Fluid Flow from a Low to a Higher Density Liquid F. WEINBERG The penetration of liquid from a low density brine solution into a higher density solution below it has been measured as a function of vertical flow velocity and the density difference of the two solutions. The flow velocity was produced by a horizontal disc rotating in the low density liquid. The results show the penetration distance and penetration rate are dependent on flow velocity and in particular are very sensitive to small changes in the density difference between the two liquids. The observations are considered in relation to liquid penetration into dendritic arrays, and fluid flow in the pool of ingots and continuously cast steel billets, during solidification.

I.

Ill.

INTRODUCTION

IN a previous investigation ~the penetration of liquid into a dendritic array under forced convection was examined in aluminum alloys and a water model system. The flow penetration was found to depend primarily on the initial flow velocity and the density difference between the interdendritic and bulk liquid. However, the individual effect of these variables on flow was not clearly established. In addition, the observed flow velocities differed significantly from calculated values derived theoretically. The present investigation was undertaken to establish the effect of the initial flow velocity and density changes in the liquid on vertical fluid flow in a water model system, without dendrite barriers being present. II.

PROCEDURE

Following the previous investigation a vertical vycor tube of 50 mm inside diameter was filled with brine to a height of 155 ram. A stainless steel disc 40 mm in diameter and 2 mm thick was positioned horizontally 5 mm below the top surface of the liquid and rotated at a measured angular velocity. The vertical flow velocity in brine of uniform density was determined by measuring the position of a nylon sphere as a function of time as it moved down the tube. The nylon sphere had a density of 1.150 x 103 kg m -3 which was slightly lower than the density of the brine used in the test. Measurements were made for disc velocities between 60 and 340 r per minute. The effect of density differences in the liquid on vertical flow was determined by filling the top 55 mm of the tube with brine of density p 1 and the lower 100 mm with colored brine of higher density 02, ensuring the two solutions did not mix. Following the start of rotation of the disc, the downward movement of the interface between the two solutions was measured as a function of time. Brine solutions having densities between 1.045 and 1.087 x 103 kg m 3 were used with disc speeds between 60 to 340 r per minute. For the case of AO = 0 the interface height was measured by following the downward movement of a group of spheres of slightly lower density than the liquid.

F. WEINBERG is Professor and Head, Department of Metallurgical Engineering, The University of British Columbia, 309-6350 Stores Road, Vancouver, British Columbia V6T 1W5, Canada. Manuscript submitted January 23, 1984.

METALLURGICAL TRANSACTIONS B

OBSERVATIONS

The rotation of the horizontal disc at the top of the liquid column results in downward flow of liquid near the tube wall and upward flow along the tube axis.' The downward and upward flow velocities were observed to be relatively constant along the tube and similar in magnitude. The flow velocities measured as a function of the speed of rotation of the disc are shown by the points in Figure 1. The calculated velocities, based on solutions of the Navier-Stokes equations,~ are shown by the solid line. There is good agreement in this case between the observed and calculated velocities. The flow penetration from low to higher density liquid for a series of values of Ap and rotational speeds between 60 and 300 r per minute is shown in Figures 2(a) through (d). In the figures the height of the interface separating the two liquids is plotted as a function of time from the start of rotation of the disc. Considering Figure 2(a) for w = 60 r per minute the penetration of flow into the higher density liquid is very sensitive to Ap. A density increase of 0.5 kg m -3 is enough to increase markedly the time required for the flow to penetrate a significant distance into the heavier liquid. With Ap = 8.4 kg m 3 there is relatively little penetration over an appreciable time interval. The flow penetration is rapid in the upper layers of the high density liquid, and slows appreciably as flow approaches the bottom of the liquid.

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VOLUME 15B, DECEMBER 1984--681

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Increasing the disc rotation speed from w = 60 to 120 r per minute (Figure 2(b)) markedly increases the penetration distance with time for a given Ap. For example, with Ap = 1 kg m -3 the time required to reach a height of 20 mm decreases from 1350 to 90 seconds as oJ increases from 60 to 120 r per minute. With higher values of Ap (greater than 41,1 kg m -3) the penetration is small. Further increases in rotational speed (Figures 2(c) and (d)) result in further marked increases in penetration distance with time. The density difference required to prevent significant penetration also increases appreciably, Interface velocities were estimated from the curves in Figure 2 and plotted as a function of density difference in Figure 3. Since the curves in Figure 2 are not linear, the velocity is only approximate. In general the slope for a given Ap and o~ was taken from the lower part of the curve, neglecting the velocity reduction near the bottom of the liquid, or the latter part of the curve which often approached linearity. In Figure 3 the interface velocity is observed 682--VOLUME 15B, DECEMBER 1984

to drop very rapidly for co = 60 r per minute with a very small increase in Ap, leveling off at a velocity of 3 • 10 -3 m m s -3. As oJ is increased the slope of the initial portion of the curve decreases; the velocity at which there is a marked change in slope increases; and the final velocities observed increase.

IV.

DISCUSSION

The present results show a very marked reduction in flow penetration and flow velocity in the higher density liquid with very small density changes, particularly for the low fluid velocities associated with low rotational speeds. This agrees with results reported by Stewart and Weinberg 2 for flow due to natural convection from pure tin to tin containing a small amount of lead. The flow velocities in the low density liquid in their case was in the order of 5 mm s which is comparable to 60 r per minute in the present case. METALLURGICAL TRANSACTIONS B

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They found extensive penetration occurred for Ap = 0.4 kg m -3 and 0.5 kg m -3 and no significant penetration at, and above, Ap = 9.6 kg m -3 consistent with the present results. The measured vertical flow velocities in this investigation for a liquid of uniform density agrees with the velocities calculated from theory. In the previous investigation of fluid flow into dendrite arrays 1 some flow velocities were measured without dendrites being present. It was found that the measured velocities were much lower than the values calculated from theory, differing from the present results. The low velocities of the earlier results are attributed to the presence of a temperature gradient in the liquid which would produce higher densities in the lower regions of the liquid. In the vertical dendritic solidification of AI 5 wt pct Cu examined in the previous investigation, the penetration of flow into the interdendritic liquid was 12 mm for co = 60 r per minute and a temperature gradient of 0.41 ~ mm i. The interface advanced at a rate of 0.069 mm s -l which would allow less than 170 seconds for the liquid to penetrate. From Figure 2(a) for o) = 60 r per minute, a density difference of 5 kg m -3 could account for this penetration in the time available. This density difference could be produced with a temperature change (for pure A1) of 21.5 ~ or a concentration increase of Cu in the melt of 0.19 wt pct, or lesser amounts of each added together. The temperature gradient in the melt, 0.41 ~ mm -~, is too small to produce a change of 21.5 ~ in less than 12 mm. However, the Cu concentration in the melt would rise by 0.19 wt pct after only 4.4 pct of solid formed, which is very early in the solidification process.

METALLURGICAL TRANSACTIONS B

During the solidification process temperature and solute gradients develop in the melt which can markedly influence the fluid flow pattern, which in turn affects the solute segregation and cast structure of the solid. Investigations have been reported describing fluid flow in the melt during the solidification of large steel ingots. 3'4'5 In all cases it was observed that flow due to natural convection was confined to the upper part of the liquid pool after the ingots had partially solidified. Similarly, observations of fluid flow in the liquid pool of continuously cast billets 6'7 show that fluid flow due to natural convection occurs only in the upper part of the pool. In both cases the present results suggest that higher density liquid exists in the lower part of the pool due to a combination of slightly lower temperatures and higher solute concentrations. Taking the flow velocities in these cases to be in the order of 5 mm s-~, co = 60 r per minute in the present investigation, a density difference of Ap = 1 kg m -3 would require a drop in temperature of 0.6 ~ for pure iron or a change in composition of 0.007 wt pct C in FeC alloys. A difference of 1 ~ between the lower and upper parts of the liquid pool is not unreasonable. Variations in the concentration of C of the order of 0.01 wt pct have been observed in as-cast small ingots. 5 In observations on directionally cast alloy steels in which radioactive P was added to the melt, fluid flow in the melt did not extend to the solid-liquid interface, s This can be accounted for by higher density liquid being present ahead of the interface due to the temperature gradient in the melt. If the density in the lower part of the pool in a steel ingot or in a continuously cast billet is a little higher than the upper part, then mechanical stirring of the upper melt or hot topping practices which enhance natural convective flow in the upper melt would have little effect on flow in the lower part of the melt. Fluid flow from the upper part would not penetrate the lower region. To develop fluid flow in the pool and enhance the properties of the steel, electromagnetic stirrers are being used in the continuous casting of steel slabs and billets. The stirrers are placed in the mold, 9 immediately below the mold, or at various positions along the liquid pool. Different magnetic field configurations are used causing flow to occur primarily parallel or perpendicular to the billet axis. The present results indicate electromagnetic stirring of liquid near the top of the pool will be confined to the upper part of the pool. Stirring at intermediate and lower positions in the pool may cause flow to extend to the lowest part of the pool depending on the magnitude of the vertical flow velocity generated and the relative density of the liquid near the pool bottom. Flow upward would be more extensive than downward. If the flow velocity of the liquid during the solidification of steel is suddenly increased due to a change in the speed of rotation of a casting, 8 electromagnetic stirring, 9 or by the impinging stream from an immersed nozzle, 1~ the interdendritic penetration increases and solute enriched liquid is removed, This results in a solute-depleted band which appears as a "white band" on the etched surface. This is consistent with the present observations that the penetration is sensitive to flow velocities, particularly in the low-velocity region. In addition, the present results indicate the same effect can result from a sudden decrease in the freezing rate since the penetration is time dependent. This would have to be verified experimentally.

VOLUME 15B, DECEMBER 1984--683

V.

SUMMARY

The penetration of low density liquid into a higher density liquid under forced convection is strongly dependent on the flow velocity, and in particular on the density difference between the two liquids. At low flow velocities, comparable to those resulting from natural convection in melts, density differences as small as 0.5 kg m -3 can very markedly decrease the distance and rate of penetration. The results account for the small penetration of liquid into the interdendritic region during solidification. The results can also account for the lack of flow from the upper to lower parts of the pool during the solidification of large ingots and continuously cast billets of steel, based on the conclusion that the liquid in the lower part of the pool has a slightly higher density than the upper part of the pool. Following this conclusion, enhanced fluid flow due to mechanical stirring, modified hot topping practice, or electromagnetic stirring near the top of the liquid pool will produce little flow in the lower part of the liquid pool.

684--VOLUME 15B, DECEMBER 1984

ACKNOWLEDGMENTS The measurements were carried out with the assistance of D. Tripp and N. Tuffrey. Support by the Natural Science and Engineering Research Council is gratefully acknowledged. REFERENCES 1. J. R Gabathuler and F. Weinberg: Metall. Trans. B, 1983, vol. 14B, pp. 733-41. 2. M.J. Stewart and F. Weinberg: J. of Crystal Growth. 1972, vol. 12, pp. 227-37. 3. A. Kohn: The Solidification of Metals, The Iron and Steel Institute, London, publication 110, 1967, pp. 356-63. 4. K.W. Andrews and C. R. Gomer: ibid., p, 363. 5. E Weinberg, J. Lair, and R. Pugh: Solidification and Casting of Metals, Metals Society, London, publication 192. 1977. pp. 334-39. 6. S.K. Morton and F. Weinberg: JISI. 1973, vot. 211, pp. 13-23. 7. J.E. Lair, J.K. Brimacombe, and F. Weinberg: lronmaking and Steelmaking, 1974. no. 1, pp. 35-42. 8. F. Weinberg and R. K. Buhr: The Solidification of Metals, The Iron and Steel Institute, London, publication 110, 1967, p. 295. 9. M. Gray, A. McLean, G. C. Weatherly, L. Beitelmam D. Campbell, M. W. Bates, and R. Hadden: Canadian Inst. of Metl. Bulletin, 1982, vol. 75, pp. 106-09. 10. E.B. Hawbolt, F. Weinberg, and J. K. Brimacombe: Metall. Trans. B, 1979, vol. 10B, pp. 229-36.

METALLURGICAL TRANSACTIONS B