The Elusiveness of HTCs

The issue of using a reliable value for the heat transfer coefficient (HTC) at the mold-casting interface for the purpose of modeling the temperature history inside a casting is a recurrent one; it has been particularly crucial in permanent mold where it is the overriding factor governing the temperature changes during filling and solidification. Innumerable measurements have been made in universities for simple geometries showing that HTC varies considerably during the process, even before the sharp drop in HTC when, most of the times, a gap forms at the mold-casting interface. A case rarely studied is when the casting is pressed against the mold by the contraction of the aluminum alloy, where HTC increases sharply. The complexity in the phenomenon cannot be practically tackled when solving the heat transfer problem so that simplified “effective’’ values of HTC are used. Since the HTCs also depend on the mold coating practice, our conviction is that these “effective values” should be determined in-house on a variety of casting shapes and sizes; this implies that the empirical determination of HTCs should be simple. In this article, a method is proposed where the recordings of two thermocouples is sufficient to determine the HTCs during the filling and the subsequent cooling phases of the process. The method will be demonstrated on the cluster of the standard ASTM B108 test bars.

Characteristics of HTCs

Modeling filling and solidification in permanent mold requires to describe the heat transfer between the casting and the mold. This is done by defining a surface HTC which, when multiplied by the contact area and the difference in temperature between the casting and the mold, gives the heat power transferred across the interface. HTC is expressed in Wm-2C-1. What can be concluded from the innumerable academic studies alluded to above is the following: 

a) The HTCs depend on the experimental set-up, however simple it may be.
b) The HTCs are dependent on time, or on the interface temperature, depending on how one chooses to plot their variation.
c) When measured continuously, for instance using the Inverse Method, the variation is erratic and cannot be described by a mathematical equation.
d) In most set-ups, there is a sharp drop in HTC at some point in the cooling process when a gap forms due to the thermal contraction of the casting.

However, if the gap formation is common in simple academic set-ups where the casting surface is free to move away from the mold, in real life, the complex shape of a casting makes it that it is inevitably pressed against the mold at some locations, resulting in a sharp increase in HTC; this happens in all cases, or the solidified casting would drop from the mold without any ejecting force necessary. 

Considering the case of the casting shown in Figure 1, one would expect that HTC1 > HTC2 > HTC3. 

Generally, most of the surface of the casting is pulled away from the mold rather than pressed against it, so that the variation of HTC with the casting surface temperature is generally represented by the simple lines shown in Figure 2, even in the most sophisticated commercial software. The formation of the gap may be considered by applying a continuous drop in HTC from the liquidus to the solidus temperatures (Figure 2a). The model used in the present work applies a step function (Figure 2b) with a drop in the value of HTC of 2/3 at the solidus temperature; it is thought to better represent the gap opening process, which is believed to be discontinuous, i.e. taking place when the internal stresses pulling the casting away from the mold overcome the adherence of the casting to the mold coating. Also, this gap opening can only take place when the casting is able to sustain substantial tensile stress, i.e. when it is close to full solidification.

If measuring the HTCs will be done on the ASTM B108 standard mold, the method applies to any mold as long as the last metal to fill the mold is accessible for temperature measurement (generally in an open riser). 

HTCs during filling have been found to be substantially less than during the cooling and solidification process, with values less than 1000 Wm-2°C-1. This has been corroborated by the fact that when the mold/casting HTC was not reduced during filling, misruns were systematically predicted which did not actually occur. This can be explained by the fact that during the early phase of the casting-mold coating contact, air is entrapped in the valleys of the peaks and valleys configuration of the coating surface, this air being expelled by the hydrostatic pressure and/or surface tension interactions  after the filling is completed.

Measuring HTCs Must Be Simple 

The method must be simple and unintrusive as it will be implemented in a production environment. In the present paper, it will be demonstrated by determining the HTCs during the filling and subsequent cooling inside the ASTM B108 standard mold used to produce a pair of 0.5’’diameter as-cast tensile test bars. However rough this approach using the “effective HTC” concept might be from a scientific standpoint, it is the most realistic to provide the closest image of the casting thermal history.

How Effective HTCs Are Measured

The principle of the method is to record the temperature-time curve in the casting at two locations, at the beginning and at the end of filling, and until complete solidification takes place. The two recordings between the beginning of filling and the end of solidification will allow, by trial and error, to determine the values of HTCs which provide the best fit between the measured and predicted temperatures, first at the end of filling (HTCfill), then on cooling until complete solidification (HTCstatic). The casting poured in the present example is shown in Figure 3.

Thermocouple TC1 is in the pouring basin, to accurately measure the pouring temperature, while TC3 is located in one of the risers. Thermocouple TC2, located in the reduced section, was used for another project. 

Points on the TC3 recording will be compared to what is predicted in the modeled solution; the values of HTCs will be changed by increment of 50 Wm-2C-1 until the “best fit” is obtained at these points on the experimental recordings.  

Details of the Experimental Procedure 

The mold was soaked in an oven to achieve a constant temperature of 400°C±5°C. The pour was done within one minute, after the three thermocouples had been placed in the cavity; their exact locations (x, y, z) was determined by x-ray images at two angles of view. The mold coating was one of the most widely used commercial “white” coating; its thickness was measured before heating up, on the flat surfaces of the mold cavity (sprue and bottom channel) at a thickness of 52 ± 15µm. The experimental recordings are shown in Figure 4. The type K thermocouple wire used, gage 24, resulted in a twisted junction 1.2mm in diameter providing a 0.8s response time in a flow of liquid metal.

Fitting Modeled and Experimental Results

The temperatures recorded by thermocouples TC1 and TC3 are shown in Figure 4. The pouring temperature, given by TC1 was 732°C and the filling time was 6.1s.

The HTC during filling (called HTCfill) was obtained by finding the best fit at the maximum temperature recorded by TC3 (671°C) while HTC between filling and solidification (called HTCstatic) was determined by finding the best fit at the solidification time recorded by TC3 (81s); the solidification temperature used for A356 was 556°C. The predicted results for the temperature history at points TC2 and TC3 are shown in Figure 5.

Using HTCfill = 550 W.m-2 °C-1 resulted in a predicted maximum temperature of 675°C for TC3, which corresponds to the end of filling, compared to 672°C experimentally. The predicted temperature distribution in the liquid metal at the end of filling is shown in Figure 6.

The predicted solidification time is shown in Figure 7. One may argue that because of the time lag in the temperature recording, the actual maximum temperature at the end of filling is higher than 671°C, in which case our value of HTCfill would be overestimated. Let us point out that in a real (usually bigger) casting, this issue would be lessened because of the much slower change in temperature after the maximum is reached.

Likewise, using HTCstatic = 1150 W.m-2 °C-1 after the end of filling results in a predicted solidification time of 78 s at TC3, compared to 82s experimentally. One may verify that the predicted end of solidification at the tip of TC1 (104 s) is reasonably close to the experimental value (108 s).

It is noteworthy that HTCfill is less than HTCstatic, probably because the air is not expelled from the valleys of the rough surface of the coating before the liquid comes to rest and the hydrostatic pressure and surface tension effects kick in.

Comparing Figure 4 and Figure 5 shows that the difference between the experimental and predicted curves is important in between the anchor points (i.e., temperature at end of filling and solidification time). This highlights the fact that the “effective” HTC does not describe the reality “second after second.” As has been demonstrated in numerous academic studies, HTC varies considerably during the process in a manner which cannot be put into equation; the straight lines in Figure 2 are oversimplifications which cannot be practically avoided.

This simple way of determining “effective” HTCs should be done in the foundry using filling and solidification modeling to design permanent mold gating/risering systems. These custom “effective” HTCs are bound to produce predictions closer to reality than values determined in a laboratory, under conditions which by no means resemble what takes place in reality. The exercise should be repeated several times on the same casting to assess its repeatability (or lack of); this will gage the degree of confidence one may attribute to the result of modeling. This uncertainty highlights the elusive nature of modeling in permanent mold, because of the mold coating variability on initial application and during the casting campaign. but also because of additional simplifying assumptions such as neglecting the heat losses to the attachments of the mold to the casting machine and the temperature losses in the liquid during tilt-pouring. 

The modeler should be particularly aware of these limitations, keeping in mind that the result of modeling is a representation “close to the reality,” never the reality. This should bring about the necessary caution when interpreting the results of a simulation.

The knowledge of HTCfill , value of HTC during filling, is particularly important for predicting misruns or cold shuts. It must be borne in mind that the numerical CFD solution of the filling problem implies hypotheses which are particular to each code, i.e. to each commercial software; therefore, the predicted filling will never be the same for two different codes, which is not the case in the absence of turbulent fluid flow. The consequence is that HTCfill will depend on the software used, which is not an issue if the same software is used to design the mold. 

HTCs In Different Foundries Are ‘All Over the Place’

The mold-casting heat transfer coefficient during filling HTCfill was found equal to 550 W.m-2 °C-1 while HTCstatic = 1150 W.m-2 °C-1 between the end of filling and full solidification. The reproducibility of these results is not expected to be particularly good; this is why, after carrying several runs, it was found appropriate to have results rounded to multiples of 50 Wm-2C-1. Figure 8 shows the value of HTC determined in 6 foundries with widely different mold coating practice; the coatings being proprietary or originating two suppliers, the applied thickness varying from less than 10µm to over 200µm. Our values (coating 52µm thick) fall within the spread of the displayed results (AFS Transactions 97-68).