Enclosed Barn Conditioning System: A Comparison Between Traditional and Indirect Evaporative Cooling

2.1 Barn heat load assessing

Firstly, the hypothetical heat load of a barn (Figure 1) sized to accommodate a population of 500 lactating cows was assessed.

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Figure 1. Simplified layout of the barn

It was assumed that the structure had an overall external surface area S_barn of 8,900 m² (including the roof and lateral walls) and a total volume V_barn of 41,700 m³. Table 1 shows the building thermal properties considered for the calculation.

Table 1. Barn thermal properties

The floor was assumed to be adiabatic. The hourly climatic conditions recorded by the weather stations near the city of Modena (one of the 5 province of Parmigiano Reggiano production) were downloaded from the Environmental Agency (ARPAE) of the Emilia-Romagna Region website (https://simc.arpae.it/dext3r). The data used refers to the period between 12:00 AM on August 15, 2018, and 12:00 AM on August 15, 2022, including air temperature T_amb, relative humidity φ_amb [%], wind velocity v, and total irradiation I. This data was used for the hourly heat loads computation for a time-span of four years, from August 15, 2018, to August 15, 2022.

2.1.1 Vapor-compression energy calculation

To calculate the electrical energy requirement of a vapor-compression chiller, it is necessary to establish the thermo-hygrometric conditions inside the barn. Specifically, a temperature of 25℃ (T_barn) and a relative humidity of 50% (φ_amb) were chosen. The number of air changes per hour n_a was fixed at two. With this information, it is possible to calculate the heat load Q_barn that needs to be removed by the chiller to reach the desired conditions, which is the sum of: external heat load Q_out due to radiation and convection with external walls and roof, the sensible heat of the air introduced into barn Q_s, the condensation enthalpy of the water that needs to be condensed Q_w, and the metabolic heat produced by the cows Q_m as indicated in Eq. (1).

$Q_{barn }=Q_{out }+Q_s+Q_m+Q_w$     (1)

To calculate Q_out, the sol-air temperature [11] was taken into account with Eq. (2).

$Q_{out }=S_{barn } \cdot U \cdot\left(T_{amb }+\Delta T_{sol }-25^{\circ} C\right) \cdot t$    (2)

U is the overall heat transfer coefficient, t is the time step considered (1 hour), and ΔT_sol  is the temperature increment due to solar irradiation. The overall heat transfer coefficient was calculated as:

$U=\frac{1}{\frac{1}{h_{barn }}+\frac{l}{\lambda}+\frac{1}{h_{out }}}$     (3)

h_out stands for the external convective heat transfer coefficient, and it was estimated as [12]:

$h_{out }=4+4 v$     (4)

ΔT_sol  was calculated as:

$\Delta T_{sol }=R_{out } \cdot F \cdot \alpha \cdot I$     (5)

F is the view factor that was considered 1 for the whole building, R_out  is the external resistance calculated as:

$R_{out }=\frac{1}{h_{out }+h_r}$     (6)

and h_r  is the radiation heat transfer coefficient, calculated as:

$h_r=\varepsilon \cdot 4 \cdot \sigma_0 \cdot T_{s-a}^3$     (7)

σ₀is the Stefan-Boltzmann constant and T_s-ais the average temperature between the air temperature and the external surface temperature, assumed in this work 5℃ higher than the air temperature. Q_s was calculated as:

$Q_s=n_a \cdot V_{barn } \cdot \rho_{air } \cdot c_{p_{air }} \cdot\left(T_{out }-T_{barn }\right)$     (8)

ρ_air is the air density and c_pair  is the air specific heat at constant pressure. V_barn is the total volume of the barn. Q_w  was calculated with Eq. (9).

$Q_w=m_w \cdot 2501.3 ~kJ / kg_{barn }$     (9)

m_w  is the mass of condensed water removed from the air entering the building, computed with Eq. (10).

$m_w=\left(\omega_{out }-\omega_{barn }\right) \cdot n_a \cdot V_{barn } \cdot \rho_{air }$     (10)

ω_out and ω_barn are the humidity ratios of the ambient and inside the barn (corresponding to 50% at 25℃). They were calculated as [13]:

$\omega=0.622 \cdot \frac{\varphi \cdot p_{\text {sat }}}{p_{\text {amb }}-\varphi \cdot p_{\text {sat }}}$     (11)

p_amb is the ambient pressure (101,325 Pa), and p_sat is the saturation pressure at the specific temperature considered (25℃ indoor, T_amb  outdoor). When the m_w results negative for a specific condition, it was assumed zero and no water addition was considered. The hourly Q_m was assumed 0.9 kWh for each cow [1, 14, 15]. Q_barn  was calculated for 8760 hours for each of the four years considered. Then, the electric consumption was calculated by dividing the total heat load by the energy efficiency ratio of the system, namely 2.5.

2.1.2 Indirect evaporative cooling energy consumption calculation

To evaluate the condition that can be reached inside the barn it was chosen an off-the-shelf evaporative cooling system, and the model considered was the Climate Wizard CW-80 Indirect Evaporative Cooler, able to process 20,880 m³/h and with a power consumption of 10 kW per unit [16].

The evaluation of the CW-80 system's performance depends on a tool offered by Seeley International. This tool allows for determining the volume of air flow and its temperature upon exiting the dry channel. These determinations rely on the temperature and humidity conditions at the heat exchanger's entrance. With knowledge of the supplied temperature and volume of air to the environment needing cooling, subsequent calculations were performed to assess the cooling capacity of an M-cycle for cooling the barn.

Once the outlet temperature of the system T_{IEC_out} (corresponding to the inlet temperature in the barn) are known, it is possible to make a simplified black box calculation to calculate the final barn temperature T_f  trough the following formula:

$T_f=T_{I E C_{out }}+\left(Q_{out }-Q_m\right) /\left(n_a \cdot V_{barn } \cdot \rho_{air } \cdot c_{p_{air }}\right)$     (12)

At this temperature it is also possible to calculate the final relative humidity knowing the absolute humidity at the outlet of the indirect evaporative cooling system that correspond to the ambient relative humidity. This because there is no water addition in the dry channel [17]. This calculation can be repeated at different air changes per hours, the higher the n_a, the lower the final temperature and the humidity. Knowing the nominal volume air flow of the system and its electric power consumption, it is possible to calculate the yearly electric energy consumption at different air changes per hour.

2.2 Temperature-humidity index (THI)

THI is a value that represents the combined effects of air temperature and humidity associated with the thermal stress level of the cows [18].

The formula used in this work for calculating the THI is the following [19]:

$T H I=\left[0.8 \cdot T_{a m b}\right]+\left[\left(\frac{\varphi}{100}\right) \cdot\left(T_{a m b}-14.4\right)\right]+46.4$     (13)

A THI ≤74 can be considered normal, a value between 74 < THI < 79 can be classified as alert condition, between 79 ≤ THI < 84 can be considered as a danger condition, and a THI ≥ 84 can be considered an emergency condition [20]. In this work, while the THI in case of compressed vapor chiller is technically imposed by the chosen temperature, the THI obtained with indirect cooling depends on the external conditions and on the number of air changes per hour.

The calculations presented above have delineated the pros and cons of both compressed vapor chillers and indirect evaporative cooling systems. The indirect evaporative cooling system offers advantages rooted in water evaporation and minimal energy consumption required to operate the main ventilators, resulting in remarkably low overall energy consumption. However, this system's performance is heavily reliant on external factors such as relative humidity and inlet air temperature, and it is not always able to maintain the target conditions unless an extremely high number of machines are installed, which remain unused for most of the year.

On the other hand, the traditional compression vapor chiller stands as a well-established and widely adopted solution capable of providing cooling power of up to MWs in standalone configurations. Its relatively lower dependence on external ambient conditions renders it suitable for various environments. Nonetheless, it consumes substantial energy, as its COP is not as high as that of the evaporative system.

A promising avenue for further research involves integrating and managing both systems throughout the day to minimize energy consumption. This combined approach could offer the flexibility of the traditional compression vapor cycle along with the enhanced efficiency of the indirect evaporative cooling system. Furthermore, the literature provides evidence of the potential benefits of using an indirect evaporative cooling system as a pre-cooler for a traditional chiller [20]. This strategy can potentially enhance the vapor compression cycle's performance by maintaining the condenser phase at a steady state, irrespective of external ambient conditions. Furthermore, a focus on evaluating these two systems from an economic point of view, both individually and in combination, would complete the feasibility analysis.