Particles In Turbulent Flow Research Articles

Clustering of fast gyrotactic particles in low-Reynolds-number flow.

Systems of particles in turbulent flows exhibit clustering where particles form patches in certain regions of space. Previous studies have shown that motile particles accumulate inside the vortices and in downwelling regions, while light and heavy non-motile particles accumulate inside and outside the vortices, respectively. While strong clustering is generated in regions of high vorticity, clustering of motile particles is still observed in fluid flows where vortices are short-lived. In this study, we investigate the clustering of fast swimming particles in a low-Reynolds-number turbulent flow and characterize the probability distributions of particle speed and acceleration and their influence on particle clustering. We simulate gyrotactic swimming particles in a cubic system with homogeneous and isotropic turbulent flow. Here, the swimming velocity explored is relatively faster than what has been explored in other reports. The fluid flow is produced by conducting a direct numerical simulation of the Navier-Stokes equation. In contrast with the previous results, our results show that swimming particles can accumulate outside the vortices, and clustering is dictated by the swimming number and is invariant with the stability number. We have also found that highly clustered particles are sufficiently characterized by their acceleration, where the increase in the acceleration frequency distribution of the most clustered particles suggests a direct influence of acceleration on clustering. Furthermore, the acceleration of the most clustered particles resides in acceleration values where a cross-over in the acceleration PDFs are observed, an indicator that particle acceleration generates clustering. Our findings on motile particles clustering can be applied to understanding the behavior of faster natural or artificial swimmers.

Heat Transfer and Pressure Drop of Nanofluid with Rod-like Particles in Turbulent Flows through a Curved Pipe.

Pressure drop, heat transfer, and energy performance of ZnO/water nanofluid with rodlike particles flowing through a curved pipe are studied in the range of Reynolds number 5000 ≤ Re ≤ 30,000, particle volume concentration 0.1% ≤ Φ ≤ 5%, Schmidt number 104 ≤ Sc ≤ 3 × 105, particle aspect ratio 2 ≤ λ ≤ 14, and Dean number 5 × 103 ≤ De ≤ 1.5 × 104. The momentum and energy equations of nanofluid, together with the equation of particle number density for particles, are solved numerically. Some results are validated by comparing with the experimental results. The effect of Re, Φ, Sc, λ, and De on the friction factor f and Nusselt number Nu is analyzed. The results showed that the values of f are increased with increases in Φ, Sc, and De, and with decreases in Re and λ. The heat transfer performance is enhanced with increases in Re, Φ, λ, and De, and with decreases in Sc. The ratio of energy PEC for nanofluid to base fluid is increased with increases in Re, Φ, λ, and De, and with decreases in Sc. Finally, the formula of ratio of energy PEC for nanofluid to base fluid as a function of Re, Φ, Sc, λ, and De is derived based on the numerical data.

Clustering of inertial particles in turbulent flow through a porous unit cell

Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred 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 the collision of particles with pore walls is modelled 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 geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers.

Rate of formation of caustics in heavy particles advected by turbulence.

The rate of collision and the relative velocities of the colliding particles in turbulent flows are a crucial part of several natural phenomena, e.g. rain formation in warm clouds and planetesimal formation in protoplanetary discs. The particles are often modelled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three-dimensional turbulent flows, we calculate the rate of formation of caustics, [Formula: see text] as a function of the Stokes number ([Formula: see text]). The best approximation to our data is [Formula: see text], in the limit [Formula: see text] where [Formula: see text] is a non-universal constant. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Controversial turbulent Schmidt number value in particle-laden boundary layer flows

When solid particles, such as sediments, are transported by a turbulent boundary layer flow, the wall-normal turbulent diffusion of particle concentration has been observed to be much higher than the turbulent diffusion of momentum (the eddy viscosity). This is characterized by a turbulent Schmidt number lower than unity. By using the few available existing direct measurements of Reynolds-averaged wall-normal particle flux and our two-phase flow large eddy simulations we demonstrate that the actual turbulent Schmidt number is indeed higher than unity. The misinterpretation may be explained by settling retardation of particles in turbulent flows compared with quiescent water.

Chemical plume tracking using an AUV with UKF based extremum seeking

Hydrothermal vent areas are unique ecosystems with high productivity and high biodiversity that are subject to ongoing research. Hydrothermal vents form in areas with increased magmatic activity where superheated, mineral rich water leaks from the seafloor. Due to the rapid cooling of the water the metal sulfides precipitate and form a black or white plume that can be sensed several hundred meters away from the vent source. Finding and reliably following such plumes with autonomous underwater vehicles (AUVs) is a challenging task since the plume does not have a smooth concentration gradient but lots of local patches due to the turbulent particle flow. This paper presents an algorithm that combines biology inspired chemotaxis with Unscented Kalman filter (UKF) based extremum seeking control (ESC). The effectiveness is demonstrated by a simulation of a physics-based AUV model in a turbulent 3D Plume model.

Asymmetry between deuterium and tritium turbulent particle flows

The asymmetry between deuterium (D) and tritium (T) turbulent particle fluxes in mixed D–T plasmas is studied with numerical simulations of nonlinear gyrokinetic turbulence in ion temperature gradient-dominated and trapped electron mode-dominated regimes. At 50–50 D–T concentration, the asymmetry, or flow separation, between D and T fluxes is such that the tritium is better confined than the deuterium in both regimes. To supplement the nonlinear simulations, an analytic quasilinear theory of the particle flux symmetry breaking is developed and is valid for general electron dynamics. This theory correctly predicts the numerically computed deviation in the ion density fraction (from 50–50), or ion density gradient (from the electron gradient), required to restore equal deuterium and tritium fluxes.

Anisotropic turbulent flow model effect on the prediction of the erosion rate of the micro particulate flow in the elbow

Turbulent particle flow is modeled using CFD to predict the erosion rate in the pipe. Anisotropic turbulence of the Reynolds Stress Model (RSM) is used in modeling turbulent fluid (natural gas) and particle (sand) flow through the Eulerian-Lagrangian equations. Since RSM can simulate the effects of anisotropy and flow history, it can better predict the behavior of particles that are dependent on the fluid flow. Also, the particle path line and their effect on erosion have been investigated at the all erosion models studied in this study. The results show that using RSM with the Tabakoff erosion model can predict maximum erosion with an error of less than 5% in the range of 47–49 degrees of elbow bend. However, other turbulence models, such as k-epsilon, are capable of delivering results with an error of more than 50% in the range of 45–49 degrees of elbow bend. Further, RSM can well simulate secondary flows, such as near-wall recirculation and dean flow.

Preferential concentration in the particle-induced convective instability

Heavy particles in turbulent flows have been shown to accumulate in regions of high strain rate or low vorticity, a process otherwise known as preferential concentration. This can be observed in geophysical flows, and is inferred to occur in astrophysical environments, often resulting in rapid particle growth which is critical to physical processes such as rain or planet formation. Here we study the effects of preferential concentration in a two-way coupled system in the context of the particle-driven convective instability. To do so, we use Direct Numerical Simulations and adopt the two-fluid approximation. We focus on a particle size range for which the latter is valid, namely when the Stokes number is $\lesssim O(0.1)$. For Stokes number above $\sim 0.01$, we find that the maximum particle concentration enhancement over the mean scales with the rms fluid velocity $u_{\rm{rms}}$, the particle stopping time $\tau_p$, and the particle diffusivity $\kappa_p$, as $u_{\rm{rms}}^2 \tau_p / \kappa_p$. We show that this scaling can be understood from simple arguments of dominant balance. We also show that the typical particle concentration enhancement over the mean scales as $(u_{\rm{rms}}^2 \tau_p/ \kappa_p)^{1/2}$. We finally find that the probability distribution function of the particle concentration enhancement over the mean has an exponential tail whose slope scales as $(u_{\rm{rms}}^2 \tau_p / \kappa_p)^{-1/2}$. We apply our model to geophysical and astrophysical examples, and discuss its limitations.

Publisher’s Note: “Accumulated densities of sedimenting particles in turbulent flows” [Phys. Fluids 32, 075104 (2020)

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Vortices as Brownian particles in turbulent flows.

Brownian motion of particles in fluid is the most common form of collective behavior in physical and biological systems. Here, we demonstrate through both experiment and numerical simulation that the movement of vortices in a rotating turbulent convective flow resembles that of inertial Brownian particles, i.e., they initially move ballistically and then diffusively after certain critical time. Moreover, the transition from ballistic to diffusive behaviors is direct, as predicted by Langevin, without first going through the hydrodynamic memory regime. The transitional timescale and the diffusivity of the vortices can be collapsed excellently onto a master curve for all explored parameters. In the spatial domain, however, the vortices exhibit organized structures, as if they are performing tethered random motion. Our results imply that the convective vortices have inertia-induced memory such that their short-term movement can be predicted and their motion can be well described in the framework of Brownian motions.

Accumulated densities of sedimenting particles in turbulent flows

We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane and analyze the deviation from homogeneity in terms of the Reynolds number and the settling velocity. We identify two regimes that arise during the early and well-mixed stages of advection. In the former regime, more inhomogeneity in the particle distribution is introduced for decreasing settling velocity or increasing Reynolds number, while the tendencies are opposite in the latter regime. A resonant-like crossover is found between these two regimes where inhomogeneity is maximal.

Development of a Momentum Transfer Coefficient in Particle Horizontal Channel Flow

Abstract A developed momentum transfer coefficient based on Wen’s 1966 model was proposed, in which the two threshold values were used to keep the continuous particle porosity function. A second-order moment gas–particle two-fluid turbulent model that coupled this coefficient, was established to model and simulate the particle horizontal channel flows. An improved Reynolds stresses transport to close fluctuation velocities correlation between gas and particle phases was set to reveal the fully anisotropic characteristics of particle dispersions. The hydrodynamics of horizontal gas–particle turbulent flow was numerically simulated and validated by experimental measurement with satisfied agreements. Distributions of particle Reynolds stresses are significantly affected by two-phase interactions, turbulent diffusions and particle collisions. Much wider size and flatter profiles distributions were obtained in terms of the horizontal and vertical root-means-square of particle velocities in comparison with Wen’s 1966 model.

Efficient calculation of the response statistics of two-dimensional fractional diffusive systems

Various natural phenomena are described by anomalous diffusion processes. Notable examples relate to the study of diffusion of tracers in particles in turbulent flows, or in the propagation of acoustic waves. In this context, the governing equations involve a fractional Laplacian operator, which replaces the classical Laplacian, and may involve nonlinear terms. This leads to problems described by fractional nonlinear diffusion equations. In general, no analytical solutions are available for determining the response of these systems. Thus, the development of approximate approaches circumventing the use of computationally demanding numerical techniques is desirable. This paper proposes a statistical linearization based approach, which allows calculating approximately, albeit iteratively, the response statistics. The method is developed using a recently proposed representation of the fractional Laplacian in conjunction with a mode expansion of the system response. It is implemented by introducing non-orthogonal eigenfunctions of the fractional Laplacian of the response, which are obtained from the linear modes of the classical diffusion equation. Such a representation allows deriving a system of nonlinear ordinary differential equations, which is linearized in a stochastic mean square sense. Then, the response statistics and power spectral density are determined by an iterative procedure. Numerical results pertaining to a system with white noise excitation demonstrate the efficiency of the proposed approximate approach. Further, comparisons with data from relevant Monte Carlo results assess the reliability of the estimated response.

Pseudo real-time continuous measurements of particle preferential concentration in homogeneous isotropic turbulence

Preferential concentration is a phenomenon where particles in turbulent flow concentrate in regions of low vorticity and high strain rate, forming clusters. This phenomenon is prevalent in nature and various industrial environments. Previous measurement systems for detecting this phenomenon have been based mostly on discrete images, and is relatively slow because of the image post processing involved. We have developed a new fast-response continuous measurement system comprised of a photomultiplier tube (PMT), custom-designed lens tube, and a continuous wave Nd:YAG laser. Experiments were conducted in a chamber that creates homogeneous isotropic turbulence with no mean flow. Image-based Voronoi analysis and box counting analysis from a high-speed camera were compared against the new PMT-based method for three Stokes number cases of near 0, 2.2, and 10. As the Stokes number was varied, the new technique showed similar results compared to the conventional camera-based methods.

Erosion of oval elbows in turbulent particulate natural gas flow with different aspect ratio of cross-sections

In this study, the erosion of the oval elbow duct pipe due to the natural gas–solid particles in the turbulent flow (k-epsilon) by (CFD) is investigated with specific consideration to the effect of the oval aspect ratio. The natural gas–solid particle turbulent flow is simulated by utilizing the two-way coupling, Eulerian–Lagrangian approach; while an enhanced wall treatment method is used because the flow has unique behavior when is close to the walls. Effects of most important erosion variable like channel geometry change, natural gas rate, and velocity on the erosion rate in all geometries were evaluated and discussed. Simulation results were verified with existing experimental results of the circular duct. Our results show that the geometry change has a severe effect on the erosion rate, and also the pipe aspect ratio has a considerable effect on the Dean Flow, the particle path line, and finally, the erosion rate of the elbow channel. Particle trajectory shows that the particles have an intense focus on inside the convex wall of the high-aspect-ratio cross-sections. Our result shows that the erosion will be decreased by reducing the aspect ratio to 0.4.

Lagrangian acceleration timescales in anisotropic turbulence

In a Lagrangian point of view, anisotropy in small time scales of turbulent flow is not yet well understood. Using Particle Tracking Velocimetry over nearly a decade in Taylor-scale based Reynolds numbers, we theoretically predict anisotropic acceleration correlation times of tracer particles in turbulent flow.

Exact results on the large-scale stochastic transport of inertial particles including the Basset history term

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.

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.

Dual mechanism model for fluid particle breakup in the entire turbulent spectrum

AbstractThis work provides an in‐depth understanding of different breakup mechanisms for fluid particles in turbulent flows. All the disruptive and cohesive stresses are considered for the entire turbulent energy spectrum and their contributions to the breakup are evaluated. A new modeling framework is presented that bridges across turbulent subranges. The model entails different mechanisms for breakup by abandoning the classical limitation of inertial models. The predictions are validated with experiments encompassing both breakup regimes for droplets stabilized by internal viscosity and interfacial tension down to the micrometer length scale, which covers both the inertial and dissipation subranges. The model performance ensures the reliability of the framework, which involves different mechanisms. It retains the breakup rate for inertial models, improves the predictions for the transition region from inertia to dissipation, and bridges seamlessly to Kolmogorov‐sized droplets.