Impingement Density Analysis on Heat Transfer and the Appearance of Edge Cracks in Conventional Slab Using Hydraulic Nozzles

Abstract

In this work, the fluid dynamics and heat transfer of two hydraulic nozzles used in the secondary cooling of the conventional slab continuous casting machine were analyzed. Impingement density maps, the jet opening angle and heat flux associated with different operating conditions (impingement distance, pressure) were experimentally determined. The opening angle and impingement density footprint were found to vary considerably in shape and magnitude with varying operating pressure and distances. Finally, it was found that when short operating distances are used, a greater heat extraction gradient occurs in the major axis of the impingement footprint, which promotes edge-cracks in the slab in plant.

1. Introduction

Hydraulic and pneumatic nozzle cooling is widely used in the secondary cooling of continuous casting as it provides a good balance in terms of its ability to remove high heat fluxes, efficiently uses liquid and obtains good uniformity in the temperature of the solidified product. Therefore, several researchers have studied parameters such as impingement density, w [1,2,3,4,5,6], speed and droplet size [2,4,5,6,7], distance between the nozzle and the part to be cooled [3,8], roughness [2,9] and the spray angle [10], among others, since these modify the way in which the nozzles extract heat, furthermore Kominek et al. [11] found that the choice of nozzles and their overlaps has a significant influence on cooling homogeneity. However, poor heat extraction can cause the appearance of defects such as internal or surface cracks that influence the quality of the solidified products [12,13]. Due to this, some studies related to the estimation of the heat transfer coefficient and heat flux have been carried out, using experimental and numerical models [14,15], in order to improve the efficiency in the cooling of metal parts [7,13,16]. Some authors have carried out experiments with direct plant data to better reproduce the phenomenon, by modifying the variables to improve cooling [12,17]. Kortbacek et al. [18] investigated the intensity of the cooling, the HTC and the impact pressure distribution by spraying using different nozzles. They found that the combination of both parameters provides a good quality correlation function. In the same way, Ito et al. [19] investigated the effect of hydraulic pressure and the flow of water from sprays produced by hydraulic nozzle on the cooling intensity through laboratory experiments and plant tests. They found that by increasing the water pressure, the average heat transfer coefficient reaches 2.8 times higher when using the same impingement density (16 m³·h⁻¹·m⁻²), and with this, the casting speed is increased by 30% without internal or superficial cracks. Arth et al. [13] mention that the casting speed is dependent on the impingement density. Many researchers agree that impingement density is the parameter that has the most influence on the cooling stage [4,20,21,22,23,24] and therefore, should be taken into consideration when designing the secondary cooling nozzle arrangement. For this reason, the main aim of this research is to analyze the impingement maps produced by two hydraulic nozzles and to quantify the heat extraction in the stainless-steel plate varying the operating conditions. In addition, we aim to elucidate the causes of edge-cracks in the slabs, according to the current operating conditions in the plant.

2. Materials and Methods

2.1. Determination of the Impingement Density

In Figure 1a the experimental setup arrangement employed to determinate the impingement density (volumetric flow of water collected per unit area) is shown. To obtain the high-water pressures required in the industry, a 6.5 HP pump was used with a working pressure range of 2.1–4.5 MPa (SHI-030-B, Shiraiwa Japan Force). The water flow and pressure were measured using a flowmeter (LZT M-15, Hong Kong, China) and a manometer with a maximum pressure of 2 MPa (Instrutek, Guadalajara, Mexico), respectively. A globe valve was used to regulate the operating conditions. The water jet was produced by means of two LECHLER hydraulic nozzles (Metzingen, Germany) used in the conventional slab continuous casting machine. To control the operating distances and heights between the hydraulic nozzle and the manifold, a three-dimensional clamping and sliding system was built. The calibration and alignment of the experimental system is very important, since it depends on this that the results of the tests carried out are reproducible. For this step, a collecting grid such as the one shown in Figure 1b was used, which consists of 153 collecting tubes arranged in 9 rows, by 17 columns. The arrangement of the water collector allows for the footprint of the nozzles studied to be covered entirely. The local water impingement density was assessed by measuring the mass of water, m in kg, collected over a prescribed period of time, t in s, in bottles connected to tubes with a cross-section area, a in m², placed at positions x–y–z_s, according to the following expression,

$$w=\frac{m}{t·a·\cos \theta }$$

(1)

where (cos θ) is the direction cosine of the angle formed between the nozzle axis and the line connecting the center of the nozzle orifice with the center of the entrance of a given collecting tube, and was introduced to consider the projected area of the collecting tubes perpendicular to the direction of motion of the drops [23]. The diameters of the collecting tubes and their separations are provided in Figure 1b.

Table 1. Experimental conditions for impingement density.

Nozzle	α (°)	zs (m)	Pressure (kPa)	Water Flow (L·s−1)
Lechler 632.604	60	0.137, 0.250	137.9	0.038
			301.6	0.058
			517.1	0.08
			999.7	0.116
Lechler 632.644	60	0.150, 0.250	137.9	0.046
			301.6	0.071
			517.1	0.1
			999.7	0.133

shows the operating distances, nozzle angle and working conditions for each of the nozzles analyzed.

2.2. Characterization of the Water Jet

Figure 1c shows the experimental scheme used to measure the angle of expansion of the water jet. The procedure consisted of preparing a supersaturated solution of 50-micron polyamide particles after which they were seeded into the water reservoir; subsequently, the flow and pressure conditions were established based on the desired experimental conditions and the jet was released into the container. Next, the laser was turned on and the plane generated by the optical lens was aligned in such a way that it falls on the water jet to illuminate the particles that will be engraved. Finally, image processing using commercial Matlab^® software. The laser used was a (Dantec Systems^®, Skovlunde, Denmark) Nd: YFL dual power 30–1000 with a maximum pulse of 2 × 30 mJ and 20 kHz. The output power of the laser is 150 W and a wavelength of 527 nm. A Speed Sense Phantom Miro M310 camera, which uses a Planar 1.4/50 mm ZF lenses (Dantec Systems^®, Skovlunde, Denmark).

2.3. Heat Transfer Measurements

Figure 1d shows the experimental system used to determine local heat fluxes. A stainless steel 304-L plate, for which the thermophysical properties are shown on

Table 2. Thermophysical properties of 304 L stainless steel [28].

T (°C)	K (W·m−1·K−1)	ρ·Cp (106 J·m−3·K−1)
50	15.9	4.0
250	17.6	4.27
500	21.8	4.70
550	23.02	4.88
750	26.4	4.82
800	26.8	4.87
850	26.4	4.86
900	26.8	4.83

, was employed. The procedure consisted of heating a rectangular plate of 0.25 × 0.1 m and a thickness of 0.013 m inside a muffle, (LINDBERG, Industrias SOLA SA de CV, Iztapalapa, Mexico) which reached a maximum temperature of 1373 K with a power of 3500 W and 220 V at 60 Hz. The metal plate was equipped with a thermocouples type “K” tip which was exposed inside the material. The thermocouples were placed in positions of known impingement density in order to determine the fluxes. These were introduced at a distance close to the cooling surface of ~0.0015 m and connected to the cooling system data acquisition from FLUKE^® NetDAQ 2645A (Everett, Washington, DC, USA) to record thermal evolution (1330–300 K). Once the homogeneous temperature of the steel plate was reached, the dew system was initialized with the desired cooling conditions and the hot steel plate was removed from the muffle and placed in front of the water jet. Thermal evolution was recorded with a sampling frequency of 20 data per second on a computer for later analysis. The heat fluxes -q were calculated by the inverse method of heat conduction in 1-D. In order to perform the calculation, the sample was subdivided into two regions of 1.5 mm (5 nodes) and 12.7 mm (15 nodes), respectively. The calculation time interval used, Δt, was 0.1 s for three future time steps (r = 3). The details of this method have already been described previously [25,26,27,28].

3. Results and Discussion

3.1. Reproducibility

The procedure for measuring the impingement density, w, requires strict control, given the degree of freedom, which could lead to highly variable results. The alignment of the collector with respect to the vertical is a fundamental variable that has to be controlled. Another major challenge is aligning the center of the nozzle with the center of the tube, due to the narrow hole at the outlet of the hydraulic nozzle. The alignment of the nozzle with the horizontal also plays an essential role for the reproducibility of the w patterns. Figure 2 shows the contours of three footprints of w, for the 632.604 nozzle using a water pressure and flow of 137.9 kPa and 0.038 L·s⁻¹, respectively, at an operating distance, z_s, of 0.25 m. It can be seen that the three footprints are very similar in size, shape and magnitude of w, obtaining a width of ~0.24 m on the x- axis, and a thickness of ~0.08 m on the y- axis for a contour with a minimum value of 2 kg·m⁻²·s⁻¹. Furthermore, the impingement density is concentrated in the center of the footprint, reaching a maximum of 12 kg·m⁻²·s⁻¹. From this analysis, it is evident that a great reproducibility was obtained in the measurement of impingement density with the proposed experimental system.

3.2. Effect of the Operating Distance on w

In Figure 3a–d, the contours of the impingement footprints obtained for two operating distances z = 0.137 m and z = 0.25 m using the same operating conditions for the 632.604 nozzle are shown. This nozzle is used in the lower part of the secondary cooling of the continuous casting machine. As can be seen in Figure 3a, for a distance of 0.137 m which is used in the industry, the impingement footprint is small and uniform concentrating the values of w in the central zone, reaching values of up to ~85 kg·m⁻²·s⁻¹. On the other hand, in Figure 3b for a separation distance of 0.25 m recommended by the manufacturer, the impingement footprint was larger on the x- axis, keeping its dimensions on the y- axis and the maximum values of w were ~20 kg·m⁻²·s⁻¹. In Figure 3c,d, the impingement maps of the nozzle 632.644 are shown using two operating distances (z = 0.15 mm and z = 0.25 m), this nozzle is used in the upper part of the secondary cooling of the continuous casting machine. A behavior similar to that presented in Figure 3a,b is shown, where it is clearly visible that for a greater operating distance (Figure 3d), the footprint area is greater, and its impingement densities decrease by ~75%. As can be seen in Figure 3c, uniform water patterns are obtained with w values of up to ~65 kg·m⁻²·s⁻¹ in the central zone. In the case of the distance z = 0.25 m in Figure 3d, the impingement footprint registered values of w of up to ~25 kg·m⁻²·s⁻¹. By applying different distances z, the fluid dynamics are modified, changing the shape and size of the footprint, as well as the impingement density w of the sprays, which is found to have a considerable effect on the extraction of heat fluxes [4,13,20,21,22,23].

To validate each of the impingement density maps, the area under the curve was integrated to estimate the volumetric flow. The procedure consisted of discretizing the footprints into small elements to reduce the error; subsequently, using an algorithm written in FORTRAN^®, the impingement density of each of the elements was numerically integrated and multiplied by its corresponding area. With the previous procedure, the water flow, W_c, was calculated and this value was compared with the measured flow W during each test and only those experiments where the error was less than 10% were taken into account. Figure 4 shows a projection of the distribution of the impingement density maps on the middle of the wide face of the continuous casting slab using different pressures and working distances for the nozzle 632.644. Figure 4a,c correspond to a working distance z = 0.15 m, which is the one used in industry. It clear that for distances close to the hot surface, the volume of water is located in very small areas, leaving certain areas without water contact (gray zone). On the other hand, it can be seen in Figure 4b,d that they are at a distance of 0.25 m, and the wetted surface area grows in the vertical direction. It is also observed that as the nozzle moves further away from the slab, the magnitude of the impingement densities decreases across the entire footprint, but in turn increases in the horizontal direction. This elongation causes a greater overlap of the impingement densities, obtaining areas where the volume of water impingement increases by the effect of the sum of the w [29] of the adjacent jets, as observed in Figure 4a′–d′. However, it is important to note that on the y-axis there is a distance of approximately 0.02 m wherein the greatest volume of water is collected. Beyond this distance, there is a large zone with values of w less than 10 kg·m⁻²·s⁻¹ which affects low heat fluxes, similar to the gray zone.

3.3. Effect of Pressure on the Size, Shape and Angle of the Footprint

In Figure 5a, the impingement maps of the 632.604 nozzle are shown at an operating distance z = 0.137 m using a water pressure range from 137.9 at 999.7 kPa and a water flow from 0.038 to 0.11 L·s⁻¹. As can be seen, by varying the pressures in the w maps, a significant change in the amplitude of the footprint was obtained, as well as a different distribution of the magnitude of density impingement w. This change in magnitude has a considerable effect on the way each of the footprints extracts heat from the hot surface, because the wetted area changes and the concentration regions of the volumetric flow of water change. In Figure 5a, it can be seen that for the lowest operating pressure (137.9 kPa) the impingement footprint has a smaller size and the distribution of the values of w were symmetric, concentrating in the central part of the footprint reaching values of up to 50 kg·m⁻²·s⁻¹. However, for a water pressure of 301.6 kPa, which is currently used in the plant, the impingement footprint had a slight increase in shape and length compared to the previous test, with a redistribution of the values of w, reaching values of up to 60 kg·m⁻²·s⁻¹ on the left side of the footprint while on the right side the maximum values were 40 kg·m⁻²·s⁻¹. On the other hand, the impingement map for a water pressure of 517.1 kPa shows a growth in the water standards on the -x axis, with maximum values of w up to 110 kg·m⁻²·s⁻¹ were slightly concentrated on the left side. Finally, with a water pressure of 999.7 kPa the footprint experienced a notable increase in size compared to previous cases with maximum impingement density values of up to 150 kg·m⁻²·s⁻¹ concentrated in the central part of the footprint. In Figure 5b, the w maps of the 632.644 nozzle with an operating distance z_s = 0.15 m which currently used in the plant in a range of water pressure from 137.9 to 999.7 kPa are shown. As can be seen in this figure for a water pressure of 137.9 kPa the area of the impingement footprint is smaller with respect to higher pressures, obtaining the maximum values (∼40 kg·m⁻²·s⁻¹) at ±0.025 m with respect to the center of the footprint. For a pressure of 301.6 kPa used in the industry, the values of w were increased compared to the previous pressures, reaching values of up to 60 kg·m⁻²·s⁻¹ which was lightly loaded to the left of the center of the footprint. For the pressure of 517.1 kPa the impingement footprint behaved very similar to the pressure of 301.6 kPa; however, its maximum values of w were 100 kg·m⁻²·s⁻¹. For the last case, with a conventional water pressure of 999.7 kPa, the flat fan-shaped impingement footprint tend to be larger, and the sprays were more uniform than in all the previous tests for this nozzle, with impingement density values w up to 180 kg·m⁻²·s⁻¹. From Figure 5, it is evident that the impingement footprint increases its amplitude mainly along the axis of symmetry x; contrasting with the fact that when the water pressure increased it did not show a change in the size of the impingement density maps [30]. The fluid-dynamic characterization of these nozzles is of great importance for the knowledge of the operators of the continuous casting machines, since by taking into account the form that the impingement footprint of the water sprays takes with each hydraulic pressure, a methodology can be proposed in controlling the water flow rate and establishing the best cooling conditions for the continuous casting machine.

Figure 6 shows the shape of the water jet for each nozzle at different pressures and flows. A treatment of images in gray scale was performed to measure the size of the opening angle, and we observed that a nozzle angle of 60° was reached only from pressures higher than 517.1 kPa. These findings indicate that at low pressures (137.9 and 301.6 kPa) the nozzle design does not meet the homogeneous cooling requirements. On the other hand, it is observed that at a pressure of 137.9 kPa no dispersion of drops at the outlet of the nozzle occurs, giving rise to the formation of a water curtain, which decreases as the pressure increases due to breakage and droplet separation. In general, oscillating impingement footprints are observed as the fluid pressure increases and this promotes an asymmetric footprint as observed in the impingement density maps.

3.4. Determination of Heat Fluxes

Figure 7 shows the local heat fluxes associated with the impingement density using two different operating conditions for the 632.644 nozzle. In Figure 7a, the heat fluxes are shown to be plotted for two local impingement densities at an operating distance of 0.15 m and a water pressure, P_w, of 137.9 kPa, while Figure 7b shown the density maps of impingement for these heat extraction conditions. The center point of the footprint registered a w of 15 kg·m⁻²·s⁻¹ and the calculated heat flux reached a maximum of ~1.17 MW·m⁻². While for a w of 7 kg·m⁻²·s⁻¹ in the area where there is a low volume of water, and the maximum heat flux was ~0.6 MW·m⁻². With this operating distance, it is shown that at a distance in the longitudinal direction of the footprint of approximately 0.06 m, there are high heat transfer gradients. Under these conditions of experimentation, that is, at a transient state and high impingement densities, the Leidenfrost point is difficult to determine due to the high heat transfer, unlike in the steady state, where the different regimes of the boiling curve can be easily identified. The last originates an uncontrolled cooling and generates defects in the slabs as internal stress which can produce edge-cracks as corroborated by the plant with edge-cracks. This was observed in the poor cooling zones on the surface of the slabs as indicated in Figure 7c. These findings have been previously mentioned by Sengupta et al. [31]. In Figure 7d,e the heat fluxes and impingement densities are shown, respectively, for an operating distance of 0.25 m and a P_w = 301.6 kPa. For this operating condition, the heat flux gradient is reduced to ~0.42 MW·m⁻². The above indicates that for the same separation distance of measurement, there is a better distribution of heat fluxes, which contributes to a greater homogeneity of heat extraction in the longitudinal direction.

To validate the measured heat fluxes, Equation (2) for one-dimensional heat diffusion in transient state [32] was solved by numerical simulation to obtain the solution of the direct heat conduction problem.

$$\frac{\partial }{\partial z}\left(k \frac{\partial T}{\partial z}\right)=\rho ·C_p\frac{\partial T}{\partial t}$$

(2)

With the solution of the inverse heat conduction problem, the heat transfer coefficient and the surface temperature were obtained as response variables. Subsequently, the heat transfer coefficient was plotted as a function of time and a trend line was fitted. The function of this trend (Equation (3)) was introduced as a user-defined function in a numerical model performed using ANSYS FLUENT^® (v15.0, ANSYS Inc., Canonsburg, PA, USA) to calculate the measurement temperature at the same location of thermocouple in the experiment, as shown in Figure 8.

$$\begin{array}{cc}\hfill h=& 1\times {10}^{-9}\left(t^9\right)-1.3\times {10}^{-7}\left(t^8\right)+6.5\times {10}^{-6}\left(t^7\right)-9.1\times {10}^{-5}\left(t^6\right)\hfill \\ & -2.3\times {10}^{-3}\left(t^5\right)+0.1\left(t^4\right)-1.3\left(t^3\right)+5.9\left(t^2\right)+13.1\left(t\right)+51.7\hfill \end{array}$$

(3)

Figure 8 shows the comparison of the measured temperature by the thermocouple and the temperature calculated on a monitor located in the same position of that obtained experimentally by the inverse heat conduction problem. A good agreement between both temperature measurements is observed. The last example indicates that the heat coefficients measured by the inverse heat conduction problem satisfactorily represents the heat fluxes measured by means of the hydraulic nozzles.

4. Conclusions

In this study, water sprays—produced by hydraulic nozzles employed in the secondary cooling of conventional slab steel—were analyzed and the following was concluded:

• By varying the operating pressure in both nozzles, large differences were obtained in the size and shape of the impingement footprint and its local values of w.
• The opening angle is directly related to the working pressure of the nozzles, which is to say, at pressures of lower than 517.1 kPa, the water jet does not lead to the angles provided in the nozzle specifications. Furthermore, we observed that the drops are sprayed at distances very close to the tip of the nozzle when the pressure is increased. This helps the droplets to arrive with sufficient momentum to impinge the collector at distances of less than 0.15 m.
• The impingement density footprint is not only affected in its shape and size, but also in the magnitude when varying the operating distance, z_s, and maintaining the same cooling conditions. This provides valuable information for the continuous casting machine operator to better control the secondary cooling process.
• When a shorter operating distance is employed, z_s, there is a greater gradient in heat removal along the longitudinal direction, which is reduced by a third when the operating distance is increased. Likewise, the overlapping of the jets improves the cooling profile in the longitudinal axis; however, current plant conditions (short distances) lead to poor cooling at the slab edges, promoting edge-cracks. In future, to simulate a more realistic cooling process in the different segments of the secondary cooling of the continuous casting of steel the authors will develop a numerical simulation with a dynamic mesh technique, employing the calculated heat transfer coefficients by these nozzles and the actual slab casting velocity.