*2.2. Theoretical Research*

Modelling of Water-Evaporative Cooling in the Unit

The water-evaporative cooling process in systems with sprayed layers can be represented as a convective heat exchange of the air flow with heat exchanger plates and a simultaneous evaporation of water from the unit surface accompanied by the absorption of vaporization heat.

The finite difference method is widely used to find a numerical solution to heat exchange problems. In a steady-state mode, the system is described by a set of parameters: the surface temperature of the unit (equal to the wet-bulb temperature), temperature

and relative humidity of the supply air. The air supply cools as heat and moisture are exchanged, approaching the cooling surface temperature, while its enthalpy (heat content) remains unchanged.

The process is limited by the exposure (the process duration), the relative humidity at the unit outlet (climate requirements) and the outdoor air parameters (the temperature and moisture content), which will determine the physical cooling potential.

For practical calculations, these parameters can be considered conditionally stationary. In the boundary layer, at the cooling surface, the relative humidity is 100%. The temperature of the unit wall is equal to the wet-bulb temperature and is assumed as constant for the considered conditions (Figure 6) [16].

**Figure 6.** Diagram of water-evaporative air cooling.

The heat and mass transfer process is characterized by equality of heat extracted from the supplied air and the heat of vaporization expended for moisture evaporation from the unit surface [31]. The cooling intensity (heat transfer) of the air supply is determined based on Newton's equation

$$q\_{\rm cool} = \mathbb{S} \cdot \mathbb{R} \cdot (t\_{\sigma} - t\_w), \tag{1}$$

where *S*—the heat exchange surface area, m2; *α*—the heat transfer coefficient average over the heat exchange surface, W/(m2·K); *to*—the outdoor air temperature, ◦C and *tw*—the heat exchange surface (wet-bulb) temperature, ◦C.

The heat transfer coefficient α is the amount of heat transferred through the unit heat transfer surface per unit time at a temperature difference of 1 ◦C [32].

In engineering calculations, it is expedient to use criterion analysis to determine its value. Thus, based on the aerodynamic similarity criteria it is possible to determine the heat transfer coefficient with high accuracy [33].

$$q\_{\rm cool} = S \cdot \overline{\pi} = Nu \frac{\left(t\_o \cdot \overline{\gamma} \cdot 10^{-5} + 0.0237\right)}{d\_{c,p}}\tag{2}$$

where *Nu*—Nusselt criterion characterizing the correlation of the intensity of heat transfer by convection and heat conduction and *de.p*—hydraulic diameter of the pipe, m.

In the considered unit, the air ducts are pipes with a rectangular cross-section. The channels of the plates are directed along the main air flow (taken conditionally as vertical), as shown in Figure 7.

**Figure 7.** Heat exchanger in cooling mode.

The equivalent diameter for a pipe of rectangular cross-section is determined by the following formula ([32], p. 189):

$$d\_{c.p} = 4\frac{A}{P} = 4\frac{b \cdot h}{2 \cdot (b + h)}\,\tag{3}$$

where *<sup>A</sup>* <sup>=</sup> *<sup>b</sup>*·*h*—cross-section area, m2; *<sup>P</sup>* = 2·(*<sup>b</sup>* <sup>+</sup> *<sup>h</sup>*)—perimeter, m; *<sup>b</sup>*—width of the tube base of a triangular cross-section, m and *h*—height of the tube of a triangular cross-section, m.

The Nusselt criterion (*Nu* = *f* Pr; Re; <sup>Δ</sup>*<sup>T</sup> T* ) is defined by the following formula:

$$Nu = 0.28 \cdot \text{Re}^{0.6} \cdot \overline{\text{Pr}}^{0.36} \cdot \left(\frac{\overline{\text{Pr}}}{\text{Pr}\_{\text{l}}}\right)^{0.25} \text{ }^{\prime} \tag{4}$$

where Re—the Reynolds criterion value for the air flow in the cooling unit; Pr—the average Prandtl criterion value for the air flow in the cooling unit and Prc —the Prandtl criterion value for the boundary layer.

The Reynolds criterion value is defined by the formula

$$\mathrm{Re} = \frac{\upsilon \cdot d\_{\varepsilon, p}}{\mathsf{v}\_{\mathrm{su}}},\tag{5}$$

where νsu—the average kinematic viscosity of the supply air, determined at an average air temperature in the unit *tav* = *to*+*tw* <sup>2</sup> .

The Prandtl criterion value for the boundary layer is defined by the following formula:

$$\text{Pr}\_{\text{l}} = \frac{\eta\_{\text{l}} \cdot c\_{\text{m}} \cdot 10^3}{t\_w \cdot 7 \cdot 10^{-5} + 0.0237} \,\text{}\,\text{}\tag{6}$$

where ηl—dynamic viscosity of the layer, Pa·sec and *cm*—specific mass heat capacity of the air, J/(kg·K).

The dynamic viscosity of the air in the boundary layer is determined by the following formula:

$$
\mathfrak{v}\_{\mathrm{l}} = \mathfrak{v}\_{\mathrm{l}} \cdot \mathfrak{o}\_{\mathrm{su}\prime} \tag{7}
$$

where νc—kinematic viscosity of air in the boundary layer, m2/s and ρsu—air density in the boundary layer, kg/m3.

The temperature of the air in the boundary layer is asymptotically close to the wall temperature and numerically may be assumed to be equal to the wet-bulb temperature. In this case, the kinematic viscosity of air in the boundary layer can be found using the following formula [34]:

$$\gamma\_1 = \frac{324 - 1.5 \cdot t\_w}{10^9} p\_0 + 16.81 + 0.048 \cdot t\_w \cdot 10^{-6} \cdot 287 \frac{t\_w + 273}{p\_0} \,, \tag{8}$$

where *t*w—wet-bulb temperature, ◦C and *p*0—atmospheric pressure, Pa.

Air's density largely depends on its temperature and pressure. The present analysis uses the atmospheric pressure, as the working pressure difference in the cooling unit is about 10–30 Pa, which is 0.01–0.03%. This analysis uses approximations of lower accuracy. Taking differential pressure of this order into account would complicate the analysis in the pursuit of imaginary accuracy. The air density of the boundary layer equals

$$\rho\_1 = \frac{p}{R(t\_w + 273)},\tag{9}$$

where *R*—gas constant, J/(kg·K).

V.P. Gavrikin and E.A. Kuranov obtained the formula to determine the wet-bulb temperature [35] resulting from the analysis of reference data [30]:

$$t\_w = \frac{-7.14 + 0.651 \cdot l}{1 + 9.7 \cdot 10^{-3} \cdot l - 3.12 \cdot 10^{-6} \cdot l^2} \tag{10}$$

where *I*—enthalpy (heat content) of the air, kJ/(kg·K).

The results obtained using the formula deviate from the tabulated values within 0.6%, which is quite sufficient for an engineering analysis.

Water-evaporative cooling takes place with the constant heat content, taking into account that enthalpy of humid air depends on the temperature and moisture content. Taking into account the availability of all initial data for outdoor air, it will be convenient to determine its heat content. The enthalpy is to be determined from the formula

$$I = c\_{d.a.} \cdot t\_o + \frac{(r + c\_v \cdot t\_o)d\_o}{1000},\tag{11}$$

where *cd.a.*–specific mass heat capacity of dry air, kJ/(kg·K).

On the other hand, in a steady-state process the heat flux can be defined as the vaporization heat of the moisture evaporated in the cooling unit, which is expressed by the following formula:

$$q\_{vap} = \frac{W \cdot \overline{\mathfrak{p}} (d\_{su} - d\_o) (r + c\_v \cdot t\_w)}{3600 \cdot 10^3},\tag{12}$$

where *W*—cooling unit capacity, m3/h; ρ—average density of the cooled air, kg/m3; *dsu* moisture content of air at the cooling unit outlet, g/kg d.a.; *do*—moisture content of outdoor

air, g/kg d.a.; *cv*—specific mass heat capacity of dry vapor, kJ/(kg·K) and *r*—specific heat of water vaporization at 0 ◦C kJ/kg.

Relationship (12) is of a deterministic nature, and its accuracy is absolute under conditions of initial data reliability. The specific humidity of the air at the unit inlet and outlet is measurable. However, in our case air parameters at the unit outlet are forecast. In a particular case, the expected moisture content of the air at the cooling unit outlet is equal to the one required by the technology. In all other cases, it is different, which is caused by the difference in the physical properties of the interacting media.

The surface may be covered with a continuous stable film (the film-wetting mode) or individual droplets or drips (the droplet-wetting mode), which determines the size of the interaction surface area. When hygroscopic materials are used, in addition to good wettability they have a certain buffer capacity, which can compensate for disturbances in the film mode.

The specific humidity of air is defined by the formula

$$d = 0.77 \frac{\text{op}}{100} e^{5516.89 \left(\frac{1}{273} - \frac{1}{273 + 7}\right)}\text{}\tag{13}$$

where ϕ—relative humidity of the air, %; *e*—the basis of natural logarithm and *t*—the air temperature, ◦C.

A similar formula is used to determine the specific humidity of air at the cooling unit outlet.

The water-evaporative cooling process is iso-enthalpic. On L.K. Ramzin's I-d diagram, it appears as a segment connecting points 1 and 2, which characterize the state of moist air before (1) and after (2) entering the cooling unit (Figure 8). It is obvious that waterevaporative cooling is possible only if the following condition is observed: *d*<sup>1</sup> < *d*2.

**Figure 8.** Water-evaporative cooling in the I-d diagram.

The average air velocity in the cooling unit is determined from the formula

$$
\overline{w} = \frac{W}{3600 \cdot \frac{\overline{S}}{2}} \tag{14}
$$

where *W*—cooling unit capacity, m3/h and *S*—cross-sectional area of the heat exchanger, m2.

In the process of heat exchange, the air temperature decreases and its density increases proportionally. The average density of the cooled air can be determined from the following formula:

$$\overline{\rho} = \frac{p}{R\left(\frac{t\_o + t\_w}{2} + 2\mathcal{T}3\right)}\tag{15}$$

The supply air temperature drop is proportional to the heat dissipated from it, provided that it does not exceed qv (the heat of vaporization, with a known difference in the specific humidity of the air) and can be found from the following system of conditions:

$$\begin{cases} \text{ By} \, q\_{\text{cool}} \le q\_{\text{rap}} t\_{su} = \frac{q\_{\text{cool}} \cdot 10^3}{0.28 \cdot W \cdot \text{\ $}}\\ \text{ If} \, q\_{\text{cool}} \succ q\_{\text{rap}} t\_{su} = \frac{q\_{\text{sup}} \cdot 10^3}{0.28 \cdot W \cdot \text{\$ }} \end{cases} \tag{16}$$

By determining the air supply temperature and taking into account its specific humidity, we can obtain the relative humidity at the cooling unit outlet:

$$\varphi\_{\rm s\!u} = \frac{100 \cdot d\_{\rm su}}{3.8 \cdot e^{5404.3 \cdot (\frac{1}{273} - \frac{1}{273 + 1})}},\tag{17}$$

where *d*su—moisture content of the air at the cooling unit outlet, g/kg of d.a.

To increase the practical value of the model, it is advisable to determine the minimum necessary water consumption for water-evaporative cooling with a given capacity under specific weather conditions, and the annual water consumption for water-evaporative cooling.

To do this, the wet flow rate for cooling one kilogram of air for specific weather conditions must be determined. Then, the sum of the required air exchange, the specific moisture consumption and the duration of specific weather conditions over a year will give the required value of the annual water consumption for water-evaporative cooling. Weather conditions vary from year to year, so climate data should be used in the design calculations.

The maximum hourly water consumption (m3/h) for evaporation is determined from the formula

$$Q\_w = W\_{\text{max}} \cdot \overline{\rho} \cdot \Delta d\_{\text{max}} \cdot 10^{-6} \,\text{}^\circ \text{} \tag{18}$$

where *W*max—air exchange rate at maximum design outdoor temperature, m3/h and Δ*d*max—the amount of moisture consumed by one kilogram of supply air during cooling at the maximum estimated outdoor temperature, g/kg of d.a.

Annual water consumption for water-evaporative cooling can be determined from the formula

$$Q\_{w.a.} = \sum\_{i=1}^{n} W\_{\mathbf{i}} \cdot \overline{\mathbf{p}} \cdot \Delta d\_{\mathbf{i}} \cdot \mathbf{r}\_{\mathbf{i}} \cdot \mathbf{1} 0^{-6} \,, \tag{19}$$

where *Wi*—air exchange required at temperature *ti* (determined from the balance of humidity and heat), m3/h; <sup>Δ</sup>*d*<sup>i</sup> <sup>=</sup> *dsu* − *do*—amount of moisture consumed by one kilogram of supply air during cooling, g/kg d.a. and τ*i*—duration of temperature period *ti*, h.

For aggregate calculations, the values of relative humidity can be obtained by linear interpolation of reference points obtained from building regulations (BR) and local building norms (LBN). For more precise calculations it is necessary to use data tables (the relationship between temperature and relative humidity) or diagrams that take into account the duration of specific combinations of temperature and relative humidity for the considered climatic zone. Such data can be found in the works of A.Y. Kreslin and other scientists.

Knowing the required air exchange rate and the permissible total aerodynamic drag or limiting the flow speed with the condition that no droplets of moisture can escape from the sprayed surfaces, we can determine the required cross-sectional area, and, consequently, the required number of units.

#### *2.3. Experimental Study*

Description of the Experimental Facilities

The climate control system using the combined climate control unit was tested in fattening sector No. 6 on Farm No. 7 of "Firma Mortadel" LLC. Indicators of test conditions are given in Table 3.

**Table 3.** Parameters and conditions of the tests.


As a control sector, we used fattening sector No. 5, having 241 pigs with a weight of 30.5 kg (20 animals per pen). The climate maintenance system was designed by FG-CLIMITED, Ontario, CA, USA, using equipment from Ag-Co Products Limited Ontario, CA, USA. The front wall has four extractor fans (one extractor from the manure channel). The air is supplied through supply valves located in the ceiling and distributed in the room at the rate of one valve per box for a total of 12. The automation system is controlled by a temperature sensor installed in the room center at a height of 1.2 m above the floor level.

The experimental sector was additionally equipped with a tested system consisting of three prototypes of a combined climate control system with a water sprinkler cooling system (Figures 9 and 10): No. 1, 2—general exchange ventilation; and No. 3—air extraction from the manure channel and a system for regulating indoor climate parameters according

to temperature and relative humidity sensors placed along the passage at a height of 1.2 m. Technical characteristics of the units are presented in Table 4.

**Figure 9.** View from the pig house roof: 1,2—UT-6000S units (for general exchange ventilation); 3—UT-3000 unit (for air extraction from the manure channel).

**Figure 10.** General view of the experimental system of climate control inside the pig house: 1,2—UT-6000C unit (for general exchange ventilation); 3—UT-3000 unit (for air extraction from the manure channel).


**Table 4.** Technical characteristics of the units.

The summer ventilation system was supplemented with an option to use the climate control units in the cooling mode.

During the test period, the outdoor air temperature ranged from −8 ◦C to +31 ◦C, and climate measurements were taken automatically by a climate control computer according to temperature and relative humidity sensors placed as shown in the diagram in Figure 11.

**Figure 11.** Control point diagram with sensors.

The climate control computer automatically maintains the specified indoor air temperature and relative humidity. Manual climate control is also possible.

As the relative humidity in the room increases, the air exchange rate smoothly increases as well. The air supply is controlled automatically by changing the speed of the fans and the degree of opening of the air inlet flaps. If the room temperature falls below the set point while the excess moisture is being removed, the heating devices are switched on. If the temperature drops further below the set point value, the ventilation level is set to the minimum value (depending on the weight and age of the animals), with the temperature taking priority.

This solution ensures the removal of excess moisture, heat and harmful gases from the house throughout the year.

#### **3. Results**

#### *Study of Water-Evaporative Cooling*

The problem was solved in Excel 2007 (Microsoft Corporation, Redmond, WA, USA). Within the variation range of relative humidity from 20 to 100% and outdoor air temperature from 20 to 50 ◦C; the calculation results are graphically presented in Figure 12.

**Figure 12.** Reduction of air temperature in the unit as a function of the temperature and relative humidity of the outdoor air.

The graph is plotted in a three-dimensional coordinate system, showing the relationship of Δ*t* = *f*(*t*, *ϕ*). The result obtained shows that the maximum cooling value is achieved at minimum relative humidity and maximum outdoor air temperature, otherwise the supply air cooling value decreases monotonically.

Over the test period, the outdoor air temperature was 30.4 ◦C and relative humidity was 31.2%. The test results are shown in Table 5. Figure 13 presents a diagram of the exhaust and supply air temperatures.


**Table 5.** Test results of the combined climate control unit in the cooling mode.

**Figure 13.** Diagram of the exhaust and air supply temperatures.

Table 5 shows that the maximum value of the air supply temperature reduction was 6.3 ◦C (in the pens closest to the units). As the distance from the units increased, the indoor air temperature increased. This effect was due to the fact that the share of cooled air (from the units) in the total ventilation system was 49%. As a result, the cooled air mixed with untreated outdoor air from the general ventilation system. Therefore, the average room temperature drop was 3.8 ◦C.

When analyzing the convergence of the results, we noted some discrepancies with the analytical data. The calculation model shows that supplied air with a temperature of 31.2 ◦C and a relative humidity of 30.4% can be cooled by 8.3 ◦C when saturated with moisture to a relative humidity of 90.0% (by 11.7 ◦C at 100.0% relative humidity).

At small values of the coefficient of spraying heat-exchange plates, we registered reduced values of the air supply temperature as compared to the calculated ones. This effect is caused by the influence of the wettability of the heat exchange surface on the efficiency of water-evaporative cooling. When the water flow rate was increased, the experimental data came close to what was theoretically possible, but this was accompanied by a detachment of moisture droplets.

The stated assumption can be proven by the fact that in sprayed layers made of hygroscopic and well-wetted cellulose, the above effect was not observed in prcatice (under condition of a sufficient water flow rate for water evaporation).

Further research is required to study the influence of the wettability of sprayed surfaces on the efficiency of water-evaporative cooling.

#### **4. Discussion**

The problem of ensuring proper climate control in livestock buildings is rather urgent and requires special attention. A considerable amount of research focuses on the development and optimization of climate control systems to increase functionality and improve technological and energy efficiency. The authors aimed to develop and test an air cooling system in a combined climate control system used in pig production. To achieve this goal, we analyzed the existing cooling systems for ventilation air, developed the design of a climate control system and a mathematical model of air cooling, made a prototype and conducted experimental research.

In the course of our research, different methods of air cooling in climate control systems were considered. For livestock farming, it is advisable to use water-evaporative cooling systems with sprayed surfaces. This variant is optimal as these systems are characterized by constructive simplicity, reliability and technological and energy efficiency. As compared to other methods of air cooling, surface-filled water-evaporative cooling systems require a minimum amount of electricity per kW of cooling. This was the main argument for the use of the water-evaporative cooling system with sprayed surfaces in the combined climate control unit.

The authors developed a mathematical model describing air cooling for the offered technical solution. The model considers a heat exchanger consisting of tubes with a rectangular cross-section. The flow of the cooled air and the refrigerant water is direct in the considered heat exchanger. The water sprayed by the nozzles wets the surface of the heat exchanger. This makes it possible to obtain a large cooling surface, which has a positive effect on cooling intensity. Based on the obtained mathematical model, we determined the theoretical values of air temperature reduction depending on outdoor air temperature and humidity.

The developed combined climate control unit with a water-evaporative cooling system was tested on the "Firma Mortadel" Ltd. farm. In the course of testing, measurements of temperature and relative air humidity were taken in the animals' pen according to the conventional procedure, and the test results confirmed expectations. The developed system decreases the air temperature.

The prototypes were tested in the operating heating and ventilation system. The capacity of the three test units was 15,000 m3/h, which provided 49% of the total capacity of the combined system. Since all the cooling units were concentrated on one side, the cooled air was unevenly distributed inside the space. To reduce this effect, it is advisable to distribute the units evenly over the space and cool the whole air supply.

The efficiency of water-evaporative cooling systems strongly depends on the climatic conditions in the region of operation. The highest efficiency is achieved in hot and arid as well as in temperate climates. Under conditions of high relative humidity—80% and above—the cooling effect tends to zero. As the cooling effect increases, so does water consumption. For example, at an outside air temperature of 40.0 ◦C and a relative humidity of 20.0%, it is possible to warm air to a temperature of 28.8 ◦C and ensure a relative humidity of 85.0%. Under these conditions, a unit with a capacity of 6000 m3 of air per hour will have a water consumption of 23 m3/h.

#### **5. Conclusions**

The analysis of the existing air cooling systems has shown that it is advisable to use water-evaporative cooling systems for livestock houses due to their simplicity, technological and energy efficiency and low requirements for operating conditions.

The comparative analysis of the energy efficiency of cooling systems has shown that systems with sprayed surfaces require a minimum amount of electric power to produce 1 kW of cold (0.003 kW/kW).

The combined climate control system includes a heat exchanger with a large heat exchange surface. Adding a heat exchanger spraying system is therefore sufficient to ensure water-evaporative cooling in the system. This system can also perform cleaning and disinfection of the unit's working surfaces as well as the inlet and outlet air of the serviced area.

To describe the cooling process in the combined climate control unit, the authors have developed a mathematical model that links air parameters at the inlet and outlet of the unit, its geometrical characteristics and performance.

The mathematical model can determine the potential cooling of the air supply and the minimum water consumption required to produce this effect. An air supply with a temperature of 31.2 ◦C and a relative humidity of 30.4% can be cooled by 8.3 ◦C when saturated with moisture to a relative humidity of 90.0% (by 11.7 ◦C at 100.0% humidity).

As the experimental research proved, the air supply was cooled by 6.3 ◦C (in the pens nearest to the units), which confirms the efficiency of water-evaporative cooling. However, additional research is required to study the influence of the wettability of the sprayed surfaces on the efficiency of water-evaporative cooling.

#### **6. Patents**

Heat recovery unit. Ilyin, I.V. and Ignatkin, I.Yu. Patent for the invention No. 2627199 C1 RU, MICROPK A01K 29/09 (2006/01). Applicant and patent holder—Russian State Agrarian University—Moscow Timiryazev Agricultural Academy—No. 2016127599; applied on 8 July 2016; issued on 3 August 2017, Bulletin No. 22-6 p.: ill.

**Author Contributions:** Software, D.S.; Validation, S.K.; Data curation, N.S. (Nikita Serov); Writing original draft, I.I.; Writing—review & editing, N.S. (Nikolay Shevkun) and A.A.; Visualization, V.P.; Project administration, I.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This article was funded by an intra-university grant from the Russian State Agrarian University—Moscow Timiryazev Agricultural Academy "Food Sovereignty" section for research projects in the field of import substitution within the framework of the "Priority 2030" strategic academic leadership program.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the authors.

**Conflicts of Interest:** The authors declare no conflict of interest.
