Simulation on Evaporation and Cooling Characteristics of Spray System

This study explored the evaporation and cooling characteristics of air pipeline spray based on computational fluid dynamics method. A geometric model of the pipeline air spray was constructed and meshed, and the Euler-Lagrange research method of the discrete phase model (DPM) was used to study the evaporation and cooling characteristics of the spray system. It was found that the length required for complete evaporation of droplets increased with the relative humidity. When the inlet temperature was 308K and the relative humidity was 40%, the evaporation length increased by 43.71% compared to when it was 20%. There was a negative correlation between the inlet temperature and the evaporation length, and when the relative humidity was 30%, the evaporation length at an inlet temperature of 323K decreased by 1.55m compared to when it was 313K. After spraying, the air temperature gradually decreased along the length of the pipe, and the cooling effect decreased as the relative humidity of the inlet air increased. When the inlet temperature was 308K and the relative humidity was 40%, the outlet temperature was 4.39K higher than when it was 20%, and the cooling effect increased as the inlet air temperature increased. When the relative humidity of the inlet air was 30%, the temperature drop at the outlet at an inlet temperature of 323K was 1.93K higher than when it was 313K.


Introduction
Gas Turbine (GT) are irreversible open cycle thermal power equipment that were initially used in jet engines and only began to be used for power generation in the 1990s [1].The performance of a gas turbine, including output power, thermal efficiency, exhaust gas flow rate, and exhaust gas temperature, largely depends on the inlet temperature of the gas.As the inlet temperature increases, the output power and thermal efficiency decrease significantly.Generally, when the working environment temperature of a gas turbine rises by 1K, the rated capacity of the gas turbine will decrease by 1%.When the intake temperature rises from 288K to 298K, the output power of the gas turbine will decrease by approximately 7% [2].In hot and humid summers, due to the high demand for electricity, gas turbine power plants need to provide more power, but the high air temperature limits the generating capacity of the gas turbine.
From a thermodynamic perspective, the capacity of a gas turbine depends on the mass flow rate of air entering the compressor.A higher mass flow rate of air can increase the capacity of the gas turbine, but the negative impact of the increased environmental temperature, reduced air density [3].Therefore, gas turbines must use inlet air cooling technology to obtain lower air temperatures, thereby increasing air density and producing high-quality airflow.This can not only improve the useful power output, but also increase the pressure ratio of the inlet air and reduce the compressor power consumption.
Evaporative inlet air cooling technology has advantages such as low investment, simple equipment, environmental friendliness, and the ability to improve the quality of inlet air.It is an effective measure for pipeline air cooling.The spray evaporation cooling process is a typical gas-liquid flow model, and numerical simulation methods are the typical means to study gas-liquid two-phase flows.Many studies have shown that the spray evaporation cooling process can be analyzed by numerical simulation.Ritchey et al [4] constructed a numerical simulation calculation framework for the inlet spray cooling technology.Within a given range of compressor operation, spray intermediate cooling can provide greater power gain than traditional intermediate cooling, and spray inlet cooling can provide performance advantages comparable to those of absorption refrigeration cooling.Lacour et al [5] established a three-dimensional numerical analysis model that describes the temperature and liquid content in the thermal spray dispersion process and used it to describe the liquid water fragmentation.They also incorporated a Gaussian model that includes particle settling and wall effects to deal with the complete dispersion process of total water.When the spray radius is close to the wind tunnel size, the cooling effect is high.
Understanding the evaporation process of droplets in pipeline and the cooling effect is of great significance to the design of spray devices.Therefore, based on computational fluid dynamics, this paper adds a spray evaporation cooling array to the existing gas turbine inlet duct, simulates the entire air intake system's evaporative cooling process, studies the evaporation trajectory of droplets inside the pipeline, and evaluates the cooling effect on the pipeline air.

Modeling and control equations
The simulation object is a straight square air duct equipped with an atomization nozzle array.The nozzles are installed at the end of the pipe, arranged in a 3x8 square array with a total of 24 nozzles.The nozzle cone angle is 90° and the injection angle is 180°.The spraying water temperature is 288K, the droplet size is 50μm, the spraying velocity is 60m/s, and the air flow velocity is 3m/s.The spraying direction is the same as the direction of air flow.Figure 1 shows the computational model, with a crosssectional size of 3mx8m for the duct and a straight length of 30m.The computational model is discretized with a grid number of 360,000.(1) Control equation of continuous phase Continuity equation: Where ρ is the density of continuous phase air, kg/m 3 ; t is the time, s; v is the velocity, m/s.Momentum equation: Where f is the Specific force, N/kg; p is the pressure, Pa; μ is the dynamic viscosity, Paꞏs; F is the source term of momentum.
Energy equation: Where e is the specific internal energy of unit mass fluid, kJ/kg; ĸ is the thermal conductivity coefficient, W/mꞏK; ɸ is the viscous dissipation function.
Conservation equation of component transport: Where D i is the diffusion coefficient of water vapor; C i is the Volume concentration of water vapor.
(2) Discrete phase control equations Momentum conservation equation and particle trajectory equation of spray water particles in a continuous phase flow field: Where ν ⃗ p is the discrete phase particle terminal velocity, m/s; v is the continuous phase velocity, m/s; ρ p is the density of discrete phase particles, kg/m 3 ; ρis the density of continuous phase, kg/m 3 ; F is the source term of momentum; F D is the unit drag force, , the simulation of this study does not consider the effect of drag force.
To investigate the evaporation and cooling effects under different temperatures and relative humidities, this study set up six different working conditions as shown in Table 1.The water supply of each working condition was selected based on the relative humidity of the air reaching 100%.

Droplet evaporation length
Figure 2 shows the trajectory of particle tracking and statistical results of the fully evaporated length for droplets under the calculation conditions of the intake temperature of 35℃ and the relative humidity of 20%.It can be seen from the figure that the droplets exchange heat with the surrounding air after injection, and their diameter gradually decreases until complete evaporation.The evaporation length of the droplets at the center of the spray is longer than that of the liquid droplets in the surrounding area, and the evaporation length of the droplets in the upper half of the model is longer than that in the lower half.This is mainly because the spray device has a conical spray area of 90°, which causes the speed of  Using the same calculation method, the evaporation length of droplets for six working conditions was statistically analyzed, and the results are shown in Table 2.Under the same intake temperature and different relative humidity conditions, with an average intake temperature of 35℃ and relative humidity of 20% and 40%, the difference in evaporation length between the two is 7.3 m.The trend of evaporation length increases with the increase of relative humidity.Under the same relative humidity and different intake temperature conditions, as compared Case 3 with Case 6, the difference in evaporation length between the two is 1.55 m, which indicates that there is a negative correlation between intake temperature and evaporation length.3 and Figure 4 show the temperature distribution cloud maps along the pipeline and at the outlet cross-section, respectively.The air temperature gradually decreases along the pipeline direction because the entire intake duct is an adiabatic wall, and heat and mass transfer can only occur between the gas and liquid phases.This demonstrates that the spray droplets absorb heat from the surrounding air and then undergo evaporation.By comparing Case 1 with Case 2, it can be found that the average temperatures at the outlet cross-sections of Case 1 and Case 2 are 294.55Kand 298.84K, respectively.The temperature in Case 2 is 4.39K higher than that in Case 1.Because the relative humidity of the incoming air in Case 2 is higher, and the amount of water supplied when the air reaches 100% relative humidity is less, requiring less heat for complete evaporation.By comparing Case 3 with Case 6, it can be seen that the average temperatures at the outlet cross-sections of Case 3 and Case 6 decrease by 12.5K and 14.43K, respectively.The temperature drop in Case 6 is 1.93K higher than that in Case 3. As the same, the intake air temperature is higher in Case 6, and more water needs to be supplied.

Conclusion
(1) The evaporation length of the central droplets after spraying in the pipeline is longer than that of the surrounding droplets, and the evaporation length of the upper droplets is greater than that of the lower droplets.The evaporation length increases with increasing relative humidity, and there is a negative correlation between the inlet air temperature and the evaporation length.
(2) After spraying in the pipeline, the air temperature gradually decreases along the pipeline direction.Under the premise of saturating water supply, the cooling effect decreases as the relative humidity of the incoming air increases and increases as the inlet air temperature increases.

Figure 1 .
Figure 1.Computational model.Numerical calculation of gas-liquid two-phase flow needs to satisfy the basic control equations of computational fluid dynamics, including continuity equation, momentum equation, energy conservation equation, transport equation, as well as the k-ε model describing turbulence and the DPM model for calculating gas-liquid two-phase flow [6-8].(1)Control equation of continuous phase Continuity equation: .1088/1742-6596/2599/1/012036 4 the liquid droplets moving forward in the surrounding to be slower than that of the center.Under the influence of gravity, the overall flow including the droplets and air is biased downward.

Figure 3 .Figure 4 .
Figure 4. Temperature cloud map at the outlet cross-section.

Table 2 .
Statistical analysis of evaporation lengths.