The current study focuses on spray cooling applied to the heat exchange components of a cooling tower. An optimization of such processes is attempted by assessing different spray flow rates and droplet sizes. For simplicity, the heat exchanger of the cooling tower is modeled as a horizontal round tube and a cooling tower spray cooling model is developed accordingly using a computational fluid dynamics (CFD) software. The study examines the influence of varying spray flow rates and droplet sizes on the heat flow intensity between the liquid layer on the surface of the cylindrical tube and the surrounding air, taking into account the number of nozzles. It is observed that on increasing the spray flow strength, the heat flow intensity and extent of the liquid film in the system are enhanced accordingly. Moreover, the magnitude of droplet size significantly impacts heat transfer. A larger droplet size decreases evaporation in the air and enhances the deposition of droplets on the round tube. This facilitates the creation of the liquid film and enhances the passage of heat between the liquid film and air. Increasing the number of nozzles, while maintaining a constant spray flow rate, results in a decrease in the flow rate of each individual nozzle. This decrease is not favorable in terms of heat transfer.

Cooling towers are extensively used and studied across various industries [

In a closed wet cooling tower, hot water flows through a coil and undergoes cooling as it interacts with the air and spray water surrounding the tube. Heat from the hot water transfers to the pipe wall through a combination of convection and conduction. The spray water forms a liquid film on the outer surface of the pipe, absorbing heat from the pipe wall. This liquid film then engages in convective heat transfer with the surrounding air, and the heat is released to the air outside the pipe. The intricate heat transfer mechanisms in cooling towers have become a central focus of research [

To mitigate the costs associated with performance testing for cooling towers, exploring alternative methods is crucial [

Spray cooling technology involves atomizing pressurized liquid into small droplets, facilitating evaporation in the air. This evaporation process requires heat absorption, causing the liquid-phase droplets to transition into the gas phase. As a two-phase heat transfer method, spray cooling efficiently harnesses the latent heat of the liquid, resulting in a significant heat transfer capacity [

In conclusion, employing CFD to simulate the heat exchange properties of closed cooling towers represents a promising research avenue. However, current studies in this domain have predominantly concentrated on two-dimensional simulations, with only a limited number focusing on three-dimensional analyses. Despite the growing interest in spray cooling technology owing to its remarkable cooling capabilities, research on its application in cooling towers, particularly concerning the direct interaction between spray droplets and heat exchange elements, is scarce. The present study aims to investigate the heat transfer efficiency of spray cooling technology on heat exchange components within closed cooling towers. To achieve this, the study focuses on analyzing the horizontal circular tube within a cooling tower using CFD numerical simulation. Specifically, it examines the impact of spray characteristics on the heat transfer properties of the liquid film and air side. This analysis involves varying parameters such as nozzle flow rate, droplet size, and the number of nozzles.

The spray model for this simulation employs a solid conical nozzle within the deformable part model (DPM) to investigate the spray cooling process. The fluid flow in the continuous phase with discrete terms can be described by the Navier–Stokes equations. Moreover, the mass and energy exchanges between the droplets and the air alter the components of the continuous phase, necessitating the tracking of component transport equations.

Continuous-phase fluids must adhere to the equations of conservation of mass, momentum, and energy. Additionally, considering that the evaporation of droplets alters the volume fraction of the air phase, it is essential to introduce the component transport equation, which is expressed as follows [

(1) Conservation of mass equation

where

(2) Conservation of momentum equation

where

(3) Conservation of energy equation

where

(4) Species transport

where

For laminar flow:

where

For turbulent flow:

where

A discrete-phase droplet moving through continuous-phase air will experience the combined effects of gravity, air resistance, and buoyancy. The equations of motion for a discrete-phase droplet can be described by Newton’s second law [

where

where

The droplets are assumed to be spherical for this simulation; therefore, the droplet resistance can be expressed as follows [

The Reynolds number of a droplet with respect to air can be expressed as follows:

The Reynolds averaging method is commonly employed in engineering applications for turbulence calculation, offering various turbulence models in CFD. Among these models, the realizable

The realizable

Turbulent viscosity of air

where

and

where

Prior to the discrete droplets colliding with the heated wall in the study, the droplets travel through the continuous phase’s air and exchange heat with it via the processes of convection, thermal radiation, and droplet evaporation. Considering that radiative heat transfer is neglected in this simulation, the heat balance equation of the droplet particles can be written as the sum of the sensible heat change and the latent heat change [

where

In this simulation, discrete-phase droplets undergo evaporation, engaging in heat and mass exchange with the continuous-phase air. Hence, a two-way coupling method is utilized to compute both the continuous and discrete phases. The mass, momentum, and energy exchange between droplets and the continuous phase per unit volume are integrated into the three conservation equations. The formulas for computing mass, momentum, and energy exchange between continuous and discrete phases are outlined as follows [

where

The heat load in this simulation equals the heat dissipation of the hot water inside the horizontal circular tube, as the hot water within the tube is cooled by the spray droplets and air outside the tube. Consequently, the heat of the hot water inside the tube primarily transfers to the liquid film or air outside the tube through the tube wall, and the heat absorbed by the liquid film is eventually transferred to the air. The following formula can be used to determine the heat dissipation of the horizontal circular tube:

where

The heat transfer within the system must comply with Newton’s law of cooling, as the heat from the hot water inside the tube is conveyed to the liquid film outside the tube, ultimately transferring the heat to the air [

The area of the liquid film in contact with the air is not always equal to the area of the tube’s outer wall. Researchers often employ the formula developed by Zalewski et al. [

Considering that the external shell is adiabatic, the heat released from the hot water inside the tube must equal the heat absorbed by the air according to the principle of conservation of energy. Consequently, the heat transfer coefficient

The ambient temperature is set to 298.15 K, the working pressure to 1 atm, and the gravitational effect is accounted for using ^{2}/s. The temperature and flow rate of the hot water within the tube are 333.15 K and 0.5 m/s, respectively. The air outside the tube has a temperature of 298.15 K and a flow rate of 2 m/s.

The DPM cone model is utilized to generate the spray droplets, and

Nozzle height (mm) | Nozzle flow (kg/s) | Average spray speed (m/s) | Spray cone angle (°) | Droplet diameter (mm) | Droplet temperature (°C) |
---|---|---|---|---|---|

100 | 0.01 | 30 | 60 | 0.1 | 25 |

0.02 | 0.07 | ||||

0.03 | 0.04 | ||||

0.04 | 0.02 |

In this simulation, the Fluent3D numerical simulation model is employed, and the finite volume method is utilized to discretize the governing equations. Throughout the simulation process, the SIMPLEC algorithm is utilized to couple the pressure field and the velocity field due to its superior convergence [

The precision of CFD computations heavily relies on the quality of the mesh employed. The simulation accounts for convective heat transfer occurring between the air and the exterior wall of the tube, as well as between the fluid inside the tube and the tube’s wall. Additionally, spray droplets adhere to the surface of the horizontal circular tube, forming a thin layer of liquid that subsequently undergoes evaporation. To ensure accuracy in the heat transfer calculation and capture the realism of droplet adhesion, conducting a mesh refinement procedure on the tube wall and adding a boundary layer to the fluid within and outside the tube during the simulation is essential. The expansion boundary layer is apparent on both the inner and outer surfaces of the tube wall in

Various methods are employed for mesh quality evaluation, with average slope and quadrature quality being the most commonly used metrics [

To ensure the calculation’s accuracy remains independent of grid quality, we conduct a verification of grid independence. This involved using the average surface temperature and thickness of the liquid film at the exit of the horizontal circular tube as reference points, under specific working conditions.

To validate the accuracy of the simulation results for this model, we utilize the simulation settings from Zeng et al. [^{2} at a nozzle flow of 2.52 × 10^{−3} kg/s, resulting in an average heat flow density of 3579.1 W/m^{2} per tube. Comparatively, for a single horizontal circular tube in this simulation, the heat flow density is 3984.053 W/m^{2}, with a relative error of 11.31%. Hence, the simulation of this single-pipe model is considered to have exhibited a certain level of accuracy.

Spray distance | Nozzle flow | Spray velocity | Spray cone angle | Droplet diameter | Droplet temperature |
---|---|---|---|---|---|

196 mm | 2.52 × 10^{−3} kg/s |
4 m/s | 30° | 0.02 mm | 20°C |

We validate our simulation by comparing it with that of Zeng et al.’s study [

Changes in the spray flow rate influence both the thickness of the liquid film and the heat transfer within the system.

The spray emitted from a single nozzle onto the surface of the cylindrical tube generates only a thin layer of liquid in the sprayed region. However, increasing the number of nozzles can lead to a wider dispersion of the liquid layer on the surface of the round tube, thereby improving water evaporation and cooling of the material inside.

This study simplifies the heat transfer process in a cooling tower by focusing on a horizontal circular tube. The heat transfer characteristics of the tube surface and the liquid coating on the air side are analyzed. The study investigates the impact of spray flow rate, droplet size, and number of nozzles on spray efficiency.

(1) Increasing the spray flow with a single nozzle at constant wind speed and droplet size will thicken the liquid film, and maximum thickness is reached at the central region of the spray. This increase in spray flow positively impacts heat flow density and expands liquid film coverage in the system. However, continual increases in spray flow will further thicken the liquid film, consequently increasing thermal resistance and reducing heat transfer efficiency.

(2) With a single nozzle and fixed wind speed and spray flow rate, larger droplets generate a thicker liquid film. This leads to increased heat flow density and broader liquid film coverage. Smaller spray droplets tend to evaporate more readily, reducing their effective flux through the pipe wall and resulting in drier zones on the wall with lower heat flow density.

(3) Under constant wind speed, spray flow rate, and droplet size, the increase in the number of nozzles reduces the thickness of the liquid film emitted from each nozzle’s center. This increase in nozzle count enhances the extent of the liquid film, thereby improving system heat transfer. However, when the distance between nozzles is minimal, the spray from adjacent nozzles intersects, creating a boundary region. This boundary region thickens the liquid film and reduces flow velocity, hindering heat transmission. Despite a constant spray flow rate, increasing the number of nozzles disperses the liquid film more widely on the horizontal tube. However, this also reduces the discharge rate from each nozzle, resulting in a thinner liquid layer on the tube that is more susceptible to evaporation and the formation of dry regions.

Heat exchange area between the liquid film and the air, m^{2}

Surface area of the droplet, m^{2}

Resistance coefficient

Specific heat capacity, J/(kg⋅K)

Heat capacity of the species in the

Constants for the

Function of the mean strain and rotation rates, the angular velocity of the system rotation, and the turbulence fields (

Mass diffusion coefficient

Thermal diffusion coefficient

Total energy

Turbulent kinetic energy produced

Turbulent kinetic energy

Diffusion flux of species

Static pressure, Pa

Prandtl number

Heat dissipation of the horizontal circular tube, kJ/s

Reynolds number

Net rate of production of species

Turbulent Schmidt number

Energy source term

Source term produced by discrete-phase transition

User-defined source terms

Mass source term

Momentum source term

Average temperature of the liquid film, K

Average temperature of air outside the tube, K

Temperature difference in the pipe between the hot water inlet and outflow, K

Change in droplet temperature in the control volume, K

Contribution of wave expansion to the total dissipation rate in compressible turbulence

Local mass fraction of different component

Constant pressure specific heat at the average temperature of the hot water in the pipe, kJ/(kg·K)

Diameter of droplets, mm

Gravitational acceleration, m/s^{2}

Convective heat transfer coefficint, W/(m^{2}⋅K)

Convective heat transfer coefficient, W/(m^{2}⋅K)

Mass transfer coefficient, kg/(m^{2}⋅s)

Latent heat, J/kg

Enthalpy of the water vapor, J/kg

Turbulent kinetic energy

Effective thermal conductivity,

Thermal conductivity of fluid, W/(m⋅K)

Mass of the droplet, kg

Mass flux of droplets, kg/s

Average mass of droplets in control volume, kg/s

Initial mass of droplet particles, kg

Initial droplet mass flux, kg/s

Mass change of droplets when passing through each control volume, kg

Mass flow rate of hot water in the horizontal circular tube, kg/s

Number of tubes in the first row of tube bundles

System time, s

Continuous phase velocity field, m/s

Velocity of the droplet, m/s

Humidity mass ratio in the gas-phase side of the liquid–gas interface and in humid air,

Turbulent dissipation rate

Molecular viscosity of wet air, Pa⋅s

Continuous phase viscosity, Pa⋅s

Turbulent viscosity, Pa⋅s

Density, kg/m^{3}

Density of the droplet, kg/m^{3}

Turbulent Prandtl numbers

Relaxation time of the droplet

None.

This work was supported by the National Natural Science Foundation of China (Grant No. 52376069) and Shandong Province Science and Technology Small and Medium sized Enterprise Innovation Ability Enhancement Project (Grant No. 2022TSGC2596).

The authors confirm contribution to the paper as follows: study conception and design: Kaiyong Hu, Zhaoyi Chen; data collection: Yunqing Hu, Huan Sun, Zhili Sun; analysis and interpretation of results: Kaiyong Hu, Zhaoyi Chen, Jinghong Ning; draft manuscript preparation: Kaiyong Hu, Zhaoyi Chen, Tonghua Zou. All authors reviewed the results and approved the final version of the manuscript.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest to report regarding the present study.