Inertial Particles Research Articles

Modulation of interphase, cross-scale momentum transfer of turbulent flows by preferentially concentrated inertial particles

Inertial particles can interact in two ways with carrier-phase turbulence, exchanging mass, momentum, and energy. This study proposes a wavelet multiresolution framework that analyzes spectral energy transfer involving two phases and multiple scales simultaneously. Its application to preferentially concentrated particle-laden turbulence shows the role of particle clusters in spectral energy transfer as well as the physical consistency of the subgrid-scale (SGS) Stokes number useful to analyze and develop an SGS model for two-way coupled particle-laden turbulence.

The effect of instantaneous particle distributions on the gas-phase temperature in an unsteady particle-laden jet heated with high-flux radiation

Detailed simultaneous planar measurements of particle number density and gas-phase temperature were performed in radiatively heated particle-laden jet with average particle volumetric loadings in the range 0.625−−1.4×10−3, which is within the transition region between the two- and four-way coupling regimes, to evaluate the correlation between the local particle volume fraction and temperature for inertial particles with a series of diameter distributions and radiative heating powers. Utilising novel optical measurement and image processing techniques, together with Voronoi analysis, regions of high instantaneous particle number density and localised regions of high/low gas-phase temperatures were identified. The results show that the particle volume fraction measured within the identified ‘hot regions’ was more than 1.5 times greater than the mean value for each case, while within the ‘cold regions’ the particle volume fraction was typically less than the mean. Similarly, the temperature around individual particles was found to increase with an increase in the local particle volume fraction, while the variation in local gas temperature in the vicinity of particles increases with a decrease in particle diameter. Furthermore, the temperature surrounding particles that were determined to be within closely spaced cluster regions (which form in the present measurements due to the random distribution of particles in the flow) was found to be greater than that around particles outside of clusters, even for the same local particle volume fraction (measured in a radius of 0.1 times the jet pipe diameter around each particle). The particle distributions were found to closely match a random Poisson distribution, consistent with the high particle Stokes numbers (86 ≤SkD≤ 514), and are not affected by the presence of radiative heating, implying that any flow phenomena induced by thermal gradients in the flow negligibly influence the particles in the near field of the jet for the conditions investigated here.

Inertial particle under active fluctuations: Diffusion and work distributions.

We study the underdamped motion of a passive particle in an active environment. Using the phase space path integral method we find the probability distribution function of position and velocity for a free and a harmonically bound particle. The environment is characterized by an active noise which is described as the Ornstein-Uhlenbeck process (OUP). Taking two similar, yet slightly different OUP models, it is shown how inertia along with other relevant parameters affect the dynamics of the particle. Further we investigate the work fluctuations of a harmonically trapped particle by considering the trap center being pulled at a constant speed. Finally, the fluctuation theorem of work is validated with an effective temperature in the steady-state limit.

Computation of magnetized Couette–Poiseuille thermal flow of couple stress between two analogous plate with variable viscosity suspending the hafnium particles

AimsIn the presence of a magnetic field, the Couette–Poiseuille flow of a pair stress fluid between two parallel plates was thoroughly examined. The flow was caused by uniform motion of the top plate and an axial pressure gradient. The effect of Hafnium particles, both in spherical and homogeneous form, was investigated by heating the wall. For this purpose, Reynolds' model was employed. MethodologyThe modeled equations are highly nonlinear partial differential equation which are transformed to convectional differential equation using the similarity transformation. The resulting non-linear system of equations was solved by recourse to the efficient bvph2 scheme along with homotopy analysis method (HAM). NoveltyThe innovative fragment of the present study is to scrutinize the magnetized the Couette–Poiseuille nanofluid flow of a pair stress fluid between two parallel plates is thoroughly examined with variable viscosity, still not has been elaborated in the available works to date. Consequently, in the restrictive sense, the existing work is associated with available work reported by Makinde and Onyejekwe [39] and originated in exceptional agreement. Findings and conclutionsAn inverse relation was found to exist between velocity and Hartman number. The reason behind this is that the increase in temperature enfeebles the viscous forces which, consequently, results in reduction of velocity. However, it was noticed that temperature profile is adversely affected by raising the viscosity parameters and consequently the velocity is enhanced. Future suggestionIt is possible to investigate diphase flows in various geometries using inertial particles suspended in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids, which might be one of the proposed model's future uses.

Work and heat distributions of an inertial Brownian particle.

The work and heat distribution densities of a classical Brownian particle immersed in a heat bath and interacting with an external field have been extensively analyzed from different approaches. In this article, a previous method based on basic principles of stochastic dynamics is extended to derive these functions. The starting point is the inertial Langevin equationand the external field is an off-center harmonic potential driven by an external protocol. Unlike previous works where the driving is arbitrary, the so-called optimal protocol that minimizes the mechanical work is used instead. The corresponding work and heat distributions are derived through a procedure based on getting a generic Fokker-Planck equationindistinctly of the variable under consideration. The work distribution is calculated for different initial conditions and values of the friction coefficient of the thermal fluid ranging from the periodic or very low-underdamped mode up to the overdamped regime. It is a Gaussian as that of previous experiments of a particle trapped in an optical tweezers moved at constant velocity. Some aspects about the heat distribution is analyzed in terms of the statistical features of the non-Gaussian noise accompanying its dynamics to give an account of experimental results. It is concluded that the easiness in calculating the work distribution cannot be applied to heat. It requires numerical calculations.

Scale-dependent particle clustering in transitional wake flow

Dispersion and mixing of inertial point particles in the unsteady and three-dimensional wake of a circular cylinder at$Re=200$are investigated via one-way coupled simulations. The presence of streamwise-oriented vortical braids originating from the mode A instability in the transition regime has a profound impact on the particle dynamics and preferential concentration in the near wake. Particles trapped between the Kármán rollers and the streamwise braids form an inner layer of densely concentrated particles, while discrete particle clumps on the otherwise thin ribbon-like clusters between two consecutive Kármán rollers are another manifestation of the streamwise braids. The effect of particle inertia on the size of clusters and voids ascribed to centrifugal ejection is examined by volume-averaged Voronoï analysis. A distinct dependence on Stokes number ($Sk$) is seen at the cluster scale, whereas the void scale exhibits self-similarity. New physics-based threshold values of clusters and voids are distinctly different from the probability-distribution-based threshold at cluster scale. Increasing inertia is found to suppress particle acceleration more than deceleration. The particle velocity is further suppressed by the presence of the streamwise vortical braids. The effects of particle inertia vary non-monotonically in$Sk$with the strongest effect at$Sk=1$when most particles tend to reside in high-strain/low-vorticity regions.

Transport modes of inertial particles and their effects on flow structures and heat transfer in Rayleigh–Bénard convection

We investigate the flow characteristics and kinetic behaviors of particles in turbulent Rayleigh–Bénard convection particulate flows. Direct numerical simulations combined with a Lagrangian point-particle strategy were carried out in the range of Stokes numbers 2×10−4≤StL≤7.3×10−2 for Rayleigh numbers from 2×106 to 108 at the Prandtl number Pr=0.678. A two-way coupling model is employed in which the momentum exchange between the dispersed particles and the carrier fluid is taken fully into account. Based on various patterns of particle motion, we find three transport modes of inertial particles which are labeled as the circling transport (CCT) mode, the channel transport (CNT) mode, and the downpour transport (DPT) mode, respectively. These modes can switch to each other when Stokes numbers and Rayleigh numbers vary and exhibit different effects of particle motions on the flow field and heat transfer. For the CCT and DPT modes, compared with the CNT, a weakening alteration of flow structures and thermal plumes leads to no significant effect on the transport of momentum and heat. For the CNT mode, a pronounced effect of particles on enhancements of the turbulent momentum transport and heat transfer relates to the strong interaction between the particle clusters and the chaotic structures of eddies. What is more, the particles tend to homogeneously distribute for the CCT and DPT modes, although the particles exhibit different transport states. As for the CNT mode, under both preferential sweeping and centrifugal effects, particles accumulate into clusters that hover toward the region of high strain rate and the edges of eddies. We found that the averaged particle settling speeds are almost proportional to the Stokes number. The particle settling speeds are larger than the terminal velocity of Stokesian particles for the CCT and CNT modes as particles tend to settle in the downward fluid. In contrast, it becomes smaller than the terminal velocity for the DPT mode due to the drag of the upward fluid.

Characterisation of the Tyre Spray Ejected Downstream of a Bluff Automotive Body

<div class="section abstract"><div class="htmlview paragraph">Considerations of surface contamination and airborne spray are becoming increasingly significant throughout the automotive design process. Advanced driver assistance systems, such as autonomous cruise control, are growing in popularity. These systems rely on external sensors, the performance of which may be impaired by both direct obstruction and spray. Existing experimental methods of assessing front-end surface contamination and wiper performance have typically utilised fixed spray-grids positioned upstream of the vehicle. The resulting spray is largely steady in nature, in contrast to the unsteady flow-field and tyre spray that would be produced by preceding vehicles. This paper presents the numerical analysis of the spray ejected downstream of a simplified automotive body. The continuous phase (air) is solved using a DDES-based approach coupled with a Lagrangian representation of the dispersed phase (water). Two configurations are examined, a square-back configuration and a variation employing 20° rear-end side tapers. The inclusion of side tapering results in a significant change in wake topology and the resulting spray cloud. Good agreement is achieved between initial single-phase predictions of the continuous phase and existing experimental data. The spray cloud of both configurations is found to be highly unsteady, driven by vortical structures in the near- and far-wake, and is altered significantly by what are relatively minor changes to the geometry. Proper Orthogonal Decomposition reveals comparable spatial modes in the mass flux field of the dispersed phase and the continuous phase velocity field downstream of the vehicle. However, the correlation between the temporal coefficients of these modes is relatively weak. This highlights the presence of slip effects between the two phases, coming as a result of particle inertia, and the need to consider both phases simultaneously in future studies of spray dynamics.</div></div>

Intricate relations among particle collision, relative motion and clustering in turbulent clouds: computational observation and theory

Abstract. Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision–coagulation, on particle clustering and particle relative motion. We perform direct numerical simulation (DNS) of coagulating particles in isotropic turbulent flow in the regime of small Stokes number (St=0.001–0.54) and find that, due to collision–coagulation, the radial distribution functions (RDFs) fall off dramatically at scales r∼d (where d is the particle diameter) to small but finite values, while the mean radial component of the particle relative velocity (MRV) increases sharply in magnitude. Based on a previously proposed Fokker–Planck (drift-diffusion) framework, we derive a theoretical account of the relationship among particle collision–coagulation rate, RDF and MRV. The theory includes contributions from turbulent fluctuations absent in earlier mean-field theories. We show numerically that the theory accurately accounts for the DNS results (i.e., given an accurate RDF, the theory could produce an accurate MRV). Separately, we also propose a phenomenological model that could directly predict MRV and find that it is accurate when calibrated using fourth moments of the fluid velocities. We use the model to derive a general solution of RDF. We uncover a paradox: the past empirical success of the differential version of the theory is theoretically unjustified. We see a further shape-preserving reduction of the RDF (and MRV) when the gravitational settling parameter (Sg) is of order O(1). Our results demonstrate strong coupling between RDF and MRV and imply that earlier isolated studies on either RDF or MRV have limited relevance for predicting particle collision rate.

Effect of electrostatic forces on the dispersion of like-charged solid particles transported by homogeneous isotropic turbulence

The effect of electrostatic forces on the dispersion of small like-charged inertial particles transported by a homogeneous isotropic turbulent flow is analysed by means of direct numerical simulations coupled with the Lagrangian tracking of charged particles. The results show that particle dispersion decreases for increasing charge. Since turbulent particle dispersion is related to the intensity of particle agitation and to the Lagrangian particle integral time scale, we analyse the effects of electrostatic forces on these two quantities. Particle agitation decreases for increasing particle charge. In fact, particle kinetic energy is not directly modified by electrostatic forces, which are conservative, it is rather the particle entrainment by fluid turbulence that is modified. To support this claim, one shows that the fluid–particle velocity covariance is destructed by electrostatic forces, a destruction can be predicted by drawing an analogy between inter-particle collisions and Coulomb collisions. As expected, electrostatic forces decorrelate particle velocities leading to a decrease of the Lagrangian particle integral time scale. Finally, one shows that the analogy with inter-particle collisions allows us to predict the reduction of particle dispersion.

Transport of condensing droplets in Taylor-Green vortex flow in the presence of thermal noise.

We study the role of phase change and thermal noise in particle transport in turbulent flows. We employ a toy model to extract the main physics: Condensing droplets are modelled as heavy particles which grow in size, the ambient flow is modelled as a two-dimensional Taylor-Green flow consisting of an array of vortices delineated by separatrices, and thermal noise are modelled as uncorrelated Gaussian white noise. In general, heavy inertial particles are centrifuged out of regions of high vorticity and into regions of high strain. In cellular flows, we find, in agreement with earlier results, that droplets with Stokes numbers smaller than a critical value, St<St_{cr}, remain trapped in the vortices in which they are initialized, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the Péclet number Pe characterizing the amplitude of thermal noise and the condensation rate Π to study their effects on the critical Stokes number for droplet trapping, as well as on the final states of motion of the droplets. We find that the imposition of thermal noise, or of a finite condensation rate, allows droplets of St<St_{cr} to leave their initial vortices. We find that the effects of thermal noise become negligible for growing droplets and that growing droplets achieve ballistic motion when their Stokes numbers become O(1). We also find an intermediate regime prior to attaining the ballistic state, in which droplets move diffusively away from their initial vortices in the presence of thermal noise.

Asymmetric Solid–Liquid Two-Phase Flow around a NACA0012 Cascade in Sediment-Laden Flow

Sediment abrasion may cause the removal of material and efficiency loss to hydraulic machinery (hydro-turbine, pump, etc.), which may worsen the internal flow and endanger the safe operation of the machines. As abrasion is caused by the impact of sediment on the solid surface, the movement of particles determines the wear intensity. To understand the wear mechanism of hydraulic machinery, the motion characteristics of the asymmetric solid–liquid two-phase flow in a sediment-laden flow around NACA0012 cascades were studied. The laser particle imaging velocimetry (PIV) method was used to measure the flow of quartz particles with median diameters d50 of 82.7 μm, 65.9 μm, and 31.8 μm near the wall of cascades at an impact angle of 10° in a Venturi circuit. The flow characteristics and velocity slip between solid and liquid phases, as well as the effects of particle size and the Reynolds number on velocity slip, were analyzed. The results showed that: (1) the flow is asymmetrically distributed in front of the cascade’s leading edge at a 10° impact angle, and there is strong velocity slip between solid and liquid phases; (2) under the influence of particle inertia, the velocity of the solid phase is higher than that of the liquid phase in the deceleration stage, while the velocity of the solid phase is lower than that of liquid phase in the acceleration stage; (3) in the process of approaching the leading edge, the velocity difference between the solid and liquid phase increases by about 10% and the angle difference increases by about 8.8°.

Markov property of Lagrangian turbulence

Based on direct numerical simulations with point-like inertial particles, with Stokes numbers St = 0, 0.5, 3, and 6, transported by homogeneous and isotropic turbulent flows, we present in this letter for the first time evidence for the existence of Markov property in Lagrangian turbulence. We show that the Markov property is valid for a finite step size larger than a Stokes-number-dependent Einstein-Markov coherence time scale. This enables the description of multi-scale statistics of Lagrangian particles by Fokker-Planck equations, which can be embedded in an interdisciplinary approach linking the statistical description of turbulence with fluctuation theorems of non-equilibrium stochastic thermodynamics and local flow structures. The formalism allows estimation of the stochastic thermodynamics entropy exchange associated with the particles Lagrangian trajectories. Entropy-consuming trajectories of the particles are related to specific evolution of velocity increments through scales and may be seen as intermittent structures. Statistical features of Lagrangian paths and entropy values are thus fixed by the fluctuation theorems.

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.

Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics.

We investigate the formation and stability of a pair of identical soft capsules in channel flow under mild inertia. We employ a combination of the lattice Boltzmann, finite element and immersed boundary methods to simulate the elastic particles in flow. Validation tests show excellent agreement with numerical results obtained by other research groups. Our results reveal new trajectory types that have not been observed for pairs of rigid particles. While particle softness increases the likelihood of a stable pair forming, the pair stability is determined by the lateral position of the particles. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.

Enhanced settling and dispersion of inertial particles in surface waves

Particulate matter in the environment, such as sediment, marine debris and plankton, is transported by surface waves. The transport of these inertial particles is different from that of fluid parcels described by Stokes drift. In this study, we consider the transport of negatively buoyant particles that settle in flow induced by surface waves as described by linear wave theory in arbitrary depth. We consider particles that fall under both a linear drag regime in the low Reynolds number limit and in a nonlinear drag regime in the transitional Reynolds number range. Based on an analysis of typical applications, we find that the nonlinear regime is the most widely applicable. From an expansion in the particle Stokes number, we find kinematic expressions for inertial particle motion in waves, and from a multiscale expansion in the dimensionless wave amplitude, we find expressions for the wave-averaged drift velocities. These drift velocities are analogous to Stokes drift and can be used in large-scale models that do not resolve surface waves. We find that the horizontal drift velocity is reduced relative to the Stokes drift of fluid parcels and that the vertical drift velocity is enhanced relative to the particle terminal settling velocity. We also demonstrate that a cloud of settling particles released simultaneously will disperse in the horizontal direction. Finally, we discuss the accuracy of our expressions by comparing against numerical simulations, which show excellent agreement, and against experimental data, which show the same trends.

Accelerated decay of a Lamb–Oseen vortex tube laden with inertial particles in Eulerian–Lagrangian simulations

We investigate the effect of inertial particles on the stability and decay of a prototypical vortex tube, represented by a two-dimensional Lamb–Oseen vortex. In the absence of particles, the strong stability of this flow makes it resilient to perturbations, whereby vorticity and enstrophy decay at a slow rate controlled by viscosity. Using Eulerian–Lagrangian simulations, we show that the dispersion of semidilute inertial particles accelerates the decay of the vortex tube by orders of magnitude. In this work, mass loading is unity, ensuring that the fluid and particle phases are tightly coupled. Particle inertia and vortex strength are varied to yield Stokes numbers 0.1–0.4 and circulation Reynolds numbers 800–5000. Preferential concentration causes these inertial particles to be ejected from the vortex core forming a ring-shaped cluster and a void fraction bubble that expand outwards. The outward migration of the particles causes a flattening of the vorticity distribution, which enhances the decay of the vortex. The latter is further accelerated by small-scale clustering that causes enstrophy to grow, in contrast with the monotonic decay of enstrophy in single-phase two-dimensional vortices. These dynamics unfold on a time scale that is set by preferential concentration and is two orders of magnitude lower than the viscous time scale. Increasing particle inertia causes a faster decay of the vortex. This work shows that the injection of inertial particles could provide an effective strategy for the control and suppression of resilient vortex tubes.

Effects of the path history on inertial particle pair dynamics in the dissipation range of homogeneous isotropic turbulence

The relationship between inertial particle pair dynamics in the dissipation range and local turbulence characteristics is investigated using direct numerical simulations in homogeneous isotropic turbulence at a Reynolds number of 110 based on the Taylor microscale. Seventeen million sub-Kolmogorov-sized particles with Stokes numbers of 0.5, 1.0, 1.5, and 2.0 are tracked backward in time to investigate the formation of the relative velocity of inertial particles in the dissipation range. The numerical experiment shows that particle pairs take different paths and sample different underlying flows depending on the intensity of the local turbulence activity at final locations where the distance between particles is much smaller than the Kolmogorov length scale. Taking different paths depending on the intensity of the local turbulence activity is described by the sling time, which is defined as the time when particle pairs are slung out from the underlying flow. Particle pairs with shorter sling time values than the characteristic time scale of particles are detached from the dissipation range of flow and approach each other in a ballistic fashion. In contrast, the large-scale flow guides particle pairs with longer sling time than the characteristic time scales. In particular, particle pairs forming caustics with the same sling time are detached from similar flows regardless of the magnitude of particle relative velocities. Samplings of similar flows at sling moments cause the scaling relationship between relative velocities of particles and sling time. These behaviors of particle pairs, especially for pairs with caustics in relative velocities, are also observed in the range of considered Stokes numbers. The relationship between the intensity of the local turbulence activity and the paths taken by particles highlights the importance of considering a preferential sampling of flow in understanding inertial particle pair dynamics.

Invariant manifold approach for quantifying the dynamics of highly inertial particles in steady and time-periodic incompressible flows.

The dynamics of finite-sized particles with large inertia are investigated in steady and time-dependent flows through the numerical solution of the invariance equation, describing the spatiotemporal evolution of the slow/inertial manifold representing the effective particle velocity field. This approach allows for an accurate reconstruction of the effective particle divergence field, controlling clustering/dispersion features of particles with large inertia for which a perturbative approach is either inaccurate or not even convergent. The effect of inertia on heavy and light particles is quantified in terms of the rate of contraction/expansion of volume elements along a particle trajectory and of the maximum Lyapunov exponent for systems exhibiting chaotic orbits, such as the time-periodic sine-flow on the 2D torus and the time-dependent 2D cavity flow.

Particle Focusing in a Straight Microchannel with Non-Rectangular Cross-Section.

Recently, studies on particle behavior under Newtonian and non-Newtonian fluids in microchannel have attracted considerable attention because particles and cells of interest can be manipulated and separated from biological samples without any external force. In this paper, two kinds of microchannels with non-rectangular cross-section were fabricated using basic MEMS processes (photolithography, reactive ion etching and anisotropy wet etching), plasma bonding and self-alignment between two PDMS structures. They were used to achieve the experiments for inertial and elasto-inertial particle focusing under Newtonian and non-Newtonian fluids. The particle behavior was compared and investigated for different flow rates and particle size in the microchannel with rhombic and equilateral hexagonal cross section. We also investigated the influence of Newtonian fluid and viscoelastic fluid on particle migration in both microchannels through the numerical simulation. The experimental results showed the multi-line particle focusing in Newtonian fluid over a wide range of flow rates, but the single-line particle focusing was formed in the centerline under non-Newtonian fluid. The tighter particle focusing appeared under non-Newtonian fluid in the microchannel with equilateral hexagonal cross-section than in the microchannel with rhombic cross section because of the effect of an obtuse angle. It revealed that particles suspended in the channel are likely to drift toward a channel center due to a negative net elasto-inertial force throughout the cross-sectional area. Simulation results support the present experimental observation that the viscoelastic fluid in the microchannel with rhombic and equilateral hexagonal cross-section significantly influences on the particle migration toward the channel center owing to coupled effect of inertia and elasticity.