Effects of Surface Conditions on Spray Cooling Characteristics

Abstract

The influence of surface conditions such as scale thickness and surface roughness on water spray cooling and air jet cooling characteristics was investigated experimentally. SUS304 stainless steel with the thickness of 20 mm was used as the cooled sample. An artificial scale layer was formed on the sample surface by thermal-spraying using Al₂O₃ powder. The thickness of the Al₂O₃ layer was varied from 50 µm to 210 µm. A sample without an artificial scale layer was also studied; in this case, the surface was roughened by shot blasting up to 20 µmRa.

As a result, the artificial scale layer showed a thermal resistance function in both water spray cooling and air jet cooling. In water spray cooling, the characteristics of which depend on surface temperature, the cooling rate during film boiling and the apparent quenching temperature at the interface increased with Al₂O₃ scale thickness. Surface roughness enhanced the cooling rate during film boiling and resulted in a higher quenching temperature in spray cooling. In air jet cooling, heat flux increases with surface roughness, but this tendency can be seen only with larger flow rates. Surface roughness has a much stronger influence on heat flux in water spray cooling, even though the average heat flux is not as large. In this research, the heat flux during impingement of water droplets was estimated to be much higher than that in air jet cooling. This is thought to explain the difference in the influence of surface roughness on cooling characteristics with the two cooling methods.

1. Introduction

Recently, high tensile strength steel sheets have been applied in a wider range of auto body parts than ever in order to improve automotive fuel efficiency and collision safety, while high strength steel plates are now used as materials for linepipes in severe environments such as in deeper water and under high pressure operating conditions in response to increasing demand for energy resources. To achieve the targeted mechanical properties and microstructures, steel companies are developing and applying TMCP (Thermo Mechanical Control Process) technologies in which the temperature of the steel is controlled by water cooling on the run-out table in hot strip mills and in the accelerated cooling device in plate mills. For example, at the hot strip run-out table, pipe laminar cooling of the top side and spray cooling of the bottom side are usually applied.

In the past, the targeted microstructure was mainly ferrite and pearlite after cooling in the hot strip mill. Recently, technologies for high tensile steel sheets which have bainite or mixed structures have progressed remarkably. While hot-rolled sheets which consist of the bainitic structure are cooled to, for example, 450°C, the cooling condition can shift from film boiling to transition boiling. Once transition boiling occurs, heat flux increases drastically and uncontrollably. Hence, it is important to evaluate cooling characteristics such as the heat transfer coefficients in film, transition and nucleate boiling and the quenching temperature at which film boiling shifts to transition boiling in order to ensure uniform, accurate cooling to a targeted temperature by adjusting the water flow rate and cooling time.

Based on this background, various studies have been conducted^{1,2,3,4,5,6,7)} on water cooling of steel materials, focusing on the shifting phenomena of boiling conditions. Mitsutsuka¹⁾ conducted a spray cooling experiment with carbon steel and correlated the relationship between the heat transfer coefficient and water flow density in terms of the surface temperature of the steel, but did not consider the effect of scale thickness or surface roughness. To investigate the effect of scale thickness, Tamari et al.⁶⁾ and Kato et al.⁷⁾ independently conducted similar experiments with various conditions of heating time and nickel content. The quenching temperature increased with scale thickness in both experiments. Moreover, those results might include the effect of surface roughness, which inevitably changes depending on scale thickness.

Okubo et al.²⁾ conducted a mist cooling experiment using SUS303 stainless steel with artificial undulations on its surface as the specimen. The result showed that the cooling rate during film boiling decreased and the quenching temperature increased with the number of undulations.

In this paper, the effects of scale thickness and surface roughness on cooling characteristics, including the heat transfer coefficients during film, transition and nucleate boiling and the quenching temperature, were investigated separately by cooling experiments with various scale thicknesses and surface roughnesses. The water spray cooling experiment was conducted using SUS304 stainless steel as the base material, on which a surface metallic oxide layer, as an artificial scale layer, was formed by thermal spraying, or the surface was roughened by shot blasting. A variety of scale thicknesses and surface roughness values were examined.

An air jet cooling experiment was also conducted. The mechanism by which scale thickness and surface roughness affect spray cooling characteristics was investigated by comparing the air jet and spray cooling results. The cooling ability of a single spray droplet colliding with the steel surface was also estimated.

2. Experimental Procedure and Conditions

2.1. Specimen

Table 1 shows the main specifications of the specimens used in the experiments. SUS304 stainless steel was used as the base material to eliminate unstable factors such as transformation and scale formation and peeling. The specimen dimensions were 20 mm in thickness, 140 mm in width and 130 mm in length.

Table 1. Surface condition of specimen.

Coating layer	Thickness (μm)	Roughness (μmRa)
Al2O3	50	1.6
	100	1.5
	170	1.3
	210	1.4
Non-coating		3.0
		10.2
		20.1

Base material: SUS304 20^t×140^W×130^L mm

To investigate the effect of scale thickness, artificial scale layers with various thicknesses were formed on the specimen surface by thermal spraying using metallic oxide powder. To eliminate unstable factors such as removal and growth of scale during experiments, Al₂O₃ powder was used which has high thermal and chemical stabilities. The thickness of the Al₂O₃ layer was varied from 50 μm to 210 μm by adjusting the thermal spraying time. The specimens were polished to about 1.5 μmRa after thermal spraying.

On the other hand, to investigate the effect of surface roughness, different specimens of the base material without the artificial scale layer were prepared, and their surfaces were roughened to values from 3 μmRa to 20 μmRa by shot blasting. The real surface area of the actual three-dimensional roughness profile, which was measured by a laser microscope (VK-X105, KEYENCE Ltd.), was calculated. The measured area was 2.4 mm (2270 scan) × 1.7 mm (1640 scan) with magnification of 50x at the center of the specimen. Table 2 shows surface area ratio, which is defined as the real surface area divided by the measured (nominal) one. The surface area ratio increased with the surface roughnesses ranging between 1.96 and 2.81.

Table 2. Surface area ratio observed by a laser microscope.

Roughness (μmRa)	3.0	10.2	20.1
Surface area ratio	1.96	1.98	2.81

A thermocouple with a diameter of 0.5 mm was embedded 2 mm below the base material surface to measure the heating and cooling temperatures.

2.2. Water Spray Cooling Experiment

Figure 1 shows the apparatus used in the water spray cooling experiment. Table 3 shows the experimental conditions. Cooling water from the spray nozzle, which was installed above the specimen and had a squarely spreading angle of 50°, was pumped from the tank, in which the temperature of the water was maintained at 30°C, and was sprayed at a predetermined water flow rate. The water temperature, which was initially 30°C at the outlet of the spray nozzle, was cooled down between 28 and 29°C until the sprayed water reached the sample surface. The water flow density was changed from 0.00167 to 0.0117 m³/m²s by adjusting the injection distance between 530 and 200 mm at the constant total flow rate of 0.0004 m³/s to keep the same conditions in terms of spray droplet diameter and velocity. The water flow density was evaluated by dividing the total flow rate by the square injection area for the spreading angle of 50°. The calculated values were confirmed by actual measurement using a measuring box, in which 20 mm square cells were arranged in lines so that the water flow density distribution of the nozzle was uniform at the injection distance of 265 mm in an area of 175 mm square, corresponding to the spreading angle of 37°. The mean diameter and velocity of the spray droplets at the injection distance of 200 mm were determined to be 330 μm and 10 m/s, respectively, by using the phase-Doppler technique.

Fig. 1.

Experimental apparatus of spray cooling.

Table 3. Experimental conditions in spray cooling tests.

Reheating temperature	620°C
Cooling start temperature	560°C
Water temperature	30°C
Water flow density	0.00167, 0.00667, 0.0117 m3/m2 s
Injection distance	530, 265, 200 mm
Mean droplet diameter	330 μm
Mean droplet velocity	10 m/s

The specimens were heated to 620°C in an electric furnace under a nitrogen atmosphere, and were then taken out from the furnace and placed under the spray nozzle. The cooling water was sprayed at the predetermined water flow density onto the closed shutter, and when the sample temperature decreased to 560°C, the shutter was opened and water spray cooling was applied until the specimen temperature decreased to room temperature.

2.3. Air Jet Cooling Experiment

Figure 2 shows the apparatus used in the air jet cooling experiment. Air was pressurized with the compressor, and then jetted at 20°C from the air cooling header. The header surface had 2.5 mm diameter holes with a 20 mm pitch in the width direction and 17 mm pitch in the longitudinal direction. The injection distance was 15 mm. The air flow density was changed from 1.67 to 6.17 Nm³/m²s by adjusting the valve. The mean air velocity at the outlet was from 106 to 339 m/s. In the experiment, the specimen was oscillated in the longitudinal direction within the jetting surface of the header to smooth the air jet cooling.

Fig. 2.

Experimental apparatus of air jet cooling.

The experimental conditions are listed in Table 4. The heating conditions were basically the same as that in section 2.2. The heated specimen was taken out from the furnace and placed on the carriage. The specimen was then oscillated at the velocity of 0.05 m/s with the stroke of 120 mm and period of 4.8 s. When the temperature of the specimen decreased to 560°C, the specimen was cooled to room temperature at the full air flow density.

Table 4. Experimental conditions in air jet cooing tests.

Cooling area	150 mm×250 mm
Injector hole	ϕ2.5 20×17 mm pitch
Reheating temperature	620°C
Cooling start temperature	560°C
Air temperature	20°C
Air flow density	1.67, 2.83, 3.83, 6.17 Nm3/m2 s
Injection distance	15 mm
Transferring speed	0.05 m/s

2.4. Estimation of Thermal Histories at Base Metal Surface

The thermal histories at the base metal surface, which corresponds to the interface between the base material and the artificial scale layer in the case of the thermal sprayed specimens, were estimated from the histories measured with thermocouples in order to evaluate the effect of surface conditions on cooling characteristics.

Assuming that the specimen was cooled uniformly in the longitudinal and width directions, the calculated condition was simplified to a one-dimensional problem in the thickness direction. From the heat conduction equation, temperature T (K) at distance Y (m) from the center of thickness of the base metal can be represented by Eq. (1).   

$$\frac{\partial T}{\partial t}=\frac{\lambda }{c\rho }\frac{{\partial }^{2}T}{\partial Y^2}$$(1)

Where, t is time (s), λ is thermal conductivity (W/mK), c is specific heat (J/kgK) and ρ is the density of the material (kg/m³). The values of c, λ and ρ in reference⁸⁾ were used.

From Fourier’s law, the heat flux q (W/m²) at a surface (Y=±h/2, h: thickness) can be represented by Eq. (2).   

$$q=-\lambda \frac{\partial T}{\partial Y}$$(2)

The heat flux in natural convection, water spray and air jet cooling is expressed by Eqs. (3), (4), (5), respectively:   

$$q=q_{rad}+q_1$$(3)

  

$$q_{rad}=\sigma \epsilon (T_s{}^4-T_a{}^4)$$(4)

  

$$q_1=\alpha (T_s-T_a)$$(5)

Where, q_rad is heat flux by radiation, q₁ is heat flux in natural convection, water spray and air jet cooling, σ is the Stefan-Boltzmann constant (5.67×10⁻⁸ W/m²K⁴), T_s (K) is the base metal surface temperature and T_a (K) is air or water temperature.

Applying the equations above to an analytical method of a one-dimensional inverse heat conduction problem following Monde et al.,⁹⁾ a heat transfer analysis was conducted to match the calculated thermal history to the measured history at the point 2 mm below the metal surface. Since the scale layer was too thin and its thermal conductivity was not clarified precisely, the analysis was conducted without considering the scale layer,⁷⁾ and the heat transfer coefficient was calculated.

3. Experimental Results

3.1. Water Spray Cooling

3.1.1. Effect of Scale Thickness

Figure 3 shows the experimental results for various scale thicknesses of Al₂O₃ at the water flow density of 0.00167 m³/m²s. The thermal history in Fig. 3(a) is the calculated result for the interface between the scale layer and the base metal.¹⁹⁾ For instance, in the case of the 50 μm scale thickness, film boiling was observed from the beginning until 36 s, corresponding to the quenching temperature of 365°C, and the cooling rate was low. Subsequently, transition boiling with a significant cooling rate occurred above approximately 130°C, after which the cooling rate decreased again during nucleate boiling. Because the thermal history is a calculated result, the quenching point at which transition boiling began on the base metal surface should be denoted as “apparent.” The apparent quenching temperature is summarized in Fig. 3(b). The apparent quenching temperature increased linearly with larger thicknesses of the scale layer, changing from 365 to 458°C, as qualitatively shown in Kato et al.⁷⁾ Figure 3(c) shows the cooling rate on the interface during film boiling from 530 to 490°C. The cooling rate was almost the same or slightly higher with larger scale thicknesses, as qualitatively shown in Tamari et al.⁶⁾

Fig. 3.

Effects of scale thickness on spray cooling characteristics (Scale type Al₂O₃, Water flow density 0.00167 m³/m²s).

3.1.2. Effect of Surface Roughness

Figure 4 shows the effect of surface roughness on cooling characteristics. The quenching temperature in Fig. 4(a) increased with the water flow rate and surface roughness.²⁰⁾ The effect of surface roughness was more significant at 10 μmRa and 20 μmRa than at 3 μmRa. The cooling rate during film boiling from 530 to 400°C increased with surface roughness, and a more significant influence was observed with high water flow rates, as shown in Fig. 4(b).

Fig. 4.

Effects of surface roughness on spray cooling characteristics (Non-coating).

3.2. Air Jet Cooling

3.2.1. Effect of Scale Thickness

Figure 5 shows the calculated thermal histories at the interface and heat fluxes with the scale thicknesses of 50 μm and 210 μm. The interfacial temperature decreased gradually in both cases, as shown in Fig. 5(a), but the cooling rate was slightly lower with the 210 μm scale thickness. In Fig. 5(b), the heat flux was highest just after the beginning, then decreased in an approximately linear manner as cooling progressed, implying that heat transfer was almost constant independent of the interfacial temperature.

Fig. 5.

Effect of scale thickness on air jet cooling (Scale type Al₂O₃, Air flow density 3.83N m³/m²s).

3.2.2. Effect of Surface Roughness

Figure 6(a) shows the calculated surface thermal histories and heat fluxes with the surface roughness values of 3 μmRa and 20 μmRa. The surface temperature decreased gradually, and the cooling rate was slightly lower with the 3 μmRa roughness, displaying the same tendency as in Fig. 5. The calculated heat transfer coefficient from the starting temperature of 560°C to 150°C increased with the flow rate in Fig. 6(b). When the air flow density was large, the heat transfer coefficient increased slightly with surface roughness, but the difference was not as intense as that during film boiling in Fig. 4(b).

Fig. 6.

Effect of surface roughness on air jet cooling (Non-coating).

4. Discussion

4.1. Effect of Scale Thickness on Spray Cooling

As shown in Fig. 3(b), the apparent quenching temperature at the interface between the scale and the base material varied depending on the scale thickness. Nishio et al.¹⁰⁾ conducted an immersion cooling experiment in which a copper material with a low thermal conductive material as an additional layer on its surface was immersed in a liquid nitrogen pool, and showed that the quenching temperature rose with the thickness of the additional layer when the additional layer was thin, but reached a constant value when the additional layer was increased to a certain thickness.

From this, it was hypothesized that the quenching temperature was constant at the scale surface in the experiment in this paper because the scale layer was sufficiently thick. That is, the reason for the increase in the apparent quenching temperature with scale thickness, as shown in the temperature distribution shown in Fig. 7(b), might be that the scale layer behaved as a thermal resistance material. Therefore, a new heat transfer calculation was conducted considering the scale layer, which was neglected in Chapters 2 and 3, in order to compare the temperatures at the scale surface and the interface under the various experimental conditions.

Fig. 7.

Schematic illustration of temperature distribution at quenching point.

From the air jet cooling experiment in Fig. 5, with the scale thicknesses of 50 and 210 μm, the thermal conductivity in the artificial scale layer of Al₂O₃ was identified as coinciding with the experimental thermal history of the point 2 mm below the interface. The heat transfer coefficient on the scale surface was assumed to be 1100 W/m²K, and the thermal conductivity in the scale layer was assumed to be constant regardless of the temperature and scale thickness. The calculated thermal conductivity of the artificial scale layer of Al₂O₃ was 1.4 W/mK, which was much smaller than the 32 W/mK value of a sintered body,¹¹⁾ but slightly close to the 3 W/mK of a thermal spraying layer.¹²⁾ Takeuchi et al.¹²⁾ stated that the binding rate of Al₂O₃ particles in a thermal spraying layer is smaller than that of a sintered body. The condition of the thermal spraying layer may be different depending on the spraying condition. The thermal conductivity of the artificial layer in this paper was assumed to be smaller than that reported by Takeuchi due to a difference in porosity.

Using the identified thermal conductivity of 1.4 W/mK in the artificial scale layer of Al₂O₃, the effect of the scale thickness on the apparent quenching temperature at the interface was analyzed. First, in Fig. 8, based on the measured data with the scale layer thickness of 50 μm, the results of the above-mentioned inverse analysis in which the effect of the scale layer was neglected (hereinafter referred to as “experimental data”) are plotted as the heavy grey line, showing the relationship between the interfacial temperature and heat flux. Heat flux increased gradually during film boiling, displaying slight fluctuation, increased drastically at 365°C, and then reached its peak value at 192°C.

Fig. 8.

Modeling of relationship between surface or interface temperature and heat flux (Scale type Al₂O₃, Water flow density 0.00167 m³/m²s, Scale thickness 50 μm).

Modelling the experimental heat flux by a polygonal line, as shown by the thin line in Fig. 8, and taking it as the relationship between the scale surface temperature and heat flux, the experimental conditions were analyzed considering the heat transfer in the scale layer so that the calculated thermal history at the interface between the scale layer and the base material matched the experimental data in the case of the scale layer thickness of 50 μm.

Figure 9 shows the calculated results with the scale thicknesses of 50 μm and 210 μm, compared with the experimental results. In the experiment, the quenching temperature at the interface (referred to above as “apparent quenching temperature”) was 365°C for the 50 μm scale thickness and 485°C for the 210 μm thickness. The corresponding calculated results were 365°C and 410°C. Assuming that the quenching temperature at the scale surface was the same in the two cases, the calculation model showed qualitative agreement with the experimental results in terms of the quenching temperature at the interface. However, in the case of the scale layer thickness of 210 μm, there was a large difference between the calculated and experimental results regarding the thermal history after the quenching point. This difference might be caused by the assumption of average heat flux with the condition of 50 μm scale thickness. That is, since spray cooling is the result of intermittent cooling by discrete droplets, when a droplet impacts on the specimen, the regional and instantaneous heat flux is expected to be much larger than the average value in Fig. 8. Therefore, a microscopic investigation of the quenching temperature will be needed in order to clarify the reason for this difference.

Fig. 9.

Comparison of thermal histories at interface between simulations and experiments.

In addition, in Fig. 8, the calculated cooling rate with the scale thickness of 210 μm reached its peak at the interfacial temperature of 380°C and then decreased. The cooling curve after the peak crossed the curve for the scale thickness of 50 μm. However, in the experiment, as shown in Fig. 3(a), the cooling curves overlapped under all the conditions of scale thickness from 50 to 210 μm. Assuming as shown in Fig. 10(a) that the thermal conductivity in the scale layer increases as the temperature of the scale layer decreases below a certain value, the calculated results showed good agreement with the experiment even in the case of the scale thickness of 210 μm, as shown in Fig. 10(b). The reason of this temperature dependency of the thermal conductivity in the scale layer is not clear. It might be caused by a phase transformation of Al₂O₃, or void formation in the scale layer. Hayashi et al.¹³⁾ investigated thermal conductivity of Al₂O₃ fiber and indicated the effect of phase of Al₂O₃ and void fraction on thermal conductivity could not be ignored. Also, the temperature dependency of Al₂O₃ may change significantly, depending on how the coating layer is prepared. Therefore, detailed investigation of the temperature dependency of thermal conductivity in Al₂O₃ spray layer, including the influence of phase transformation and void formation, will be needed.

Fig. 10.

Simulated results of temperature histories at the interface considering varying conductivity of scale layer.

In actual cooling phenomena in steels with the scales, further investigations are necessary, not only on thermal conductivities of scale elements FeO, Fe₃O₄ and Fe₂O₃, but also on the combined effect of scale layers. Also, there is a difficulty on dealing with fracture and removal of scale layer during the cooling process, to estimate the effect of scale thickness on spray cooling characteristics quantitatively.

4.2. Effect of Surface Roughness on Spray Cooling

The following will discuss the mechanism in air jet cooling, in which heat transfer coefficient increased with surface roughness under the condition of a large flow density, as shown in Fig. 6(b).

Figure 11 shows a schematic illustration of the temperature distribution inside the base material and the cooling medium. The overall heat transfer coefficient K (W) of the cooling surface and the intersection of the base material is calculated as shown in Eq. (6).   

$$K=\frac{\lambda }{\text{h}}{\text{A}}_{\text{0}}\left(T_b-T_s\right)=\alpha {\text{A}}_{\text{s}}\left(T_s-T_a\right)$$(6)

Where, T_s is the temperature of the cooling surface, T_a is the temperature of the cooling medium, A₀ is the area of intersection of the base material, A_s is the surface area of the base material, T_b is the temperature of the cooled surface and h is the thickness of the base material. Eliminating T_s, the following is obtained:   

$$K=\frac{1}{\left(\frac{h}{\lambda {\text{A}}_{\text{0}}}+\frac{1}{\alpha {\text{A}}_s}\right)}\left(T_b-T_a\right)$$(7)

Therefore, the total thermal resistance R (K/W) is expressed by Eq. (8).   

$$R=\frac{h}{\lambda {\text{A}}_{\text{0}}}+\frac{1}{\alpha {\text{A}}_s}$$(8)

In Eq. (8), the first term of the right side expresses the resistance of thermal conductivity, and the second term expresses the resistance of heat transfer coefficient. The ratio of the two terms can be expressed as the Biot number Bi multiplied with the ratio of the cross section:   

$$Bi=\frac{\alpha h}{\lambda }$$(9)

  

$$\frac{h/\left(\lambda {\text{A}}_{\text{0}}\right)}{1/\left(\alpha {\text{A}}_{\text{s}}\right)}=\frac{\alpha h}{\lambda }\frac{{\text{A}}_{\text{s}}}{{\text{A}}_{\text{0}}}=Bi\frac{{\text{A}}_{\text{s}}}{{\text{A}}_{\text{0}}}$$(10)

Fig. 11.

Schematic illustration of thermal conduction and thermal resistances.

Figure 12 shows the relationship between the air flow rate and Biot number in air jet cooling with the surface roughness of 3 μmRa. The Bio number increased with the air flow rate, implying that the resistance of thermal conductivity was larger than the resistance of heat transfer coefficient, meaning the thermal conductivity rate-limiting state. In this condition, the surface temperature of the cooled material becomes very close to the temperature of the cooling medium, and the temperature gradient directly under the surface becomes large, resulting in a condition where the region from which the heat is deducted becomes thin and the isothermal lines of the temperature distribution become parallel following the surface configuration. In this condition, a rougher surface leads to a larger real surface area with a more intense fin effect. Consequently, air jet cooling becomes more efficient.

Fig. 12.

Relationship between air flow rate and Biot number (Non-coating, Surface roughness 3 μmRa).

On the other hand, a small Biot number does not lead to the thermal conductivity rate-limiting state. In this case, it is expected that the region from which the heat is deducted becomes relatively thick, resulting in a lower effect of surface roughness on cooling efficiency.

Comparing Figs. 4 and 6, the effect of surface roughness on the base material was evidently different in air jet cooling and water spray cooling. In Fig. 13, the difference is exemplified for the conditions of a similar cooling rate during film boiling in water spray cooling and air jet cooling. In air jet cooling, the thermal history was not particularly different under the surface roughness conditions of 3 μmRa and 20 μmRa. The effect of surface roughness was noticed in the case of the large flow rate, as in Fig. 6. On the other hand, during film boiling in water spray cooling, the difference in the thermal histories was obvious. The cooling rate in film boiling with 20 μmRa was three times larger than that with 3 μmRa. In water spray cooling, the local heat transfer coefficient at which the droplet collides with and contacts the specimen surface is much larger than the values in Fig. 6, leading to an intense effect of the surface roughness of the base material on the cooling rate.

Fig. 13.

Effect of surface roughness on thermal histories (Spray cooling: 0.00667 m³/m²s, Air jet cooling: 6.17N m³/m²s).

4.3. Local Heat Flux when Spray Droplet Contacts Material Surface

As discussed in sections 4.1 and 4.2, the local cooling ability was noticeably high during film boiling in water spray cooling, leading to a more intense effect of scale thickness and surface roughness than those estimated by the calculation and measured in air jet cooling. Therefore, the local heat flux of a water spray droplet colliding with and contacting the specimen surface was estimated.

Many references regarding the behavior of droplets colliding with high temperature surfaces exist in the literature.^{14,15,16,17,18)} Hatta et al.¹⁵⁾ sprayed water droplets on the surface of heated alloy 625 and investigated their behavior, then showed that the droplets broke apart after the collision when the Weber number was more than 50. Negeed et al.¹⁸⁾ used SUS304 stainless steel specimens with various surface roughnesses from 0.04 μmRa to 10 μmRa, heated from 100°C to 600°C, on which single droplets with varying Weber numbers from 4.2 to 156 were sprayed. Based on observation of the droplet behavior by a high speed camera, they proposed an experimental equation in terms of the contact radius and time of the droplet.

In the experimental conditions shown in Table 3, in which the water temperature was 30°C, the mean droplet diameter was 330 μm and the mean droplet velocity was 10 m/s, the Weber number was calculated to be 460, implying that the droplet which collided on the specimen surface broke apart, making it difficult to evaluate local heat flux accurately. Therefore, the minimum heat flux q_min (W/m²) of a water spray droplet colliding with and contacting the specimen surface was estimated by Eq. (11).   

$$q_{min}=\frac{Q_d}{A_{max}\tau }$$(11)

Where, Q_d (J) is the cooling amount during droplet contact, A_max (m²) is the maximum contact area when the droplet and material are in contact and τ (s) is contact time. Here, the equations proposed by Negeed et al. were used for A_max and τ, since those equations were based on an experiment with SUS304 specimens with varying surface roughnesses and considered breakup of the droplets after collision.   

$$d_{max}=1.834d_0{Re}^{-0.130}W{e}^{0.318}$$(12)

  

$$A_{max}=\frac{\pi }{4}{d}_{max}{}^2$$(13)

  

$$\tau =7.121\left(\frac{d_0}{V_d}\right){Re}^{-0.262}{\text{We}}^{0.369}$$(14)

Where, d_max (m) is the maximum diameter during droplet contact, d₀ (m) is the droplet diameter before collision, Re is the Reynolds number, We is the Weber number and V_d (m/s) is the droplet collision speed. In the experimental conditions in Table 3, the maximum diameter during collision d_max is 1.5 mm, the maximum area of contact A_max is 1.7 mm² and contact time τ is 0.262 ms.

The amount of cooling by a single droplet Q_d was calculated using the efficiency of the evaporative heat of the total amount of sprayed water. The heat flux q_e (W/m²) necessary to evaporate all the sprayed water with water flow density W (m³/m²s) is given by Eq. (15).   

$$q_e=W{\rho }_{w}L+W{\rho }_w{C}_p\mathrm{\Delta }T$$(15)

Where, ρ_w (kg/m³) is the density of the cooling water, L (J/kg) is latent heat of vaporization, Cp (J/kgK) is the specific heat of the cooling water and ΔT (K) is the temperature difference between the cooling water and the saturation temperature. With the water flow density of 0.00667 m³/m²s, assuming that all the cooling water evaporates, the heat flux is 17 MW/m². Figure 14 shows the relationship between the surface temperature and the heat flux with the water flow density of 0.00667 m³/m²s and the surface roughness of 3 μmRa. At surface temperatures from 330°C to 550°C during film boiling, the mean heat flux was 0.32 MW/m². This corresponds to 1.9% of the heat flux needed to evaporate all the sprayed water.

Fig. 14.

Relationship between surface temperature and heat flux (Spray cooling 0.00667 m³/m²s, Non-coating, Surface roughness 3 μmRa).

On the other hand, the amount of heat Q_dmax (J) to evaporate a single droplet is:   

$$Q_{dmax}=\frac{4}{24}\pi d_0{}^3{\rho }_w\left(L+C_p\mathrm{\Delta }T\right)$$(16)

From this equation, Q_dmax of a single droplet with a diameter of 330 μm is 48 mJ. Assuming that the droplet contributes to cooling only by collision with the specimen and the cooling ability of the droplet after breakup is negligible, using the efficiency of the spray cooling experiment, the cooling amount of the single droplet Q_d is 0.92 mJ.

Assigning those values in Eq. (11), the minimum heat flux of the sprayed droplets colliding with and contacting the specimen is 2.1 MW/m². This value is 6.4 times larger than the average heat flux of 0.32 MW/m² during film boiling in Fig. 14, and is considered to be verified by the maximum heat flux of 1.6 MW/m² in Fig. 14, confirming that the specimen was cooled rapidly only when the droplets were in contact with the specimen.

In water spray cooling, from Eq. (5), the heat transfer coefficient was 5095 W/m²K at the surface temperature of 440°C. In air jet cooling, the heat transfer coefficient was about 1500 W/m²K with the air flow density of 6.17 Nm³/m²s, from which the effect of surface roughness appeared. The heat transfer coefficient of the spray droplets colliding with the material is 3.4 times larger than that in air jet cooling, implying that the effect of surface roughness on the heat transfer coefficient became more noticeable due to the large Biot number.

5. Conclusion

A spray cooling experiment and an air jet cooling experiment were conducted to investigate the effect of scale thickness and surface roughness, which are recognized as characteristics of the steel surface, on spray cooling characteristics. A SUS304 specimen with the thickness of 20 mm was used as the base material, on which an artificial surface scale layer of metallic oxide was formed by thermal spraying, or the surface was roughened by shot blasting. The conclusions obtained by comparing cooling characteristics are listed below.

(1) Both in water spray cooling and in air jet cooling, the artificial scale layer behaved as a thermal resistance layer. In air jet cooling, the heat transfer coefficient was almost constant at all surface temperatures. The cooling rate of the specimens decreased as the scale thickness increased. However, in water spray cooling, in which the heat transfer coefficient was dependent on the surface temperature, the cooling rate of the specimen during film boiling was almost constant regardless of the scale thickness or was slightly dependent on scale thickness. The quenching temperature at the interfacial temperature also increased with scale thickness.

(2) In the case of a large flow density in air jet cooling, the heat transfer coefficient increased with surface roughness. A similar tendency was observed with water spray cooling, but the rate of change in the heat transfer coefficient with surface roughness was larger.

(3) The estimated instantaneous heat flux of a single droplet during film boiling was 6.4 times the average heat flux. To clarify the spray cooling characteristics, it will be necessary to investigate the behavior of a single droplet and its cooling ability in detail.

References

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