Session H1: General Fluid Dynamics II

Crown sealing and buckling instability during sphere impact

We present results from an experimental investigation of the classical crown splash and sealing phenomena observed during the impact of spheres onto quiescent liquid pools for a range of ambient pressures. A 6-metre tall vacuum chamber was used to provide the required ambient conditions from atmospheric conditions down to 1/16th of an atmosphere. We pay particular attention to the above-surface crown formation and ensuing dynamics, including the buckling instability of the crown just before seal. In addition, we have observed the very rapid motions of the ejecta formed immediately after impact, using ultra-high-speed imaging at frame rates over 400,000 fps, which reveals qualitative differences at reduced pressures.   

Dripping like Pollock

In this investigation we have reproduced, in a controlled manner, the dripping technique used by Jackson Pollock to creat abstract paintings.We drip a fluid jet on top of a horizontal surface, varying the height from the substrate, the liquid flow rate and the displacement speed of the nozzle. We are able to reproduce the coiling and dripping instabilities which characterize the characteristic patterns of Pollock's paintings. We also found that the non Newtonian properties of the paints are of great importance to create these patterns. Since the fluid jets are rapidly stretched, the sudden increase of extensional viscosity plays an important role to produce the characteristic Pollock patterns. Some preliminary results will be shown and discussed.   

Entropic Lattice Boltzmann Methods for Fluid Mechanics: Thermal, Multi-phase and Turbulence

With its roots in statistical mechanics and kinetic theory, the lattice Boltzmann method (LBM) is a paradigm-changing innovation, offering for the first time an intrinsically parallel CFD algorithm. Over the past two decades, LBM has achieved numerous results in the field of CFD and is now in a position to challenge state-of-the art CFD techniques [1]. Major restyling of LBM resulted in an unconditionally stable entropic LBM which restored Second Law (Boltzmann H theorem) in the LBM kinetics and thus enabled affordable direct simulations of fluid turbulence [2, 3]. In this talk, we shall review recent advances in ELBM as a practical, modeling-free tool for simulation of complex flow phenomenon. We shall present recent simulations of fluid turbulence including turbulent channel flow, flow past a circular cylinder, creation and dynamics of vortex tubes, and flow past a surface mounted cube. Apart from its achievements in turbulent flow simulations, ELBM has also presented us the opportunity to extend lattice Boltzmann method to higher order lattices which shall be employed for turbulent, multi-phase and thermal flow simulations. A new class of entropy functions are proposed to handle non-ideal equation of state and surface tension terms in multi-phase flows. It is shown the entropy principle brings unconditional stability and thermodynamic consistency to all the three flow regimes considered here. Acknowledgements: ERC Advanced Grant ``ELBM'' and CSCS grant s437 are deeply acknowledged. References: [1] Chikatamarla et al, J.Fluid.Mech, 656 (2010); Physica.A,392(2013) [2] Chikatamarla and Karlin, Phys.Rev.Lett., 010201 (2006); Phys.Rev.Lett, 190601 (2006). [3] Karlin et al, Europhys. Letters, 47, no. 2, p. 182, 1999.   

Validation of X-Ray CT-measured Liquid Concentration against LIF

Dense spray near the nozzle exit requires more research. X-Ray Computed Tomography (CT) technique has shown that it could capture spray patterns similar to that of a conventional Shadowgraphy; however, liquid density measured with the X-Ray CT technique lacks validation. Thus, the objective of the current study is to validate liquid density measured with the X-Ray CT technique against that of the conventional Laser-Induced Fluorescence (LIF) method. Water solution with 150 parts per billion (ppb) of Rhodamine WT dye is sprayed into a cold spray chamber by using a pressure swirl atomizer. An Nd:YAG laser with a light-sheet optics is used to fluoresce Rhodamine WT dye in water spray and a high-speed CMOS camera with a filter is employed to measure quantitative liquid concentrations approximately thirty (30) nozzle diameters downstream. The intensity of fluorescence correlates linearly with the amount of Rhodamine WT dye in the water, enabling mass distribution measurement of the liquid spray. As the X-Ray CT technique measures liquid mass distribution, the X-Ray CT measured spray density can be validated by the proven conventional LIF method.   

Steady and Unsteady Size-Dependent Couple Stress Creeping Flow

As an inevitable consequence of non-central forces acting at the atomic level, couple-stresses appear within the framework of continuum mechanics, and force-stress must be considered as a general non-symmetric tensor. Based upon recent theoretical work, the couple-stress tensor is shown to be skew-symmetric, as is its energy conjugate mean curvature rate tensor. Within this fully consistent couple stress continuum theory applied to fluid flow, there appears a material length scale $l$ that becomes increasingly important as the characteristic geometric dimension of the problem reduces. In the present work, we study the effects of this theory for creeping incompressible flows by developing fundamental point force and point couple solutions, along with boundary integral representations for both the steady and unsteady cases. In addition, we develop the corresponding boundary element methods and solve several problems that highlight the size-dependent nature of these flows, which may be most relevant to a range of micro- and nano-scale technologies.   

Numerical simulation of the induced magnetic field within a rotating concentric annulus with self gravity

In order to study the GEODYNAMO is necessary to know the behavior of the natural convection of the electrical conducting fluid confined in a rotating spherical shell. In this work, the convective patterns within this geometry are presented. Natural convection is induced by a temperature difference between the inner sphere and outer sphere and a gravitational field which varies like $ 1/r^3 $. The patterns presented are known as Busse cells and are moving around the rotational axis. The magnetic fields induced by previously mentioned convective patterns are presented. These magnetic fields are obtained by solving the equations of MHD. The free-divergence magnetic field is obtained by using a Lagrange multiplier scheme. All the equations are solved based on a spectral element method (SEM). To avoid the singularity at the poles, the cubed-sphere algorithm is used to generate the mesh. The obtained magnetic fields are similar to the results reported by other research groups.   

Turbulent flows interacting with groups of obstacles

The interaction between a turbulent incoming flow and patches of obstacles (with circular cross section in plan view with diameter $D$) that contain a number of individual cylinders ($N_c$ is the number of cylinders and $d$ is their diameter) with different void-fractions ($\phi$ = $N_cd^2/D^2$) are studied. Streamwise-spanwise plane PIV measurements, at the mid-height of the patches, of the wakes generated by the different void-fractions show that the three-dimensionality of the patches and the incoming turbulence lead to different results compared to the laminar 2D cases available in literature. In particular, for void-fraction $\phi>0.1$, no steady recirculation region is detected behind the obstacles, and even for lower $\phi$, its streamwise length is drastically reduced. Furthermore, for higher $\phi$ ($> 0.15$), the wakes are not comparable with the one of a solid cylinder with the same height and diameter, as it happens for the laminar 2D cases. Results from vertical PIV measurements along the symmetry plane of the patches will also be discussed.   

Transitioning from a single-phase fluid to a porous medium: a boundary layer approach

Pressure-driven laminar channel flow is a classic problem in fluid mechanics, and the resultant Poiseuille flow is one of the few exact solutions to the Navier-Stokes equations. If the channel interior is a porous medium (governed by Darcy's law) rather than a single-phase fluid, the resultant behaviour is plug flow. But what happens when these two flow regions are coupled, as is the case for industrial membrane filtration systems or biological tissue engineering problems? How does one flow transition to the other? We use asymptotic methods to investigate pressure-driven flow through a long channel completely blocked by a finite-length porous obstacle. We analytically solve for the flow at both small and large Reynolds number (whilst remaining within the laminar regime). The boundary layer structure is surprisingly intricate for large Reynolds number. In that limit, the structure is markedly different depending on whether there is inflow or outflow through the porous medium, there being six asymptotic regions for inflow and three for outflow. We have extended this result to a wide class of 3D porous obstacles within a Hele-Shaw cell. We obtain general boundary conditions to couple the outer flows, and find that these conditions are far from obvious at higher order.   

Swirling flows with imposed radial flow - a model for a cold accretion disk?

There is a lot of current interest in exploring whether Keplerian-type flows ($dI/dr > 0$ but $d\Omega/dr < 0$ where $I$ is the angular momentum and $\Omega$ the angular velocity) can harbour nontrivial hydrodynamic flows in order to explain the inferred presence of turbulence in cold accretion disks (e.g. Balbus, Nature 2011). Invariably, the very small (accreting) inflow is neglected in accretion disk models. I will discuss how this could be a dangerous omission by building upon recent work (Gallet et al. 2010, Ilin \& Morgulis 2013) which shows linear instability of otherwise-stable Taylor-Couette flows when radial flow is imposed.