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 (2018)]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly-inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.
Two dimensional channel flow simulations of FENE-P fluid in the elasto-inertial turbulence regime reveal distinct regimes ranging from chaos to a steady travelling wave which takes the form of an arrowhead structure. This coherent structure provides new insights in the polymer/flow interactions driving EIT, which are observed in a set of controlled numerical experiments and the study of transfer between elastic and turbulent kinetic energy.
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 goal of the present study is: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bi-dimensional instability in three-dimensional EIT flows and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of FENE-P fluid flows are performed in two- and three-dimensional channels. The Reynolds number is set to $\mathrm{Re}_τ= 85$ which is sub-critical for 2D flows but beyond transition for 3D ones. The polymer properties correspon…
Viscoelastic microfluidic devices are promising for various microscale procedures such as particle sorting and separation. In this study, we perform three dimensional computational investigation of a particle in a viscoelastic channel flow by considering combined inertial and elastic effects. We calculate equilibrium positions of the particle in the microchannel for a wide range of Reynolds and Weissenberg numbers, which are important in the design of microfluidic devices. The results provide an insight into the motion of cells and particles and explain the findings of previous experiments. Fu…
Turbulence generally arises in shear flows if velocities and hence inertial forces are sufficiently large. In striking contrast, viscoelastic fluids can exhibit disordered motion even at vanishing inertia. Intermediate between these cases, a novel state of chaotic motion, `elasto-inertial turbulence' (EIT), has been observed in a narrow Reynolds number interval. We here determine the origin of EIT in experiments and show that characteristic EIT structures can be detected across an unexpectedly wide range of parameters. Close to onset a pattern of chevron shaped streaks emerges in excellent agr…
Dynamic properties of elasto-inertial turbulence (EIT) are studied in a Taylor-Couette geometry. EIT is a chaotic flow state that develops upon both non-negligible inertia and viscoelasticity. A combination of direct flow visualisation and torque measurement allows to verify the earlier onset of EIT compared to purely inertial instabilities (and inertial turbulence). The scaling of the pseudo-Nusselt number with inertia and elasticity is discussed here for the first time. Variations in the friction coefficient, temporal frequency spectra, and spatial power density spectra highlight that EIT un…
This movie illustrates the recent numerical and experimental discovery of a new state of turbulence in dilute polymer solutions, Elasto-Inertial Turbulence. Elasto-inertial turbulence is characterized by a chaotic flow state in which both inertial and elastic effects, whose relative contributions vary with the Reynolds number, control the flow dynamics.
Elasto-inertial turbulence is a new state of turbulence found in flows with polymer additives . The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The resulting mechanism of interactions between polymer dynamics and the flow helps resolve a long…
Turbulence is ubiquitous in nature yet even for the case of ordinary Newtonian fluids like water our understanding of this phenomenon is limited. Many liquids of practical importance however are more complicated (e.g. blood, polymer melts or paints), they exhibit elastic as well as viscous characteristics and the relation between stress and strain is nonlinear. We here demonstrate for a model system of such complex fluids that at high shear rates turbulence is not simply modified as previously believed but it is suppressed and replaced by a new type of disordered motion, elasto-inertial turbul…
We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increas…
Recently, the nature of viscoelastic drag-reducing turbulence (DRT), especially maximum drag reduction (MDR) state, has become a focus of controversy. It has long been regarded as polymers-modulated inertial turbulence (IT), but is challenged by the newly proposed concept of elasto-inertial turbulence (EIT). This study is to re-picture DRT in parallel plane channels by introducing dynamics of EIT based on statistical and budget analysis for a series of flow regimes from the onset of DR to EIT. Energy conversion between velocity fluctuations and polymers as well as polymeric pressure redistribu…
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…
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.
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 …
Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely-elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is a size of the particles. The critical size is estimated for a strong clustering (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a weak clustering associat…
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…
Elasto-inertial turbulence (EIT) is a new, two-dimensional chaotic flow state observed in polymer solutions with possible connections to inertialess elastic turbulence and drag-reduced Newtonian turbulence. In this Letter, we argue that the origins of EIT are fundamentally different from Newtonian turbulence by finding a dynamical connection between EIT and an elasto-inertial linear instability recently found at high Weissenberg numbers (Garg et al. Phys. Rev. Lett. 121, 024502, 2018). This link is established by isolating the first known exact coherent structures in viscoelastic parallel flow…
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…
The breakup of inertial, solid aggregates in an incompressible, homogeneous and isotropic three-dimensional turbulent flow is studied by means of a direct numerical simulation, and by a Lagrangian tracking of the aggregates at varying Stokes number and fluid-to-particle density ratio. Within the point-particle approximation of the Maxey-Riley-Gatignol equations of motion, we analyse the statistics of the time series of shear and drag stresses, which are here both deemed as responsible for particle breakup. We observe that, regardless of the Stokes number, the shear stresses produced by the tur…
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…
Surface distortions to an otherwise planar channel flow introduce vorticity perturbations. We examine this scenario in viscoelastic fluids, and identify new mechanisms by which significant vorticity perturbations can be generated in both inertialess and elasto-inertial channel flows. We focus on the case where the lengthscale of the surface distortion is much longer than the channel depth, where we find significant departure from plane shear (Page & Zaki, J. Fluid Mech. 801 2016) due to the non-monotonic base-flow streamwise-normal elastic stress. In inertialess flows, a purely elastic respons…
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…
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…
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…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of artificial diffusion (AD) for numerical stability in hyperbolic problems, which alters the physical nature of the system. This study presents a hybrid numerical procedure that integrates an upwind total variation diminishing (TVD) finite-difference scheme, which is known for its stability in hyperbolic problems, for the polymer stress convection term into an overall …
Two-dimensional statistically stationary isotropic turbulence with an imposed uniform scalar gradient is investigated. Dimensional arguments are presented to predict the inertial range scaling of the turbulent scalar flux spectrum in both the inverse cascade range and the enstrophy cascade range for small and unity Schmidt numbers. The scaling predictions are checked by direct numerical simulations and good agreement is observed.
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 relative dispersion of pairs of inertial particles in incompressible, homogeneous, and isotropic turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number $Re_λ \sim 200$ and 400. The evolution of both heavy and light particle pairs is analysed at varying the particle Stokes number and the fluid-to-particle density ratio. For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle ve…
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…
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…
