Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session H32: Particle-Laden Flows: Non-Spherical Particles |
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Chair: Alfredo Soldati, Universita Degli Studi di Udine Room: 2020 |
Monday, November 24, 2014 10:30AM - 10:43AM |
H32.00001: Consequences of a double zero eigenvalue for the rotational motion of a prolate spheroid in shear flow Tomas Rosen, Arne Nordmark, Cyrus K. Aidun, Fredrik Lundell The rotational motion of a single prolate spheroidal particle in a linear shear flow provides fundamental knowledge necessary to understand both rheology and orientation distributions of suspensions including elongated particles. In this work, we present results from both direct numerical simulations using the lattice Boltzmann method and stability analysis using Comsol Multiphysics. It has been found that particle and fluid inertia cause different stable rotational states.\footnote{Ros\'{e}n \textit{et al.}, J. Fluid Mech. \textbf{738}, 563 (2013).}$^,$\footnote{Ros\'{e}n \textit{et al.}, J. Fluid Mech., submitted (2014).} The transitions between these originate from the fact that the Log-rolling particle (particle aligned with vorticity) has a double zero eigenvalue for a certain choice of particle Reynolds number $Re_p=Re_{PF}$ and solid-to-fluid density ratio $\alpha=\alpha_{DZ}$. The consequence is that particles with $\alpha>\alpha_{DZ}$, will always go to a planar rotation (symmetry axis perpendicular to vorticity), while lighter particles can assume a stable periodic or chaotic state which is non-planar. Since $\alpha_{DZ}$ is decreasing with aspect ratio, we find further that only planar states exist for particles of low aspect ratio (length/width). [Preview Abstract] |
Monday, November 24, 2014 10:43AM - 10:56AM |
H32.00002: Chaotic orbits tracked by a 3D asymmetric immersed solid at high Reynolds numbers using a novel Gerris-Immersed Solid (DNS) Solver Pei Shui, St\'{e}phane Popinet, Prashant Valluri, Rama Govindarajan The motion of a neutrally buoyant ellipsoidal solid with an initial momentum has been theoretically predicted to be chaotic in inviscid flow by Aref (1993). On the other hand, the particle could stop moving when the damping viscous force is strong enough. This work provides numerical evidence for 3D chaotic motion of a neutrally buoyant general ellipsoidal solid and suggests criteria for triggering this motion. The study also shows that the translational/rotational energy ratio plays the key role on the motion pattern, while the particle geometry and density aspect ratios also have some influence on the chaotic behaviour. We have developed a novel variant of the immersed solid solver under the framework of the Gerris flow package of Popinet et al. (2003). Our solid solver, the Gerris Immersed Solid Solver (GISS), is capable of handling 6 degree-of-freedom motion of particles with arbitrary geometry and number in three-dimensions and can precisely predict the hydrodynamic interactions and their effects on particle trajectories. The reliability and accuracy have been checked by a series of classical studies, testing both translational and rotational motions with a vast range of flow properties. [Preview Abstract] |
Monday, November 24, 2014 10:56AM - 11:09AM |
H32.00003: Rotational motion of elongated particles in isotropic turbulent flow: statistical perspective Lihao Zhao, Helge Andersson, Evan Variano We consider the rotational motion of non-spherical particles in turbulent flow, comparing the statistics of particles' angular velocity to the corresponding quantities computed in the fluid phase. We use numerical (DNS) and laboratory measurements for particles that are both larger and smaller than the Kolmogorov lengthscale. The particles are spheroids or rods, with aspect ratios between 1 and 10. We will discuss the subtleties of defining a meaningful Stokes number for these particles, focusing on the effect of asphericity and the fact that our interest is in rotation and not translation. Comparing the probability density function of angular velocity between fluid and particle phase indicates that the angular velocity of particles has a narrower distribution than that of the fluid phase, and that. particles do respond to extreme events in the fluid phase. The first four moments of the PDFs are analyzed, and these show that the ``filtering'' effect is very similar between DNS and lab experiments, despite differences in particle sizes and mass. We propose a nondimensional curve for predicting the magnitude of the filtering effect, and discuss the implications of this curve for the definition of Stokes number, as discussed earlier. [Preview Abstract] |
Monday, November 24, 2014 11:09AM - 11:22AM |
H32.00004: Flow of a flexible fiber past an obstacle Hector Lopez, Jean Pierre Hulin, Harold Auradou, Veronica D'Angelo The transport of flexible biological or man made fibers by a flow is of interest in view of their potential applications in many different industrial fields. Here we study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiber follow closely those of the local flow velocity. The ratios of the curvatures of the fibers by the corresponding curvatures of the streamlines reflect a balance between elastic and viscous forces: this ratio is shown experimentally to be determined by a dimensionless Sperm number (Sp) combining the characteristic parameters of the flow (transverse velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the fiber (diameter, effective length, Young's modulus). The effective length is either the fiber length (short fiber case) or the characteristic size of the obstacle (long fiber case). For low values of Sp the ratio of the curvatures increases linearly with Sp. For values higher than 250, the fiber and the streamlines have the same curvature. [Preview Abstract] |
Monday, November 24, 2014 11:22AM - 11:35AM |
H32.00005: Particle motion inside Ekman and B\"{o}dewadt boundary layers Matias Duran Matute, Steven van der Linden, GertJan van Heijst We present results from both laboratory experiments and numerical simulations of the motion of heavy particles inside Ekman and B\"{o}dewadt boundary layers. The particles are initially at rest on the bottom of a rotating cylinder filled with water and with its axis parallel to the axis of rotation. The particles are set into motion by suddenly diminishing the rotation rate and the subsequent creation of a swirl flow with the boundary layer above the bottom plate. We consider both spherical and non-spherical particles with their size of the same order as the boundary layer thickness. It was found that the particle trajectories define a clear logarithmic spiral with its shape depending on the different parameters of the problem. Numerical simulations show good agreement with experiments and help explain the motion of the particles. [Preview Abstract] |
Monday, November 24, 2014 11:35AM - 11:48AM |
H32.00006: The effect of shear flow on the rotational diffusivity of a single axisymmetric particle Brian Leahy, Donald Koch, Itai Cohen Colloidal suspensions of nonspherical particles abound in the world around us, from red blood cells in arteries to kaolinite discs in clay. Understanding the orientation dynamics of these particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in simple shear flow, the orientation dynamics of Brownian nonspherical particles are poorly understood at large shear rates. Here, we analytically calculate the time-dependent orientation distributions of particles confined to the flow-gradient plane when the rotary diffusion is small but nonzero. For both startup and oscillatory shear flows, we find a coordinate change that maps the convection-diffusion equation to a simple diffusion equation with an enhanced diffusion constant, simplifying the orientation dynamics. For oscillatory shear, this enhanced diffusion drastically alters the quasi-steady orientation distributions. Our theory of the unsteady orientation dynamics provides an understanding of a nonspherical particle suspension's rheology for a large class of unsteady flows. For particles with aspect ratio 10 under oscillatory shear, the rotary diffusion and intrinsic viscosity vary with amplitude by a factor of $\approx 40$ and $\approx 2$, respectively. [Preview Abstract] |
Monday, November 24, 2014 11:48AM - 12:01PM |
H32.00007: Non-spherical aerosol transport under oscillatory shear flows at low-Reynolds numbers Lihi Shachar Berman, Yann Delorme, Philipp Hofemeier, Steven Frankel, Josue Sznitman Most airborne particles are intrinsically non-spherical. In particular, non-spherical particles with high aspect ratios, such as fibers, are acknowledged to be more hazardous than their spherical counterparts due to their ability to penetrate into deeper lung regions, causing serious pulmonary diseases. Not only do particle properties such as size, shape, and density have a major impact on particle transport, for non-spherical aerosols, their orientations also greatly influence particle trajectories due to modified lift and drag characteristics. Until present, however, most of our understanding of the dynamics of inhaled particles in the deep airways of the lungs has been limited to spherical particles only. In the present work, we seek to quantify through numerical simulations the transport of non-spherical airborne particles and their deposition under oscillatory shear flows at low Reynolds numbers, characteristic of acinar airways. Here, the Euler--Lagrangian model is used to solve the translational movement of a fiber, whereas the Eulerian rotational equations are introduced and solved to predict detailed unsteady fiber orientations. Overall, our efforts provide new insight into realistic dynamics of inhaled non-spherical aerosols under characteristic breathing motions. [Preview Abstract] |
Monday, November 24, 2014 12:01PM - 12:14PM |
H32.00008: Relative motion between rigid fibers and fluid in turbulent channel flow Cristian Marchioli, Alfredo Soldati We examine how rigid fibers with different length and inertia translate and rotate relative to the surrounding fluid in presence of non-linear mean shear and flow anisotropy. Two observables will be investigated: the fiber-to-fluid translational velocity (slip velocity) and angular velocity (slip spin). Slip velocity and slip spin statistics are extracted from DNS of turbulence at $Re_{\tau}=150$ coupled with Lagrangian tracking of prolate ellipsoids with Stokes number $1 < St < 100$, and aspect ratio $1< \lambda <50$. We find that elongation has quantitative effects on the statistics, particularly for fibers with small $St$. As $St$ increases, differences due to the aspect ration vanish and the relative motion is controlled by fiber inertia through preferential concentration. Inertial effects show up in the different distribution of slip velocities observed when fibers are trapped in sweeps/ejections or segregated in near-wall fluid streaks. The corresponding conditional PDFs are found to be non-Gaussian, suggesting that relative motions cannot be modeled as a standard diffusion process at steady state. This is evident in the strong shear region, where fiber anisotropy adds to flow anisotropy to induce strong deviations on fiber dynamics with respect to spherical particles. [Preview Abstract] |
Monday, November 24, 2014 12:14PM - 12:27PM |
H32.00009: Measuring the orientation and rotation rate of 3D printed particles in turbulent flow Greg Voth, Guy G. Marcus, Shima Parsa, Stefan Kramel, Rui Ni, Brendan Cole The orientation distribution and rotations of anisotropic particles plays a key role in many applications ranging from icy clouds to papermaking and drag reduction in pipe flow. Experimental access to time resolved orientations of anisotropic particles has not been easy to achieve. We have found that 3D printing technology can be used to fabricate a wide range of particle shapes with smallest dimension down to 300 $\mu $m. So far we have studied rods, crosses, jacks, tetrads, and helical shapes. We extract the particle orientations from stereoscopic video images using a method of least squares optimization in Euler angle space. We find that in turbulence the orientation and rotation rate of many particles can be understood using a simple picture of alignment of both the vorticity and a long axis of the particle with the Lagrangian stretching direction of the flow. [Preview Abstract] |
Monday, November 24, 2014 12:27PM - 12:40PM |
H32.00010: Spin, slip, and settle: effects of shape on motion for Taylor-scale particles in homogeneous isotropic turbulence Margaret Byron, Yiheng Tao, Isabel Houghton, Evan Variano We fabricate hydrogel cylinders of varying aspect ratios and suspend them in homogeneous isotropic turbulence at high Reynolds number. Cylinders are nearly neutrally buoyant and refractive-index-matched to water, with characteristic lengthscales that are close to the Taylor microscale. We simultaneously image these cylinders and the surrounding fluid for stereoscopic PIV measurement, permitting calculation of instantaneous particle slip velocity. We measure the particles' settling velocity in quiescent flow and compare this to both the calculated slip velocities and empirically-predicted settling velocities. Particle rotation is determined via the solid-body rotation equation and compared with fluid-phase properties (vorticity, shear, et al). We find that the aspect ratio of the cylinder has only a weak effect on its expected value of angular velocity magnitude, and further examine the influence of aspect ratio on slip and settling velocities. Lastly, we discuss applications of our results to problems of underwater navigation in aquatic organisms. [Preview Abstract] |
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