Session KE: Multiphase Flows: General II

On a multi-phase modeling framework for sediment transport

Understanding sediment transport in the heterogeneous environment, including river, beach, estuary, shelf and submarine canyon, is crucial to the preservation and restoration of coastal ecosystem. A multi-phase modeling framework is developed in order to study sediment transport driven by a variety forcing (current, tide, wave and gravity-driven flow) with a range of sediment characteristics. As an example, constitutive relation for intergranular interaction (particle stress) based on kinetic theory of granular flow is adopted in a two-phase model and is shown to be capable of modeling wave-induced sheet flow transport in the sandy-beach environments. Recently, to further model typical fine sediment transport processes of long timescales (e.g., tidal), spatial inhomogeneity, and multiple sediment classes, the two-phase model is rationally simplified. The simplified model is much efficient yet robust to retain essential mechanisms of fluid-sediment and intergranular interactions. Adopting rheological closure based on viscous suspension, preliminary results indicate that the model captures field observed lutocline behavior of fluid mud under tidal flow and wave-supported gravity-driven fluid mud on the continental shelf.   

Sediment dynamics over rippled beds in oscillatory flow: Experiments

The University of Maryland Oscillatory Sediment Flume (UMOSF) is an experimental facility built to investigate sediment transport mechanics within an oscillatory turbulent boundary layer is over a mobile sediment bed. The range of sediment size and density as well as the flow oscillation amplitude and period is selected in the current work to study flows which generate rippled bed forms. The measurement technique utilizes a simultaneous two-phase PIV method to examine fluid-particle interactions, focusing on the suspension mechanisms and to obtain statistics to describe the two-way coupling. Specifically, measurements will focus on the upslope face, crest and recirculation zone of the ripple, where previous simulations for steay flow\footnote{Chang \& Scotti, \textit{J. Turbulence}, \textbf{4}(019), pp.1-21, (2003).} have shown the strongest regions of suspension, injection into the boundary region, and mixing with the outer flow to occur. Results of these experiments are closely coordinated with ongoing numerical simulations, and discussed in a companion presentation.   

Sediment dynamics over rippled beds in oscillatory flow: Numerical results

The dynamic motion of solid particles is an important phenomena in a wide range of applications such as: coastal erosion, sand dune motion or fluidized bed. In these applications, an important issue is the effect of the wall-shape on the dynamical behavior of the dispersed phase and on the sediment deposition. In this study, Direct Numerical Simulations of steady fluid flow over a ripple have been coupled with Lagrangian tracking of discrete solid particles. The forces acting on the particles are reduced to the drag and the lift force induced by the fluid a flow. The particles are initially randomly distributed in the computational domain. On the bottom boundary, a saltating model is introduced to account for particle-wall interaction. Both steady and oscillatory conditions are considered, and the results are compare with ongoing experimental results discussed in a companion presentation.   

Modeling Sediment Transport under Waves

Modeling studies of the flux of sediment at the sea bed under energetic waves are presented. The transport of sediment is crucial to predicting many coastal engineering processes, such as erosion around structures and prediction of beach profiles. We model a two-phase system containing water and sediment particles approximated as a mixture having variable density and viscosity that depends on the local sediment concentration. We use a control volume approach on a three-dimensional staggered grid to solve the equations numerically. The expression for the stress-induced diffusion coefficient developed by Nir {\&} Acrivos for sediment flow is used and the Richardson {\&} Zaki relationship is used to the calculate sediment settling velocity as a function of concentration. The turbulent dynamics of an initially stationary densely packed sand layer are examined and model results are compared with experimental data collected in two lab experiments. The model also does a reasonable job of predicting concentration profiles and suspension properties across the bottom boundary layer.   

Concentration distribution in gravity driven mixing of two fluids in a tilted tube

The concentration distribution in the mixing zone of interpenetrating light and heavy fluids in a tilted tube is studied by laser induced fluorescence as a function of the tilt angle $\theta$ from vertical. At low $\theta$, the flow is turbulent, resulting in efficient mixing across the tube. With increasing $\theta$, a concentration difference appears across the tube section due to the transverse component of gravity. At large $\theta$, this segregation is efficient enough for the concentration contrast at the fronts to become equal to the global density difference between the two original fluids. At still larger tilt angles, there is no mixing between fluids but a stable parallel counterflow controlled by viscous dissipation in the bulk of the fluids. In the two first regimes, the local concentration contrast $\delta \rho$ at the interpenetration fronts is shown to be directly related to the front velocity through $V_f \propto \delta \rho/\rho$. This confirms that these regimes correspond to a local balance between inertia and gravity at the front.   

Effect of inertia and gravity on the turbulence in a suspension

A theoretical model is presented for the effect of particle inertia and gravity on the turbulence in a homogeneous suspension. It is an extension of the one-fluid model developed by L'vov, Ooms and Pomyalov (2003), in which the effect of gravity was not considered. In the extended model the particles are assumed to settle in the fluid under the influence of gravity due to the fact, that their density is larger than the fluid density. The generation of turbulence by the settling particles is described, special attention being paid to the turbulence intensity and spectra. A comparison is made with DNS calculations and experimental data. Also a sensitivity study is carried out to investigate at which conditions the gravity effect becomes important. With the model it is possible to calculate the significance of the two-way coupling effect as function of the relevant dimensionless groups. Also an explanation in physical terms is given.   

Solidification and the Effects of Internal Heat Generation

Solutions using the integral method are presented for solid-liquid phase change in materials that generate internal heat. This problem is solved for cylindrical, spherical, plane wall and semi-infinite slab geometries. The analysis assumes a temperature profile in the solid phase and constant temperature boundary conditions on the exposed surfaces. We derive differential equations governing the solidification thickness for the geometries as functions of the Stefan number and the internal heat generation (IHG). For cylindrical, spherical, and plane wall geometries, the solidification layer obtains a steady-state value which is related to the inverse of the square root of the IHG. The solutions to the semi-infinite slab geometry problem show that when the surface is cooled to below the freezing point, a solidification layer forms along the edge and begins to grow until it reaches a maximum, then begins remelt. The problem has application to diverse fields such as nuclear energy, materials processing, geophysical fluids, and bioengineering.   

Numerical Simulations of Solidification in a Convecting Supercooled Melt

We present a 2-D phase-field model with convection induced by a flow field applied to freezing into a supercooled melt of pure substance, nickle. Four-fold anisotropy is introduced to the interfacial energy. Renormalization group theory is applied to the phase-field model with convection to produce an efficient computational procedure for treating multiscales in both time and space. Numerical procedures and details of numerical parameters employed are provided, and convergence of the numerical method is demonstrated by conducting grid-function convergence tests. Dendrite structures, temperature fields, pressure fields, streamlines and velocity vector fields are presented at several different times during the dendrite growth process. Comparisons of dendrites and temperature fields with and without convection indicate that the flow field has a significant effect on the growth rate of the dendrites; in particular, it inhibits growth. In addition, the flow field influences the dendritic structural morphologies and thickness of the interface. Moreover, the dendrites behave as a solid body in the flow leading to stagnation points and other interesting flow features.   

Simulations of densely-packed cloth motion in water

Fluid-structure simulations of densely-packed immersed fabric model the clothes washing process. We have modified the Immersed Boundary Method (Peskin 1977) to handle the known but complex geometry of the washing machine and agitator as well as the unknown cloth structure immersed in the fluid. Extending the technique to three-dimensions has required improved computational efficiency and causes geometric singularities when cloth that is not sufficiently extensible bends in two directions. We present some preliminary comparisons to primarily two-dimensional experiments in the dilute cloth limit. Computational difficulties caused by cloth permeability and bending stiffness will be discussed.   

Numerical method for interaction among fluid, multi-particle and complex structures

We propose a numerical method for dealing with interactions among fluid, multiple particles and complex structures. This method is based on the level set method, the CIP method and DEM. In the formulation, the structures are represented on a grid by using the level set method. The interactions of particles and structures are calculated by a method based on the discrete element method. The method can treat the interaction among fluid, multi-particle and complex structures robustly.