My research focuses on the casting process optimization of a spray pump volute body, which is a critical component in nuclear power plant safety systems. The primary challenge was to eliminate internal shrinkage defects that appeared during sand casting production. Through numerical simulation using AnyCasting software, I analyzed the original manufacturing process, identified the root causes of sand foundry defects, and proposed systematic improvements to the gating, risering, and chilling systems. Additionally, I optimized the process parameters using orthogonal experimental design and refined the chemical composition of ZG06Cr13Ni4Mo martensitic stainless steel. Finally, I performed microstructural simulations using the CAFE method to investigate the influence of pouring temperature on grain formation. The optimized process was validated by both numerical simulation and actual production, successfully eliminating shrinkage porosity and meeting all quality requirements. This research demonstrates how modern simulation tools can effectively solve sand foundry defects in complex steel castings.
1. Introduction
The spray pump volute body is an essential part of the containment spray system in nuclear power stations. It directly or indirectly affects nuclear safety, therefore demanding exceptional quality and reliability. The casting is made of ZG06Cr13Ni4Mo, a low-carbon martensitic stainless steel with complex phase transformation behavior. The component has a complex geometry with significant wall thickness variations, ranging from 7 mm to 90 mm, making it prone to shrinkage defects during solidification. In the actual production environment, the factory encountered severe issues with internal porosity, leading to high scrap rates and economic losses. My objective was to investigate the formation mechanisms of these sand foundry defects and develop a robust casting process to eliminate them.
The research approach involved several stages. First, I performed a thorough analysis of the original casting process using three-dimensional modeling and numerical simulation. Second, I predicted the locations and causes of potential defects by simulating the filling and solidification processes. Third, I implemented improvements to the riser design, gating system, and external chills based on simulation results. Fourth, I applied orthogonal experimental design to determine the optimal pouring temperature, pouring time, and mold preheating temperature. Fifth, I optimized the alloy composition using JMatPro software and statistical methods. Sixth, I conducted a comprehensive numerical validation of the new process, followed by actual production trials. Finally, I performed microstructure simulations using the CAFE method to understand the solidification grain structure and its relationship with process parameters.
2. Numerical Methods and Software
The casting process simulation was carried out using AnyCasting, a commercial software based on the finite difference method (FDM). This method discretizes the computational domain into a structured grid and approximates partial differential equations using finite difference approximations. The fundamental principle is the replacement of derivatives with difference quotients. For a continuous function y = f(x), the derivative is defined as:
$$ \frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{f(x+\Delta x) – f(x)}{\Delta x} \tag{1} $$
In numerical simulations, the forward, backward, or central difference approximations are used. The truncation error depends on the scheme. The AnyCasting software employs a control volume approach to construct the discretized equations, which ensures physical conservation and handles complex geometries effectively. The software consists of several modules: anyPRE for preprocessing and mesh generation, anyMESH for grid editing, anyDBASE for material database management, anySOLVER for computational fluid dynamics and heat transfer calculations, and anyPOST for post-processing and visualization.
For shrinkage defect prediction, AnyCasting applies various criteria based on temperature gradients, solid fraction gradients, and residual melt modulus. The core idea is to evaluate whether isolated liquid regions exist during solidification that cannot be fed by the riser. The formation of shrinkage porosity can be attributed to the lack of liquid feeding in the final stages of solidification when dendritic networks block the flow channels.
3. Casting Description and Original Process
3.1 Component Characteristics
The spray pump volute body is a medium-sized hub-type casting with a maximum outer diameter of 755 mm, inner diameter of 315 mm, and height of 338 mm. The wall thickness varies from 7 mm to 90 mm, creating large thermal gradients during solidification. The component has a symmetrical structure with bottom flanges, external protrusions, and internal spiral cavities that complicate feeding paths. The total weight of the casting is approximately 350 kg.
The material ZG06Cr13Ni4Mo has the chemical composition listed in Table 1 and the mechanical properties in Table 2. This steel is known for its excellent toughness, corrosion resistance, and castability, but its phase transformation behavior, including martensitic transformation and reversed austenite formation, can lead to substantial volumetric changes and difficulty in sound casting production.
| Element | C | Si | Mn | S | P | Cr | Ni | Mo |
|---|---|---|---|---|---|---|---|---|
| Content | ≤0.06 | 1.0 | 1.0 | 0.02 | 0.03 | 12.0–13.5 | 3.5–4.5 | 0.4–0.7 |
| Property | Yield Strength (MPa) | Tensile Strength (MPa) | Elongation (%) |
|---|---|---|---|
| Value | ≥350 | ≥750 | ≥15 |
3.2 Original Casting Process Design
The original process was designed based on conventional engineering experience. The pouring position was selected with the bottom flange surface (the critical machined surface) facing downward to ensure good feeding and dense structure. The parting line was set at the maximum outer diameter to simplify molding. The gating system was a bottom-fill arrangement using refractory brick tubes: pouring cup, sprue (φ70 mm), cross runner (φ50 mm), and two ingates (φ50 mm) feeding directly into the bottom blind risers. This design aimed for fast, smooth filling and to promote directional solidification.
Two tiers of risers were used: one open riser at the top (1# riser: φ110×165 mm) and three blind risers at the bottom flange protrusions (2#: φ100×150 mm, 3#: φ120×180 mm, 4#: φ150×380 mm). External chills made of 45# steel (120×50×50 mm, 8 pieces) were placed on the bottom flange to enhance local cooling and extend the feeding distance of the risers. The mold was made of resin-bonded sand, and a coating of water-based and alcohol-based refractory material was manually applied.
Despite this conventional design, the trial production revealed internal shrinkage cavities in the casting, particularly at the bottom protrusions after machining, which is a typical manifestation of sand foundry defects.
4. Numerical Simulation of the Original Process
4.1 Preprocessing and Mesh Generation
I created the three-dimensional solid models of the casting, gating system, risers, and chills using UG NX software and exported them in STL format. These models were imported into AnyCasting’s anyPRE module. A variable mesh scheme was adopted to balance accuracy and computational efficiency: fine cells for the complex internal cavities and thick sections, and coarse cells for the gating system and mold. The total mesh count was 1,662,648 cells. The mesh quality was verified with cross-sectional views.
4.2 Simulation Parameters
Table 3 summarizes the key boundary conditions and process parameters used in the original process simulation. The heat transfer coefficients between different material pairs were specified. The pouring temperature was set at 1580°C, and the filling time was 18 seconds.
| Parameter | Value |
|---|---|
| Material | ZG06Cr13Ni4Mo |
| Pouring temperature | 1580°C |
| Mold material | Furan resin sand |
| Pouring time | 18 s |
| Liquid stream diameter | 50 mm |
| Heat transfer coefficient (casting-mold) | Temperature-dependent |
| Heat transfer coefficient (casting-chill) | 3000 W/(m²·K) |
| Heat transfer coefficient (mold-chill) | 1000 W/(m²·K) |
4.3 Filling Process Analysis
The filling simulation showed that the molten metal entered the mold smoothly from the bottom through the blind risers and rose progressively. The flow front remained nearly horizontal, indicating a good filling pattern. However, at the central spiral thin-wall cavity, there was potential flow convergence that could trap gas, leading to blowhole defects. The particle tracking analysis confirmed no vortex formation, but the risk of air entrapment was noted in the mid-section thin walls.
4.4 Temperature Field and Solidification Analysis
I examined the temperature evolution during solidification. At the end of filling (18 s), temperatures ranged from 1580°C at the ingates to about 1454°C near the chills, showing that the chills had initiated local cooling. The solidification progressed from the bottom and walls toward the center and risers. However, the simulation predicted that the casting would not achieve a truly directional solidification because of complex geometry. I identified three isolated liquid regions:
- Region 1: at the large wall-thickness junction in the middle of the casting, where the feeding path to both top and bottom risers was blocked.
- Region 2: at the top surface under the open risers, where the riser froze before the casting section.
- Region 3: inside the bottom blind risers, which was not a defect but indicated incomplete feeding.
The residual melt modulus criterion predicted a high probability of shrinkage cavities in those locations. The defect probability map showed porosity at the top-riser junction, at the middle thickened section, and inside the bottom protrusions. These predictions matched the actual ultrasonic inspection of the trial casting, where shrinkage defects were found exactly at the bottom protrusion holes after machining. This validated the numerical model and confirmed the presence of severe sand foundry defects.
5. Optimization of Casting Process
5.1 Riser System Improvement
To improve feeding efficiency, I replaced the open top riser with an insulating and exothermic riser sleeve. The sleeve thickness was selected according to Table 4 based on the riser diameter. For the top riser (φ110 mm), a 25 mm thick insulating sleeve was used. Additionally, I added a new insulating blind riser (5# riser: φ160×240 mm) at the center through-hole to feed the inner wall region. The new riser also had an insulating sleeve with a thickness of 35 mm. This modification extended the solidification time of the risers, ensuring that they remained liquid longer than the casting sections they fed.
| Riser diameter (mm) | <150 | 151–200 | 201–300 | 301–400 | 401–600 | 601–800 |
|---|---|---|---|---|---|---|
| Sleeve thickness δ (mm) | 25 | 35 | 40 | 50 | 60 | 80 |
5.2 Gating System Modification
I increased the number of ingates from two to three to improve the distribution of molten metal and to feed the new central riser. The ingate diameter was kept at 50 mm, and the cross runners were rearranged accordingly. The sprue remained unchanged. The modified gating system allowed faster, more balanced filling and better utilization of the added riser. The bottom-fill design preserved the advantage of smooth filling and reduced turbulence.
5.3 Chill Addition and Redesign
External chills were added at several critical locations to promote directional solidification and reduce feeding distances:
- Original bottom flange chills (1# chills) were retained.
- New conformal chills (4# chills: R430×10.5°×40 mm, two pieces) were placed between the blind risers and the corresponding casting protrusions to refine the grain structure and eliminate shrinkage in those protrusions.
- Round steel chills (3# chills: φ32 mm, two pieces) were inserted at the inner arc junctions near the large sand core to weaken the local hot spot and eliminate the isolated liquid region.
- Additional chills (2# chills: R400×10.5°×40 mm, two pieces) were placed on the inside of the corresponding protrusions to refine the local microstructure.
These chills increased the cooling rate in targeted regions, ensuring that the solidification front advanced from the chilled areas toward the risers.
6. Process Parameter Optimization
6.1 Orthogonal Experimental Design
I selected three key process parameters as factors: pouring temperature (A), pouring time (B), and mold preheating temperature (C). Each factor was studied at three levels, and an L₉(3⁴) orthogonal array was used. The objective was to minimize the residual melt modulus, which correlates with shrinkage defects. Table 5 lists the factor levels, and Table 6 presents the experimental matrix and results.
| Level | A: Pouring temperature (°C) | B: Pouring time (s) | C: Mold preheating temperature (°C) |
|---|---|---|---|
| 1 | 1550 | 14 | 0 |
| 2 | 1565 | 18 | 12.5 |
| 3 | 1580 | 22 | 25 |
| Run | A (°C) | B (s) | C (°C) | Residual Melt Modulus |
|---|---|---|---|---|
| 1 | 1 (1550) | 1 (14) | 1 (0) | 3.1785 |
| 2 | 1 | 2 (18) | 2 (12.5) | 1.7204 |
| 3 | 1 | 3 (22) | 3 (25) | 1.7054 |
| 4 | 2 (1565) | 1 | 2 | 1.7115 |
| 5 | 2 | 2 | 3 | 1.7187 |
| 6 | 2 | 3 | 1 | 1.7045 |
| 7 | 3 (1580) | 1 | 3 | 1.7138 |
| 8 | 3 | 2 | 1 | 1.7191 |
| 9 | 3 | 3 | 2 | 1.7058 |
Using range analysis, I calculated the K and k values for each factor level and the range R. The results are summarized in Table 7. The larger the R, the more significant the factor. The impact order was A > B > C, i.e., pouring temperature was the most influential, followed by pouring time, and mold preheating temperature was the least influential. The optimal combination was A₂B₃C₃, meaning pouring temperature 1565°C, pouring time 22 s, and mold preheating temperature 25°C.
| Factor | A | B | C |
|---|---|---|---|
| K₁ | 6.6043 | 6.6038 | 6.6021 |
| K₂ | 5.1347 | 5.1582 | 5.1377 |
| K₃ | 5.1387 | 5.1157 | 5.1379 |
| k₁ | 2.2014 | 2.2013 | 2.2007 |
| k₂ | 1.7116 | 1.7194 | 1.7126 |
| k₃ | 1.7129 | 1.7052 | 1.7126 |
| Range R | 0.4961 | 0.4898 | 0.4881 |
| Optimal level | A₂ | B₃ | C₃ |
7. Chemical Composition Optimization
The chemical composition of ZG06Cr13Ni4Mo plays a decisive role in determining the final microstructure (martensite vs. residual austenite). A key parameter is the martensite start temperature Mₛ. A higher Mₛ ensures complete transformation to martensite at room temperature, reducing residual austenite. The Mₛ temperature can be estimated using the empirical formula:
$$ M_s = 561 – 474[\%C] – 33[\%Mn] – 17[\%Si] – 17[\%Cr] – 21[\%Mo] \tag{2} $$
I optimized the contents of C, Cr, Ni, Si, and Mo using an L₁₆(4⁵) orthogonal array with Mₛ as the response. The factor levels are shown in Table 8. The results, including the calculated Mₛ for each combination, are presented in Table 9. The range analysis (Table 10) revealed the order of influence: Ni > C > Cr > Mo > Si. The optimal combination was found to be C₂A₁B₂E₂D₂, which corresponds to: C = 0.015%, Cr = 12.5%, Ni = 3.8%, Si = 0.4%, Mo = 0.5%. To avoid segregation, the Ni/Cr equivalent ratio was controlled between 0.36 and 0.44.
| Level | C (%) | Cr (%) | Ni (%) | Si (%) | Mo (%) |
|---|---|---|---|---|---|
| 1 | 0.015 | 12.00 | 3.45 | 0.20 | 0.40 |
| 2 | 0.030 | 12.50 | 3.80 | 0.40 | 0.50 |
| 3 | 0.045 | 13.00 | 4.15 | 0.60 | 0.60 |
| 4 | 0.060 | 13.50 | 4.50 | 0.80 | 0.70 |
| Run | C | Cr | Ni | Si | Mo | Mₛ (°C) |
|---|---|---|---|---|---|---|
| T1 | 1 | 1 | 1 | 1 | 1 | 250.1 |
| T2 | 1 | 2 | 2 | 2 | 2 | 239.3 |
| T3 | 1 | 3 | 3 | 3 | 3 | 227.4 |
| T4 | 1 | 4 | 4 | 4 | 4 | 213.5 |
| T5 | 2 | 1 | 2 | 3 | 4 | 233.0 |
| T6 | 2 | 2 | 1 | 4 | 3 | 240.2 |
| T7 | 2 | 3 | 4 | 1 | 2 | 216.1 |
| T8 | 2 | 4 | 3 | 2 | 1 | 223.1 |
| T9 | 3 | 1 | 3 | 4 | 2 | 221.1 |
| T10 | 3 | 2 | 4 | 3 | 1 | 212.5 |
| T11 | 3 | 3 | 1 | 2 | 4 | 233.8 |
| T12 | 3 | 4 | 2 | 1 | 3 | 225.3 |
| T13 | 4 | 1 | 4 | 2 | 3 | 208.2 |
| T14 | 4 | 2 | 3 | 1 | 4 | 214.0 |
| T15 | 4 | 3 | 2 | 4 | 1 | 221.8 |
| T16 | 4 | 4 | 1 | 3 | 2 | 228.7 |
| Factor | C | Cr | Ni | Si | Mo |
|---|---|---|---|---|---|
| k₁ | 232.575 | 228.100 | 238.200 | 226.375 | 226.875 |
| k₂ | 228.100 | 226.500 | 229.850 | 226.100 | 226.300 |
| k₃ | 223.175 | 224.775 | 221.400 | 225.400 | 225.275 |
| k₄ | 218.175 | 222.650 | 212.575 | 224.150 | 223.575 |
| Range R | 14.400 | 5.450 | 25.625 | 2.225 | 3.300 |
| Order | Ni > C > Cr > Mo > Si | ||||
Using JMatPro software, I calculated the thermophysical properties of the optimized alloy, such as density, thermal conductivity, enthalpy, and fraction solid, based on the updated composition. These data were exported and imported into the AnyCasting database for subsequent simulation.
8. Simulation and Validation of the Optimized Process
8.1 Numerical Simulation Setup
I developed a new three-dimensional model of the optimized casting process, including insulating riser sleeves, additional chills, and modified gating system. The mesh was regenerated with 1,720,128 cells. The simulation parameters are listed in Table 11. The mold preheating temperature was 25°C, pouring temperature 1565°C, and pouring time 22 s, according to the optimization results.
| Parameter | Value |
|---|---|
| Pouring temperature | 1565°C |
| Pouring time | 22 s |
| Mold preheating temperature | 25°C |
| Casting material | ZG06Cr13Ni4Mo (optimized composition) |
| Mold material | Furan resin sand |
| Heat transfer coefficient (casting-riser sleeve) | 100 W/(m²·K) |
| Heat transfer coefficient (sleeve-mold) | 100 W/(m²·K) |
8.2 Filling and Solidification Results
The filling simulation showed a smoother and more uniform rise of the metal front compared to the original process. The additions of the third ingate improved flow distribution and allowed even faster filling. During solidification, the chills successfully created multiple oriented solidification fronts. The isolated liquid regions that existed in the original process were completely eliminated; instead, the last remaining liquid was confined to the risers, as desired. The defect prediction probability indicated no shrinkage cavities in the casting body. The total solidification time was reduced to about 990 s due to the enhanced cooling by the chills.
8.3 Production Verification
The optimized process was implemented in the factory. The resulting castings exhibited excellent surface quality and internal soundness. Ultrasonic inspection confirmed the absence of any shrinkage porosity or other internal discontinuities. The castings met all customer requirements, validating the effectiveness of the improvements in eradicating sand foundry defects.
9. Microstructure Simulation of ZG06Cr13Ni4Mo
9.1 Phase Transformation Analysis
Using the vertical section phase diagram of the Fe-C-12.5Cr-4.5Ni-0.5Si-0.6Mn system, I deduced the equilibrium solidification path of ZG06Cr13Ni4Mo: liquid → liquid + ferrite → ferrite → austenite + ferrite → austenite → martensite. The complex transformation leads to significant volumetric changes and affects feeding behavior. The solidus temperature was calculated as 1445°C and liquidus as 1490°C.
9.2 CAFE Model and Governing Equations
I employed the CAFE (Cellular Automaton Finite Element) method to simulate the grain structure formation. This model couples macroscopic heat transfer with microscopic nucleation and growth. The macroscopic heat conduction equation is given by:
$$ \rho C_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right) + \rho \Delta H \frac{\partial f_s}{\partial t} \tag{3} $$
where ρ is density, Cₚ heat capacity, λ thermal conductivity, fₛ solid fraction, and ΔH latent heat.
For solute diffusion, I chose the Lever rule model because of the high diffusivity of alloy elements in steel:
$$ C_L = \frac{C_0}{1 – f_s(1-k)} \tag{4} $$
where C₀ is the initial composition, k is the equilibrium partition coefficient.
The continuous nucleation model proposed by Rappaz was used. The grain density increment is described by a Gaussian distribution:
$$ \frac{dn}{d(\Delta T)} = \frac{n_{\text{max}}}{\sqrt{2\pi}\Delta T_\sigma} \exp\left[-\frac{(\Delta T – \Delta T_N)^2}{2\Delta T_\sigma^2}\right] \tag{5} $$
where n_max is the maximum nucleation site density, ΔT_N is the average undercooling for nucleation, and ΔT_σ is the standard deviation.
The dendritic tip growth kinetics were described by the KGT model, simplified to a polynomial form:
$$ v(\Delta T) = a_2 \Delta T^2 + a_3 \Delta T^3 \tag{6} $$
For the present alloy, the coefficients were calculated from the solidification parameters: a₂ = 0, a₃ = 1.8707×10⁻⁵ m·s⁻¹·K⁻³.
9.3 Simulation Setup for Microstructure
I performed simulations for three different pouring temperatures: 1550°C (Process A), 1565°C (Process B), and 1580°C (Process C). All other conditions were kept constant. The calculation domain was selected at the top flange area with dimensions 40 mm × 10 mm × 5 mm. The Gaussian nucleation parameters were: volume nucleation density n_v,max = 3×10¹¹ m⁻³, mean undercooling ΔT_v,N = 15 K, standard deviation ΔT_v,σ = 4.8 K; surface nucleation density n_s,max = 3×10⁹ m⁻², ΔT_s,N = 2 K, ΔT_s,σ = 1 K.
9.4 Simulation Results and Discussion
Figure 9 shows the grain structures at the specified cross-section for the three processes. All exhibited a predominantly columnar dendritic structure with some equiaxed grains at the center. The grain orientations deviated from the ideal <100> direction by angles ranging from 0° to 55°. Table 12 summarizes the grain statistics.
| Process | Pouring temp. (°C) | Number of grains | Average radius (m) | Max grain area (m²) | Average grain area (m²) |
|---|---|---|---|---|---|
| A | 1550 | 204 | 1.07770×10⁻³ | 7.16×10⁻⁶ | 1.98020×10⁻⁶ |
| B | 1565 | 193 | 1.08497×10⁻³ | 7.95×10⁻⁶ | 2.07254×10⁻⁶ |
| C | 1580 | 185 | 1.11056×10⁻³ | 6.64×10⁻⁶ | 2.13904×10⁻⁶ |
As the pouring temperature increased, the grain count decreased from 204 to 185, and the average grain size increased. This is because a higher pouring temperature leads to a lower nucleation rate and slower cooling, giving the grains more time to grow. The maximum grain area first increased then decreased, with Process C showing the smallest maximum area but a greater shape factor variation. Overall, Process B (1565°C) provided the most uniform grain structure, balancing grain size and shape distribution. This aligns with the process parameter optimization results, confirming that the optimal pouring temperature 1565°C also yields the best microstructure.
The study illustrates that controlling the pouring temperature is essential not only for avoiding macro shrinkage defects but also for refining the solidification structure. The CAFE simulation allowed me to predict the final grain morphology and to understand the relationship between process parameters and microstructure, offering a powerful tool to prevent sand foundry defects at the microscopic level.
10. Conclusions
In this research, I successfully identified and eliminated the sand foundry defects in the spray pump volute body casting. The key conclusions are as follows:
- The original sand casting process produced shrinkage porosity at predictable locations, which was accurately simulated by AnyCasting software, confirming the reliability of numerical simulation for defect prediction.
- Systematic improvements in riser design (insulating sleeves, additional risers), gating system modification, and strategic placement of external chills effectively established directional solidification and removed the feeding bottlenecks.
- Orthogonal experimental design revealed that pouring temperature has the greatest influence on casting quality, followed by pouring time, while mold preheating temperature has a relatively minor effect. The optimal parameters were found to be 1565°C pouring temperature, 22 s pouring time, and 25°C mold preheating temperature.
- Chemical composition optimization using JMatPro and orthogonal experiments, with martensite start temperature as the criterion, led to a composition of 0.015% C, 12.5% Cr, 3.8% Ni, 0.4% Si, and 0.5% Mo, ensuring a fully martensitic structure at room temperature and minimizing residual austenite.
- Production trials confirmed that the optimized process completely eliminated shrinkage defects, improving yield and meeting all quality requirements.
- CAFE microstructure simulations showed that increasing pouring temperature reduces grain count and increases grain size. The pouring temperature of 1565°C yields the most uniform grain structure, consistent with the macro-level optimization.
- The combination of numerical simulation, statistical design, and production validation provides a powerful methodology for eliminating sand foundry defects in complex steel castings.
Future work could extend the microstructure simulation to other alloy compositions and casting geometries, and integrate more advanced models for segregation and thermal stress. The successful application of these techniques in this project demonstrates their great potential for improving casting quality in industrial production.