Numerical Simulation of Sand Casting for Dredging Pump Shell

1. Introduction

The dredging industry has a long history, evolving from ancient canal construction to modern marine engineering. Among various dredging equipment, the cutter suction dredger plays a dominant role, with the dredge pump serving as its core component. The pump shell, as the primary flow-passing component, directly affects the service life and overall working efficiency of the dredging pump. However, domestic pump shells exhibit several deficiencies compared to imported ones, such as poor wear resistance, significant cavitation, low dimensional accuracy, and frequent maintenance requirements. Therefore, improving the casting quality of dredging pump shells has become a critical challenge in the domestic dredging industry.

In recent decades, casting CAE technology has transformed the traditional trial-and-error approach into a modern scientific methodology. Numerical simulation allows engineers to analyze the intricate physical and chemical phenomena occurring during the casting process, including fluid flow, heat transfer, and solidification. By simulating the transient flow characteristics such as temperature and velocity, along with quality indicators like shrinkage porosity and grain structure, engineers can accurately predict the evolution of various fields during casting, optimize process parameters, and significantly enhance the quality of sand casting parts.

The objective of this work is to systematically design and optimize the casting process for a dredging pump shell using the commercial simulation software ProCAST. The research encompasses gating system design, filling process analysis, solidification simulation, stress-strain analysis, and final process optimization.

2. Gating System Design

2.1 Design Principles and Classification

The gating system serves as the channel through which molten metal flows into the mold cavity. It controls the filling velocity and time, ensures continuous and smooth filling, prevents slag and gas inclusion, and regulates the temperature distribution to achieve directional solidification. An improperly designed gating system can lead to defects such as cold shuts, slag inclusions, gas porosity, shrinkage, and deformation. Statistics indicate that approximately 30% of casting rejects are caused by poor gating system design.

Gating systems are classified based on two criteria: the cross-sectional area ratio and the injection position. According to the area ratio, systems are categorized as:

Closed system: $\sum A_{直} > \sum A_{横} > \sum A_{内}$, providing good slag retention but causing severe turbulence
Open system: $\sum A_{直} < \sum A_{横} < \sum A_{内}$, offering smooth filling but weaker slag control
Semi-closed system: $\sum A_{内} < \sum A_{直} < \sum A_{横}$, balancing filling stability and slag retention

According to the injection position, systems are classified as top gating, bottom gating, and step gating. For steel castings like the pump shell, the open-type step gating system is often preferred as it provides a favorable temperature gradient while maintaining reasonable filling stability.

2.2 Casting Process Design of the Pump Shell

The material of the pump shell is ZG35 medium carbon cast steel. Its chemical composition is presented in Table 1.

Table 1 Chemical Composition of ZG35 (wt.%)
Element	C	Si	Mn	S	P
Content	0.32–0.42	0.20–0.45	0.50–0.80	≤0.04	≤0.04

The pump shell has a main wall thickness of 85 mm, a minimum wall thickness of 75 mm, and overall dimensions of 3595 mm × 3376 mm × 1240 mm. The structure incorporates stiffening ribs to prevent sand inclusion, deformation, and cracking, while also enhancing mechanical properties and reducing weight. The threaded holes of 30 mm diameter on the end face are not cast due to their small size, while the 60 mm diameter holes on the lifting lug are cast to reduce machining costs.

Two gating system schemes were proposed:

Scheme 1 – Step gating system: Three bottom ingates and one upper ingate with circular cross-sections
Scheme 2 – Bottom gating system: Three bottom ingates with circular cross-sections

2.3 Gating System Calculations

The pump shell was poured using a single ladle with a single nozzle of 100 mm diameter. The average flow rate of molten metal was determined as 195 kg/s based on Table 2.

Table 2 Average Flow Rate of Ladle Nozzle
Nozzle diameter/mm	30	40	50	60	70	80	100
Flow rate/kg·s⁻¹	10	27	55	90	120	150	195

The pouring time is calculated as:

$$t = \frac{G}{N \cdot n \cdot q}$$

where G is the casting weight (kg), N is the number of ladles, n is the number of nozzles per ladle, and q is the average flow rate (kg/s). The riser velocity of molten metal in the mold is given by:

$$v = \frac{C}{t}$$

where C is the casting height (mm) and t is the pouring time (s). The calculated riser velocity was checked against the minimum values in Table 3, confirming that the pouring time is appropriate.

Table 3 Minimum Rising Speed for Steel Castings
Casting weight/t	≤5	5–15	15–35	35–65	65–100	>100
Simple structure/mm·s⁻¹	15	10	8	8	7	6
Medium structure/mm·s⁻¹	20	15	12	10	9	8
Complex structure/mm·s⁻¹	25	20	16	14	12	10

For the open step gating system, the cross-sectional area ratios follow:

$$\sum A_k : \sum A_z : \sum A_h : \sum A_n = 1 : 2 : 1.8\text{–}2.2 : 2\text{–}2.5$$

where $A_k$ is the control cross-section, $A_z$ is the sprue area, $A_h$ is the bottom runner area, and $A_n$ is the bottom ingate area. Using the ladle nozzle area as the control section, the sprue diameter was set at 140 mm, the runner at 160 mm, the bottom ingate at 100 mm, and the upper ingate at 140 mm. For Scheme 2, the ingate diameter was set at 120 mm with the same sprue and runner dimensions.

3. Filling Process Simulation

3.1 Mathematical Model

The filling process simulation requires solving the governing equations of fluid flow and heat transfer. The continuity equation for incompressible flow is:

$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$

The Navier-Stokes equations, which express the conservation of momentum, are formulated as:

$$\rho \left(\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y}\right) = -\frac{\partial p}{\partial x} + \mu \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\right) + \rho g_x$$

The energy equation accounting for heat transfer during filling is:

$$\rho C_p \left(\frac{\partial T}{\partial t} + u\frac{\partial T}{\partial x} + v\frac{\partial T}{\partial y}\right) = \lambda \left(\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2}\right)$$

The SOLA-VOF method was employed to solve the velocity-pressure fields and track the free surface. This method combines the SOLA algorithm for pressure correction with the Volume of Fluid technique for interface tracking.

3.2 Model Preparation and Simulation Setup

The three-dimensional model of the pump shell was created using Creo 3.0 software. The geometry was then processed in GeoMESH to repair the free edges, overlapping surfaces, and other geometric discontinuities. The repaired model was subsequently imported into the MeshCAST module for finite element mesh generation. An uneven mesh distribution was adopted, with finer meshes in regions of high geometric gradient, such as the pump tail, and coarser meshes for the mold to balance accuracy and computational efficiency.

The material ZG35 was not available in the ProCAST database; therefore, its thermophysical properties were calculated using the software’s property calculation module. The liquidus temperature was 1503°C, the solidus temperature was 1412°C, and the latent heat was 250.8 J/g. The mold material was silica sand selected from the database.

Table 4 Summary of Thermal Properties of ZG35
Property	Value
Liquidus temperature	1503°C
Solidus temperature	1412°C
Latent heat	250.8 J/g
Pouring temperature	1560°C
Initial temperature of sand mold	20°C
Pouring velocity	1.0 m/s

Interfaces between the casting and the gating system were set as EQUIV type, allowing continuity of temperature and velocity fields. Interfaces between the casting and the mold were set as COINC type, with a heat transfer coefficient of $h = 500 \, \text{W/(m²·K)}$.

3.3 Results of Scheme 1 – Step Gating System

The filling simulation of the step gating system revealed that during the initial stages, molten metal entered the cavity through the bottom ingates. However, at approximately 30% filling, the upper ingate began to fill prematurely before the metal level reached its height. This led to high-velocity flow from the upper ingate, causing significant erosion of the mold wall and splashing, which could produce inclusions and sand defects.

Despite this issue, the temperature field analysis showed a favorable bottom-to-top temperature gradient starting from approximately 40% filling. The final casting temperature remained around 1510°C, indicating only a minimal temperature drop of 50°C during the entire pouring process. This characteristic reduces the oxidation of the molten steel and diminishes the risk of shrinkage defects.

3.4 Results of Scheme 2 – Bottom Gating System

The bottom gating system demonstrated smooth and stable filling throughout the process. The velocity of the flow front remained low, preventing mold wall erosion and air entrapment. However, the temperature field analysis revealed significant issues. The molten metal temperature dropped to below 1500°C when the mold cavity was barely filled, and in some regions, the temperature fell below 1420°C. At the end of pouring, the main body temperature dropped to 1480°C, with some areas at the bottom already reaching below the solidus temperature and beginning to solidify.

The prolonged filling time caused excessive heat loss, increasing the risk of oxidation and the formation of oxide films. Moreover, the lack of a proper temperature gradient during solidification would likely result in shrinkage defects, which would severely compromise the quality of the sand casting parts.

3.5 Comparison and Selection

The comparison of the two gating schemes is summarized in Table 5:

Table 5 Comparison of Two Gating System Schemes
Aspect	Scheme 1 (Step)	Scheme 2 (Bottom)
Filling stability	Moderate, minor turbulence	Excellent, smooth
Temperature gradient	Favorable (bottom-to-top)	Unfavorable (unordered)
Temperature drop	Small (~50°C)	Large (~80°C+)
Mold erosion	Moderate at upper ingate	Minimal
Risk of oxidation	Low	High
Risk of shrinkage	Low	High

Although Scheme 1 exhibited premature filling of the upper ingate due to improper runner sizing, its favorable temperature distribution and minimal temperature loss made it the superior choice. The gating system dimensions were recalculated to ensure sequential filling without excessive erosion, and the step gating system was ultimately adopted.

4. Riser and Chilling System Design

4.1 Design Principles

The riser system must compensate for the volumetric contraction of the molten metal during solidification. Key principles include:

The riser should solidify later than the region it feeds
The riser must store sufficient molten metal for feeding
Risers should be placed above or beside thermal centers
Riser dimensions should be as small as possible while ensuring feeding efficiency

4.2 Modulus Calculation and Feeding Channel Determination

The Chvorinov rule establishes the relationship between solidification time and modulus:

$$t_s = k \cdot M^2$$

where $M$ is the modulus (volume-to-surface area ratio) and $k$ is the solidification coefficient. The pump shell was divided into five geometric elements:

Element ① – Flange (L-shaped joint): M₁ = 1.88 cm
Element ② – Stiffening ribs (T-shaped joint): M₂ = 5.7 cm
Element ③ – Curved transition (L-shaped plate): M₃ = 8.4 cm
Element ④ – Pump shell wall (85 mm plate): M₄ = 4.25 cm
Element ⑤ – End plate (90 mm plate): M₅ = 4.5 cm

The solidification sequence is ① → ④ → ⑤ → ③ → ②. Thus, elements ②, ③, ⑤ form feeding channels that require additional molten metal compensation. Chills were placed on element ② to reduce its effective modulus to $0.9M_2 = 5.1$ cm, while top risers were placed above element ③, and additional risers were positioned on elements ④ and ⑤.

4.3 Riser Dimensions Calculation

The basic modulus method was employed for riser sizing:

$$M_R = f \cdot M_C$$

where $M_R$ is the riser modulus, $M_C$ is the casting modulus, and $f$ is the enlargement factor (1.1 for top blind risers, 1.2 for open risers). For riser #1 at element ③ with $M_C = 8.4$ cm:

$$M_R = 1.1 \times 8.4 = 9.24 \, \text{cm}$$

The riser volume was verified using the feeding capacity criterion. The shrinkage volume of the casting and riser is:

$$V_s = \varepsilon (V_c + V_R)$$

where $\varepsilon$ is the solidification shrinkage rate, $V_c$ is the casting volume, and $V_R$ is the riser volume. A standard type II cylindrical open riser was selected with dimensions: D = 400 mm, H = 500 mm.

For risers #2 (five risers on elements ④ and ⑤) with $M_C = 4.5$ cm:

$$M_R = 1.2 \times 4.5 = 5.4 \, \text{cm}$$

The feeding capacity calculation using the perimeter quotient method:

$$q = \frac{A_c}{V_c^{2/3}}$$

with $q = 640$ yielded the casting volume that each riser could feed. Five standard type II risers with diameter D = 300 mm and height H = 375 mm were selected.

4.4 Chilling System Design

External chills were designed to accelerate local cooling and improve directional solidification. The chill weight was calculated from heat balance:

$$W_{chill} = V_c \cdot \rho_m \cdot [L + c_p \cdot \Delta T]$$

The surface area of chills was determined from the modulus reduction criterion:

$$A_{chill} = \frac{M_{geometric} – M_{applied}}{M_{applied} – M_{adjacent}} \cdot A_c$$

For the stiffening ribs with geometric modulus 5.7 cm, chill thickness was determined as 0.75 times the rib thickness, following the air-gap condition formula. Each chill was segmented into 5 blocks to reduce the risk of hot tearing, with dimensions of 200 mm × 100 mm × 60 mm and a mass of approximately 9.36 kg each.

5. Solidification Simulation and Stress-Strain Analysis

5.1 Solidification Simulation Results

The solidification simulation was performed using ProCAST with the temperature and stress fields solved sequentially. Figure 5-1 shows the temperature distribution at different solidification fractions. The following observations were made from the simulation results:

The stiffening ribs solidified very early due to the chilling effect, with their temperature dropping below the solidus immediately after filling
At 50% solidification, the bottom region had started solidifying while the upper region remained largely molten
A significant problem was identified: the mold provided better cooling on the external surfaces than the internal sand cores, resulting in a higher internal temperature and violating the desired directional solidification pattern
By 85% solidification, the casting body was nearly fully solidified, but the riser necks had already frozen, prematurely terminating the feeding process

The fraction solid distribution confirmed the temperature field results. At 70% solidification, several isolated liquid regions formed, particularly between risers #2-1 and #2-2, indicating that the riser spacing exceeded the effective feeding distance. The riser neck region of riser #1 also showed a high fraction solid, losing its feeding capacity prematurely.

Table 6 Riser Solidification Sequence Analysis
Riser	Last solidification region	Issue identified
#1	Riser center	Neck solidifies prematurely
#2-1	Riser center	Neck solidifies prematurely
#2-2	Riser center	Satisfactory
#2-3	Riser center	Satisfactory
#2-4	Riser center	Neck solidifies prematurely
#2-5	Riser center	Satisfactory

The cooling curves recorded from thermocouples placed in riser #1 showed that the cooling rate followed the sequence: $2 < 3 < 1 < 4 < 5 < 6$. Ideally, the cooling rate should increase monotonically from the casting to the riser center. The anomalous cooling of point 2 relative to point 1 confirmed poor riser design.

5.2 Shrinkage Porosity Prediction

The shrinkage porosity was predicted using the Niyama criterion:

$$N = \frac{G}{\sqrt{R}}$$

where $G$ is the temperature gradient and $R$ is the cooling rate. For steel castings, the critical Niyama value is typically $\text{cm·s}^{1/2}/\text{°C}$. Regions with Niyama values below this threshold are considered prone to shrinkage porosity. The simulation results revealed:

Shrinkage defects were primarily concentrated in the riser bodies and ingates
Significant porosity also appeared in the main casting body, particularly in the bottom region
The bottom region lacked proper feeding due to an insufficient upward temperature gradient
Shrinkage occurred at the roots of risers #1, #2-1, and #2-4 due to premature neck solidification
The stiffening ribs were free from porosity, confirming the effectiveness of the chills
Porosity at the flange bottom was attributed to insufficient feeding distance from riser #1

5.3 Stress-Strain Analysis

The stress-strain simulation required high-temperature mechanical properties of ZG35, including Young’s modulus, yield stress, Poisson’s ratio, and plastic modulus. These were calculated using ProCAST’s property estimation module and are shown as temperature-dependent curves.

The stress analysis revealed that the highest equivalent stress occurred at the flange regions due to the wall thickness difference between the flange and the pump tube. The temperature gradient during solidification created a thin shell at the sand corner interface, creating stress concentration. The maximum equivalent stress exceeded the yield strength of ZG35 at the corresponding temperature, indicating a potential hot tearing risk. The ingate regions also exhibited elevated stress levels, although these remained well below the yield limit. The deformation analysis showed:

No significant deformation in the main pump body due to the presence of stiffening ribs
Considerable deformation at the flange region due to differential cooling between flange and pump tube
The riser design failed to achieve simultaneous solidification of different wall thicknesses

6. Casting Process Optimization

6.1 Optimization Strategy

Based on the simulation results, the following optimization measures were implemented:

Table 7 Optimization Measures and Rationale
System	Original design	Optimized design	Rationale
Gating	1 upper ingate, Ø140 mm	2 upper ingates, Ø130 mm	Reduce premature filling and erosion
Gating	Vertical upper ingate	Inclined upward ingate	Improve directional temperature distribution
Gating	Sprue Ø140 mm	Sprue Ø150 mm	Reduce filling time
Riser	Ordinary risers	Insulating risers with exothermic powder	Increase feeding efficiency
Riser	No padding	Padding added at riser #1 and #2-1	Extend feeding distance
Chill	Original chill layout	Additional chills at bottom of casting	Improve bottom-to-top temperature gradient
Chill	No chill at flange	Chills on lower half of flange	Prevent shrinkage and hot tearing
Chill	No chill between #2-2 and #2-3	Chills between risers #2-2 and #2-3	Create artificial end zone for feeding

The padding material was set as the same entity as the casting with EQUIV interface. The insulating sleeve was assigned the material property “Insulation” with a lower thermal conductivity, and the exothermic powder was set as “Exothermic” material.

6.2 Simulation Results of Optimized Process

The filling simulation of the optimized process showed significant improvements:

Molten metal entered smoothly through the bottom ingates, with the liquid level rising steadily
The upper ingates began feeding precisely when the metal level reached their height
The bottom ingates nearly closed when the upper ingates began operation, creating a natural transition
No splash, air entrapment, or excessive mold erosion was observed
The temperature field displayed a well-established bottom-to-top gradient throughout the filling process
The final casting temperature was approximately 1520°C, indicating a minimal temperature drop of only 40°C

The solidification simulation of the optimized process demonstrated marked improvements:

The stiffening ribs still solidified rapidly under the chilling effect, as expected
At 50% solidification, the bottom region and flange lower half had solidified while the upper region remained molten, confirming the establishment of directional solidification
The region between risers #2-2 and #2-3 solidified earlier due to the added chills, effectively creating the desired end zone
At 70% solidification, isolated liquid regions formed around each riser, but the riser necks remained open, allowing continuous feeding
At 85% solidification, the casting body was completely solid, while the riser centers still contained liquid, confirming that the risers were the last to solidify
The shrinkage porosity distribution showed defects only in the risers and ingates, with the casting body being completely sound
No shrinkage was observed in the flange bottom or the previously problematic regions

7. Conclusions and Outlook

7.1 Conclusions

This thesis systematically investigated the casting process design and optimization for the dredging pump shell using numerical simulation. The following conclusions were drawn:

The structural analysis confirmed that the pump shell design is reasonable for sand casting. The wall thickness exceeds the minimum castable thickness for ZG35 steel, and the stiffening ribs effectively prevent deformation and cracking
Two gating schemes were evaluated through filling simulation. The bottom gating system provided excellent filling stability but resulted in poor temperature distribution and excessive temperature drop. The step gating system, despite initial design flaws, offered a favorable temperature gradient and minimal temperature loss. After modifying the upper ingate design, the step gating system was successfully adopted
The solidification simulation revealed that the original riser system suffered from insufficient feeding distance and premature neck solidification. The chill layout was also inadequate for achieving directional solidification. These deficiencies led to the formation of isolated liquid regions and subsequent shrinkage defects in the casting body
Stress analysis identified the flange region as the most critical area, exhibiting high equivalent stress and deformation due to differential cooling between the flange and the tube. This necessitated additional chilling and padding in the optimized design
The optimized process incorporated two upper ingates, insulating risers with exothermic powder, additional chills at the bottom and between risers, and padding at critical risers. The re-simulation confirmed that these modifications effectively eliminated shrinkage defects and produced sound sand casting parts that meet the technical requirements

7.2 Outlook

While this research has successfully optimized the casting process for the dredging pump shell, certain limitations and future research directions should be acknowledged:

The computational model simplified certain geometric features such as casting fillets. Future simulations should retain more geometric details to improve the fidelity of the thermal and flow field predictions
The thermophysical properties of ZG35 were calculated using software estimation rather than experimental measurements. Experimental verification of these properties would enhance the reliability of the simulation results
This study focused on macro-scale simulations of temperature, flow, and stress fields. Micro-scale simulation of grain structure evolution would provide additional insight into the relationship between process parameters and final material properties
Environmental factors such as ambient temperature and humidity can significantly affect casting quality. These parameters should be incorporated into future simulations to account for seasonal variations in production