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

Abstract

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.

Stokes number effects on particle slip velocity in wall-bounded turbulence and implications for dispersion models

“…This behavior has been observed also in a spatially developing turbulent boundary layer 16 where the globally averaged rms ratios may exceed unity and, consistently with our findings, increase with St. Rms ratios close to unity are observed at the wall in Figs. 3(c) We conclude our discussion by considering the fluid-particle velocity covariance, an important quantity in Lagrangian 3 and Eulerian models, 6,8 e.g., to compute integral time scales. For the present analysis, the streamwise and wall-normal components, u f u p and w f w p , respectively, are the most interesting.…”

“…When the particle velocity differs from that of the surrounding fluid, e.g., due to particle inertia 1 or gravity, 2 significant decorrelation of the fluid velocity fluctuations along the particle trajectory occurs and a particle slip velocity can be observed. The particle slip velocity vector, defined as u = u f − u p with u f the fluid velocity at the particle location (referred to as fluid velocity seen hereinafter), is a primary variable in two-fluid modeling of particle-laden flows, 3,4 for which new data might provide useful guidance. Its importance has long been recognized 5 with reference to crossing trajectory effects on the time decorrelation tensor of u f , a crucial parameter for the development of Lagrangian stochastic models of particle dispersion, for instance in gas-solid turbulent flows, 2 but also for the closure of Eulerian models.…”

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

“…Though the purpose of our analysis is not directly about two-way coupling effects, the above discussion is interesting to reveal that, for a given stochastic model, Clearly, formulations in terms of so-called 'fluctuations' can easily become intricate with many terms, making their manipulation slippery while they do not necessarily clarify the physical picture. Thus, contrary to some statements [67,68], a more practical way to account for the velocity of the fluid seen is to retain formulations in terms of the instantaneous velocity.…”

“…As already mentioned above, a recent proposal introduced a new formulation for the velocity of the fluid seen [68]. Using the present notations, this proposal consists in simulating U s as the solution of the following stochastic differential equation…”

Prediction of Extrathoracic Aerosol Deposition using RANS-Random Walk and LES Approaches

“…These models contain terms which inherently avoid the appearance of spurious drifts through the introduction of a mean-pressure gradient in the stochastic differential equation for the instantaneous velocity. Improvements of this original model have been lately incorporated to extend this approach to non-homogeneous flows by, e.g., Arcen and Tanière (2009). Walpot et al (2007) have additionally conducted a DNS and Particle Tracking Velocimetry investigation and described an innovative methodology to accurately determine the Langevin coefficients in nonhomogenous media.…”