Acceleration statistics of inertial particles in turbulent flow

Turbulent transport of material inclusions plays an important role in many natural and industrial situations. Being able to accurately model and predict the dynamics of dispersed particles transported by a turbulent carrier flow, remains a challenge. One critical and difficult point is to develop models which correctly describe the dynamics of particles over a wide range of sizes and densities. Our measurements show that acceleration statistics of particles dispersed in a turbulent flow do exhibit specific, and so far unpredicted, size and density effects and that they preserve an extremely robust turbulent signature with lognormal fluctuations, regardless of particles size and density. This has important consequences in terms of modeling for the turbulent transport of dispersed inclusions.     

Where do inertial particles go in fluid flows?

We derive a general reduced-order equation for the asymptotic motion of finite-size particles in unsteady fluid flows. Our inertial equation is a small perturbation of passive fluid advection on a globally attracting slow manifold. Among other things, the inertial equation implies that particle clustering locations in two-dimensional steady flows can be described rigorously by the Q parameter, i.e., by one-half of the squared difference of the vorticity and the rate of strain. Use of the inertial equation also enables us to solve the numerically ill-posed problem of source inversion, i.e., locating initial positions from a current particle distribution. We illustrate these results on inertial particle motion in the Jung-Tél-Ziemniak model of vortex shedding behind a cylinder in crossflow.     

Transport of inertial particles in a turbulent flow around spherical dimples

The problem on the emission of dust particles from a spherical dimple on a flat horizontal wall with a turbulent stream of a viscous incompressible fluid flowing around it is investigated numerically. With the help of a passive element of control, three various schemes of internal steady flows are reproduced for a dimple with the relative depth h = 0.25, which testifies to the nonuniqueness of the scheme of 3D flow around deep dimples. It is shown that the process of carrying out inertial particles into an external stream depends substantially on the type of internal flow of the scheme implemented in the dimple.     

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.     

On clustering of aerosol particles in homogeneous turbulent shear flows

The objective of this paper is to present a model for predicting clustering of aerosol particles in uniformly sheared turbulent flows laden with small heavy particles. The background of the model for predicting clustering is based on a kinetic equation for the two-point probability density function of the relative velocity distribution of two particles. The effect of clustering of particles in homogeneous turbulent shear flows is demonstrated and compared with known results of direct numerical simulations. It is shown that the universality of the clustering process can take place if the characteristic cluster size is smaller than the shear scale.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

Coexistence of inertial competitors in chaotic flows

We investigate the dynamics of inertial particles immersed in open chaotic flows. We consider the generic problem of competition between different species, e.g., phytoplankton populations in oceans. The strong influence from inertial effects is shown to result in the persistence of different species even in cases when the passively advected species cannot coexist. Multispecies coexistence in the ocean can be explained by the fact that the unstable manifold is different for each advected competitor of different size.     

Lyapunov exponents and information dimension of the mass distribution in turbulent compressible flows

Turbulent density fluctuations in isothermal highly compressible turbulent flows are highly clumped and can be quantified by the scaling properties of powers of the mass distribution. This Eulerian quantity can be related to Lagrangian properties of the system given by the Lyapunov exponents of tracer particles advected with the flow. Using highly resolved numerical simulations, we show that the Kaplan-Yorke conjecture holds within numerical uncertainties.     

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D 237, 1998 (2008)]. They can serve as numerical algorithms to compute maximum entropy states and minimum enstrophy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.     

Selective sensitivity of open chaotic flows on inertial tracer advection: catching particles with a stick

We investigate the effects of finite size and inertia of a small spherical particle immersed in an open unsteady flow which, for ideal tracers, generates transiently chaotic trajectories. The inertia effects may strongly modify the chaotic motion to the point that attractors may appear in the configuration space. These studies are performed in a model of the two-dimensional flow past a cylindrical obstacle. The relevance to modeling efforts of biological pathogen transport in large-scale flows is discussed. Since the tracer dynamics is sensitive to the particle inertia and size, simple geometric setups in such flows could be used as a particle mixture segregator separating and trapping particles.     

Superpersistent chaotic transients in physical space: advective dynamics of inertial particles in open chaotic flows under noise

Superpersistent chaotic transients are characterized by an exponential-like scaling law for their lifetimes where the exponent in the exponential dependence diverges as a parameter approaches a critical value. So far this type of transient chaos has been illustrated exclusively in the phase space of dynamical systems. Here we report the phenomenon of noise-induced superpersistent transients in physical space and explain the associated scaling law based on the solutions to a class of stochastic differential equations. The context of our study is advective dynamics of inertial particles in open chaotic flows. Our finding makes direct experimental observation of superpersistent chaotic transients feasible. It also has implications to problems of current concern such as the transport and trapping of chemically or biologically active particles in large-scale flows.     

Evaporating droplets in turbulent reacting flows

Three-dimensional direct numerical simulations are carried out to determine the effects of turbulence on the preferential segregation of an evaporating spray and then to study the evolution of the resulting mixture fraction topology and propagating flame. First, the mixing between an initially randomly dispersed phase and the turbulent gaseous carrier phase is studied with non-evaporating particles. According to their inertia and the turbulence properties, the formation of clusters of particles is analyzed (formation delay, cluster characteristic size and density). Once the particles are in dynamical equilibrium with the surrounding turbulent flow, evaporation is considered through the analysis of the mixture fraction evolution. Finally, to mimic ignition, a kernel of burnt gases is generated at the center of the domain and the turbulent flame evolution is described.     

Noise- and inertia-induced inhomogeneity in the distribution of small particles in fluid flows

The dynamics of small spherical neutrally buoyant particulate impurities immersed in a two-dimensional fluid flow are known to lead to particle accumulation in the regions of the flow in which vorticity dominates over strain, provided that the Stokes number of the particles is sufficiently small. If the flow is viewed as a Hamiltonian dynamical system, it can be seen that the accumulations occur in the nonchaotic parts of the phase space: the Kolmogorov-Arnold-Moser tori. This has suggested a generalization of these dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use a bailout embedding of the standard map to mimic the dynamics of neutrally buoyant impurities subject not only to drag but also to fluctuating forces modeled as white noise. We find that the generation of inhomogeneities associated with the separation of particle from fluid trajectories is enhanced by the presence of noise, so that they appear in much broader ranges of the Stokes number than those allowing spontaneous separation. (c) 2002 American Institute of Physics.     

Helicity generation in turbulent MHD flows

We study turbulent flow of a conducting liquid in a uniform external magnetic field. It is shown that intense helicity generation is possible in the presence of a mean shear flow. It is noted that even though the mean helicity of the initial flow can be zero, the presence of internal topological structure of the flow, for example the presence of helicity of different signs at different scales, is nevertheless necessary for helicity generation. Zh. éksp. Teor. Fiz. 114, 946–955 (September 1998)     

Effects of forcing in three-dimensional turbulent flows

We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power-law spectrum, E(f)(k) approximately k(3-y). Numerical simulations are performed at different resolutions up to 512(3). We show that at varying the spectrum slope y, small-scale turbulent fluctuations change from a forcing independent to a forcing dominated statistics. We argue that the critical value separating the two behaviors, in three dimensions, is y(c)=4. When the statistics is forcing dominated, for yy(c), we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of universality in turbulent flows.