# Particulate Matter Dispersion Modeling in Agricultural Applications: Investigation of a Transient Open Source Solver

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## Abstract

**:**

`WALE`and

`dynamicKeq`) in the main regions. The inflow turbulence generator could create a stable and accurate boundary layer for the mean vertical velocity and vertical profile of the turbulent Reynolds stresses R

_{11}. The validation of the Lagrangian solver showed mixed results, with partly good agreements (simulation results within the measurement uncertainty), and partly high deviations of up to 80% for the concentration of particles. The higher deviations were attributed to an insufficient turbulence regime of the used validation case, which was an experimental chamber. For the simulation case of PM dispersion from manure application on a field, the solver could capture the influence of features such as size and density on the dispersion. The investigated solver is especially useful for further investigations into time-dependent processes in the near-source area of PM sources.

## 1. Introduction

## 2. Materials and Methods

`typewriter`font.

#### 2.1. Solving the Flow Field Phase

`OpenFOAM`contains a library with a broad range of SGS scale turbulence models. For this study, we investigated the models of Smagorinsky, TKE, dynamic TKE, and the wall-adapting local eddy viscosity (

`Smagorinsky, oneEqTKE, dynTKE`and

`WALE`, respectively).

#### 2.2. Solving the Particle Phase

## 3. Validation of the Solver

#### 3.1. Validation of the Flow Solver

#### 3.1.1. Geometry

#### 3.1.2. Meshing

`blockMesh`and

`snappyHexMesh`. At first, the domain was meshed with more cells near the bottom wall by grading the cells along the height of the domain. The domain was meshed with 260 × 92 × 70 (coarse), 313 × 110 × 70 (medium) and 375 × 130 × 85 cells (fine). Mesh refinement was performed around the buildings and the canyon formed by the buildings. A single-refinement region was created for the coarse mesh and the mesh was refined two times for medium and fine meshes.

#### 3.1.3. Boundary Conditions

_{μ}= 0.09.

`zeroGradient`). At the outlet, the boundary condition for velocity was set to

`zeroGradient`and the pressure to

`fixedValue`. The top, front and back boundaries are set as

`symmetryPlane`, meaning a free-slip condition. The boundaries’ bottom and buildings are considered walls, where the velocity is set to zero.

#### 3.1.4. Solver Setup and Turbulence Modeling

`linearUpwind`schemes, and the time variable was discretized with the second-order

`backward`scheme, which are both described in [41].

`kEqn`,

`dynamicKEqn`,

`WALE`, and

`Smagorinsky`, all described in Section 2.1.

_{H}= 4.7 m/s, the flow passes through the entire domain five times in 5 s and, in the region of interest, near the buildings, the flow passes through approximately 40 times. Hence, a period of 5 s was considered sufficient for the entire simulation.

#### 3.1.5. Mesh Convergence

_{z}/U

_{H}are −0.05, −0.1 and −0.15. Hence, the normalized vertical velocities are measured from the simulations at x/H = 0.1425, 0.2 and 0.2525 and compared with the experimental results, as in Figure 3. From the figure, the large influence of the grid size can clearly be seen. At x/H = 0.2525, the relative errors for coarse, medium and fine meshes are 37%, 15% and 4%, respectively. Hence, for all the following simulations, the fine mesh was chosen.

#### 3.1.6. Validation Results of the Flowfield

`kEqn`and

`Smagorinsky`in Figure 4a,b and the non-equilibrium SGS models

`dynkEqn`and

`WALE`in Figure 4c,d. Both equilibrium models failed to predict the spatial distribution of velocity contours accurately, especially for the positive-velocity region near building A. Here, both models predicted the velocitiy maxima near the edges of the building whereas, in the experiment, the velocitiy maxima were high near the middle region of the building. On the other hand, the non-equilibrium models WALE and dynamicKEqn performed very well when reproducing the experimental results. On the side of building B, a very good agreement can be seen for the negative velocities towards the middle region, with no noticeable difference between experimental and simulation results for

`dynamicKEqn`. However, near the wall region, all SGS models showed larger deviations from the experimental data. The highest deviations can be seen at the height of z/H = 0.6; the relative error was, depending on the compared velocity contour, in the range of 5–20%. Possible reasons for this are discussed in Section 5.1.

#### 3.2. Validation of the Particle Transport

^{3}, with a mean diameter of 10 μm and nominal diameter range between 2 and 20 μm, were injected for a time period of 1800 s. Air-flow velocity and particle concentration were measured using Phase Doppler Anemometry (PDA). The particle concentration was measured at 27 different locations in the mid-plane of the model room along three different x positions.

#### 3.2.1. Computational Domain and Meshing

#### 3.2.2. Particle Injection and Simulation

^{3}. The particles were simulated with Gravity, Drag and Pressure forces. Boundary interactions were set to an escape condition when particles reach the outlet, or rebound condition when particles reached the walls.

`pimpleLPTFoam`, in combination with the drag model of Putnam (

`sphereDrag`) and

`MPPICFoam`using the Ergun–Wen–Yu drag model (

`ErgunWenYuDrag`). The multi-phase particle in Cell method [43] is similar to the Discrete Parcel Method (DPM). In DPM, the particle interactions are directly resolved, whereas in MPPIC, particle–particle interactions are represented by models, which utilise the mean values calculated on the Eulerian mesh.

`pimpleLPTFoam`was originally introduced by the Chair of Modeling and Simulation (LeMoS) at the University of Rostock [44,45] for dilute particle-laden flows by combining a DPM-based particle-tracking approach, including four-way phase-coupling capabilities, with the standard OpenFOAM solver

`pimpleFoam`.

`kEpsilon`model for 1850 s. The particles were injected from 20 s until 1820 s. In the case of LES, the

`dynamicKEqn`turbulence model was used, since it produced better results in the flow-field validation case, as shown in Section 3.1.6.

#### 3.2.3. Validation Results of the Particle Transport

_{x}from the experiment is compared to the RANS and LES simulations along three lines at x = 0.2, 0.4 and 0.6 m in the mid-plane in Figure 6. The velocity profile from the RANS simulation with the

`kEpsilon`turbulence model predicted the experimental velocity profile very precisely along all three lines. For LES simulation, the velocity profile was time-averaged and then compared. Even though the LES simulation began from the converged solution of the RANS simulation, the velocity along the inlet tends to increase further than the expected experimental values. LES was able to perform well near the wall region and in the region below the inlet, but the velocity values are overpredicted along the inlet. The possible reasons for this are discussed in Section 5.2.

`PimpleLPTFoam`and

`MPPICFoam`, show nearly identical results, with the exception of two measurement points at sampling line x = 0.2 m on height 0.3 m and 0.32 m. For all three sampling lines, the simulations underestimated the particle concentrations in the lower two thirds of the domain, with relative errors in the range between −37% (x = 0.2 m, H = 0.22 m) and −80% (x = 0.6, H = 0.22 m). A possible explanation for this could be the previously discussed overprediction of velocity in the region of the inlet jet. This could have accelerated the particles more strongly towards the opposite wall than in the experiment, leading to less dispersion occurringin the region below the inlet.

## 4. Modelling of Particulate Matter Dispersion from Manure Application

#### 4.1. Computational Domain

`symmetryPlane`, the bottom was considered as

`wall`, and inlet and outlet as

`patch`. Two meshes were considered for the simulation. The domain was first meshed with a small number of cells, and then then refined using the solver’s in-built

`refineMesh`utility. The cells were graded along the z-direction, so that the mesh near the bottom wall was fine, with a nearly uniform aspect-ratio. The mesh consisted of 19,995,000 hexahedral cells.

#### 4.2. Turbulent Inlet

_{11}, which is defined as the time-average of the square of the velocity fluctuations in x-direction: ${R}_{11}=\overline{{u}_{X}^{\prime}\xb7{u}_{x}^{\prime}}$, with ${u}_{x}^{\prime}={u}_{x}-\overline{{u}_{x}}$. As can be seen, R

_{11}is closely related to the turbulence intensity in x-direction. U

_{x}and R

_{11}were chosen because they are considered to be two of the most important characteristics for a modeled windfield in the guidelines for Physical modelling of flow and dispersion processes in the atmospheric boundary layer [51].

#### 4.3. Solver Setup

`dynamicKEqn`turbulence model was used, with

`pimpleLPTFoam`solver. The flow field was simulated for a period of 400 s without particles. The period of 400 s was chosen, assuming the average wind speed to be 5 m/s, so that the flow passes through the domain four times. Second-order

`linearUpwind`schemes were used for the

`div(phi,U)`and

`div(phi,k)`terms. The case setup and the solver can be found and downloaded in [52] for further use by the reader. The simulation was performed with 420 processors on the SUPERMUC at Leibniz Supercomputing Centre running for 8 h with a maximum Courant number of 1. After 400 s, the particles were injected and the simulation was continued for further 120 s, which then required another 8 h of simulation time. During the particle phase, the results were written out every 5 s. Even though

`pimpleLPTFoam`and

`MPPICFoam`were able to produce similar results, as discussed in Section 5.2,

`pimpleLPTFoam`was chosen as the solver, as it was convenient to use with the

`turbulentDFSEMInlet`boundary condition.

#### 4.4. Particle Properties

^{3}, and the density of the aerosolized particulate matter was estimated as 130 kg/m

^{3}. The size distribution of the particulate matter was measured and is shown in Figure 10.

^{−6}) and the volume fraction is of the order of 1 × 10

^{−15}. The particles were modeled with drag and gravitational force, and without collision between the particles. The particle phase was simulated for a period of 120 s, and the spatial distribution of particle concentration in the domain was estimated afterwards. Particles of diameters ranging from 0.25 to 10 μm, with a total of 24 particle sizes, were analyzed at 1012 positions. In the x-direction, the particles were analyzed from x = 50 to x = 500 m for every 10 meters; in y-direction, the particles were analyzed from y = −25 m to y = 25 m for every 5 m; in the z-direction, the particles were analyzed at z = 0.5 m and z = 1.5 m. The regions of analysis were spheres of volume 1 m

^{3}.

#### 4.5. Results

#### 4.5.1. Atmospheric Boundary Layer

_{11}was also stable throughout the domain with a good match with the experimental results for heights up to approximately 25 m. The good agreement of this turbulent characteristic at the first sampling position at x = 125 m indicates, that vortices are correctly produced by the

`DFSEM`generator and transported without decay from the inlet to the outlet. However, for regions above 25 m, higher deviations from the experimental values occur, with an inverse trend. The reason for this might be the geometry of the computational mesh, which is concentrated towards the ground, resulting in smaller cells in the bottom region, and coarser cells with higher aspect ratios towards the top. The sensitivity of the

`DFSEM`turbulence generator on the cell size and geometry should, therefore, be investigated further.

#### 4.5.2. Influence of Size of Particulate Matter

#### 4.5.3. Influence of Density

^{3}and 316.6 kg/m

^{3}were simulated with the same initial conditions and mesh as described before. The time averaged particulate matter concentration was spatially averaged over the y-direction and plotted as in Figure 16. The difference between the PM10 concentrations at z = 0.5 m is small. At x = 70 m, the difference is only 0.7 and similar difference is observed in other points, which are not visible. The concentration of PM10 with 316.6 kg/m

^{3}is high at z = 0.5 m.

#### 4.5.4. Risk Estimation

^{3}by using the density and volume of the particulate matter. For computational cost-effective simulations, the injected particle mass was 0.0066 μg per second. To use the AQI under the assumption of a hazardous environment directly at the source, the simulated concentration results were proportionally increased such that the injected particle mass was 100 μg per second.

## 5. Discussion

#### 5.1. Flowfield

`WALE`and

`dynamicKEqn`. Larger deviations were only seen in the near-wall regions. This may be due to the presence of ${y}^{+}$ values in the buffer region. Even though

`nutUSpaldingWallFunction`was used to compensate the ${y}^{+}$ values, a better mesh refinement could have resulted in more accurate results and should be investigated in further simulations. Alternatively, so-called detached eddy simulations (DES, a mixed approach of RANS for simulating the near-wall flow, and LES for simulating the non-wall-affected flow) could improve the wall-near results and simultaneously reduce computational effort, which is described, e.g., in [36].

`dynamicKEqn`model showed an error of only 4%. This is a good indicator for the advantages of transient LES over steady-state RANS in the context of complex flows, which will be discussed further in Section 5.4. The

`dynamicKEqn`model was also validated in a previous study to simulate the flow inside a naturally ventilated dairy barn and was found to perform very well for the most important characteristics [55]. Future studies on the coupling of indoor and outdoor flow will, therefore, focus on this turbulence model.

#### 5.2. Particle Dispersion

`PimpleLPTFoam`and

`MPPICFoam`is rather reliable for an assessment of trends (e.g., general effectiveness of flow barriers) than for the derivation of absolute values as needed, e.g., in civil protection applications. A bottleneck here is the lack of high-quality datasets under realistic turbulent conditions, which can be used for validatation.

#### 5.3. Application Example

`DFSEM`inlet boundary condition was able to create a vertical velocity profile, which matched the experimental data very well. The profile was stable throughout the domain, which is important for the dispersion studies and indicates a fully developed turbulent boundary layer from the beginning. This is usually achieved only after a longer simulated inflow section with natural turbulence generation or a recycling strategy, where the velocity values from the outlet are mapped and superimposed on the inlet [56,57,58]. These strategies require a considerable amount of computational effort. By using the synthetic turbulence generator

`DFSEM`, this effort was not required; hence, this boundary condition is a promising tool for further efficient investigations of atmospheric dispersion processes. Up to a height of 25 m (which covers the usual region of interest when investigating near source immissions) the Reynolds stresses R

_{11}were in good agreement with the experimentally derived initial conditions throughout the domain. However, for regions above this height, larger deviations were seen, which could lead to inaccurate dispersion simulations. These deviations are likely due to an interaction between the

`DFSEM`and a non-uniform mesh. Hence, the sensitivity of generated eddies on the grid aspect ratio should be further investigated on unstructured meshes.

#### 5.4. Performance: Cost-Benefit Ratio

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ART | Aerosols and reactive trace gases |

AQI | Air quality index |

CFD | Computational fluid dynamics |

COSMO | Consortium for Small Scale Modelling Europe |

DEM | Detached-eddy simulation |

DFSEM | Divergence-free synthetic eddy method |

DPM | Discrete parcel method |

DWD | German Weather Service |

LDA | Laser Doppler anemometry |

LES | Large eddy simulation |

LPT | Lagrangian particle tracking |

MPPIC | Multiphase particle-in-cell method |

OpenFOAM | Open Source Field Operation and Manipulation |

PDA | Phase Doppler anemometry |

PISO | Pressure implicit with splitting of operator |

PM | Particulate matter |

SEM | Synthetic eddy method |

SGS | Subgrid scale |

SIMPLE | Semi-implicit method for pressure linked equations |

TKE | Turbulence kinetic energy |

(U)RANS | (Unsteady) Reynolds-averaged Navier-Stokes equations |

USEPA | United States Environmental Protection Agency |

UV | Ultraviolet |

WALE | Wall-adapting local eddy-viscosity model |

## References

- Arslan, S.; Aybek, A. Particulate Matter Exposure in Agriculture. In Air Pollution; Haryanto, B., Ed.; IntechOpen: Rijeka, Croatia, 2012; Chapter 3. [Google Scholar]
- World Health Organisation. Burden of Disease from Ambient Air Pollution; Global Health Observatory Data; World Health Organisation: Geneva, Switzerland, 2014; Available online: https://www.who.int/airpollution/data/AAP_BoD_results_March2014.pdf (accessed on 5 September 2021).
- Aarnink, A.; Ellen, H. Processes and Factors Affecting Dust Emissions from Livestock Production. In How to Improve Air Quality; Wageningen University & Research: Wageningen, The Netherlands, 2007; Available online: https://research.wur.nl/en/publications/processes-and-factors-affecting-dust-emissions-from-livestock-pro (accessed on 5 September 2021).
- Lelieveld, J.; Evans, J.S.; Fnais, M.; Giannadaki, D.; Pozzer, A. The contribution of outdoor air pollution sources to premature mortality on a global scale. Nature
**2015**, 525, 367–371. [Google Scholar] [CrossRef] [PubMed] - Bundesamt, S. Wirtschaftsduenger Tierischer Herkunft in Landwirtschaftlichen Betrieben/Agrarstrukturerhebung-Fachserie 3 Reihe 2.2.2-2016; Statistisches Bundesamt: Wiesbaden, Germany, 2017. Available online: https://www.destatis.de/DE/Themen/Branchen-Unternehmen/Landwirtschaft-Forstwirtschaft-Fischerei/Produktionsmethoden/Publikationen/Downloads-Produktionsmethoden/wirtschaftsduenger-2030222169005.html (accessed on 5 September 2021).
- Funk, R.; Reuter, H.I.; Hoffmann, C.; Engel, W.; Öttl, D. Effect of moisture on fine dust emission from tillage operations on agricultural soils. Earth Surf. Process. Landf. J. Br. Geomorphol. Res. Group
**2008**, 33, 1851–1863. [Google Scholar] [CrossRef] - Maffia, J.; Dinuccio, E.; Amon, B.; Balsari, P. PM emissions from open field crop management: Emission factors, assessment methods and mitigation measures—A review. Atmos. Environ.
**2020**, 226, 117381. [Google Scholar] [CrossRef] - Takai, H.; Pedersen, S.; Johnsen, J.O.; Metz, J.; Koerkamp, P.G.; Uenk, G.; Phillips, V.; Holden, M.; Sneath, R.; Short, J.; et al. Concentrations and emissions of airborne dust in livestock buildings in Northern Europe. J. Agric. Eng. Res.
**1998**, 70, 59–77. [Google Scholar] [CrossRef][Green Version] - Cambra-López, M.; Aarnink, A.J.; Zhao, Y.; Calvet, S.; Torres, A.G. Airborne particulate matter from livestock production systems: A review of an air pollution problem. Environ. Pollut.
**2010**, 158, 1–17. [Google Scholar] [CrossRef] [PubMed] - Kabelitz, T.; Ammon, C.; Funk, R.; Münch, S.; Biniasch, O.; Nübel, U.; Thiel, N.; Rösler, U.; Siller, P.; Amon, B.; et al. Functional relationship of particulate matter (PM) emissions, animal species, and moisture content during manure application. Environ. Int.
**2020**, 143, 105577. [Google Scholar] [CrossRef] [PubMed] - Kabelitz, T.; Biniasch, O.; Ammon, C.; Nübel, U.; Thiel, N.; Janke, D.; Swaminathan, S.; Funk, R.; Münch, S.; Rösler, U.; et al. Particulate matter emissions during field application of poultry manure-The influence of moisture content and treatment. Sci. Total Environ.
**2021**, 780, 146652. [Google Scholar] [CrossRef] - Mostafa, E.; Nannen, C.; Henseler, J.; Diekmann, B.; Gates, R.; Buescher, W. Physical properties of particulate matter from animal houses—Empirical studies to improve emission modelling. Environ. Sci. Pollut. Res.
**2016**, 23, 12253–12263. [Google Scholar] [CrossRef] [PubMed] - McEachran, A.D.; Blackwell, B.R.; Hanson, J.D.; Wooten, K.J.; Mayer, G.D.; Cox, S.B.; Smith, P.N. Antibiotics, bacteria, and antibiotic resistance genes: Aerial transport from cattle feed yards via particulate matter. Environ. Health Perspect.
**2015**, 123, 337–343. [Google Scholar] [CrossRef][Green Version] - Ferziger, J.H.; Perić, M.; Street, R.L. Computational Methods for Fluid Dynamics; Springer: Berlin/Heidelberg, Germany, 2002; Volume 3. [Google Scholar]
- Van Dop, H.; Nieuwstadt, F.; Hunt, J. Random walk models for particle displacements in inhomogeneous unsteady turbulent flows. Phys. Fluids
**1985**, 28, 1639–1653. [Google Scholar] [CrossRef] - Nimmatoori, P.; Kumar, A. Dispersion Modeling of Particulate Matter in Different Size Ranges Releasing from a Biosolids Applied Agricultural Field Using Computational Fluid Dynamics. Adv. Chem. Eng. Sci.
**2021**, 11, 180–202. [Google Scholar] [CrossRef] - Quinn, A.; Wilson, M.; Reynolds, A.; Couling, S.; Hoxey, R. Modelling the dispersion of aerial pollutants from agricultural buildings—An evaluation of computational fluid dynamics (CFD). Comput. Electron. Agric.
**2001**, 30, 219–235. [Google Scholar] [CrossRef] - Wang, M.; Lin, C.H.; Chen, Q. Advanced turbulence models for predicting particle transport in enclosed environments. Build. Environ.
**2012**, 47, 40–49. [Google Scholar] [CrossRef] - Blocken, B. LES over RANS in building simulation for outdoor and indoor applications: A foregone conclusion? In Building Simulation; Springer: Berlin/Heidelberg, Germany, 2018; Volume 11, pp. 821–870. [Google Scholar]
- Deetz, K.; Klose, M.; Kirchner, I.; Cubasch, U. Numerical simulation of a dust event in northeastern Germany with a new dust emission scheme in COSMO-ART. Atmos. Environ.
**2016**, 126, 87–97. [Google Scholar] [CrossRef] - Vogel, B.; Vogel, H.; Bäumer, D.; Bangert, M.; Lundgren, K.; Rinke, R.; Stanelle, T. The comprehensive model system COSMO-ART–Radiative impact of aerosol on the state of the atmosphere on the regional scale. Atmos. Chem. Phys.
**2009**, 9, 8661–8680. [Google Scholar] [CrossRef][Green Version] - Faust, M.; Wolke, R.; Münch, S.; Funk, R.; Schepanski, K. A new Lagrangian in-time particle simulation module (Itpas v1) for atmospheric particle dispersion. Geosci. Model Dev.
**2021**, 14, 2205–2220. [Google Scholar] [CrossRef] - Smagorinsky, J. General circulation experiments with the primitive equations. Mon. Wea. Rev.
**1963**, 91, 99–164. [Google Scholar] [CrossRef] - Nicoud, F.; Ducros, F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust.
**1999**, 62, 183–200. [Google Scholar] [CrossRef] - Yoshizawa, A.; Horiuti, K. A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows. J. Phys. Soc. Jpn.
**1985**, 54, 2834–2839. [Google Scholar] [CrossRef] - Yoshizawa, A. Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids
**1986**, 29, 2152–2164. [Google Scholar] [CrossRef] - Kim, W.W.; Menon, S. A new dynamic one-equation subgrid-scale model for large eddy simulations. In 33rd Aerospace Sciences Meeting and Exhibit; Aerospace Research Central: Reno, NV, USA, 1995; p. 356. [Google Scholar]
- Dyna, C. Multi-Phase Flows and Discrete Phase Models. Available online: http://www.cfdyna.com/Home/of_multiPhase.html (accessed on 5 September 2021).
- Michaelides, E.E.; Crowe, C.T.; Schwarzkopf, J.D. (Eds.) Multiphase Flow Handbook; Taylor & Francis Inc.: Abingdon, UK, 2016. [Google Scholar]
- Putnam, A. Integrable form of droplet drag coefficient. ARS J.
**1961**, 31, 1467–1470. [Google Scholar] - Gidaspow, D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions; Academic Press, Inc.: Cambridge, MA, USA, 1994. [Google Scholar]
- Wen, Y.; Yu, Y. Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser.
**1966**, 162, 100–111. [Google Scholar] - Cameron, T.; Alexander, Y.; Foss, J. Springer Handbook of Experimental Fluid Mechanics; Springer: Berlin/Heidelberg, Germany, 2007; p. 289. [Google Scholar]
- Elghobashi, S. On predicting particle-laden turbulent flows. Appl. Sci. Res.
**1994**, 52, 309–329. [Google Scholar] [CrossRef] - Gromke, C.; Buccolieri, R.; Di Sabatino, S.; Ruck, B. Dispersion study in a street canyon with tree planting by means of wind tunnel and numerical investigations–evaluation of CFD data with experimental data. Atmos. Environ.
**2008**, 42, 8640–8650. [Google Scholar] [CrossRef] - De Villiers, E. The Potential of Large Eddy Simulation for the Modeling of Wall Bounded Flows; Imperial College of Science, Technology and Medicine: London, UK, 2006. [Google Scholar]
- Liu, F. A Thorough Description of How Wall Functions Are Implemented in OpenFOAM; Technical Report; Chalmers University of Technology: Gothenburg, Sweden, 2017. [Google Scholar]
- Issa, R.I. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys.
**1986**, 62, 40–65. [Google Scholar] [CrossRef] - Patankar, S.V.; Spalding, D.B. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. In Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion; Elsevier: Amsterdam, The Netherlands, 1983; pp. 54–73. [Google Scholar]
- Holzmann, T. Mathematics, Numerics, Derivations and OpenFOAM
^{®}; Holzmann CFD: Augsburg, Germany, 2016; pp. 95–112. [Google Scholar] [CrossRef] - The OpenFOAM Foundation. OpenFOAM User Guide Version 4.0. 2016. Available online: https://cfd.direct/openfoam/user-guide-v4/ (accessed on 5 September 2021).
- Chen, F.; Simon, C.; Lai, A.C. Modeling particle distribution and deposition in indoor environments with a new drift–flux model. Atmos. Environ.
**2006**, 40, 357–367. [Google Scholar] [CrossRef] - Andrews, M.J.; O’Rourke, P.J. The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Int. J. Multiph. Flow
**1996**, 22, 379–402. [Google Scholar] [CrossRef] - Kasper, R.; Turnow, J.; Kornev, N. Numerical modeling and simulation of particulate fouling of structured heat transfer surfaces using a multiphase Euler-Lagrange approach. Int. J. Heat Mass Transf.
**2017**, 115, 932–945. [Google Scholar] [CrossRef] - Kasper, R.; Turnow, J.; Kornev, N. Multiphase Eulerian–Lagrangian LES of particulate fouling on structured heat transfer surfaces. Int. J. Heat Fluid Flow
**2019**, 79, 108462. [Google Scholar] [CrossRef] - Poletto, R.; Craft, T.; Revell, A. A new divergence free synthetic eddy method for the reproduction of inlet flow conditions for LES. Flow Turbul. Combust.
**2013**, 91, 519–539. [Google Scholar] [CrossRef] - Jarrin, N.; Prosser, R.; Uribe, J.C.; Benhamadouche, S.; Laurence, D. Reconstruction of turbulent fluctuations for hybrid RANS/LES simulations using a synthetic-eddy method. Int. J. Heat Fluid Flow
**2009**, 30, 435–442. [Google Scholar] [CrossRef][Green Version] - Bex, C.C.; Pinon, G.; Slama, M.; Gaston, B.; Germain, G.; Rivoalen, E. Lagrangian Vortex computations of turbine wakes: Recent improvements using Poletto’s Synthetic Eddy Method (SEM) to account for ambient turbulence. J. Phys. Conf. Ser.
**2020**, 1618, 062028. [Google Scholar] [CrossRef] - Saha, C.K.; Yi, Q.; Janke, D.; Hempel, S.; Amon, B.; Amon, T. Opening Size Effects on Airflow Pattern and Airflow Rate of a Naturally Ventilated Dairy Building—A CFD Study. Appl. Sci.
**2020**, 10, 6054. [Google Scholar] [CrossRef] - Janke, D.; Yi, Q.; Thormann, L.; Hempel, S.; Amon, B.; Nosek, Š.; Van Overbeke, P.; Amon, T. Direct Measurements of the Volume Flow Rate and Emissions in a Large Naturally Ventilated Building. Sensors
**2020**, 20, 6223. [Google Scholar] [CrossRef] - VDI. Environmental Meteorology-Physical Modelling of Flow and Dispersion Processes in the Atmospheric Boundary Layer-Application of Wind Tunnels; Guideline; Verein Deutscher Ingenieure: Duesseldorf, Germany, 2000. [Google Scholar]
- Janke, D.; Swaminathan, S.; Hempel, S.; Kasper, R.; Amon, T. Sample Case Files for the Particulate Matter Dispersion Modeling in Agricultural Applications. 2021. Available online: https://github.com/ssacfd/ATB_particletransport (accessed on 5 September 2021).
- Lin, J.J.; Noll, K.E.; Holsen, T.M. Dry deposition velocities as a function of particle size in the ambient atmosphere. Aerosol Sci. Technol.
**1994**, 20, 239–252. [Google Scholar] [CrossRef][Green Version] - United States Environmental Protection Agency. Air Quality Guide for Particle Pollution. 2015. Available online: https://www.airnow.gov/publications/air-quality-index/air-quality-guide-for-particle-pollution/ (accessed on 5 September 2021).
- Janke, D.; Caiazzo, A.; Ahmed, N.; Alia, N.; Knoth, O.; Moreau, B.; Wilbrandt, U.; Willink, D.; Amon, T.; John, V. On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn. Comput. Electron. Agric.
**2020**, 175, 105546. [Google Scholar] [CrossRef] - Nozawa, K.; Tamura, T. Simulation of rough-wall turbulent boundary layer for LES inflow data. In Second Symposium on Turbulence and Shear Flow Phenomena; Begel House Inc.: Danbury, CT, USA, 2001. [Google Scholar]
- Nozawa, K.; Tamura, T. Large eddy simulation of the flow around a low-rise building immersed in a rough-wall turbulent boundary layer. J. Wind Eng. Ind. Aerodyn.
**2002**, 90, 1151–1162. [Google Scholar] [CrossRef] - Lund, T.S.; Wu, X.; Squires, K.D. Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys.
**1998**, 140, 233–258. [Google Scholar] [CrossRef][Green Version] - Esmen, N.A.; Corn, M. Residence time of particles in urban air. Atmos. Environ. (1967)
**1971**, 5, 571–578. [Google Scholar] [CrossRef] - Sehmel, G.A. Particle eddy diffusivities and deposition velocities for isothermal flow and smooth surfaces. Aerosol Sci.
**1973**, 4, 125–138. [Google Scholar] [CrossRef] - Van Buggenhout, S.; Van Brecht, A.; Özcan, S.E.; Vranken, E.; Van Malcot, W.; Berckmans, D. Influence of sampling positions on accuracy of tracer gas measurements in ventilated spaces. Biosyst. Eng.
**2009**, 104, 216–223. [Google Scholar] [CrossRef]

**Figure 2.**Geometry for flow field validation. (

**a**) Overview of the computational domain. (

**b**) Detailed view on the cross section of the two buildings forming a street canyon.

**Figure 3.**Mesh convergence study for the flow field validation. The three measurement points from the experiment of [35] were located on a horizontal line in the street canyon on a height of 0.7 H. The values on the ordinate are the normalized velocities in z-direction, with U

_{H}as the reference velocity at the inlet on the reference height H. Experimental data from [35], Elsevier, 2008.

**Figure 4.**Comparison of simulation and experimental results for four different subgrid scale turbulence models. (

**a**,

**b**) show the static models, (

**c**,

**d**) the dynamic models. The normalized vertical velocity, with U

_{H}as a reference, is shown, which is the inlet velocity at height H. The contours from the experiment are plotted as solid lines and those from simulations as dotted lines, where colors indicate the velocity values.

**Figure 6.**Comparison of the vertical profiles for the velocity in x-direction. Dots and dashed black lines were formed with data from the experiment of [42], Elsevier, 2006. Red lines are the simulated velocities from the RANS approach, green lines are the time-averaged results from the LES approach.

**Figure 8.**Comparison of measured and simulated particle concentrations with data from the experiment of [42]. The particle concentration values were normalized with the measured particle concentrations at the inlet of the test room or the computational domain. For the simulations with the two solvers

`PimpleLPTFoam`and

`MPPICFoam`, particle concentrations were computed as the time average of 1800 s simulation time. Experimental data from [42], Elsevier, 2006.

**Figure 9.**Sketch of the domain used for the simulation of the application example. Particles were injected at x = 50 m at three different lateral points y = [−0.25, 0, 0.25] m at a height of 1.5 m.

**Figure 10.**Particle size distribution injected in the application example. The size distribution was obtained from experiments with aerosolized manure in a wind tunnel, as described in [10].

**Figure 11.**View on the instantaneous flowfield after 400 s of simulation. (

**a**) shows the iso-contours for Q = 0.01 s

^{−2}, which is the 2nd invariant of the velocity gradient tensor. Surface coloring is carried out in accordance with mean velocity, as shown in the color bar. (

**b**) shows the vorticity of the flowfield after 400 s on a section on the XZ-plane at y = 0, with a height up to z = 40 m.

**Figure 12.**Development of the vertical profiles of (

**a**) velocity, and (

**b**) Reynolds stress R

_{11}at four different locations along the domain in x-direction. Colored lines are the simulation results and time-averaged over 400 s. Black dots are values set at the inlet, derived from atmospheric boundary layer wind tunnel experiments [49].

**Figure 13.**Spread of particles at 120 s from x = 50 m to x = 200 m (Front view with x axis along horizontal and z axis along vertical). The coloring indicates the age of the particles.

**Figure 15.**Volume fraction of PM10 for different heights at 120 s (top view of the domain with x axis along horizontal and y axis along vertical).

Fine | Medium | Coarse | |
---|---|---|---|

Min | 0.44 | 0.71 | 1.42 |

Max | 61.80 | 79.76 | 167.71 |

Avg | 10.94 | 13.04 | 25.28 |

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## Share and Cite

**MDPI and ACS Style**

Janke, D.; Swaminathan, S.; Hempel, S.; Kasper, R.; Amon, T. Particulate Matter Dispersion Modeling in Agricultural Applications: Investigation of a Transient Open Source Solver. *Agronomy* **2021**, *11*, 2246.
https://doi.org/10.3390/agronomy11112246

**AMA Style**

Janke D, Swaminathan S, Hempel S, Kasper R, Amon T. Particulate Matter Dispersion Modeling in Agricultural Applications: Investigation of a Transient Open Source Solver. *Agronomy*. 2021; 11(11):2246.
https://doi.org/10.3390/agronomy11112246

**Chicago/Turabian Style**

Janke, David, Senthilathiban Swaminathan, Sabrina Hempel, Robert Kasper, and Thomas Amon. 2021. "Particulate Matter Dispersion Modeling in Agricultural Applications: Investigation of a Transient Open Source Solver" *Agronomy* 11, no. 11: 2246.
https://doi.org/10.3390/agronomy11112246