# The Influence of Droplet Distribution Coverage and Additives on the Heat Transfer Characteristics of Spray Cooling under the Influence of Different Parameters

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[4]. The heat flux per unit volume of some high-power chips can exceed 500 W/cm

^{2}[5]. Application of a new and efficient heat transfer method is a matter of urgency. In the year 2017, the heat flux of high-performance electronic chips was expected to reach 190 W/cm

^{2}by 2020 [6]. What is worse, the microminiaturization of the electronic equipment has greatly shrink the heat dissipation area, which has led to a heat flux of up to 10

^{3}W/cm

^{2}in recent years [7].

^{3}W/cm

^{2}), as one of the most competitive technologies in the field of high heat flux cooling and airborne electronic equipment cooling. Closed-loop spray cooling technology is currently listed by NASA as one of the research priorities for future airborne thermal control systems [8], and the investigation has successfully approached the goal of 10

^{3}W/cm

^{2}[9]. Spray cooling is widely used in medical, metallurgy, chip cooling, aerospace and other fields [10], and liquid nitrogen spray cooling can be used in some specific environments to achieve greater cooling capacity instantaneously [11]. The non-uniformity of droplet distribution in spray cooling and its effect on heat transfer performance were investigated by Cheng et al. [12] and Xie et al. [13]. Meanwhile, the effects of nozzle arrays [14], splash injection [15], and liquid film flow [16] were studied by some scholars. In each case, references are provided for the enhancement of spray heat transfer.

_{2}O

_{3}nanofluid jets and horizontal circular surfaces and showed that presenting the data in Reynolds number captures the effect of nozzle height and jet diameter, and presenting the data in Pecoret number correlates the nanofluid concentration with a single criterion number.

## 2. Materials and Methods

#### 2.1. Experimental Equipment

^{2}. The flow rate of the medium can be changed by changing the flow adjustment valve and observing the flow meter, and the heat on the heating surface is exchanged with the spray droplets. Four K-type thermocouples with 8 mm spacing are arranged vertically in the heating block for temperature measurement, as shown in Figure 2, and the temperature is collected by a Keysight DAQ970A data acquisition instrument (Keysight Technologies, Inc., Santa Rosa, CA, USA). During the experiment, the internal image of the spray chamber is captured in real-time by the OSG030-815UM (Weihong Image (Shenzhen) Co., Ltd., Shenzhen, China) industrial high-speed camera of the visualization system.

#### 2.2. Data Processing

^{2}, λ is the thermal conductivity of copper, W/(cm∙K), and $\frac{\Delta T}{\Delta y}$ is the temperature distribution gradient in the axial direction of the heating block.

_{W}is the temperature at the surface of the simulated heat source, °C, T

_{1}is the temperature measured by thermocouple K

_{1}, °C, and y

_{1}is the distance between thermocouple K

_{1}and the surface of the heat source, mm.

^{2}∙K), T

_{in}is the nozzle inlet temperature of the cooling medium, °C.

_{i}is the mass concentration of each component, λ

_{i}is the thermal conductivity of each component, W/(m·K).

_{i}is the dynamic viscosity of each component, Pa·s.

_{i}is the density of each component, kg/m

^{3}.

_{i}is the constant pressure specific heat of each component, J/kg·K.

^{2}).

_{m}is the mass flow rate of the medium, kg/s, A is the area covered by the spray, m

^{2}.

^{2}∙K), D is the spray coverage diameter, m, λ is the thermal conductivity, W/(m·K).

_{i}is the constant pressure specific heat of each component, J/(kg·K).

#### 2.3. Uncertainty Analysis

_{1}~X

_{M}are all the variables associated with this parameter.

^{2}, λ is the thermal conductivity of copper, W/(cm∙K), T is the measured temperature of the thermocouple, °C, y is the distance of the thermocouple from the surface of the heat source, mm, and b is the slope value after linear fitting of the temperature, °C/mm.

_{W}is the temperature at the surface of the simulated heat source, °C, T

_{1}is the temperature measured by thermocouple K

_{1}, °C, and ΔT is the distance between thermocouple K

_{1}and the surface of the heat source, mm.

^{2}∙K), q is the heat flux of the simulated heat source surface, W/cm

^{2}, T

_{W}is the temperature at the surface of the simulated heat source, °C, T

_{in}is the nozzle inlet temperature of the cooling medium, °C.

## 3. Results and Discussion

#### 3.1. Effect of Heat Flux Variation on Heat Transfer Performance

^{2}and stabilizes at 50 min. In the process of changing the transient surface heat transfer coefficient with heat flux of 100 W/cm

^{2}, 150 W/cm

^{2}and 200 W/cm

^{2}, it appears that the heat transfer coefficient first rises and then decreases, and finally stabilizes. The trend is more obvious in the case of 150 W/cm

^{2}and above. Combined with the visualization and analysis process, it can be found that when the system starts to operate, the surface heat flux increases sharply, causing a significant increase in the heat transfer coefficient. With increasing heat flux, smaller droplets evaporate rapidly on the heating surface to produce a vapor layer, and the heat exchange between some droplets and the heat source surface is resisted by the vapor. As time increases, as the droplet’s own velocity overcomes the effect of vapor on heat exchange, the hindering effect of a small number of small droplets evaporating and the overall cooling heat exchange reach a state of equilibrium. Therefore, the transient heat transfer coefficients tend to be stable after 60 min.

^{2}, 100 W/cm

^{2}, 150 W/cm

^{2}, and 200 W/cm

^{2}are shown in Figure 6. It can be observed that there is little difference in the internal state of the spray chamber at low heat fluxes. In the heating heat flux of 150 W/cm

^{2}, the surface temperature of the heat source has reached the boiling point of water, and water vapor appears in the chamber. The entire chamber is filled with water vapor when the heating heat flux is 200 W/cm

^{2}. The increase in water vapor causes the pressure inside the chamber to increase, and the boiling point of water to rise, which to a certain extent blocks the boiling heat exchange on the surface of the heat source. Therefore, fluctuations in the heat transfer coefficient can occur when heating with large heat flux.

#### 3.2. Effect of Coverage on Heat Transfer Performance by Changing Flow Rate

^{2}heating heat flux are shown in Figure 7. As can be seen from the nozzle product manual and computer measurements, in this experimental system, when the Ge Qiang 1/8 1 mm nozzle flow rate is 25 L/h, the spray cone angle is 25°, as illustrated in Figure 7a. The droplet jet cannot overcome gravity’s acceleration when the flow rate is too low, so a complete spray cone cannot be formed and a corresponding coverage cannot be calculated. The spray cone angle is 30° when the flow rate is 30 L/h, 40 degrees when the flow rate is 35 L/h, and 45 degrees when the flow rate is 40 L/h. By setting nozzle coverage to 100% at a flow rate of 40 L/h, it is possible to determine a nozzle height of 2.89 cm. With this height fixed, reducing the flow rate to 35 L/h and 30 L/h, the corresponding coverage rates can be calculated as 77% and 42%, respectively.

^{2}). From Figure 8, Figure 9, Figure 10 and Figure 11, it can be seen that the transient surface heat transfer coefficient increases with the increase in coverage at different heating heat fluxes when the medium flow rate is increased, and the phenomenon is more obvious especially at high heat fluxes. When the heating heat flux is low, the heat exchange on the surface of the heat source is not completely in the boiling zone, the greater the flow rate, the greater the droplet velocity, and the greater the number of instantaneous droplets. As a result, at this time, some droplets that are not ready to boil will prevent the surface from boiling, causing a fluctuation of the surface heat transfer coefficient at a higher flow rate. While when the heat flux is 150 W/cm

^{2}and above, the surface heat exchange is all carried out in the boiling zone, more droplets at higher flow rates will accelerate heat transfer. Hence this part of the surface heat transfer coefficient increases more smoothly, and the higher the flow rate, the larger the transient surface heat transfer coefficient. In addition, Figure 10 and Figure 11 also verify the conclusion in Section 2.1 that the surface heat transfer coefficient first increases and then decreases and eventually plateaus at high heat fluxes.

^{2}and below, the surface heat transfer coefficient first increases and then slightly decreases with the increase in coverage. As can be seen from Figure 8, Figure 9, Figure 10 and Figure 11, the transient surface heat transfer coefficient fluctuates for large flow rates and small heating heat fluxes. Therefore, the steady-state heat transfer coefficient also decreases. Figure 12 also further verifies the above conclusion.

#### 3.3. Effect of Coverage on Heat Transfer Performance by Changing Height

^{2}and 100 W/cm

^{2}is consistent. When the nozzle height is small, the upper part of the spray cone where the droplets are dense exchange heat with the heating surface at the center of the larger heat flux. The droplets in the center of the heating surface push the liquid to flow around to cover the whole heating surface, with good boiling state and high heat exchange efficiency. When the nozzle height is slightly increased, the heating surface remains in the dense droplet area and the droplet coverage area expands, thus the heat transfer coefficient increases. The nozzle height continues to be increased and the droplet coverage is increased, but the spray cone above the heated surface has been parabolic, with fewer droplets in the center of the heated surface. At this time, better heat transfer performance only appears at the edge of the heating block. Thus, the overall heat transfer coefficient is reduced.

#### 3.4. Effect of Cationic Surfactant (CTAB)–Water Mixture on the Heat Transfer Performance

^{2}·K is reached at the concentration of 200 ppm, which is 29.3% higher than the heat transfer coefficient of 1.47 W/cm

^{2}·K of pure water. Beyond this point, the concentration continued to increase, and the heat transfer coefficient decreased continuously, and when the concentration reaches 300 ppm, the heat transfer deteriorated.

#### 3.5. Effect of Ethanol–Water Mixture on the Heat Transfer Performance

^{2}·K is reached at 4% ethanol volume fraction, which is 21.8% higher than that of pure water.

#### 3.6. Effect of CTAB–Ethanol–Water Mixture on the Heat Transfer Performance

^{2}·K is reached at the CTAB concentration of 200 ppm, which is 23.8% higher than that of pure water. With the concentration of 250 ppm, the heat transfer coefficient is lower than that of pure water.

#### 3.7. Dimensionless Criterion Correlation Equations Based on Experimental Parameters

#### 3.8. Further Application Potential for Airborne Systems

## 4. Conclusions

- (1)
- Both the transient surface heat transfer coefficient and the steady-state surface heat transfer coefficient of the simulated heating source increase as the heating heat flux increases. During the initial operation of the system under high heat flux conditions, some of the droplets will rapidly produce vapor that blocks heat transfer, resulting in a situation where the transient heat transfer coefficient increases sharply and then decreases slightly and subsequently reaches an equilibrium state.
- (2)
- Both transient and steady-state surface heat transfer coefficients increase with increasing flow rate at high heat flux. In the case of large flow rate and small heating heat flux, the transient surface heat transfer coefficient fluctuates and the steady-state heat transfer coefficient decreases, so the heat transfer coefficient increases first and then decreases slightly with the coverage rate.
- (3)
- When the spray coverage does not exceed the heating surface, the temperature distribution on the surface of the simulated heat source is not uniform due to the properties of the heating surface and the velocity characteristics of the spray cone. Because of the non-uniformity of the temperature distribution on the surface of the simulated heating source and the different morphology of the spray cone, optimal heat transfer performance can be achieved at lower nozzle height and smaller surface coverage.
- (4)
- The addition of cationic surfactants (CTAB), ethanol and CTAB–ethanol mixtures all contributed to the enhancement of surface heat transfer. The addition of the CTAB–water mixture showed the greatest enhancement. The optimum enhanced heat transfer concentrations existed for all three solutions with maximum enhancement of 29.3%, 21.8% and 23.8%, respectively. However, heat transfer deterioration occurs in several solutions if the additive concentration is too high.
- (5)
- The higher accuracy and adaptability of the dimensionless criterion correlation formula that integrates Re, Pr and size coefficient. It shows that the dimensional parameters such as spray height and coverage cannot be neglected in the prediction of heat transfer ability.
- (6)
- If it is desired to enhance heat transfer by varying the flow rate, the coverage can be increased at high heat fluxes and reduced appropriately at low and medium heat fluxes. If the heat transfer is enhanced by changing the nozzle height, the nozzle height should be reduced appropriately to reduce the coverage, encouraging the complete coverage surface in the dense area of liquid droplets. If heat transfer is enhanced by additives, the additive concentration needs to be controlled in the optimal range.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of spray system. 1 liquid storage tank; 2 micro high-pressure pump; 3 flow adjustment valve; 4 flow meter; 5 pressure gauge; 6 stop valve; 7 spray chamber; 8 nozzle; 9 observation window; 10 reflector; 11 fill light; 12 heating rod; 13 waste liquid collection tank; 14 high-speed camera; 15 data acquisition instrument; 16 heating power regulator; 17 computer.

**Figure 4.**Transient surface heat transfer coefficient with change of heat flux at a flow rate of 40 L/h.

**Figure 5.**The influence of the change of heating heat flux on the steady-state surface heat transfer coefficient at a flow rate of 40 L/h.

**Figure 6.**Visualization images of the influence of the change of heating heat flux on the inside of the spray chamber at a flow rate of 40 L/h: (

**a**) 50 W/cm

^{2}; (

**b**) 100 W/cm

^{2}; (

**c**) 150 W/cm

^{2}; (

**d**) 200 W/cm

^{2}.

**Figure 7.**Visualization images of the influence of flow rate change on spray coverage at a heating heat flux of 100 W/cm

^{2}: (

**a**) flow rate 25 L/h; (

**b**) flow rate 30 L/h, coverage 42%; (

**c**) flow rate 35 L/h, coverage 77%; (

**d**) flow rate 45 L/h, coverage 100%.

**Figure 8.**The influence of coverage rate of changing flow rate at 50 W/cm

^{2}on transient surface heat transfer coefficient.

**Figure 9.**The influence of coverage rate of changing flow rate at 100 W/cm

^{2}on transient surface heat transfer coefficient.

**Figure 10.**The influence of coverage rate of changing flow rate at 150 W/cm

^{2}on transient surface heat transfer coefficient.

**Figure 11.**The influence of coverage rate of changing flow rate at 200 W/cm

^{2}on transient surface heat transfer coefficient.

**Figure 12.**The influence of the coverage rate of the flow rate change on the steady-state surface heat transfer coefficient.

**Figure 13.**Visualization images of the effect of nozzle height change on spray coverage at a flow rate of 40 L/h: (

**a**) height 1.16 cm, coverage16%; (

**b**) height 1.73 cm, coverage 36%; (

**c**) height 2.31 cm, coverage 64%; (

**d**) height 2.89 cm, coverage 100%.

**Figure 14.**The influence of the coverage rate of changing height at 50 W/cm

^{2}on the transient surface heat transfer coefficient.

**Figure 15.**The influence of the coverage rate of changing height at 100 W/cm

^{2}on the transient surface heat transfer coefficient.

**Figure 16.**Visualization images of spray cone shape: (

**a**) solid dense cone, coverage16%; (

**b**) solid dense cone and hollow parabolic cone.

**Figure 17.**The influence of the coverage rate of the nozzle height change under different heat fluxes on the steady-state surface heat transfer coefficient.

**Figure 18.**The steady-state heat transfer coefficients of spray cooling at different CTAB concentrations.

**Figure 19.**Visualization images of the foam inside the chamber at different CTAB concentrations: (

**a**) 50 ppm; (

**b**) 100 ppm; (

**c**) 150 ppm; (

**d**) 200 ppm; (

**e**) 250 ppm; (

**f**) 300 ppm.

**Figure 21.**The steady-state heat transfer coefficients of spray cooling at different ethanol concentrations.

**Figure 22.**Visualization images of the foam inside the chamber at different ethanol concentrations: (

**a**) 4%; (

**b**) 6%; (

**c**) 8%.

**Figure 23.**The steady-state heat transfer coefficients of the ethanol–water mixture at different CTAB concentrations.

**Figure 24.**Visualization images of the foam inside the chamber of the ethanol–water mixture at different CTAB concentrations: (

**a**) 20 ppm; (

**b**) 40 ppm; (

**c**) 60 ppm.

**Figure 25.**Comparison of fitted and experimental values when fitting the correlation equation using Re and Pr.

**Figure 26.**Comparison of fitted and experimental values when fitting the correlation equation using Re, Pr and h/D.

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**MDPI and ACS Style**

Niu, Q.; Wang, Y.; Kang, N.
The Influence of Droplet Distribution Coverage and Additives on the Heat Transfer Characteristics of Spray Cooling under the Influence of Different Parameters. *Appl. Sci.* **2022**, *12*, 9167.
https://doi.org/10.3390/app12189167

**AMA Style**

Niu Q, Wang Y, Kang N.
The Influence of Droplet Distribution Coverage and Additives on the Heat Transfer Characteristics of Spray Cooling under the Influence of Different Parameters. *Applied Sciences*. 2022; 12(18):9167.
https://doi.org/10.3390/app12189167

**Chicago/Turabian Style**

Niu, Qian, Yu Wang, and Na Kang.
2022. "The Influence of Droplet Distribution Coverage and Additives on the Heat Transfer Characteristics of Spray Cooling under the Influence of Different Parameters" *Applied Sciences* 12, no. 18: 9167.
https://doi.org/10.3390/app12189167