In the field of advanced manufacturing, lost wax investment casting stands out as a near-net-shape process ideal for producing complex and high-integrity components. The precision of this method, however, hinges on accurately predicting thermal behavior during solidification, particularly the interfacial heat transfer coefficient (HTC) between the metal and the mold. This coefficient is critical for numerical simulations that aim to forecast defects like shrinkage and porosity, yet obtaining reliable HTC values remains challenging due to its dependence on material properties, process parameters, and dynamic interfacial conditions. In this study, we investigate the HTC for ZL114A aluminum alloy during solidification in a lost wax investment casting setup. By combining experimental temperature measurements with inverse modeling in ProCAST software, we derive a temperature-dependent HTC profile and validate its accuracy against实测 data. Our approach not only enhances simulation fidelity but also provides a framework for optimizing process parameters in aluminum alloy investment casting, ultimately reducing development cycles and improving product quality.
The solidification process in lost wax investment casting involves complex heat transfer phenomena, where high-temperature molten metal loses heat to the cooler ceramic shell. This non-steady-state heat exchange governs the microstructure and integrity of the final casting. To model this accurately, we rely on the Fourier heat conduction equation, which forms the basis of our numerical analysis. The general form of this equation accounts for transient heat flow and latent heat release during phase change:
$$ \rho c_p \frac{\partial T}{\partial t} = \lambda \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right) + \rho L \frac{\partial f_s}{\partial t} $$
Here, \( \rho \) represents density, \( c_p \) is the specific heat capacity, \( \lambda \) denotes thermal conductivity, \( T \) is temperature, \( t \) is time, \( L \) is the latent heat of fusion, and \( f_s \) is the solid fraction. This equation is solved with initial conditions set by the initial temperature distribution and boundary conditions that describe heat exchange at interfaces. Specifically, at the metal-mold interface, the boundary condition is expressed as:
$$ -\lambda_1 \frac{\partial T}{\partial n} = h_c (T_c – T_m) $$
where \( \lambda_1 \) is the thermal conductivity of the metal, \( \frac{\partial T}{\partial n} \) is the temperature gradient normal to the interface, \( h_c \) is the interfacial HTC, \( T_c \) is the casting temperature at the interface, and \( T_m \) is the mold temperature. Similarly, heat transfer from the mold to the ambient environment is given by:
$$ -\lambda_2 \frac{\partial T}{\partial n} = h_m (T_w – T_e) $$
with \( \lambda_2 \) as the mold thermal conductivity, \( h_m \) as the mold-environment HTC (typically set to 10 W·m⁻²·K⁻¹ for air), \( T_w \) as the mold surface temperature, and \( T_e \) as the ambient temperature. These equations underscore the importance of accurately determining \( h_c \), as it directly influences temperature field predictions.
To inversely calculate the HTC, we employed Beck’s nonlinear estimation method, which minimizes the difference between simulated and measured temperatures over discrete time steps. The objective function is defined as:
$$ f(h_M) = \sum_{j=1}^{J} \sum_{i=0}^{N} C_j \left( T_{j, M+i}^m – T_{j, M+i}^c \right)^2 $$
where \( h_M \) is the HTC assumed constant over \( N \) time steps starting from time \( M \), \( T^m \) and \( T^c \) are the measured and calculated temperatures at sensor locations \( j \), and \( C_j \) is a weighting factor. This inverse approach allows us to derive HTC values that best match experimental observations, providing a more realistic input for simulations.
Our experimental setup involved a ZL114A aluminum alloy cast into a ceramic shell typical of lost wax investment casting processes. The shell consisted of a zircon flour face layer, mullet transition layers, and high岭土 backup layers, sealed with a slurry, resulting in a uniform thickness of 6 mm. The alloy was poured at 710°C into a preheated shell at 200°C, with a gravity pouring time of 5 seconds. Key thermophysical properties of the materials, essential for simulations, are summarized in Table 1. These parameters, which vary with temperature, were sourced from literature and software databases to ensure accuracy.
| Property | ZL114A Alloy | Ceramic Shell |
|---|---|---|
| Liquidus Temperature (K) | 886 | – |
| Solidus Temperature (K) | 830 | – |
| Latent Heat (J·kg⁻¹) | 431,000 | – |
| Thermal Conductivity (W·m⁻¹·K⁻¹) | 80–175 | 4–7 |
| Specific Heat (kJ·kg⁻¹·K⁻¹) | 0.90–1.05 | 0.7–1.0 |
| Density (kg·m⁻³) | 2,400–2,700 | 2,200–2,300 |
Temperature data were acquired using thermocouples positioned at the center of cylindrical castings (60 mm diameter × 380 mm length) at heights of 80 mm, 180 mm, and 280 mm from the base, as illustrated in the experimental schematic. A KR3141-SOT data logger recorded the casting temperatures, while a SK-BX1640 thermal imager monitored the shell surface temperatures at designated regions. This dual measurement approach captured the dynamic thermal history essential for inverse analysis.
The temperature curves obtained from the experiments revealed distinct phases of cooling. In the casting, temperatures dropped rapidly post-pouring, followed by a plateau between 350 s and 850 s due to latent heat release during solidification, and then a linear decline as the casting cooled further. Shell temperatures showed similar trends but with variations between regions; for instance, areas closer to the initial metal entry points exhibited higher temperatures, gradually converging over time due to heat conduction. These data, when plotted, provided a reliable basis for the inverse calculation of HTC.
Using the measured temperature profiles as input, we performed inverse modeling in ProCAST to determine the HTC as a function of temperature. The results, plotted in Figure 1, indicate that the HTC evolves through three distinct stages: (1) above the liquidus temperature, it remains relatively constant, reflecting intimate metal-mold contact; (2) between the liquidus and solidus temperatures, it decreases sharply as solidification initiates and an air gap forms due to metal contraction; and (3) below the solidus temperature, it declines gradually as solid-state shrinkage continues. This behavior aligns with theoretical expectations for lost wax investment casting, where interfacial conditions change dynamically with temperature.
To validate the derived HTC, we incorporated it into a ProCAST simulation of the same casting geometry. The finite element model, meshed with 3 mm surface elements and over 1 million volume elements, was solved using the updated HTC values. A comparison between simulated and experimental temperatures, as shown in Table 2, demonstrates excellent agreement, with maximum deviations of 10°C for the metal and 15°C for the shell. This close match confirms the accuracy of our inverse approach and the reliability of the HTC for predictive simulations.
| Parameter | Maximum Temperature Difference (°C) |
|---|---|
| Metal Temperature | 10 |
| Shell Temperature | 15 |
Further analysis of the HTC profile highlights its sensitivity to process variables in lost wax investment casting. For instance, the initial high HTC values correspond to efficient heat transfer when the metal is fully liquid, but as solidification progresses, the formation of an air gap impedes heat flow, leading to the observed decline. This phenomenon is captured by the inverse model, which accounts for real-time interfacial changes. Additionally, we explored the impact of shell thickness and material properties on HTC, noting that thicker shells generally reduce HTC due to increased thermal resistance, consistent with findings in similar studies.
The mathematical framework for our inverse analysis not only improves simulation accuracy but also offers insights into optimizing casting parameters. By iteratively refining the HTC using Beck’s method, we minimize errors in temperature predictions, which is crucial for defect prevention in aluminum alloy castings. Moreover, the derived HTC values can be generalized to other lost wax investment casting scenarios with similar materials and geometries, enhancing the versatility of our approach.
In conclusion, our study successfully determines the interfacial heat transfer coefficient for ZL114A aluminum alloy in a lost wax investment casting process through a combination of experimental measurements and inverse numerical modeling. The HTC, characterized by three temperature-dependent stages, provides a more accurate input for ProCAST simulations, as validated by the close agreement between predicted and actual temperatures. This methodology not only advances the precision of thermal simulations but also supports the optimization of casting processes, reducing trial-and-error efforts and promoting higher quality outcomes in aluminum alloy investment casting. Future work could extend this approach to other alloys or complex geometries, further refining the understanding of heat transfer in lost wax investment casting.