# Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles

## Abstract

In this paper, we study systematically the effects of forcing time scale in the large-scale stochastic forcing scheme of Eswaran and Pope [“An examination of forcing in direct numerical simulations of turbulence,” Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in terms of altered flow Reynolds number and the changing range of flow length scales present in the turbulent flow. We argue that removing this dependence is important when studying the Reynolds number dependence of the turbulent collision statistics. The results are alsomore »

- Authors:

- Institute of Meteorology and Water Management - National Research Institute, 61 Podlesna Street, 01-673 Warsaw (Poland)
- Department of Mechanical Engineering, University of Delaware, Newark, Delaware 19716-3140 (United States)
- (United States)
- Department of Engineering Technology, Old Dominion University, 214 Kaufman Hall, Norfolk, Virginia 23529 (United States)
- (China)

- Publication Date:

- OSTI Identifier:
- 22403209

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COLLISIONS; COMPUTERIZED SIMULATION; CONCENTRATION RATIO; DISTRIBUTION FUNCTIONS; ENERGY LOSSES; PARTICLES; REYNOLDS NUMBER; SPATIAL DISTRIBUTION; STATISTICS; STOCHASTIC PROCESSES; TURBULENT FLOW; VELOCITY

### Citation Formats

```
Rosa, B., E-mail: bogdan.rosa@imgw.pl, Parishani, H., Department of Earth System Science, University of California, Irvine, California 92697-3100, Ayala, O., Wang, L.-P., and The State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074.
```*Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles*. United States: N. p., 2015.
Web. doi:10.1063/1.4906334.

```
Rosa, B., E-mail: bogdan.rosa@imgw.pl, Parishani, H., Department of Earth System Science, University of California, Irvine, California 92697-3100, Ayala, O., Wang, L.-P., & The State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074.
```*Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles*. United States. doi:10.1063/1.4906334.

```
Rosa, B., E-mail: bogdan.rosa@imgw.pl, Parishani, H., Department of Earth System Science, University of California, Irvine, California 92697-3100, Ayala, O., Wang, L.-P., and The State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074. Thu .
"Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles". United States.
doi:10.1063/1.4906334.
```

```
@article{osti_22403209,
```

title = {Effects of forcing time scale on the simulated turbulent flows and turbulent collision statistics of inertial particles},

author = {Rosa, B., E-mail: bogdan.rosa@imgw.pl and Parishani, H. and Department of Earth System Science, University of California, Irvine, California 92697-3100 and Ayala, O. and Wang, L.-P. and The State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074},

abstractNote = {In this paper, we study systematically the effects of forcing time scale in the large-scale stochastic forcing scheme of Eswaran and Pope [“An examination of forcing in direct numerical simulations of turbulence,” Comput. Fluids 16, 257 (1988)] on the simulated flow structures and statistics of forced turbulence. Using direct numerical simulations, we find that the forcing time scale affects the flow dissipation rate and flow Reynolds number. Other flow statistics can be predicted using the altered flow dissipation rate and flow Reynolds number, except when the forcing time scale is made unrealistically large to yield a Taylor microscale flow Reynolds number of 30 and less. We then study the effects of forcing time scale on the kinematic collision statistics of inertial particles. We show that the radial distribution function and the radial relative velocity may depend on the forcing time scale when it becomes comparable to the eddy turnover time. This dependence, however, can be largely explained in terms of altered flow Reynolds number and the changing range of flow length scales present in the turbulent flow. We argue that removing this dependence is important when studying the Reynolds number dependence of the turbulent collision statistics. The results are also compared to those based on a deterministic forcing scheme to better understand the role of large-scale forcing, relative to that of the small-scale turbulence, on turbulent collision of inertial particles. To further elucidate the correlation between the altered flow structures and dynamics of inertial particles, a conditional analysis has been performed, showing that the regions of higher collision rate of inertial particles are well correlated with the regions of lower vorticity. Regions of higher concentration of pairs at contact are found to be highly correlated with the region of high energy dissipation rate.},

doi = {10.1063/1.4906334},

journal = {Physics of Fluids (1994)},

number = 1,

volume = 27,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}