2013 Volume 53 Issue 12 Pages 2192-2196
We numerically analyze the cooling process of a steel plate in a run out table (ROT). As a preliminary attempt to obtain the best cooling capacity in a facility with limited space (i.e., the length of the ROT), the number of nozzles representing the quantity of supplied cooling water, and the spacing between the nozzles, are changed for several cases without changing other factors. Thus, the effects of the nozzle arrangement on cooling performance are investigated. Cooling histories of the plate, the heat flux on the plate’s surface, shapes of the residual water distribution, and cooling capacity are obtained for various cases.
After hot rolling, a steel plate (or strip) at a temperature of around 800 to 950°C enters a run out table (ROT) at a certain speed. Then the plate exits via ROT after being cooled through various cooling methods such as a curtain jet, spray, circular jet, and so on. Usually, spray cooling is used for roll cooling or descaling of the plate’s surface, and jet cooling is used for plate cooling since it can effectively transport its momentum to the plate’s surface. For better uniform cooling in the width direction of the steel plate, the curtain jet method is often applied. However the thickness of the curtain cannot be kept uniform in the width direction because of its inherent flow instability, and this can break the cooling uniformity in the width direction. The circular jet, because of its inherent non uniform water supply characteristics in the width direction, can lead to inhomogeneous mechanical or metallurgical properties of the product. However, this problem has been greatly reduced by rearrangement of the nozzle array pattern. Because the circular jet can provide more efficient cooling capacity per unit volume flow rate of the cooling water, it has been more widely used recently.
The cooling process in the ROT is nearly the last process in the entire steel-making process. The mechanical and metallurgical properties of the steel plate strongly depend on its cooling history. Thus, a thorough understanding of the heat transfer characteristics of the cooling process is needed to obtain the desired product quality. Because the temperature of the steel plate is much higher than the saturation temperature of the cooling water, boiling heat transfer occurs on the plate’s surface. According to the temperature range of the plate’s surface, three different boiling modes exist: nucleate boiling, transition boiling, and film boiling. Furthermore, the boiling mode in a specific area can temporally be changed according to the thermal condition on the plate’s surface. Heat transfer characteristics in each boiling mode have been studied extensively by many researchers.1,2,3,4) They conducted experiments on the laboratory scale or in relatively large pilot scale facilities that include impinging water jets on test specimens. Also, the thickness of the Leidenfrost steam layer in film boiling mode has been theoretically and experimentally predicted at the stagnation point.5,6,7)
In addition to the boiling modes, there are many important parameters affecting the heat transfer in a ROT cooling process; these include the finishing mill exit temperature, jet velocity, water temperature, flow rate, plate speed, metallurgical phase transformation, and cooling water supplying mechanism. Chen et al. investigated the effect of a moving plate on cooling performance and suggested the best arrangement of the cooling system for circular and planar jets.8,9) Jondhale conducted a pilot scale experiment to examine the effect of the nozzle-to-nozzle distance in the width direction, plate speed, and cooling water flow rate on heat transfer.10) Zhang et al. determined cooling performance with respect to the variation of the plate’s initial temperature, the ROT speed, the cooling water flow rate, and the header arrangement.11)
Recently, in related industrial fields, the cooling water supplying capacity of ROT facilities has continuously been increased to meet the need to develop novel products having much higher strength and smaller grain sizes. Most facilities constructed since the late 1990s have a cooling water supply capacity of over 20 kg/m2s of mass flux based on plate surface area. As the feed water flow rate increases, the residual water that remains on the plate’s surface forms a larger water level on the plate, and the convective flow sweeping the plate’s surfaces becomes stronger. It is known that the cooling performance of a system seems to be saturated by increasing the amount of supplied cooling water, and this phenomenon is verified in the previous study.12) Therefore, it is necessary to determine the appropriate quantity of supplied cooling water to maximize the cooling capacity in the limited space of a cooling facility.
We changed the spacing between the nozzles in the plate’s running direction and the quantity of cooling water (by changing the number of nozzles) to obtain the best cooling performance under the limited length of the ROT facility. This is a preliminary attempt to design a cooling system with optimal cooling performance. The cooling process was simulated by applying a numerical method suggested by Park.13) We obtained the shape of the residual water, the cooling history of the plate, the cooling efficiency, and the average heat flux for various cases. From our results, we determined the nozzle arrangement that shows the maximum cooling capacity among the cases.
We applied Park’s effective thermal conductivity model12) to simulate the boiling heat transfer between the moving hot plate and the cooling water. Because the temperature of the plate is much higher than the Leidenfrost temperature at which film boiling begins, we assumed that the heat transfer between the plate and the cooling water occurs only in the film boiling mode. When the Leidenfrost steam layer exists on the plate’s surface, it acts as a thermal resistance that obstructs the heat transfer between the plate’s surface and the cooling water. By considering the effect of the steam layer, the thermal conductivity in the first row of cells above the plate’s surface was replaced with the effective thermal conductivity. The thickness of the steam layer can be obtained by iterative calculations using Park’s model.12) In addition to boiling heat transfer, this numerical model can account for the effect of other important factors related to the ROT cooling process such as the steel strip’s run and the free surface motion of the residual water.
The numerical model makes it possible to investigate the ROT cooling process under conditions that are similar to real industry situations. From the numerical analysis results, the exclusive effect of a certain factor (plate running speed, nozzle arrangement, etc.) can be analyzed without varying the other factors. This is almost impossible to achieve in experiments due to the inherent uncertainties in the experimental method. We can obtain useful data related to the cooling process such as the shape of the residual water, average temperature of the plate, average heat flux, and cooling efficiency using the present numerical simulation. The validity of the numerical model was verified in a previous study by comparing the numerical results with experimental results from other researchers.14)
The phase transformation of the steel plate is another crucial factor that affects the cooling process and the quality of products. However, since we focused on the heat transfer between the plate’s surface and the cooling water, phase transformation and the corresponding heat generation were neglected in the present numerical study.
Figure 1 indicates the typical grid system used in this numerical analysis as a calculation domain. Six nozzles were placed in the plate running direction, and the grid was stretched around the nozzles as shown in the figure. In our numerical analysis, the interval between the nozzles was constant in the plate running direction. The sizes of the interval were set to 110, 170, 230, 290, 350, 410, and 470 mm in each case. Except for the nozzle intervals, all other operating conditions were set to be the same in every case. Because the nozzle was placed repeatedly in the width direction, symmetry conditions were set on the side of the grid system as shown in Fig. 1(b). Thus, only one period in the width direction was adopted as a calculation domain. The length and width of the grid system are 3 m and 30 mm, respectively. The distance between the nozzles and the plate’s surface is 300 mm. The cooling water is injected from the nozzle exit at a rate of 5.56 m/s.
Computational domain in (a) isometric view and (b) expanded top view.
Since the lower side jet (upward jet) is in the direction opposite to that of gravity, the cooling rates of the upper and lower side jets are different. Only one half of the plate’s thickness, including the top side, was selected as the computational domain by assuming that the cooling effects on both sides are equal. The thickness of the steel plate is 12.5 mm, running at a speed of 1 m/s. The thermal properties of the steel plate were assumed to be constant. The incoming temperature of the plate was set to 850°C.
In our numerical simulation, the effects of boiling heat transfer, free surface flow, and the running plate were fully considered. Figure 2 shows the shape of the residual water for the various nozzle interval cases when the flow reached nearly steady state. The injected cooling water cools the running hot steel plate, and then flows upstream and downstream on the plate. The plate is initially at 850°C and is cooled along the plate’s running direction. At 12 s, the shape and motion of the residual water become nearly steady. Regardless of the nozzle interval, the levels of residual water are very similar in all cases, as shown in Fig. 2. Thus, we can estimate that the impinging pressure values on the plate’s surface also have similar values for all of the cases. The color in Fig. 2 represents temperature. The lowest temperature of the plate increases as the interval increases. In the cases of 110 mm and 470 mm, the lowest temperatures of the plate’s surface are 280 and 350°C, respectively.
Shape of residual water layers for various nozzle intervals.
The temperature histories at 1 mm and 5 mm below the plate’s surface are shown in Fig. 3. These data were obtained from the z=0 mm plane, which is directly under the nozzles. From x=0 to x=0.3 m, the plate is cooled only by residual water; thus, the temperature decreases slowly. The water jet cooling begins after x=0.3 m and we note that the temperature starts to decrease sharply, as shown in Fig. 3(a). In the case of 110 mm, because the interval of the nozzles is very short, the plate temperature on the –1 mm plane falls sharply to the lowest temperature in the jet-cooling zone. For other cases, because the plate undergoes cooling and heat retrieval repeatedly, the temperature on the –1 mm plane greatly fluctuates until the end of the jet-cooling zone. After the jet-cooling zone, the plate is cooled only by residual water again. However, because the heat retrieval effect exceeds the cooling effect due to the residual water, the temperatures at the –1 mm plane are recovered in all cases. At a location 5 mm below the plate’s surface, the temperatures decrease only slightly until x=0.3 m, where the jet-cooling zone starts. Also, after x=0.3 m, the temperatures do not fluctuate and decrease continuously.
Temperature drop histories on (a) a plane 1 mm under the plate’s surface and (b) a plane 5 mm under the plate’s surface at the z=0 mm plane for various nozzle intervals.
In Fig. 4, the variations of the average temperatures of the plate are plotted along the plate’s running direction for various nozzle intervals. The average temperatures at each x positions are calculated in the plate’s cross section areas normal to the plate running direction. We can note that initial average temperature of 850°C decreases continuously. However, their decreasing rates are certainly different in the jet-cooling regions and the residual water-cooling regions. In the case of 110 mm, because the nozzles are positioned very closely, the average temperature of the plate decreases at the greatest rate in the narrow jet-cooling zone. After jet cooling, the decreasing rate of the average temperature decreases significantly. In the case of 470 mm, because of the long interval of the nozzle, strong and mild cooling appears repeatedly and the lowest average exit temperature is achieved. The difference in the average exit temperature between the 110 and 470 mm cases is about 13°C. We note that the cooling capacity can be severely superposed by clustering the cooling water supplying nozzle, such as in the 110 mm case.
Average temperature of the y-z plane of the plate for various nozzle intervals.
The average heat flux on the plate’s surface is shown in Fig. 5 with respect to the various nozzle intervals. In previous research,14) when the interval between the nozzles was increased or decreased according to certain ratios in the plate running direction, we confirmed that the average heat flux was nearly a maximum value in the case of a constant nozzle interval. To determine the optimal size of the constant nozzle interval, the interval was increased by 60 mm from 110 to 470 mm in this study. As the nozzle interval increases, the average heat flux also increases almost linearly. In the case of 470 mm, the average heat flux is 19.8% greater than that of the 110 mm case. This is because the heat inside the plate is sufficiently released toward the plate’s surface when the nozzle interval is long enough. That is, even if there is a sufficiently long nozzle interval in the plate’s running direction, the temperature near the plate’s surface continues to recover until it meets the next water jet.
Average heat flux on the plate’s surface for various nozzle intervals.
Initially, the number of nozzles in the plate’s running direction was set to six for all cases. Then, the number of nozzles was increased to be inversely proportional to the nozzle interval. For nozzle intervals of 110 and 470 mm, 25 and 6 nozzles, respectively were adopted over the whole ROT domain of 3 m. All other operating conditions were the same as before. The simulation results for the residual water shape are shown in Fig. 6. Because the water flow rate increases in proportion to the number of nozzles, we found that the level of residual water also increases with the number of nozzles. Such a high water level and strong flow of residual water can disturb the impact of the water jets on the plate’s surface. As we estimated from Fig. 6, the impinging pressure on the plate’s surface became lower as the number of nozzles increases, and the amount of supplied cooling water increases. This phenomenon affects the cooling performance.
Shape of residual water layers for various numbers of nozzles.
In Fig. 7, the variations of average temperatures of the plate in the y-z plane are plotted along the plate’s running direction for various numbers of nozzles. When the number of nozzles is increased from 6 to 12, the average temperature of about 30°C decreases. However, there is no significant decrease in the average temperature between the cases of 12 and 25 nozzles. The case of 12 nozzles shows a higher cooling rate rather than the case of 25 nozzles near the entrance region, where x is less than 1.5 m. This means that to supply more cooling water by increasing the number of nozzles has a limitation in terms of enhancing the cooling capacity. It can be analyzed that the thick residual water layer and the strong counter-flow of the residual water hinder the effective impingement of the water jets on the plate’s surface, as shown in Fig. 6.
Average temperature of the y-z plane of the plate for various numbers of nozzles.
Figure 8 shows the average heat flux of the plate’s surface and the cooling efficiency of the system. Here, the cooling efficiency is defined as the heat removal from the plate’s surface per unit mass of supplied cooling water. As shown in Fig. 8, the cooling efficiency monotonically decreases as the number of nozzles increases; i.e., a smaller amount of supplied cooling water produces higher cooling efficiency. This is the same conclusion given by Zhang et al.11)
Average heat flux on the plate’s surface and cooling efficiency for various numbers of nozzles.
The average heat flux does not increase monotonically by increasing the number of nozzles, and is maximized in the case of 16 nozzles. Although the cooling water flow rate in the case of 25 nozzles is the largest, its average heat flux is lower for 12, 16, and 20 nozzles. Therefore, to design a system with optimal cooling capacity in the limited space of the facility (3 m in the plate running direction in this study), simply increasing the quantity of cooling water is not a good idea, and full consideration of the heat transfer between the running plate and the cooling water, including the hydrodynamic behavior of the residual water, must be made.
For a ROT after hot rolling, the cooling process of the steel strip using circular water jets was numerically analyzed by applying Park’s numerical model.12) As a preliminary attempt to design the cooling system with optimal cooling performance in the limited space of the facility, the number of nozzles and the spacing between the nozzles were changed for several cases without changing other operating conditions.
First, the effect of the nozzle interval was tested. The six nozzles were placed with different nozzle intervals in the plate running direction, and the same amount of cooling water was supplied for all cases. The case with the nozzles evenly placed over the whole length of the facility showed the best cooling capacity, since the case had enough time and space for the interior heat to be exposed to the outside of the plate. Thus, the cooling capacity of the supplied water could be used effectively.
Next, to achieve the best cooling capacity in a limited length of ROT, we examined cases in which the nozzles were evenly placed in the whole ROT domain, and the number of nozzles was varied from 6 to 25. The cooling capacity was maximized at a specific number of nozzles (i.e., a specific amount of supplied water). We found that the cooling capacity in a given spacing was closely related to the hydrodynamic behavior of the residual water.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (the Grant 2013059593).
