A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers

TL;DR

This paper introduces a simple stochastic quadrant model that predicts heavy particle transport and deposition in turbulent boundary layers, accurately matching experimental data without adjustable parameters.

Contribution

The model directly incorporates ejection and sweeping events using a Markov chain approach based on fluid velocity statistics, offering improved predictions over existing models.

Findings

Deposition rates closely match experimental measurements.

Model outperforms CRW and Langevin-based models in predicting deposition.

Provides detailed statistics on particle near-wall behavior.

Abstract

We present a simple stochastic quadrant model for calculating the transport and de- position of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a fully developed channel flow. Individual particles are tracked through the boundary layer via their interactions with a succession of random eddies found in each of the quadrants of the fluid Reynolds shear stress domain in a homogeneous Markov chain process. In this way we are able to account directly for the influence of ejection and sweeping events as others have done but without resorting to the use of adjustable parameters. Deposition rate predictions for a wide range of heavy particles predicted by the model compare well with benchmark experimental measurements. In addition deposition rates are compared with those obtained from continuous random walk (CRW) models and Langevin equation based ejection and sweep models which noticeably give sig- nificantly lower deposition rates. Various statistics related to the particle near wall behavior are also presented. Finally we consider the model limitations in using the model to calculate deposition in more complex flows where the near wall turbulence may be significantly different.