In this paper, we present a comprehensive study on the solidification and shrinkage behavior of a diffuser casting used in a containment spray pump, which is a critical component in nuclear power plants. The casting is made of ZG0Cr13Ni4Mo, a low-carbon martensitic stainless steel. Due to its complex geometry, including a spiral flow channel and significant wall thickness variations, the casting is prone to shrinkage defects and dimensional inaccuracies. We utilized UG NX8.0 for three-dimensional modeling and AnyCasting simulation software to analyze the filling and solidification processes. The initial process design was evaluated, and defects such as shrinkage porosity and misalignment were identified. To address these issues, we proposed modifications to the riser and chill systems, and performed parameter optimization via orthogonal experiments. Additionally, dimensional deviations were corrected by adjusting core box dimensions based on three-dimensional scanning data. Our findings demonstrate that the improved process design effectively eliminates shrinkage defects and achieves the required dimensional accuracy. The methodology presented here offers valuable insights for similar castings in the sand casting foundry industry.
1. Introduction
The containment spray system (EAS) is a safety system in pressurized water reactors (PWRs) designed to reduce pressure and temperature inside the containment in the event of a loss-of-coolant accident. The diffuser is a key component of the containment spray pump, which is a nuclear-grade safety pump. The diffuser is classified as an internal component of the pump that does not bear pressure, and it is manufactured using ZG0Cr13Ni4Mo, a low-carbon martensitic stainless steel. This material offers excellent mechanical properties, good corrosion resistance, and outstanding weldability, making it suitable for critical service in nuclear power plants. However, its high alloy content leads to a relatively large solidification shrinkage, which makes the casting process challenging, especially for complex geometries.
The diffuser casting has a cylindrical shape with a maximum diameter of 740 mm and a height of 620 mm. The wall thickness varies from 12 mm to 55 mm, and the internal architecture features a spiral flow path, which is essential for the hydraulic performance of the pump. The dimensional tolerances are stringent, requiring compliance with ISO8062/CT11. The casting must be free from defects such as shrinkage cavities, porosity, cracks, and sand inclusions. Moreover, the casting undergoes non-destructive examinations including radiographic and penetrant testing, as well as tensile and impact tests.
The traditional trial-and-error approach in a sand casting foundry is inefficient for such a complex component. Therefore, we adopted computer-aided engineering (CAE) techniques to simulate the casting process and optimize the design. This study focuses on the solidification and shrinkage analysis of the diffuser casting, followed by process optimization and dimensional correction.
2. Theoretical Basis
2.1 Heat Transfer During Solidification
During the solidification of a casting, heat is transferred through three fundamental modes: conduction, convection, and radiation. In a sand casting foundry, the mold (typically resin-bonded sand) has a much lower thermal conductivity than the molten metal. Consequently, the cooling rate of the casting is primarily controlled by the heat dissipation capacity of the mold. The governing differential equation for transient heat conduction in three dimensions is given by:
$$ \frac{\partial}{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(\lambda \frac{\partial T}{\partial z}\right) + \dot{q} = c\rho \frac{\partial T}{\partial t} $$
where \(\lambda\) is the thermal conductivity, \(T\) is the temperature, \(\dot{q}\) is the internal heat generation rate, \(c\) is the specific heat capacity, \(\rho\) is the density, and \(t\) is time. For the sand casting of steel, the heat transfer at the metal-mold interface is dynamic, involving an interfacial thermal resistance. In the present simulation, the heat transfer coefficient was treated as a function of temperature to improve accuracy.
2.2 Shrinkage of Castings
All metals undergo contraction during cooling from the liquid state to room temperature. The total shrinkage can be divided into three stages: liquid shrinkage, solidification shrinkage, and solid-state shrinkage. The volumetric shrinkage \(\varepsilon_V\) and linear shrinkage \(\varepsilon_l\) are defined as:
$$ \varepsilon_V = \frac{V_0 – V_1}{V_0} \times 100\% $$
$$ \varepsilon_l = \frac{l_0 – l_1}{l_0} \times 100\% $$
where \(V_0\), \(V_1\) and \(l_0\), \(l_1\) are the volumes and lengths at temperatures \(t_0\) and \(t_1\), respectively. In steel castings, the solidification shrinkage is significant, and if not compensated by risers, it leads to internal porosity. The shrinkage of alloy steels is influenced by the content of alloying elements. Table 1 presents the effect coefficients of elements on the solidification shrinkage of steel.
| Element | Mn | Cr | Si | Al | W | Ni |
|---|---|---|---|---|---|---|
| Coefficient | +0.0585 | +0.12 | +1.03 | +1.70 | -0.53 | -0.0354 |
The casting shrinkage rate, often called the patternmaker’s allowance, is defined as:
$$ \varepsilon = \frac{L_M – L_J}{L_J} \times 100\% $$
where \(L_M\) is the pattern (or core box) dimension and \(L_J\) is the actual casting dimension. For sand casting foundry processes, typical values for cast steel range from 1.3% to 2.3%, but the actual value depends on the part geometry, mold rigidity, and cooling conditions.
2.3 Numerical Simulation of Casting Processes
Numerical simulation has become a powerful tool in modern foundry practice. By solving the conservation equations for mass, momentum, and energy, casting simulation software can predict mold filling, solidification, and defect formation. The finite difference method (FDM) is commonly employed, where the computational domain is discretized into a structured grid. We selected AnyCasting software for this study because of its robust capabilities in handling complex geometries and its accurate defect prediction models.
3. Initial Process Design
3.1 Casting Material
The diffuser casting is made of ZG0Cr13Ni4Mo, which corresponds to CA-6NM grade. The chemical composition is listed in Table 2. The liquidus and solidus temperatures are approximately 1490°C and 1455°C, respectively. The material exhibits a martensitic transformation during cooling, which causes a volumetric expansion of about 0.54%.
| C | Si | Mn | S | P | Cr | Ni | Mo |
|---|---|---|---|---|---|---|---|
| ≤0.06 | 0.30-0.80 | ≤1.00 | ≤0.020 | ≤0.030 | 12.00-13.50 | 3.50-4.50 | 0.40-0.70 |
3.2 Initial Gating and Riser Design
The initial process was designed for a sand casting foundry using resin-bonded sand molds. The casting was oriented with the large flange at the bottom and the small end at the top to facilitate progressive solidification. A three-part molding was adopted because of the complex geometry. The gating system was bottom-gated to ensure smooth filling and avoid sand erosion. Ceramic tubes with a diameter of 60 mm were used for the runner system, and the sprue had a diameter of 60 mm. The pouring time was calculated based on the casting weight and the nozzle diameter of the ladle:
$$ t = \frac{G}{N n q} $$
where \(G\) is the total weight of metal (810 kg after accounting for expansion), \(N\) and \(n\) are the number of ladles and nozzles (both 1), and \(q\) is the pouring rate (27 kg/s for a 40 mm nozzle). This yields a pouring time of 30 s. The rise speed of the metal in the mold was checked:
$$ V = \frac{C}{t} = \frac{901}{30} = 30 \text{ mm/s} $$
which exceeds the minimum allowable rise speed of 25 mm/s for complex castings.
Risers were designed using the modulus method. Three open risers (100×200 mm) were placed on the top flange, eight blind risers (Φ100×150 mm) around the bottom, and one insulating riser (Φ110×165 mm) on the central core to feed the hot spot at the modified through-hole. Two external chills (60×60×30 mm) were placed on the side steps.
4. Numerical Simulation of Initial Process
4.1 Pre-processing
The solid models of the casting, gating system, risers, and chills were exported in STL format and imported into AnyCasting. Non-uniform mesh was generated, resulting in 3,334,992 cells. The material database was supplemented with the thermal-physical properties of ZG0Cr13Ni4Mo. The main simulation parameters are listed in Table 3.
| Parameter | Value |
|---|---|
| Pouring temperature | 1570°C |
| Pouring time | 25 s |
| Ladle nozzle diameter | 40 mm |
| Initial mold temperature | 20°C |
4.2 Filling Simulation
The filling simulation (Figure 1) shows that the mold filled smoothly with a planar liquid metal front. Slight turbulence could be observed only in the bottom blind risers that were not directly connected to the ingate, but this does not affect the casting quality. The air entrainment analysis indicated good venting behavior, and no air porosity defects were predicted.
4.3 Solidification and Defect Prediction
The solidification simulation predicted a solidification time of 4433 seconds. The temperature distribution at the start of solidification is shown in Figure 2. The chills effectively accelerated cooling at the stepped locations. However, the residual melt modulus analysis revealed two problematic regions: the lower inner circumferential area and the bottom flange inner wall. Both areas exhibited isolated liquid regions, indicating insufficient feeding from the risers. The shrinkage porosity predicted by the simulation matched the defects observed in the actual casting produced by the sand casting foundry, validating the accuracy of the simulation model.
## 5. Process Optimization
### 5.1 Modified Riser and Chill Design
To eliminate the shrinkage defects, we improved the feeding system as follows:
– **External chills:** A ring of 10 chills (80×30×30 mm) were uniformly placed on the lower inner surface of the casting to accelerate cooling and extend the end zone.
– **Additional blind riser:** A blind riser (Φ100×150 mm) was added at the middle of the bottom flange, directly attached via three necks, to provide localized feeding. The riser modulus was calculated using:
$$ M_r = f M_c $$
with \(f=1.2\) and \(M_c=1.25\) cm, giving \(M_r=1.5\) cm.
The modified process also retained the existing gating system since filling was already satisfactory.
### 5.2 Simulation of Modified Process
The improved design was re-simulated. As shown in Figure 3, the solidification sequence is now progressive from the bottom to the top, with the risers solidifying last. The shrinkage porosity previously observed at the inner surface and bottom flange was completely eliminated; any residual isolated liquid was confined to the risers. Thus, the modified process is expected to produce a sound casting.
## 6. Orthogonal Experiment for Process Parameter Optimization
In order to find the optimal casting parameters, we designed an orthogonal experiment. The factors considered were pouring temperature (A), pouring time (B), and initial mold temperature (C), each at three levels. The residual melt modulus was used as the response variable, since a smaller value indicates fewer shrinkage defects. Table 4 lists the factors and levels.
| Level | A: Pouring temp (°C) | B: Pouring time (s) | C: Mold initial temp (°C) |
|---|---|---|---|
| 1 | 1550 | 28 | 20 |
| 2 | 1560 | 30 | 60 |
| 3 | 1570 | 32 | 100 |
The \(L_9(3^4)\) orthogonal array was adopted, and the experiments were conducted via simulation. The results are presented in Table 5.
| Run | A | B | C | Residual melt modulus (cm) |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1.9200 |
| 2 | 1 | 2 | 2 | 1.9306 |
| 3 | 1 | 3 | 3 | 1.9404 |
| 4 | 2 | 1 | 2 | 1.9657 |
| 5 | 2 | 2 | 3 | 1.9759 |
| 6 | 2 | 3 | 1 | 1.9524 |
| 7 | 3 | 1 | 3 | 2.0147 |
| 8 | 3 | 2 | 1 | 1.9878 |
| 9 | 3 | 3 | 2 | 1.9986 |
A range analysis was performed, and the results are summarized in Table 6.
| Statistics | A | B | C |
|---|---|---|---|
| t1 | 1.930 | 1.967 | 1.953 |
| t2 | 1.965 | 1.965 | 1.965 |
| t3 | 2.000 | 1.964 | 1.977 |
| R | 0.070 | 0.003 | 0.024 |
| Rank | A > C > B |
The analysis of variance (ANOVA) indicated that factor A (pouring temperature) has a highly significant effect, factor C is significant, while B is not significant. The optimal combination was A3 B1 C3, i.e., pouring temperature 1570°C, pouring time 28 s, and mold initial temperature 100°C. These parameters were subsequently implemented in the sand casting foundry for production.
## 7. Dimensional Deviation Correction
### 7.1 Causes of Dimensional Errors
The diffuser casting must meet the ISO8062/CT11 dimensional tolerance. After initial production, three-dimensional scanning revealed that the external dimensions were within tolerance, but the internal flow channel exhibited deviations up to -4.62 mm at certain locations. The main cause was that a single constant shrinkage rate of 1.5% used in the initial design was not applicable to all sections of this complex casting. The geometry, local cooling rates, and resistance during contraction cause non-uniform shrinkage. In addition, the martensitic transformation induces volumetric expansion, further complicating the dimensional behavior.
### 7.2 Correction of Core Box Dimensions
To correct the dimensions, we determined the actual shrinkage rates at the deviating locations using the measured casting dimensions and the original pattern dimensions. For example, at a location with a basic size of 286 mm and a deviation of -4.62 mm, the original core box dimension was:
$$ L_M = (1 + 0.015) \times 286 = 290.29 \text{ mm} $$
The actual shrinkage rate was calculated as:
$$ \varepsilon = \frac{290.29 – (286 – 4.62)}{286 – 4.62} \times 100\% = 3.17\% $$
The allowable tolerance for 286 mm is ±3.1 mm, so the acceptable core box dimension ranges from:
$$ L_{M1} = (1 + 0.0317) \times (286 – 3.1) = 291.88 \text{ mm} $$
to:
$$ L_{M2} = (1 + 0.0317) \times (286 + 3.1) = 295.07 \text{ mm} $$
The same procedure was applied to other deviated locations. Table 7 lists the measured deviations, computed shrinkage rates, and selected core box modifications. These modifications were implemented by grinding or applying epoxy resin to the core boxes, depending on whether the dimension needed to be reduced or increased.
| Deviation (mm) | Casting size (mm) | Tolerance (mm) | Original core box size (mm) | Actual ε (%) | Min. core box (mm) | Max. core box (mm) | Selected modifier (mm) |
|---|---|---|---|---|---|---|---|
| -4.62 | 286 | 6.2 | 290.29 | 3.2 | 291.88 | 295.07 | 3.0 |
| -4.32 | 325 | 6.2 | 329.88 | 2.9 | 331.24 | 334.43 | 3.0 |
| +6.53 | 336 | 6.2 | 341.04 | 0.4 | 331.57 | 334.66 | 8.0 |
| +4.24 | 345.5 | 6.2 | 350.68 | 0.3 | 346.54 | 349.65 | 2.5 |
| -4.66 | 231.5 | 5.6 | 234.97 | 3.6 | 236.93 | 239.83 | 3.5 |
| -3.49 | 231.5 | 5.6 | 234.97 | 3.1 | 235.79 | 238.68 | 2.5 |
| -3.57 | 315 | 6.2 | 319.73 | 2.7 | 320.63 | 323.51 | 2.5 |
| -5.31 | 179 | 5.6 | 181.69 | 4.6 | 184.31 | 187.23 | 4.0 |
| -4.14 | 179 | 5.6 | 181.69 | 3.9 | 183.07 | 185.98 | 3.0 |
After correcting the core boxes, a second casting was made and scanned. The new dimensional measurements showed that all deviations were within the specified tolerance, confirming the effectiveness of the corrective measures.
## 8. Production Verification and Conclusions
The optimized process was verified in an actual production run at a sand casting foundry. The castings produced using the modified riser/chill design and the optimal process parameters were free from shrinkage cavities and porosity, as confirmed by radiographic and ultrasonic tests. Dimensional re-scanning verified that all features met the ISO8062/CT11 requirements. The process improvements led to a significant reduction in scrap rate and rework cost, while maintaining the high quality required for nuclear-grade components.
In summary, this study demonstrates the powerful synergy of numerical simulation and systematic experimental design in solving complex casting problems. The key conclusions are:
1. The initial process design produced shrinkage defects at the lower inner ring and bottom flange due to insufficient feeding. Adding external chills and a blind riser effectively eliminated these defects.
2. Orthogonal experimental analysis revealed that pouring temperature has the greatest influence on shrinkage defects, followed by mold initial temperature and pouring time. The optimal parameters are 1570°C pouring temperature, 28 s pouring time, and 100°C mold initial temperature.
3. Dimensional deviations in complex castings cannot be adequately compensated by a single shrinkage allowance. A location-specific correction based on actual shrinkage measurements is necessary to meet stringent tolerances.
4. AnyCasting simulation proved to be a reliable tool for predicting defects and optimizing the sand casting foundry process, reducing the need for costly trial runs.
The methods described here can be extended to other castings of similar complexity, especially those made of high-shrinkage alloys such as martensitic stainless steels. The integration of CAD, CAE, and statistical optimization is essential for modern high-quality foundry production.