In the present study, I conducted a comprehensive numerical simulation of the temperature field during the solidification process of an aluminum alloy wheel produced via sand casting foundry technology. The sand casting foundry approach is widely adopted for its flexibility in producing complex geometries, such as electric vehicle wheels. However, defects like shrinkage porosity and surface imperfections often arise due to improper thermal management. To address these challenges, I established a mathematical model, a geometric model, and a finite element simulation model for the temperature field during solidification. The nonlinear characteristics of material properties and boundary conditions were fully considered, and the latent heat of crystallization was treated using the equivalent specific heat method. Using the finite element simulation software ProCAST, I numerically simulated the temperature field evolution. The results revealed that the three-dimensional temperature distribution could dynamically reflect the thermal changes during solidification, providing valuable insights for process optimization in sand casting foundry applications.
1. Introduction
The sand casting foundry process for aluminum alloy wheels involves pouring molten metal into a sand mold, where solidification occurs under gravity. The temperature field plays a crucial role in determining the final quality of the casting. A non-uniform temperature distribution can lead to hot spots, uneven shrinkage, and defect formation. Therefore, numerical simulation of the temperature field is essential for predicting and optimizing the solidification behavior. In this work, I focused on the sand casting foundry of ZL104 aluminum alloy wheels, utilizing ProCAST to model the transient thermal phenomena. The study aimed to capture the dynamic temperature changes from pouring to complete solidification, thereby offering a reference for improving casting quality and determining optimal process parameters in sand casting foundry environments.
2. Mathematical Model of Solidification Heat Transfer
The governing equation for transient heat conduction in the sand casting foundry process is the Fourier heat conduction equation, which accounts for heat transfer in three dimensions. Assuming isotropic thermal conductivity, the equation is given by:
$$
\rho c_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(\lambda \frac{\partial T}{\partial z}\right) + \dot{Q}
$$
where \(\rho\) is the density, \(c_p\) is the specific heat at constant pressure, \(\lambda\) is the thermal conductivity, \(T\) is the temperature, \(t\) is time, and \(\dot{Q}\) represents the internal heat source term due to latent heat release during solidification. For the sand casting foundry of aluminum alloys, the latent heat is significant and must be handled appropriately. I employed the equivalent specific heat method, which modifies the specific heat in the solidification range to account for the latent heat release:
$$
\dot{Q} = \rho L \frac{\partial f_s}{\partial t} = \rho L \frac{\partial f_s}{\partial T} \cdot \frac{\partial T}{\partial t}
$$
Here, \(L\) is the latent heat of fusion, and \(f_s\) is the solid fraction. Assuming a linear relationship between solid fraction and temperature within the mushy zone (between liquidus temperature \(T_l\) and solidus temperature \(T_s\)), we have:
$$
f_s = \frac{T_l – T}{T_l – T_s}
$$
The initial condition for the simulation is:
$$
T(x,y,z,t)|_{t=0} = T_0
$$
where \(T_0\) is the initial pouring temperature. The boundary condition at the casting-mold interface is described by a convective heat transfer coefficient \(h\):
$$
-\lambda \frac{\partial T}{\partial n}\bigg|_S = h (T_1 – T_2)
$$
where \(T_1\) and \(T_2\) are the temperatures of the casting and mold at the interface, respectively. In the sand casting foundry process, the interfacial heat transfer coefficient is temperature-dependent, as determined by the Tikhonov regularization method:
$$
h = \begin{cases}
800 & (t > 600^\circ C) \\
6t – 2800 & (550^\circ C < t \leq 600^\circ C) \\
3.5t – 1425 & (450^\circ C \leq t \leq 550^\circ C) \\
t – 300 & (350^\circ C \leq t < 450^\circ C) \\
50 & (t < 350^\circ C)
\end{cases}
$$
where \(t\) is the casting surface temperature in degrees Celsius.
3. Geometric Model and Finite Element Mesh
The geometric model of the aluminum alloy wheel was constructed based on actual dimensions (153 mm diameter × 54 mm height) used in sand casting foundry production. The wheel geometry includes three main regions: the rim, the hub, and the mounting plate. The sand mold was also modeled as a cylindrical enclosure. I used the MeshCAST module within ProCAST to generate finite element meshes. The element type was tetrahedral, and the total number of nodes and elements for the casting part were 10,962 and 49,284, respectively. The mesh density was refined near critical areas such as the rim-hub junction and the hub-mounting plate junction to capture steep thermal gradients typical in sand casting foundry processes.
4. Material Properties and Process Parameters
The alloy chosen for this simulation is ZL104, whose chemical composition is presented below. The liquidus and solidus temperatures of ZL104 are 595°C and 555°C, respectively. The thermal conductivity and density as functions of temperature are shown schematically (not reproduced here). For the sand mold, the thermophysical properties were assumed constant, as summarized in Table 1.
Table 1: Chemical Composition of ZL104 Alloy (mass %)
| Si | Mn | Mg | Fe | Other | Al |
|---|---|---|---|---|---|
| 8.0–10.5 | 0.2–0.5 | 0.17–0.35 | 0.0–0.6 | <0.5 | Balance |
Table 2: Thermophysical Properties of Sand Mold Material (constant)
| Property | Value |
|---|---|
| Thermal conductivity (W·m⁻¹·°C⁻¹) | 0.52 |
| Density (kg·m⁻³) | 1630 |
| Specific heat (J·kg⁻¹·°C⁻¹) | 1120 |
Processing parameters used in the sand casting foundry simulation:
- Pouring temperature: 682°C (within the range of 670–700°C)
- Pouring velocity: 200 mm/s (within the range of 100–300 mm/s)
- Initial mold temperature: 25°C (room temperature)
- Total simulation time: 5000 s
5. Results and Discussion
The simulation provided detailed temperature field evolution over time. The total solidification time was approximately 4888 s. Figure 4 (described in text) shows the temperature contours at various time steps from 0.1 s to 150 s. At 0.1 s, the molten aluminum began filling the mold at 682°C. By 0.3 s, partial filling occurred with a temperature drop to 678°C due to contact with the cooler sand mold. At 5 s, the mold was completely filled, and the temperature remained near 679°C because of continuous metal flow. After filling, heat dissipation dominated, and by 20 s, the minimum temperature dropped to 653°C, still above the liquidus. At 50 s and 100 s, temperatures were 644°C and 638°C, respectively. At 150 s, the minimum temperature reached 624°C, but no solidification had started yet. Figure 5 (described) shows the temperature variation at different node positions during the first 150 s.
Solidification began around 300 s, as indicated by the minimum temperature of 583°C crossing below the liquidus. The progression of the temperature field from 300 s to 5000 s is illustrated in Figure 6 (described). At 1000 s, the minimum temperature was 572°C; at 1700 s, it dropped to 466°C; at 2400 s, it reached 304°C. The cooling rate increased during this period due to the growing solid fraction enhancing heat transfer. From 3100 s to 4500 s, the temperature decreased more slowly as the system approached thermal equilibrium. At 5000 s, the casting temperature was nearly 58°C, i.e., ambient temperature. The entire solidification process in this sand casting foundry simulation aligns well with industrial observations.
To quantitatively analyze the thermal behavior, I selected five key nodes representing different regions of the wheel: Node 1263 (inside rim), Node 944 (outer rim edge), Node 1362 (rim-hub junction), Node 306 (mid-spoke), and Node 14 (spoke-mounting plate junction). Their positions are indicated in Figure 7 (described). Table 3 summarizes the node locations.
Table 3: Locations of Key Nodes
| Node ID | Location |
|---|---|
| 1263 | Inner rim |
| 944 | Outer rim edge |
| 1362 | Rim-hub junction |
| 306 | Mid-spoke |
| 14 | Spoke-mounting plate junction |
Figure 8 (described) shows the temperature evolution for these nodes during two time intervals: 0–150 s and 300–4888 s. In the first 5 s, all nodes experienced negligible temperature change due to filling. Between 5 s and 150 s, temperatures decreased moderately, with Node 14 (near the gate) cooling fastest because of early heat exchange with the mold. During the solidification phase (300–1000 s), the temperature drop was gradual (average cooling rate ~0.01°C/s). Between 1000 s and 3000 s, a steeper decline occurred (average cooling rate ~0.12°C/s) as the solid fraction increased. After 3000 s, the cooling rate slowed again due to diminishing thermal gradients. At the end of solidification (4888 s), all nodes reached approximately 58°C.
The temperature differences among nodes were most pronounced during the early cooling stage. For instance, at 300 s, Node 14 was at 583°C while Node 1263 was at 590°C, a difference of 7°C. At 1000 s, the spread was about 5°C. By 2000 s, the difference reduced to 2°C, indicating a more uniform temperature field. This homogenization is typical in sand casting foundry processes where the mold acts as a heat sink but also provides gradual cooling.
6. Conclusion
In this work, I successfully performed a three-dimensional numerical simulation of the temperature field during the solidification of an aluminum alloy wheel produced by sand casting foundry. The finite element model, incorporating nonlinear material properties and temperature-dependent interfacial heat transfer coefficients, accurately captured the dynamic thermal behavior. Key findings include:
- The filling stage lasted approximately 5 s, and solidification commenced around 300 s. Total solidification time was about 4888 s.
- The cooling rate was initially slow (0–150 s), then increased during the main solidification period (1000–3000 s), and finally decreased as the casting approached ambient temperature.
- Regions near the pouring gate (spoke-mounting plate junction) cooled faster than other areas, leading to earlier solidification.
- The numerical results provide a reliable basis for predicting temperature gradients, determining solidification times, and optimizing process parameters in sand casting foundry operations.
This study demonstrates that numerical simulation is a powerful tool for understanding and improving the sand casting foundry process, ultimately enhancing the quality of aluminum alloy wheels.