3.1. Mesh Details
Dairy cows are mainly housed in naturally ventilated dairy barns with large openings, connected directly to the ambient, turbulent weather conditions. This makes the measurements of volume flow rate from these buildings challenging. Hence, a substantial amount of time was spent in the design of representative meshes to increase the accuracy of CFD results. If an optimum distance between the dairy barn and the boundary of the control volume is not sufficiently secured, faster airflow streams could be compared with the natural airflow resulting in unreal airflow around the leeward vent opening [
22]. Thus, the size of the CFD domain used during the simulations was chosen in order to ensure that the position of the outer boundaries did not compromise the CFD solution.
A tetrahedral mesh was built in commercial ANSYS ICEM CFD
® and tests of different meshes were carried out using this software. Various sizes of tetrahedral meshes were used, and after several levels of previously evaluated refinement, no significant differences (
p-value < 0.05) in the air velocity and temperature were encountered. Thus, the selected mesh was composed of 162,191 nodes and 683,222 elements (
Figure 7). Such a meshing system was found to conform easily to the exact boundary of the scale model. The convergence of the solution was carefully verified by monitoring the transport equation residuals throughout the simulation.
In the present study, the authors decided to use the standard
k–ε model to model the natural ventilation in the CBP. Previous studies [
24] have shown that the standard
k–ε model predicts reasonably well the airflow patterns in an experimental naturally ventilated livestock building.
3.2. Validation of the Measured and Simulated Values
The values of air velocity, using five ridge openings and air speed of 0.1 and 1.0 m s
−1, gave a fair correlation of measured versus simulated values. Values of R
2 and the regression equation are shown in
Table 4. Good correlations were observed between measured and simulated values of air temperature, using five ridges opening and air speed of 0.1 and 1.0 m s
−1. In both conditions, for the linear and angular coefficients significant differences were detected (
t test,
p-value > 0.05).
A good relationship was observed between measured and simulated values using air speed of 0.1 m s
−1 and four wind directions tested. The adjusted equations of air velocity and temperature had the lowest R
2 of 0.559 and 0.627, respectively (
Table 4). Overall, the wind directions performed similarly with the exception of East to West, which produced the largest values of air velocity and temperature measured. In this treatment, there was a positive and linear relationship between the average of measured and simulated air velocity (slope = 0.8239, R
2 = 0.559) and temperature (slope = 0.4663, R
2 = 0.627). The results show a good correlation between measured and simulated air velocity at four wind directions tested (
Table 4). These were demonstrated by the correlation coefficients (R
2). In both conditions, these equations showed the linear and angular coefficients significant (
t test,
p-value > 0.05).
Given that the absolute average errors calculated between air velocities and temperature measurements and simulated values were very close to or less than 0.21 m s−1 and 1.53 °C, respectively, the accuracy values of the anemometer (±0.01 m s−1) and thermometer (±1.0 °C) at that magnitude of these errors would have little influence on the final result for the calculation of the variables studied. Thus, the computer models can be considered suitable for the proposed use.
3.3. Computational Simulation
A real CBP barn found in Kentucky (1.35 m × 1.20 m × 0.27 m) with five different ridge types and four wind directions was used in CFD simulations, where the average air velocity outside the CBP barn was 0.04 m s−1 and heat flux of the floor (all compost area) was 0.1 W m−2. The inlet air velocity used in the model was computed using similitude theory, obtaining a value of 0.1 m s−1.
The calculated values obtained using similitude theory for an open CBP barn without dairy cattle and subjected to natural ventilation were used to assign the boundary conditions of the model: 0.1 m s−1 average inlet air speed, 6.9 °C air inlet temperature, 101.325 kPa atmospheric pressure and 0.1 W m−2 heat flux floor.
The air velocity distribution in a vertical plan situated in the center of the barn allows us to determine the inside air speed more precisely.
Figure 8 shows the simulated air velocity vectors vertically inside and around of CBP barns equipped with closed ridge (CLR) using a different wind direction. Visually, the simulation results for east to west wind direction were very similar to west to east wind direction, thus, only the east to west wind direction is shown.
Figure 8A shows the air entering the CBP barn through the ridge opening at one side, and then coming out through the sidewall opening located at the other side. So, the airflow velocity was reduced due to the presence of the wall and fences on both sides of the barn. It resulted in an internal vortex at the center of the feed alley and compost area.
Figure 8B shows the effect of airflow the compost surface area near the alleyway. In
Figure 8C, it can be seen a considerable variation in the direction of the air velocity vectors. Inside of the trusses structure, it can be seen that the main flow tends to turn opposite to the main wind direction. As result, the vortex of the airflow promoted the worst conditions of air circulation. A strong vortex is developed at the top of the ridge structure when the wind direction occurred along the length of the CBP. The vortex occupies almost the whole cavity in the ridge structure due to the inversed flow created through the central surface bedding area. The building geometry is a crucial aspect to achieve efficient natural ventilation and indoor thermal comfort in a CBP environment.
Vortex paths are important, especially in the surface of compost bedding where turbulent fluctuations dominate over the mean flow [
25]. Measurements in a full-scale set-up of this kind are challenging, not the least due to the variation of wind direction during averaging periods.
Figure 9 shows the simulated air velocity vectors vertically inside and around of CBP barns equipped with open ridge (OPR) using different wind directions. According to
Figure 9A,B, these barns produced higher ridge vent flows for the south to north and north to south wind directions at wind velocities above 0.07 m s
−1. Wind direction comparisons indicated that south winds consistently produced the highest ridge vents flows (
Figure 8A), while the east and west winds generated the lowest ridge vent flows (
Figure 9C). It can be seen that the main flow tended to turn opposite the main wind direction. In all cases, the roof presents a complicated area to model due to turbulent shear layers and ridge vent openings zones. However, this is likely to be the least important face for ventilation calculation in most animal facilities. A similar effect was observed by other researchers [
23].
Figure 10 shows the simulated results of CBP barn equipped with open ridge with chimney (ORC) in different wind directions.
Figure 10A,B shows considerable variation in the direction of the air velocity vectors, and consequently the flow is far from being two-dimensional. Near the ridge opening, it can be seen that vortex was located above the roof in the right (
Figure 10A) and left (
Figure 10B) side. From the
Figure 10B, the north wind direction, which produced the highest ridge vent flows, also generated high air velocities inside the structure. The contour plot of wind speed revealed periodic air recirculation zone above the building due to the flow redirection caused by the chimney. Due to a portion of the high-speed, incoming airflow becomes incorporated in the indoor flow regime. This airflow recirculation was highly influenced by the velocity of the short-circuiting flow beneath the roof.
Distribution of air velocity on the compost area in winds direction east to west (
Figure 10C) was more uniform than the other directions tested. In this case, the air movement tended to stabilize, generating lower air velocity above the compost area. The amount of obstruction of the building is known to have an impact on the flow that crosses the structure, whereby potentially affecting air velocity values [
15]. Due to the size of the heat source and the geometric of the building, the flow was forced over the ridge vent.
The flow near the floor was decelerated due to the stagnation point at the fence and wall that directed the airflow to the top of the building.
Figure 11 shows the simulated results of CBP barn equipped with elevated ridge (ELR) in different wind directions. The east and west wind directions present the higher ridge vent outlet flow (
Figure 11C). The wind flows up the windward wall surface and above the roof of the barns with east and west winds (
Figure 11C) but hits the roof inside the barn with south and north winds (
Figure 11A,B). In addition, a lower pressure area was created above the roof in the east and west winds than in the south and north winds, thereby generating higher ridge opening flows.
Figure 12 shows a representation of air velocity vectors distribution vertically when overshot ridge (OVR) was equipped in different wind directions. The recirculation zone of the airflow formed above the roof in simulated barn with south winds (
Figure 12A) was smaller than simulated barn with north winds (
Figure 12B). Therefore, as can be seen in
Figure 12C, the recirculation zone was situated after the barn at windward gable wall height in the simulated barn with east and west winds. The south and north winds direction created the lowest air velocity values differences (
Figure 12A,B) and east and west winds produced the highest air velocity values differences (
Figure 12C). Airflow entered through both sides the opening wall and owing to density differences between the inside and outside air, it immediately dropped to the floor. Single-sided ventilation tended to show comparatively lower air change rates but increased recirculation zone intensity on the surface of cover (
Figure 12A,B). This airflow then travelled toward the center of the building, heating up as it passed over the compost area before it eventually rose. A similar observation has already been reported by Norton et al. [
17].
Figure 13 shows the air velocity distribution in a vertical plan situated in the center of the CBP barn simulated equipped with different types of ridge vents for four wind directions. As evidenced in
Figure 13A for the CBP barn equipped with closed ridge (CLR), the higher air velocity values was observed near to the compost area in east and west winds. However, in the near ridge region, both these winds directions failed to perform well with air velocity values around 0.1 m s
−1. The findings were sensitive to slight wind direction changes and therefore significant variation was found for all parameters measured. For the CBP barn equipped with open ridge (OPR;
Figure 13B), the examination of the air velocity inside the barn above the compost bedding surface demonstrated that the values were very close at 0.2 m height from the ground. However, it can be observed that the air velocity values in the directions of the southerly and northerly winds rapidly increase in the ridge area. For the CBP barn equipped with open ridge with chimney (ORC;
Figure 13C), the air velocity value above the compost area was lower in the south and north wind direction due to the drag effect of the sidewall planks. The air velocity values were lower near ridge opening in the east and west wind direction. For the CBP barn equipped with an elevated ridge (ELR),
Figure 13D shows that the average air speed in the space between the top of the compost area and the barn roof was approximately half that of the outside wind, for all wind directions. Air velocity was much lower inside the barn than outside and its flow through ridge opening was systematically higher in the south and north wind directions. Finally, for the CBP barn equipped with overshot ridge (OVR;
Figure 13E), the air velocity shows approximately the same values at 0.02 m above the compost area for all the wind directions tested, but values strongly decreased near the ridge opening in the east and west wind direction, then increased progressively from the ridge opening.
3.4. Evaluation of the Types of Ridge Vents and Wind Direction
Maintaining active composting in a compost bedded pack barn is a real challenge during the winter months. It becomes difficult to start or restart a compost bedded pack barn in winter with low bacterial activity as the heat losses can easily outweigh the heat generated. Due to this, to select the best condition of ventilation in the winter weather, the CFD models were evaluated in the function of five types of ridge vents (CLR, OPR, ORC, ELR and OVR) and four wind directions (north, south, east and west) to promote greater percentage heated surfaces of the floor.
The analyses of variance for the five types of ridge vents and the four wind directions as a function of the percentage of heated floor area are shown in
Table 5. No statistically significant differences were found (
p > 0.05) between the types of ridge vents (
p-value = 0.716) and the wind direction (
p-value = 0.874).
Heating area percentage is an indicator of the efficiency of the composting process. This is achieved by an adequate selection of ridge opening and wind direction that maintains ideal microbiological conditions in terms of aeration and temperature with a range of 45–60 °C. The mean values of percentage of the heated floor area in the five types of ridge vents and the four wind directions are shown in
Table 6. Statistically significant evidence was found to state that the means of the heating area percentage between simulations differed (Tukey test;
p-value < 0.05). The highest percentage of heated floor of the surface area inside the CFD models were observed in treatments ORC and west to east wind direction. The type of ridge vent and wind direction that promoted greater cooling surface of the floor were the treatments ELR and the south to north wind direction. These results showed that the best ridge vent and wind direction in the winter weather were observed in the open ridge with chimney (ORC) and west to east, respectively.
This work provided the designer with practical knowledge on the behavior of natural ventilation due to wind direction and thermal buoyancy forces acting in the CBP under different ridge vent openings. By applying CFD simulation and experimental investigation, a methodology was prepared to determine the behavior of airflow caused by thermal buoyancy and wind direction. The innovation of the methodology can be described by the fact that some equations were formed to estimate air velocity and air temperature and determine which ridge vent opening was most efficient.
3.5. Cattle Dairy Compost Barn Building Validation Tests
In
Figure 14, the behavior of the air velocity measurements in five real CBP barns with different roof types present in Kentucky was estimated in
Table 4. Results showed that the empirical equation to determine V
air was statistically significant (
p-value < 0.0001) and it presented the lowest coefficient of determination of 0.8157 (
Figure 14D), being subsequently validated via a
t test (
p-value > 0.05). The adjusted equations were statistically significant (F test,
p-value < 0.0001), providing an average error of 0.38 m/s.
The variability of the V
air real measured and simulated was higher for the OVR (
Figure 14D), which presented an average and standard deviation equal to 0.63 ± 0.39 m/s and 0.58 ± 0.42 m/s, respectably. In such a CBP, the area with the lowest V
air was observed in the north face, over the bed area, due to the structure of the barn that blocks and redirecting the air flow.
In the ELR (
Figure 14C), the real and simulated air velocity values showed a lower average (0.56 and 0.52 m/s, respectably) and variation equal to 0.37 and 0.32 m/s, respectably. The region with the lowest V
air occurred near the north face.
The worst situation was verified for the CBP with ORC (
Figure 14E), where V
air was less than 0.60 m/s in 48.9% of the barn area. On the other hand, in CBP equipped with OVR (
Figure 14D), V
air was greater than 1.0 m/s in 58.4% (real) and 42.1% (simulated) of areas respectively, showing that the systems used promoted the increase of such an attribute to levels close to adequate in most of the facilities.
The minimum and maximum average airflow velocities were 0.05 and 1.1 m/s, respectively. In all case, natural ventilation on this face of the barn became reduced, reducing heat exchanges with the environment and making surface temperature of bed composting lower.
In all CBP facilities evaluated, the V
air was lower than the recommended (
Figure 14). According to Black et al. (2013), in CBP facilities, the ventilation should be provided such that the V
air is close to 1.8 m/s throughout the entire CBP, so that it can dry the bed, remove gases and favor the heat exchanges between the animal and the environment.
The results also show that the use of mechanical ventilation in tropical conditions is necessary for the proper functioning of the system, since only the natural ventilation was not sufficient to promote Vair values according to the recommendation for CBP barns.