Heat transfer of a modified surface with a dispersed coolant flow

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Introduction
The rapid development of powerful electronics, power plants and engines has led to the fact that the characteristics of these systems have become limited by the possibilities of heat removal.Modern electronics can generate heat flows up to 10 MW/m 2 , which must be removed with a minimum coolant flow.The use of a phase transition allows the heat removal by a dispersed flow to reach a high heat flux density.This method has proven to be effective in a variety of applications.However, heat removal and spray heat removal efficiency need to be further improved in order to meet the requirements of next generation ultra high power power plants.The development of surface properties and structures, which is provided by modern production technologies, can significantly affect the interaction of the dispersed flow and the wall, which becomes the most promising cooling method.However, the mechanisms of spray cooling with improved thermal properties of the surface are diverse and ambiguous.An analysis of experimental data on structured surfaces shows that dispersed flow cooling can provide a maximum heat flux above 10 MW/m 2 at a heat transfer coefficient reaching 60 kW/(m 2 •K) [1].
For dispersed water cooling of structured surfaces, a large scatter of data was obtained both in terms of heat transfer coefficients and in terms of maximum heat fluxes [1].Most experimental and numerical studies in the field of dispersed cooling are devoted to the study of sprays formed by a single nozzle [2][3].For single-phase modes, this method of cooling has been studied quite thoroughly [4][5].However, as can be seen from the * Corresponding author: schteling@gmail.comreview article [1], the dispersed cooling mode at surface temperatures above the liquid saturation temperature is actively studied, and many authors obtain ambiguous results regarding both the maximum heat flux density and its efficiency.
This article presents an experimental study of the heat transfer process of a modified surface with a dispersed coolant flow under conditions of ultrahigh heat flows.For the study, an experimental stand was used that simulates the energy-loaded surfaces of thermonuclear installations.The paper compares the experimental data for a modified surface containing regular structures and for a surface without structures and having the 6th roughness class.
Review article [1] gives many options for studying spray cooling of various modified surfaces.Previous studies have not considered structures of similar geometry under spray cooling conditions.Also, in most of the above studies, the heat flux density does not exceed 2 MW/m 2 , while in the current study, the heat flux density reaches 7 MW/m 2 .At the same time, the design of the experimental setup provides a heat exchange surface of 10 cm 2 , while the surface itself is oriented vertically, which more satisfies the conditions of industrial power plants.These facts distinguish this study from others.

Description of the experimental stand
Figure 1 shows a schematic view of an experimental stand for studying heat removal from a structured surface with a high temperature when it is cooled by a dispersed coolant flow.This experimental stand includes a hydraulic circuit, an induction heating system, test section with a modified surface, an information acquisition and processing system, and an experimental chamber.The pressure in the coolant circuit (distilled water) can vary in the range p = (0.1 ÷ 1.5) MPa, which, when using various atomizing devices (nozzles), allows you to control the flow of the coolant in a wide range.

Construction of the test section
A schematic representation of the working area is shown in fig. 2. Fastening of the working area (1) to the wall of the experimental chamber (2) is carried out using a magnetically transparent ceramic flange (3) made of heat-insulating ceramics.The cylindrical part of the working area is heated by induction currents using an induction coil (4).The working section is made of copper and has the shape of a cylinder, turning into a truncated cone, with a smaller diameter.17 rods made of Armco iron ( 5) are integrated into the cylindrical part of the working section.This design makes it possible to significantly increase the efficiency of induction heating and increase the supplied heat flux density.The nozzle ( 6) is fixed on a branch pipe, which allows changing its location in the experimental chamber.In the above experiments, the nozzle sprays the coolant onto a flat surface of a truncated cone, the diameter of which is 35 mm (the heat exchange area is ~10 cm 2 ).
On fig. 3 shows the location of thermocouples in the working area.Four groups of thermocouples are located in pairs in two sections of the working area x 1 = 3 mm and x 2 = 7 mm.

The design of the nozzle
Fig. 4 shows a scheme of the hydraulic nozzle used in this series of experiments.The nozzle consists of: a body (1), an insert containing an outlet orifice (2) and a swirler insert (4), which together form a conical mixing chamber (3).The inserts are fixed with a stopper (5).
The insert (Fig. 5) contains one central channel 0.4 mm in diameter and four tangential channels 0.6 mm wide and 0.4 mm deep.The liquid is supplied simultaneously through the central and tangential channels.Thus, the streams collide and break up in the mixing chamber, creating a dispersed stream at the exit of the nozzle, which forms a spray cone in the form of a filled cone.The orifice nozzle diameter is 0.6 mm.Measurements carried out by the IPI method (Interferometric Particle Imaging) showed that the average droplet diameter dk was 35 μm in the spray cone section located at a distance of 35 mm from the nozzle at a coolant pressure of 2•10 5 Pa.

Modified surface structure
A regular structure consisting of truncated pyramids was deposited on the heat exchange surface of the working section by knurling (Fig. 6).The knurling tool (roller) is shown in fig. 7. The knurling of the structures was carried out sequentially in the transverse and longitudinal directions.The choice of modification is due to its fairly simple implementation (including for industrial conditions, which is especially important for the energy sector), as well as the regularity of the formed structures.The size of the structures in this case corresponds to the current task of studying the heat transfer of macrostructures with a dispersed coolant flow.

Results of the experimental study 4.1 The experimental procedure
With the specified heater power, a steady heat-transfer mode was set, and its onset was detected when the target temperature stopped to increase for a sufficiently long period of time (approximately 100 s).Concurrently with this, the test section surface was cooled with a distilled water spray (at the established coolant pressure and flowrate, and constant inlet coolant temperature of approximately 26 °C).After that, the heating power was changed with the coolant pressure and flowrate remained the same, and the experiment was repeated.If it was not possible to reach a steady mode with the next increase of the power level, i.e., if the test section temperature showed an unlimited growth, it was considered that the limit removed heat flux was achieved at the given cooling parameters.After that, new spray cooling parameters were set, and the experiments were repeated [6].

Method for calculating thermophysical characteristics
The following is a brief summary of the computational technique and the main results of the experiments.
To evaluate the efficiency of heat transfer, the heat flux density and heat transfer coefficient were calculated for each experimental regime.
The heat flux density is calculated as: , T T  average temperatures in sections x 1 and x 2 , λ -thermal conductivity of copper.The heat transfer coefficient is estimated as follows: (2); where T w is the wall temperature, T S is the saturation temperature at atmospheric pressure.

Experimental results
Fig. 9 shows the obtained experimental dependences of the heat flux density on the temperature of the irrigated wall.The description of the graph indicates the coolant parameters for each mode, where p is excess pressure of the coolant at the nozzle inlet, G is mass flow rate of the coolant, j is average irrigation density, T in is initial temperature of the coolant.On the dependences presented, the boundaries of heat transfer modes are marked: I -effective heat transfer mode, which corresponds to nucleate boiling (the most intense vaporization is observed), II -transitional heat transfer mode, III -film heat transfer mode.Heat transfer curves № 1-3 was obtained on a surface that does not contain structures and has the 6th roughness class (the size of inhomogeneities on the surface is no more than 5 μm), heat transfer curves 4-6 were obtained on a modified surface containing the structures described in Section 3.
The results obtained showed a slight drop in the heat flux density on the modified surface, relative to the unmodified surface, with similar operating parameters of the coolant.There is also a decrease in the maximum heat flux density for all regimes on a structured surface.Fig. 10 shows graphs of the dependence of the heat transfer coefficient on the temperature of the irrigated wall.On the graphs, one can observe an increase in the heat transfer coefficient for regimes on a modified surface, relative to regimes with an unmodified surface, which is associated with a lower temperature of the irrigated wall at an equal heat flux density.This slight increase in the heat transfer coefficient for the case of a modified surface, with a heat flux density corresponding to the unmodified surface, can also be observed in the dependence shown in Fig. 11.Fig. 12 shows graphs of the dependence of the maximum heat flux density on the irrigation density.As can be seen from this dependence, an increase in the irrigation density leads to an increase in the maximum heat flux density for both the modified and unmodified surface.The nature of the dependence is similar for both types of surface.However, with a similar irrigation density, the maximum values of the heat flux density on the modified surface are lower, which can also be associated with inefficient cooling of the entire area of the modified surface.Fig. 13 shows graphs of the dependence of the maximum heat transfer coefficient on the irrigation density.As can be seen from this dependence, the maximum values of the heat transfer coefficient at a given irrigation density are higher when the modified surface is cooled.This is due to the lower average temperature of the modified surface during irrigation, which is indirectly due to the non-isothermal nature of the structures of the modified surface.

Conclusions
 The selected structure for surface modification did not give significant results in increasing the heat transfer efficiency.This may be due to the nonoptimal size of the inhomogeneity, which under the experimental conditions was an order of magnitude larger than the average diameter of the dispersed flow droplets. A slight decrease in the heat flux density, as well as the surface temperature with identical regime parameters, may be due to the uneven temperature distribution along the structure profile on the modified surface.Despite the fact that this indirectly leads to an increase in the heat transfer coefficient, a decrease in the critical temperature negatively affects the technical applicability of the dispersed cooling method. The choice of the optimal surface modification to increase the efficiency of dispersed cooling directly depends on the parameters of the irrigating spray.
The work was supported by the Russian Science Foundation grant №. 23-19-00476.

Fig. 3 .
Fig. 3. Location of thermocouples in the test section.

Fig. 7 .
Fig. 7. Photo of the knurling roller.The geometry of the structures and their characteristic dimensions are shown in fig.8.

Fig. 10 .
Fig. 10.Dependence of the heat transfer coefficient on the temperature of the irrigated wall.

Fig. 11 .
Fig. 11.Dependence of the heat transfer coefficient on the heat flux density.

Fig. 12 .
Fig. 12. Dependence of the maximum heat flux density on the irrigation density.

Fig. 13 .
Fig. 13.Dependence of the maximum heat transfer coefficient on the irrigation density.