In this work, I investigate the solidification shrinkage behavior and casting process optimization of a diffuser component used in a containment spray pump. The diffuser is a critical sand casting part made of ZG0Cr13Ni4Mo, a low-carbon martensitic stainless steel. This material exhibits excellent mechanical properties and corrosion resistance, but its large solidification shrinkage often leads to shrinkage defects in complex sand casting parts. My research combines CAD/CAE simulation with practical production validation to eliminate shrinkage porosity, improve dimensional accuracy, and optimize process parameters. I first introduce the theoretical basis of heat transfer and shrinkage during solidification. Then I describe the initial casting process design and use AnyCasting software to numerically simulate the mold filling and solidification processes. The simulation results predict shrinkage defects at the bottom flange and inner ring, which are consistent with actual casting defects. To solve these problems, I propose an improved process with additional external chills and a blind riser. I also apply an orthogonal experiment to determine the optimal parameters: pouring temperature 1570°C, pouring time 28 s, and initial mold temperature 100°C. Furthermore, I analyze the dimensional deviations of the castings and correct the core box dimensions based on measured shrinkage rates. The production verification shows that the improved process successfully eliminates shrinkage defects and meets the stringent size requirements of nuclear-grade equipment. This study demonstrates the effectiveness of numerical simulation and systematic optimization for producing high-quality sand casting parts.
1. Introduction
The containment spray system is a crucial safety feature in pressurized water reactor nuclear power plants. It provides cooling water to the containment atmosphere during loss-of-coolant accidents, thereby reducing pressure and removing radioactive iodine. The diffuser is a key component of the containment spray pump, and it is classified as a nuclear-grade mechanical part. The diffuser is a sand casting part produced from ZG0Cr13Ni4Mo, a low-carbon martensitic stainless steel with the Chinese designation ZG0Cr13Ni4Mo. This steel is widely used in pump casings, impellers, and other hydraulic components because of its excellent strength, toughness, fatigue resistance, and cavitation erosion resistance.
Due to the nuclear safety requirements, the diffuser casting must pass strict inspections, including tensile testing, impact testing, liquid penetrant testing, radiographic testing, and dimensional inspection. The casting is not permitted to have defects such as peeling, cracks, sand holes, shrinkage cavities, or porosity. Moreover, because the pump performance strongly depends on the internal flow channel geometry, the dimensional tolerance is very tight. The diffuser has a complex structure with helical flow passages, a maximum height of 620 mm, and wall thicknesses ranging from 12 mm to 55 mm. Such a large structural gradient, combined with the high shrinkage of alloyed steel, makes it difficult to achieve sound and dimensionally accurate sand casting parts.
In my project, I attempt to solve the production difficulties encountered by a company that manufactures this diffuser. The initial casting process produced shrinkage defects and unacceptable dimensional variations. My approach involves three major steps: (1) numerical simulation of the initial process to reveal defect mechanisms; (2) optimization of the feeding system (risers and chills) and process parameters; (3) dimensional correction of the core box based on three-dimensional scanning data. The outcome is a reliable casting process that produces excellent sand casting parts, with no shrinkage defects and with dimensions within the specified tolerance bands.
2. Theoretical Basis of Solidification and Shrinkage
2.1 Heat Transfer During Solidification
Heat transfer occurs through conduction, convection, and radiation. During casting solidification, all three modes can be present. The governing differential equation for heat conduction in a solidifying body is:
$$ \frac{\partial}{\partial x}\left(\lambda\frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(\lambda\frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(\lambda\frac{\partial T}{\partial z}\right)+\dot{q}=c\rho\frac{\partial T}{\partial t} \tag{1} $$
where \( \lambda \) is the thermal conductivity, \( T \) is the temperature, \( \dot{q} \) is the rate of internal heat generation, \( c \) is the specific heat, \( \rho \) is the density, and \( t \) is time. For constant \( \lambda \), Eq. (1) simplifies to:
$$ \lambda\left(\frac{\partial^{2}T}{\partial x^{2}}+\frac{\partial^{2}T}{\partial y^{2}}+\frac{\partial^{2}T}{\partial z^{2}}\right)+\dot{q}=c\rho\frac{\partial T}{\partial t} \tag{2} $$
The solidification process is characterized by three simultaneous transmissions: heat transfer, momentum transfer, and mass transfer. These coexist in the moving solid-liquid interface and the metal-mold interface.
For sand casting parts using resin-bonded sand molds, the thermal conductivity of the mold is much lower than that of the molten metal. Therefore, the cooling rate is controlled mainly by the heat extraction capability of the sand mold. The interfacial thermal resistance between the metal and mold is usually negligible compared to the thermal resistance of the sand mold itself. As a result, the temperature gradient across the casting cross-section is small, and the ability of the sand mold to conduct heat governs the solidification speed.
2.2 Shrinkage Mechanisms
When a metal cools from the pouring temperature to room temperature, it undergoes three stages: liquid shrinkage, solidification shrinkage, and solid shrinkage. The volumetric shrinkage \( \varepsilon_{V} \) and linear shrinkage \( \varepsilon_{l} \) are defined as:
$$ \varepsilon_{V} = \frac{V_{0}-V_{1}}{V_{0}}\times 100\% \tag{3} $$
$$ \varepsilon_{l} = \frac{l_{0}-l_{1}}{l_{0}}\times 100\% \tag{4} $$
where \( V_{0}, V_{1} \) and \( l_{0}, l_{1} \) are the volumes and lengths at temperatures \( t_{0} \) and \( t_{1} \), respectively.
The total shrinkage comprises liquid contraction, solidification contraction, and solid contraction. The first two stages are responsible for the formation of shrinkage cavities and porosity. Solid contraction can lead to dimensional deviations and distortion if the casting is constrained by the mold.
For steel sand casting parts, alloying elements significantly influence the solidification shrinkage. The influence coefficients of some elements are listed in Table 1.
| Element | Mn | Cr | Si | Al | W | Ni |
|---|---|---|---|---|---|---|
| Coefficient | +0.0585 | +0.12 | +1.03 | +1.70 | −0.53 | −0.0354 |
For ZG0Cr13Ni4Mo stainless steel, the high chromium and silicon contents increase the shrinkage rate. This material has a notable crystalline range, with a liquidus temperature of 1490°C and a solidus temperature of 1455°C. The dendritic network that forms during solidification restricts liquid flow and makes it difficult for risers to compensate for volumetric contraction, leading to shrinkage porosity in complex regions.
The casting contraction rate \( \varepsilon \) (also called patternmaker’s shrinkage) is used to dimension the pattern. It is defined as:
$$ \varepsilon = \frac{L_{M}-L_{J}}{L_{J}}\times 100\% \tag{5} $$
where \( L_{M} \) is the pattern dimension and \( L_{J} \) is the final casting dimension. The pattern working dimension is then:
$$ L_{M} = \left(1+\varepsilon\right)L_{J} \tag{6} $$
Typical values of contraction allowance for sand casting parts are given in Table 2.
| Alloy | Free contraction (%) | Restrained contraction (%) |
|---|---|---|
| Gray iron, small/medium | 1.0 | 0.9 |
| Ductile iron, pearlitic/ferritic | 0.9–1.1 / 0.8–1.0 | 0.6–0.8 / 0.4–0.6 |
| Cast steel, carbon/low alloy | 1.6–2.0 | 1.3–1.7 |
| Cast steel, Cr high-alloy | 1.3–1.7 | 1.0–1.4 |
| Cast steel, austenitic | 2.0–2.3 | 1.7–2.0 |
In practice, the exact shrinkage of a given casting depends on its geometry, mold rigidity, cooling conditions, and other factors. For complex sand casting parts with tight dimensional tolerances, one must obtain the actual shrinkage by trial production and then correct the pattern or core box accordingly.
3. Description of the Diffuser Casting
3.1 Function and Requirements
The diffuser is a component of the containment spray pump. The pump is a vertical barrel-type pump with a nominal flow rate of 850 m3/h and a head of 131 m. The diffuser is a stationary part that converts kinetic energy of the fluid into pressure energy. It is a sand casting part manufactured from low-carbon martensitic stainless steel ZG0Cr13Ni4Mo. According to RCC-M 3201, the chemical composition requirements are listed in Table 3.
| Element | C | Si | Mn | S | P | Cr | Ni | Mo |
|---|---|---|---|---|---|---|---|---|
| Requirement | ≤0.06 | 0.30–0.80 | ≤1.00 | ≤0.020 | ≤0.030 | 12.00–13.50 | 3.50–4.50 | 0.40–0.70 |
The mechanical properties after proper heat treatment are given in Table 4.
| Yield strength \( \sigma_{s} \) (MPa) | Ultimate tensile strength \( \sigma_{b} \) (MPa) | Elongation \( \delta \) (%) |
|---|---|---|
| 550 | 760 | 15 |
The casting must be free from defects such as shrinkage cavities, porosity, cracks, sand inclusion, and cold shuts. The required dimensional accuracy is ISO 8062/CT11. The diffuser has a complex geometry with an outer diameter of 740 mm and a height of 620 mm. It contains a helical flow channel that is formed by complex cores. Because of the large wall-thickness differences, the casting is prone to hot spots and solidification shrinkage.
3.2 Initial Casting Process Design
The initial process was designed with the casting in a large-end-down orientation. Because of the complex shape, a three-box molding method was employed. The pattern was split into two halves. The mold material and cores were made of resin-bonded sand. The pouring system was a bottom-gating system with ceramic tubes to avoid sand erosion and oxidation. The gating dimensions were chosen based on a 40 mm diameter ladle nozzle. The initial riser design included three open risers at the top flange, one insulating riser above the central hole, and eight blind risers around the bottom flange. External chills were placed on two bosses. The initial casting contraction allowance was set uniformly to 1.5% in all directions.
The total cast weight was approximately 750 kg. The pouring temperature was 1570°C and the nominal pouring time was 25 s.
4. Numerical Simulation of the Initial Process
4.1 Modeling and Meshing
I used NX 8.0 to create three-dimensional models of the casting, gating system, risers, chills, and cores. The models were exported in STL format and imported into the AnyCasting simulation software. A non-uniform mesh was generated with 3,334,992 cells, ensuring at least two cells across the thinnest walls. The casting material was defined in a user database using the thermal-physical properties of ZG0Cr13Ni4Mo. The mold material was resin-bonded sand. The interface heat-transfer coefficients were specified as temperature-dependent functions. The main parameters are shown in Table 5.
| Parameter | Value |
|---|---|
| Pouring temperature | 1570°C |
| Pouring time | 25 s |
| Ladle nozzle diameter | 40 mm |
| Mold type | Resin sand (three-box) |
4.2 Mold Filling Results
The filling process was simulated for 25 s. The results indicated a smooth and stable rise of the molten metal in the mold. The gas venting was satisfactory, with no obvious entrapment. Small vortices were observed only inside four blind risers that were not connected to ingates, but these did not affect the casting quality. Therefore, the filling system itself did not introduce defects.
4.3 Solidification Results and Defect Prediction
The solidification simulation predicted that the casting would fully solidify in 4433 s. The temperature field at the start of solidification showed a bottom-to-top decreasing temperature gradient, which is detrimental for directional solidification. However, due to the large risers, the temperature distribution reversed during later stages, providing acceptable feeding. The simulation predicted shrinkage defects in two regions: the inner ring lower surface and the bottom flange inner wall. These defects are shown in the residual melt modulus results. The predicted locations correlated well with defects observed in actual production. The solidification sequence also revealed an isolated liquid region at the bottom flange after 519 s, which could not be fed due to early closure of the feeding channel. The inner ring region is about 329 mm away from the insulating riser bottom, making feeding difficult, especially because this area is surrounded by sand cores with poor heat dissipation.
5. Optimization of Casting Process and Parameters
5.1 Improvements to the Feeding System
To eliminate the shrinkage defects, I adopted two main measures:
(1) Additional blind riser at the bottom flange. A blind riser with a diameter of 100 mm and height of 150 mm was added in the middle of the bottom flange. The riser neck was designed with a modulus satisfying the ratio \( M_{C}:M_{N}:M_{r}=1:1.1:1.2 \). For the flange hot spot with \( M_{C}=1.25\,\text{cm} \), the riser modulus becomes \( M_{r}=1.2\times1.25=1.5\,\text{cm} \). The riser was connected to the flange via three necks, each 100 mm × 53 mm in cross-section. Using a riser efficiency of \( \eta=14\% \) for side risers, the maximum compensable volume is given by:
$$ V_{C\max} = \frac{\eta}{1-\eta} V_{r} \tag{7} $$
where \( V_{r} \) is the riser volume. With \( V_{r}=1.18\,\text{L} \), \( V_{C\max}=0.192\,\text{L} \). The actual shrinkage volume required is \( V_{s}=3140.2 \times 0.045 = 141.3\,\text{cm}^{3} = 0.141\,\text{L} \), which is less than \( V_{C\max} \), so the riser is adequate.
(2) External chills on the inner ring. Ten external chills, each 80 mm × 30 mm × 30 mm, were uniformly placed on the lower inner ring surface. The chills accelerate local cooling, create an artificial end effect, and extend the feeding distance of the insulating riser to the inner ring region.
The gating system and parting line remained unchanged because the filling simulation showed satisfactory performance.
5.2 Simulation of the Improved Process
I repeated the numerical simulation with the improved riser and chills. The filling behavior remained stable. The solidification analysis showed that the new bottom blind riser solidified after the bottom flange, providing effective feeding. The external chills successfully increased the cooling rate at the inner ring and eliminated the isolated liquid region. The residual melt modulus prediction showed no shrinkage porosity in the previously defective areas. The shrinkage was now confined to the risers, which are removed after solidification.
5.3 Orthogonal Experiment for Process Parameters
To find the optimal processing conditions, I carried out a three-factor, three-level orthogonal experiment. The factors and levels are listed in Table 6.
| Level | A: Pouring temperature (°C) | B: Pouring time (s) | C: Initial mold temperature (°C) |
|---|---|---|---|
| 1 | 1550 | 28 | 20 |
| 2 | 1560 | 30 | 60 |
| 3 | 1570 | 32 | 100 |
I used the standard \( L_{9}(3^{4}) \) orthogonal array. The evaluation index was the residual melt modulus, which indicates the amount of isolated liquid remaining. Smaller values correspond to less shrinkage porosity. The results are summarized in Tables 7–9.
| Trial | A | B | C | Residual melt modulus |
|---|---|---|---|---|
| 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 | B | C | |
|---|---|---|---|
| \( t_{1} \) | 1.930 | 1.967 | 1.953 |
| \( t_{2} \) | 1.965 | 1.965 | 1.965 |
| \( t_{3} \) | 2.000 | 1.964 | 1.977 |
| Range \( R \) | 0.070 | 0.003 | 0.024 |
| Order | A > C > B | ||
| Optimal | A3 | B1 | C3 |
| Source | Sum of squares \( S \) | df | Mean square | F ratio |
|---|---|---|---|---|
| A | 0.002710 | 2 | 0.001355 | 903.33 |
| B | 0.000014 | 2 | 0.000007 | 4.67 |
| C | 0.000836 | 2 | 0.000418 | 278.67 |
| Error | 0.000003 | 2 | 0.0000015 |
Since \( F_{0.01}(2,2)=99 \) and \( F_{0.1}(2,2)=9 \), factors A and C are statistically significant, whereas factor B is not significant. The optimal combination is A3 B1 C3, i.e., pouring temperature of 1570°C, pouring time of 28 s, and initial mold temperature of 100°C. This combination gives the smallest residual melt modulus and thus the soundest casting.
6. Dimensional Deviation Correction
6.1 Causes of Dimensional Deviations
Even with a good feeding system, the final dimensions of a sand casting part may deviate from the design because of the complex interactions of shrinkage, mold expansion, pattern wear, core deformation, and internal stresses. In this case, the diffuser casting had a uniform contraction allowance of 1.5% in all directions. However, the actual shrinkage was not uniform due to the varying wall thickness and restraint conditions. Three-dimensional scanning showed that the external surfaces were within tolerance, but the internal flow-channel surfaces exhibited substantial deviations, some exceeding the allowed tolerances. This is because the internal geometry is formed by sand cores, and the core dimensions were based on the same uniform shrinkage value, which did not account for local variations.
The martensitic transformation in ZG0Cr13Ni4Mo also contributes to volume changes. When austenite transforms to martensite, the crystal structure changes from face-centered cubic to body-centered cubic, decreasing the atomic packing factor from 0.74 to 0.68. This expansion is about 0.54% and can influence the final dimensions of the casting.
6.2 Determination of Core Box Correction Parameters
To correct the dimensional deviations, I used the measured dimensions from three-dimensional scanning to calculate the actual linear shrinkage at each deviated location. According to the ISO 8062/CT11 tolerance standard, the permissible deviations depend on the basic size. For example, for a basic size of 286 mm, the tolerance is 6.2 mm. The original core box dimension was calculated as:
$$ L_{M} = \left(1+0.015\right)\times 286 = 290.29\,\text{mm} \tag{8} $$
If the actual casting dimension was measured as \( 286-4.62=281.38\,\text{mm} \), the actual shrinkage rate becomes:
$$ \varepsilon = \frac{290.29-281.38}{281.38}\times 100\% = 3.17\% \tag{9} $$
To bring the casting within the tolerance band, the new core box dimension should be between the minimum and maximum allowable values. The allowable casting dimension ranges from \( 286-3.1 \) to \( 286+3.1 \). Thus the minimum and maximum core box dimensions are:
$$ L_{M1} = \left(1+0.0317\right)\times 282.9 = 291.88\,\text{mm} \tag{10} $$
$$ L_{M2} = \left(1+0.0317\right)\times 289.1 = 295.07\,\text{mm} \tag{11} $$
I applied this procedure to all deviated locations. Table 10 summarizes the measured deviations, calculated shrinkage rates, and the recommended core box dimensions. In practice, a middle value within this range was chosen to provide a safety margin, and the final correction was rounded to a convenient machining value.
| Deviation (mm) | Casting size (mm) | Tolerance (mm) | Original pattern size (mm) | Actual shrinkage (%) | Min pattern size \( L_{M1} \) (mm) | Max pattern size \( L_{M2} \) (mm) |
|---|---|---|---|---|---|---|
| −4.62 | 286 | 6.2 | 290.29 | 3.17 | 291.88 | 295.07 |
| −4.32 | 325 | 6.2 | 329.88 | 2.9 | 331.24 | 334.43 |
| +6.53 | 336 | 6.2 | 341.04 | 0.4 | 331.57 | 334.66 |
| +4.24 | 345.5 | 6.2 | 350.68 | 0.3 | 346.54 | 349.65 |
| −4.66 | 231.5 | 5.6 | 234.97 | 3.6 | 236.93 | 239.83 |
| −3.49 | 231.5 | 5.6 | 234.97 | 3.1 | 235.79 | 238.68 |
| −3.57 | 315 | 6.2 | 319.73 | 2.7 | 320.63 | 323.51 |
| −5.31 | 179 | 5.6 | 181.69 | 4.6 | 184.31 | 187.23 |
| −4.14 | 179 | 5.6 | 181.69 | 3.9 | 183.07 | 185.98 |
After modifying the core boxes according to these dimensions, the subsequent production run was scanned again. The second scan showed that the deviations were almost completely eliminated, and the few remaining minor deviations were acceptable after local grinding or welding repair (followed by post-weld heat treatment). Thus, the core box corrections successfully brought the sand casting parts into compliance with the ISO 8062/CT11 requirements.
7. Conclusion
In this project, I have systematically analyzed and optimized the casting process for a diffuser component made of ZG0Cr13Ni4Mo low-carbon martensitic stainless steel, which is a challenging sand casting part for nuclear applications. The main conclusions from my work are as follows:
(1) Numerical simulation using AnyCasting accurately predicted the shrinkage porosity locations in the original process. The defects were attributed to insufficient feeding at the bottom flange and the inner ring, caused by long feeding distances, early closure of feeding paths, and poor local cooling.
(2) The addition of a bottom blind riser and ten external chills effectively eliminated the shrinkage porosity. The modified process ensures directional solidification and adequate feeding for all hot spots.
(3) The orthogonal experiment showed that the pouring temperature has the greatest influence on casting soundness, followed by the initial mold temperature, while the pouring time has a negligible effect. The optimal process parameters are a pouring temperature of 1570°C, a pouring time of 28 s, and an initial mold temperature of 100°C.
(4) Uniform contraction allowance is not sufficient for complex sand casting parts. By measuring actual dimensions and calculating local shrinkage rates, I corrected the core box dimensions and achieved the required ISO 8062/CT11 tolerance.
(5) The combined use of CAD/CAE simulation, statistical parameter optimization, and dimensional feedback is an effective approach to produce high-quality sand casting parts with minimal trial runs and reduced cost.
This research provides a valuable reference for the production of complex stainless steel castings with similar material and geometry challenges.