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Casting-Chill Interface Heat Transfer during Solidification of an Aluminum Alloy EULOGIO VELASCO, JESUS TALAMANTES, SIGIFREDO CANO, SALVADOR VALTIERRA, JUAN FRANCISCO MOJICA, and RAFAEL COLAS Unidirectional solidification tests on an aluminum alloy were conducted with a computer-controlled instrumented rig. The alloys employed in this study were poured into isolated ingot molds (made of recrystallized alumina and covered with ceramic fiber) placed on top of a steel plate, coated either with a graphite- or ceramic-based paint in order to avoid sticking of the material. Thermal evolution during the test was captured by type-K thermocouples placed at different positions in both the ingot and the plate. The bottom surface of the plate was either cooled with water or left to cool in air. The heat-transfer coefficients across the aluminum-steel interface were evaluated by means of a finitedifference model. It was concluded that the heat-transfer rate depends on the conditions at the interface, such as the type of coating used to protect the plate, and the solidification reactions occurring on the aluminum during its solidification.

I. INTRODUCTION

MATHEMATICAL modeling as a productive tool is being employed nowadays in a huge number of industries around the world.[1,2,3] The principal uses of this technique are in[3] developing new products or processes, improving the quality of parts or products as the knowledge of the process is gained, reduction in production costs as the variability of the process is decreased, etc. Foundries can achieve the greatest benefits by implementing a direct approach to modeling,[4–9] in order to gain knowledge about the interaction between the different phenomena that take place during the solidification of complex pieces. The microstructure which develops in a cast depends on its solidification rate,[10,11,12] and, since the solidification rate depends on the rate at which the heat flows at the castingmold interfaces,[13–18] it is possible to establish a direct link between the microstructure and the type and characteristics of the mold employed to produce the pieces. The heat-transfer conditions during solidification are complex, since the boundary conditions between the piece being cast and its mold change with time. It can be assumed that an intimate contact between the metal and mold exists while the former is liquid, but, as solidification proceeds, the metal shrinks, forming an air gap at the interface, which reduces the heat-transfer rate to the surrounding media.[13–18] The goal of this work is to study the heat-transfer conditions that develop during solidification of an aluminum alloy poured into an experimental rig that forces unidimensional heat flow and how they are affected by solidification kinetics. EULOGIO VELASCO, Process Engineer, SALVADOR VALTIERRA, Research and Development Manager, and JUAN FRANCISCO MOJICA, Technology Vice-President, are with Corporativo Nemak, S.A. de C.V., ´ ´ ´ 66000 Garcıa, N.L., Mexico. JESUS TALAMANTES, Graduate Student, ´ ´ ´ formerly with Facultad de Ingenierıa Mecanica y Electrica, Universidad ´ ´ Autonoma de Nuevo Leon, is with the Department of Mechanical Engineering, The University of Sheffield, Sheffield S1 3JD, United Kingdom. SIGIFREDO CANO, Process Engineer, formerly with Corporation Nemak, is with Mahle, Inc., Morristown, TN 37815. RAFAEL COLAS, Professor, ´ ´ ´ is with the Facultad de Ingernierıa Mecanica y Electrica, Universidad ´ ´ Autonoma de Nuevo Leon, 66451 Cd. Universitaria, N.L., Mexico. Manuscript submitted November 12, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS B

II. EXPERIMENTAL AND MODELING PROCEDURES Three different solidification tests were made with the aid of a computer-controlled instrumented rig, which consisted of a 51-mm-thick steel plate and a mast used to hold a series of type-K (chromel-alumel) thermocouples at different heights. These thermocouples were connected to solid-state devices, which convert the electromotive force generated by the couple into a linear scale ranging from 0 to 5 V. The output from these devices was then fed into an analog-digital board installed in a compatible computer. Figure 1 shows, schematically, the positions at which the thermocouples were inserted. Cooling of the bottom surface of the steel was accelerated by water in two trials, and the steel was left to cool in air in a third trial. The aluminum alloy was poured into an ingot mold made of recrystallized alumina of 150-mm diameter and 300-mm height, which was covered with a ceramic fiber blanket in order to assure unidirectional solidification by reducing heat losses through the radial direction. The chemical composition of the alloys is reported in Table I, whereas the testing conditions are shown in Table II. The thermocouples of interest in this study are those placed into or in contact with the steel plate. The one on its top was fixed with the aid of steel wire. The position of this device, as well as of those located within the ingot, was confirmed by cutting the ingot in half. The thermocouple in contact with the bottom surface was also fixed to it with steel wire and was protected from the water stream (when it was employed) with a steel washer. It is worth mentioning that the temperature sensed by this device was confirmed to be that of the steel plate, rather than that of the water, by cutting off the water stream (toward the end of the test); the temperature increase which followed was similar to that registered by the thermocouple placed into the steel plate (Figure 2). The solidification kinetics of the alloy were studied by means of thermal analysis, in which the instantaneous cooling rate (dT/dt)[19,20,21] is assumed to be equal to the derivative of a series of successive quadratic polynomials adjusted by the least-squares method into an even number of data VOLUME 30B, AUGUST 1999—773

Fig. 1—Diagram showing the positions at which the thermocouples were installed.

Table I. Chemical Composition (Weight Percent) of the Alloy Test I II III

Si

Cu

Fe

Mn

Mg

Zn

Ti

Sr

7.79 3.76 0.859 0.491 0.376 0.749 0.172 0.0127 7.93 3.68 0.912 0.540 0.378 0.663 0.183 0.0175 8.08 3.63 0.843 0.438 0.353 0.668 0.191 0.0102

Table II. Testing Conditions Temperatures (C)

Time (s)

Test

Bottom Cooling

Pouring

Water

Ambient

Pouring

Total

I II III

air water water

635 649 696

— 35 30

35 31 30

12 11 11

1650 2800 3100

Fig. 3—Heat flow in the steel plate; l is not shown because it is normal to the diagram.

Heat conduction within the steel plate was calculated with a finite-difference model (explicit formulation), which divides the plate into m elements or nodes of equal volume. Figure 3 shows the one-dimensional array used to calculate the heat flowing from the casting (Q3) to the bottom surface of the plate (Q4). Heat flow through the element marked as n during a given time interval (dt) is given by Q1 5 (Tn 2 Tn21)

elkd t d

[1a]

Q2 5 (Tn11 2 Tn)

elkd t d

[1b]

where Q1 and Q2 are the heat flowing from or into, respectively, the element of dimensions d, e, and l; Tn11, Tn , and Tn21 are the temperatures at the n 1 1, n, and n 2 1 nodes, respectively, and k is the temperature-dependent thermal conductivity of the steel.[23] Heat flowing from the plate at the bottom surface is calculated by hb 5 Hb(Ts 2 Tb)

Fig. 2—Temperature increase recorded by the thermocouples placed into the plate and in contact with its bottom surface, which results from cutting of the stream of water.

points.[22] The critical temperatures of transformation were determined by plotting the cooling rate as a function of time or temperature.[21] 774—VOLUME 30B, AUGUST 1999

[2]

where Hb and hb are, respectively, the heat-transfer coefficient and the heat flow, and Ts and Tb are, respectively, the temperatures at the plate surface (measured by the thermocouple) and that of water or air. In a similar way, the heat flowing into the plate is calculated by ht 5 Ht(Ta 2 Ts)

[3]

where Ht and ht are heat-transfer coefficient and flow, and Ta is the temperature of the aluminum alloy, which in this work is related to the temperature measured by the thermocouple located at the interface, and Ts is that of the steel surface, which is calculated by the model. METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 4—Thermal evolution recorded by the thermocouples located at the center and bottom surface of the steel plate.

Heat gained (Q3) or lost (Q4) by either surface can then be calculated by Q* 5 h* eldt

[4]

where the subscript asterisk is used to indicate either surface. The temperature at the end of the time interval (T n*) is given by T *n 5 Tn 1

(Q delrs

[5]

where (Q is the amount of heat lost or gained by a node, and r and s are, respectively, the temperature-dependent density and specific heat of the steel.[23] The model will be stable as long as the thermal gradient does not penetrate more than one element per iteration. It is assumed that the critical conditions occur toward the aluminum interface. Heat flowing into the external node is computed with a second-degree polynomial fitted through the center of the plate and the external node and at Ts (Eq. [3]) at the interface. Following this, the time between iterations, which is dependent on the thermophysical properties of the steel and on the number of elements into which the plate was divided, is given by[24]

dt # d 2

(m 2 0.75) rs 2mk

[6]

the 0.75 value comes from the assumption that the temperature distribution toward the surface follows a parabolic distribution with respect to distance. III. RESULTS AND DISCUSSION Development of a one-dimensional thermal gradient during solidification was confirmed by examination of the microstructures of the ingot mold. This was done on samples close to its bottom surface, i.e., those in contact with the steel plate, and at different heights. It was found that the radial variation of different microstructural aspects (dendritic arm spacing, degree of modification, etc.) was negligible in comparison to that which took place along its height. Figure 4 shows the thermal evolution of the steel plate for the three tests. It can be seen how the data recorded at METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 5—Thermal evolution measured in the three tests by the thermocouple located in the upper surface of the steel plate.

the bottom surface, in the tests in which water cooling was employed (c and e), do not increase very much, in contrast to the test in which the bottom surface was cooled by air (a), in which it follows the increase in temperature recorded by the thermocouple placed at the center of the steel plate (b). Figure 5 shows the temperatures recorded by the thermocouples which were placed in contact with the steel plate upper surface in the three different tests. Curve a, corresponding to the first test, is plotted only up to 600 seconds, since that particular thermocouple broke down. The curves indicate that solidification proceeds at a higher rate in test II (curve b), than at tests I and III (curves a and c, respectively), which can be attributed to the effect of water cooling and the use of a more-conductive coating, in the second case. Another aspect to notice in Figure 5 is the change in slope and curvature in each test, especially in the one marked as b (test II), which shows the characteristic increase in temperature of an exothermic reaction,[19,21] which, in the present case, corresponds to formation of the eutectic Al 1 Si. One of the difficulties in modeling heat transfer during solidification is that of coupling microstructural and thermal phenomena, since it is expected that the heat-transfer coefficient will be higher during the early stages of solidification than later on, mainly due to the air gap formed by metal shrinkage.[13–18] Solidification of the aluminum alloy in contact with the steel plate was followed by thermal analysis; Figures 6 and 7 show the method used to obtain the critical points of transformation[19,20,21] in test II. The points marked as A in both figures correspond to the start of dendritic growth, whereas points B and C are associated with the start and finish of the eutectic reaction. Evaluation of the heat-transfer coefficients at the aluminum-plate interface was carried out with the aid of the finitedifference model described in the previous section. Figure 8 shows the display of the simulation at 1000 seconds after the start of test II. Data from the simulation are presented in four different sections; the first one, upper-left corner, shows the temperature-time plots for the values measured (points) and the corresponding predictions from the model (lines); both sets of data are correlated in the graph located in the upper-right corner. At the lower-left corner, two different plots are shown: the derivative of the cooling curve for the VOLUME 30B, AUGUST 1999—775

Fig. 6—Derivative of the cooling curve marked as b in Fig. 5 as a function of time.

Fig. 7—Derivative of the cooling curve marked as b in Fig. 5 as a function of temperature.

Fig. 9—Predicted temperature evolution within the steel plate during test I.

Fig. 10—Predicted temperature evolution within the steel plate during test II.

Fig. 11—Predicted temperature evolution within the steel plate during test III. Fig. 8—Computer simulation of the solidification of test II.

aluminum close to the interface, corresponding to Figure 6, and the values of Ht (Eq. [3]) required to achieve the correlation shown in the upper graphs. The array shown in the lower-right hand corner side is used to visualize the changes in temperature that take place in the steel plate during the simulation. The three numbers displayed to the right of the array correspond to the temperatures measured by the 776—VOLUME 30B, AUGUST 1999

thermocouples. It is worth noticing that the changes in value of Ht correlate to the solidification reactions taking place in the aluminum (Figures 6 and 7). The program, whose display is shown in Figure 8, was used to plot the thermal gradients developed within the steel plate as a function of time. Predictions and measurements (marked as individual points) for the three tests are shown in Figures 9 through 11. For the sake of clarity, the time METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 12—Heat-transfer coefficients required at the interface in order to reproduce the experimental data shown in Fig. 4. Data from Ref. 25 is added for comparison.

scale in these figures starts at the right-hand side. It is worth noticing the difference in the magnitude and shape of the thermal distribution within the plate as the bottom surface of the plate is left to cool in air or water (Figures 9 and 10, respectively) or as the coating changes from graphite to mica (Figures 10 and 11, respectively). Figure 12 plots the heat-transfer coefficients, as a function of time and temperature, which had to be applied to the aluminum-plate interface in order to achieve a good agreement between the values measured at the center and at the bottom surface of the plate and those predicted by the model. The values recommended by a developer of computer code[25] are included for comparison. Deducing the heat-transfer coefficient as a function of transient temperatures is treated as an inverse problem,[18,26–29] which requires the elaboration of mathematical models of more-complex formulation than the one developed for the present work. Unfortunately, such models concentrate more on the actual mathematics of the problem, rather than on deducing the underlaying mechanisms responsible for such phenomena. Efforts have been made to understand the functional dependence of the interfacial heat-transfer coefficient on casting conditions,[13–18,30–33] and it has been found that the heat transfer first increases to a maximum value and then decreases,[18,30–33] but, up until now, a clear explanation of such behavior has not been offered. An advantage of the experimental arrangement is the capacity for capturing readings from different thermocouples. These data are used to deduce the time and temperature dependence of the heat-transfer coefficients, since, as can be seen from Figure 8, the temperatures at the center and at both surfaces of the plate are known, and the thermal gradients can be calculated by Eqs. [1] through [5], once two sets of heat-transfer coefficients (Hb and Ht) are prescribed. It is worth mentioning that the values of Ht found in this work agree with those reported elsewhere.[30–34] The present model assumes that the heat-transfer coefficient at the aluminum-steel plate depends on the solidification kinetics, since its value is kept constant while the alloy is liquid and increases as soon as the dendrites start to form (Figure 9). For the sake of simplicity, the heat-transfer coefficient was kept constant at this value (which might not be correct, but simplifies the calculations); the model assumes that the transfer rate decreases as soon as the eutectic forms, with a further decrease once the alloy is fully solid. Although the eutectic reaction starts before the cooling METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 13—(a) through (d ) Solidification mechanisms that affect the heattransfer rate to the mold.

rate becomes zero (point B in Figure 6), the model takes the time at which this occurs as the start of solidification of the eutectic (Figure 8). The assumptions presented in the previous paragraph can be justified with the aid of the diagram of Figure 13. The low heat-transfer rates found at the early period of the test might be due to the lower conductivity of the liquid,[35] as compared to that of the solid (a). The transfer rate will be increased as the dendritic network develops (b), because nucleation occurs at the interface and, as the individual dendrites grow and develop the secondary branches, the transfer rate will be enhanced. The decrease in the heattransfer coefficient as the eutectic starts to form (c) might be due to shrinkage of the solid crust, the establishment of a layer of lower thermal conductivity (since the thermal conductivity of Si is lower than that of the Al), or by the heat evolution produced by this reaction (Figures 5 through 7). Once the interfacial layer has fully developed, the transfer rate will decrease as the gap generated by the shrinkage grows (d).[36] Figure 12 indicates that the heat-transfer coefficient depends on both time and temperature, but, in order to use these data in a sensible way, an understanding of the solidification kinetics under a given set of conditions is required. For instance, the cooling curves (Figure 5) indicate that the use of a coating made from silicates has a much greater effect than does a graphite-based coating on the steel plate which was left to cool on air. Although in both experiments the temperature at the top surface of the plate reaches its saturation at around 200 seconds (Figures 9 and 11), the value achieved in test I (graphite paint and air cooling) is around 100 8C higher than that in test III (mica coating and water cooling). IV. CONCLUSIONS A computer-controlled experimental rig was developed to study the behavior of an aluminum casting alloy during unidirectional solidification, which was achieved by insulating an ingot mold placed on top of a steel plate. A heat-transfer finite-difference model was developed to VOLUME 30B, AUGUST 1999—777

calculate the thermal gradients which develop in the steel plate. Although the model is rather simple, it allows coupling of heat-transfer phenomena and solidification kinetics. Both the solidification kinetics and heat-transfer coefficients were affected by the use of water cooling and the type of coating employed. It is concluded that the solidification kinetics affect the heat-transfer rate, with the highest value encountered as the dendritic network develops. The transfer coefficient is reduced when solidification of the eutectic proceeds and is further reduced as the metal shrinks and an isolating gap of air forms.

ACKNOWLEDGMENTS The authors acknowledge the support given by CONACYT and the facilities provided by Nemak, S.A. de C.V.

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