Smart Inertial Particles

We performed a numerical study to train smart inertial particles to target specific flow regions with high vorticity through the use of reinforcement learning algorithms. The particles are able to actively change their size to modify their inertia and density. In short, using local measurements of the flow vorticity, the smart particle explores the interplay between its choices of size and its dynamical behaviour in the flow environment. This allows it to accumulate experience and learn approximately optimal strategies of how to modulate its size in order to reach the target high-vorticity regions. We consider flows with different complexities: a two-dimensional stationary Taylor-Green like configuration, a two-dimensional time-dependent flow, and finally a three-dimensional flow given by the stationary Arnold-Beltrami-Childress helical flow. We show that smart particles are able to learn how to reach extremely intense vortical structures in all the tackled cases.Comment: Published on Phys. Rev. Fluids (August 6, 2018

Flow Navigation by Smart Microswimmers via Reinforcement Learning

Smart active particles can acquire some limited knowledge of the fluid environment from simple mechanical cues and exert a control on their preferred steering direction. Their goal is to learn the best way to navigate by exploiting the underlying flow whenever possible. As an example, we focus our attention on smart gravitactic swimmers. These are active particles whose task is to reach the highest altitude within some time horizon, given the constraints enforced by fluid mechanics. By means of numerical experiments, we show that swimmers indeed learn nearly optimal strategies just by experience. A reinforcement learning algorithm allows particles to learn effective strategies even in difficult situations when, in the absence of control, they would end up being trapped by flow structures. These strategies are highly nontrivial and cannot be easily guessed in advance. This Letter illustrates the potential of reinforcement learning algorithms to model adaptive behavior in complex flows and paves the way towards the engineering of smart microswimmers that solve difficult navigation problems.Comment: Published on Physical Review Letters (April 12, 2017

Helicoidal particles in turbulent flows with multi-scale helical injection

We present numerical and theoretical results concerning the properties of turbulent flows with strong multi-scale helical injection. We perform direct numerical simulations of the Navier-Stokes equations under a random helical stirring with power-law spectrum and with different intensities of energy and helicity injections. We show that there exists three different regimes where the forward energy and helicity inertial transfers are: (i) both leading with respect to the external injections, (ii) energy transfer is leading and helicity transfer is sub-leading and (iii) both are sub-leading and helicity is maximal at all scales. As a result, the cases (ii-iii) give flows with Kolmogorov-like inertial energy cascade and tuneable helicity transfers/contents. We further explore regime (iii) by studying its effect on the kinetics of point-like isotropic helicoids, particles whose dynamics is isotropic but breaks parity invariance. We investigate small-scale fractal clustering and preferential sampling of intense helical flow structures. Depending on their structural parameters, the isotropic helicoids either preferentially sample co-chiral or anti-chiral flow structures. We explain these findings in limiting cases in terms of what is known for spherical particles of different densities and degrees of inertia. Furthermore, we present theoretical and numerical results for a stochastic model where dynamical properties can be calculated using analytical perturbation theory. Our study shows that a suitable tuning of the stirring mechanism can strongly modify the small-scale turbulent helical properties and demonstrates that isotropic helicoids are the simplest particles able to preferentially sense helical properties in turbulence

Caustics in turbulent aerosols form along the Vieillefosse line at weak particle inertia

Caustic singularities of the spatial distribution of particles in turbulent aerosols enhance collision rates and accelerate coagulation. Here we investigate how and where caustics form at weak particle inertia, by analysing a three-dimensional Gaussian statistical model for turbulent aerosols in the persistent limit, where the flow varies slowly compared with the particle relaxation time. In this case, correlations between particle- and fluid-velocity gradients are strong, and caustics are induced by large, strain-dominated excursions of the fluid-velocity gradients. These excursions must cross a characteristic threshold in the plane spanned by the invariants $Q$ and $R$ of the fluid-velocity gradients. Our method predicts that the most likely way to reach this threshold is by a unique ``optimal fluctuation'' that propagates along the Vieillefosse line, $27R^2/4 +Q^3=0$. We determine the shape of the optimal fluctuation as a function of time and show that it is dominant in numerical statistical-model simulations even for moderate particle inertia.Comment: 12 pages, 3 figure

Inertial torque on a small spheroid in a stationary uniform flow

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle shape is varied from oblate (aspect ratio λ = 1 / 6 ) to prolate ( λ = 6 ) , and we consider low and moderate particle Reynolds numbers ( Re ≤ 50 ) . We demonstrate that the angular dependence of the torque, predicted theoretically for small particle Reynolds numbers, remains qualitatively correct for Reynolds numbers up to Re ∼ 10 . The amplitude of the torque, however, is smaller than the theoretical prediction, the more so as Re increases. For Re larger than 10, the flow past oblate spheroids acquires a more complicated structure, resulting in systematic deviations from the theoretical predictions. Overall, our numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in a turbulent flow.publishedVersio

Analysis of the correlation dimension for inertial particles

We obtain an implicit equation for the correlation dimension which describes cluster- ing of inertial particles in a complex flow onto a fractal measure. Our general equation involves a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid appears as additive noise. When the long-time limit of the propagator is considered our equation reduces to an existing large-deviation formalism from which it is difficult to extract concrete results. In the short-time limit, however, our equation reduces to a solvability condition on a partial differential equation. In the case where the inertial particles are much denser than the fluid, we show how this approach leads to a perturbative expansion of the correlation dimension, for which the coefficients can be obtained exactly and in principle to any order. We derive the perturbation series for the correlation dimension of inertial particles suspended in three-dimensional spatially smooth random flows with white-noise time correlations, obtaining the first 33 non-zero coefficients exactly

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