One of the most enigmatic science question concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number as the ratio of particle diffusivity and turbulent eddy viscosity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced when predicted with existing literature model. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate the turbulent particle diffusivity while direct measurements and simulations of turbulent particle flux support the occurrence of settling retardation.
Chaotic and turbulent dispersion of passive heavy inertial particles in homogeneous two-dimensional turbulence with Ekman drag has been studied using notions of the effective diffusivity and distributed chaos. Results of recent direct numerical simulations have been used for this purpose. Effect of the Stokes number value on the applicability of these notions to the dispersion of passive heavy inertial particles has been briefly discussed.
We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space singularities of the deformation tensor, and random uncorrelated motion. We discuss how the phase- and real-space singularities are related. Their formation is well understood in terms of a local theory. We discuss implications for random uncorrelated motion. Our results are supported by results of direct numerical simulations of inertial particles in model fl…
We show that viscoelastic plane Poiseuille flow becomes linearly unstable in the absence of inertia, in the limit of high elasticities, for ultra-dilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues upto a Reynolds number ($Re$) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultra-dilute …
The aim of this Letter is to characterize the flow regimes of suspensions of finite-size rigid particles in a viscous fluid at finite inertia. We explore the system behavior as function of the particle volume fraction and the Reynolds number (the ratio of flow and particle inertia to viscous forces). Unlike single phase flows where a clear distinction exists between the laminar and the turbulent states, three different regimes can be identified in the presence of a particulate phase, with smooth transitions between them. At low volume fractions, the flow becomes turbulent when increasing the R…
We report experimental results on the dynamics of heavy particles of the size of the Kolmogorov-scale in a fully developed turbulent flow. The mixed Eulerian structure function of two-particle velocity and acceleration difference vectors <δv\cdotδa_p> was observed to increase significantly with particle inertia for identical flow conditions. We show that this increase is related to a preferential alignment between these dynamical quantities. With increasing particle density the probability for those two vectors to be collinear was observed to grow. We show that these results are consistent wit…
Turbophoresis leading to preferential concentration of inertial particles in regions of low turbulent diffusivity is a unique feature of inhomogeneous turbulent flows, such as free shear flows or wall-bounded flows. In this work, the theory for clustering of weakly inertial particles in homogeneous turbulence is extended to the inhomogeneous case of a turbulent channel flow. The inhomogeneity contributes to the cluster formation in addition to clustering in homogeneous turbulence. A space-dependent rate for the creation of inhomogeneous particle concentration is derived in terms of local stati…
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization usi…
We present experimental observations of the spatial distribution of large inertial particles suspended in a turbulent swirling flow at high Reynolds number. The plastic particles, which are tracked using several high speed cameras, are heavier than the working fluid so that their dynamics results from a competition between gravitational effects and turbulent agitation. We observe two different regimes of suspension. At low rotation rate, particles are strongly confined close to the bottom and are not able to reach the upper region of the tank whatever their size or density. At high rotation ra…
Direct numerical simulations are used to study the interaction of a stream of small heavy inertial particles with the laminar and turbulent wakes of an immobile sphere facing an incompressible uniform inflow. Particles that do not collide with the obstacle but move past it, are found to form preferential concentrations both in the sphere boundary layer and in its wake. In the laminar case, the upstream diverging flow pattern is responsible for particle clustering on a cylinder that extends far downstream the sphere. The interior of this surface contains no particles and can be seen as a shadow…
In turbulent flows subject to strong background rotation, the advective mechanisms of turbulence are superseded by the propagation of inertial waves, as the effects of rotation become dominant. While this mechanism has been identified experimentally, the conditions of the transition between the two mechanisms are less clear. We tackle this question experimentally by tracking the turbulent front away from a solid wall where jets enter an otherwise quiescent fluid. Without background rotation, this apparatus generates a turbulent front whose displacement recovers the $z(t)\sim t^{1/2}$ law class…
The existence of a quiescent core (QC) in the center of turbulent channel flows was demonstrated in recent experimental and numerical studies. The QC-region, which is characterized by relatively uniform velocity magnitude and weak turbulence levels, occupies about $40\%$ of the cross-section at Reynolds numbers $Re_τ$ ranging from $1000$ to $4000$. The influence of the QC region and its boundaries on transport and accumulation of inertial particles has never been investigated before. Here, we first demonstrate that a QC is unidentifiable at $Re_τ= 180$, before an in-depth exploration of partic…
We report experimental results on the relative motion of pairs of solid spheric particles with initial separations in the inertial range of fully developed turbulence in water. The particle densities were in the range of $1 \lessapprox ρ_{p}/ρ_{f} \lessapprox 8$, \textit{i.e.}, from neutrally buoyant to highly inertial; and their sizes were of the Kolmogorov scale. For all particles, we observed a Batchelor like regime, in which particles separated ballistically. Similar to the Batchelor regime for tracers, this regime was observed in the early stages of the relative separation for times $t \l…
In particle-laden turbulent flows the turbulence in carrier fluid phase gets affected by the dispersed particle phase for volume fraction above $10^{-4}$ and hence reverse coupling or two-way coupling becomes relevant in that volume fraction regime. In a recent study by Muramulla $et.al.^1$, a discontinuous decrease of turbulence intensity is observed in a vertical particle-laden turbulent channel-flow for a critical volume fraction O($10^{-3}$). The collapse of turbulent intensity is found out to be a result of catastrophic reduction of turbulent energy production rate. Mechanistically, parti…
The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modelled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions amongst inertial beads result in a non-trivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, non-interacting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (…
This study is concerned with the statistics of vertical turbulent channel flow laden with inertial particles for two different volume concentrations ($Φ_{V} = 3 \times 10^{-6}$ and $Φ_{V} = 5 \times 10^{-5}$) at a Stokes number of $St^{+} = 58.6$ based on viscous units. Two independent direct numerical simulation models utilizing the point-particle approach are compared to recent experimental measurements, where all relevant nondimensional parameters are directly matched. While both numerical models are built on the same general approach, details of the implementations are different, particula…
In this paper we investigate both theoretically and numerically the forward in time (FIT) and backward in time (BIT) dispersion of fluid and inertial particle pairs in isotropic turbulence. Fluid particles are known to separate faster BIT than FIT in three-dimensional turbulence, and we find that inertial particles do the same. However, we find that the irreversibility in the inertial particle dispersion is in general much stronger than that for fluid particles. For example, the ratio of the BIT to FIT mean-square separation can be up to an order of magnitude larger for inertial particles than…
We study the rotational dynamics of {\it inertial} disks and rods in three-dimensional, homogeneous isotropic turbulence. In particular, we show how the alignment and the decorrelation time-scales of such spheroids depend, critically, on both the level of inertia and the aspect ratio of these particles. These results illustrate the effect of inertia---which leads to a preferential sampling of the local flow geometry---on the statistics of both disks and rods in a turbulent flow. Our results are important for a variety of natural and industrial settings where the turbulent transport of asymmetr…
An asymptotic solution is derived for the motion of inertial particles exposed to Stokes drag in an unsteady random flow. This solution provides the finite-time Lyapunov exponents as a function of Stokes number and Lagrangian strain- and rotation-rates autocovariances. The sum of these exponents, which corresponds to a concentration-weighted divergence of particle velocity field, is considered as a measure of clustering. For inertial particles dispersed in an isotropic turbulent flow our analysis predicts maximum clustering at an intermediate Stokes number and minimal clustering at small and l…
Previous studies on nonspherical particle-fluid interaction were mostly confined to elongated fiber-like particles, which were observed to induce turbulence drag reduction. However, with the presence of tiny disk-like particles how wall turbulence is modulated and whether drag reduction occurs are still unknown. Motivated by those open questions, we performed two-way coupled direct numerical simulations of inertialess spheroids in turbulent channel flow by an Eulerian-Lagrangian approach. The additional stress accounts for the feedback from inertialess spheroids on the fluid phase. The results…
The role of initial separation for inertial range scaling of turbulent two-particle dispersion is reassessed in light of recent results. (slightly expanded version of Comment published in Physical Review Letters).
The theory of inertial manifolds (IM) is used to develop reduced-order models of turbulent combustion. In this approach, the dynamics of the system are tracked in a low-dimensional manifold determined in-situ without invoking laminar flame structures or statistical assumptions about the underlying turbulent flow. The primary concept in approximate IM (AIM) is that slow dominant dynamical behavior of the system is confined to a low-dimension manifold, and fast dynamics respond to the dynamics on the IM instantaneously. Decomposition of slow/fast dynamics and formulation of an AIM is accomplishe…
We study the dynamics of neutrally buoyant particles with diameters varying in the range [1, 45] in Kolmogorov scale units (eta) and Reynolds numbers based on Taylor scale between 580 and 1050. One component of the particles' velocity is measured using extended Laser Doppler Velocimetry at the center of a Von-Karman (VK) flow, acceleration is derived by differentiation. We find that although the particle acceleration variance decreases with increasing their diameter with scaling close to (D/eta)^-2/3, in agreement with previous observations, the characteristic time of acceleration autocorrelat…
By tracking small particles in the bulk of an intensely turbulent flow, we show that even a very small concentration of long-chain polymers disrupts the usual turbulent energy cascade. The polymers affect scales much larger than their physical size, from the dissipation range to the inertial range. The effect depends strongly on the polymer concentration. While the dissipative-scale statistics change continuously as the polymer concentration is increased, the inertial-range energy transfer rate is only altered by the polymer additives when the concentration is above a threshold (approximately …
We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale flow geometries. To this end, we combine direct numerical simulations of homogeneous and isotropic turbulence and of the Taylor-Green flow, with particle tracking velocimetry in a von Kármán experiment. While flows have different topologies (as nulls cluster differently), particles behave similarly in all cases, indicating that Taylor-scale neutrally buoyant …
We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is non-local both in space and time, i.e. the closure terms are parametrized in terms of the spatial neighborhood of the resolved quantities but also their history. The data-driven scheme is complemented with a physical constrain expressing the energy conservation property of the nonlinear advection terms. We show that the adoption of this physical constrain not only increases the accuracy of the closure scheme but also impr…
In a one-dimensional model for a turbulent aerosol (inertial particles suspended in a random flow) we compute the distributions of particle-velocity gradients and the rate of caustic formation at finite but small Kubo numbers Ku, for arbitrary Stokes numbers St. Our results are consistent with those obtained earlier in the limit of small Ku and and large St, such that Ku^2 St remains constant. We show how finite-time correlations and non-ergodic effects influence the inertial-particle dynamics at finite but small Kubo numbers.
Transport equations for heavy inertial particles in turbulent boundary layers may be derived from an underlying phase-space probability density function (PDF) equation. These equations, however, are unclosed, and the standard closure approach is to use a quasi-Normal approximation (QNA) in which the fourth moments are approximated as behaving as if the velocities were Normally distributed. Except for particles with weak inertia, the QNA leads to large quantitative errors, and is not consistent with the known asymptotic predictions of Sikovsky (Flow Turbulence Combust, vol. 92, 2014, pp. 41-64)…
We present the extension of a modeling technique for Lagrangian tracer particles [B. Viggiano et al., J. Fluid Mech.(2020), vol. 900, A27] which accounts for the effects of particle inertia. Thereby, the particle velocity for several Stokes numbers is modeled directly by a multi-layered Ornstein-Uhlenbeck process and a comparison of key statistical quantities (second-order velocity structure function, acceleration correlation function, and root mean square acceleration) to expressions derived from Batchelor's model as well as to direct numerical simulations (DNS) is performed. In both approach…
We compute the joint distribution of relative velocities and separations of identical inertial particles suspended in randomly mixing and turbulent flows. Our results are obtained by matching asymptotic forms of the distribution. The method takes into account spatial clustering of the suspended particles as well as singularities in their motion (so-called 'caustics'). It thus takes proper account of the fractal properties of phase space and the distribution is characterised in terms of the corresponding phase-space fractal dimension D_2. The method clearly exhibits universal aspects of the dis…
The problem of an accurate Eulerian-Lagrangian modeling of inertial particle dispersion in Large Eddy Simulation (LES) of turbulent wall-bounded flows is addressed. We run Direct Numerical Simulation (DNS) for turbulent channel flow at shear Reynolds numbers equal to 150 and 300 and corresponding a-priori and a-posteriori LES on differently coarse grids. We then tracked swarms of different inertia particles and we examined the influence of filtering and of Sub-Grid Scale (SGS) modeling for the fluid phase on particle velocity and concentration statistics. We also focused on how particle prefer…
We investigate the mechanisms by which inertial particles dispersed at semi-dilute conditions cause significant drag-reduction in a turbulent channel flow at $\mathrm{Re}_τ= 180$. We consider a series of four-way coupled Euler-Lagrange simulations where particles having friction Stokes number $\mathrm{St}^+ = 6$ or 30 are introduced at progressively increasing mass loading from $M=0.2$ to 1.0. The simulations show that $\mathrm{St}^+ = 30$ particles cause large drag-reduction by up to 19.74\% at $M=1.0$, whereas $\mathrm{St}^+ = 6$ particles cause large drag increase by up to 16.92\% at $M=1.0…
We propose an experimental study on the gravitational settling velocity of dense, sub-Kolmogorov inertial particles under different background turbulent flows. We report Phase Doppler Particle Analyzer measurements in a low-speed wind tunnel uniformly seeded with micrometer scale water droplets. Turbulence is generated with three different grids (two consisting on different active-grid protocols while the third is a regular static grid), allowing us to cover a very wide range of turbulence conditions in terms of Taylor-scale based Reynolds numbers ($Re_λ\in [30-520]$), Rouse numbers ($Ro \in […
We study pair dispersion in a three-dimensional incompressible high Reynolds number turbulent flow generated by Fourier transforming the dynamics of the Gledzer-Ohkitani-Yamada (GOY) shell model into real space. We show that GOY shell model can successfully reproduce both the Batchelor and the Richardson-Obukhov regimes of turbulent relative dispersion. We also study how the crossover time scales with the initial separations of a particle pair and compare it to the prediction by Batchelor.
We study intermittency of circulation moments in turbulent superfluid helium by using experimental grid turbulence and numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. More precisely, we compute the velocity circulation $Γ_r$ in loops of size $r$ laying in the inertial range. For both, experimental and numerical data, the circulation variance shows a clear Kolmogorov scaling $\langle Γ_r^2 \rangle \sim r^{8/3}$ in the inertial range, independently of the temperature. Scaling exponents of high-order moments are comparable, within error bars, to previously reported anomalous…
Traditional large eddy simulation is based on Kolmogrov's hypothesis, and done in the inertial range. In inertial range the LES model coefficient is scale-invariant. In many cases, such as computing in the boundary layer, the filter scale is not in the inertial range, and the model coefficient changes drastically with the filter scale, thus the assumption of scale-invariance is not proper. In this paper, we propose a general principle of constraint, and then we deduce two concrete constraints based on the existing spectrum theory and priori data. The constrained dynamic Smogorinsky model can p…
We analyze the evolution of the distribution, both in the phase space and in the physical space, of inertial particles released by a spatially-localized (punctual) source and advected by an incompressible flow. The difference in mass density between fluid and particles is assumed as small, and represents the basic parameter for a regular perturbative expansion. By means of analytical techniques such as Hermitianization, we derive a chain of equations of the advection--diffusion--reaction type, easily solvable at least numerically. Our procedure provides results also for finite particle inertia…
Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centered cubic porous unit cell on the transport, clustering, and deposition of fine particles at different Stokes numbers ($St = 0.01, 0.1, 0.5, 1, 2$) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and collision of particles with pore walls is modeled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geo…
In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-meter wide ellipsoid filled with water is brought to solid body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is injected into the resonant inerti…
Particles with density different from that of the advecting turbulent fluid cluster due to the different response of light/heavy particles to turbulent fluctuations. This study focuses on the quantitative characterization of the segregation of dilute poly-disperse inertial particles evolving in turbulent flow, as obtained from Direct Numerical Simulation of the Navier-Stokes equations. We introduce an indicator of segregation amongst particles of different inertia and/or size, from which a length scale r_{seg} quantifying the degree of segregation of two different types of particles is deduced…
We quantify the strength of the waves and their impact on the energy cascade in rotating turbulence by studying the wave number and frequency energy spectrum, and the time correlation functions of individual Fourier modes in numerical simulations in three dimensions in periodic boxes. From the spectrum, we find that a significant fraction of the energy is concentrated in modes with wave frequency $ω\approx 0$, even when the external forcing injects no energy directly into these modes. However, for modes for which the period of the inertial waves $τ_ω$ is faster than the turnover time $τ_\textr…
Two-way coupled direct numerical simulations are used to investigate the effects of inertial particles on self-sustained, turbulent coherent structures (i.e. the so-called the regeneration cycle) in plane Couette flow at low Reynolds number just above the onset of transition. Tests show two limiting behaviors with increasing particle inertia, similar to the results from the linear stability analysis of saffman, 1962: low-inertia particles trigger the laminar-to-turbulent instability whereas high-inertia particles tend to stabilize turbulence due to the extra dissipation induced by particle-flu…
The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple, low-dimensional dynamical system representation of Lagrangian evolution of velocity gradients in fluid turbulence, at least for short times. Here we derive a new restricted Euler dynamical system for the velocity gradient evolution of inertial particles such as solid particles in a gas or droplets and bubbles in turbulent liquid flows. The model is derived in t…
We investigate the transport of inertial particles by cellular flows when advection dominates over inertia and diffusion, that is, for Stokes and Péclet numbers satisfying $\mathrm{St} \ll 1$ and $\mathrm{Pe} \gg 1$. Starting from the Maxey--Riley model, we consider the distinguished scaling $\mathrm{St} \, \mathrm{Pe} = O(1)$ and derive an effective Brownian dynamics approximating the full Langevin dynamics. We then apply homogenisation and matched-asymptotics techniques to obtain an explicit expression for the effective diffusivity $\overline{D}$ characterising long-time dispersion. This exp…
The statistics of velocity differences between very heavy inertial particles suspended in an incompressible turbulent flow is found to be extremely intermittent. When particles are separated by distances within the viscous subrange, the competition between quiet regular regions and multi-valued caustics leads to a quasi bi-fractal behavior of the particle velocity structure functions, with high-order moments bringing the statistical signature of caustics. Contrastingly, for particles separated by inertial-range distances, the velocity-difference statistics is characterized in terms of a local …
We present experimental observations of the velocity and spatial distribution of inertial particles dispersed in the turbulent downward flow through a vertical channel at $Re_τ = 235$ and $335$. The working fluid is air laden with size-selected glass micro-spheres, with Stokes numbers $St = O(10)$ and $O(100)$ based on the Kolmogorov and viscous time scales, respectively. Cases at solid volume fractions $ϕ_v = 3{\times}10^{-6}$ and $5{\times}10^{-5}$ are considered. In the more dilute regime, the particle concentration profile shows near-wall and centerline maxima compatible with a turbophoret…
We present a generalization of turbulent pair dispersion to large initial separations ($η< r_0 < L$), by introducing a new time scale, $τ_{v_0}$, that reflects the persistence of initial conditions at time $τ=0$. Results of 3D Lagrangian tracking experiments at moderate Reynolds numbers show that pairs, for which the new time scale is shorter than the eddy turnover time scale, separate as in the Richardson superdiffusive regime, $\langle Δr^2 \rangle \propto τ^3$. The analysis of delay times (time interval to cross $Δr = ρ\, r_0$) of these conditionally sampled pairs exhibit $ρ^{2/5}$ scaling.
The phenomenon of turbulent thermal diffusion in temperature-stratified turbulence causing a non-diffusive turbulent flux of inertial and non-inertial particles in the direction of the turbulent heat flux is found using direct numerical simulations (DNS). In simulations with and without gravity, this phenomenon is found to cause a peak in the particle number density around the minimum of the mean fluid temperature for Stokes numbers less than 1, where the Stokes number is the ratio of particle Stokes time to turbulent Kolmogorov time at the viscous scale. Turbulent thermal diffusion causes the…
