In the pursuit of achieving strategic goals such as carbon peak and carbon neutrality, turbocharging technology has emerged as a critical solution for energy conservation and emission reduction. The automotive turbocharger turbine is increasingly evolving toward precision, lightweight, and thin-walled designs. However, reducing blade thickness to enhance aerodynamic performance often leads to defects like misruns during the lost wax investment casting process, resulting in increased scrap rates and production costs. Numerical simulation technology offers a viable alternative to traditional trial-and-error methods, enabling optimization of product processes, improvement of quality, and reduction of development costs. This study focuses on enhancing simulation accuracy by incorporating key thermal physical parameters and boundary conditions, which are decisive for reliable results. We explore the application of measured data and inverse calculation methods to refine the numerical simulation of lost wax investment casting for automotive turbocharger turbines.
The accuracy of numerical simulations in lost wax investment casting heavily relies on precise input parameters, including the thermal properties of the alloy and mold, as well as the interfacial heat transfer coefficient (IHTC) between the casting and the mold. Previous research has developed theoretical models to improve simulation fidelity, but comprehensive studies on essential parameters like IHTC remain limited. In this work, we employ a combination of experimental measurements and numerical inverse methods to determine these parameters. The Beck nonlinear estimation algorithm is utilized to compute the temperature-dependent IHTC, ensuring that the simulated temperature fields align closely with experimental data. This approach not only validates the simulation’s reliability but also provides a reference for similar applications in lost wax investment casting processes.
To establish a mathematical foundation for the inverse calculation of IHTC, we adopt the Beck nonlinear estimation method. This iterative optimization technique minimizes the discrepancy between simulated and measured temperature fields. The convergence criterion is defined as follows:
$$ s(h) = \sum_{i=1}^{N_t} \sum_{j=1}^{N_m} \left( \frac{T_{\text{meas}}(x_j, t_i) – T_{\text{calc}}(x_j, t_i, h)}{\sigma_T} \right)^2 + \sum_{k=1}^{N_h} \left( \frac{h_k – h_{0,k}}{\sigma_k} \right)^2 $$
where \( T_{\text{meas}}(x_j, t_i) \) represents the measured temperature at location \( x_j \) and time \( t_i \), \( T_{\text{calc}}(x_j, t_i, h) \) is the calculated temperature from the forward simulation, \( h_k \) denotes the IHTC values to be determined, \( h_{0,k} \) is the initial guess for IHTC, \( \sigma_T \) is the measurement error, and \( \sigma_k \) is the maximum allowable change in \( h \) during iteration. The minimization of \( s(h) \) yields the optimal IHTC, which is then used in subsequent simulations to enhance accuracy. This method accounts for the complex heat transfer mechanisms in lost wax investment casting, such as conduction, radiation, and convection, across different temperature ranges.
The experimental phase involves measuring the thermal physical parameters of the Inconel713C alloy and the ceramic mold, conducting temperature measurement tests during solidification, and setting up numerical simulations. The alloy, a γ′-precipitation strengthened nickel-based superalloy, is chosen for its high-temperature strength and fatigue resistance, making it suitable for turbocharger applications. The mold consists of a primary layer and five backup layers, composed of zircon sand and quartz-based materials. Key thermal properties, including solidus and liquidus temperatures, specific heat capacity, and thermal conductivity, are determined using differential scanning calorimetry (DSC), laser flash analysis, and transient plane source methods. The density of the alloy and mold are measured as \( 7.915 \times 10^3 \, \text{kg/m}^3 \) and \( 2.49 \times 10^3 \, \text{kg/m}^3 \), respectively. Thermal conductivity is calculated using the formula:
$$ \lambda = \alpha \rho c $$
where \( \lambda \) is thermal conductivity, \( \alpha \) is thermal diffusivity, \( \rho \) is density, and \( c \) is specific heat capacity. The following table summarizes the testing methods and instruments used for these measurements:
| Parameter | Temperature Range (°C) | Method | Instrument |
|---|---|---|---|
| Alloy Solidus/Liquidus | 25–1500 | Differential Scanning Calorimetry | NETZSCH STA 449F3 |
| Alloy Specific Heat and Thermal Conductivity | 25, 800, 1000 | Laser Flash Method | NETZSCH LFA427 |
| Mold Thermal Conductivity | 25, 800, 1000 | Transient Plane Source Method | Hot Disk TPS 2500S |
For the temperature measurement test during solidification, a vacuum induction melting furnace is employed, equipped with a temperature acquisition system using B-type platinum-rhodium thermocouples. The thermocouples are pre-embedded in the mold at specific locations near the casting-mold interface to capture real-time temperature data during the lost wax investment casting process. The setup includes a QuadTemp multi-channel temperature recorder with a 1-second sampling interval. The procedure involves heating the mold to a preheat temperature, melting the alloy, and pouring it into the mold while recording temperatures. This data is crucial for the inverse calculation of IHTC.
Numerical simulations are performed using ProCAST software, with a focus on the filling and solidification stages. The geometry includes a cluster of three turbines with a gating system, meshed at 4 mm element size. The mold thickness is set to 6 mm using shelling functions. Initial conditions are defined based on experimental observations: the molten metal in the induction coil is at 1545°C, while the outer metal is between solidus and liquidus temperatures at 1310°C, and the mold preheat temperature is 850°C. The IHTC is initially set to 2000 W/(m²·K) based on literature, and the inverse module in ProCAST is used to optimize this value by comparing simulated and measured temperature fields. The optimized IHTC is then applied in forward simulations to predict defects such as misruns in the turbine blades.
The results from thermal property measurements reveal important insights. The DSC analysis of Inconel713C shows a liquidus temperature of 1328°C and a solidus temperature of 1300°C, determined from the heating curve. However, comparisons with Scheil model calculations indicate discrepancies due to experimental cooling rates and assumptions in the model. The specific heat capacity and thermal conductivity measurements are plotted against calculated values, demonstrating that experimental data below 1000°C are more accurate for simulation inputs. For the mold, thermal diffusivity and specific heat capacity vary with temperature, but overall thermal conductivity decreases as temperature increases, attributed to moisture evaporation and pore expansion in the porous ceramic material. The table below compares measured and calculated values for the alloy’s solidus and liquidus temperatures:
| Parameter | Measured Value (°C) | Calculated Value (°C) |
|---|---|---|
| Solidus | 1300 | 1180 |
| Liquidus | 1328 | 1340 |
The temperature measurement during solidification captures the cooling curve, showing an initial rapid temperature drop due to convective heat loss, followed by a slower decline during vacuum conditions, and a release of latent heat between 1300°C and 1330°C. This data is used as input for the inverse simulation, leading to the determination of the IHTC as a function of temperature. The optimized IHTC values are as follows: 62 W/(m²·K) at 200°C, 275 W/(m²·K) at 1300°C, 1000 W/(m²·K) at 1340°C, and 1050 W/(m²·K) at 1545°C. These values reflect the three stages of heat transfer in lost wax investment casting: direct conduction at high temperatures, mixed modes during solidification, and radiation/convection at lower temperatures.
Comparisons between simulated and measured temperature fields at the turbine bottom show that the optimized input conditions reduce the average temperature difference from 106.65°C to 5.67°C, indicating high accuracy. Additionally, the simulation predicts misrun defects at the blade tips, which align with actual casting observations. The filling process simulation illustrates that the blade tips are the last to fill and first to solidify, making them prone to defects. The inclusion of optimized parameters in the lost wax investment casting simulation effectively captures these phenomena, as shown in the solid fraction analysis. For instance, the optimized simulation reveals potential misruns, whereas the initial simulation does not, underscoring the importance of accurate input data.
Further analysis of the lost wax investment casting process involves evaluating the thermal behavior during solidification. The inverse-calculated IHTC demonstrates a significant increase at temperatures above 1300°C, corresponding to the liquidus point where metal-mold contact is intimate. Below this temperature, the formation of a solid shell and air gaps reduces heat transfer, leading to lower IHTC values. This behavior is consistent with theoretical models and highlights the nonlinear nature of heat transfer in lost wax investment casting. The formula for IHTC variation can be approximated as a piecewise function, but for simulation purposes, the discrete values are integrated into the software database.
In conclusion, this study successfully enhances the numerical simulation of lost wax investment casting for automotive turbocharger turbines by incorporating measured thermal physical parameters and an inversely calculated IHTC. The Beck nonlinear estimation method proves effective in determining temperature-dependent IHTC, resulting in simulated temperature fields and defect predictions that closely match experimental data. This approach not only validates the simulation’s reliability but also provides a framework for optimizing other lost wax investment casting processes. Future work could explore dynamic boundary conditions and multi-scale modeling to further improve accuracy in complex geometries.
The implications of this research extend to industrial applications, where reduced prototyping costs and improved product quality are critical. By leveraging advanced measurement techniques and inverse algorithms, manufacturers can achieve higher precision in lost wax investment casting, contributing to sustainable manufacturing practices. The repeated emphasis on lost wax investment casting throughout this study underscores its significance in modern turbine production, and the methodologies presented here can be adapted to similar alloys and mold materials. Overall, the integration of experimental data with numerical simulation represents a robust strategy for advancing lost wax investment casting technology.