In this thesis, I focus on the numerical simulation of the solidification process for large steel casting, aiming to improve the accuracy and reliability of defect prediction through parameter optimization. The work covers the establishment of a material thermo-physical property database, the inverse determination of interfacial heat-transfer coefficients between casting and mold, the quantitative evaluation of Niyama criterion for shrinkage porosity prediction, and the industrial application to a large steel casting frame. The research is based on two typical steel casting materials: ZG0Cr13Ni4Mo and ZG230-450. Large steel casting products are essential in energy, marine, metallurgical, and petrochemical industries, and their production often involves high cost and long lead time. Therefore, numerical simulation has become a key technology to replace the traditional trial-and-error approach. However, the accuracy of simulation for large steel casting is often limited by the lack of reliable input parameters. This study addresses these issues by performing controlled experiments and inverse calculations to obtain parameter values that are specifically suitable for large steel casting geometries.
The thesis begins with a comprehensive review of the development of casting simulation technology. From early heat transfer calculations to modern coupled flow, thermal, and stress simulations, the field has matured significantly. Commercial software packages such as ProCAST, MAGMAsoft, and InteCAST are widely used in foundry industries. However, for large steel casting, several challenges remain. First, the material property database built into commercial software is usually based on foreign standards, and the properties of domestic steel casting grades are not readily available. Second, the interfacial heat-transfer coefficient between the steel casting and the mold is often treated as a constant or a simple linear function, which is inadequate for large steel casting because of the significant gas gap formed at the interface during cooling. Third, the critical values of Niyama criterion for predicting shrinkage porosity in large steel casting are not well established. Many studies have reported values for small steel castings, but large steel casting exhibits different cooling rates and thermal gradients, leading to different critical thresholds. This thesis aims to fill these gaps.
To construct the database, I chose Microsoft Access as the database management system due to its relational model, user-friendly interface, and wide compatibility. The database contains five modules: steel casting material properties, mold material properties, refractory material properties, interfacial heat-transfer coefficient data, and shrinkage porosity criterion values. Each material module consists of two types of data tables. The first type stores temperature-independent parameters such as chemical composition, liquidus temperature, solidus temperature, latent heat, and density at room temperature. The second type stores temperature-dependent properties including thermal conductivity, specific heat, thermal diffusivity, and enthalpy. For steel casting materials, the temperature-dependent table includes density variation with temperature as well. Figure 2-2 in the original thesis illustrates the data table structure, but here I present a representative schema in Table 1.
| Field Name | Data Type | Description |
|---|---|---|
| MaterialName | Text | Steel casting grade (primary key) |
| Standard | Text | National standard or internal specification |
| ChemicalComposition | Text | Main alloying elements and ranges |
| LiquidusTemperature | Number | Liquidus temperature in °C |
| SolidusTemperature | Number | Solidus temperature in °C |
| LatentHeat | Number | Latent heat in kJ/kg |
| DensityRoom | Number | Density at room temperature in g/cm³ |
| Reference | Text | Source of data |
The design of the database allows the user to add or delete material types through forms. For each material, a corresponding temperature-dependent property table is automatically created. The database also includes a module for interfacial heat-transfer coefficients. This module stores the interface type (defined by the pair of materials on both sides) and the temperature-dependent heat-transfer coefficient data. Another module stores the Niyama criterion critical values and critical feeding solid fraction for different steel casting grades. The main interface provides navigational buttons to access each module. The database significantly improves the efficiency of data preparation for large steel casting simulation.
Regarding the data collection, I measured the thermo-physical properties of ZG0Cr13Ni4Mo and ZG230-450 using the laser flash method. The laser flash method is a non-steady-state technique that directly measures thermal diffusivity. A small disk-shaped specimen with a thickness of 3 mm and a diameter of 12 mm is used. The rear surface temperature rise is recorded after a laser pulse heats the front surface. The thermal diffusivity \(\alpha\) is calculated by the formula:
$$ \alpha = \frac{1.37 L^2}{\pi^2 t_{1/2}} $$
where \(L\) is the specimen thickness and \(t_{1/2}\) is the time required for the rear surface temperature to reach half of its maximum value. The specific heat was measured using differential scanning calorimetry (DSC). Once the thermal diffusivity and specific heat are known, the thermal conductivity can be computed using the relationship:
$$ \lambda(T) = \alpha(T) \cdot \rho(T) \cdot C_p(T) $$
The measured data for ZG0Cr13Ni4Mo are listed in Table 2.
| Temperature (°C) | Thermal diffusivity (10⁻⁶ m²/s) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) |
|---|---|---|---|
| 200 | 4.98 | 575 | 22.2 |
| 300 | 4.90 | 569 | 21.7 |
| 400 | 4.80 | 590 | 21.9 |
| 500 | 4.63 | 649 | 23.3 |
| 600 | 4.33 | 708 | 23.7 |
| 700 | 3.93 | 745 | 22.7 |
| 750 | 3.83 | 783 | 23.3 |
| 800 | 4.79 | 591 | 22.3 |
| 900 | 5.12 | 593 | 23.5 |
| 1000 | 5.27 | 595 | 24.3 |
| 1100 | 5.46 | 612 | 25.9 |
| 1200 | 5.44 | 611 | 25.7 |
For ZG230-450, the measured properties are presented in Table 3.
| Temperature (°C) | Thermal diffusivity (10⁻⁶ m²/s) | Specific heat (J/kg·K) | Thermal conductivity (W/m·K) |
|---|---|---|---|
| 100 | 11.8 | 473 | 44.1 |
| 200 | 10.7 | 507 | 42.2 |
| 300 | 9.53 | 540 | 40.2 |
| 400 | 8.40 | 586 | 38.4 |
| 500 | 7.30 | 650 | 36.6 |
| 600 | 6.20 | 697 | 33.7 |
| 700 | 4.87 | 795 | 30.2 |
| 750 | 4.14 | 905 | 29.2 |
| 800 | 4.31 | 752 | 25.3 |
| 850 | 4.94 | 646 | 24.9 |
| 900 | 5.25 | 605 | 24.8 |
| 1000 | 5.78 | 573 | 25.8 |
The liquidus temperature of ZG0Cr13Ni4Mo is 1490 °C and the solidus temperature is 1455 °C. The latent heat is 272 kJ/kg, and the room-temperature density is 7.743 g/cm³. For ZG230-450, the liquidus is 1508.25 °C, the solidus is 1459.01 °C, the latent heat is 241.7 kJ/kg, and the density is 7.795 g/cm³. For other materials, I used the ProCAST database calculation module. By inputting the chemical composition, the module can generate temperature-dependent data using the Lever rule or the Schiel model. For large steel casting with long solidification time, the Lever model is more appropriate. The calculated data include thermal conductivity, density, enthalpy, solid fraction, and liquidus/solidus temperatures.
The second major part of this thesis is the study of interfacial heat-transfer coefficient between the large steel casting and the mold. The interfacial heat-transfer coefficient is crucial for accurate temperature field simulation. In large steel casting, the interfacial condition evolves from perfect contact to partial contact, and finally to complete separation with a gas gap. This evolution significantly affects heat transfer. Direct measurement of the interfacial heat-transfer coefficient is impossible, so I employed an inverse method using ProCAST. The inverse problem is formulated as follows: given measured temperatures inside the casting and mold, estimate the heat-transfer coefficient at the interface. The mathematical model is based on minimizing the least-squares residual between measured and simulated temperatures. The objective function is:
$$ F(h) = \sum_{i=1}^{N_t} \sum_{j=1}^{N_m} \frac{1}{\sigma_T^2} \left[T_{ij}^m – T_{ij}^c(h)\right]^2 + \sum_{k=1}^{N_h} \frac{1}{\sigma_h^2} \left[h_k – h_k^0\right]^2 $$
where \(T_{ij}^m\) is the measured temperature at node \(j\) at time \(i\), \(T_{ij}^c\) is the corresponding calculated temperature, \(h\) is the vector of unknown heat-transfer coefficients, \(\sigma_T\) is the temperature measurement error, \(h_k^0\) is an initial guess, and \(\sigma_h\) is a regularization parameter. ProCAST’s inverse module iteratively updates the heat-transfer coefficient until the objective function is minimized.
To perform the experiment, I designed a test casting with large steel casting characteristics. The test casting consisted of four plates with thicknesses of 100 mm, 150 mm, 200 mm, and 250 mm, as shown in the original thesis. Three risers were placed on the top: a cylindrical riser, a small cylindrical riser, and an insulating riser. The mold material was furan resin sand. The pouring temperature was 1550 °C. Six thermocouples were installed at specific positions near the casting-mold interface. Type B thermocouples (platinum-rhodium) were used inside the casting because of the high temperature, while Type K thermocouples were used inside the mold. Temperature data were recorded using an intelligent scanner connected to a computer with data acquisition software. In addition to temperature, the gas gap width at the interface was measured using displacement sensors. The displacement sensor was a linear potentiometer with a measurement range of 10 mm, installed in a ceramic tube and connected to a rod that touched the casting surface through a hole in the mold.
Figure 3-11 in the original thesis shows the measured temperature curves for ZG0Cr13Ni4Mo. The curves indicate a reasonable cooling behavior. The gas gap measurements are shown in Figure 3-12. At position one (free contraction interface), the gap remained zero for the first 50 minutes, meaning that the casting and the mold were in complete contact. After 50 minutes, the gap began to increase almost linearly with time. At 120 minutes, the rod stopped moving due to friction, but the gap could be estimated from the contraction. The gap width as a function of time was fitted as:
$$ L(t) = \begin{cases} 0, & 0 \le t \le 50 \\ 0.00654 t – 0.303, & t \ge 50 \end{cases} $$
where \(L\) is in millimeters and \(t\) is in minutes. At position two (constrained contraction), the gap remained zero until 90 minutes, then increased to about 0.05 mm at 110 minutes, and then decreased because of overall contraction, eventually returning to near contact after 130 minutes. These measurements confirm that the interfacial gap is dynamic and complex in large steel casting.
For the inverse calculation, I built a three-dimensional model of the test casting and mold using Pro/E and meshed it with MeshCAST. The mesh was refined near the thermocouple locations. The material properties were assigned using the measured data and ProCAST database data. The initial interface heat-transfer coefficient was set to 500 W/m²/°C for all four temperature points. The pouring temperature was set to 1550 °C, and the initial mold temperature was 25 °C. The flow field was calculated first to obtain the initial temperature distribution for solidification. The inverse calculation used the temperature data from one thermocouple as the measured input. After several iterations, the converged interfacial heat-transfer coefficients were obtained. Table 4 lists the values at four interface temperatures.
| Interface temperature (°C) | Heat-transfer coefficient (W/m²/°C) |
|---|---|
| 1100 | 490 |
| 1200 | 530 |
| 1350 | 620 |
| 1450 | 760 |
These values show a clear decreasing trend with decreasing temperature. At 1450 °C, the casting is nearly liquid and the interface is fully contacted, so the heat-transfer coefficient is high (760 W/m²/°C). At 1350 °C, a thin solid shell has formed, and partial separation occurs, reducing the coefficient to 620 W/m²/°C. As the gap grows, the coefficient further drops to 530 W/m²/°C at 1200 °C and 490 W/m²/°C at 1100 °C. The relationship between the interfacial heat-transfer coefficient and the gas gap width is shown in Figure 3-26 in the original thesis. I summarize the correspondence in Table 5.
| Gas gap (mm) | Contact state | Heat-transfer coefficient (W/m²/°C) |
|---|---|---|
| 0 | Complete contact (liquid) | 760 |
| 0 | Partial contact (solid shell) | 620 |
| 0.254 | Complete separation | 530 |
| 0.65 | Complete separation | 490 |
It is interesting to note that when the gas gap is zero at both 1450 °C and 1350 °C, the heat-transfer coefficient differs. This is because at 1350 °C, even though the macroscopic gap is zero, micro-scale gaps exist between the solidified surface and the mold due to surface roughness and contraction. The effective contact area is reduced, leading to a lower effective heat-transfer coefficient. Once the gas gap is fully developed, further increase in gap width has a diminishing effect on the interfacial heat-transfer coefficient, as the dominant heat transfer mode becomes radiation and gas conduction with large thermal resistance.
The third major contribution of this thesis is the determination of Niyama criterion critical values for large steel casting. The Niyama criterion is widely used to predict shrinkage porosity in steel casting. It is expressed as:
$$ \frac{G}{\sqrt{R}} < C_{Niyama} $$
where \(G\) is the temperature gradient, \(R\) is the cooling rate, and \(C_{Niyama}\) is the critical value. In ProCAST, the criterion is defined as a mapping factor:
$$ M = \frac{G}{\sqrt{L}} $$
where \(L\) is the cooling rate. The units of \(M\) are °C¹ᐟ² s¹ᐟ² cm⁻¹. The critical value determines the threshold below which porosity is expected. For large steel casting, the critical value differs from that of small castings because of differences in cooling conditions and thermal gradients.
In this study, I poured two test castings one made of ZG0Cr13Ni4Mo and one made of ZG230-450. After solidification, the castings were examined using ultrasonic testing to detect internal shrinkage porosity. The ultrasonic equipment was a CTS-22 flaw detector with a 2 MHz probe. The inspection was performed by a professional testing department. The detected shrinkage defects were reconstructed in 3D using Pro/E to visualize their locations and sizes. Then I simulated the solidification process of the test castings using ProCAST with the measured material properties and the interfacial heat-transfer coefficient obtained earlier. After the temperature field calculation, I computed the Niyama number for every node. In the post-processing module, I adjusted the upper limit of the color scale to see which regions would be predicted as porous. By comparing the predicted porosity distribution with the ultrasonic inspection results, I determined the critical Niyama value for each material.
For ZG0Cr13Ni4Mo, the comparison was performed on a cross-section through the center of the plates. Figure 4-7 in the original thesis shows the ultrasonic inspection result and simulated porosity with upper limits of 20, 25, and 30 (in °C¹ᐟ² s¹ᐟ² cm⁻¹). The best agreement was obtained when the upper limit was between 25 and 30. Converting these values to the conventional units of °C¹ᐟ² min¹ᐟ² cm⁻¹, the critical Niyama value for large steel casting ZG0Cr13Ni4Mo is in the range of 3.2 to 3.87. For ZG230-450, the comparison indicated a critical value of approximately 25 °C¹ᐟ² s¹ᐟ² cm⁻¹, which is equivalent to 3.2 °C¹ᐟ² min¹ᐟ² cm⁻¹. These values are higher than the values reported in the literature for small steel castings, which are typically around 0.8 to 1.0 °C¹ᐟ² min¹ᐟ² cm⁻¹. The reason is that large steel casting has a much slower cooling rate and smaller temperature gradients, so the Niyama number tends to be lower for the same defect condition. Therefore, a higher critical value is needed to correctly identify porosity-prone regions. The obtained critical values were stored in the database for future use.
Finally, I applied the optimized parameters to a real industrial large steel casting: a large rolling mill frame weighing 120 tons. The frame dimensions were 9645 mm × 4470 mm × 700 mm, with a central window of 6610 mm × 1470 mm × 700 mm. The material was ZG230-450. The original casting process used four insulating risers, four gates, and two chill blocks on the ears. The mold was made of chromite sand for face layer and silica sand for backing. The pouring temperature was 1550 °C. The original process was suspected to produce shrinkage porosity in the regions between the risers because of insufficient feeding. To improve the solidification pattern, I proposed adding four chill blocks (800 mm × 800 mm × 400 mm) below the casting between the risers. These chill blocks would accelerate cooling at the bottom and promote progressive solidification from bottom to top, which helps feeding through the risers.
I simulated both the original process (with only ear chill blocks) and the improved process (with additional chill blocks between risers). The material properties used in the simulation were the measured data for ZG230-450 and the interfacial heat-transfer coefficient from the database. The initial temperature was set to 1550 °C, and the mold temperature was 25 °C. The casting was assumed to be instantly filled. Figure 4-14 in the original thesis shows the temperature fields at different times on a horizontal section at mid-height. In the original process, a large hot spot appeared between the risers and remained for a long time, indicating a wide mushy zone that is prone to shrinkage porosity. In the improved process, the additional chill blocks effectively eliminated the hot spot, and the temperature distribution was more uniform, with a steeper temperature gradient toward the risers.
To quantify the shrinkage porosity, I computed the Niyama criterion using the critical value determined earlier. In the post-processing, I set the upper limit to 25 (in ProCAST units) and displayed the regions where \(M < 25\). Figure 4-17 shows that the original process predicted extensive shrinkage porosity in the areas between the risers, especially near the center of the frame. The improved process showed almost no shrinkage porosity in the cross-sections, as shown in Figure 4-18. The simulation results demonstrate that the additional chill blocks create a favorable temperature gradient that allows the risers to feed the solidifying contraction effectively. The actual production after implementing the improved process was inspected by ultrasonic testing, and the result was “qualified” with no unacceptable defects. This confirms that the optimized parameters and the proposed process modification are effective for large steel casting production.
In conclusion, this thesis provides a systematic study of parameter optimization for numerical simulation of large steel casting solidification. The main contributions are:
1. A comprehensive material property database has been established using Microsoft Access, covering steel casting materials, mold materials, refractory materials, interfacial heat-transfer coefficients, and shrinkage porosity criteria. The database facilitates data retrieval and management for simulation.
2. The thermo-physical properties of ZG0Cr13Ni4Mo and ZG230-450 have been experimentally measured using the laser flash method and DSC. These data are reliable and suitable for large steel casting simulation.
3. The interfacial heat-transfer coefficient between large steel casting and furan resin sand has been determined by the inverse method. The coefficient decreases from 760 W/m²/°C at 1450 °C to 490 W/m²/°C at 1100 °C. The relationship with the gas gap width has been identified, providing a physical explanation for the variation.
4. The critical Niyama values for shrinkage porosity prediction in large steel casting have been quantified: 3.2–3.87 °C¹ᐟ² min¹ᐟ² cm⁻¹ for ZG0Cr13Ni4Mo and 3.2 °C¹ᐟ² min¹ᐟ² cm⁻¹ for ZG230-450. These values are essential for correctly predicting shrinkage porosity in heavy-section steel casting.
5. The optimized parameters have been applied to a 120-ton large steel casting frame. The simulation using the determined critical values successfully predicted the shrinkage porosity distribution. The process improvement with additional chill blocks eliminated the porosity, demonstrating the practical value of the research.
Through this research, I have solved key parameter problems in numerical simulation for large steel casting. The results provide theoretical guidance and practical tools for foundry engineers to improve the quality of large steel casting products. Future work may extend the database to more materials and explore the influence of casting geometry on interfacial heat-transfer coefficients and criterion values. Additionally, coupled simulation of shrinkage porosity and hot tearing could be beneficial for complex large steel casting structures.