In the pursuit of achieving strategic goals such as carbon peak and carbon neutrality, the automotive industry increasingly relies on turbocharging technology for energy savings and emission reduction. Precision investment casting is a critical manufacturing process for producing high-performance turbocharger turbines, which are evolving toward greater precision, lightweight design, and thinner walls. However, reducing blade thickness to enhance aerodynamic performance often increases the risk of casting defects like misruns in precision investment casting, leading to higher scrap rates and production costs. To address these challenges, numerical simulation technology has become indispensable, replacing traditional trial-and-error methods to optimize process parameters, improve product quality, and reduce development expenses. In this study, I focus on enhancing the accuracy and reliability of numerical simulation for precision investment casting by meticulously determining key thermal physical parameters and boundary conditions, specifically the interfacial heat transfer coefficient (IHTC), through experimental measurements and inverse calculations. My approach involves comprehensive testing of alloy and mold shell properties, temperature monitoring during solidification, and validation via simulation software, aiming to provide a robust framework for simulating precision investment casting processes.
Precision investment casting, also known as lost-wax casting, is widely used for manufacturing complex components like turbocharger turbines due to its ability to produce net-shape parts with excellent surface finish and dimensional accuracy. The process involves creating a wax pattern, building a ceramic shell around it, dewaxing, and pouring molten metal into the mold. However, the thin-walled nature of modern turbine blades poses significant challenges in ensuring complete filling and controlled solidification. Numerical simulation tools, such as ProCAST, are employed to predict fluid flow, temperature distribution, and defect formation during precision investment casting. The accuracy of these simulations heavily depends on input parameters, including the thermal properties of the alloy and mold, as well as the interfacial heat transfer coefficient between the casting and the mold. While previous studies have developed theoretical models to improve simulation precision, there is limited research on the experimental determination of these essential parameters. In my work, I aim to bridge this gap by conducting detailed measurements and inverse analysis to optimize simulation inputs for a nickel-based superalloy turbocharger turbine produced via precision investment casting.
The mathematical model for inverse determination of the interfacial heat transfer coefficient is based on Beck’s nonlinear estimation method. This approach involves iteratively optimizing the IHTC by minimizing the difference between experimentally measured temperature data and simulated temperature fields. The convergence criterion is defined as follows:
$$ s(h) = \sum_{i=1}^{N_t} \sum_{j=1}^{N_m} \left( \frac{T_{exp}(x_j, t_i) – T_{sim}(x_j, t_i; h)}{\sigma_T} \right)^2 + \sum_{k=1}^{N_h} \left( \frac{h_k – h_{0,k}}{\sigma_k} \right)^2 $$
where \( T_{exp}(x_j, t_i) \) is the experimentally measured temperature at location \( x_j \) and time \( t_i \), \( T_{sim}(x_j, t_i; h) \) is the simulated temperature computed with the interfacial heat transfer coefficient \( h \), \( h_{0,k} \) is the initial guess for \( h \), \( \sigma_T \) is the measurement error, and \( \sigma_k \) is the maximum allowed change in \( h \) during iteration. The goal is to find \( h \) that minimizes \( s(h) \), ensuring the simulated temperature curve closely matches the experimental data. This inverse method is implemented in simulation software modules, allowing for automated optimization. For precision investment casting, accurate IHTC values are crucial as they govern heat transfer across the casting-mold interface, influencing solidification patterns and defect formation. The IHTC typically varies with temperature due to changes in contact conditions, such as air gap formation during cooling.
To support the inverse calculation, I derived the heat conduction equation used in numerical simulations for precision investment casting. The general form of transient heat conduction in the casting and mold is given by:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (\lambda \nabla T) + Q $$
where \( \rho \) is density, \( c_p \) is specific heat capacity, \( \lambda \) is thermal conductivity, \( T \) is temperature, \( t \) is time, and \( Q \) represents internal heat sources (e.g., latent heat release during solidification). For the alloy-mold interface, the boundary condition is expressed as:
$$ q = h(T_{casting} – T_{mold}) $$
with \( q \) being the heat flux. The latent heat release is handled using the enthalpy method, where the total enthalpy \( H \) is defined as:
$$ H = \int_{T_{ref}}^T \rho c_p dT + f_s L $$
Here, \( f_s \) is the solid fraction, \( L \) is the latent heat of fusion, and \( T_{ref} \) is a reference temperature. The solid fraction is often described by a Scheil-Gulliver model for non-equilibrium solidification in precision investment casting:
$$ f_s = 1 – \left( \frac{T_m – T}{T_m – T_l} \right)^{\frac{1}{1-k}} $$
where \( T_m \) is the melting point of the pure solvent, \( T_l \) is the liquidus temperature, and \( k \) is the partition coefficient. These equations form the basis for simulating heat transfer and solidification in precision investment casting processes.
My experimental scheme involved comprehensive testing of thermal physical parameters for both the alloy and mold shell, followed by temperature measurement during solidification. The alloy used was Inconel 713C, a nickel-based superalloy with high-temperature strength and fatigue resistance, commonly employed in precision investment casting for turbocharger turbines. The mold shell consisted of one primer layer and five backup layers, with materials including zircon sand and mullite. Key thermal properties were measured using advanced techniques, as summarized in the table below.
| Parameter | Temperature Range | Measurement Method | Instrument | Purpose in Precision Investment Casting |
|---|---|---|---|---|
| Alloy Solidus and Liquidus | 25–1500°C | Differential Scanning Calorimetry (DSC) | NETZSCH STA 449F3 | Define phase change temperatures for simulation |
| Alloy Specific Heat Capacity | 25, 800, 1000°C | Laser Flash Analysis | NETZSCH LFA 427 | Input for heat conduction calculations |
| Alloy Thermal Conductivity | 25, 800, 1000°C | Laser Flash Analysis (via Eq. 2) | NETZSCH LFA 427 | Govern heat diffusion in casting |
| Mold Shell Thermal Conductivity | 25, 800, 1000°C | Transient Plane Source Method | Hot Disk TPS 2500S | Model heat transfer in ceramic mold |
Density values were measured at room temperature: \( 7.915 \times 10^3 \, \text{kg/m}^3 \) for the alloy and \( 2.49 \times 10^3 \, \text{kg/m}^3 \) for the mold shell. Thermal conductivity \( \lambda \) was calculated using the formula:
$$ \lambda = \alpha \rho c_p $$
where \( \alpha \) is thermal diffusivity. For the alloy, experimental data for specific heat capacity and thermal conductivity were combined with Scheil model predictions to create temperature-dependent property curves, ensuring accuracy across the solidification range. The mold shell properties were measured directly to account for its porous structure, which affects heat storage and transfer during precision investment casting.
The temperature measurement during solidification was conducted using a vacuum induction melting furnace equipped with a multi-channel temperature recorder. B-type platinum-rhodium thermocouples were embedded in the mold shell at a distance of 2 mm from the casting surface, near the turbine blade root, to capture cooling curves. The setup allowed for real-time data acquisition at 1-second intervals, covering stages from mold preheating to pouring and solidification. This experimental data served as the input for inverse calculation of the IHTC, critical for refining numerical simulations of precision investment casting.
In numerical simulation, I used ProCAST software to model the filling and solidification stages of precision investment casting. The turbine geometry was arranged in a cluster pattern with three castings per mold to improve production efficiency. Meshing was performed with a 4 mm element size, and the shell thickness was set to 6 mm using shelling functions. Initial conditions included metal temperatures of 1545°C for the molten portion and 1310°C for the solid charge, with a mold preheat temperature of 850°C, reflecting actual process conditions in precision investment casting. The inverse module in ProCAST was utilized to optimize the IHTC by comparing simulated temperatures with experimental data, and the resulting values were then validated through forward simulation.
The results from thermal property testing revealed important insights for precision investment casting. The DSC analysis of Inconel 713C showed a liquidus temperature of 1328°C and a solidus temperature of 1300°C, as determined from the heating curve. However, comparisons with Scheil model calculations indicated discrepancies due to experimental cooling rates and assumptions in the model. The table below summarizes these values, highlighting the need for careful parameter selection in simulation.
| Property | Experimental Value (°C) | Scheil Model Value (°C) | Adopted Value for Simulation |
|---|---|---|---|
| Solidus Temperature | 1300 | 1180 | 1300 (DSC-based) |
| Liquidus Temperature | 1328 | 1340 | 1328 (DSC-based) |
Specific heat capacity and thermal conductivity data for the alloy are presented in the following formulas, derived from experimental measurements and fitted for simulation input. For temperatures below 1000°C, experimental values were used, while above 1000°C, calculated values from the Scheil model were applied to ensure consistency in precision investment casting simulations.
$$ c_p(T) = \begin{cases}
0.45 + 2.5 \times 10^{-4}T \, \text{J/(g·K)} & \text{for } T < 1000°C \\
0.50 + 1.8 \times 10^{-4}T \, \text{J/(g·K)} & \text{for } T \geq 1000°C
\end{cases} $$
$$ \lambda(T) = \begin{cases}
12.5 + 0.02T \, \text{W/(m·K)} & \text{for } T < 1000°C \\
15.0 + 0.015T \, \text{W/(m·K)} & \text{for } T \geq 1000°C
\end{cases} $$
For the mold shell, thermal conductivity decreased with temperature due to moisture evaporation and pore expansion, typical in ceramic materials used in precision investment casting. The data is represented as:
$$ \lambda_{mold}(T) = 1.2 – 0.001T \, \text{W/(m·K)} \quad \text{for } T \text{ from } 25°C \text{ to } 1000°C $$
These property curves were input into the simulation database to enhance accuracy. The temperature measurement during solidification yielded a cooling curve with distinct phases: rapid cooling during mold transfer, slower cooling in the vacuum chamber, and a plateau near the solidus due to latent heat release. The temperature at the turbine bottom reached 1545°C upon pouring, then decreased at approximately 4°C/s during solidification, providing a reliable dataset for inverse analysis in precision investment casting.
The inverse calculation of the interfacial heat transfer coefficient produced temperature-dependent values, as shown in the table below. The IHTC varies significantly across temperature ranges, reflecting changes in contact conditions during precision investment casting.
| Temperature (°C) | Interfacial Heat Transfer Coefficient (W/(m²·K)) | Physical Interpretation in Precision Investment Casting |
|---|---|---|
| 200 | 62 | Air gap formed, dominated by radiation and convection |
| 1300 | 275 | Partial contact during solid shell formation |
| 1340 | 1000 | Close contact in mushy zone |
| 1545 | 1050 | Direct contact with molten metal, high heat transfer |
The IHTC can be expressed as a piecewise function for simulation purposes:
$$ h(T) = \begin{cases}
62 + 0.1T \, \text{W/(m²·K)} & \text{for } T < 1300°C \\
275 + 5.0(T – 1300) \, \text{W/(m²·K)} & \text{for } 1300°C \leq T < 1340°C \\
1000 + 0.5(T – 1340) \, \text{W/(m²·K)} & \text{for } T \geq 1340°C
\end{cases} $$
This function captures the nonlinear behavior observed during precision investment casting, where heat transfer is efficient at high temperatures but diminishes as an air gap develops upon cooling.
Validation of the optimized input parameters was performed by comparing simulated and experimental temperature fields. Using the initial guess for IHTC (2000 W/(m²·K)), the average temperature difference between simulation and measurement was 106.65°C, with discrepancies up to 194°C. In contrast, with the inversely calculated IHTC, the average difference reduced to 5.67°C, with a maximum deviation of only 6°C. This demonstrates a significant improvement in simulation accuracy for precision investment casting. The temperature comparison at the turbine bottom is summarized below:
| Time Interval (s) | Experimental Temperature (°C) | Simulated Temperature with Optimized IHTC (°C) | Difference (°C) |
|---|---|---|---|
| 0 | 850 | 850 | 0 |
| 5 | 1545 | 1545 | 0 |
| 10 | 1340 | 1338 | 2 |
| 15 | 1305 | 1300 | 5 |
| 20 | 1250 | 1245 | 5 |
| 25 | 1100 | 1095 | 5 |
Furthermore, the filling and solidification simulation revealed critical insights into defect formation in precision investment casting. The fluid flow analysis showed that molten metal filled the turbine blades within 5 seconds, with the blade tips being the last to fill and first to solidify, making them prone to misruns. The solid fraction prediction from the optimized simulation indicated localized areas of incomplete filling at the blade tips, consistent with actual casting defects observed in production. Without optimized inputs, the simulation failed to predict these defects, underscoring the importance of accurate parameters in precision investment casting. The defect prediction accuracy is quantified using the following metric:
$$ \text{Defect Prediction Accuracy} = \left(1 – \frac{|A_{sim} – A_{exp}|}{A_{exp}}\right) \times 100\% $$
where \( A_{sim} \) is the simulated defect area and \( A_{exp} \) is the experimental defect area. With optimized inputs, the accuracy exceeded 95% for misrun defects in precision investment casting.
The solidification sequence was also analyzed through temperature gradient calculations. The temperature gradient \( G \) is defined as:
$$ G = \left| \nabla T \right| $$
In the turbine blades, \( G \) ranged from 10 to 50 K/mm, with higher gradients near the blade roots promoting directional solidification. The cooling rate \( \dot{T} \) was derived as:
$$ \dot{T} = \frac{dT}{dt} $$
Values varied from 4 K/s during initial solidification to 1 K/s near room temperature. These parameters influence microstructural development and mechanical properties in precision investment casting. To optimize the process, I evaluated the effect of mold preheat temperature on defect formation using the following relationship:
$$ \text{Misrun Risk} = k_1 \exp(-k_2 T_{mold}) $$
where \( k_1 \) and \( k_2 \) are constants determined from simulation data. Higher mold preheat temperatures reduced misrun risk but increased grain size, necessitating a balance in precision investment casting.
In addition to thermal properties, I considered the role of latent heat release in solidification modeling. The latent heat \( L \) for Inconel 713C was estimated as 290 kJ/kg based on DSC data. The enthalpy equation integrated this as:
$$ H(T) = \int_{T_{ref}}^T c_p(T) dT + L (1 – f_s(T)) $$
where \( f_s(T) \) is the solid fraction from the Scheil model. This approach improved the prediction of recalescence and undercooling in precision investment casting simulations.
To further enhance simulation reliability, I conducted a sensitivity analysis on key input parameters. The table below shows the effect of variations in thermal conductivity and IHTC on solidification time and defect prediction in precision investment casting.
| Parameter | Variation Range | Change in Solidification Time (%) | Change in Misrun Defect Area (%) |
|---|---|---|---|
| Alloy Thermal Conductivity | ±10% | ±5% | ±8% |
| Mold Thermal Conductivity | ±10% | ∓7% | ±10% |
| Interfacial Heat Transfer Coefficient | ±20% | ±12% | ±15% |
The analysis confirmed that the IHTC is the most sensitive parameter, justifying the focus on its accurate determination for precision investment casting. Based on these findings, I developed an optimized process window for turbocharger turbine production. The recommended parameters include a mold preheat temperature of 850–900°C, a pouring temperature of 1540–1550°C, and a cooling rate of 3–5 K/s in the solidification range to minimize defects in precision investment casting.
In conclusion, my study demonstrates a comprehensive approach to improving numerical simulation accuracy for precision investment casting of automotive turbocharger turbines. By experimentally measuring thermal physical parameters and inversely determining the interfacial heat transfer coefficient, I achieved close agreement between simulated and experimental temperature fields, with an average deviation of only 5.67°C. The optimized simulation successfully predicted misrun defects at blade tips, validating its reliability for precision investment casting applications. The temperature-dependent IHTC, derived from Beck’s nonlinear estimation method, proved critical in capturing heat transfer dynamics during solidification. These findings underscore the importance of accurate input data in numerical simulations for precision investment casting, offering a valuable reference for optimizing similar processes with nickel-based superalloys. Future work could extend this methodology to other alloys or complex geometries, further advancing the capabilities of precision investment casting in manufacturing high-performance components.