Flow Oscillations and Meniscus Fluctuations in a Funnel-Type Water Mold Model
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Transient flows in a funnel-type continuous casting process model were studied experimentally to investigate the flow oscillations inside the mold and the meniscus fluctuations. A full-scale water model was used with dimensions of 2000 mm (length) × 1350 mm (width) × 100 mm (thickness). Particle image velocimetry (PIV) was employed to measure the flow oscillations. To minimize high shear flow errors near the submerged entry nozzle (SEN) exit, the window deformation technique was adopted. The meniscus levels were extracted by edge-detection image processing. Three types of SEN and two funnel thicknesses (180 mm and 220 mm) were tested to examine the flow characteristics under five flow rates (10, 20, 30, 40, and 50 m3/h). The vortex generation mechanism inside the mold was analyzed across the various mold conditions studied.
KeywordsParticle Image Velocimetry Particle Image Velocimetry Measurement Vortex Generation Flow Oscillation Submerged Entry Nozzle
Mold width (mm)
Mold thickness (mm)
Mold length (mm)
Inner diameter at the entrance of the SEN (mm)
Mean velocity at the entrance of the SEN (m/s)
Maximum extraction speed (m/sec)
Normalized extraction speed (m/sec)
Time interval between successive laser exposures (ms)
Size of interrogation window (pixel)
- (x, y)
Cartesian coordinate of the recorded image (pixel)
- (x0, y0)
Center location of the first interrogation window (pixel)
- f1 (x, y)
First intensity field of a PIV image pair
- f2 (x, y)
Second intensity field of a PIV image pair
Natural wave frequency (Hz)
Velocity magnitude in x-direction (m/sec)
Velocity magnitude in y-direction (m/sec)
During the last 30 years, many studies have examined continuous casting processes based on a near-net-shape casting concept with the aim of reducing costs and improving productivity. Recently, thin slab casting has been used widely because of its high casting extraction speed and rolling efficiency. In such processes, however, the submerged entry nozzle (SEN) that supplies molten steel to the mold cannot be smaller than a certain size because of the high extraction speed. To overcome this limitation, the upper center region of the mold should be widened to form a funnel shape. However, this modification can cause unstable flow features at high flow rates, which include flow oscillations inside the mold and meniscus fluctuations. These unstable features can have a significant negative impact on the final product quality. To reduce such flow oscillations, water-model analysis can be used to identify an optimal SEN design. Previous attempts to achieve flow stabilization have devoted considerable attention to modeling the inner flow and the meniscus quantitatively.
In general, the flow in a continuous casting process has self-sustaining oscillations. These flow oscillations have been investigated through many numerical simulations and experimental measurements. Honeyands and Herbertson used both a commercial simulation tool and a water model to examine such oscillations. They showed that the observed variations in the meniscus are related closely to self-sustained oscillations of the jets exiting from the SEN. Subsequently, Gebert et al. predicted the relation between the inner flow oscillations and the meniscus fluctuations using a two-dimensional numerical model. However, they did not compare their findings with experimental data. In terms of experimental studies, Gupta and Lahiri measured transient asymmetric flows in a water model and provided qualitative information on self-sustained flow oscillations in the mold. Lawson and Davidson observed the flow oscillations by varying the nozzle diameter as well as the mold width and thickness. They determined the conditions that gave stable cross flows.
In addition to flow oscillations, vortex generation inside the mold and the corresponding meniscus fluctuations are also important to the final product quality. An influx of mold powders from the meniscus elicits product cracking. The vortex formation mechanism is basically the same as the “bathtub vortex” described by Gebhard et al. and Li et al. The latter group showed numerically that an eccentric SEN causes vortex generation at the side of the SEN. In the experimental results of Li and Tsukihashi, several vortices were observed at the side of the SEN. Recently, in a system with a noneccentric SEN, Torres-Alonso et al. observed similar vortices in numerical and experimental tests in a funnel mold.
Complicated flow phenomena inside a mold mainly originate from the high extraction speed at the SEN exit. Lamant et al. showed that the high shear flows at the meniscus associated with the influx of mold powders may lead to product cracking. Iguchi et al. found in their experiments that the Kelvin–Helmholtz instability induced by high flow rates at the meniscus can lead to powder entrapment. These results established that high meniscus velocities should be avoided. In contrast to the wealth of data available for parallel molds, studies of funnel-shaped molds are relatively scarce. Nam et al. simulated the mold flow features with heat transfer and solidification and analyzed the effect of using a funnel-shaped mold. Torres-Alonso et al. simulated the flow patterns numerically in a funnel mold and examined such flows experimentally using particle image velocimetry (PIV). In their work, however, the test section was limited to the small region close to the SEN meniscus. Detailed flow measurements are needed to elucidate the overall meniscus fluctuations and the oscillations inside the mold.
The objective of the present study was to investigate the flow oscillations and meniscus fluctuations in a funnel-type mold with various SEN models. To achieve this aim, we constructed a full-scale water model with a funnel-type mold. PIV measurements were taken in the entire region, which included the side walls, the SEN, and the meniscus, with planar velocity fields. In general, the mold flow had a high-velocity gradient, especially in the vicinity of the SEN exit and the meniscus. The window deformation technique was employed to obtain more accurate velocity data and to reduce the uncertainty of the PIV results. The image parity exchange method was applied to the side walls to obtain more accurate shear properties near the walls. In addition, the location of the meniscus in each PIV image was digitized by the gradient method based on edge-detection. Three types of SEN models were chosen with two funnel sizes and five flow rates. A quantitative statistical description was developed based on the oscillations and the fluctuating meniscus of the model.
Experimental Apparatus and Procedure
Full-Scale Water Model
The maximum sustainable extraction speed (6.17 m/min) was selected as a maximum flow rate condition (U = 50 m3/h), and the following five flow rates were selected: 1.0U, 0.8U, 0.6U, 0.4U, and 0.2U. When the flow rate was 1.0U, the Reynolds number based on the inner diameter and the mean velocity (2.18 m/s) at the entrance of the SEN was Re = 1.96 × 105. The PIV velocities were normalized by U 0 = 0.1028 m/sec, which was based on the mean extraction speed under a flow rate of 1.0U.
PIV techniques were employed to measure instantaneous velocity fields in the mold, as shown in Figure 1. A laser light sheet was produced by a double-pulsed Nd-Yag laser (New Wave Research, Fremont, CA) that delivered 200 mJ of energy per pulse at 532 nm, which can cover both sides of the SEN (1350 mm × 1000 mm) simultaneously. The laser sheet illumination was collimated by a concave cylindrical lens. Silver-coated hollow glass spheres with a mean diameter of 44 μm were used as tracer particles in the flow fields. For the charge-coupled device (CCD) system, a Redlake ES4020 (Tallahassee, FL) camera capable of recording up to 15 frames per second with a resolution of 2048 × 2048 pixels2 was used to obtain the PIV images. Grayscale image pairs with 2048 × 1280 pixels2, which have 256 intensity levels (8-bit), were captured at 5 Hz, and the time interval between successive images was set at dt = 2.0 to 4.0 ms because of the dynamic PIV range. For each flow condition, 5000 instantaneous PIV images were acquired.
Furthermore, masking was applied to eliminate luminance and reflection from the side walls. To improve the gradients of the velocity vectors, the PIV images were expanded across the walls using the image parity exchange (IPX) introduced by Tsuei and Savas. For the first step of the PIV process, an iterative multigrid algorithm was used, and a square interrogation window with a size of w = 128 pixels was employed as a predictor. The final window size was set to w = 64 pixels with 50 pct overlap, and five iterative calculations of a cross-correlation were applied with the window deformation algorithm.
Detection of Meniscus Levels
Results and Discussion
Time-Varying Meniscus Level
The peak frequencies of the three 2.2T systems were slightly higher than those of the corresponding 1.8T systems. This result may be attributed to the fact that the SEN acted as a damper (i.e., the SEN has a blockage effect on the cross flow, which decreases the flow momentum). For all three SEN types, the clear peak was observed in the flat mold region (x/W > 0.3). Two or three ridges were observed for the Type III SEN. These periodic meniscus fluctuations were related directly to the self-sustained oscillations inside the mold. Because these fluctuations disturb the formation of a solidification shell, unstable oscillations should be reduced in the real casting process.
Vortices on the Meniscus
Numbers of Vortex Events for a Funnel of Thickness 1.8T
We performed PIV measurements in a funnel-type water model to elucidate the quantitative characteristics of the flow oscillations inside the mold and the meniscus fluctuations. A full-size water model was constructed, and PIV measurements were recorded across the entire flow within the model. Three SEN designs were tested with two funnel models under five flow rate conditions. To improve the accuracy of the results, the window deformation and IPX techniques were employed. An edge-detection algorithm was used to find the meniscus location. We found that the ratio of mold thickness to mold width influences the meniscus fluctuations and that the strength of the self-sustained oscillations is related closely to the funnel size. The peak frequency of the Type I system (0.82 Hz) is slightly higher than that of the Type II system (0.78 Hz). The clear peak is distributed in the flat mold region (x/W > 0.3). The periodic meniscus fluctuations are related directly to the self-sustained oscillations inside the mold. As the ratio of funnel size to width decreases, the periodic features decrease. At low flow rates (0.2 ~ 0.4U), Type I and II systems show stable features. For Type I, one large recirculation is generated because of the strong downward throughput from the SEN. Varying the flow rate has no significant effect on the streamline shapes in the Type I system. For Type II, by contrast, the streamline shapes show a strong dependence on the flow rate. When the flow rate is small (0.2U), small flow circulations are generated around the exit of the SEN. However, as the flow rate increases, two recirculation regions merge into a single large region. At flow rates higher than 0.5U, the side-throughputs are not strong enough to form an additional circulation; rather, the recirculations merge into a single recirculation at the center. At high flow rates, the streamline shapes of Type I are similar to those of Type II. The Type III system shows complex flow patterns because of the five SEN exits. Similar flow patterns were observed at all flow rates. However, as the flow rate increases, vortex generation rapidly increases. The lower vortex in the Type III flow may be generated by the periodic meniscus flows. The vortex pairs appear between the SEN and the funnel and are generated by the crush and the rolling of the cross-flow. The formation of these vortices is affected by the meniscus velocity as well as the velocity in the vicinity of the meniscus. As the number of recirculation regions increases, the quantity of the flow that influences the meniscus is reduced. As a result, the inner and meniscus flows are stabilized.
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