Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow

TL;DR

This paper develops a probabilistic model for scalar dispersion from concentrated sources in turbulent channel flow, accurately capturing velocity and concentration statistics through advanced stochastic and micromixing models.

Contribution

It introduces a joint PDF model combining Langevin dynamics, elliptic relaxation, and micromixing models, with no-slip wall conditions, validated against DNS and experimental data.

Findings

Accurately reproduces velocity and scalar concentration statistics.

Demonstrates effectiveness of the joint PDF approach with wall effects.

Validates models against high-Reynolds-number DNS and experiments.

Abstract

Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is represented by a large number of Lagrangian particles. A stochastic near-wall PDF model combines the generalized Langevin model of Haworth & Pope with Durbin's method of elliptic relaxation to provide a mathematically exact treatment of convective and viscous transport with a non-local representation of the near-wall Reynolds stress anisotropy. The presence of walls is incorporated through the imposition of no-slip and impermeability conditions on particles without the use of damping or wall-functions. Information on the turbulent timescale is supplied by the gamma-distribution model of van Slooten et al. Two different micromixing models are compared that incorporate the effect of small scale mixing on the transported scalar: the widely used interaction by exchange with the mean (IEM) and the interaction by exchange with the conditional mean (IECM) model. Single-point velocity and concentration statistics are compared to direct numerical simulation and experimental data at Re_\tau=1080 based on the friction velocity and the channel half width. The joint model accurately reproduces a wide variety of conditional and unconditional statistics in both physical and composition space.