Rotational diffusion of particles in turbulence (original) (raw)
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Orientation statistics of small particles in turbulence
New Journal of Physics, 2011
The statistics of the alignment of axisymmetric microscopic particles in fully developed turbulent flow is studied numerically and theoretically. Direct numerical simulations (DNS) of turbulent flows demonstrate that rod-like particles are more strongly aligned with the vorticity vector than with the principal strain axis. To elucidate this property, we compare the evolution obtained in a turbulent flow with a simpler model, where the velocity gradient of the flow is replaced by a fluctuating random matrix, whose temporal correlations reproduce the properties observed in DNS. In contrast with the DNS results, this model exhibits a strong alignment of the rods with the direction of the fastest stretching of the symmetric part of the random matrix. We argue that the correlation between the rod axis and the vorticity vector arises from similarities between the equations of motion governing these quantities.
Dynamics of particles advected by fast rotating incompressible turbulent fluid flow is studied. Fast rotation and particle inertia imply the divergent particle velocity field and result in both intermittency in spatial distribution of particles and formation of the large-scale inhomogeneous structures. A nonzero mean helicity of fluid flow causes an additional mean nondiffusive turbulent flux of inertial particles. In-termittency in the systems with and without external pumping is studied. Fast rotation causes anomalous scaling already in the second moment of inertial particle number density and may result in excitation of a small-scale instability of inertial particle distribution, which leads to the formation of small-scale particle clusters. We discuss the relevance of our results for atmospheric, astrophysical, and industrial turbulent rotating flows. [S0031-9007(98)07241-X]
Rotation of Nonspherical Particles in Turbulent Channel Flow
Physical Review Letters, 2015
Effects of particle inertia, particle shape, and fluid shear on particle rotation are examined using direct numerical simulation of turbulent channel flow. Particles at the channel center (nearly isotropic turbulence) and near the wall (highly sheared flow) show different rotation patterns, and surprisingly different effects of particle inertia. Oblate particles at the center tend to rotate orthogonally to their symmetry axes whereas prolate particles rotate around their symmetry axes. This trend is weakened by increasing inertia, so that highly-inertial oblate spheroids rotate nearly isotropically about their principle axes at the channel center. Near the walls, inertia does not move the rotation of spheroids towards isotropy, but rather reverses the trend, causing oblate spheroids to rotate strongly about their symmetry axes and prolate spheroids to rotate normal to their symmetry axes. The observed phenomena are mostly ascribed to preferential orientations of the spheroids.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous, and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For large-scale forcing, the spatial distribution of particle orientations forms large-scale structures, which are absent for intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For intermediate-scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate increases as the aspect ratio increases.
Statistics of velocity and preferential accumulation of micro-particles in boundary layer turbulence
Nuclear Engineering and Design, 2005
The distribution of inertial particles in turbulent flows is strongly non-homogeneous and is driven by the structure of the underlying carrier flow field. In this work, we use DNS combined with Lagrangian particle tracking to characterize the effect of inertia on particle preferential accumulation. We compare the Eulerian statistics computed for fluid and particles of different size, and observe differences in terms of distribution patterns and deposition rates which depend on particle inertia. Specifically, different statistics are related to the selective interaction occurring between particles and coherent flow structures. This selective response causes a preferential sampling of the flow field by the particles and eventually leads to the well-known phenomenon of long-term particle accumulation in the boundary layer. We try to measure particle preferential accumulation with a Lagrangian parameter related to the rate of deformation of an elemental volume of the particle phase along a particle trajectory. In the frame of the Lagrangian approach, this parameter is mathematically defined as the particle position Jacobian, J(t), computed along a particle path. This quantity is related to the local compressibility/divergence of the particle velocity field. Lagrangian statistics of J(t) show that compressibility increases for increasing particle response times τ + p (up to τ + p = 25 and within the time span covered by the simulation). (A. Soldati). not sufficient and more sophisticated models are required.
Physics of Fluids, 2012
The prediction of solid bodies transport (such as algae, debris, sediment grains, or corrosion deposits) is a necessary requirement in many industrial or environmental processes. The physical processes involved cover a wide range of processes, from tidal flow to turbulent eddies and particle drag. A stochastic model was therefore developed to link the different scales of the physical processes where it was assumed that the particles are dilute enough that they do not affect the flow or the motion of other particles while being large enough that each particle does not follow exactly the fluid motions (i.e., macro-particles). The stochastic model is built in such a way that it uses Reynolds-averaged fluid properties to predict trajectories of individual particles. This model was then tested using experimental measurements obtained for isotropic particles released in semi-homogeneous turbulence. The turbulent flow was generated using a pair of oscillating grids and was characterized using particle image velocimetry measurements. The trajectories of the particles were measured using a pair of high resolution cameras. The comparison between the experimental data and different numerical models gives satisfactory results.
Deviation-angle and trajectory statistics for inertial particles in turbulence
Physical review. E, 2016
Small particles in suspension in a turbulent fluid have trajectories that do not follow the pathlines of the flow exactly. We investigate the statistics of the angle of deviation ϕ between the particle and fluid velocities. We show that, when the effects of particle inertia are small, the probability distribution function (PDF) P_{ϕ} of this deviation angle shows a power-law region in which P_{ϕ}∼ϕ^{-4}. We also find that the PDFs of the trajectory curvature κ and modulus θ of the torsion ϑ have power-law tails that scale, respectively, as P_{κ}∼κ^{-5/2}, as κ→∞, and P_{θ}∼θ^{-3}, as θ→∞: These exponents are in agreement with those previously observed for fluid pathlines. We propose a way to measure the complexity of heavy-particle trajectories by the number N_{I}(t,St) of points (up until time t) at which the torsion changes sign. We present numerical evidence that n_{I}(St)≡lim_{t→∞}N_{I}(t,St)/t∼St^{-Δ} for large St, with Δ≃0.5.
Response Behavior of Nonspherical Particles in Homogeneous Isotropic Turbulent Flows
Advanced Computational Fluid Dynamics for Emerging Engineering Processes - Eulerian vs. Lagrangian [Working Title]
In this study, the responsiveness of nonspherical particles, specifically ellipsoids and cylinders, in homogeneous and isotropic turbulence is investigated through kinematic simulations of the fluid velocity field. Particle tracking in such flow field includes not only the translational and rotational components but also the orientation through the Euler angles and parameters. Correlations for the flow coefficients, forces and torques, of the nonspherical particles in the range of intermediate Reynolds number are obtained from the literature. The Lagrangian time autocorrelation function, the translational and rotational particle response, and preferential orientation of the nonspherical particles in the turbulent flow are studied as function of their shape and inertia. As a result, particle autocorrelation functions, translational and rotational, decrease with aspect ratio, and particle linear root mean square velocity increases with aspect ratio, while rotational root mean square velocity first increases, reaches a maximum around aspect ratio 2, and then decreases again. Finally, cylinders do not present any preferential orientation in homogeneous isotropic turbulence, but ellipsoids do, resulting in preferred orientations that maximize the cross section exposed to the flow.
Physics of Fluids, 2012
In this study, we investigate the effect of “biased sampling,” i.e., the clustering of inertial particles in regions of the flow with low vorticity, and “filtering,” i.e., the tendency of inertial particles to attenuate the fluid velocity fluctuations, on the proba- bility density function of inertial particle accelerations. In particular, we find that the concept of “biased filtering” introduced by Ayyalasomayajula et al. [“Modeling iner- tial particle acceleration statistics in isotropic turbulence,” Phys. Fluids 20, 0945104 (2008)], in which particles filter stronger acceleration events more than weaker ones, is relevant to the higher order moments of acceleration. Flow topology and its connec- tion to acceleration is explored through invariants of the velocity-gradient, strain-rate, and rotation-rate tensors. A semi-quantitative analysis is performed where we assess the contribution of specific flow topologies to acceleration moments. Our findings show that the contributions of regions of high vorticity and low strain decrease sig- nificantly with Stokes number, a non-dimensional measure of particle inertia. The contribution from regions of low vorticity and high strain exhibits a peak at a Stokes number of approximately 0.2. Following the methodology of Ooi et al. [“A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence,” J. Fluid Mech. 381, 141 (1999)], we compute mean con- ditional trajectories in planes formed by pairs of tensor invariants in time. Among the interesting findings is the existence of a stable focus in the plane formed by the second invariants of the strain-rate and rotation-rate tensors. Contradicting the results of Ooi et al., we find a stable focus in the plane formed by the second and third invariants of the strain-rate tensor for fluid tracers. We confirm, at an even higher Reynolds number, the conjecture of Collins and Keswani [“Reynolds number scaling of particle clustering in turbulent aerosols,” New J. Phys. 6, 119 (2004)] that iner- tial particle clustering saturates at large Reynolds numbers. The result is supported by the theory presented in Chun et al. [“Clustering of aerosol particles in isotropic turbulence,” J. Fluid Mech. 536, 219 (2005)]. ⃝C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4744993\]
Statistical Model for the Orientation of Nonspherical Particles Settling in Turbulence
Physical Review Letters, 2017
The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parametrization of the distribution of ice crystals in clouds, and potentially lead to an improved understanding of radiation reflection or particle aggregation through collisions in clouds.