Session L25: Particle-laden Flows IV

Simulated tornado debris tracks: implications for inferring corner flow structure

A large collection of three-dimensional large eddy simulations of tornadoes with fine debris have been recently been performed as part of a longstanding effort at West Virginia University to understand tornado corner flow structure and dynamics. Debris removal and deposition is accounted for at the surface, in effect simulating formation of tornado surface marks. Physical origins and properties of the most prominent marks will be presented, and the possibility of inferring tornado corner flow structure from real marks in the field will be discussed.   

Numerical simulation of a bidisperse turbidity current interacting with a Gaussian bump

We study a particle-laden lock-exchange current interacting with a Gaussian bump by means of DNS simulations. Our software package TURBINS employs an immersed boundary implementation of the Boussinesq Navier-Stokes equations for the fluid motion, coupled to transport equations for the particle concentration fields. The suspension includes two particle sizes with a settling velocity ratio of 10. As the current travels over the bottom topography, we record instantaneous deposit profiles and wall shear stress contours. As the current impinges on the obstacle, it becomes strongly three-dimensional. Comparison of the final deposit profiles near the Gaussian bump against the case of a flat surface shows a smaller influence of the topography on the fine particles than on the coarse ones. Due to lateral deflection, deposition generally decreases near the bump, while increasing away from it. Some distance downstream of the obstacle, the deposit profiles lose their memory of the bump and become nearly uniform again. Instantaneous wall shear stress profiles are employed in order to estimate the critical conditions at which bedload transport and/or particle resuspension can occur in various regions.   

Modelling Submarine Turbidity Currents

When a large scale pyroclastic flow enters the ocean it leads to the spreading of sediment across the deep ocean through particle laden flows known as turbidity currents. Turbidity currents are driven by gravitational forces associated with a density difference caused by the presence of suspended particles. This generates a flow which transports the suspended particles, but which progressively slows as they sediment to the underlying boundary. We adopt a shallow layer model in which vertical accelerations are neglected and employ a three equation system that expresses the conservation of fluid and particulate mass and formulates a balance of momentum for a current flowing down an incline. Importantly we include the effects of entrainment of surrounding fluid into the flow. Solutions are constructed using numerical means and they reveal the strong dependence of run out length on the rate of entrainment. Further, the prediction of the distribution of the deposit from the flow compares favourably with field data from the July 2003 event from Soufri\`{e}re Hills volcano, Montserrat.   

Convective instability in sedimentation

We investigate the convective sedimentation in a stably stratified saltwater using linear stability analysis and 3D direct numerical simulation. We consider sediment particle with grain diameter in the range of 1.5 to 60 $\mu$m. Equilibrium Eulerian approach and dilute flow assumption are adopted to simplify the governing equations of the two-phase system (Balachandar and Eaton 2009, Annul Rev. Fluid Mech.). A semi-empirical closure of particle diffusivity due to long-range interaction is adopted (Segre et al. 2007, Phys. Rev. Lett.). For a fixed salt diffusivity, the particle phase can act as either slow or fast diffusing agent in a double-diffusive system depending on the particle diameter. Additionally, the settling-driven mechanism can also trigger instability. Linear stability analysis is carried out as the guideline for 3D numerical simulation. Simulation results indicate different finger patterns for different particle settling velocity and sediment concentration. For fine particle, where the double-diffusive mechanism plays an important role, the instability is enhanced by the settling. The finger size is on centimeter scale and the finger pattern is more nonlinear and asymmetric. For large particle, the interfacial instability appears long after the particles pass the density interface induced by salt where Rayleigh-Taylor instability takes place and finger pattern is more symmetric. Fully nonlinear analysis with 3D direct numerical simulations will be presented in the meeting.   

Particle jet formation during explosive dispersal of solid particles

Previous experimental studies have shown that when a layer of solid particles is explosively dispersed, the particles often develop a non-uniform spatial distribution. The instabilities within the particle bed and at the particle layer interface likely form on the timescale of the shock propagation through the particles. The mesoscale perturbations are manifested at later times in experiments by the formation of coherent clusters of particles or jet-like particle structures, which are aerodynamically stable. Experiments have been carried out in spherical and cylindrical geometry to investigate the influence of particle diameter and density and the ratio of particle to high explosive mass on the relative tendency for instabilities to develop in the expanding particle cloud. The number of particle jets that form tends to scale with a particle compaction Reynolds number corresponding to the ratio of inertial to frictional forces of the particle system. Below a critical Reynolds number, the expanding particle cloud remains stable.   

Shear stress and particle removal measurements of a turbulent air jet impinging normally upon a surface

When a jet of air impinges normally upon a surface, it imposes a shear stress parallel to the wall in all directions from the impingement point. Particle removal from that surface is assumed to be mainly due to that imposed shear stress. ~But that shear stress has been difficult to measure and has, in the past, been inferred from particle removal rates.~ Here we make a basic measurement of mean shear stress imposed upon a planar wall by a normally-impinging turbulent air jet using the technique of oil-film interferometry. The resulting shear-stress distribution is then compared with the removal rates of latex microspheres from a planar glass surface as a function of the distance from jet impingement normalized by the height of the nozzle above the surface.~ The particle removal experiments are carried out with sparse (few particle collisions) particle distributions. These experiments show that the efficiency of particle removal is directly but not linearly related to the imposed shear stress. A distinct shear stress threshold was found, below which little or no particle removal occurred.   

Large-Scale Simulations of Realistic Fluidized Bed Reactors using Novel Numerical Methods

Turbulent particle-laden flows in the form of fluidized bed reactors display good mixing properties, low pressure drops, and a fairly uniform temperature distribution. Understanding and predicting the flow dynamics within the reactor is necessary for improving the efficiency, and providing technologies for large-scale industrialization. A numerical strategy based on an Eulerian representation of the gas phase and Lagrangian tracking of the particles is developed in the framework of NGA, a high- order fully conservative parallel code tailored for turbulent flows. The particles are accounted for using a point-particle assumption. Once the gas-phase quantities are mapped to the particle location a conservative, implicit diffusion operation smoothes the field. Normal and tangential collisions are handled via soft-sphere model, modified to allow the bed to reach close packing at rest. The pressure drop across the bed is compared with theory to accurately predict the minimum fluidization velocity. 3D simulations of the National Renewable Energy Lab's 4-inch reactor are then conducted. Tens of millions of particles are tracked. The reactor's geometry is modeled using an immersed boundary scheme. Statistics for volume fraction, velocities, bed expansion, and bubble characteristics are analyzed and compared with experimental data.   

Large-Scale Eulerian-Lagrangian Simulations of Turbulent Particle-Laden Riser Flows

Turbulent gas-particle flows play fundamental roles in a wide range of technical systems. Understanding and predicting particle-laden turbulent flows is key to ensuring optimal performance and improving the design of devices such as fluidized bed reactors. In this work, a Lagrangian description of the particles is combined with state-of-the-art schemes for high-fidelity turbulence simulations in order to enable predictive numerical modeling of particle cluster formation in turbulent riser flows. The simplified riser configuration of He et al is used to answer several key questions regarding meso-scale structures in risers, in particular regarding (1) the onset of instability, especially in the limit of low volume fractions, (2) the role played by the drag model formulation (in particular the dependence of the drag law on void fraction) and (3) the collision model in the formation and dynamics of particle structures. Simulation results are compared with experimental results in terms of cluster size and shape, as well as gas and particle statistics. Then, a wall-free fully periodic configuration is considered and differences in cluster statistics are discussed.   

Porosity-Permeability Relations in Granular, Fibrous and Tubular Porous Media

A Voronoi diagram-based stochastic geometry generator was developed to generate porous media models of granular, fibrous and tubular types. By adjusting geometry parameters such as number of random seeds and width of channels between grains or radius of fibers/tubes, homogenous and isotropic models of porous media with specified porosity can be accurately generated. The relation of porosity to geometry parameters was proven to be repeatable, and additional manipulations on geometries were built in, including creation of anisotropy and heterogeneity. A parallelized Lattice Boltzmann simulator with nearly ideal speedup was developed and employed to study porosity-permeability relations. Simulation data obtained in the porosity range of 0.01-0.4 revealed that properly normalized permeability in tubular porous media is higher than that in the granular type when porosity becomes greater than 0.1, which can be explained by its more efficient use of the pore space to conduct the flow. Simulation data obtained from fibrous media in solid volume fraction range of 0.01-0.4 agreed with published results, and showed a rapid change with solid volume fraction in the dilute limit.   

Modeling enduring contact in Direct Numerical Simulations of incipient motion of granular beds

A boundary integral method for fast Direct Numerical Simulations of particle-laden flow on Cartesian grids is used here to model the incipient motion of particle beds forced by a steady current. The particle hydrodynamic force is determined numerically by resolving the flow around individual particles. Analytical lubrication force corrections are added during collisions when the interstitial gap becomes smaller than the grid step. The mechanical force normal and tangential to the contact between particles is modeled by a linear elastic-plastic law and a history dependent friction law, respectively. Resolving fluid-structure interaction effects during collisions is numerically expensive because the collision time scale is two orders of magnitude smaller than the maximum time step for numerical stability of the viscous flow. We improve the numerical efficiency with an acceleration-based control of the time step so that the maximum time step is used for enduring contacts with low particle acceleration. Quantitative comparison for sediment motion initiation is made with laboratory data.