# The Simultaneous Analysis of Droplets’ Impacts and Heat Transfer during Water Spray Cooling Using a Transparent Heater

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[9]. In addition, this coolant has a low cost and high environmental friendliness, and is simple and safe to use.

## 2. Materials and Methods

#### 2.1. Experimental Setup and Transparent Heater Construction

^{2}and the spray irrigated the vertically oriented sapphire surface. The density of the supplied heat flux was measured according to the current passed through the heater and the potential difference between the silver current leads, also deposited by the ion sputtering technique along the edges of the ITO heater. At this stage of the study, the single-phase heat transfer during spray cooling without the development of boiling was studied, and the maximum heat flux density was 133 kW/m

^{2}.

#### 2.2. Spray Flow Parameters

_{d}and d

_{d}are the density and size of the droplets, V

_{f}is the velocity of a spray flow, µ

_{a}is the dynamic viscosity of the gas phase, and d

_{0}is the orifice diameter of a spray nozzle. The estimations show that, for the spray flow studied in the paper the value of St number (3) varies in the range of 50–1300, which identifies it as inertial flow. Here, the velocity of droplets was estimated using the high-speed video recording from the side of the spray flow.

#### 2.3. High-Speed Video and Infrared Recordings

#### 2.4. Measurement Uncertainties

## 3. Results

#### 3.1. Irrigation Patterns

#### 3.2. Droplet Sizes

_{0.5}) and Sauter mean diameter (d

_{32}) were determined, the last of which is defined as follows [41]:

_{i}is the number of droplets with a diameter of d

_{i}. Figure 5b demonstrates the dependence of the d

_{32}value on the liquid flow rate. It can be seen that, with an increase in the liquid flow rate in the investigated range, the Sauter mean diameter increases and the obtained dependence d

_{32}(Q) with an accuracy of ±25% is described by a linear function.

#### 3.3. Droplet Impact on Liquid Film

#### 3.4. Droplet Flux Density

^{2}) was selected, and the number of droplets falling onto the surface within the boundaries of this area was counted for 500–800 ms. It is important to note that this technique makes it possible to count all droplets that come onto the surface, as even small droplets cause wave disturbances of the liquid film, which are clearly distinguishable in high-speed video frames (Figure 6a). The error of determining the droplet flux density in such way for small liquid flow rates directly depends on the statistical error. At high flow rates (more than 1.5 mL/s), counting the number of droplets becomes more difficult owing to the large number of local “events”. In this case, the maximum measurement error of the $\dot{N}$ is up to 20%. However, it should be noted here that this value can be reduced, including through the use of automatic image processing algorithms, as well as neural networks, which will increase the sampling and improve the measurement accuracy.

#### 3.5. Heat Transfer Rate

^{2}are presented. The obtained temperature distribution indicates that there is a difference in temperature values at the center and at the periphery of the heating area. However, this difference for the presented case is no more than 3 °C, but it can increase with an increase in the heat flux density. This fact, in our opinion, is primarily owing to the non-uniform distribution of the droplet flux density over the surface, as demonstrated earlier (Figure 7).

_{0}is the initial liquid temperature. Figure 9a shows the dependences of the HTC value on the heat flux density at various liquid flow rates. It seen that the intensity of single-phase heat transfer during spray cooling weakly depends on the heat flux in the studied range. At the same time, an increase in the flow rate leads to a noticeable increase in the intensity of heat transfer (Figure 9b).

_{32}) are used as characteristic scales of velocity and length, respectively:

## 4. Conclusions

- –
- The study of the droplet size distribution was carried out and the dependence of the Sauter diameter on the liquid flow rate for the studied irrigation modes was obtained.
- –
- The droplet flux density for various flow rates was studied. It has been shown that this parameter can differ significantly depending on the impact surface region. This makes it possible to assess the degree of irrigation irregularity even in the case of a full cone spray.
- –
- Various possible scenarios of interaction between droplets and a liquid film forming on the surface were shown, such as the formation of small-scale capillary waves for small droplets, as well as the appearance of craters and splashing crown in the case of large ones.
- –
- Based on the data of high-speed infrared recording, the intensity of heat transfer during spray cooling for various heat flux densities and the liquid flow rates was analyzed. It was shown that, for the studied regimes, the value of the heat transfer coefficient is weakly dependent on the heat flux and is determined primarily by the flow rate.
- –
- Comparison of the obtained experimental data on the intensity of single-phase heat transfer during spray cooling with existing models was performed. It was shown that data can be described within the model of [49] with a modified numerical coefficient. In addition, based on a comparative analysis of existing approaches, an analogy in the mechanisms that determine the intensity of heat transfer during spray cooling and nucleate boiling was shown.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Liquid flow rates for the studied spray cooling regimes. The error bars are presented for the Q values.

**Figure 3.**Prospects of using a transparent impact surface for studying the hydrodynamic parameters of spray irrigation.

**Figure 4.**The various patterns during spray irrigation of the transparent impact surface investigated in the paper.

**Figure 5.**(

**a**) Droplet size distribution during spray irrigation (Q = 0.5 mL/s); (

**b**) Sauter mean diameter dependence on the flow rate.

**Figure 6.**Various scenarios of the droplet impacts on the liquid film observed during spray cooling (Q = 0.5 mL/s): (

**a**) small-scale wave disturbance caused by small droplets; (

**b**) crater formation; (

**c**) splashing crown.

**Figure 7.**The dependence of the droplet flux density on the liquid flow rate for various impact surface areas.

**Figure 8.**(

**a**) The time-averaged IR thermography frame and (

**b**) corresponding temperature distribution of the heating during spray cooling (Q = 1.7 mL/s, q = 45 kW/m

^{2}).

**Figure 9.**The dependence of the heat transfer coefficient during spray cooling on (

**a**) heat flux density and (

**b**) liquid flow rate.

**Figure 10.**The comparison of the obtained data on the heat transfer intensity during spray cooling with the existing correlations (q = 45 kW/m

^{2}).

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**MDPI and ACS Style**

Serdyukov, V.; Miskiv, N.; Surtaev, A. The Simultaneous Analysis of Droplets’ Impacts and Heat Transfer during Water Spray Cooling Using a Transparent Heater. *Water* **2021**, *13*, 2730.
https://doi.org/10.3390/w13192730

**AMA Style**

Serdyukov V, Miskiv N, Surtaev A. The Simultaneous Analysis of Droplets’ Impacts and Heat Transfer during Water Spray Cooling Using a Transparent Heater. *Water*. 2021; 13(19):2730.
https://doi.org/10.3390/w13192730

**Chicago/Turabian Style**

Serdyukov, Vladimir, Nikolay Miskiv, and Anton Surtaev. 2021. "The Simultaneous Analysis of Droplets’ Impacts and Heat Transfer during Water Spray Cooling Using a Transparent Heater" *Water* 13, no. 19: 2730.
https://doi.org/10.3390/w13192730