Particle Velocity Correlation Research Articles

EXPERIMENTAL STUDY OF LAGRANGIAN MIXING IN WEAKLY DISSIPATIVE TIDAL CHANNELS

Estuaries are extremely dynamic environments, allowing wildlife to grow in a wide variety of ecosystems because of the interaction of masses of water with different characteristics. In particular, coastal bays and estuaries are characterized by flows driven by hydraulic unbalance such as baroclinic pressure gradients, river inflows and wind stresses, and tidal waves. Here, following a reductionist approach, we examine dispersion processes in a physical model of a tidal channel bounded by an inlet mouth, with tides as the dominant forcing. The presence of a tidal inlet can generate macro-vortices that during a tidal cycle may influence the momentum and mass transport on relatively large distances (Awaji et al. (1980), Awaji (1982), Branyon et al. (2022)). Moreover, tides tend to produce non-monotonic particle velocity correlation leading to possible particle looping trajectories that also reflect on a looping character of the Lagrangian integral time scales, differently from the classical statistically steady or homogeneous turbulence (Enrile et al. (2019)). Our goal is to examine the dispersion regimes by means of two-dimensional velocity measurements at the free surface reproduced in a large-scale physical model as a starting point for Lagrangian analysis. We show how the presence of a tidal inlet generates complex flow patterns depending on the character of the forcing tides. Furthermore, the mixed nature of tides may be crucial to dispersion processes, as it enhances the ability of the flow to transport mass in the direction of the main flow.

Particle motion within the viscous sublayer of a turbulent shear flow

The motion of isolated heavy particles on the bottom wall of a turbulent shear flow is investigated experimentally (using high-frequency particle tracking) and correlated to that of the fluid (from high-resolution LDV measurements). Numerous particle diameters, particle densities, and flow velocities are considered, where the particles remain within the viscous sublayer (particle Reynolds number lower than 10). It is shown that fluid flow fluctuations within the viscous sublayer (varying Couette flow) induce particle velocity fluctuations of the same magnitude, slightly smaller. The mean particle velocity, standard deviation, and Lagrangian correlation time are found to scale with the viscous scales. Particles roll and slide without takeoff, unlike what happens in viscous laminar flow where the lift force may overcome the immersed particle weight. Arguments are given for this difference. Probability density functions for the streamwise and spanwise velocity are found to follow Gamma and Gaussian laws, respectively, which also scale with the viscous scales.

Experimental analysis of particle velocity and acceleration in vertical dilute phase pneumatic conveying

Many parameters need to be investigated in order to reduce power consumption, product degradation and flawless operation of pneumatic conveying systems. Particle velocity in vertical conveying is one such parameter that we are focussing on in this study. Many correlations were developed to predict particle velocity in steady state zone. Still, they lacked in consistency for finding any correlation that would explain particle velocity in acceleration zone as well as in fully developed flow. In this study, an experimental system was developed with 5 m vertical test section having 50 mm ID of pipe. Materials selected were representing a large range of Archimedes number (102–107). Very small quantities (Diluted) of various materials were manually fed into the upward conveying airflow using a piston forced particle feeder. Particle velocities were measured in acceleration as well as in fully developed region. Visuals of particle flow were recorded using high-speed camera and analyzed by a Matlab programme, specially developed for this analysis. Terminal velocity analysis (up-ss = ua–uT) has been used to predict steady state velocity. Terminal velocity analysis was found to have good agreement with previously published data by using its (terminal velocity) true value. Correlation of particle velocity and acceleration length was developed based on the investigation of statistical velocity distribution at different locations in vertical test section. The developed parameters of vertical conveying in this study have been compared with horizontal conveying results of [1]. Different relative curves (horizontal and vertical) were developed and a new threshold velocity (VH-identical velocity) was added to the master curve developed by [2]. These developed correlations and curves will help in designing and operation of pneumatic conveying systems.

Wave-Induced Reynolds Stress in Three-Dimensional Nearshore Currents Model

ABSTRACT Chun, H. and Suh, K.-D., 2016. Wave-induced Reynolds stress in three-dimensional nearshore currents model. This paper presents the formulation of the wave-induced Reynolds stress (WIRS), i.e. the correlation of horizontal and vertical water particle velocities, based on the Airy's wave theory. Even though the correlation of the velocities is zero in a constant-depth water, it has a nonzero value if there are slopes on the bottom and mean water level. Comparison of the vertical gradient of the WIRS term with the horizontal gradient of wave-forcing terms shows that the two terms have the same order of magnitude, which in turn is comparable to that of the radiation stress in the surf zone. For the three-dimensional computation of nearshore currents, the WIRS term is incorporated into a three-dimensional ocean model in the σ coordinates. The numerical model is then applied to two laboratory experiments. To see the effect of the WIRS term on the mean flow, numerical simulations without this term are a...

Overview of existing Langevin models formalism for heavy particle dispersion in a turbulent channel flow

The purpose of the paper is to compare two successful families of stochastic model for the prediction of inertial particles dispersion in a turbulent channel flow. Both models are based on the Langevin equation; nevertheless, they were developed following different paths. The first model considered is named “Drift Correction model (DCM)”, and the second one is the “Generalized Langevin Model (GLM)”. To examine the capabilities of both models, a comparison of the results predicted by the DCM- and GLM-type dispersion models with those extracted from a Direct Numerical Simulation (DNS) is conducted. In the limit of vanishing particle inertia, both models can accurately predict second-order statistics. It is also noticed, as not expected, that they are very similar when they are written in the same functional form. The comparison has also been conducted with DNS data of a particle-laden channel flow. The comparison of particle statistics (such as concentration, mean and rms particle velocity, third-order particle velocity correlations) shows that both stochastic models give very satisfactory results up to second-order statistics. The DCM- and GLM-type dispersion models studied can capture the main physical mechanisms that govern particle-laden turbulent channel flows.

Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

We investigate the response of large inertial particle to turbulent fluctuations in an inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding particle dynamics and may permit stochastic process modelization using two-time models (for instance, Sawford’s). As particles are tracked over long times in the quasi-totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration.

Fluctuating hydrodynamics in periodic domains and heterogeneous adjacent multidomains: Thermal equilibrium.

We first study fluctuating hydrodynamics (FH) at equilibrium in periodic domains by use of the smoothed dissipative particle dynamics (SDPD) method. We examine the performance of SDPD by comparing it with the theory of FH. We find that the spatial correlation of particle velocity is always the Dirac δ function, irrespective of numerical resolution, in agreement with the theory. However, the spatial correlation of particle density has a finite range of r(c), which is due to the kernel smoothing procedure for the density. Nevertheless, this finite range of correlation can be reduced to an arbitrarily small value by increasing the resolution, that is, reducing r(c), similarly to how the smoothing kernel converges to the Dirac δ function. Moreover, we consider temporal correlation functions (CFs) of random field variables in Fourier space. For sufficient resolution, the CFs of SDPD simulations agree very well with analytical solutions of the linearized FH equations. This confirms that both the shear and sound modes are modeled accurately and that fluctuations are generated, transported, and dissipated in both thermodynamically and hydrodynamically consistent ways in SDPD. We also show that the CFs of the classical dissipative particle dynamics (DPD) method with proper parameters can recover very well the linearized solutions. As a reverse implication, the measurement of CFs provides an effective means of extracting viscosities and sound speed of a DPD system with a new set of input parameters. Subsequently, we study the FH in truncated domains in the context of multiscale coupling via the domain decomposition method, where a SDPD simulation in one subdomain is coupled with a Navier-Stokes (NS) solver in an adjacent subdomain with an overlapping region. At equilibrium, the mean values of the NS solution are known a priori and do not need to be extracted from actual simulations. To this end, we model a buffer region as an equilibrium boundary condition (EBC) at the truncated side of the SDPD simulation. In the EBC buffer, the velocity of particles is drawn from a known Gaussian distribution, that is, the Maxwell-Boltzmann distribution. Due to the finite range of spatial correlation, the density of particles in the EBC buffer must be drawn from a conditional Gaussian distribution, which takes into account the available density distribution of neighboring interior particles. We introduce a Kriging method to provide such a conditional distribution and hence preserve the spatial correlation of density. Spatial and temporal correlations of SDPD simulations in the truncated domain are compared to that in a single complete domain. We find that a gap region between the buffer and interior is important to reduce the extra dissipation generated by the artificial buffer at equilibrium, rendering more investigations necessary for thermal fluctuations in the multiscale coupling of nonequilibrium flows.

Correlations in Single File Diffusion: Open and Closed Systems

We present a discussion of positional and velocity correlations of particles in single-file diffusion, based on some earlier work. We consider two physical situations: (a) An open system of N hard-core particles on an infinite line. (b) A large system with a fixed density of hard-core particles at an arbitrary temperature. In the first case (a), moments and correlations show unusual behavior. The average displacement of a particle is nonzero and grows as t1/2. Furthermore it depends on the position of the particle. Particles on the right of center are pushed right and those on the left are pushed left. The mean-square displacement also depends on the position. The diffusion constant is small for particles around the center but grows rapidly toward edges. Certain correlations in particle displacement grow with separation. For the second case (b) we give exact results for velocity-velocity auto-correlator of a tagged particle and establish that with time this correlator becomes negative and approaches zero as a power-law t-3/2 at long times. The mobility of the tagged particle is shown to decrease rapidly with density as has been observed in experiments. [Formula: see text] Special Issue Comments: This article presents mathematical results on the dynamics in expanding files, and constant density files. This article is connected to the Special Issue articles about advanced statistical properties in single file dynamics29 and files with force and advanced formulations.30

Characteristics of a new dust coordinate sensor

A new in-beam dust coordinate sensor (DCS) at the Colorado Center for Lunar Dust and Atmospheric Studies (CCLDAS) dust accelerator facility has been constructed and is now in use. The dust sensor operates by measuring the image charges induced on two planes of wire electrodes by passing charged dust particles. Applications for the DCS include the quantitative evaluation and improvements of the focusing and steering elements of the accelerator, and the correlation of particle velocity and mass with impact sites using precision particle location. For focusing and steering improvements, particle positions to 0.25 mm are plotted in real-time. It is possible to determine a typical particle’s position within the beamline to < 0.1 mm. The design, simulation and results of the DCS are further discussed.

A geometric model for the spatial correlation of an acoustic vector field in surface-generated noise

Spatial correlation of sound pressure and particle velocity of the surface noise in horizontally stratified media was demonstrated, with directional noise sources uniformly distributed on the ocean surface. In the evaluation of particle velocity, plane wave approximation was applied to each incident ray. Due to the equivalence of the sound source correlation property and its directivity, solutions for the spatial correlation of the field were transformed into the integration of the coherent function generated by a single directional source. As a typical horizontally stratified media, surface noise in a perfect waveguide was investigated. Correlation coefficients given by normal mode and geometric models show satisfactory agreement. Also, the normalized covariance between sound pressure and the vertical component of particle velocity is proportional to acoustic absorption coefficient, while that of the surface noise in semi-infinitely homogeneous space is zero.

Multi-scale analysis on particle fluctuation velocity near the minimum pressure drop in a horizontal pneumatic conveying

Multi-scale characteristics of particle fluctuation velocity at the MPD (minimum pressure drop) air velocity in the acceleration and fully-developed regimes are experimentally investigated. The high-speed particle image velocimetry (PIV) is first used to measure the fluctuating particle velocities at the MPD air velocity in a horizontal pneumatic conveying. Then the fluctuating particle velocities in the acceleration and fully-developed regimes are analyzed by the continuous wavelet transform and orthogonal wavelet multi-resolution technique. It is found that the wavelet components of low frequency dominate the fluctuating energy of axial particle velocity in the bottom part of the pipe, and contribute about 70% and 84% to the acceleration and fully-developed regimes, respectively. The more contribution to the fluctuating energy of vertical particle velocity, however, comes from the wavelet components of high frequency, accounting for about 82%. The low frequency component of auto-correlation suggests a large-scale particle flow in both acceleration regime and fully-developed regime. The low frequency wavelet component also makes a large contribution to spatial correlation of axial particle velocity, which increases from the acceleration regime to fully-developed regime. The PDF of low frequency components are asymmetrical near the bottom of the pipe, but the PDF of the relatively high frequency exhibits symmetry and the spread of the PDF evidently shrinks for increasing frequencies, implying a reducing fluctuation of high frequency component.

Velocity correlations of a discrete-time totally asymmetric simple-exclusion process in stationary state on a circle

The discrete-time version of totally asymmetric simple-exclusion process (TASEP) on a finite one-dimensional lattice is studied with the periodic boundary condition. Each particle at a site hops to the next site with probability 0≤p≤1 if the next site is empty. This condition can be rephrased by the condition that the number n of vacant sites between the particle and the next particle is positive. Then the average velocity is given by a product of the hopping probability p and the probability that n≥1. By mapping the TASEP to another driven diffusive system called the zero-range process, it is proved that the distribution function of vacant sites in the stationary state is exactly given by a factorized form. We define k-particle velocity correlation function as the expectation value of a product of velocities of k particles in the stationary distribution. It is shown that it does not depend on positions of k particles on a circle but depends only on the number k. We give explicit expressions for all velocity correlation functions using the Gauss hypergeometric functions. Covariance of velocities of two particles is studied in detail, and we show that velocities become independent asymptotically in the thermodynamic limit.

Multipoint concentration statistics for transport in stratified random velocity fields

We determine the full multipoint concentration statistics for superdiffusive transport in a steady stratified random velocity field. Using a Lagrangian approach, we derive explicit analytical expressions for the multipoint moments of concentration and specifically for the concentration variance, which is a measure for concentration uncertainty. The multipoint concentration moments are fully characterized by the Lagrangian mean velocity and by the one and two particle velocity correlations. While the relative variance at the center of mass of the mean concentration is constant, it increases exponentially with time and distance from the center of mass. This implies that small concentration values are particularly uncertain, which can pose a serious practical concern as these are typically the earliest and latest to arrive at a point.

A second-order moment method of dense gas–solid flow for bubbling fluidization

Abstract A gas–solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid–particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229–263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1–041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas–solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241–253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158–168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1–2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241–253] and 1.1–4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158–168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour–Daniel lecture. Powder Technology 148, 123–141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241–253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158–168].

Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift velocity in the limits of low and high particle inertia, is derived. It is also shown that some previously proposed stochastic models are not compatible with this transport equation in the limit of high particle inertia. The drift and diffusion parameters of these stochastic differential equations are then estimated using direct numerical simulation (DNS) data. It is observed that, contrary to the conventional modeling, they are highly space dependent and anisotropic. To investigate the performance of the present stochastic model, a comparison is made with DNS data as well as with two different stochastic models. A good prediction of the first and second order statistical moments of the particle and fluid seen velocities is obtained with the three models considered. Even for some components of the triple particle velocity correlations, an acceptable accordance is noticed. The performance of the three different models mainly diverges for the particle concentration and the drift velocity. The proposed model is seen to be the only one which succeeds in predicting the good evolution of these latter statistical quantities for the range of particle inertia studied.

Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence

The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1–46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic Eulerian approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St K = 0.17 and 2.2 . In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St K = 2.2 , particle number density and RUE spatial distribution predicted by the mesoscopic Eulerian approach are more smooth with respect to the ones measured from the Lagrangian simulations results. Similarly, the Eulerian approach underestimates the mesoscopic kinetic energy for the high wavenumber modes while the agreement remains very good for the low wavenumber modes. For both cases, the mesoscopic Eulerian approach provides a good prediction of the time dependent particle and fluid-particle velocity correlations measured by spatial averaging in the whole computational domain.

One‐Dimensional Modeling of Transport in Soils with Depth‐Dependent Dispersion, Sorption and Decay

Macroscopic spatial variations in advection velocity lead to an increase in dispersion with increasing travel distance or depth. In soils, this increase goes along with a decrease in decay and sorption of organic substances. We used three different one‐dimensional models that make different assumptions about the dispersion process to compare predicted leaching in a 1‐m‐deep soil profile with layers with different sorption and decay parameters. The first two convective–dispersive models assume that dispersion results from microscopic variations in solute particle velocities that are not correlated across soil layer boundaries. The third model, a stream tube model (STM), assumes that the particle velocity remains constant along its trajectory and is perfectly correlated in different layers. The three models were parameterized to predict the same inert tracer breakthrough curve (BTC) at 1‐m depth. The first convective–dispersive model assumes a constant dispersion coefficient (“homogeneous” convection–dispersion equation [CDE]). The second model uses different dispersion coefficients in the different layers (“layered” CDE) to predict the same inert tracer BTCs as the STM at the layer boundaries. Despite similar predictions of inert tracer BTCs, the models predicted different BTCs of reactive substances at 1‐m depth. The different predictions by the STM and layered CDE illustrate the importance of the correlation of solute particle velocities in different soil layers. They also point to a fundamental problem related to the use of a CDE with a depth‐dependent dispersion to mimic a dispersion process caused by macroscopic variations in particle velocities.

Multi-sources distinguishing of vector transducer via differential evolution

Vector transducer can simultaneously measure components of particle velocity as well as pressure at some point in sound field. In this paper, a series of equations are obtained from the correlation of particle velocity and pressure of the incident wave field, the error of each equation with white noise is studied, and Differential Evolution is used in solving the equations to distinguish multi-sources. Results of computer simulation show that Differential Evolution has more superiority than Genetic Algorithms on the rate and precision of convergence under the same condition.

Optimal design of a cold spray nozzle by numerical analysis of particle velocity and experimental validation with 316L stainless steel powder

The optimization of exit diameter of a cold spray nozzle under different spray conditions was investigated numerically for the first time. The optimal expansion ratio is influenced by the gas conditions, particle size, nozzle divergent section length and throat diameter. The optimal expansion ratio increases with the increases in gas pressure and nozzle divergent length. It decreases with the increases in gas temperature, particle size and nozzle throat diameter. The optimal expansion ratio using He is less than that using N 2 under the same operating conditions. The experiment with a 316L stainless steel powder indicates that a dense 316L stainless steel coating with a high microhardness can be deposited with an optimized nozzle using air as an accelerating gas owing to the high particle velocity. The good correlation of particle velocity with the coating microstructure and microhardness confirmed the optimal design method.

Autocorrelations from the scale dependence of transverse-momentum fluctuations in Hijing-simulated Au–Au collisions at [formula omitted

We present measurements of the scale (bin-size) dependence of event-wise mean transverse momentum 〈pt〉 fluctuations for Au–Au collisions at sNN=200GeV simulated with the Hijing-1.37 Monte Carlo. We invert those scale distributions to obtain autocorrelation distributions on pseudorapidity η and azimuth ϕ difference variables (ηΔ,ϕΔ). The autocorrelations have a simple structure dominated by a same-side (on azimuth) peak with similar widths on the two difference variables. With jet quenching imposed, the same-side peak widths increase slightly in both directions, and the amplitude is substantially reduced. The same-side peaks are attributed to minijets, observed in this study as local velocity correlations of charged particles with pt<2GeV/c.