One-Particle Stochastic Lagrangian Model for Turbulent Dispersion in Horizontally Homogeneous Turbulence (original) (raw)
Related papers
Lagrangian Stochastic Models For Turbulent Dispersion In The Atmospheric Boundary Layer
Boundary-Layer Meteorology, 2000
A one-particle three-dimensional stochastic Lagrangian model for transport of particles in a horizontally-homogeneous atmospheric surface layer with arbitrary one-point probability density function of Eulerian velocity fluctuations is suggested. A uniquely defined Lagrangian stochastic model in the class of well-mixed models is constructed from physically plausible assumptions. These assumptions are: (i) in the neutrally stratified horizontally homogeneous surface layer, the vertical motion is mainly controlled by eddies whose size is of order of the current height; and (ii), the streamwise drift term is independent of the crosswind velocity. Numerical simulations for neutral stratification have shown a good agreement of our model with the well-known Thomson's model, with Flesch and Wilson's model, and with experimental measurements as well. However there is a discrepancy of these results with the results obtained by Reynolds' model.
A Stochastic Model of Particle Dispersion in a Turbulent Gaseous Environment
Combustion and Flame, 1998
The prediction of particle dispersion by interactions with a turbulent gaseous fluid is an important, yet difficult, problem. This paper presents a new model to predict the motion of particles in a turbulent flow. This model, which solves for the probability density function (pdf) for particle velocity, treats the impact of the turbulence on the velocity pdf as a diffusion process. Particle concentrations are, in turn, found from the velocity distributions. Comparisons between the model predictions and both analytical and experimental results are presented. Results are reported for flows of homogeneous, isotropic turbulence; for grid-generated turbulence; and for round jets. This study includes a large range of particle diameters and densities. Good agreement is found between the predictions and measurements.
A Lagrangian stochastic model for nonpassive particle diffusion in turbulent flows
Mathematical and Computer Modelling, 1995
In this paper, we present a Lagrangian stochastic model for heavy particle dispersion in turbulence. The model includes the equation of motion for a heavy particle and a stochastic approach to predicting the velocity of fluid elements along the heavy particle trajectory. The trajectory crossing effect of heavy particles is described by using an Ito type stochastic differential equation combined with a fractional Langevin equation. The comparison of the predicted dispersion of four heavy particles with the observations shows that the model is potentially useful but requires further development.
A stochastic model for dispersion and concentration distribution in homogeneous turbulence
Journal of Fluid Mechanics, 1988
A new approach to contaminant diffusion in homogeneous turbulence is proposed. This approach is based on solving for the Lagrangian trajectories of many particles taking into account the interaction among their velocities. The velocity field at a given instant is composed of many ‘eddies’ distributed randomly and uniformly in space. The velocity of each eddy is proportional to the cube root of its size. In this way the calculated Eulerian correlation function between any two points is consistent with observations. The present model is used to calculate concentration fluctuations, concentration averages and intermittency as functions of location and time. Results were found to be in accordance with experimental measurements. Probability distributions as functions of time and location are also calculated.
The 14th International Conference on Interdisciplinarity in Engineering—INTER-ENG 2020, 2020
The stochastic behavior of wind speed is a particular characteristic of wind energy production, which affects the degradation mechanism of the turbine, resulting in stochastic charging on the wind turbine. A model stochastic is used in this study to evaluate the efficiency of wind turbine power of whatever degree given fluctuating wind turbulence data. This model is based on the Langevin equations, which characterize, by two coefficients, drift and diffusion functions. These coefficients describe the behavior of the transformation process from the input wind speed to the output data that need to be determined. For this present work, the computation of drift and diffusion functions has been carried out by using the stochastic model to assess the output variables in terms of the torque and power curves as a function of time, and it is compared by the classical method. The results show that the model stochastic can define the efficiency of wind turbine generation more precisely.
Single-particle dispersion in stably stratified turbulence
Physical Review Fluids, 2018
We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in the horizontal direction is a combination of a continuoustime eddy-constrained random walk process with a contribution to transport from horizontal winds. Transport at times larger than the Lagrangian turnover time is not universal and dependent on these winds. The models yield results in good agreement with direct numerical simulations of stratified turbulence, for which single-particle dispersion differs from the well studied case of homogeneous and isotropic turbulence.
An efficient Lagrangian stochastic model of vertical dispersion in the convective boundary layer
Atmospheric Environment, 1999
We consider the one-dimensional case of vertical dispersion in the convective boundary layer (CBL) assuming that the turbulence field is stationary and horizontally homogeneous. The dispersion process is simulated by following Lagrangian trajectories of many independent tracer particles in the turbulent flow field, leading to a prediction of the mean concentration. The particle acceleration is determined using a stochastic differential equation, assuming that the joint evolution of the particle velocity and position is a Markov process. The equation consists of a deterministic term and a random term. While the formulation is standard, attention has been focused in recent years on various ways of calculating the deterministic term using the well-mixed condition incorporating the Fokker-Planck equation. Here we propose a simple parameterisation for the deterministic acceleration term by approximating it as a quadratic function of velocity. Such a function is shown to represent well the acceleration under moderate velocity skewness conditions observed in the CBL. The coefficients in the quadratic form are determined in terms of given turbulence statistics by directly integrating the Fokker-Planck equation. An advantage of this approach is that, unlike in existing Lagrangian stochastic models for the CBL, the use of the turbulence statistics up to the fourth order can be made without assuming any predefined form for the probability distribution function (PDF) of the velocity. The main strength of the model, however, lies in its simplicity and computational efficiency. The dispersion results obtained from the new model are compared with existing laboratory data as well as with those obtained from a more complex Lagrangian model in which the deterministic acceleration term is based on a bi-Gaussian velocity PDF. The comparison shows that the new model performs well.
Stochastic Lagrangian Models for Two-Particle Relative Dispersion in High-Reynolds Number Turbulence
Monte Carlo Methods and Applications, 1997
s-A new stochastic model (a diffusion approximation) for the relative dispersion of pair of particles in high-Reynolds-number incompressible turbulence is proposed. An attempt is made to uniquely define the coefficients of SDE governing the relative dispersion process under a closure assumption about the quasi-one dimensional model. An approach for constructing a diffusion approximation of the relative dispersion taking into account the intermittency is proposed.
Lagrangian stochastic models for turbulent relative dispersion based on particle pair rotation
Journal of Fluid Mechanics, 2008
The physical picture of a fluid particle pair as a couple of material points rotating around their centre of mass is proposed to model turbulent relative dispersion in the inertial range. This scheme is used to constrain the non-uniqueness problem associated to the Lagrangian models in the well-mixed class and the properties of the stochastic process derived are analysed with respect to some turbulent velocity characteristics. A simple illustrative Markov model is developed in stationary homogeneous isotropic turbulence and the particle separation statistics are compared with direct numerical simulation data. In spite of the simplicity of the model, a consistent comparison is observed in the inertial range, supporting the formulation proposed.