# Enhancement of Chiller Performance by Water Distribution on the Adiabatic Cooling Pad’s Mesh Surface

^{*}

## Abstract

**:**

## 1. Introduction

^{2}residential house reduced the total energy consumption by 75% compared to traditional air conditioners. The cost of an evaporative cooling system for hot and dry climate regions is about 88% lower than that of a traditional conventional cooling system that uses electricity for cooling [13]. The results of the studies [14,15,16] showed an improvement in the performance of the entire air conditioning system—the cooling capacity improved from 5 to 18.6% using a direct evaporative cooling approach. In addition to the advantages described in the revised studies, the direct evaporative cooling system has its disadvantages, such as increased water consumption and the need of water preparation, as evaporation leaves the minerals in the air in the form of fine dust. For cooling towers this is a fairly inexpensive process involving coarse cleaning—cleaning is mainly provided to prevent scale formation—then the nozzles of the adiabatic system require microfilters and osmotic filtration. As a result, not only the system costs increase, but so do the operating costs. Although the price of water is not comparable to the cost of electricity, it is still constantly rising worldwide. Water consumption efficiency for cooling ranges from 0.45 MJ/L to 2 MJ/L [17]; it is obvious that older and cheaper adiabatic cooler models tend to use more water than the more recent and more advanced ones. Adiabatic cooler companies, as well as their end-users, need to consider water losses throughout the year, as they will be higher during the hot seasons. In the study [18], the water loss of an adiabatic cooler in summer is 5.2 L per hour. The report [19] examines about 100 published studies on evaporative cooling systems. The energy saving potential of the cooling process in this review was determined to range between 50–80% and systems effectiveness—between 80–110%. An extensive literature review indicates gaps in the research on the water atomization process and there is a significant need to develop improved water distribution systems that could enhance adiabatic cooling process performance. The authors also analyzed the available numerical studies on water mist technology in the adiabatic cooling process [20,21,22] and also identified the research gap in this field. As the wetting efficiency depends directly on the degree of water atomization, that is, on the size of the obtained droplets [23,24], the most optimal for evaporative cooling are spiral type nozzle [25], but the volume of sprayed water distribution is limited in many areas [26]. Another disadvantage of these nozzles is the non-homogeneity of the water distribution on the adiabatic cooling pad’s mesh surface: the lower the water flow rate, the lower the surface wettability and cooling capacity [27]; as such, by increasing the wettability, the cooling performance was further improved [28]. Authors also note that many issues, due to the multifactorial nature of the ongoing processes, remain poorly understood. The process of spraying a liquid jet is characterized by a complex physical phenomenon, which consists in crushing a liquid jet into a large number of drops and distributing these droplets in space; considering the ongoing processes of heat and mass transfer, it makes it practically impossible to use analytical methods and create a reliable theory. Full-scale tests are quite expensive and do not fully provide a complete picture of the ongoing complex physical phenomena. Known works using computational fluid dynamics (CFD) methods are mainly performed in a two-dimensional problem setting, and refer to specific special cases of problem solving. The purpose of this study is to develop a technique for numerical simulation of the distribution of a dropping liquid (water), taking into account heat and mass transfer on the mesh surface of an adiabatic cooler, to improve the performance of air conditioning equipment. To achieve this goal, modern methods of computational fluid dynamics (CAD/CFD) are used in a three-dimensional formulation of the problem. The mathematical description is based on non-stationary Navier–Stokes equations, taking into account heat transfer, which were solved numerically using the finite volume method. To find the desired numerical solution, a continuous non-stationary mathematical model of physical processes is discretized both in space and in time. Taking into account the complexity of the problem under consideration, for each considered diameter of the dropping liquid the following indicators were determined: velocity, viscosity, density, Reynolds criterion, which are included in the equations of heat and mass transfer coefficients, and spraying efficiency. Due to the limited experimental data, the grid convergence method was used to estimate the accuracy of the obtained solution.

## 2. Materials and Methods

#### 2.1. CAD Approach

#### 2.1.1. Physical Definition of the Problem

^{3}/h or Q = 0.00025–0.000666 m

^{3}/s. This type of nozzle is used to distribute water in coolers.

^{3}/s) flows from pipeline 1 to mixing chamber 2 of the tangential nozzle, where the water is swirled and discharged through outlet port 3 (nozzle) into the airspace. When the liquid film comes out of the nozzle, it disintegrates, forming a single flare (jet) in the form of a cone and not limited by solid walls.

^{3}/s, for case 2—Q = 0.000666 m

^{3}/s. The ambient temperature (air) T

_{AIR}and the temperature of the liquid (water) T

_{WATER}entering the pipeline and then into the nozzles are equal to each other. T

_{AIR}= T

_{WATER}= 293.20 K (20 °C). Ambient pressure is equal to atmospheric p = 101325 Pa, density ρ = 1.2041 kg/m³, dynamic viscosity μ = 1.85 × 10

^{−5}Pa∙s, specific heat capacity at constant pressure Cp = 1005 J/(kg∙deg).

_{WATER}= 293.20 K (20 °C), density ρ = 998.16 kg/m³, dynamic viscosity μ = 0.0010014 Pa∙s, specific heat capacity Cp = 4184.4 J/(kg∙deg). The metal mesh is modelled as an isotropic porous body (the permeability of the medium is the same in all directions inside the medium). The effective porosity of the medium is determined by Equation (1), as the volume fraction of the pores connected together Vpores in the total volume of the porous medium Vtotal:

^{3}; L—length of the body in this direction, mm. The dependence of the pressure difference ΔP (Pa) on the flow rate of the liquid V (m/s) is shown in Figure 3.

_{partical}= 293.20 K (20 °C), density ρ = 998.16 kg/m

^{3}, diameter-d = 100 µm and d = 500 µm, as well as the total mass flow (amount of particle mass, introduced by the fraction into the fluid per unit time) for the case of volume flow Q = 0.00025 m

^{3}/s-mass flow m = 0.249 kg/s, for Q = 0.000666 m

^{3}/s-m = 0.6376 kg/s. In particle motion calculation, gravity was taken into account, which was specified using the components of the gravitational acceleration vector in the global coordinate system.

#### 2.1.2. Mathematical Formulation of the Problem

_{H}—source of heat per unit volume, qi—diffusion flow of heat, δij—Kronecker symbol, τ

_{ij}—tensor of viscous shearing stresses, ${\tau}_{ij}^{R}\equiv -\rho {u}_{i}{u}_{j}$—stress tensor in the Reynolds model, μL—dynamic coefficient of viscosity, μ

_{t}—coefficient of turbulent viscosity, y—distance from the solid wall, g

_{i}—components of gravitational acceleration in the direction of x

_{i}; ${\sigma}_{c},{\sigma}_{B},{\sigma}_{k},{\sigma}_{\epsilon},{C}_{B},{C}_{\mu},{C}_{\epsilon 1},{C}_{\epsilon 2}$—empirical constants; Cp—specific heat capacity at constant pressure; λ—coefficient of thermal conductivity of gas (fluid); Pr = μcp/λ—Prandtl number; for laminar flow the parameters k, μ

_{t}, ε—are equal to zero; x, y, z—current coordinates; summing takes place using the suffix numbers i, j = x, y, z.

#### 2.1.3. Methods for Processing the Results of Numerical Calculations

^{3}); w—the speed of droplet movement (m/s).

## 3. Results and Discussion

^{3}/s (Figure 6a), and Q = 0.000666 m

^{3}/s (Figure 6b) with and without installed metal pad mesh in front of the nozzle. Liquid particle diameter d = 500 µm Figure 6a,b. Liquid particle diameter d = 100 µm Figure 7a,b.

^{3}/s, a low mass transfer coefficient Sh is typical for both the first and second nozzles. However, the installed metal pad mesh increases the Sh coefficient for both nozzles by ≈15%.

^{3}/s, compared to particles d = 100 µm, there is a noticeable increase in the coefficient Sh ≈ by 70–80%. At the same time, with a metal pad mesh for d = 500 µm, Sh increases by 20–40%.

^{3}/s, for particles d = 500 µm and d = 100 µm, compared with Q = 0.00025 m

_{3}/s. The Sh coefficient increases, and the installed metal pad mesh increases Sh ≈ up to 30%.

^{3}/s (Figure 9a), and Q = 0.000666 m

^{3}/s (Figure 9b) with and without installed metal pad mesh in front of the nozzle. Liquid particle diameter d = 500 µm Figure 8a,b. Liquid particle diameter d = 100 µm Figure 9a,b.

^{3}/s, Q = 0.000666 m

^{3}/s, a low heat transfer coefficient Nu is relevant for both the first and second nozzles. At d = 500 µm and the same liquid flow rates, the heat transfer coefficient Nu increases significantly compared to particles d = 100 µm and can reach 90%. It is connected with the increase in the Reynolds number included in Equation (14).

^{3}/s and d =100 µm, d = 500 µm, at the first nozzle η = 0.054. However, the installed metal pad mesh, in all other cases, improves the efficiency value by ≈30–40%.

^{3}); σ—the force of the surface tension of the liquid (N/m).

^{3}/s, the value of the average value of the criterion Re

_{d = 500}along the trajectory of the liquid particle for d = 500 µm is much higher than its value, compared to Re

_{d = 100}for particles d = 100 µm. That is, Re

_{d = 500}> Re

_{d = 100}or Re

_{d = 500}= 1560 > Re

_{d = 100}= 9.45. A similar picture is also observed for the Weber test: We

_{d = 500}> We

_{d}

_{= 100}or We

_{d = 500}= 486 > We

_{d = 100}= 11.58.

_{d = 100}for d = 100 µm almost doubles Re(mesh)

_{d = 100}> Re

_{d = 100}, Re(mesh)

_{d = 100}= 22.76 > Re

_{d = 100}= 9.45. For d = 500 µm, 1.2 times Re(mesh)

_{d = 500}> Re

_{d = 500}, Re(mesh)

_{d = 500}= 1967 > Re

_{d = 500}= 1560. In this case, the criterion We decreases, and for d = 100 µm is We(mesh)

_{d = 100}= 7.9, i.e., tends to the minimum value We

_{Kp}= 7. Presumably, passing through the additional mesh (obstacle) the velocity of liquid particles decelerates and breaks up. The average droplet velocity at a distance from the nozzle outlet to the exit from the additional mesh is two times less than in the calculations without the mesh w(mesh) < w, w(mesh) = 0.85 m/s < w = 1.6 m/s.

_{d = 500}= 386 < We

_{d = 500}= 486, taking into account that the criterion We (mesh) is in the range 10 < We < 104, then the form of droplet destruction occurs in the same way, as in the case considered above, for d = 500 µm, We d = 500.

^{3}/s are presented: (

**a**) without metal pad mesh and (

**b**) with metal pad mesh. The figures show that the installation of the metal pad mesh somewhat narrows the liquid jet, but at the same time, when it reaches the pre-cooler pad, it reduces the intensity of vortex formation and the liquid flow passes through the pad mesh more evenly.

^{3}/s: (c) without metal pad mesh and (d) with metal pad mesh. In the case with a lower flow rate, for the scenario with metal pad mesh, there is noticeably less intense vortex formation above the pre-cooler pad. It is also observed that there is less obvious compression of the jet and a more uniform distribution of the fluid flow velocity, when passing through the metal mesh.

^{3}/s and for Q = 0.000666 m

^{3}/s: (c) without metal pad mesh and (d) with metal pad mesh. The figure shows that the mass concentration of water is more evenly distributed in the adiabatic cooler for the case with the installed metal pad mesh. Presumably, such a distribution is achieved by less intense vortex formation above the pre-cooler.

^{3}/h −2.4 m

^{3}/h. Working pressure p = 29.42–343 kPa.

- −
- The theoretical jet opening angle was calculated according to the well-known method described in [44]. The obtained numerical solution well matched with the results of the theoretical calculation of the jet, and the error does not exceed 10%. Jet opening angle (theoretical) φ
_{teoret}= 20°, numerical calculation φ_{nc}= 22°. Figure 15 shows visualization of the distribution of a steady liquid jet for a volumetric flow rate Q = 0.00025 m^{3}/s: (a) numerical calculation (visualization is presented in the form of a dropping liquid), (b) experiment. Figure 15a shows that the shape of the outflowing jet, at the outlet of the nozzle, has a small section of a cylindrical shape, and further downstream the jet opens up, taking a full cone-shaped shape. A similar flow was observed in the experiment (see Figure 15b). - −
- The speed of the drops w along the trajectory are not uniform and as the jet breaks up it is w = 0.5–3 m/sec. Drops of a smaller diameter d = 100 mkm create a cylindrical jet, at d = 500 mkm a conical jet, in the general case, creating a full-cone jet. The result of the calculation is well matched with the manufacturer experimental visualized data of the considered type of nozzle.

^{3}/h, there are two zones of disintegration of liquid droplets: in the first zone 1 Weber criterion 0.1 ≤ We∙Re

^{−0.5}≤ 0.8 (zone 1), division into 2–4 drops occur, the “bag” is destroyed and chaotic fragmentation; in the second zone 0.8 ≤ We∙Re

^{−0.5}≤ 10, droplets are destroyed with a breakdown of the surface layer, giving a very fine spray along with large secondary particles separated from the original drop. In this case the calculated working pressure is in the range p = 102.32–104.82 kPa; it does not exceed the working pressure, according to the manufacturer datasheet of the nozzle.

_{2}emissions produced by power plants. Increasing the area of the pre-cooler pad, by using the metal mesh intended as cooling pads of various shapes, will significantly reduce fossil fuel consumption during peak loads. The distribution of water on the adiabatic cooling pad’s mesh surface also plays an important role in the performance of an evaporative cooler. In addition, precise control of water atomization helps to reduce the environmental impact of cooling processes by reducing water consumption.

## 4. Conclusions

- It was revealed in the considered design cases, that when the liquid is supplied through the pipeline to the nozzles from one side in the presented design they do not work evenly.
- Assessment of the accuracy of the problem under consideration showed agreement with the results of theoretical studies and manufacturer experimental visualized data.
- The results of calculating the mass transfer coefficient showed that for particles d = 100 μm, Q = 0.00025 m
^{3}/s, and Q = 0.000666 m^{3}/s, a relatively low mass transfer coefficient Sh ≈ 3.3–3.5 is typical. The installation of metal pad mesh allowed to increase Sh ≈ 15%. For particles d = 500 µm, compared to particles d = 100 µm, the Sh coefficient increased by 70–80%, and the additional metal mesh increased Sh factor by another 20–40%. - Heat transfer coefficient Nu for d = 500 µm compared to particles d = 100 µm increased by 90% and the additional metal mesh increased Nu by another 20–40%.
- The atomization efficiency has its own value for each nozzle and the highest atomization efficiency was observed at liquid flow rate Q = 0.00025 m
^{3}/s and d = 100 µm, d = 500 µm. An additional metal pad mesh, in all other cases considered, improved the efficiency value by ≈30–40%. - Visualization patterns of the fluid flow rate showed that at the jet periphery, upon impact with an adiabatic pre-cooler pad, return flows were formed, which, presumably, affected the uniformity of the liquid mass concentration in the pre-cooler itself. The installation of an additional metal pad mesh makes it possible to reduce vortex formation above the pre-cooler pad and, as a result, to equalize the uniformity of the distribution of the mass concentration of the liquid.
- Processing the simulation results, it was found that the use of metal pad mesh promotes the smoothest and most uniform water distribution of pre-cooling pad that improves environmental benefit by increasing efficiency values by ≈20–40% and reducing the water consumption of the system by ≈15–20%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**Mass transfer coefficient Sh, d = 500 µm: (

**a**) Q = 0.00025 m

^{3}/s; (

**b**) Q = 0.000666 m

^{3}/s.

**Figure 7.**Mass transfer coefficient Sh, d = 100 µm: (

**a**) Q = 0.00025 m

^{3}/s; (

**b**) Q = 0.000666 m

^{3}/s.

**Figure 8.**Heat transfer coefficient Nu, d = 500 µm: (

**a**) Q = 0.00025 m

^{3}/s; (

**b**) Q = 0.000666 m

^{3}/s.

**Figure 9.**Heat transfer coefficient Nu, d = 100 µm: (

**a**) Q = 0.00025 m

^{3}/s; (

**b**) Q = 0.000666 m

^{3}/s.

**Figure 13.**Fluid flow rate distribution patterns for: Q = 0.00025 m

^{3}/s: (

**a**) without metal pad mesh and (

**b**) with metal pad mesh; Q = 0.000666 m

^{3}/s: (

**c**) without metal pad mesh and (

**d**) with metal pad mesh.

**Figure 14.**The distribution of mass concentration of water for: Q = 0.00025 m

^{3}/s: (

**a**) without metal pad mesh and (

**b**) with metal pad mesh; Q = 0.000666 m

^{3}/s: (

**c**) without metal pad mesh and (

**d**) with metal pad mesh.

**Figure 15.**Visualization of the distribution of a steady liquid jet for a volume flow Q = 0.00025 m

^{3}/s. (

**а**) Numerical calculation, (

**b**) experiment.

Q = 0.00025 | Sh | Q = 0.000666 | Sh | |
---|---|---|---|---|

d = 0.0001 | f1 | 3.311782 | f1 | 3.509563 |

f2 | 3.320845 | f2 | 3.676473 | |

f1 mesh | 3.942006 | f1 mesh | 4.540239 | |

f2 mesh | 3.943016 | f2 mesh | 4.930458 | |

d = 0.005 | f1 | 16.11704 | f1 | 24.17137 |

f2 | 19.87923 | f2 | 27.27551 | |

f1 mesh | 28.44891 | f1 mesh | 28.66047 | |

f2 mesh | 25.21438 | f2 mesh | 34.43927 |

Q = 0.00025 | Nu | Q = 0.000666 | Nu | |
---|---|---|---|---|

d = 0.0001 | f1 | 0.719422 | f1 | 0.927462 |

f2 | 0.728958 | f2 | 1.099443 | |

f1 mesh | 1.369552 | f1 mesh | 1.992825 | |

f2 mesh | 1.372388 | f2 mesh | 2.396427 | |

d = 0.005 | f1 | 14.17148 | f1 | 22.49213 |

f2 | 18.05553 | f2 | 25.70276 | |

f1 mesh | 26.90797 | f1 mesh | 27.19304 | |

f2 mesh | 23.56767 | f2 mesh | 33.09933 |

Q = 0.00025 | η | Q = 0.000666 | η | |
---|---|---|---|---|

d = 0.0001 | f1 | 0.054693 | f1 | 0.016712 |

f2 | 0.037475 | f2 | 0.010037 | |

f1 mesh | 0.020881 | f1 mesh | 0.04781 | |

f2 mesh | 0.023857 | f2 mesh | 0.031201 | |

d = 0.005 | f1 | 0.054693 | f1 | 0.000359 |

f2 | 0.000796 | f2 | 0.00024 | |

f1 mesh | 0.002619 | f1 mesh | 0.000906 | |

f2 mesh | 0.001852 | f2 mesh | 0.000664 |

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**MDPI and ACS Style**

Borodinecs, A.; Lebedeva, K.; Sidenko, N.; Prozuments, A.
Enhancement of Chiller Performance by Water Distribution on the Adiabatic Cooling Pad’s Mesh Surface. *Clean Technol.* **2022**, *4*, 714-732.
https://doi.org/10.3390/cleantechnol4030044

**AMA Style**

Borodinecs A, Lebedeva K, Sidenko N, Prozuments A.
Enhancement of Chiller Performance by Water Distribution on the Adiabatic Cooling Pad’s Mesh Surface. *Clean Technologies*. 2022; 4(3):714-732.
https://doi.org/10.3390/cleantechnol4030044

**Chicago/Turabian Style**

Borodinecs, Anatolijs, Kristina Lebedeva, Natalja Sidenko, and Aleksejs Prozuments.
2022. "Enhancement of Chiller Performance by Water Distribution on the Adiabatic Cooling Pad’s Mesh Surface" *Clean Technologies* 4, no. 3: 714-732.
https://doi.org/10.3390/cleantechnol4030044