Session PK: Fluid-Driven Particle Flows

Effect of dynamic bed topography on turbulent flow structure in a gravel-bed river

A series of flume experiments were conducted at St. Anthony Falls Laboratory, University of Minnesota to study the effect of bedform dynamics on the flow over a gravel bed comprised of a wide distribution of grain sizes. Instantaneous high-frequency velocities were sampled using ADV at a frequency of 200 Hz, while the simultaneous bed elevations were sampled using SONAR transducers at a frequency of 0.1 Hz. Spectral analysis of the measured velocity fluctuations reveals the existence of two distinct power-law scaling regimes. At high frequencies, an inertial subrange of turbulence with Kolmogorov scaling is observed. At low frequencies, another scaling regime with spectral slope of about -1.1 is found. This range is the signature of the evolving multi-scale bed topography on the near-bed velocity fluctuations. The two scaling ranges are separated by a spectral gap, i.e., a range of intermediate scales with no energy contribution. The high-frequency limit of the spectral gap corresponds to the integral scale of turbulence. The low-frequency end of the gap corresponds to the scale of the smallest bedforms identified by the velocity sensor, which depends on the position of the sensor. Comparison with spectral densities of bed elevations also shows that relatively low-resolution velocity measurements collected near the channel bed can be used to estimate the travel time of the largest bedforms.   

The effects of woody debris on streambed morphology: flume experiments on the spatial patterns of fluid flow and sediment transport around woody debris

The interaction of woody debris, fluid flow and sediment transport in rivers creates local streambed morphology, such as large pools that are important fish habitat and sediment deposits that bury and stabilize wood. We present the results of 300 experimental runs characterizing the fluid flow field around individual stationary model wood on an immobile bed. Fluid flow patterns on the bottom boundary layer, where bedload sediment transport occurs, were visualized using solid dye crystals. We find that: 1) the presence of roots leads to greater areas of predicted sediment scour and deposition; 2) the amount of predicted sediment scour and deposition are exponentially related to the root cross-sectional area, oriented orthogonal to flow; 3) as root porosity decreases the amount of predicted sediment scour and deposition decrease and the predicted sediment deposit moves away from the roots. Ongoing sediment transport experiments, building on the fluid flow experiments, are investigating the volumes and spatial patterns of sediment scour and deposition around woody debris.   

Nonlinear convection in a mushy layer: Chimney spacing and optimal brine fluxes

The rapid solidification of any binary alloy leads to the formation of a chemically reactive porous medium, or mushy layer, comprised of a dendritic solid phase threaded by a concentrated fluid. An important geophysical example is sea ice, where solid ice crystals are separated by dense salty brine, the buoyancy-driven drainage of which has important implications for the ocean thermohaline circulation, and the long time bulk mechanical and electromagnetic properties of the sea ice matrix itself. It is known that convection and local dissolution lead to flow focusing in drainage channels devoid of solid, or chimneys. The spacing of chimneys and resulting brine fluxes evolve over time. We consider nonlinear convection within a mushy layer, applying a numerical model of directional solidification to investigate the spacing mechanism for fully developed chimneys. The resulting dynamics yields insight into the evolution of solute fluxes from growing mushy layers.   

Direct Numerical Simulation of Turbulent Flow over Sandy Rippled Beds

The presence of ripples on the seafloor affects the turbulent dynamics of bottom boundary layer (BBL) flow. The difference in the roughness length scales of a planar and rippled sand bed produces quantifiable differences in the turbulent BBL. A complete understanding of the effect of suspended sediment concentration on turbulence modulation is currently unknown. We use mixture theory to implement a three-dimensional BBL model that simulates the coupled interaction between the fluid and sediment. The mixture theory approach treats the fluid-sediment mixture as a single continuum with effective properties that parametrize the fluid-sediment and sediment-sediment interactions. We compare two-dimensional and three-dimensional simulations with existing laboratory measurements of fluid velocity and sediment concentration over rippled sand beds. We find that the vortex dynamics over sand ripples are highly three-dimensional. Two-dimensional flow simulations are inadequate for the numerical modeling of turbulent flow over sand ripples. We also find that suspended sediment concentration influences the production of turbulence; therefore, accurate simulation of turbulent flow over sandy beds must include an adequate description of fluid-sediment interactions.   

Experimental Studies on the Saltating Sand Particle Transport and Wind-Sand Interaction

Saltation is the major transport mode of wind-blown sand particles, accounting for about 75{\%} of total sand transport through saltation, suspension and surface creep. The complex interactions among the saltating sand particles, the particles on the surface and the turbulent flow have not been fully understood owing to lack of experimental data. Various state-of-the-art flow measurement techniques were applied to comprehensively examine three different types of natural sand in a simulated atmospheric boundary layer. Firstly, digital high-speed photography was used to capture images of the saltating sand particles at 2000 frames per second, which resolved the particle motion adjacent to the sand bed surface. Secondly, instantaneous velocities of the saltating sand particles were extracted from the high-speed particle images using the particle tracking velocimetry (PTV). The particle resultant velocity, concentration and the stream-wise mass flux were evaluated as a function of height. Finally, the velocity fields of wind and wind-blown sand particles were simultaneously measured by using the PTV and the particle imaging velocimetry (PIV), respectively. This experimental study shed new lights on the complicated saltation motion, and will be helpful in enhancing formulation of theoretical models and development of effective control measures of wind erosion.   

Blowing in the wind: aeolian dunes in modulated gravity

Barchan dunes can be found in the desert under steady wind conditions. They translate in the direction of the wind while their shape remains unchanged. These remarkable natural patterns are the result of the interaction between sand and wind where the wind deposits the sand in heaps, which, in turn, change the properties of the turbulent wind. These crescent-shaped dunes have a minimal length in the order of ten meters, which renders laboratory experiments almost impossible. Their length scale is set by the details of the sand-wind interaction. In nature, smaller dunes do not evolve into the typical barchan shape. Our experimental approach produces dramatically scaled down dunes. The idea is to modulate gravity by vertical oscillation of the sand bed. Our tiny dunes travel in the turbulent boundary layer of an open windtunnel. Particle image velocimetry on their surface reveals the flux of creeping sand, while measurement of sand grains flying through the air using a high speed camera quantifies the key mechanism that moves sand by wind: saltation. We will contrast our findings with several theories that predict the shape of dunes on earth and other planets of our solar system.   

Theoretical and Experimental Investigation of Lunar and Martian Regolith Simulant Dynamic Response to Rocket Plume Impingement

An investigation of rocket plume impingement on the regolith of the Moon and Mars is being conducted both theoretically and experimentally. Experimental results (1)and data from the Apollo landings inspired a theoretical model at ORBITEC : the ABL (Ablating Boundary Layer) model that assumes that regolith erosion and entrainment occurs in the thin boundary layer. The resulting crater streamlines itself with curve formed by extremization of the Lagrangian : L = (Z')$^{2}$+ Z$^{2}$ where Z(r) and Z(r)' are a depth variable and its radial derivative respectively. The actual depth profile z (r) in this model is derived from the formula z=Log ( 1+ Z/Z$_{o})$ where Z$_{o}$ is a constant. For light soils the model reduces to z$\sim $ Z/Z$_{o}$ and cantenary profiles result, exponential density profiles (2) give conoidal craters. (1) Experimental tests of the ABL model performed at Duke have shown good agreement. Further theoretical modeling and experimental data will be presented. (1) Metzger P., Lane, J., Immer C. and Clements, S. '6$^{th}$ International Conference on Case Histories in Geotechnicla Engineeering , Arlinton VA August 11-16, 2008. (2) Bresson~L. M., Moran~C. J., and Assoline,~S. Soil Sci. Soc. of Am. Jou, 2004,~vol.~68,~4,~pp.~1169-1176.   

Granular Crater Formation

This project characterizes crater formation in a granular material by a jet of gas impinging on a granular material, such as a retro-rocket landing on the moon. We have constructed a 2D model of a planetary surface, which consists of a thin, clear box partially filled with granular materials (sand, lunar and Mars simulants...). A metal pipe connected to a tank of nitrogen gas via a solenoid valve is inserted into the top of the box to model the rocket. The results are recorded using high-speed video. We process these images and videos in order to test existing models and develop new ones for describing crater formation. A similar set-up has been used by Metzger et al.\footnote{P. T. Metzger et al. Journal of Aerospace Engineering (2009)} We find that the long-time shape of the crater is consistent with a predicted catenary shape (Brandenburg). The depth and width of the crater both evolve logarithmically in time, suggesting an analogy to a description in terms of an activated process: $dD/dt = A \exp(-aD)$ ($D$ is the crater depth, $a$ and $A$ constants). This model provides a useful context to understand the role of the jet speed, as characterized by the pressure used to drive the flow. The box width also plays an important role in setting the width of the crater.   

Euler-Lagrange Simulations of Particle Interactions with Coherent Vortices in Turbulent Boundary Layers

The overarching interest of the current investigations is numerical modeling of particle entrainment and deposition near sandy beds as relevant to the problem of rotorcraft brownout. Numerical simulations are being performed using an Euler-Lagrange method. Solution of the incompressible gas-phase flow field is accomplished using a fractional-step numerical method; the particulate phase is advanced using Discrete Particle Simulation. The particular flow field of interest models a rotor wake and is comprised of coherent vortices embedded in a turbulent boundary layer. The particles, once suspended, interact with the coherent wake vortices characterizing the rotor flow, and with the finer scale turbulence generated near the ground. The primary objectives are two-flow. First, to gain insight into the particle-vortex dynamics that influence transport near the bed and, second, to advance understanding of the mesoscopic particle velocity field. The latter objective requires very large particle ensembles in order to recover an Eulerian description of the particle field, important to advancing other simulation strategies for two-phase flows. Predictions of the flows for a range of particle and flow parameters will be presented.