# Development of a CFD Model to Simulate Natural Ventilation in a Semi-Open Free-Stall Barn for Dairy Cows

^{*}

## Abstract

**:**

## 1. Introduction

^{®}. Next, Ansys ICEM 17.1

^{®}software tool was used in order to obtain the mesh of both the modelled objects and other elements outside the barn (i.e., trees and rural buildings). The same software tool made it possible to set boundary conditions. Finally, Ansys Fluent 17.1

^{®}software tool was used to simulate indoor natural ventilation by using as simulation parameters airflow velocities collected by a meteorological station nearby the barn. Due to the difficulty of the modelling phase, this study focused on a relevant cross-section of the building that intercepted the decubitus area of the animals, where they spent 8–10 h a day. This cross-section was also significant for the analysis of the internal microclimatic conditions.

## 2. Materials and Methods

#### 2.1. The Barn Under Study and Acquisition Data Systems

^{2}, which were located on the North-East wall of the building and gave access to the boxes for calves and heifers. Other two areas along the North-East wall were used as offices for herd management. Finally, with regard to the main building components, the flooring was in concrete, the bearing structure consisted of steel pillar and beams, and the roof was composed of steel trusses and corrugated fibre cement sheet roofing. Sensors were positioned inside the resting area, where the animals spent most of their time, which was therefore significant with regard to the potential effects of natural ventilation on animal welfare, and outside the barn, nearby the chimney, for testing the CFD model also in extreme conditions due to the presence of high turbulence. The heights of the probes were, respectively, equal to 2.50 m (inside the barn) and 7.50 m (outside the barn, about 1 m above the chimney).

^{−1}), the average hourly wind speed (ms

^{−1}), and the average hourly wind direction (°). The incoming wind velocity profile showed wind-speed growth along with height increase [24]. In this study, to build a wind velocity profile, an equilibrium boundary layer was assumed, and data acquired by the meteorological station were used in the power law reported in the following Equation (1):

_{ref}is the mean velocity at the considered reference height, Y

_{ref}is the reference height, and α is the power law exponent.

#### 2.2. CFD Analysis

#### 2.2.1. 3D Modelling

^{®}software tool (2016 Autodesk In., San Rafael, CA, USA). The axes of the Cartesian coordinate system were set parallel to the longitudinal axis of the barn. As reported in the guidelines referred to the best practice, in this modelling phase the case study was reproduced with an adequate level of detail. The term “adequate” means that the level of detail should be enough to reflect the real situation, but not too much for not having too many cells in the meshing phase. In fact, this would imply an excessive computational cost [25]. Many simplifications were made in order to reach this goal. All the small internal elements–such as trusses, low walls, fans, and steel pillars–were excluded or simplified. The floor was considered at a single height, and the corrugated fibre cement sheet roofing was simplified and modelled without any undulations. The barn was modelled as an empty building, i.e., without dairy cows. The surrounding trees and other rural buildings were reproduced as simple geometries, i.e., parallelepiped and prisms (Figure 4). Regarding the trees, only the foliage and not the trunk was considered. Finally, all the solids were reduced to surfaces. In this phase, the computational domain was also modelled. The computational domain should be large enough to permit flow development, avoiding at the same time flow artificial accelerations in the region of interest. As suggested by Franke et al. [25], the computational domain was built as a parallelepiped. Taken as reference, the height of the building equal to H, the inlet surface, and the vertical and the lateral extensions were set equal to 5 times H (5H) from the building closest to the perimeter of the domain. The outflow boundary was positioned at least at 20 times H (20H) downwind the building.

#### 2.2.2. Mesh Characteristics and CFD Modelling

^{®}software tool to build the mesh and assign the boundary conditions. The mesh used was hexahedral, and the grid was unstructured since it was very flexible compared to the structured one for building complex geometries. Rules given by literature guidelines were followed to choose the cells parameters (i.e., ratio and spacing). The number of cells is equal to about 7.95 million (8.15 million nodes). Symmetry boundary conditions have been considered on the top and lateral sides of the computational domain in order to enforce a parallel flow [1,26,27,28,29,30]. At the boundary upwind of the barn, a velocity inlet boundary condition has been used, while downwind of the barn, i.e., where the fluid leaves the computational domain, an outflow boundary condition, corresponding to a fully developed flow [31], has been used to force all derivatives of the flow variables to vanish [25] (Figure 5). The boundary conditions regarding solids and grounds have been set as walls, and those regarding openings and foliage have been set as interior.

^{®}software tool, which made it possible to apply turbulence model, porous media, and solver setting. The Navier–Stokes equations represent the fundamental equations of fluid dynamics and form the basis of CFD modelling [32]. During the process of CFD modelling, one important step was to select the appropriate turbulence models to describe the turbulent flow. The standard k-ε model turbulence model, i.e., a semi-empirical model based on transport equations for the turbulent kinetic energy and its dissipation rate, has been used, with dissipation rate profiles specified as

_{v}is the von Karman’s constant, z

_{0}is the surface roughness, and u

_{*}is the friction velocity, calculated from a specified velocity U

_{ref}at a reference height. The turbulent kinetic energy for inlet boundary was derived from

_{µ}is an empirical constant. This turbulence model was chosen due to its simple format and robust performance, and because of its favourable convergence behaviour and reasonable accuracy [33,34]. The realizable and the standard K-ε turbulence model were both simulated: it was observed that the simulated results were very close to each other, so the second one was chosen due to it having lower computational costs. The Standard Wall Functions by Launder and Spalding [35] were chosen as wall treatment for solid surfaces.

_{i}is equivalent to pressure gradient, µ is air dynamic viscosity (Nsm

^{−2}), α is the permeability (m

^{2}), ρ is the air density (kgm

^{−3}), |u| is the magnitude of the velocity, C

_{2}is the inertial resistance factor, k

_{r}is a dynamic parameter that depends on porosity and shape of the barrier elements, and W is the width of vegetative barrier (m). In particular, the term $\frac{\mu}{\alpha}{u}_{i}$ is the viscous loss term and ${C}_{2}\frac{1}{2}\rho \left|u\right|{u}_{i}$ is the inertial loss term.

#### 2.2.3. Mesh Sensitivity

## 3. Results and Discussion

#### 3.1. Setting of Model Parameters by Data Analyses

^{−1}to 9.60 ms

^{−1}, with mean values and standard deviation equal to 3.85 ms

^{−1}and 2.59 ms

^{−1}, respectively.

_{ref}, Y

_{ref,}and α were used:

- A mean velocity U
_{ref}at reference height equal to 3.85 ms^{−1}; - A reference height Y
_{ref}equal to 10 m; - A power law exponent α equal to 0.14.

_{0}was set equal to 0.019, and u

_{*}was set equal to 0.236 ms

^{−1}, taking as reference a height of 10 m. The turbulent kinetic energy for inlet boundary was set as a constant value, derived from Equation (3), where C

_{µ}is an empirical constant taken equal to 0.09 [26]. With regard to porosity, in this research it was not directly estimated. According to Gan and Salim [43], the porosity value of 0.96 was assumed. According to Guo and Maghirang [36], viscous loss term in Equation (4) was ignored, so the viscous resistance was set as 0. According to previous research [44], C

_{d}was set equal to 0.25 and dSA was set equal to 1.6 m

^{−1}, so the final pressure loss coefficient is 0.4 m

^{−1}. Finally, model convergence was not assumed to be reached until both the velocity magnitude at the monitoring points and the residual had stabilized [2]. The iteration steps necessary to reach a convergent solution were about 1500. After the simulation was completed, the balance of mass was checked.

#### 3.2. Validation of the Model

#### 3.3. Mesh Sensitivity

#### 3.4. Study of Air Velocity Distribution in the Barn

^{−1}in the resting areas, service alley, and feeding alley, that housed dairy cows. With regard to box for calves, average air velocity was equal to 0.67 ms

^{−1}(Figure 12).

## 4. Conclusions

- Know the air velocity in areas considered most sensitive for the presence of animals;
- Find, in a future research based on the results of this study, alternative design configurations, with the aim to discover the best condition for the well-being of users and animals.

^{®}; then, it was imported into Ansys ICEM CFD 17.1

^{®}to build the unstructured mesh and to assign the boundary condition. Finally, the numerical simulations were carried out by using the Ansys-Fluent 17.1

^{®}program. A limitation not concerning the modelling process is that the experiment was conducted under isothermal cases. This choice, together with the simplification concerning the model, would not affect the objective of the present study, because for the authors all the elements that strongly affect the airflow development and air velocity distribution were taken into account, as reported in some past studies [2]. By using the described CFD methodology, a representation of the airflow distribution was given. It was considered good because it reflected the real condition inside the barn, where the internal distribution of the spaces and the position of the openings strongly impact the air velocity, and because of the comparison carried out between measured and simulated data. Therefore, the methodology applied in this paper could represent an example of how to study the natural ventilation of livestock buildings having similar characteristics. Since the modelled air velocity distribution in the barn fitted the real one well, the CFD model was considered reliable to study other transversal and longitudinal sections, by adding other anemometers. Future implementations should also regard the increase of the geometry complexity, or the study of gas distribution according to the study of airflow distribution. Furthermore, future studies will be carried out in order to evaluate the residence time of the air at each point of the model through the concept of “age of air”.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 6.**(

**a**) Prevailing air velocity in the reference week and (

**b**) prevailing magnitude in the reference week.

**Figure 7.**(

**a**) Downwind mesh comparison, (

**b**) mesh comparison inside the barn, and (

**c**) upwind mesh comparison.

**Figure 10.**(

**a**). Plane A—air velocity distribution (ms

^{−1}) and (

**b**) Plane A—air velocity vectors distribution (ms

^{−1}).

**Figure 11.**(

**a**) Plane B-air velocity distribution (ms

^{−1}) and (

**b**) Plane B-air velocity vectors distribution (ms

^{−1}).

Sicilian Provinces | Number of Livestock Farms |
---|---|

Trapani | 170 |

Palermo | 964 |

Messina | 698 |

Caltanissetta | 188 |

Enna | 420 |

Catania | 397 |

Ragusa | 1472 |

Syracuse | 569 |

Number of Livestock Farms | ||||
---|---|---|---|---|

Sicilian Provinces | Cattles and Buffaloes Housing | Pigs Housing | Laying Hens Housing | Broilers Housing |

Trapani | 113 | 9 | 65 | 13 |

Palermo | 813 | 47 | 139 | 25 |

Messina | 458 | 143 | 191 | 30 |

Caltanissetta | 164 | 6 | 28 | 2 |

Enna | 394 | 21 | 16 | 3 |

Catania | 303 | 48 | 91 | 29 |

Ragusa | 1389 | 159 | 60 | 19 |

Syracuse | 535 | 52 | 38 | 6 |

N. Simulation | Air Velocity at Weather Station (10 m height) (ms ^{−1}) | Air Velocity Outside the Barn (ms^{−1})(Sensor B) | Air velocity Inside the Barn (ms^{−1})(Sensor A) | ||||
---|---|---|---|---|---|---|---|

MEASURED | SIMULATED | RELATIVE ERROR % | MEASURED | SIMULATED | RELATIVE ERROR % | ||

1 (27/04-22:00) | 1.90 | 1.14 | 1.38 | 18.84 | 0.24 | 0.29 | 16.90 |

2 (28/04-02:00) | 2.90 | 1.83 | 2.08 | 13.02 | 0.40 | 0.45 | 12.31 |

3 (28/04-06:00) | 2.70 | 2.04 | 1.89 | 7.56 | 0.44 | 0.44 | 0.32 |

4 (28/04-07:00) | 2.70 | 1.96 | 1.89 | 3.64 | 0.46 | 0.44 | 5.00 |

5 (28/04-19:00) | 6.40 | 3.94 | 4.59 | 15.31 | 0.98 | 0.98 | 0.08 |

6 (28/04-20:00) | 6.00 | 3.43 | 4.31 | 22.82 | 0.79 | 0.91 | 14.70 |

7 (28/04-21:00) | 7.80 | 3.38 | 5.58 | 49.21 | 0.89 | 1.19 | 29.13 |

8 (28/04-22:00) | 7.90 | 4.51 | 5.66 | 22.65 | 1.07 | 1.20 | 11.36 |

9 (29/04-00:00) | 5.80 | 4.06 | 4.17 | 2.68 | 0.95 | 0.88 | 7.71 |

10(29/04-01:00) | 6.80 | 4.27 | 4.89 | 13.45 | 1.10 | 1.03 | 6.35 |

11(29/04-02:00) | 8.20 | 5.50 | 5.89 | 6.89 | 1.23 | 1.26 | 2.07 |

12(29/04-03:00) | 6.80 | 4.45 | 4.89 | 9.48 | 1.02 | 1.03 | 0.98 |

13(29/04-05:00 | 8.50 | 3.97 | 6.08 | 42.04 | 0.89 | 1.29 | 36.98 |

14(29/04-06:00) | 8.50 | 4.13 | 6.08 | 38.17 | 0.87 | 1.29 | 39.22 |

15(30/04-00:00) | 2.00 | 1.16 | 1.44 | 21.30 | 0.32 | 0.31 | 4.23 |

16(30/04-01:00) | 2.50 | 1.45 | 1.80 | 21.65 | 0.27 | 0.38 | 35.59 |

17(30/04-02:00) | 2.00 | 1.34 | 1.44 | 7.48 | 0.32 | 0.31 | 1.98 |

18(01/05-01:00) | 2.80 | 2.00 | 2.01 | 0.54 | 0.45 | 0.43 | 4.72 |

19(01/05-02:00) | 2.00 | 1.99 | 1.44 | 32.04 | 0.39 | 0.31 | 23.36 |

20(01/05-05:00) | 1.40 | 0.93 | 0.98 | 5.43 | 0.32 | 0.24 | 29.61 |

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**MDPI and ACS Style**

Tomasello, N.; Valenti, F.; Cascone, G.; Porto, S.M.C.
Development of a CFD Model to Simulate Natural Ventilation in a Semi-Open Free-Stall Barn for Dairy Cows. *Buildings* **2019**, *9*, 183.
https://doi.org/10.3390/buildings9080183

**AMA Style**

Tomasello N, Valenti F, Cascone G, Porto SMC.
Development of a CFD Model to Simulate Natural Ventilation in a Semi-Open Free-Stall Barn for Dairy Cows. *Buildings*. 2019; 9(8):183.
https://doi.org/10.3390/buildings9080183

**Chicago/Turabian Style**

Tomasello, Nicoletta, Francesca Valenti, Giovanni Cascone, and Simona M. C. Porto.
2019. "Development of a CFD Model to Simulate Natural Ventilation in a Semi-Open Free-Stall Barn for Dairy Cows" *Buildings* 9, no. 8: 183.
https://doi.org/10.3390/buildings9080183