Regions Of High Vorticity Research Articles

Experimental study on a non-dilute two-phase coflowing jet: Dynamics of particles in the near flow field

The dynamics of particles in multi-phase jets has been widely studied due to its importance for a broad range of practical applications. The present work describes an experimental investigation on an initially non-dilute two-phase jet, aimed at improving the understanding in this field. A two-color PDPA has been employed to measure simultaneously the velocity and size of particles. The measurements are post-processed to check the reliability of the results and to derive information on particle volume flux as an indication of their concentration. Acoustic forcing is applied in order to control coherent structures, which are responsible for mixing and transport phenomena, and also to get phase-locked measurements. Phase-averaged statistics enabled to freeze the jet structure, not visible in the time-averaged data. The results along the jet centerline confirm that drag forces and the spread angle of the jet initially control particle dispersion, very near the nozzle exit ( x/ D < 4). However, as the vortical structures evolve forming tongue-shaped structures, the total particle volume flux is augmented when these structures connect with the main stream ( x/ D > 5). This is due to an increase of the number of smaller size particles, even when a decrease of the number of larger size particle is observed. Further analysis at five cross-stream sections across two consecutive vortices confirm that small particles are convected around the coherent structure and then incorporated to the main stream, increasing the particle concentration at the jet core. On the other hand, the number of larger particles (as well as their contribution to axial volume flux) starts to decay in regions of high azymuthal vorticity. This behaviour is partly ascribed to the transversal lift force, associated to the large spatial gradients observed in these regions. Saffman and Magnus forces have been estimated to be comparable or even greater than radial drag forces. The results suggest that the Saffman force might accelerate particles in radial direction, inducing a high radial volumetric flow rate from high to low axial velocity regions.

A spectral projection method for the analysis of autocorrelation functions and projection errors in discrete particle simulation

AbstractDiscrete particle simulation is a well‐established tool for the simulation of particles and droplets suspended in turbulent flows of academic and industrial applications. The study of some properties such as the preferential concentration of inertial particles in regions of high shear and low vorticity requires the computation of autocorrelation functions. This can be a tedious task as the discrete point particles need to be projected in some manner to obtain the continuous autocorrelation functions.Projection of particle properties on to a computational grid, for instance, the grid of the carrier phase, is furthermore an issue when quantities such as particle concentrations are to be computed or source terms between the carrier phase and the particles are exchanged. The errors committed by commonly used projection methods are often unknown and are difficult to analyse. Grid and sampling size limit the possibilities in terms of precision per computational cost.Here, we present a spectral projection method that is not affected by sampling issues and addresses all of the above issues. The technique is only limited by computational resources and is easy to parallelize. The only visible drawback is the limitation to simple geometries and therefore limited to academic applications.The spectral projection method consists of a discrete Fourier‐transform of the particle locations. The Fourier‐transformed particle number density and momentum fields can then be used to compute the autocorrelation functions and the continuous physical space fields for the evaluation of the projection methods error. The number of Fourier components used to discretize the projector kernel can be chosen such that the corresponding characteristic length scale is as small as needed. This allows to study the phenomena of particle motion, for example, in a region of preferential concentration that may be smaller than the cell size of the carrier phase grid.The precision of the spectral projection method depends, therefore, only on the number of Fourier modes considered. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Triple-point shear layers in gaseous detonation waves

Recent experiments have shown intriguing regions of intense luminescence or ‘hotspots’ in the vicinity of triple-point shear layers in propagating gaseous detonation waves. Localized explosions have also been observed to develop in these fronts. These features were observed in higher effective activation energy mixtures, but not in lower effective activation energy mixtures. The increased lead shock oscillation through a cell cycle in higher activation energy mixtures may result in a significantly increased disparity in the induction time on either side of the triple-point shear layer, and thus an enhanced mixing between reacted and non-reacted streams supported by Kelvin–Helmholtz instability. The relation between the shear-layer instability and the mixture effective activation energy is analysed by carrying out a spatial linear stability study for three mixtures with different activation energies and injection conditions that correspond to the experimental conditions. The role of vortical structures associated with Kelvin–Helmholtz instability in the formation of localized ignition is investigated by performing two-dimensional Navier–Stokes simulations with detailed chemical kinetics and transport. In the low activation energy mixture, large-scale vortical structures are observed to occur downstream of the induction distance; these structures do not have a noticeable effect on the reaction. In higher effective activation energy mixtures, a thin transverse ignition front develops near the interface between the two gas streams and results in a combustion structure decoupled from the entrainment region. The decoupling leads to attenuation of the instability growth rate when compared to frozen calculations, and a reduced heat release in the high vorticity region. The analysis indicates the instability plays a modest role in ignition events for high activation energy mixtures. The formation of localized explosions observed in high activation energy systems is instead linked to the impossibility of a one-dimensional reactive combustion wave supported by the injection conditions. In the absence of curvature effects and stream-tube divergence, a system of shock waves is formed which spreads the ignition to the cold gas stream.

Surface current effects on the fetch‐limited growth of wave energy

To study the fetch‐limited growth of wind wave energy over a region with significant lateral shear of the current field, this study exploited data obtained from two linear phased‐array High Frequency (HF) radar systems. Both the near‐surface currents and wave energy and period were mapped over the highly sheared inshore boundary of the Florida Current. The wave energy growth during two periods when the winds were steady for &gt;12 hours and were directed offshore was computed over a range of fetches from 5 to 45 km. The observed energy growth rates were significantly (∼50 %) lower than predicted by the Donelan et al. (1992) empirical formulation over the high vorticity region. The reduced growth rate was consistent with a shift of the wind stress direction into the current direction due to refraction of the wave field. Dimensionless wave energy increased by as much as 100% over neighboring values when the vertical component of the surface current vorticity was a global minimum. While trapping and enhancement of wave energy is predicted by wave ray theory, it has never before been confirmed within the Florida Current with coincident wave and current measurements.

Regularity criteria for the generalized viscous MHD equations

In this paper, we consider regularity criteria for solutions to the 3D generalized MHD equations with fractional dissipative term −(−Δ)αu for the velocity field and −(−Δ)βb for the magnetic field. For the case α=β, it is proved that if the velocity field belongs to Lp,q with 2α/p+3/q⩽2α−1 or the gradient of velocity field belongs to Lp,q with 2α/p+3/q⩽3α−1 on [0,T], then the solution remains smooth on [0,T]. The significance is that there is no restriction on the magnetic field. Moreover, the norms ‖u‖Lp,q and ‖Λαu‖Lp,q are scaling dimension zero for 2α/p+3/q=2α−1 and 2α/p+3/q=3α−1 respectively. For 1⩽β⩽α, we find that the minimum sum of α and β to guarantee the global existence of smooth solutions is 52. Furthermore, we show that the weak solution actually is strong if the corresponding vorticity field ω=∇×u satisfies certain condition in the high vorticity region.

Large eddy simulation of particle settling in the ocean mixed layer

The settling process of suspended particles in the turbulent flow was investigated by analyzing the Lagrangian motion of a large number of particles in the ocean mixed layer simulated by large eddy simulation (LES), focusing on the role of Langmuir circulation (LC). At the beginning, particles released near the surface are swept down rapidly following the downward jets in the presence of LC, contrary to the case of the horizontally uniform downward propagation in the absence of it. The strong vertical mixing by LC keeps the particle concentration almost uniform after the initial period in the presence of LC, while its mean concentration continues to decrease through particle settling. Under the influence of turbulence in the ocean mixed layer, the particle settling velocity W is always smaller than ws, and W∕ws decreases with decreasing ws∕u∗, where ws is the terminal velocity of a particle in the still fluid and u∗ is the frictional velocity. The presence of LC causes a further decrease of W ultimately, and the difference between the cases with and without LC is the largest at ws∕u∗∼1. The analysis of LES data reveals that particles spend more time in upward flows and that more particles tend to accumulate in the high vorticity region in the presence of LC. It suggests that particle trapping is more likely when the length scale of vortices is larger, which may lead to the decrease of W in the presence of LC. It was also found that the preferential concentration occurs away from the regions of high horizontal vorticity and divergence when ws∕u∗∼1.

Geometry of particle paths in turbulent flows

We use the intrinsic geometrical characteristics of space curves, i.e. curvature and torsion, to describe the paths of particles passively advected in a turbulent flow. We find that curvature increases with the Reynolds number and that the maxima in vorticity and curvature times local velocity are linearly correlated. Fluctuations around the maximal values in runs at a fixed Reynolds number are only weakly correlated, and the distributions are fairly wide, so that it is not possible to conclude that a tightly wound spiral has to correspond to a region of high vorticity.

Numerical research on heat transfer enhancement for high Prandtl-number fluid

The molten salt, Flibe, has been recommended as a candidate coolant material in the blanket system of the FFHR fusion reactor though it is high Prnadtl-number ( Pr) fluid that leads to low heat transfer performance. This paper, describes the results of numerical simulations performed in order to estimate the effects of cylinders as obstructions for heat-transfer enhancement in high- Pr fluid duct flow. Two-dimensional thermofluid simulations were performed for cases with 44, 24 and 48 cylinders, respectively, inserted perpendicularly to the fluid flow, and acting as heat transfer enhancers between parallel plates. From these analyses, the flow contraction created by the cylinders causes a high-vorticity around the heated wall. This high-vorticity plays an important role in the heat-transfer enhancement. In the high-vorticity region, the momentum perpendicular to a wall has a large gradient along the stream direction. In fact, the fluid flows down while rotating and “washing” the heated wall. This effect is also governed by the arrangement of cylinders. A staggered arrangement is adopted in the case with 44 cylinders, while square arrangement is employed in the cases with 24 and 48 cylinders. The enhancement of perpendicular flow is very effective when using a staggered arrangement, procuring a higher heat transfer downstream of the cylinders. The estimated pressure drop for high- Pr fluid flow was larger for the with 44 cylinders than for the cases with 24 and 48 cylinders. This result indicates that the heat transfer of high- Pr fluid flow strongly depends on the effect of flow stirring caused by obstructions.

Clustering of aerosol particles in isotropic turbulence

It has been recognized that particle inertia throws dense particles out of regions of high vorticity and leads to an accumulation of particles in the straining-flow regions of a turbulent flow field. However, recent direct numerical simulations (DNS) indicate that the tendency to cluster is evident even at particle separations smaller than the size of the smallest eddy. Indeed, the particle radial distribution function (RDF), an important measure of clustering, increases as an inverse power of the interparticle separation for separations much smaller than the Kolmogorov length scale. Motivated by this observation, we have developed an analytical theory to predict the RDF in a turbulent flow for particles with a small, but non-zero Stokes number. Here, the Stokes number (. Predictions of the analytical theory are compared with two types of numerical simulation: (i) particle pairs interacting in a local linear flow whose velocity varies according to a stochastic velocity gradient model; (ii) particles interacting in a flow field obtained from DNS of isotropic turbulence. The agreement with both types of simulation is very good. The theory also predicts the RDF for unlike particle pairs (particle pairs with different Stokes numbers). In this case, a second diffusion process occurs owing to the difference in the response of the pair to local fluid accelerations. The acceleration diffusivity is independent of the pair separation distance; thus, the RDF of particles with even slightly different viscous relaxation times undergoes a transition from the power law behaviour at large separations to a constant value at sufficiently small separations. The radial separation corresponding to the transition between these two behaviours is predicted to be proportional to the difference between the Stokes numbers of the two particles. Once again, the agreement between the theory and simulations is found to be very good. Clustering of particles enhances their rate of coagulation or coalescence. The theory and linear flow simulations are used to obtain predictions for the rate of coagulation of particles in the absence of hydrodynamic and colloidal particle interactions.

Fin whales Balaenoptera physalus and minke whales Balaenoptera acutorostrata exploit a tidally driven island wake ecosystem in the Bay of Fundy

Marine predators forage in tidally induced oceanographic features, where they exploit predictable aggregations of prey. Very little, however, is known about how the physical forcing within these features affects their behaviour at a fine scale. During the summers of 2000 and 2002, we combined a series of cliff-top observations and boat-based surveys to describe the movements of fin whales Balaenoptera physalus and minke whales Balaenoptera acutorostrata within a predictable island wake occurring near Grand Manan Island in the Bay of Fundy, Canada. We recorded the loca- tion of fin and minke whales as they surfaced in or near the wake. We also examined the movements of individual fin whales using focal follow techniques to assess their habitat use within 3 distinct oceanographic regions (non-wake habitat, eddy habitat and free stream habitat) of the study area. Fin and minke whale occurrence was highest during flood tides and lowest during the mid-ebb phases. Fin (33) and minke whale (64) sightings were concentrated in areas characterised by slower current velocities — the region influenced by the eddy system formed within the wake. Nine individ- ual fin whales, identified through photographs, spent a disproportionate amount of time within the eddy habitat portion of the study area, with occasional forays into free stream habitat. Foraging in the high-vorticity regions of the wake likely allows whales to exploit higher prey concentrations than in the free stream habitat or non-wake habitat.

Preferential concentration of particles in isotropic turbulence: a comparison of the Lagrangian and the equilibrium Eulerian approaches

In this brief note, we present a study of the preferential concentration of particles in isotropic turbulence using the fast Eulerian method [Int. J. Multiph. Flow 27 (2001) 1199]. The advantage of the fast Eulerian method is that it obviates the need to solve additional governing equations for the particulate phase. For small particle response times, Ferry and Balachandar [Int. J. Multiph. Flow 27 (2001) 1199] show that a unique equilibrium Eulerian particle velocity field, v( x, t), independent of initial conditions can be obtained. The resultant expansion in τ p is an explicit function of the fluid velocity field, u( x, t), and its spatial and temporal derivatives. In the current work, a truncated expansion of the particle velocity field, accurate to O( τ p), is used to calculate statistics of particle dispersion and preferential accumulation in isotropic turbulence. These statistics are compared with those from the Lagrangian evolution of particles. There is good agreement for small τ p, where the theory is best applicable. Preferential concentration properties of dense particles as well as bubbles are studied. It is demonstrated that instantaneous velocities of exact Lagrangian particles agree well with those evaluated by interpolating the Eulerian particle velocity field to the particle positions. In addition, particles evolved using the Eulerian velocity field exhibit similar long-time spatial distribution as the exact particles, indicating that there is no accumulation of errors in time. Specifically, the concentration of dense particles in high strain-rate regions and of bubbles in high vorticity regions is accurately captured by the Eulerian method.

Preferential concentration of particles in a fully developed turbulent square duct flow

The preferential concentration of dense particles in a downward, fully developed turbulent square duct flow at Re τ =360, based on mean friction velocity and duct width, is studied using large eddy simulations. Due to the low volume fractions involved (maximum volume fraction <10 −5), one-way coupled simulations are performed, i.e., two-way coupling and particle–particle collisions are not considered. The continuous and the dispersed phases are treated using Eulerian and Lagrangian approaches, respectively. A finite volume based second-order accurate fractional step scheme is used to integrate the unsteady, three-dimensional Navier–Stokes equations. The subgrid stresses are modeled with a dynamic subgrid kinetic energy model, as reported previously. The particle equation of motion includes drag, lift and gravity forces and is integrated using the fourth-order accurate Runge–Kutta method. Four cross-sectional locations representative of the mean secondary flow patterns and six particle response times were chosen to study the effect of location and particle inertia on preferential concentration. To demonstrate preferential concentration, variation of vorticity magnitude, swirling strength, maximum compressional strain-rate, and ∇ u : ∇ u , and their probability distribution functions (PDF) conditioned on particle presence, with particle response time is presented. Since the square duct cross-section is inhomogeneous, we also study variation in preferential concentration with cross-sectional location. Particles are seen to accumulate in regions of high ∇ u : ∇ u and strain-rate and in regions of low swirling strength. In general, particles accumulate in regions of low vorticity magnitude. However, near the wall, the tendency of particles to accumulate in regions of high vorticity increases with response time.

Dense estimation of fluid flows

In this paper, we address the problem of estimating and analyzing the motion of fluids in image sequences. Due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids, the standard techniques from computer vision, originally designed for quasi-rigid motions with stable salient features, are not well adapted in this context. We thus investigate a dedicated minimization-based motion estimator. The cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics, which is compatible with large displacements. This term is associated with an original second-order div-curl regularization which prevents the washing out of the salient vorticity and divergence structures. The performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images. In addition, we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence.

Microscopic Approach to Cloud Droplet Growth by Condensation. Part II: Turbulence, Clustering, and Condensational Growth

The goal of this work is to answer the question of whether nonuniformity in the spatial distribution of sizes and positions of cloud droplets and/or variable vertical velocity in a turbulent medium can contribute to the broadening of the droplet size distribution. A numerical approach to simulate the growth and trajectory of several tens of thousands of cloud droplets in a turbulent environment whose properties vary from droplet to droplet is used. The finite inertia of particles in a turbulent fluid causes particles to diverge from regions of high vorticity and to converge preferentially in regions of low vorticity, thus creating strong deviations in particle concentration. As a first step, the inertia effect was examined in the context of nongrowing, sedimenting, or nonsedimenting droplets. It was found that statistically significant preferential concentration is possible in conditions typical of cloud droplets in cumulus clouds. In the absence of sedimentation, preferential concentration increases as a function of the Stokes number St. Allowing the droplets to sediment decreases preferential concentration to a degree that increases with the velocity ratio Sυ. A series of experiments including condensational growth of droplets was then performed. It was found that while the increasing preferential concentration of droplets, as a result of increasing eddy dissipation rate, does result in increases in the instantaneous dispersion of the supersaturation perturbation distribution, the width of the size distribution of droplets, which is a function of the dispersion in the time integral of the supersaturation perturbations, decreases. This result is a consequence of the decrease in decorrelation time of the supersaturation perturbations as the turbulence intensity increases. Comparison of the results herein with the observations made in quasi-adiabatic cloud cores leads one to the conclusion that the microscopic approach, even under the most favorable condition of no turbulence, produces too little broadening to explain the observations.

Numerical Study of Eastern Boundary Ventilation and Its Effects on the Thermocline Structure

Abstract Numerical experiments with idealized OGCM are carried out to investigate the oceanic eastern boundary problems. The experimental results indicate that the eastward flow due to the north–south gradient of the surface density returns to the interior region through the lower half of the mixed layer, and this return flow generates a density jump just above the thermocline. Formulation for the mixed layer depth distribution at the eastern boundary is also presented, which is derived only from the geostrophy and no-normal flow condition. This formulation agrees well with the numerical experiment, and can be an appropriate eastern boundary condition for theoretical ventilated thermocline model with no deficiency of the mass balance on the boundary. Furthermore, the effects of such eastern boundary structure on the subtropical thermocline are studied. On the shallow thermocline in the subtropics, eastern boundary ventilated region emerges, which is identified as a region of high potential vorticity. In t...

The dayside ultraviolet aurora and convection responses to a southward turning of the interplanetary magnetic field

Abstract. We examine the large-scale ultraviolet aurora and convection responses to a series of flux transfer events that immediately followed a sharp and isolated southward turning of the IMF. During the interval of interest, SuperDARN was monitoring the plasma convection in the dayside northern ionosphere, while the VIS Earth Camera and the Far Ul-traviolet Imager (UVI) were monitoring the northern hemisphere’s ultraviolet aurora. Reconnection signatures were seen in the SuperDARN HF radar data in the postnoon sector following a sharp southward turning of the IMF. The presence of flux transfer events is supported by measurements of a classic dispersed ion signature in the low-altitude cusp from the DMSP spacecraft. Subsequent to the onset of reconnection, the postnoon convection and ultraviolet aurora expanded in concert, reaching 18 MLT in half an hour. The auroral oval was found to move equatorward at the convection speed in the 16–18 MLT sector, implying that it was related directly to an adiaroic magnetospheric boundary. In the present study, we have estimated the field-aligned current response to magnetic reconnection in terms of the vorticity of the ionospheric plasma convection velocity. The convection velocities were obtained using two methods: (a) direct reconstruction of the full vector velocities from bistatic measurements of the convection by the SuperDARN HF radars in a relatively small region of the auroral zone, and (b) from global-scale spherical harmonic fits to the SuperDARN velocities deduced from the map potential model. Regions of high vorticity, which were predicted to be an estimate of a component of the total field-aligned current, agree extremely well with the images of the dayside UV aurora, indicating that, in this case, the plasma vorticity is an excellent estimator of the morphology of dayside field-aligned currents (FACs). The morphology of the aurora and ionospheric electric field in the postnoon sector supports the existence of a dayside current wedge induced in response to dayside reconnection.Key words. Magnetospheric physics (auroral phenomena; magnetosphere-ionosphere interactions; solar wind magne-tosphere interactions)

Simultaneous particle image velocimetry and infrared imagery of microscale breaking waves

We report the results from a laboratory investigation in which microscale breaking waves were detected using an infrared (IR) imager and two-dimensional (2-D) velocity fields were simultaneously measured using particle image velocimetry (PIV). In addition, the local heat transfer velocity was measured using the controlled flux technique. To the best of our knowledge these are the first measurements of the instantaneous 2-D velocity fields generated beneath microscale breaking waves. Careful measurements of the water surface profile enabled us to make accurate estimates of the near-surface velocities using PIV. Previous experiments have shown that behind the leading edge of a microscale breaker the cool skin layer is disrupted creating a thermal signature in the IR image [Jessup et al., J. Geophys. Res. 102, 23145 (1997)]. The simultaneously sampled IR images and PIV data enabled us to show that these disruptions or wakes are typically produced by a series of vortices that form behind the leading edge of the breaker. When the vortices are first formed they are very strong and coherent but as time passes, and they move from the crest region to the back face of the wave, they become weaker and less coherent. The near-surface vorticity was correlated with both the fractional area coverage of microscale breaking waves and the local heat transfer velocity. The strong correlations provide convincing evidence that the wakes produced by microscale breaking waves are regions of high near-surface vorticity that are in turn responsible for enhancing air–water heat transfer rates.

An analytical model of the dynamic lift experienced by a bubble moving off-angle to an inviscid flow field with vorticity

As a bubble traverses an inviscid flow field possessing vorticity it experiences a lift force in proportion to the cross-product of the relative velocity difference and the flow field vorticity. The proper derivation of this force construct is important in the formulation of bubble trajectory models applied to high vorticity regions such as a shear flow, but is hampered by three aspects. First, there is disagreement as to the evolutionary basis of the lift force. Second, the models of lift force are derived for a nominal one-dimensional flow case, i.e., collinear bubble velocity and flow field velocity vectors, but are applied to general three-dimensional simulations where the two velocities are not necessarily co-planar. This vectorial generalization of dynamic lift has not been validated. Third, the mathematical model to predict lift force is awkward to apply in a numerical trajectory simulations. In the present study, we argue that the lift force derives from a contouring of the kinetic energy and convective potential-rate fields. This forms the basis for a simple predictive tool which is termed a split lamina model, which is capable of extracting an analytical validation of the vectorial generalization. Conceptually, the split lamina model artificially cleaves a bubble into two separate halves along the plane of the impinging flow field velocity. As each half-bubble resides a flow field of a slightly different velocity, the force acting on respective halves is calculated by integrating the defect in kinetic energy and convective potential-rate. Upon mathematical reassembly of the halves the registered force imbalance is assigned to be the lift force. For a simple shear flow, the split lamina technique predicts the analytical lift coefficients for a sphere to within three percent of the accepted value C L =1/2. Hence, promoting a study of the off-nominal flow conditions, the 3D vectorial generalization of Auton (1987. Journal of Fluid Mechanics, 183, 199–218) is subsequently validated by applying the velocity potential derived in Schrage (1998. Ph.D. thesis, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, May). For moderate three dimensionality, the split lamina model emulates the vectorial generalized lift force to within 10 percent. To simplify the conventional cross-product format, the lift force is compacted as an adjunct force tensor K which operates on the bubble relative velocity difference vector to describe the force in accordance with F L = ρV( a) K ( u − v).

A fast Eulerian method for disperse two-phase flow

We propose a variant of the Eulerian method for two-phase flow that is valid for small particle response time τ. For small τ, the particle velocity field v ( x ,t) approaches a unique, equilibrium field, independent of initial conditions. A precise inequality is derived specifying how small τ must be for this to occur. When it does, v ( x ,t) depends only on local fluid quantities (velocity and its spatial and temporal derivatives), and may be expressed as an expansion in τ. We derive an expansion which generalizes those of previous researchers. The first-order truncation of this expansion may be computed efficiently, so by using it to approximate v, the method avoids the need to solve additional partial differential equations, and therefore is much faster than the standard Eulerian method. Results from a direct numerical simulation of turbulent channel flow indicate that this first-order approximation of v is sufficiently accurate. Static tests performed at one time-instance show the actual velocities of particles evolved in a Lagrangian fashion are estimated well by evaluating the first-order approximation of v at the particles' positions. In particular, turbophoresis is represented accurately. Dynamic tests examine the effect of using the first-order approximation of v to evolve particles. The distribution of particles evolved in this way differs little from that of particles evolved using the standard Lagrangian method, indicating that static errors do not accumulate over time. In particular, the approximate method accurately captures preferential concentration in regions of high strain and low vorticity. Analogous results hold for bubbles. Therefore, for sufficiently small particles of any density, the first-order approximation to v is accurate, so the proposed variant of the Eulerian method is both accurate and fast.

Effect of inter-particle spacing on turbulence modulation by Lagrangian PIV

Abstract Turbulence modulation by solid particles in a fully developed channel flow was investigated by Lagrangian measurement technique. Digital particle image velocimetry (DPIV) and a high-speed CCD camera mounted on a shuttle moving with particle mean streamwise velocity were used to simultaneously detect particle and fluid information among particles. Two classes of particles at particle volumetric fraction up to 3.32×10 −4 were employed to provide characteristic values of length ratio and distance between particles, i.e., inter-particle spacing. Turbulence augmentation by particles greater than the Kolmogorov micro-length-scale was induced by a region of high strain rate and high vorticity located on both sides of the particles. The rapid distortion theory (RDT) applied to dispersed two-phase turbulent flows substantiates the observed directional non-isotropic structure with an increase in particle volumetric fraction. The enstrophy production was enhanced with decreasing values of inter-particle spacing, yielding an increase in the enstrophy among particles.