Metal–shell heat transfer from a thermocouple – and the model finds the misrun at the blade tips

The turbine wheel of an automotive turbocharger is a typical critical nickel-alloy casting: a heavy hub, thin blades, an equiaxed structure, vacuum melting, a ceramic shell. Wheel blades are getting thinner for aerodynamics, and with that the chance of a misrun grows, and scrap with it.

A group from Jiangsu University and the engineering company Wuxi Vane Wheel Engineering set out to find why their ProCAST model did not see that misrun. The answer lay in the boundary condition between metal and mould – the heat transfer coefficient h. It is usually taken from the literature and set as one number for the whole process. The authors measured it: they put a thermocouple in the mould, recovered h from the temperature record and recomputed the pour.

How the trial was set up

The wheels are cast in Inconel 713C, a γ′-strengthened nickel alloy, by remelting cut master-alloy bars in a single-chamber vacuum induction furnace. Melting and pouring happen in one cycle: the crucible is bonded to the wax cluster before shelling and becomes part of the mould. Part of the bar sits inside the induction coil and part outside it. Three ingates run from the crucible to three wheels.

The shell has six coats: a face coat of zircon slurry (ZrSiO₄ + SiO₂) with zircon sand stucco and five backup coats of silica slurry with mullite. In the model it is 6 mm thick.

The thermocouple is led through a hole in the shell into the hub of one wheel; the junction sits in the metal, 2 mm from the mould interface. It is a type B thermocouple: platinum–rhodium wires in a twin-bore alumina tube, the junction welded with an oxy-hydrogen torch, the rest of the length protected by ceramic beads. A QuadTemp logger records the temperature once a second.

What the thermocouple recorded

The record starts when the mould leaves the preheating furnace at 1010 °C. During transfer the mould cools by about 6 °C per second, under vacuum before pouring by 2 °C per second, and at pouring it is at 850 °C. At pouring the thermocouple reads 1545 °C. Then the metal cools by about 4 °C per second, releases its latent heat between 1330 and 1300 °C and afterwards cools steadily at about 1 °C per second.

Alloy and shell properties

Before fitting h, the authors measured what is usually also taken from a database. The alloy solidus and liquidus by differential scanning calorimetry (NETZSCH STA 449F3, 25 to 1500 °C). The alloy specific heat and conductivity by laser flash (NETZSCH LFA 427), the shell conductivity by the transient plane source method (Hot Disk TPS 2500S), at 25, 800 and 1000 °C. At room temperature the alloy density is 7,915 kg/m³ and the shell density 2,490 kg/m³.

Calorimetry gave a solidus of 1300 °C and a liquidus of 1328 °C, a Scheil calculation 1180 and 1340 °C. The authors put the gap down to the small sample (111.3 mg) and the 10 °C/min rate, at which undercooling lowers the liquidus, and to the Scheil model with no diffusion in the solid underestimating the solidus. The model received the calorimetric solidus and the Scheil liquidus – 1300 and 1340 °C. One detail does not add up: the curve in Fig. 4 is a heating curve, while undercooling happens on cooling. And the liquidus was read at the top of the melting peak, which usually lies below the end of melting. The final 1340 °C is unaffected, but it shows how easy it is to be ten degrees off when reading a liquidus from calorimetry.

For the alloy, the calculated specific heat came out below the measured one and the calculated conductivity above it. Below 1000 °C the model received the measured values, above it the calculated ones.

On heating, the shell conducts heat half as well: 0.83 W/(m·K) at 25 °C and 0.39 at 1000 °C. The authors put this down to porosity: at room temperature the shell holds moisture, which leaves on heating, and the pores expand. The specific heat behaves oddly – 0.743, 1.277 and 0.27 kJ/(kg·K) at 25, 800 and 1000 °C. The almost fivefold drop between 800 and 1000 °C is worth rechecking before such values go into your own model.

What went into the model

1300°Csolidus from calorimetry

1340°Cliquidus from a Scheil calculation

850°Cshell at the moment of pouring

1545°Cmetal in the hub at pouring

The heat transfer coefficient

Next came the inverse problem, by Beck's nonlinear estimation method: the model adjusts h until its curve matches the recorded one. In ProCAST this is the inverse module. The starting value of 2,000 W/(m²·K) came from a 2011 study by Dong et al. on single-crystal blades. The mesh was 4 mm. At the start the metal inside the coil was at 1545 °C, outside the coil at 1310 °C, between solidus and liquidus. The mould was at 850 °C.

Measured heat transfer coefficient

1,050W/(m²·K)at 1545 °C

1,000W/(m²·K)at 1340 °C

275W/(m²·K)at 1300 °C

62W/(m²·K)at 200 °C

The authors split the curve into three stages. While the metal is liquid, from 1545 to 1340 °C, it is pressed against the shell, heat flows by conduction, the resistance is low and h is high. Between 1340 and 1300 °C the casting forms a skin and shrinks, the mould expands as it heats, and a gap opens in places – h drops sharply. Below 1300 °C the skin thickens, the gap becomes continuous, heat leaves by radiation and through the gas in the gap, and h falls with temperature. The result is on the cover of this entry: even at pouring the measured h is almost half the 2,000 the model started from.

What changed in the model

In the hub the model with h = 2,000 differed from the thermocouple by 28 to 194 °C, 106.65 °C on average: the metal in it cooled noticeably faster than in reality. With the fitted h the difference is 2 to 6 °C, 5.67 °C on average.

The model fills the mould like this. For the first three seconds the liquid metal in the coil heats the still unmelted part of the bar. In the fourth second the metal runs through the ingates into the hubs and rises quickly. By the fifth second the mould is full, and the wheel solidifies in sequence, from the blade tips toward the shaft. The blade tips fill last and are the first to start freezing – that is where a misrun is most likely.

The model with h = 2,000 showed a whole wheel. The model with measured h put a misrun at the tips of two blades – where the cast wheel had it.

What follows

The coefficient was fitted and checked on the same thermocouple, so 5.67 °C is the quality of the fit, not an independent check. The paper has one independent check – the misrun location – and it carries more weight than any number: the model with measured h saw a defect that the model with a literature value did not.

There is one thermocouple, and it sits in the hub – the thickest section. In a thin blade the skin and gap form earlier, and h there may differ. For the blade tips, where the casting's fate is decided, the coefficient is carried over from the hub.

The paper leaves one question open. With h = 2,000 the metal loses heat faster – in Fig. 9 that model curve does run below the measurement – so you would rather expect the misrun in that run. It came out the other way. By the description of the method the two runs differ only in the coefficient, and the solid-fraction pictures give no time stamp. The authors do not explain this. When repeating the approach, compare the misrun in both runs and at the same moments.

The h values themselves apply to equiaxed casting of Inconel 713C into a zircon–silica shell preheated to 850 °C. For another shell and another mould temperature they have to be measured again, and for directional solidification in a Bridgman furnace all the more so. What carries over is the method: a thermocouple in the mould, an inverse problem in the same software as the main model, and a check against a real defect.