Kunlun Bai

Near-Wake Turbulent Flow Structure and Mixing Length Downstream of a Fractal Tree

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.

Turbulent Flow Structure Inside a Canopy with Complex Multi-Scale Elements

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.

Development of magnetic liquid metal suspensions for magnetohydrodynamics

A new class of materials is developed that is a liquid with both high conductivity and magnetic susceptibility for magnetohydrodynamic (MHD) applications. We develop a general method for making such suspensions and demonstrate that various magnetic and non-magnetic metal particles, from 40 nm - 500 microns in diameter, can be suspended in liquid gallium and its alloys. The method uses an acid solution to prevent oxidation of the liquid metal and metallic particles, which allows wetting and thus suspending. We can increase the magnetic permeability by a factor of 5.0 by controlling the packing fraction of magnetic particles, 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. We can independently tune the viscosity by a factor of 230 by adding non-magnetic particles, which would allow independent control of MHD effects from turbulence.

Experimental study of spectral energy fluxes in turbulence generated by a fractal, tree-like object

We report on an experimental study of the kinetic energy fluxes between scales in the turbulent near-wake flow downstream of a fractal, tree-like object. Experiments are performed in a liquid channel and data are acquired using planar Particle Image Velocimetry (PIV). The data are analyzed based on the filtering framework of relevance to Large Eddy Simulations. The flow and energy fluxes differ from the case of a canonical flow such as the cylinder wake, where typically kinetic energy is injected into turbulence by an object characterized by a single, well-defined, length-scale. For a fractal tree-like object, we find that the measured energy flux is strongly dependent on scale. In the present flow, scale-dependent injection of kinetic energy into the cascade arises from production as well as spatial transport terms. The injection rate spectrum is evaluated directly from the data by quantifying the rate of change of spectral energy flux as a function of wavenumber. The net injection rate spectrum is obser...

Ability of a low-dimensional model to predict geometry-dependent dynamics of large-scale coherent structures in turbulence.

We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent 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 [Brown and Ahlers, Phys. Fluids 20, 075101 (2008); Phys. Fluids 20, 105105 (2008)]. We test the model using Rayleigh-Bénard convection experiments in a cubic container. The model predicts a mode in which the alignment of a convection roll stochastically crosses a potential barrier to switch between diagonals. We observe this mode with a measured switching rate within 30% of the prediction.

LES modeling and experimental measurement of boundary layer flow over multi-scale, fractal canopies

In many regions the atmospheric surface layer is affected substantially by vegetation canopies. Most previous work has focused on effects of vegetated terrain characterized by a single length scale, e.g. a single obstruction of a particular size, or canopies consisting of plants, often modeled using a prescribed leaf-area density distribution with a characteristic dominant scale. It is well known, however, that typical flow obstructions such as canopies are characterized by a wide range of length scales, branches, sub-branches, etc. Yet, it is not known how to parameterize the effects of such multi-scale objects on the lower atmospheric dynamics. This work aims to study boundary layer flow over fractal, tree-like shapes. Fractals provide convenient idealizations of the inherently multi-scale character of vegetation geometries, within certain ranges of scales. Preliminary results from a large-eddy simulation (LES) and experimental study of a fractal tree canopy in a turbulent boundary layer are reported. The LES use Renormalized Numerical Simulation (Chester et al., 2007, J. Comp. Phys.) to provide subgrid parameterizations of drag forces from unresolved small-scale branches. Experiments aiming at understanding drag forces acting on fractal trees are performed in a water tunnel facility. Drag force measurements are obtained on a set of “pre-fractal” trees containing 1-5 branch generations.

Effective magnetic susceptibility of suspensions of ferromagnetic particles

The effective susceptibility χeff of suspensions of ferromagnetic particles in a liquid was measured using inductance measurements. These measurements were used to test a model that predicts how χeff varies due to demagnetization, as a function of sample aspect ratio, particle packing fraction, and particle aspect ratio [R. Skomski, G. C. Hadjipanayis, and D. J. Sellmyer, IEEE Trans. Magn. 43, 2956–2958 (2007)]. For spherical particles or cylindrical particles forcibly aligned with an external magnetic field, the model can be fitted to the measured data with agreement within 13%. This model predicts suspensions of aligned, large-aspect-ratio particles should have the largest χeff, approaching the particle material susceptibility in the limit of large particle aspect ratio. However, χeff was found to be no larger than about 4 for cylindrical iron particles of various aspect ratios, close to the value obtained for spheres. This results from the random alignment of non-spherical particles relative to the magnetic field naturally found in suspensions, which increases the demagnetization effect and limits χeff. The contribution of random particle alignments to the demagnetization effect and χeff remains to be accounted for in models.