2013 Volume 53 Issue 6 Pages 1042-1046
In the steel strip manufacturing process, a high temperature steel strip at a temperature of more than 800°C is rapidly cooled by circular impinging water jets. The cooling rate is an important parameter that characterizes the desired microstructure and mechanical properties of the steel strip. In the cooling process, the nozzle arrangement of the water jet system can be easily changed as necessary and heat transfer characteristics can be controlled by adjusting the nozzle arrangement. In this study, inline and staggered nozzle arrangements are adopted. By using the numerical method developed in a previous study, cooling behaviors such as the temperature distribution of the plate surface, the cooling history of the plate, and the average heat flux are determined and compared quantitatively for each nozzle arrangement.
In the metal processing industry, after hot rolling, the temperature of a steel plate reaches about 800 to 1000°C and is then rapidly cooled by water jets impinging on the moving steel plate. Very large heat transfer rates occur in the water jet impingement zone. Typically, a circular water jet system is used in the cooling process on the run out table (ROT) due to the system’s high cooling capacity. The cooling of hot-rolled steel involves a complicated heat transfer process with simultaneous complex physical phenomena. The cooling process involves the free surface motion of the residual water remaining on the plate and the forced convection heat transfer between the running plate and the cooling water. Moreover, because the temperature of the steel plate exceeds much higher than the saturation temperature of the cooling water, boiling heat transfer occurs.
The cooling rate is an important parameter for determining the desired microstructure and mechanical properties of the plate. Therefore, a number of studies have been conducted to obtain an accurate heat transfer rate and cooling history of the plate during the water jet cooling process. Wolf et al.1) examined a number of experimental works regarding the boiling heat transfer in a water jet and most of the experiments were carried out under a nucleate boiling condition. Ma et al.2) conducted experimental studies to characterize heat transfer with and without boiling. Liu and Wang3) studied theoretical and experimental heat transfer characteristics of film boiling at the stagnation zone by an impinging circular water jet. They concluded that transition boiling occurs for highly subcooled water jets and the onset of film boiling is strongly influenced by the degree of subcooling. By solving the inverse heat conduction problem (IHCP), Rodidou et al.4) and Xu et al.5) obtained the surface heat flux, surface temperature distribution, and boiling curve of a stationary hot plate for various operating parameters. These prior studies are important in understanding the boiling heat transfer process. However, in general, it is difficult to apply the results to practical situations in ROT due to the differences between laboratory experiment conditions and real situations. Thus, some researchers have conducted studies using real scale experiments.6,7,8,9) However, in the real scale experiments, the effects of a particular operating parameter such as water flow rate, plate running speed, initial plate temperature, and others on the cooling process could not be determined quantitatively because it is difficult to maintain uniform experimental conditions for every experiment. Also, testing costs are too high and obtaining experimental data in real time is restrictive due to the high speed and high temperature of the running plate.
Recently, Park10) developed a numerical method that handles the effects of the boiling heat transfer between the cooling water and the plate, the free surface motion of the residual water, and the running plate, simultaneously. In Park’s numerical method, it is assumed that the heat transfer between the plate and the cooling water occurs mainly in the film boiling mode due to the high temperature of the plate. Using Park’s method, the effects of the operating parameters can be analyzed quantitatively without the several uncertainties inherent in the experiments. Thus, temperature distributions, heat flux, vapor film thickness, and etc. can be easily obtained.
In the cooling process on the run out table, the nozzle arrangement of the water jet system can be easily changed as necessary and heat transfer characteristics can be controlled by adjusting the nozzle arrangement. In our study, based on previous numerical works,10,11,12) we conducted numerical simulations of the cooling process to investigate the effects of the nozzle arrangement on the cooling process. Inline and staggered nozzle arrangements were adopted in this study. For each nozzle arrangement, the temperature distribution of the plate surface, the cooling history of the plate, the average heat flux, and the thickness of the Leidenfrost steam layer were determined and compared quantitatively.
To simultaneously model the effects of boiling heat transfer between the plate and the water jets, the running plate, and the free surface motion of the residual water in our numerical analysis, Park’s numerical method10) was applied. In this paper, we introduce the basic idea of Park’s numerical method (see Ref. 10) for details).
After hot rolling, boiling heat transfer is expected between the plate surface and the cooling water. Depending on the range of the plate temperature, the boiling mode is divided into nucleate boiling, transition boiling, and film boiling. We focused on film boiling because of the high temperature of the plate surface, which is higher than the Leidenfrost temperature. A thin steam layer called the Leidenfrost steam layer occurs between the plate surface and the residual water due to the phase change of the cooling water and it is called Leidenfrost steam layer. The thickness of the steam layer is in the range of 10 to 100 μm, which was obtained by Nakanishi et al.13) and Liu et al.3) for the stagnation region. In terms of heat transfer, the steam layer plays a role in thermal resistance that obstructs the heat exchange between the plate and the cooling water. Park developed an effective thermal conductivity model to include the effect of the thermal resistance of the steam layer. This method is based on the continuity condition of heat flux in the first row of cells over the plate surface (see10) for details).
In the real situation, the plate is cooled by passing through the water jet zone with a velocity of 1 to 10 m/s. To consider the running motion of the steel plate, the moving reference frame method was used. The cooling water supplied continuously to the plate remains on the plate surface and forms a somewhat thick water level. Because this residual water plays an important role in the cooling process, the level of the residual water should be determined accurately. Therefore, in order to track the liquid-air interface (free surface), which is the interface between the residual water and the surrounding air, VOF (Volume Of Fluid) method was used in this study. The modified HRIC (High Resolution Interface Calculation) scheme was used to discretize convective terms of the VOF equation.
To calculate the flow and heat transfer, the mass, momentum, and energy conservation equations were adopted as governing equations for three-dimensional, unsteady, incompressible, turbulent flows. The standard k-ε model was used for turbulence modeling and all convective terms were discretized with a second order linear upwind scheme. During the calculation, the time step was fixed to 0.001 s from 0 to 4 s and a first order implicit scheme was used in the unsteady formulation.
Figure 1 represents the grid system for calculation domain. The length and width of the grid system is 1 m and 30 mm, respectively. The height of the system is 162.5 mm. The thickness of the steel plate in this calculation domain is 12.5 mm and the vertical distance of the nozzle exit to the plate surface is 150 mm. Because the nozzle was placed repeatedly in the width direction, to save calculation time, only one period in the width direction was adopted as a calculation domain. The diameter of the circular nozzles is 5 mm. Six nozzles were placed in the calculation domain, and the constant interval of the nozzles in the plate-running direction is 78 mm. The velocity of plate is 1 m/s and the initial entry temperature of plate is 850°C. The temperature of the water jet is 30°C and the jet velocity is 5.56 m/s. To compare the effect of the nozzle arrangement on cooling performance, inline and staggered arrangements were used as shown in Fig. 1(c). Except for the nozzle arrangement, the other conditions were the same in both nozzle arrangements. A total of 1300000 hexahedral cells were used in this calculation.
Computational domain in (a) isometric view, (b) side view, and (c) expanded top view.
In our numerical simulation, the effects of boiling heat transfer, free surface flow, and running plate were fully considered. The plate is cooled by passing it through the water jet impingement zone.
Figure 2 shows the shape of residual water stacked on the plate top surface after 4 s of cooling time for each nozzle arrangement. We note that the initially 850°C plate gets cooled down along the downstream. The thickness of the residual water affects the cooling performance because thick residual water obstructs the impingement of the water jets on the plate surface. The shape of the residual water is different in accordance with the nozzle arrangement. The thickness of the residual water is about 20 to 70 mm for both arrangements. The motion and shape of the residual water became steady after approximately 2.5 s. The high temperature plate is cooled by water jets and by residual water.
Shape of residual water layers for (a) inline arrangement and (b) staggered arrangement.
Figure 3 shows thickness distributions of the Leidenfrost steam layer above the plate. While the plate of initial temperature 850°C is cooled by cooling water, Leidenfrost steam layer is formed between the plate and cooling water. The thickness of the Leidenfrost steam layer was obtained by an iterative calculation for effective thermal conductivity within first-row cells on the plate surface. The shapes of the Leidenfrost steam layer correspond to each nozzle arrangement. In both arrangements, the minimum thickness and the maximum thickness of the Leidenfrost steam layer are similar. The minimum thickness of the Leidenfrost steam layer occurred under the nozzles due to the high impinging pressure (10000 to 16000 Pa) of water jet. The thickness of the Leidenfrost steam layer has a range roughly from 7 to 70 μm. This result is comparable to the experimental measurement of 8 ± 2 μm using a planar water jet at the stagnation point, as described by Bogdanic et al.14) and to Leidenfrost’s finding that the thickness of the steam layer is about from about 50 to 200 μm under the non-impinging condition.
Thickness distributions of Leidenfrost steam layer for (a) inline arrangement and (b) staggered arrangement.
The temperature distributions on the plate surface and on the plane 1 mm below the plate surface are shown in Fig. 4 for each nozzle arrangement. From the plate entrance region to the start of the impingement zone, the surface of the plate is cooled by residual water and the temperature is around 800°C. In the water jet impingement zone, the plate surface was cooled primarily by water jets. Distinctive cooling patterns corresponding to the nozzle arrangement are formed. The lowest temperature observed under the water jets is 260°C for the inline arrangement and 270°C for the staggered arrangement. For the inline arrangement, after the impinging water jet region, stripes caused by non-uniform temperature distributions in the width direction are observed on the plate surface and stripes of greater clarity are seen on the plane below 1mm. In the metal processing industry, many problems concerning non-uniform material properties have been reported. These non-uniform material properties may be resulted by non-uniform temperature distributions. We verify that the stripes are significantly reduced by the staggered arrangement. Therefore, for the better uniformity of the material properties, the staggered arrangement is more beneficial than the inline arrangement.
Temperature distributions on (a) plate surfaces and (b) planes 1 mm below plate surface for each nozzle arrangement.
The temperature profiles of plate surface along the plate-running direction are shown in Fig. 5. These data are obtained from the plate surface at the z = 0 mm plane, which is directly under the nozzles, and from the plate surface at the z = 15 mm plane, which is located in the center of the width direction. At the plate surface on the z = 0 mm plane, the temperature profiles are approximately consistent with each other. From x = 0 mm to the impingement zone, temperature decreases slowly. At the start of the impingement zone, the temperature decreases sharply. Then, the temperature greatly fluctuates until the end of the impingement zone. After the water jet impingement zone, the temperature is generally increased due to heat conduction from the inside of the plate. At the plate surface on the z = 15 mm plane, we confirm that temperature of the staggered arrangement is lower than that of the inline arrangement, and the temperature of the staggered arrangement fluctuates significantly at the water jet impingement zone. Temperature profiles 1 mm below the plate surface are shown in Fig. 6. Similarly to Fig. 5, the temperatures are captured from the z = 0 and 15 mm planes, respectively. The temperature profiles are almost same at a distance 1 mm under the plate surface on the z = 0 mm plane. The temperature of the staggered arrangement is lower than that of the inline arrangement at a distance 1 mm under the plate surface on the z = 15 mm plane. At a distance 1 mm under the plate surface, large temperature fluctuations are not observed for both z positions.
Temperature drop histories on plate surface for (a) z = 0 mm plane and (b) z = 15 mm plane.
Temperature drop histories on plane 1 mm under plate surface at (a) z = 0 mm plane and (b) z = 15 mm plane.
In Fig. 7, the temperature profiles in the thickness direction are shown with each nozzle arrangement at various positions in the plate-running direction. The results were obtained from the center plane of the plate in the width direction; i.e., at the z = 15 mm plane of the plate. At x = 0.1 m, because the plate is not affected directly by the water jets, the temperature profiles are almost the same. After x = 0.3 m, the temperature difference is noticeable, and the maximum difference in temperature is 65°C on the plate surface. After the water jet impingement zone, the temperature tends to recover near the surface, and which can be seen at x = 0.9 m. There are no temperature changes under 8 mm from the plate surface.
Temperature profile along thickness direction.
Figure 8 shows the surface heat flux distribution at the center of the width of the plate in the plate-running direction. At the impingement zone, the surface heat flux is locally high, and resulting in peak values. The number of peak points corresponds to the number of nozzles placed in the plate-running direction and twelve peaks were detected for the staggered arrangement. However, for the inline arrangement, because of the overlapped effect of nozzles placed on the same line in the plate-running direction, only six peaks were detected. The peak values are about 4 to 10 MW/m2 at the stagnation points where the water jets impinge on the plate surface. These data are in good agreement with results obtained by Xu et al.5) When one circular water jet impinges against a stationary hot steel plate, Xu et al. determined the heat fluxes on the plate surface using the IHCP (inverse heat conduction problem) method. The heat flux results are 4 to 12 MW/m2 near the stagnation point. The horizontal lines in the figure represent the total average surface heat flux. As can be seen from the figure, the staggered arrangement has a 7.7% higher total average heat flux than that of the inline arrangement. In other words, the cooling performance of the staggered arrangement is better than that of the inline arrangement.
Heat flux in plate-running direction.
We conducted a numerical analysis to examine the effects of a running plate, free surface motion, and boiling heat transfer simultaneously. To investigate the effects of the nozzle arrangement on the cooling process, an inline arrangement and staggered arrangement were adopted. We obtained various data from our numerical analysis such as the thickness of the Leidenfrost steam layer, temperature profile, and total average heat flux. Also we compared the cooling performances of each nozzle arrangement. After the water jets, non-uniform temperature distributions causing non-uniform material properties were observed in the inline arrangement, and were almost eliminated by the staggered arrangement. In the staggered arrangement, the total surface and interior of the plate were cooled more than with the inline arrangement. The staggered arrangement has a 7.7% greater cooling capacity. It is meaningful that we obtained a high cooling performance just by changing the nozzle arrangement and not changing other factors. In future work, the impinging water jet system could be rearranged to more diverse configurations with respect to the changes in the number of nozzles and the intervals between nozzles. Studies should be carried out to compare the cooling capacity of various nozzle arrangements and identify the optimal design for the cooling process.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (the Grant 2010-0024619).
