Pair Of Fluid Particles Research Articles

Lagrangian Particle Dispersion in a Poor Man’s Magnetohydrodynamic Turbulence Model

Lagrangian dispersion of fluid particle pairs refers to the study of how individual fluid particles disperse and move in a fluid flow, providing insights to understand transport phenomena in various environments, from laminar to turbulent conditions. Here, we explore this phenomenon in synthetic velocity and magnetic fields generated through a reduced-order model of the magnetohydrodynamic equations, which is able to mimic both a laminar and a turbulent environment. In the case of laminar conditions, we find that the average square distance between particle pairs increases linearly with time, implying a dispersion pattern similar to Brownian motion at all time steps. On the other hand, under turbulent conditions, surprisingly enough we observe a Richardson scaling, indicating a super-ballistic dispersion pattern, which aligns with the expected scaling properties for a turbulent environment. Additionally, our study reveals that the magnetic field plays an organizing role. Lastly, we explore a purely hydrodynamic case without magnetic field effects, showing that, even in a turbulent environment, the behavior remains Brownian-like, highlighting the crucial role of the magnetic field in generating the Richardson scaling observed in our model.

Chaotic advection and particle pairs diffusion in a low-dimensional truncation of two-dimensional magnetohydrodynamics

The chaotic advection of fluid particle pairs is investigated though a low-order model of two-dimensional magnetohydrodynamic (MHD), where only five nonlinearly interacting modes are retained. The model is inthrinsically inhomogeneous and anisotropic because of the influence of large-scale fluctuations. Therefore, even though dynamically chaotic, the fields are unable to form the typical scaling laws of fully developed turbulence. Results show that a super-ballistic dynamics, reminiscent of the Richardson law of particle-pairs diffusion in turbulent flows, is robustly obtained using the truncated model. Indeed, even in the strongly reduced truncation presented here, particle diffusion in MHD turbulence has the same laws as the separation of velocity of particle pairs. The inherent anisotropy only affects the scaling of diffusivity, by enhancing the diffusion properties along one direction for small time-scales. Finally, when further anisotropy is introduced in the system through Alfvén waves, fluid particles are trapped by these, and super-ballistic diffusion is replaced by Brownian-like diffusion. On the other hand, when the magnetic field is removed, the kinetic counterpart of the model does not show super-ballistic dynamics.

Particle pair dispersion and eddy diffusivity in a high-speed premixed flame

Turbulent mixing is a physical process of fundamental importance in high-speed premixed flames. This mixing results in enhanced transport of temperature and chemical scalars, leading to potentially large changes in flame structure and dynamics. To understand turbulent mixing in non-reacting flows, a number of classical theories have been proposed to describe the scaling and statistics of dispersing fluid particle pairs, including predictions of the effective, or turbulent, eddy diffusivity. Here we examine the validity of these classical theories through the study of fluid particle pair dispersion and eddy diffusivity in a highly turbulent premixed methane-air flame at a Karlovitz number of approximately 140. Using data from a direct numerical simulation and a higher-order Lagrangian tracking algorithm, particle pair centroids are seeded at different initial temperatures and separations, and then integrated forward in time. We show that scaling relations and results developed for pair dispersion in non-reacting flows remain relevant in this high-intensity premixed flame, and we identify the impacts of heat release on dispersion and eddy diffusivity.

Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network

An artificial neural network (ANN) is used to establish the relation between the resolved-scale flow field and the subgrid-scale (SGS) stress tensor, to develop a new SGS model for large-eddy simulation (LES) of isotropic turbulent flows. The data required for training and testing of the ANN are provided by performing filtering operations on the flow fields from direct numerical simulations (DNSs) of isotropic turbulent flows. We use the velocity gradient tensor together with filter width as input features and the SGS stress tensor as the output labels for training the ANN. In the a priori test of the trained ANN model, the SGS stress tensors obtained from the ANN model and the DNS data are compared by computing the correlation coefficient and the relative error of the energy transfer rate. The correlation coefficients are mostly larger than 0.9, and the ANN model can accurately predict the energy transfer rate at different Reynolds numbers and filter widths, showing significant improvement over the conventional models, for example the gradient model, the Smagorinsky model and its dynamic version. A real LES using the trained ANN model is performed as the a posteriori validation. The energy spectrum computed by the improved ANN model is compared with several SGS models. The Lagrangian statistics of fluid particle pairs obtained from the improved ANN model almost approach those from the filtered DNS, better than the results from the Smagorinsky model and dynamic Smagorinsky model.

Relative dispersion of particle pairs in turbulent channel flow

Lagrangian tracking of particle pairs is of fundamental interest in a large number of environmental applications dealing with contaminant dispersion and passive scalar mixing. The aim of the present study is to extend the observations available in the literature on relative dispersion of fluid particle pairs to wall-bounded turbulent flows, by means of particle pair tracking in direct numerical simulations (DNS) of a turbulent channel flow. The mean-square change of separation between particle pairs follows a clear ballistic regime at short times for all wall distances. The Eulerian structure functions governing this short-time separation are characterised in the channel, and allow to define a characteristic time scale for the ballistic regime, as well as a suitable normalisation of the mean-square separation leading to an overall collapse for different wall distances. Through fluid particle pair tracking backwards and forwards in time, the temporal asymmetry of relative dispersion is illustrated. At short times, this asymmetry is linked to the irreversibility of turbulence, as in previous studies on homogeneous isotropic flows. The influence of the initial separation (distance and orientation) as well as the influence of mean shear are addressed. By decomposing the mean-square separation into the dispersion by the fluctuating velocity field and by the average velocity, it is shown that the influence of mean shear becomes important at early stages of dispersion close to the wall but also near the channel centre. The relative dispersion tensor Δij is also presented and particularly the sign and time evolution of the cross-term Δxy are discussed. Finally, a ballistic cascade model previously proposed for homogeneous isotropic turbulence is adapted here to turbulent channel flows. Preliminary results are given and compared to the DNS. Future developments and assumptions in two particle stochastic models can be gauged against the issues and results discussed in the present study.

Von Kármán–Howarth and Corrsin equations closure based on Lagrangian description of the fluid motion

A new approach to obtain the closure formulas for the von Kármán–Howarth and Corrsin equations is presented, which is based on the Lagrangian representation of the fluid motion, and on the Liouville theorem associated to the kinematics of a pair of fluid particles. This kinematics is characterized by the finite scale separation vector which is assumed to be statistically independent from the velocity field. Such assumption is justified by the hypothesis of fully developed turbulence and by the property that this vector varies much more rapidly than the velocity field. This formulation leads to the closure formulas of von Kármán–Howarth and Corrsin equations in terms of longitudinal velocity and temperature correlations following a demonstration completely different with respect to the previous works. Some of the properties and the limitations of the closed equations are discussed. In particular, we show that the times of evolution of the developed kinetic energy and temperature spectra are finite quantities which depend on the initial conditions.

Two-Particle Separation in the Point Vortex Gas Model of Superfluid Turbulence

We study numerically statistical properties of the random mean square separation, Δ(t)=〈Δ2〉1/2 of fluid particle pairs in the Onsager’s point vortex gas, i.e. in a random, inviscid, two-dimensional flow generated by the motion of quantized point vortices of random polarities. This model is perhaps the simplest, two-dimensional model of superfluid turbulence in helium II at low temperatures when the normal fluid is absent. The existence of the inverse energy cascade through scales in such a system was discovered in the pioneering work by Onsager (Nuovo Cimento Suppl. 6:279, 1949). We found that the mean diffusivity of particle pairs, d〈Δ2〉/dt obeys, to a good degree of accuracy, the Richardson’s diffusion ‘four-third’ law, d〈Δ2〉/dt∼Δ4/3. We also analyzed the details of time evolution of the rms particle separation. At small time the particle separation is ballistic, while at large time, when the motion of individual particles in the considered pair becomes uncorrelated, the mean square separation follows the diffusion law, 〈Δ2〉∼t. For intermediate time we found that the root mean square separation, Δ=〈Δ2〉1/2 is very sensitive to the initial separation, due to the memory of initial separation kept by the particle pair during the initial period of exponential ballistic separation, so that the rms separation never follows the Richardson’s t3/2 scaling law. We characterized the time evolution of the rms particle separation in the vicinity of the inflexion point of the curve Δ(t) by the power law, \(\Delta\sim\gamma t^{\alpha(\Delta_{0})}\) , and found the dependence of α and γ on the initial separation Δ0, thus generalizing the Richardson’s t3/2-law for the considered two-dimensional point vortex gas.

Relative dispersion in isotropic turbulence. Part 1. Direct numerical simulations and Reynolds-number dependence

The relative dispersion of fluid particle pairs in isotropic turbulence is studied using direct numerical simulation, in greater detail and covering a wider Reynolds number range than previously reported. A primary motivation is to provide an important resource for stochastic modelling incorporating information on Reynolds-number dependence. Detailed results are obtained for particle-pair initial separations from less than one Kolmogorov length scale to larger than one integral length scale, and for Taylor-scale Reynolds numbers from about 38 to 230. Attention is given to several sources of uncertainty, including sample size requirements, value of the one-particle Lagrangian Kolmogorov constant, and the temporal variability of space-averaged quantities in statistically stationary turbulence.Relative dispersion is analysed in terms of the evolution of the magnitude and angular orientation of the two-particle separation vector. Early-time statistics are consistent with the Eulerian spatial structure of the flow, whereas the large-time behaviour is consistent with particle pairs far apart moving independently. However, at intermediate times of order several Kolmogorov time scales, and especially for small initial separation and higher Reynolds numbers, both the separation distance and its rate of change (called the separation speed) are highly intermittent, with flatness factors much higher than those of Eulerian velocity differences in space. This strong intermittency is a consequence of relative dispersion being affected by a wide range of length scales in the turbulent flow as some particle pairs drift relatively far apart. Numerical evidence shows that substantial dispersion occurs in the plane orthogonal to the initial separation vector, which implies that the orientation of this vector has, especially for small initial separation, only limited importance.

Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence

Turbulent diffusion of a pair of fluid particles in 3-dimensional homogeneous and isotropic turbulence was studied using a high-resolution direct numerical simulation (DNS) with 10243 grid points. The DNS showed that the mean square of the distance δx between the two fluid particles grows with time t as 〈|δx|2〉∼Cεt3 in the inertial subrange, which is in agreement with Richardson (1926) and Obukhov (1941), where C≈0.7 and ε is the mean dissipation rate per unit mass. A simple Lagrangian closure approximation for 〈|δx|2〉 is shown to be in good agreement with the DNS.

The evaluation of a Lagrangian model for turbulent transport and chemistry

A Lagrangian two-particle model for the relative diffusion and mixing of two reactive species is proposed. It describes the relative motion of a pair of fluid particles and includes the possibility for chemical interaction. The model was tested for consistency in simple geometrical configurations and has been compared to experimental data, Eulerian first- and second-order closure models as well as to other Lagrangian models. The transport algorithm was adapted in order to accommodate dispersion in decaying grid turbulence so that a comparison could be made with a series of wind tunnel measurements of the reaction of NO with O3. Three chemical closures are formulated and compared with experimental results. It appears that the formation of the reaction product is sensitive for both the description of the dispersion process and the chemical closure and that an accurate assessment of chemical closures is only possible with an accurate description of the dispersion process.

Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence

The scaling properties of one- and two-point statistics of the acceleration, pressure, and pressure gradient are studied in incompressible isotropic turbulence by direct numerical simulation. Ensemble-averaged Taylor-scale Reynolds numbers (Rλ) are up to about 230 on grids from 323 to 5123. From about Rλ 40 onwards the acceleration variance normalized by Kolmogorov variables is found to increase as Rλ1/2. This nonuniversal behavior is traced to the dominant irrotational pressure gradient contributions to the acceleration (whereas the much weaker solenoidal viscous part is universal). Longitudinal and transverse two-point correlations of the pressure gradient differ according to kinematic constraints, but both (especially the latter) extend over distances of intermediate scale size large compared to the Kolmogorov scale. These extended-range properties essentially provide the Eulerian mechanism whereby (as found in recent work) the accelerations of a pair of fluid particles can remain significantly correlated for relatively long periods of time even as they move apart from each other. Although a limited inertial range is attained in the energy spectrum, little evidence for classical inertial scaling is found in acceleration correlations and pressure structure functions. The probability density function (PDF) of pressure fluctuations has negatively skewed tails that exhibit a stretched-exponential form. Pressure gradient statistics show a rapid increase in intermittency with Reynolds number, characterized by widening tails in the PDF and large flatness factors. The practicality of computing acceleration correlations from velocity structure functions is also assessed using direct numerical simulations (DNS); within some resolution limitations good agreement is obtained with experimental data in grid turbulence at comparable Reynolds number.

THE SCREENING POTENTIALS OF ION-DIPOLE SYSTEM ADSORBED IN ION-DIPOLAR DISORDERED MATRICES

The effects of quenched disorder on the fluid properties have received increased attention in recent years. In theoretical studies the matrix-fluid system is considered as a special binary mixture in which the matrix is treated as a rigid set of obstacles,obtained by quenching an equilibrium configuration of particles (usually noted as species “0”) with the fluid molecules (noted as species “1”) at equilibrium in the presence of quenched particles. Resulting from the applying of the replica trick the description of the original matrix-fluid system was replaced by a multicomponent equilibrium (s+1) component mixture for which it was possible to use the standard methods of liquid-state theory (the integral equations, cluster expansions ets.). The specific feature of such (s+1)-component mixture is that a pair of fluid particles from different replicas has no interaction and at the end of calculation it takes the limit s → 0, assuming that there is no problem in performing the analytical continuation for noninteger values of s.

On the Lagrangian turbulent dispersion models based on the Langevin equation

A Lagrangian approach is used to describe turbulent two-phase particulate flows. Special attention focuses on a currently used model based on the Langevin equation with instantaneous relative velocity of fluid and particles. A detailed analysis of the model is performed and its drawbacks are discussed. Afterwards, a novel model for particle dispersion in homogeneous turbulence is proposed. It is built on physical arguments quite different from those underlying the previous model: rather than instantaneous relative velocities, averaged characteristics of the motion of solid–fluid particle pairs are considered. The new model accounts for both inertia and external force effects. It is validated by comparison with existing experimental data on particle dispersion in grid turbulence and with large-eddy simulations of homogeneous turbulence.

Fluid particle dispersion in homogeneous turbulent shear flow

The dispersion of Lagrangian fluid particle pairs in homogeneous turbulent shear flow is studied by a direct numerical simulation using 256×1282 grid points. It is emphasized that anisotropy requires the effects of both magnitude and orientation of the initial separation vector on two-particle statistics to be considered separately, especially at early times when these statistics are primarily determined by the Eulerian structure of the velocity gradient fluctuations. The effects of initial particle positions and pair separation on displacement and dispersion statistics are examined in relation to classical theory. Particle-pair dispersion is found to be most effective in the streamwise direction, and especially so for particle pairs initially separated in the direction of the mean velocity gradient. Similarly, two-particle velocity correlations are anisotropic, being strongest in the streamwise component but weakest in the cross-stream component. The particle-pair separation distance probability density function differs significantly from a Gaussian form used in most dispersion models for air-quality applications. It is hoped that the new results will be helpful for extending two-particle stochastic models to anisotropic turbulent flows.

Stochastic Lagrangian Models of Relative Dispersion of a Pair of Fluid Particles in Turbulent Flows

Article Stochastic Lagrangian Models of Relative Dispersion of a Pair of Fluid Particles in Turbulent Flows was published on January 1, 1995 in the journal Monte Carlo Methods and Applications (volume 1, issue 2).

Direct numerical simulation of two-particle relative diffusion in isotropic turbulence

The relative diffusion of fluid particle pairs in statistically stationary isotropic turbulence is studied by direct numerical simulation, at a Taylor-scale Reynolds number of about 90. The growth of two-particle separation exhibits asymptotic stages at small and large diffusion times. Through the two-particle separation, particle–pair velocity correlations are closely related to the Eulerian spatial structure of the turbulence. At large times, the square of the separation distance has a chi-square probability distribution. At the moderate Reynolds number of the simulations, for this asymptotic distribution to be reached before the particles begin to move independently of each other, the initial separation must be small compared to the Kolmogorov scale. In an inertial frame moving with the initial particle velocities, the velocity increments of two fluid particles become uncorrelated only if their initial velocities are uncorrelated, which requires their initial separation be large compared to the integral length scale. For sufficiently large initial separations, the relative velocity increments and mean-square dispersion in this moving frame display a resemblance to inertial range scaling, but with a proportionality constant that is much smaller than classical estimates. At large times, the degree of preferential alignment between the separation and relative velocity vectors is weak, but the product of the separation distance and the velocity component projected along the separation vector is sustained on average.

Relative Diffusion of a Pair of Fluid Particles in Turbulence

Relative Diffusion of a Pair of Fluid Particles in Turbulence

Relative Diffusion of a Pair of Fluid Particles in Turbulence

The effective Hamiltonian method is used to find the distribution function describing the positions as a function of time of a given pair of fluid particles subject to convection in steady, incompressible, statistically isotropic turbulent flow. By assuming a joint Gaussian distribution for the velocity field, a reasonable time dependence is obtained for the statistical average of the distance between the pair of fluid particles. The basis for Richardson's four-thirds law is indicated and the proportionality constant C * is shown to be related to the Kolmogorov constant C by C * =3 1/3 C 1/2 /2 1/2 .

Two-body dynamics in fluids as probed by interaction-induced light scattering

The relative dynamics of particle pairs in fluids is investigated both theoretically and by simulation experiments. The physical implications of this analysis are important in all interaction-induced phenomena and illustrated in the case of the pair time correlation function relevant to collision-induced light scattering in atomic fluids.

A Numerical Investigation of Tetroon versus Fluid Particle Dispersion in the Convective Planetary Boundary Layer

Abstract Data from Deardorff's (1974) turbulence model are used in simulations of fluid particle and tetroon dispersion in the convective atmospheric boundary layer with −h/L ≫ 1, where h is the mixed-layer depth. It is found that the lateral spread σy(t) of tetroons about the mean wind direction is virtually identical to that of fluid particles for travel times t < ze/w*, where w* is the convective velocity scale and ze(<h) is the altitude of release, and also the equilibrium level of the tetroons. The rms lateral separation ly21/2; of tetroon and fluid particle pairs also are equal for travel times less than ze/w*. At larger travel times, both the σy and ly2 profiles of tetroons increase at slower rates than those of fluid particles. The simulations indicate that this is a consequence of the inability of tetroons to follow fluid particles through the turnaround zone z ≤ 0.2h where the kinetic energy of downward moving fluid is transformed into horizontal motion. Based on this finding it is shown that th...