We demonstrate how to suspend various magnetic and non-magnetic particles in liquid metals and characterize their properties relevant to magnetohydrodynamics (MHD). The suspending method uses an acid as a flux to eliminate oxidation from both metal particles and liquid, which allows the particles to be wetted and suspend into the liquid if the particles have higher conductivity than the liquid. With this process we were able to suspend a wide range of particle materials and sizes from 40 nm to 500 µm, into three different liquid metal bases, and volume fractions φ up to the liquid-solid transition φc. By controlling the volume fraction of iron particles in liquid eGaIn, we increased the magnetic permeability by a factor of 5.0 and the electrical conductivity by 13% over that of the pure liquid metal, which gives these materials the potential to exhibit strong MHD effects on the laboratory scale that are usually only observable in the cores of planets and stars. By adding non-magnetic zinc particles, we increased the viscosity by a factor of 160 while keeping the magnetic and electrical properties nearly constant, which would allow independent control of MHD effects from turbulence. We show that the suspensions flow like Newtonian fluids up to the volume fraction of the liquid-solid transition φc.
We test the ability of a general low-dimensional model for turbulence to predict geometrydependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations, which are derived as a function of boundary geometry from the Navier-Stokes equations [1,2]. We test the model using Rayleigh-Bénard convection experiments in a cubic container. The model predicts a new mode in which the alignment of a convection roll switches between diagonals. We observe this mode with a measured switching rate within 30% of the prediction.Large-scale coherent flow structures in turbulencesuch as convection rolls in the atmosphere -are ubiquitous and can play a dominant role in heat and mass transport. A particular challenge is to predict dynamical states and their change with different boundary geometries, for example in the way that local weather patterns depend on the topography of the Earth's surface. However, the Navier-Stokes equations that describe flows are impractically difficult to solve for turbulent flows, so lowdimensional models are desired.It has long been recognized that the dynamical states of large-scale coherent structures are similar to those of low-dimensional dynamical systems models [3] and stochastic ordinary differential equations [4][5][6][7]. However, such models tend to be descriptive rather than predictive, as parameters are typically fit to observations, rather than derived [8]. In particular, dynamical systems models tend to fail at quantitative predictions of new dynamical states in regimes outside where they were parameterized. In this letter we demonstrate a proof-of-principle that a general low dimensional model can quantitatively predict the different dynamical states of large-scale coherent structures in different geometries.The model system is Rayleigh-Bénard convection, in which a fluid is heated from below and cooled from above to generate buoyancy-driven convection [9,10]. This system exhibits robust large-scale coherent structures that retain the same organized flow structure over long times. For example, in upright cylindrical containers of aspect ratio 1, a large-scale circulation (LSC) forms. This LSC consists of temperature and velocity fluctuations which, when coarse-grain averaged, collectively form a single convection roll in a vertical plane [11], as shown in Fig. 1a. Various dynamics of the LSC have been reported, including spontaneous meandering of the orientation θ 0 in a horizontal plane, and an advected oscillation which appears as a torsional or sloshing mode [12][13][14][15][16][17][18]. As an example of different dynamical states in different geometries, if instead the axis of the cylinder is aligned horizontally, θ 0 tends to align with the longest diagonals of the cell, and oscillates periodically between diagonals and around individual corners [19]. While there are several low-dimensional models for LSC dynamics [20][21][22][23], only one by Brown & Ahlers has made predictions dependent on container ge...
In order to study the turbulence structure behind a multiscale tree-like element in a boundary layer, detailed particle image velocimetry measurements are carried out in the near-wake of a fractal-like tree. The tree is a pre-fractal with five generations, each consisting of three branches and a scale-reduction factor of 1/2 between consecutive generations. Detailed mean velocity and turbulence stress profiles are documented, as well as their downstream development. Scatter plots of mean velocity gradient (transverse shear in the wake) and Reynolds shear stress exhibit a good linear relation at all locations in the flow. Therefore, in the transverse direction of the wake evolution, the data support the Boussinesq eddy-viscosity concept. The measured mixing length increases with streamwise distance, in agreement with classic wake expansion rates. Conversely, the measured eddy viscosity and mixing length in the transverse direction decrease with increasing elevation, which differs from the behaviours measured in the vertical direction in traditional boundary layers or in canopy flows studied before. In order to find an appropriate single length scale to describe the wake evolution behind a multiscale object, two models are proposed, based on the notion of superposition of scales. One approach is based on the radial spectrum of the object while the second is based on its length-scale distribution evaluated using fractal geometry tools. Both proposed models agree well with the measured mixing length. The results suggest that information about multiscale clustering of branches must be incorporated into models of the mixing length for flows through single or sparse canopies of multiscale trees.
Particle image velocimetry laboratory measurements are carried out to study mean flow distributions and turbulent statistics inside a canopy with complex geometry and multiple scales consisting of fractal, tree-like objects. Matching the optical refractive indices of the tree elements with those of the working fluid provides unobstructed optical paths for both illuminations and image acquisition. As a result, the flow fields between tree branches can be resolved in great detail, without optical interference. Statistical distributions of mean velocity, turbulence stresses, and components of dispersive fluxes are documented and discussed. The results show that the trees leave their signatures in the flow by imprinting wake structures with shapes similar to the trees. The velocities in both wake and non-wake regions significantly deviate from the spatially-averaged values. These local deviations result in strong dispersive fluxes, which are important to account for in canopy-flow modelling. In fact, we find that the streamwise normal dispersive flux inside the canopy has a larger magnitude (by up to four times) than the corresponding Reynolds normal stress. Turbulent transport in horizontal planes is studied in the framework of the eddy viscosity model. Scatter plots comparing the Reynolds shear stress and mean velocity gradient are indicative of a linear trend, from which one can calculate the eddy viscosity and mixing length. Similar to earlier results from the wake of a single tree, here we find that inside the canopy the mean mixing length decreases with increasing elevation. This trend cannot be scaled based on a single length scale, but can be described well by a model, which considers the coexistence of multi-scale branches. This agreement indicates that the multi-scale information and the clustering properties of the fractal objects should be taken into consideration in flows inside multi-scale canopies.
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