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

## Abstract

We present a simple stochastic quadrant model for calculating the transport and deposition 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 models and Langevin equation based ejection and sweep models which noticeably give significantly 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.

- Authors:

- School of Mechanical and Systems Engineering, Newcastle University, Stephenson Building, Claremont Road, Newcastle upon Tyne NE1 7RU (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22403232

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Fluids (1994)

- Additional Journal Information:
- Journal Volume: 27; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-6631

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY LAYERS; DEPOSITION; EDDY CURRENTS; FLOW RATE; FLUCTUATIONS; GRAPH THEORY; LANGEVIN EQUATION; MARKOV PROCESS; NEUTRAL-PARTICLE TRANSPORT; PARTICLE TRACKS; PARTICLES; REYNOLDS NUMBER; SHEAR; STATISTICS; STRESSES; TURBULENCE

### Citation Formats

```
Jin, C., Potts, I., and Reeks, M. W., E-mail: mike.reeks@ncl.ac.uk.
```*A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers*. United States: N. p., 2015.
Web. doi:10.1063/1.4921490.

```
Jin, C., Potts, I., & Reeks, M. W., E-mail: mike.reeks@ncl.ac.uk.
```*A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers*. United States. doi:10.1063/1.4921490.

```
Jin, C., Potts, I., and Reeks, M. W., E-mail: mike.reeks@ncl.ac.uk. Fri .
"A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers". United States. doi:10.1063/1.4921490.
```

```
@article{osti_22403232,
```

title = {A simple stochastic quadrant model for the transport and deposition of particles in turbulent boundary layers},

author = {Jin, C. and Potts, I. and Reeks, M. W., E-mail: mike.reeks@ncl.ac.uk},

abstractNote = {We present a simple stochastic quadrant model for calculating the transport and deposition 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 models and Langevin equation based ejection and sweep models which noticeably give significantly 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.},

doi = {10.1063/1.4921490},

journal = {Physics of Fluids (1994)},

issn = {1070-6631},

number = 5,

volume = 27,

place = {United States},

year = {2015},

month = {5}

}