Measurement of the heat transfer coefficient in gas spray cooling with low liquid flow rate

. The rapid development of high power electronic, energy systems has led us to the fact that the performance of these systems is limited by their cooling capacity. Spray cooling is one of the most effective methods for cooling heated surfaces. The efficiency of heat transfer from the heated surface depends on many of the integral parameters of the flows (flow rates of liquid, gas, their thermophysical properties, surface properties), and on the size and distribution of droplets formed in the nozzle, their density and velocity, the properties of the surface and material of heated objects, and the temperature value. In this work, the efficiency of heat transfer from a heated copper surface by a rarefied gas-spray flow created by two similar types of nozzles in the mode of a small amount of liquid supplied is experimentally studied.


Introduction
The interaction of droplets with a heated wall is an important process that occurs in a large number of existing and new technologies.Spray cooling is a very efficient technology that outperforms all other traditional cooling methods, especially those that do not involve a phase change and do not use the latent heat of vaporization.However, the effectiveness of spray cooling depends on a large number of parameters, including spray characteristics such as droplet size, velocity and number density, thermal properties of the fluid, surface properties, and the temperature range and thermal properties of the materials used.Indeed, substrate temperature can have a significant effect on the hydrodynamics of droplet and splash impact, an aspect that is rarely taken into account in model development.This process is extremely complex, so most design rules today are highly empirical in nature [1][2][3][4].
Due to the complexity of the problem, the hydrodynamics of liquid films created by aerosols and the heat transfer associated with this have not been fully studied.An important requirement in general, but especially in the case of aerosol cooling of electronic equipment, is uniform heat removal from the surface and the absence of hot spots.According to the classification [4], at different heat fluxes, both boiling and non-boiling modes are possible.At high heat fluxes, a large flow rate of liquid in the spray is required, and at the same time, its droplets must be small.The droplet size is determined by the diameter of the nozzle or nozzles, if there are several.At the same time, with a decrease in the diameter of the nozzle, the flow rate of the liquid decreases.Actually, for each heat transfer task of a particular device, there is an optimal heat transfer system.To date, no universal model has been developed that predicts the effectiveness of spray cooling in a significant range of operating parameters.However, the cooling capacity and efficiency of spray cooling needs to be further improved to meet the requirements of next generation heavy duty applications [4][5][6].
Rarefied gas-spray cooling has a predominant application when all the liquid used is evaporated in the heat exchange process.In this case, with heat transfer without boiling, simple empirical dependences of the process are possible.

Experimental setup
To measure the characteristics of the spray, we made a setup, the scheme of which is shown in Figure 1.Air is supplied from a compressor through a flow regulator, water is supplied from a syringe pump to control low liquid flow and has a room temperature of 25°C.The resulting spray falls onto a stainless-steel plate, in the middle of which there is a hole for the thin end of a copper heater with an area of 1 cm 2 .In the narrow part of the heater and in the steel plate, there are thermocouples to control the surface temperature and heat fluxes falling on the heater surface and spreading over the surface of the steel plate.From these thermocouples, the heat flux removed by the spray and the surface temperature of the heater are calculated.
The nozzle device is schematically shown in Figure 2(a).Inside the nozzle there is a channel for water supply, made of a steel tube into which a capillary is inserted (Figure 2(b)).The air enters the outer wide part of the nozzle and at the exit the gas stream breaks off small drops of water, which are then transferred to the heater.For experiments 2 nozzles were made with different diameters of the inner capillary (0.25 mm and 0.5 mm), through which water is supplied.During the heat transfer coefficient measurement, the gas flow rate varied from 5 to 15 l/min (at normal pressure), water -from 0.5 to 2 ml/min.Thus, the mass flow rate of gas exceeded the mass flow rate of water by about 10-30 times.
During the experiment, the flow rates of liquid and gas, the power released on the heater were set.Based on the measured temperatures, the generated heat flux and the surface temperature of the heater were calculated.Since the spray is rarefied and, as a result, the heat fluxes are small, it is problematic to determine the critical heat flux by surface heating, since heating will take a very long time.The heat transfer coefficient was determined in the experiment by the formula: HTC = q/(Tw -Tin), ( where the heat flux q is determined from the measured readings of thermocouples in the thin heater neck and the steel substrate.The surface temperature was determined by approximating the measured values of thermocouple indicators in the neck of the heater.

Results
Figure 3 shows the values of the heat transfer coefficient at a gas flow rate of 5 liters per minute, depending on the flow rate of the supplied liquid for a nozzle with a capillary of 0.25 mm.With an increase in the flow rate of the liquid, an increase in the heat transfer coefficient is first observed, followed by its stabilization at the investigated flow rates.The same dependence takes place for an injector with a capillary of 0.5 mm.The heat transfer coefficient, which weakly depends on the flow rate of liquid or gas, is reached when the surface temperature does not exceed the boiling point.This also explains the abnormally high heat transfer coefficient at a heater power of 30 W. Figure 4 shows the values of the heat transfer coefficient from the heated surface at a water flow rate of 0.5 ml per minute, depending on the gas flow rate.As well as with an increase in water flow, an increase in heat transfer coefficients with an increase in gas flow is observed.When the surface is cooled below the boiling point, the heat transfer coefficient weakly depends on the flow rate of gas and liquid.For a nozzle with a capillary of 0.5 mm, at air flow rates of 15 l/min and higher, the spraying mode becomes unstable, highly pulsating, and chaotic; therefore, for such a nozzle, only modes with flow rates of 5 and 10 l/min were studied.At a water flow rate of 0.5 ml/min and a gas flow rate of 10 l/min, a pulsating regime is observed, and the fluctuations gradually increase and decrease over time.
Therefore, the heat flux and substrate temperature can be determined only from the average temperatures of the thermocouples.However, the average values are in good agreement with the results of experiments without pulsations (Figure 5.) The dependence of the heat transfer coefficient on the liquid flow rate remains the same as for the nozzle with a 0.25 mm capillary.With an increase in the gas flow rate (filled points), the heat transfer coefficient increases, and the greatest increase is achieved at low heat fluxes, which corresponds to the cooling of the surface temperature below the boiling point.The dependence of the heat transfer coefficient on the gas flow rate for the second nozzle is shown in Figure 6.The dependence on water and gas flow for different nozzles can be summarized by the dependence of the heat transfer coefficient on the surface temperature.As described above, as the temperature increases, the heat transfer coefficient decreases.Moreover, this drop is different for different heating capacities.But at the same time, for the same power supplied to the heater, regardless of the type of nozzle and the flow rates of liquid and gas, the heat transfer coefficient decreases linearly with increasing temperature, as shown in Figure 7.Moreover, the points from the experiments with both nozzles lie on the same straight line.

Conclusions
Thus, when the surface is cooled with a rarefied spray, the heat transfer coefficient increases with an increase in the flow rate of liquid and gas for various nozzle geometries.However, this growth slows down greatly when the surface temperature cools below the boiling point of the liquid.This is due to the fact that a smaller part of the water has time to evaporate from the substrate, and the heat of the liquid-vapor interfacial transition for water is much greater than the heat of increasing temperature from 25 °C to 100 °C and the gas cannot greatly increase the evaporation rate, since the remnants of unevaporated water are simply blown off from the heater.At the same time, the heat transfer coefficient decreases with increasing substrate temperature, and not along a hyperbola, as one would expect with a constant heat flux to the heater, but linearly.This is due to the fact that as the temperature rises, most of the heat flux spreads into the steel substrate and is not removed by the spray.Linear, 50W

Fig. 1 .
Fig. 1.Scheme of the experimental setup for measuring the heat flux removed by the spray.

Fig. 2 .
Fig. 2. Scheme of a gas spray nozzle (a) and a photograph of a capillary for water supply (b).

Fig. 3 .
Fig. 3. Dependence of the heat transfer coefficient on the liquid flow rate for a nozzle with a capillary of 0.25 mm at a gas flow rate of 5 l/min.

Fig. 4 .
Fig. 4. Dependance of the heat transfer coefficient on the gas flow rate with different water flow rates.

Fig. 5 .
Fig.5.Dependence of the heat transfer coefficient on the liquid flow rate for an injector with a 0.5 mm capillary at various gas flow rates.

Fig. 6 .
Fig.6.Dependence of the heat transfer coefficient on the gas flow rate at the heater power 50 W.A sharp increase in the heat transfer coefficient corresponds to a decrease in temperature below the boiling point.

Fig. 7 .
Fig. 7. Dependence of the heat transfer coefficient on the surface temperature.Points with different liquid and gas flow rates and different nozzles lie on the same straight line.