Large steel castings play a vital role in the equipment manufacturing industry, particularly in power generation, marine engineering, metallurgy, and petrochemical applications. The production of high-quality large steel castings is challenging due to the complex solidification process, which often leads to defects such as shrinkage porosity and macro-segregation. Numerical simulation has become an indispensable tool for predicting these defects and optimizing casting processes. However, the accuracy of simulation depends heavily on the quality of input parameters, including thermophysical properties of materials, interfacial heat-transfer coefficients, and criteria values for shrinkage prediction. This thesis addresses these critical issues by establishing a comprehensive database, measuring key thermophysical properties, determining interfacial heat-transfer coefficients through inverse modeling, and quantifying Niyama criterion thresholds for large steel castings. The findings have been applied to optimize the casting process of a large steel frame, demonstrating significant improvements in quality and reliability.
1. Introduction
Large steel castings are key components in heavy machinery, such as rolling mill frames, turbine runners, and hydraulic press columns. The production of these castings involves substantial material and energy consumption, and any internal defect can lead to catastrophic failure. Traditional trial-and-error methods for process design are insufficient for large steel castings due to their high cost, long production cycles, and complex solidification behavior. Numerical simulation, supported by accurate material data and boundary conditions, has emerged as a powerful tool for optimizing casting processes and ensuring soundness.
The solidification of large steel castings differs significantly from that of small or medium castings. The cooling rates are much slower, leading to a long mushy zone and a higher tendency for shrinkage porosity. The interfacial heat-transfer coefficient between the casting and the mold is a crucial boundary condition that governs heat extraction during solidification. However, this coefficient is difficult to determine experimentally because it depends on the local gap formation, contact pressure, temperature, and material properties. Furthermore, the Niyama criterion, widely used for porosity prediction, requires a critical threshold value that is geometry- and material-dependent. For large steel castings, published threshold values are often inappropriate because they are derived from small castings.
This study focuses on two typical steel grades used in large castings: ZG0Cr13Ni4Mo (a martensitic stainless steel) and ZG230-450 (a carbon steel). The objectives are:
- To build a database of thermophysical properties for materials used in the simulation of large steel castings.
- To measure the thermophysical properties of the two typical steel grades using the laser flash method.
- To determine the interfacial heat-transfer coefficient between the casting and mold as a function of temperature and air gap width using inverse simulation in ProCAST.
- To establish the critical Niyama criterion values for porosity prediction in large steel castings.
- To apply the obtained parameters to optimize the casting process of a large steel frame.
The structure of this thesis is as follows: Chapter 2 describes the establishment of the material thermophysical property database. Chapter 3 presents the experimental measurement and inverse calculation of interfacial heat-transfer coefficients. Chapter 4 discusses the determination of Niyama criterion values and the application to a large steel frame. The final section summarizes the conclusions.
2. Database of Thermophysical Properties
2.1 Framework of the Database
The database was developed using the ACESS relational database management system, which is well-suited for managing structured data and allows for easy querying, updating, and maintenance. The database is designed to store all essential data for the numerical simulation of large steel castings, including thermophysical properties of cast steel, mold materials, and refractory materials, as well as interfacial heat-transfer coefficients and shrinkage prediction criterion values. The overall framework is illustrated in Figure 1 (conceptual). The database consists of five main modules:
- Cast steel material properties module
- Mold material properties module
- Refractory material properties module
- Interfacial heat-transfer coefficient module
- Shrinkage porosity criterion values module
Each module contains two types of data tables: basic property tables (temperature-independent) and temperature-dependent property tables. The basic tables include fields such as material name, composition, liquidus temperature, solidus temperature, latent heat, and density. Temperature-dependent tables include thermal conductivity, specific heat, thermal diffusivity, and enthalpy as functions of temperature. The database was populated with data from three sources: direct experimental measurement, ProCAST material calculation, and literature data.
2.2 Experimental Measurement of Thermophysical Properties
For the two typical steel grades, ZG0Cr13Ni4Mo and ZG230-450, the thermal diffusivity and specific heat were experimentally measured. Thermal diffusivity was determined using the laser flash method, which is a non-steady-state technique. In this method, a small disc-shaped sample is subjected to a short laser pulse on one surface, and the temperature rise on the opposite surface is recorded. The thermal diffusivity (α) is calculated from the half-time (t1/2) when the rear surface temperature reaches half of its maximum value:
$$ \alpha = \frac{1.37 L^2}{\pi^2 t_{1/2}} \approx \frac{0.139 L^2}{t_{1/2}} \tag{1} $$
where L is the sample thickness. The specific heat (Cp) was measured using differential scanning calorimetry (DSC). Subsequently, the thermal conductivity (λ) was derived using the relation:
$$ \lambda(T) = \alpha(T) \cdot C_p(T) \cdot \rho(T) \tag{2} $$
where ρ is the density. The measured temperature-dependent properties for ZG0Cr13Ni4Mo are summarized in Table 1.
| 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 |
Similarly, for ZG230-450, the measured data are listed in Table 2.
| 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 |
These measured values were used directly in the simulation of large steel castings. For other mold and refractory materials, literature data and ProCAST’s database were adopted. The ProCAST software provides a thermodynamic calculation module that can generate thermophysical properties based on alloy composition. For instance, the liquidus and solidus temperatures, latent heat, and solid fraction curves were obtained using the Lever rule for the two steel grades. The database ensures that all these data are readily accessible for future simulations.
3. Interfacial Heat-Transfer Coefficient
3.1 Mathematical Model for Inverse Calculation
The interfacial heat-transfer coefficient (h) between the casting and the mold is a critical boundary condition. Since it cannot be directly measured, it is often estimated by solving an inverse heat conduction problem (IHCP). The forward problem is defined by the heat conduction equation with known material properties, initial conditions, and boundary conditions. In the inverse problem, the temperature history at certain interior points is measured, and the unknown boundary condition (h) is adjusted until the calculated temperatures match the experimental measurements.
ProCAST’s inverse module minimizes a least-squares objective function:
$$ F(h) = \sum_{i=1}^{N_t} \sum_{j=1}^{N_m} \frac{1}{\sigma_T^2} \left[ T_{ij}^m – T_{ij}^c(h) \right]^2 + \sum_{k=1}^{N_h} \frac{1}{\sigma_h^2} \left[ h_k – h_k^0 \right]^2 \tag{3} $$
where Tijm is the measured temperature at node j and time i, Tijc is the corresponding calculated temperature, σT is the measurement error, hk are the unknown heat-transfer coefficients, hk0 are initial guesses, and σh is a regularization parameter. When F(h) approaches zero, the obtained h values are considered the equivalent interfacial heat-transfer coefficients.
3.2 Experimental Setup
To investigate the heat transfer for large steel castings, an experimental casting with dimensions representative of large components was designed. The test casting consisted of four plates of different thicknesses: 100 mm, 150 mm, 200 mm, and 250 mm, with a height of 400 mm. Three risers were attached: two regular sand risers and one insulating riser. The mold material was furan resin-bonded sand. The casting material was ZG0Cr13Ni4Mo. The pouring temperature was 1550°C.
Thermocouples were placed at several locations inside the casting and the mold, as well as near the interface. Platinum-rhodium (B-type) thermocouples were used for the casting interior, and K-type thermocouples for the mold. Additionally, displacement sensors were installed to measure the air gap width at two locations: one free-shrinkage interface and one constrained-shrinkage interface. Temperature data were recorded automatically using a data acquisition system.
3.3 Measurement Results and Air Gap Evolution
Figure 2 (not shown) presents the measured temperature curves at various positions. The air gap width evolution at the free-shrinkage interface is approximated by the following piecewise function:
$$ x_g(t) = \begin{cases} 0 & 0 \le t \le 50 \\ 0.00654 t – 0.303 & t \ge 50 \end{cases} \tag{4} $$
where xg is in mm and t is in minutes. At the constrained interface, the gap remained nearly zero for the first 90 minutes, then increased to about 0.05 mm, and later decreased due to casting contraction, indicating partial contact.
3.4 Inverse Calculation Using ProCAST
The finite element mesh for the experimental casting system was generated using ProCAST’s MeshCAST module. The casting and mold geometries were created in Pro/E and imported as surface files. The mesh was refined near thermocouple locations to improve accuracy. The material properties for the mold and insulation were assigned from the database. The initial interfacial heat-transfer coefficient was set as a function of temperature with initial values of 500 W/m²·°C at four temperature nodes.
The inverse calculation was performed using measured temperature data from a thermocouple located at the center of the thickest plate. The regularization parameters were kept at default values. The iteration continued until the residual became acceptably small. The resulting interfacial heat-transfer coefficients are given in Table 3.
| Temperature (°C) | h (W/m²·°C) |
|---|---|
| 1450 | 760 |
| 1350 | 620 |
| 1200 | 530 |
| 1100 | 490 |
Figure 2 shows the relationship between the interfacial heat-transfer coefficient and temperature. The coefficient decreases significantly as the interface cools. This behavior is attributed to the formation of an air gap and the transition from complete contact to partial contact and finally to complete separation.
The effect of air gap width on the heat-transfer coefficient was also analyzed. At 1450°C, where the casting is still liquid and in complete contact with the mold, the coefficient is 760 W/m²·°C. At 1350°C, a partial contact condition with micro-gaps leads to a reduction to 620 W/m²·°C. When the gap reaches 0.25 mm, the coefficient drops to 530 W/m²·°C. Further increasing the gap to 0.65 mm causes only a minor reduction to 490 W/m²·°C, indicating that the coefficient becomes less sensitive to gap size for wider gaps. The relationship is depicted in Figure 3 (not shown).
4. Shrinkage Porosity Prediction and Application
4.1 Niyama Criterion
The Niyama criterion is widely used for predicting shrinkage porosity in steel castings. It is defined as:
$$ \text{Niyama} = \frac{G}{\sqrt{R}} \tag{5} $$
where G is the local temperature gradient (K/cm) and R is the cooling rate (K/s). A threshold value (CNiyama) is used: if the local Niyama value is less than the threshold, porosity is likely to form. The critical value depends on the alloy and casting geometry, especially for large steel castings where solidification is slow.
4.2 Determination of Critical Values
To establish appropriate critical values for large steel castings, two experimental castings of ZG0Cr13Ni4Mo and ZG230-450 were produced, and their porosity distributions were detected using ultrasonic testing. The experimental casting geometry was the same as that used in the heat-transfer experiments. After solidification, the castings were sectioned and examined. The actual porosity locations were compared with predictions from ProCAST using different Niyama thresholds. By adjusting the threshold in the post-processor, the best match was obtained when the predicted shrinkage regions corresponded to the ultrasonic indications.
For ZG0Cr13Ni4Mo, the critical Niyama value was found to be in the range of 25–30 °C1/2·s1/2·cm-1. In traditional units (where R is in °C/min), this corresponds to 3.2–3.87 °C1/2·min1/2·cm-1. For smaller sections, the lower value is appropriate, while for larger sections, the upper value should be used.
For ZG230-450, the critical Niyama value was determined to be 25 °C1/2·s1/2·cm-1, i.e., 3.2 °C1/2·min1/2·cm-1. These values are higher than those commonly cited for small steel castings (0.8–1.0), confirming that large steel castings require different criteria due to their slower cooling and longer local solidification times.
4.3 Application to a Large Steel Frame
The validated parameters (thermophysical properties, interfacial heat-transfer coefficient, and Niyama thresholds) were applied to simulate the solidification of a large rolling mill frame weighing 120 tons, made of ZG230-450. The original casting process had two chill blocks placed on the lugs. To improve feeding between the risers, an alternative process was proposed with four additional chill blocks (800 mm × 800 mm × 400 mm) placed under the casting between the risers. Numerical simulations were performed for both schemes.
The temperature field evolution was compared at various times. The original scheme showed a large “simultaneous solidification” region between the risers, which is prone to shrinkage porosity. The alternative scheme, with additional chills, promoted a more directional solidification pattern from the bottom upward and from the ends toward the center, significantly reducing the simultaneous solidification zone. Consequently, the feeding path was improved, and the tendency for dispersed shrinkage porosity was minimized.
The Niyama criterion was then used to predict porosity for both schemes. Using the critical value determined for ZG230-450, the original scheme displayed large regions below the threshold, indicating likely porosity in the area between risers. In contrast, the modified scheme showed no critical porosity regions. The optimized process was implemented in production, and ultrasonic inspection confirmed the absence of unacceptable shrinkage defects. This demonstrates the validity of the determined criteria and the importance of using accurate input parameters for numerical simulation of large steel castings.
5. Conclusions
In this thesis, a systematic approach was adopted to improve the numerical simulation of solidification for large steel castings. The following conclusions can be drawn:
- A comprehensive database of thermophysical properties for materials used in the simulation of large steel castings was established using ACESS. The database includes cast steels, mold materials, and refractory materials, as well as interfacial heat-transfer coefficients and shrinkage criterion values. The database facilitates quick access to reliable data for simulation.
- The thermophysical properties of ZG0Cr13Ni4Mo and ZG230-450 were experimentally measured using the laser flash method and DSC. The resulting thermal conductivity, thermal diffusivity, and specific heat as functions of temperature were incorporated into the database and used in simulations.
- Interfacial heat-transfer coefficients between ZG0Cr13Ni4Mo and a furan resin sand mold were determined by inverse analysis in ProCAST. The coefficient decreases from 760 W/m²·°C at 1450°C to 490 W/m²·°C at 1100°C. The relationship between the coefficient and air gap width was quantified; the coefficient is highly sensitive to the initial formation of the gap but less sensitive when the gap exceeds about 0.25 mm.
- The critical Niyama criterion values for porosity prediction in large steel castings were established by comparing ultrasonic inspection results with simulation predictions. For ZG0Cr13Ni4Mo, the critical value ranges from 25 to 30 °C1/2·s1/2·cm-1 (3.2–3.87 °C1/2·min1/2·cm-1), while for ZG230-450, it is 25 °C1/2·s1/2·cm-1 (3.2 °C1/2·min1/2·cm-1). These values are larger than those for small steel castings and are more appropriate for large-section components.
- Application of the obtained parameters to simulate the casting of a large steel frame demonstrated that the optimized chill placement reduces shrinkage porosity. The successful production and inspection of the frame validated the accuracy of the parameters and the simulation methodology.
The methodologies and results presented in this thesis provide reliable input parameters for the numerical simulation of large steel castings, which is essential for defect prediction and process optimization in heavy industry. Future work could extend the database to more steel grades and further refine the interfacial heat-transfer model to account for local variations due to geometry and casting orientation.