Thin-walled turbine wheels are among the most demanding investment castings in a turbocharger. They must survive exhaust temperatures above 850 °C, rotational speeds of roughly \(6\times10^{4}\) to \(12\times10^{4}\) r/min, and service lives of \(10^{3}\) to \(10^{4}\) h. Reducing blade thickness improves transient response and aerodynamic efficiency, but it also narrows the casting window: the same thin sections that reduce inertia are prone to misruns, cold shuts, and hot tears during solidification. For a 0.548 kg Inconel 713C turbine with a 0.6 mm blade-tip wall, the manufacturing problem is therefore not simply one of filling a mold. It is one of controlling heat extraction, interfacial heat transfer, and solidification sequence closely enough that thin blades fill completely while heavy hubs remain sound.
Process envelope and alloy selection
The turbine consists of ten curved blades and a central disc, with a maximum envelope of 86 mm and a height of 60.8 mm. The blade wall tapers from the root toward the tip, reaching a minimum of 0.6 mm. The alloy is Inconel 713C, a cast nickel-base superalloy selected for high-temperature strength, creep resistance, and oxidation resistance in exhaust service. Its specified composition is summarized in Table 1.
Table 1. Nominal composition of the Inconel 713C alloy used for the turbine casting (wt.%).
| Element | C | Si | Mn | Al | Co | Cr | Fe | Mo | Nb+Ta | Ti | Zr | Ni |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Content | 0.12 | 0.4 | 0.23 | 6.0 | ≤1.0 | 13.0 | ≤1.8 | 4.2 | 2.3 | 0.6 | 0.1 | Balance |
Investment casting was chosen because it provides near-net-shape geometry, smooth surfaces, and dimensional tolerances in the CT4–CT8 range, with a tolerance band of roughly 0.4–1.6 mm for this envelope. As-cast surface roughness was specified at \(Ra\) 6.3–3.2 μm, improving to \(Ra\) 1.6–0.8 μm after finishing. A minimum wall thickness of 0.6 mm is acceptable for a 50–100 mm superalloy investment casting because sharp or locally thin features may be 30–50% thinner than the general minimum. The design also used fillets of 1–4 mm at section transitions and a 2 mm internal fillet at the blade root and hub blends to reduce hot spots and stress concentration.
The pattern tooling was built around a rotating-disc die with inner and outer sliding blocks. These blocks formed the curved blade cavities, while the rotating disc opened and closed the die. Ejection was assisted by air through the die body, avoiding manual extraction of the thin blade pattern. The wax pattern used a filled formulation containing 20 wt.% rosin, 20 wt.% vinyltoluene–α-methylstyrene, 24 wt.% paraffin, 16 wt.% carnauba wax, and 20 wt.% pentaerythritol. The solid filler was intended to reduce wax shrinkage and preserve the 0.6 mm tip edges during shell building. The ceramic shell consisted of one zircon face coat and five silica–mullite backup layers, a construction chosen for adequate strength during dewaxing, preheating, and pouring.
Gating design and the shift from a four-part stack to a three-part cluster
The first gating concept used a central sprue with direct ingates feeding the turbine hub. Four turbines were assembled on one sprue, with metal entering the shaft region and feeding the parts through 19 mm diameter ingates. The sprue was 250 mm long and 22 mm in diameter, with a flared 50 mm pouring cup and a sprue well to reduce jetting. The design was intended to provide a short feed path into the heavy hub while keeping the gating ratio sufficient for shrinkage feeding.
Filling and solidification simulations revealed a practical weakness in that layout. Metal accelerated to about 1.818 m/s in the sprue and slowed to about 0.227 m/s after the sprue well. The lower pair of turbines filled first, followed by the upper pair, and filling of the four-part assembly was completed at about 6.24 s. Although the simulation did not show severe gas entrapment, the long sprue produced a high metallostatic head and a strong impact on the shell. More importantly, the vertical stacking created a systematic filling and cooling difference between lower and upper parts. The last-fed regions were the sprue and the turbine shaft, where shrinkage porosity concentrated. The process yield was only 57.1%.
The revised design changed both the thermal geometry and the filling direction. A top-poured cluster of three turbines was adopted, with each turbine axis set at 130° to the centerline of the sprue. A sprue well was retained to buffer the initial metal stream. In simulation, the modified layout reduced the filling velocity to about 1.009 m/s, roughly 0.8 m/s lower than the original design, and produced a more uniform front through the blade cavities. The solidification sequence ran from the thin blades toward the hub and finally into the sprue, so that the sprue continued to feed the hub during contraction. Predicted shrinkage porosity in the turbine body was eliminated, and the process yield increased to 72.9%. Table 2 summarizes the comparison.
Table 2. Comparison of the initial and revised investment-casting gating designs for the Inconel 713C turbine.
| Feature | Initial design | Revised design |
|---|---|---|
| Module arrangement | Four turbines stacked along a 250 mm central sprue | Three turbines around a top-poured sprue; turbine axis at 130° to sprue centerline |
| Filling behavior | Peak velocity about 1.818 m/s; lower parts filled before upper parts | Filling velocity about 1.009 m/s; more uniform front and reduced turbulence |
| Solidification and feeding | Blades froze toward hub; shrinkage concentrated in shaft and sprue | Sequential freezing from blade to hub to sprue; turbine-body shrinkage eliminated in simulation |
| Part-to-part consistency | Lower and upper castings experienced different fill and cooling histories | More uniform thermal history among the three castings |
| Process yield | 57.1% | 72.9% |
The baseline casting simulation used a pouring temperature of 1550 °C, a shell preheat of 850 °C, a filling rate of 0.6338 kg/s, and an assumed constant casting–shell interfacial heat-transfer coefficient of 2000 W m\(^{-2}\) K\(^{-1}\). Those assumptions were adequate for comparing gating layouts, but not for predicting thin-blade misruns with high confidence. The next step was therefore to replace the assumed thermal boundary conditions with measured and inversely determined values.
Thermophysical properties and interfacial heat transfer
The accuracy of a casting simulation depends strongly on the temperature-dependent properties of both the alloy and the shell, and on the heat-transfer coefficient at their interface. Differential scanning calorimetry in argon at 10 °C/min, using a 111.3 mg sample, gave a solidus of 1300 °C and a liquidus of 1328 °C. A Scheil solidification calculation for the same composition gave a lower solidus near 1180 °C and a liquidus near 1340 °C. The difference is consistent with the assumptions of the Scheil model, which neglects back diffusion in the solid, and with undercooling in the small DSC sample. For simulation, the measured solidus and a liquidus in the 1328–1340 °C range were used rather than the unadjusted Scheil values.
Specific heat and thermal conductivity were measured by the laser-flash method at 25, 800, and 1000 °C. The measured specific heat was higher than the Scheil-calculated value, while the measured thermal conductivity was lower. Because the Scheil model becomes less reliable below the solidus, measured values were used up to 1000 °C and calculated values were used above that range. The room-temperature density of the alloy was \(7.915\times10^{3}\) kg m\(^{-3}\). For the shell, the transient plane-source method gave a room-temperature density of \(2.49\times10^{3}\) kg m\(^{-3}\). The measured shell conductivity decreased with increasing temperature, a trend consistent with moisture loss and pore expansion in a porous refractory body.
The interfacial heat-transfer coefficient is defined as
$$h=\frac{q}{A\,(T_{\mathrm{cast}}-T_{\mathrm{mold}})},$$
where \(q\) is the heat flow, \(A\) is the heat-transfer area, and \(T_{\mathrm{cast}}\) and \(T_{\mathrm{mold}}\) are the local casting and mold temperatures. This coefficient is not a fixed material constant. During solidification, the casting contracts and the shell expands, opening a gap that changes from intimate contact to partial contact and finally to radiation- and convection-dominated heat transfer. Direct measurement of the transient heat flux is difficult, so \(h\) was determined by the Beck nonlinear inverse method. A B-type platinum–rhodium thermocouple was embedded 2 mm from the casting–shell interface at the turbine bottom, and the measured cooling curve was used to drive the inverse calculation. The objective function minimized the difference between measured and computed temperatures:
$$S(h)=\sum_{i=1}^{N_t}\sum_{j=1}^{N_m}\frac{\left[T_{ij}^{m}-T_{ij}^{c}(h)\right]^2}{\sigma_T^2}+\sum_{k=1}^{N_h}\frac{\left(h_k-h_k^0\right)^2}{\sigma_k^2}.$$
Here \(T_{ij}^{m}\) is the measured temperature at point \(j\) and time \(i\), \(T_{ij}^{c}(h)\) is the corresponding computed temperature, \(h_k^0\) is the initial estimate of the interfacial coefficient, and the \(\sigma\) terms weight the measurement and parameter uncertainties. The inverse solution gave the temperature-dependent coefficients listed in Table 3.
Table 3. Inversely determined casting–shell interfacial heat-transfer coefficient for Inconel 713C investment casting.
| Temperature (°C) | Interfacial heat-transfer coefficient (W m\(^{-2}\) K\(^{-1}\)) |
|---|---|
| 1545 | 1050 |
| 1340 | 1000 |
| 1300 | 275 |
| 200 | 62 |
The temperature dependence follows the expected contact–gap transition. Between 1545 and 1340 °C, the liquid metal and shell remain in close contact and conduction dominates, so \(h\) is high, about 1000–1050 W m\(^{-2}\) K\(^{-1}\). Between 1340 and 1300 °C, a solidifying skin forms, the casting begins to contract, and the shell expands; the interface becomes partial contact and \(h\) falls sharply to about 275 W m\(^{-2}\) K\(^{-1}\). Below 1300 °C, the gap widens and radiation and air convection control heat transfer, so \(h\) continues to decrease with temperature, reaching about 62 W m\(^{-2}\) K\(^{-1}\) at 200 °C.
Validation against instrumented casting trials
The measured properties and inverse \(h\) were returned to the material database, and the same casting geometry was simulated again. At the turbine-bottom thermocouple location, the original database inputs produced a poor match: the minimum temperature difference was 28 °C, the maximum was 194 °C, and the mean difference was 106.65 °C. With the measured thermophysical properties and the inversely determined interfacial coefficient, the minimum difference fell to 2 °C, the maximum to 6 °C, and the mean to 5.67 °C. Table 4 summarizes the comparison.
Table 4. Measured versus simulated temperature at the turbine-bottom location for two input-property sets.
| Simulation input set | Minimum ΔT (°C) | Maximum ΔT (°C) | Mean ΔT (°C) |
|---|---|---|---|
| Initial database properties and constant \(h=2000\) W m\(^{-2}\) K\(^{-1}\) | 28 | 194 | 106.65 |
| Measured properties and inverse temperature-dependent \(h\) | 2 | 6 | 5.67 |
The improvement was not limited to the thermocouple trace. The original input set predicted a complete blade profile with no filling defect. The revised simulation predicted a local misrun at the blade tip, and the actual trial casting showed a corresponding unfilled region at the same location. This agreement is more meaningful than a good temperature match alone because it shows that the coupled thermal boundary conditions were accurate enough to reproduce a thin-section filling failure.
Misrun and hot-tearing mechanisms
The predicted misrun occurred in blade cavities located near the top of the cluster. Two representative nodes, A and B, were examined in the filling simulation. Their maximum flow velocities were \(6.76\times10^{-2}\) and \(2.72\times10^{-2}\) m s\(^{-1}\), respectively, and flow at those locations was essentially confined to the interval from 4.08 to 4.26 s. At 4.26 s, the temperatures at nodes A and B were 1300 and 1297 °C. For this alloy, a solid fraction of 0.7 corresponds to about 1305 °C, and once the solid fraction exceeds roughly 0.7, the mush loses practical flowability. Both nodes were therefore below the flow-arrest threshold when the local driving pressure was still required to complete the tip. The interface coefficient was also in its steep transition region, so heat loss to the shell was high. With no downstream superheated metal available to replenish the tip, the cavity stopped filling.
Two additional factors reinforced the effect. The affected blades sat near the top of the module, where the metallostatic head was lower. The thin blade section also increased viscous resistance as the metal cooled, while the high surface-to-volume ratio accelerated heat loss. The result was a self-reinforcing sequence: cooling raised viscosity, viscosity reduced the local flow rate, and the reduced flow rate allowed further cooling before the tip could be filled.
Hot tearing followed a different but related thermal path. The stress simulation used a thermal-elastic–plastic formulation in which the material behaves elastically below yield and plastically above yield, with yield strength and elastic modulus falling toward zero near the melting point. The computed effective stress concentrated at the blade tip and at regions of high blade curvature, then shifted toward the root as solidification progressed. The peak effective stress at the tip was \(3.69\times10^{-2}\) MPa. Although this absolute value is small compared with the elevated-temperature strength of the alloy, the spatial concentration and evolution of the stress field were used as a hot-tear indicator rather than the magnitude alone.
The actual trial castings showed short, tortuous cracks at the lower part of the blades in regions of large curvature. The crack openings were wider at the outer surface and narrower toward the interior, and the fracture surfaces were dark gray and oxidized, which is characteristic of hot tearing. Fluorescent penetrant inspection also revealed fine indications about 2 mm long that were invisible to the unaided eye. These locations coincided with the predicted stress-concentration zones. The mechanism is consistent with constrained contraction: the thin tip, the heavier root, and the massive hub cool at different rates, and because they remain part of one rigid casting, the resulting tensile stress must be accommodated by local plastic strain. When the mushy region exhausts its ductility, a hot tear forms.
Process window and production implications
The two dominant defects respond differently to pouring temperature and shell preheat. A higher pouring temperature improves fill and delays flow arrest, while a higher shell preheat reduces the thermal gradient between metal and mold and lowers the driving force for hot tearing. To identify a practical window, a two-factor, three-level simulation matrix was evaluated: pouring temperatures of 1450, 1500, and 1550 °C, and shell preheats of 800, 850, and 900 °C. The results are given in Table 5.
Table 5. Simulated filling, shrinkage, and stress response of the turbine casting over the pouring-temperature and shell-preheat window.
| Pouring temperature (°C) | Shell preheat (°C) | Misrun in fraction-solid result | Total porosity (cm³) | Maximum effective stress (\(10^{-2}\) MPa) |
|---|---|---|---|---|
| 1450 | 800 | Yes | 1.380 | 3.85 |
| 1450 | 850 | Yes | 1.223 | 3.69 |
| 1450 | 900 | Yes | 1.031 | 3.55 |
| 1500 | 800 | No | 1.452 | 5.77 |
| 1500 | 850 | No | 1.443 | 5.83 |
| 1500 | 900 | No | 1.392 | 5.35 |
| 1550 | 800 | No | 1.153 | 2.92 |
| 1550 | 850 | No | 1.002 | 2.67 |
| 1550 | 900 | No | 1.000 | 2.22 |
At 1450 °C, the casting remained incomplete at all three shell preheats, even though the lower thermal gradient gave relatively low effective stress. At 1500 °C and above, the blades filled completely. The shrinkage porosity in all nine cases remained concentrated in the sprue, which is the last region to solidify, and the total porosity varied only modestly. At a fixed pouring temperature, increasing the shell preheat reduced the total porosity. The best overall combination was 1550 °C pouring temperature with 900 °C shell preheat: no misrun, the lowest porosity in the matrix at 1.000 cm³, and the lowest maximum effective stress at \(2.22\times10^{-2}\) MPa.
For production, the result supports a window centered on 1550 °C pouring and 900 °C shell preheat for this thin-walled Inconel 713C turbine. The pouring temperature is roughly 210–220 °C above the liquidus, which is high enough to maintain flow through the 0.6 mm tip but also high enough to warrant attention to grain coarsening and shell stability. The shell preheat must therefore be controlled as carefully as the pouring temperature: it is not merely a filling aid, but a variable that changes the thermal gradient that drives hot tearing.
The broader process chain also matters. The shell must retain strength through dewaxing and preheating, the vacuum induction remelting step must deliver consistent superheat, and the castings must be cleaned and inspected after shot blasting and gate removal. Fluorescent penetrant inspection is particularly important for this geometry because hot tears and incomplete fusion at the blade tip can be too small to detect visually. The combination of a three-part cluster, a 130° turbine-to-sprue orientation, measured thermophysical properties, and an inverse interfacial heat-transfer coefficient provides a more reliable basis for setting that process window than a constant-\(h\) simulation or a purely trial-and-error gating revision.
The remaining data gap is the high-temperature property range. Specific heat and thermal conductivity were measured only to 1000 °C, and the liquid properties were represented using calculated values. Induction melting of the master alloy was also modeled as a thermal problem rather than a coupled electromagnetic–thermal problem, which limits the fidelity of the initial melt temperature field. Extending the property database above 1000 °C and coupling the induction field to the thermal solution would further improve the prediction of filling and hot tearing in thin-walled nickel-base investment castings.