Simultaneous PIV and LIF measurements in stratified flows using pulsed lasers

We examine the problem of performing simultaneous and coplanar Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF) measurements in a stratified fluid initially at rest. Our focus is on enabling detailed velocity and density measurements in long internal waves and gravity currents, through relatively small modifications of typical existing PIV systems comprising pulsed lasers, using dye concentration as a proxy for fluid density. Several issues have limited such measurements. These include: (1) variations in the laser intensity and beam structure between laser pulses; (2) PIV particles concentrating preferentially at their neutral buoyancy depth, thereby yielding nonuniform dye illumination; and (3) the need to maintain a constant index of refraction across large stratified fluid volumes. Here we focus on an experimental setup comprising a stratified layer overlaying a deep homogeneous region. We produce long internal waves using a lock-release setup, in order to investigate the structure of waves comprising recirculating fluid regions (known as ``trapped cores''), which are of current interest in oceanographic applications. We maintain a short optical path and use velocity information from PIV data to minimize index-of-refraction issues. We exploit the fact that the system is initially at rest to devise a mapping that links apparent and actual dye concentration, thus sidestepping nonuniform illumination issues due to particle clustering. Finally, we devise a procedure to correct for laser power variations along each ray in the sheet

Laboratory experiments and simulations for solitary internal waves with trapped cores

Author Posting. © The Author(s), 2014. This is the author's version of the work. It is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 757 (2014): 354-380, doi:10.1017/jfm.2014.501.We perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15 % of the overall fluid depth) overlaying a deep homogeneous layer. We consider waves propagating near a free surface, as well as near a rigid no-slip lid. In the free-surface case, all trapped-core waves exhibit a strong shear instability. We propose that Marangoni effects are responsible for this instability, and use our velocity measurements to perform quantitative calculations supporting this hypothesis. These surface-tension effects appear to be difficult to avoid at the experimental scale. By contrast, our experiments with a no-slip lid yield robust waves with large cores. In order to consider larger-amplitude waves, we complement our experiments with viscous numerical simulations, employing a longer virtual tank. Where overlap exists, our experiments and simulations are in good agreement. In order to provide a robust definition of the trapped core, we propose bounding it as a Lagrangian coherent structure (instead of using a closed streamline, as has been done traditionally). This construction is less sensitive to small errors in the velocity field, and to small three-dimensional effects. In order to retain only flows near equilibrium, we introduce a steadiness criterion, based on the rate of change of the density in the core. We use this criterion to successfully select within our experiments and simulations a family of quasi-steady robust flows that exhibit good collapse in their properties. The core circulation is small (at most, around 10 % of the baroclinic wave circulation). The core density is essentially uniform; the standard deviation of the density, in the core region, is less than 4 % of the full density range. We also calculate the circulation, kinetic energy and available potential energy of these waves. We find that these results are consistent with predictions from Dubreil-Jacotin–Long theory for waves with a uniform-density irrotational core, except for an offset, which we suggest is associated with viscous effects. Finally, by computing Richardson-number fields, and performing a temporal stability analysis based on the Taylor–Goldstein equation, we show that our results are consistent with empirical stability criteria in the literature.Funding from NSF grant OCE-1029672 is gratefully acknowledged. P.L.F. is thankful for support from the Postdoctoral Scholar program at the Woods Hole Oceanographic Institution, and for funding from the Devonshire Foundation

An affordable, open-source, microscale conductivity and temperature probe for density measurements in stratified flows

In stratified flows, conductivity (combined with temperature) is often used to measure density. The conductivity probes typically used can resolve very fine spatial scales, but can be fragile, expensive to replace, and sensitive to environmental noise. A complementary instrument, comprising a low-cost and robust probe, would prove valuable in a wide range of applications where resolving extremely small spatial scales is not needed. We propose using micro-USB connectors as the actual conductivity sensors; these have five gold-plated microelectrodes that can be readily exposed for two-wire or four-wire measurements. To take advantage of our choice of sensor, we design a custom electronic board for simultaneous acquisition from four sensors, with conductivity resolution of 0.1%, comparable to typical existing probes. We demonstrate our system through stratified flow experiments. The multi-channel capability can be used to approximately reconstruct density fields, whereas the customizable design enables measuring density near complex boundaries

Micro-USB Connector Pins as Low-Cost, Robust Electrodes for Microscale Water Conductivity Sensing in Oceanographic Research

Motivated by the widespread need to sense water conductivity in oceanography, as well as in other applications in fluid dynamics and environmental monitoring, we propose using the exposed gold-plated pins of readily available micro-USB connectors as miniaturized, parallel finger electrodes. Since the electrodes are 600 μm apart, they grant sub-mm spatial resolution, suitable for most applications. Standard micro-USB cables are an ideal, ready-to-use solution, since they are shielded, are preassembled in different lengths, and enable 2 and 4-wire measurements. In order to take full advantage of these USB probes, we have designed a custom, open-source 4-channel measuring circuit, named "Conduino", consisting of a low-noise (SNR = 60 dB) shield board coupled to an Arduino microcontroller. Experimental results demonstrate sensing performances comparable with state-of-the-art reference instrumentation (0.1% resolution in the 0.1-15 S/m range), with significantly lower cost and increased versatility and reliability

Design and testing of an affordable desktop wind tunnel

Wind tunnels are a key source of data collection, but their cost and size can be a significant obstacle to their acquisition and usage, especially for applications such as instrument calibration, instruction, or in-class demonstrations. Here we propose a design for a cost-effective, desktop wind tunnel. This design takes advantage of readily available, inexpensive materials. Special consideration was taken to allow the wind tunnel to be serviceable, as well as giving the operator the ability to change key features without a complete redesign. There are three main sections, the first being a fan enclosure, which holds seven ducted fans in a hexagonal array. The second section holds honeycomb flow straighteners, and provides an enclosed volume suitable for larger, lower-speed experiments. The third section is a contraction, terminating in a 2in x 2in, higher-speed square section. The wind tunnel has a footprint of approximately 13.5in x 5.5in, making it small enough to be portable and to fit on a desk. An off-the-shelf masked stereolithography apparatus (MSLA) 3D printer was used to prepare the parts. This allows the wind tunnel to be built for under \$500; even including the cost of a 3D printer, the overall cost remains under \$1,000. This design is able to produce flow at up to 44.1 m/s, enabling a variety of aerodynamic demonstrations

An entrainment model for fully-developed wind farms: effects of atmospheric stability and an ideal limit for wind farm performance

While a theoretical limit has long been established for the performance of a single turbine, no corresponding upper bound exists for the power output from a large wind farm, making it difficult to evaluate the available potential for further performance gains. Recent work involving vertical-axis turbines has achieved large increases in power density relative to traditional wind farms (Dabiri, J.O., J. Renew. Sust. Energy 3, 043104 (2011)), thereby adding motivation to the search for an upper bound. Here we build a model describing the essential features of a large array of turbines with arbitrary design and layout, by considering a fully-developed wind farm whose upper edge is bounded by a self-similar boundary layer. The exchanges between the wind farm, the overlaying boundary layer, and the outer flow are parameterized by means of the classical entrainment hypothesis. We obtain a concise expression for the wind farm’s power density (corresponding to power output per unit planform area), as a function of three coefficients, which represent the array thrust and the turbulent exchanges at each of the two interfaces. Before seeking an upper bound on farm performance, we assess the performance of our simple model by comparing the predicted power density to field data, laboratory measurements and large-eddy simulations for the fully-developed regions of wind farms, finding good agreement. Furthermore, we extend our model to include the effect of atmospheric stability on power output, by using a parameterization (which had been previously developed in the context of geophysical fluid dynamics) relating entrainment coefficients to local Froude numbers. Our predictions for power variation with atmospheric stability are in agreement with field measurements and large-eddy simulations. To the best of our knowledge, this constitutes the first quantitative comparison between an atmospheric-stability-dependent theory and field data. Finally, we consider an ideal limit for array operation, whereby turbines are designed to maximize momentum exchange with the overlying boundary layer. This enables us to obtain an upper bound for the performance of large wind farms, which we determine to be an order of magnitude larger than the output of contemporary turbine arrays.Churchill Colleg

Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces

Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible, by creating adverse Marangoni stresses. Yet, testing this hypothesis is challenging. Careful experiments with purified water show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. This suggests that other physical processes, such as thermal Marangoni stresses or interface deflection, could explain the lower performance. To test the surfactant hypothesis, we perform the first numerical simulations of flows over a SHS inclusive of surfactant kinetics. These simulations reveal that surfactant-induced stresses are significant at extremely low concentrations, potentially yielding a no-slip boundary condition on the air--water interface (the "plastron") for surfactant amounts below typical environmental values. These stresses decrease as the streamwise distance between plastron stagnation points increases. We perform microchannel experiments with thermally-controlled SHSs consisting of streamwise parallel gratings, which confirm this numerical prediction. We introduce a new, unsteady test of surfactant effects. When we rapidly remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients formed in the loading phase. This demonstrates the significance of surfactants in deteriorating drag reduction, and thus the importance of including surfactant stresses in SHS models. Our time-dependent protocol can assess the impact of surfactants in SHS testing and guide future mitigating designs.Comment: 25 pages including supplemental information, 7 figures; videos available on reques

Consolidation of freshly deposited cohesive and non-cohesive sediment: particle-resolved simulations

We analyze the consolidation of freshly deposited cohesive and non-cohesive sediment by means of particle-resolved direct Navier-Stokes simulations based on the Immersed Boundary Method. The computational model is parameterized by material properties and does not involve any arbitrary calibrations. We obtain the stress balance of the fluid-particle mixture from first principles and link it to the classical effective stress concept. The detailed datasets obtained from our simulations allow us to evaluate all terms of the derived stress balance. We compare the settling of cohesive sediment to its non-cohesive counterpart, which corresponds to the settling of the individual primary particles. The simulation results yield a complete parameterization of the Gibson equation, which has been the method of choice to analyze self-weight consolidation.Comment: 16 pages, 9 figures, accepted for Physical Review Fluid

Pairwise interaction of spherical particles aligned in oscillatory flow

We present a systematic simulation campaign to investigate the pairwise interaction of two mobile, monodisperse particles submerged in a viscous fluid and subjected to monochromatic oscillating flows. To this end, we employ the immersed boundary method to geometrically resolve the flow around the two particles in a non-inertial reference frame. We neglect gravity to focus on fluid-particle interactions associated with particle inertia and consider particles of three different density ratios aligned along the axis of oscillation. We systematically vary the initial particle distance and the frequency based on which the particles show either attractive or repulsive behavior by approaching or moving away from each other, respectively. This behavior is consistently confirmed for the three density ratios investigated, although particle inertia dictates the overall magnitude of the particle dynamics. Based on this, threshold conditions for the transition from attraction to repulsion are introduced that obey the same power law for all density ratios investigated. We furthermore analyze the flow patterns by suitable averaging and decomposition of the flow fields and find competing effects of the vorticity induced by the fluid-particle interactions. Based on these flow patterns, we derive a circulation-based criterion that provides a quantitative measure to categorize the different cases. It is shown that such a criterion provides a consistent measure to distinguish the attractive and repulsive arrangements.Comment: 37 pages, 19 figure