of the force closure models is presented. Specifically, equations for the disturbance field created by the presence of particles are first derived based on the inter-phase momentum coupling force in a finite-volume formulation. Solution to the disturbance field is obtained using two approaches: (i) direct computation of the disturbance velocity and pressure using the reaction force due to particles at computational control volumes, and (ii) a linearized, approximate computation of the disturbance velocity field, specifically applicable for low Reynolds number flows. In both approaches, the computed disturbance field is used to obtain the undisturbed fluid velocity necessary to model the aerodynamic forces on the particle. The two approaches are thoroughly evaluated for a single particle in an unbounded and wall-bounded flow on uniform, anisotropic, as well as unstructured grids to show accurate computation of the particle motion and inter-phase coupling. The approach is straightforward and can be applied to any numerical formulation for particle-laden flows including Euler-Lagrange as well as Euler-Euler formulations., Comment: 31 pages, 8 figures

Accurate prediction of spray atomization process using an Euler-Lagrange (EL) approach is challenging because of high volume fraction of the liquid phase in dense regimes. This would in reality displace a remarkable portion of the gaseous phase which is commonly ignored in the standard EL approaches. In addition, deformation of droplet due to the interaction of aerodynamic force, surface tension and viscous forces is typically neglected in modeling dense sprays. In this work, to capture the volumetric displacement effects using an EL approach, the spatio-temporal changes in the volume fraction of the gaseous phase are taken into account. This leads to zero-Mach number, variable density equations that give rise to a source term in both momentum and continuity equations. It is shown that the continuity source term increases the velocity and dynamics of the carrier phase close to the nozzle. However, owing to the jet spread and dispersion of droplets, these effects decrease further downstream. In order to quantify the droplet deformation effects, different models are compared together with an experimental data. Different breakup regimes are studied in order to identify the best model for each regime. The shape deformation effect is isolated by performing a single droplet injected into the cross flow with flow conditions similar to the bag-type breakup. A significant deviation in the motion of droplet is observed compared to a case where deformation is neglected.

Accurate prediction of a dense spray using an Euler-Lagrange approach is challenging because of high volume fraction of the dispersed phase due to subgrid cluster of droplets. To accurately model dense sprays, one needs to capture this effect by taking into account the spatio-temporal changes in the volume fraction of the carrier phase due to the motion and presence of the dispersed phase. This leads to zero-Mach number, variable density equations which are commonly neglected in the standard two-way coupling spray simulations. Using pressure-based solvers, this gives rise to a source term in the pressure Poisson equation and a non-divergence free velocity field. To validate the predictive capability of such approach, an atomized non-evaporating dilute particulate round jet is first examined using Large Eddy Simulation coupled with Point-Particle approach and then higher volume loadings up to 38% are investigated with and without taking into account the volumetric displacement effects. It is shown that for volume loadings above 5%, the volumetric displacement effects enhance dynamics of the flow resulting in a higher stream-wise mean and r.m.s. velocities compared to the results of standard two-way coupling. This is more pronounced for the near field of the jet where local volume fraction of the dispersed phase is relatively high. This enhancement is conjectured to be due to the velocity divergence effect due to the modified continuity equation where spatio-temporal variations in volume fraction of the carrier phase increases velocity in the regions of high void fraction.

The accuracy of Euler-Lagrange point-particle models employed in particle-laden fluid flow simulations depends on accurate estimation of the particle force through closure models. Typical force closure models require computation of the slip velocity at the particle location, which in turn requires accurate estimation of the undisturbed fluid velocity. However, when the fluid and particle phases are two-way coupled the fluid velocity field is disturbed by the presence of the particle. A common practice is to use the disturbed velocity to compute the particle force which can result in errors as much as 100% in predicting the particle dynamics. In this work, a general velocity correction scheme is developed that facilitates accurate estimation of the undisturbed fluid velocity in particle-laden fluid flows with and without no-slip walls. The model can handle particles of different size, arbitrary interpolation functions, anisotropic grids with large aspect ratios, and wall-bounded flows. The present correction scheme is motivated by the recent work of Esmaily & Horwitz (JCP, 2018) on unbounded particle-laden flows. Modifications necessary for wall-bounded flows are developed such that the undisturbed fluid velocity at any wall distance is accurately recovered, asymptotically approaching the unbounded scheme for particles far away from walls. A detailed series of verification tests were conducted on settling velocity of a particle in parallel and perpendicular motions to a no-slip wall. A range of flow parameters and grid configurations; involving anisotropic grids with aspect ratios typically encountered in particle-laden turbulent channel flows, were considered in detail. When the wall effects are accounted for, the present correction scheme reduces the errors in predicting the near-wall particle motion by one order of magnitude smaller values compared to the unbounded correction schemes.

Modeling of a dense spray regime using an Euler-Lagrange approach is challenging because of local high volume loading. A cluster of droplets, that are assumed subgrid, can lead to locally low void fractions for the fluid phase. Under these conditions, spatio-temporal changes in the fluid volume fractions should be considered in an Euler-Lagrange, two-way coupling model. This leads to zero-Mach number, variable density governing equations. Using pressure-based solvers, this gives rise to a source term in the pressure Poisson equation and a non-divergence free velocity field. To test the validity and predictive capability of such an approach, a round jet laden with particles is investigated using Direct Numerical Simulation coupled with point-Particle based model and compared with available experimental data for a particulate turbulent round jet with $Re_j=5712$. Standard force closures including drag, lift, Magnus effect, pressure, added mass as well as viscous torque acting on each individual particle are employed in the Point-Particle based model. In addition, volume displacement effects due to the presence of solid particles or liquid droplets, which is commonly neglected in the standard two-way coupling, are taken into account in both continuity and inter-phase momentum transfer to accurately capture the underlying structure of particle-turbulence interactions. Prediction results are in well agreement with the corresponding experiment.