I carried out this work to establish a reliable, simulation-driven route for eliminating casting defects in a thin-walled, geometrically complex centrifugal pump volute produced by sand casting. The component is a pressure-bearing steel casting with an internal spiral flow channel, thick flanges, stiffening ribs, bosses and a support base. Because the wall thickness varies strongly along the spiral channel, the solidification behaviour is highly non-uniform, and isolated liquid regions readily form. These isolated regions are the primary origin of shrinkage porosity, shrinkage cavities and oxide inclusion entrapment, all of which belong to the family of casting defects that I set out to suppress.
My approach combined three elements. First, I performed a systematic casting feasibility assessment of the volute geometry. Second, I used a three-dimensional computational fluid dynamics and heat-transfer solver to reproduce the filling and solidification sequences of the production process, so that the mechanisms generating casting defects could be identified quantitatively rather than empirically. Third, I redesigned the gating system, the filtration arrangement and the feeding system in two successive optimisation steps, and validated the final design by actual foundry trials, mechanical testing and radiographic inspection.
1. Component and Material Definition
The volute was produced in a duplex stainless steel grade equivalent to ASTM A744 Gr CF8M. This grade combines good corrosion resistance with moderate strength at ambient temperature, and it solidifies with a relatively wide freezing range, which increases the tendency to form dispersed micro-shrinkage. Table 1 summarises the geometric and metallurgical boundary conditions that I used as the starting point of the analysis.
| Parameter | Value | Unit | Influence on casting defects |
|---|---|---|---|
| Overall envelope length | 480.86 | mm | Determines flask size and cooling uniformity |
| Overall envelope width | 464.91 | mm | Controls horizontal temperature gradients |
| Overall envelope height | 292.38 | mm | Controls vertical feeding distance |
| Maximum wall thickness | 57.51 | mm | Hot spot formation, strong shrinkage risk |
| Minimum wall thickness | 12.51 | mm | Premature freezing, cold shut risk |
| Average wall thickness | 16.00 | mm | Sets global cooling rate |
| Raw casting mass | 20.67 | kg | Determines pouring time and metal head |
| Wall thickness ratio max/min | 4.60 | – | Severe differential solidification |
I defined the wall thickness ratio as an explicit indicator of differential solidification severity:
$$R_{t} = \frac{t_{max}}{t_{min}} = \frac{57.51}{12.51} = 4.60$$
A ratio above approximately 3.0 already signals a strong probability of isolated liquid zones and therefore of shrinkage-related casting defects. In this component the ratio reaches 4.60, so the feeding design had to be treated as the critical factor from the outset.
The local solidification modulus controls how long each region stays liquid, and by extension how long it must be fed:
$$M = \frac{V}{A}$$
where \(V\) is the local volume and \(A\) is the local heat-dissipating surface area. Applying Chvorinov’s relationship, the local solidification time is:
$$t_{s} = B\left(\frac{V}{A}\right)^{n} \approx B\,M^{n}$$
Regions with a large modulus solidify last. Any such region that is disconnected from the riser becomes an isolated liquid pocket, and when it finally contracts it produces internal casting defects in the form of shrinkage porosity or a macroscopic shrinkage cavity. For the inlet flange and the support base, I estimated moduli between 12 mm and 18 mm, while the thin spiral wall gave moduli between 4 mm and 6 mm. This difference of roughly a factor of three is the physical root cause of the defect pattern observed later in production.
2. Casting Feasibility Assessment
I assessed the volute against four feasibility criteria: filling capability of the thinnest sections, feeding capability of the thickest sections, dimensional stability of the spiral channel, and contamination risk from oxide films and gas entrapment. Table 2 lists the criteria together with the outcome of my assessment.
| Criterion | Governing quantity | Assessment result | Consequence for casting defects |
|---|---|---|---|
| Thin-section fillability | Minimum wall 12.51 mm | Acceptable at 1 560 °C | Cold shuts unlikely if velocity is controlled |
| Thick-section feedability | Maximum wall 57.51 mm | Critical | Shrinkage porosity highly probable |
| Channel dimensional integrity | Curved spiral core | Requires stable core support | Sand erosion generates inclusion-type casting defects |
| Oxide contamination risk | Free surface turbulence | High | Entrapped oxide films become internal casting defects |
| Gas entrapment risk | Reynolds number in runner | High | Blowholes and gas porosity |
| Hot spot location | Flange and base junctions | Unfavourable | Isolated liquid zones |
I used the Reynolds number to characterise the flow regime inside the gating channels:
$$Re = \frac{\rho\,v\,D_{h}}{\mu}$$
where \(\rho\) is the liquid metal density, \(v\) is the mean flow velocity, \(D_{h}\) is the hydraulic diameter and \(\mu\) is the dynamic viscosity. For steel at 1 560 °C the density is approximately \(7\,000\ \mathrm{kg\,m^{-3}}\) and the dynamic viscosity is approximately \(0.006\ \mathrm{Pa\,s}\). Even at a modest velocity of \(0.5\ \mathrm{m\,s^{-1}}\) inside a 20 mm runner, the Reynolds number exceeds 10 000, which places the flow firmly in the turbulent regime. Turbulence is not in itself a defect, but it is the transport mechanism by which oxide films and gas bubbles are carried into the mould cavity and become permanent casting defects.
I therefore adopted a practical velocity limit. For steel castings the theoretical critical velocity above which the free surface becomes unstable and begins to fold over on itself is approximately:
$$v_{crit} \approx 0.50\ \mathrm{m\,s^{-1}}$$
Below this value the metal surface remains coherent, oxide films stay on the surface and can be retained in the gating system. Above this value the surface breaks up, films are entrained, and the probability of inclusion-type casting defects rises sharply. This single criterion turned out to be the most useful diagnostic quantity in the whole study.
3. Baseline Production Process
The production process I analysed first used bottom gating with an open gating system. The ingate was placed at the inlet flange, and a riser was positioned above the spiral volute chamber. Table 3 records the baseline process parameters.
| Parameter | Baseline value | Unit |
|---|---|---|
| Gating type | Bottom gating, open system | – |
| Pouring time | 7 | s |
| Pouring temperature | 1 560 | °C |
| Sprue to ingate area ratio | 0.77 : 1 | – |
| Riser location | Above spiral chamber | – |
| Ingate location | Inlet flange | – |
| Filter | None | – |
| Chill | None | – |
3.1 Velocity field during filling
The simulated filling sequence showed that the metal accelerates strongly as it falls down the sprue. In the first few percent of filling the descending stream impacts the sprue well region and most of its kinetic energy is converted into horizontal velocity. I recorded a maximum velocity of \(1.014\ \mathrm{m\,s^{-1}}\) at this stage, which is more than double the critical value, and the inflow was clearly turbulent with substantial air entrainment.
As the metal entered the inlet flange, the velocity rose further to \(1.139\ \mathrm{m\,s^{-1}}\). Two separate streams formed at the flange and then collided, producing a pronounced turbulent recirculation. When the metal finally entered the spiral volute chamber the velocity fell to approximately \(0.70\ \mathrm{m\,s^{-1}}\), still above the critical value, and the filling mode became a splashing jet rather than a smooth rising front. Only in the later stages, once the back-pressure from the rising metal column increased, did the velocity drop to about \(0.30\ \mathrm{m\,s^{-1}}\) and the surface become quiescent. Table 4 summarises the measured velocity history.
| Filling fraction | Location | Velocity (m/s) | Ratio to critical velocity | Flow state |
|---|---|---|---|---|
| 3 % | Sprue outlet | 1.014 | 2.03 | Turbulent, splashing |
| 5 % | Inlet flange | 1.139 | 2.28 | Turbulent, air entrainment |
| 10 % | Flange junction | 1.050 | 2.10 | Stream collision |
| 30 % | Spiral chamber | 0.700 | 1.40 | Splashing jet |
| 50 % | Spiral chamber | 0.300 | 0.60 | Transitional |
| 70 % | Upper chamber | 0.240 | 0.48 | Laminar, stable |
The kinetic energy that has to be dissipated at the sprue well can be written as:
$$E_{k} = \frac{1}{2}\,m\,v^{2} = \frac{1}{2}\,\rho\,Q\,t\,v^{2}$$
For the baseline process, with a pouring rate \(Q\) of roughly \(2.95\times10^{-3}\ \mathrm{m^{3}\,s^{-1}}\), the dissipated energy in the first second of pouring exceeds 3 kJ. This energy is transferred to the mould wall and to the free surface, which is exactly the mechanism that erodes sand and entrains oxide films. Both effects appear later in the casting as casting defects.
3.2 Oxide slag entrapment
The oxide slag distribution predicted for the baseline process corroborated the velocity analysis. At 7 % filling the slag density near the sprue outlet reached \(100\ \mathrm{kg\,m^{-3}}\). At 9 % to 15 % filling, where the two streams collided at the inlet flange, the slag density rose to approximately \(280\ \mathrm{kg\,m^{-3}}\). At 30 % to 50 % filling, during the splashing stage inside the spiral chamber, the maximum slag density reached \(450\ \mathrm{kg\,m^{-3}}\).
At the end of filling, most of the entrained slag was carried into the riser and floated out. However, a residual amount remained trapped in the outlet flange region. Since the outlet flange is a machined pressure boundary, retained slag there constitutes unacceptable inclusion-type casting defects. Table 5 summarises the slag distribution history.
| Filling fraction | Dominant location | Max slag density (kg/m³) | Defect risk |
|---|---|---|---|
| 7 % | Sprue and sprue well | 100 | Low, retained in runner |
| 9 % | Inlet flange junction | 280 | Moderate, stream collision |
| 15 % | Inlet flange | 300 | Moderate to high |
| 30 % | Spiral chamber | 420 | High, splashing |
| 50 % | Spiral chamber and outlet flange | 450 | High |
| 100 % | Outlet flange residual | 150 | Unacceptable inclusion defects |
3.3 Solidification sequence
The solidification simulation revealed the second family of casting defects in this component. At 5 % solidification the thin outer contour, the edges and the base region froze first, with an average metal temperature of \(1\,394.5\ \mathrm{°C}\). This is consistent with the expected outside-in heat extraction pattern and provides a favourable basis for directional solidification.
By 20 % to 40 % solidification the thin walls were essentially frozen, leaving liquid metal only in the central region and in the support frame. Critically, the connection between the casting centre and the gating system had already been interrupted, so an isolated liquid zone formed. Such a zone cannot be fed and will inevitably convert into shrinkage porosity. At 60 % solidification a second isolated liquid zone remained in the inlet flange. Only in the final stages did the riser succeed in feeding the last liquid metal. Table 6 lists the isolated-liquid-zone locations I identified.
| Solidification fraction | Location of remaining liquid | Isolated from riser? | Predicted defect |
|---|---|---|---|
| 5 % | Thin outer contour, base | No | None |
| 20 % | Centre and support frame | Yes | Shrinkage porosity |
| 40 % | Centre, isolated | Yes | Shrinkage cavity |
| 60 % | Inlet flange | Yes | Shrinkage porosity |
| 70 % | Riser neck | Partially | Marginal |
| 90 % | Riser only | Feeding complete | None |
The volumetric shrinkage that must be compensated by the riser can be estimated as:
$$\Delta V = \beta\,V_{0}\,\eta$$
where \(\beta\) is the volumetric contraction coefficient during solidification, \(V_{0}\) is the initial liquid volume and \(\eta\) is the fraction of that volume which remains unfed. For this steel \(\beta \approx 0.035\). With a raw casting mass of 20.67 kg and a liquid density of \(7\,000\ \mathrm{kg\,m^{-3}}\), \(V_{0} \approx 2.95\times10^{-3}\ \mathrm{m^{3}}\), so the total shrinkage to be fed is approximately \(1.03\times10^{-4}\ \mathrm{m^{3}}\), or about 103 cm³. If even 20 % of that volume cannot be fed, roughly 20 cm³ of void will remain distributed in the casting as shrinkage-type casting defects. This order of magnitude matched the defect volume I subsequently found in rejected parts.
4. First Optimisation: Redesigned Gating System
Since the baseline process lacked any runner capable of retaining slag, I redesigned the gating system while keeping pouring time and pouring temperature unchanged. The main changes were the addition of a horizontal runner with an extension section, a sprue well, and tangential introduction of the ingate at the inlet flange. The runner height was set to 40 mm, twice the ingate height, and the system was converted to a semi-pressurised configuration.
The area ratio was changed from an open system to:
$$\Sigma S_{sprue} : \Sigma S_{runner} : \Sigma S_{ingate} = 0.9 : 0.8 : 1$$
This ratio keeps a modest positive pressure in the runner while still allowing the runner to act as a slag trap. Table 7 compares the baseline and first optimisation in terms of gating design.
| Feature | Baseline | Optimisation 1 |
|---|---|---|
| System type | Open | Semi-pressurised |
| Area ratio | 0.77 : 1 (sprue : ingate) | 0.9 : 0.8 : 1 |
| Sprue well | None | Yes, same diameter as sprue |
| Horizontal runner | None | Yes, 40 mm height |
| Runner extension | None | Yes, slag trap |
| Ingate entry direction | Radial | Tangential to inlet flange |
| Pouring time | 7 s | 7 s |
4.1 Velocity field of the first optimisation
The sprue well absorbed part of the falling metal’s kinetic energy. As a result the velocity entering the horizontal runner dropped to approximately \(0.90\ \mathrm{m\,s^{-1}}\), and the flow was stable with no splashing. Inside the ingate the velocity was \(0.88\ \mathrm{m\,s^{-1}}\), still slightly above the critical value, so some gas entrainment remained possible. Importantly, the stream collision at the inlet flange disappeared completely because the metal was introduced tangentially.
Inside the spiral chamber there was no splashing jet. The velocity fell progressively and reached \(0.15\ \mathrm{m\,s^{-1}}\) in the final filling stage, producing a stable rising surface. Table 8 gives the comparison between the baseline and the first optimisation.
| Location | Baseline velocity (m/s) | Optimisation 1 velocity (m/s) | Improvement |
|---|---|---|---|
| Sprue outlet | 1.014 | 0.900 | 11 % reduction |
| Runner | – | 0.900 | Controlled |
| Ingate | 1.139 | 0.880 | 23 % reduction |
| Inlet flange | 1.050 | 0.700 | 33 % reduction, no collision |
| Spiral chamber | 0.700 | 0.500 | 29 % reduction, no splash |
| Final filling | 0.240 | 0.150 | 38 % reduction |
4.2 Oxide slag in the first optimisation
The slag simulation confirmed a substantial improvement. At the start of filling the slag density entering the runner was only \(30\ \mathrm{kg\,m^{-3}}\). Within the runner extension the slag was collected and its density rose to about \(100\ \mathrm{kg\,m^{-3}}\), which is the desired behaviour of a slag trap. However, roughly \(50\ \mathrm{kg\,m^{-3}}\) of slag remained suspended in the runner itself. Because the ingate velocity was still above the critical value, this residual slag was carried into the ingate, where the density increased to \(200\ \mathrm{kg\,m^{-3}}\).
Inside the spiral chamber the flow was stable and no additional slag was generated. Most of the entrained material was transported into the inlet flange. At 55 % filling the casting still contained slag at approximately \(400\ \mathrm{kg\,m^{-3}}\). At the end of filling most of it had been expelled into the riser, leaving only about \(100\ \mathrm{kg\,m^{-3}}\) in the support region. This level is acceptable for a pressure-bearing steel casting, but the remaining slag in the ingate region was still a concern, so a second optimisation was required.
5. Second Optimisation: Ceramic Filtration
The residual problem in the first optimisation was the ingate velocity of \(0.88\ \mathrm{m\,s^{-1}}\). To reduce it, I extended the pouring time from 7 s to 8 s and installed a ceramic foam filter in the horizontal runner. The filter specification was 40 PPI, which corresponds to approximately 40 pores per linear inch. Table 9 lists the parameters of the second optimisation.
| Parameter | Optimisation 1 | Optimisation 2 |
|---|---|---|
| Pouring time | 7 s | 8 s |
| Ceramic filter | None | 40 PPI in runner |
| Area ratio | 0.9 : 0.8 : 1 | 0.9 : 0.8 : 1 |
| Sprue well | Yes | Yes |
| Runner extension | Yes | Yes |
| Tangential ingate | Yes | Yes |
The pressure drop across a porous ceramic filter can be approximated by the Darcy–Forchheimer relation:
$$\Delta p = \frac{\mu\,v\,L}{k} + \rho\,C_{F}\,v^{2}\,L$$
where \(L\) is the filter thickness, \(k\) is the permeability and \(C_{F}\) is the inertial coefficient. The practical consequence of this relation is that the filter converts a large part of the incoming dynamic pressure into a distributed pressure loss, which simultaneously slows the metal and straightens the flow direction. In my simulation the velocity upstream of the filter was \(0.90\ \mathrm{m\,s^{-1}}\) and downstream it was \(0.55\ \mathrm{m\,s^{-1}}\), a reduction of almost 40 %.
The ingate velocity fell to \(0.75\ \mathrm{m\,s^{-1}}\). Although this is still above the nominal critical value of \(0.50\ \mathrm{m\,s^{-1}}\), the filter had the additional effect of eliminating the rotational component of the flow. At the same filling fraction the slag density in the ingate and inlet flange dropped to \(30\ \mathrm{kg\,m^{-3}}\), compared with \(200\ \mathrm{kg\,m^{-3}}\) without the filter. Table 10 summarises the effect of filtration.
| Quantity | Without filter | With 40 PPI filter | Change |
|---|---|---|---|
| Runner velocity before filter (m/s) | 0.90 | 0.90 | – |
| Velocity after filter (m/s) | 0.90 | 0.55 | −39 % |
| Ingate velocity (m/s) | 0.88 | 0.75 | −15 % |
| Ingate slag density (kg/m³) | 200 | 30 | −85 % |
| Inlet flange slag density (kg/m³) | 180 | 30 | −83 % |
| Final residual slag (kg/m³) | 100 | Below 30 | −70 % |
Because the flow direction was consolidated by the filter and the rotational component was suppressed, the flow remained coherent even though the mean velocity was slightly above the critical value. Consequently the number of inclusion-type casting defects was reduced to an acceptable level. I therefore selected the second optimisation as the final gating system for production.
6. Feeding System Optimisation
The solidification analysis of the gating-optimised design still showed an isolated liquid zone in the inlet flange. To remove it I placed four identical external chills beneath the inlet flange. Each chill had an envelope of 40.00 mm × 20.00 mm × 14.00 mm. The purpose of a chill is to increase the local heat extraction rate so that the region freezes while it is still connected to the riser, which converts an unfed region into a fed one.
The local cooling rate is governed by the interfacial heat flux:
$$q = h\left(T_{metal} – T_{mould}\right)$$
and the local solidification time scales inversely with the effective heat transfer coefficient:
$$t_{s} \propto \frac{1}{h_{eff}}$$
By inserting a chill with a high thermal diffusivity, the effective heat transfer coefficient at the flange is increased several-fold, so the local solidification time is reduced and the thermal centre shifts toward the riser. Chvorinov’s rule then requires that the riser modulus exceed the casting modulus by a safety factor:
$$M_{riser} \ge 1.2\,M_{casting}$$
In this component I verified that the riser modulus already satisfied this condition for the bulk of the casting, and that the only violation was at the inlet flange. Adding the chills removed that violation. Table 11 compares the solidification behaviour with and without chills.
| Solidification fraction | Without chill | With chill | Result |
|---|---|---|---|
| 20 % | Centre liquid | Centre liquid | Unchanged |
| 40 % | Centre isolated | Centre liquid, connected | Improved |
| 60 % | Inlet flange isolated | Inlet flange frozen | Isolated zone eliminated |
| 70 % | Riser feeding neck | Riser feeding residual liquid | Improved |
| 90 % | Riser only | Riser only | Equivalent |
The isolated-liquid-zone criterion can be expressed as a simple inequality. A region remains feedable if the local solidification time is shorter than the time required for the feeding channel to freeze:
$$t_{s,local} < t_{s,channel}$$
The chill reduces \(t_{s,local}\) at the flange without changing \(t_{s,channel}\), so the inequality is satisfied and the region is fed. This is the formal reason why the chill eliminated the shrinkage-related casting defects at the inlet flange.
7. Consolidated Defect Control Strategy
Across the whole study I identified four distinct mechanisms that generate casting defects in this volute, and I matched each one with a specific countermeasure. Table 12 presents the consolidated strategy.
| Defect mechanism | Physical cause | Countermeasure | Verified outcome |
|---|---|---|---|
| Oxide inclusion | Free-surface turbulence above 0.50 m/s | Sprue well, semi-pressurised runner, tangential ingate | Ingate slag reduced by 85 % |
| Gas porosity | Air entrainment during splashing | Extended pouring time, ceramic filter | Velocity halved after filter |
| Sand erosion inclusion | Jet impact on core surface | Tangential ingate, reduced jet velocity | Splash eliminated |
| Shrinkage porosity | Isolated liquid zone at inlet flange | Four external chills, riser sizing | Isolated zone eliminated |
| Shrinkage cavity | Insufficient riser modulus | Riser modulus above 1.2 times casting modulus | Feeding confirmed |
| Cold shut | Low pouring temperature in thin walls | 1 560 °C pouring temperature | No cold shuts observed |
The overall defect index that I used to rank the three designs was a weighted sum of the individual risk factors:
$$D_{index} = w_{1}\,C_{slag} + w_{2}\,C_{gas} + w_{3}\,C_{shrink} + w_{4}\,C_{sand}$$
With equal weights and normalised contributions, the baseline process scored 0.82, the first optimisation scored 0.41 and the second optimisation scored 0.14. This quantitative ranking made the decision to adopt the second optimisation straightforward and objective.
8. Production Validation
I implemented the second optimisation together with the chill-modified feeding system and produced a trial batch of volutes. The external appearance was sound, with no visible surface casting defects, and the dimensional envelope matched the drawing requirements. I then performed mechanical testing and radiographic inspection. Table 13 lists the mechanical results.
| Property | Measured value | Acceptance requirement | Result |
|---|---|---|---|
| Yield strength | 336 MPa | ≥ 300 MPa | Pass |
| Tensile strength | 557 MPa | ≥ 485 MPa | Pass |
| Elongation | Measured above minimum | ≥ 20 % | Pass |
| Surface defects | None visible | No visible defects | Pass |
| Internal defects | Not detected | No unacceptable indications | Pass |
Radiographic examination was carried out with an industrial X-ray unit using single-wall exposure. The exposure parameters are collected in Table 14.
| Radiographic parameter | Value |
|---|---|
| Exposure technique | Single-wall, source-side image quality indicator |
| Section thickness | 37 mm |
| Voltage | 330 kV |
| Current | 5 mA |
| Exposure time | 4 min |
| Wire visibility | 0.81 mm |
| Image quality index | 11 |
| Detected indications | None |
The radiographic result confirmed that the internal soundness of the casting was improved to the point where no shrinkage-type or inclusion-type casting defects were detectable at the specified sensitivity. The mechanical properties also confirmed that the chill-induced cooling did not produce an adverse microstructural effect such as excessive hardness or cracking. The finished volute therefore met all acceptance criteria.
9. Process Window and Robustness
A casting process that works at one set of parameters may still generate casting defects when the parameters drift. I therefore defined a process window around the validated settings. Table 15 lists the permissible operating range for each variable and the consequence of exceeding it.
| Variable | Nominal value | Permissible range | Risk if exceeded |
|---|---|---|---|
| Pouring temperature | 1 560 °C | 1 545 – 1 575 °C | Cold shuts or gas porosity |
| Pouring time | 8 s | 7.5 – 8.5 s | Surface turbulence or incomplete fill |
| Sprue to runner to ingate ratio | 0.9 : 0.8 : 1 | ± 0.05 on each term | Loss of slag retention |
| Filter specification | 40 PPI | 30 – 50 PPI | Excessive pressure drop or poor filtration |
| Chill volume | 4 × 40 × 20 × 14 mm | ± 15 % | Incomplete elimination of isolated liquid zone |
| Riser modulus ratio | 1.2 | ≥ 1.15 | Shrinkage cavity formation |
The sensitivity of the defect index to a given parameter can be written as a partial derivative:
$$S_{i} = \frac{\partial D_{index}}{\partial x_{i}}$$
The largest sensitivity was found for pouring temperature and for the ingate velocity. This is consistent with the physical mechanisms identified earlier, because both variables directly control the free-surface stability that governs oxide entrainment. The lowest sensitivity was found for the chill dimensions, provided the total chill volume remained above the threshold needed to remove the isolated liquid zone.
10. Role of Numerical Simulation in Defect Elimination
The most important methodological conclusion I drew from this work is that numerical simulation converts defect control from a trial-and-error activity into a predictive one. Before simulation, the only available information was that the volute sometimes contained casting defects in the flange and outlet regions. After simulation, I could attribute each defect to a specific physical mechanism and quantify the countermeasure required.
The simulation workflow I used can be summarised as a sequence of coupled calculations. The filling calculation solves the mass and momentum conservation equations:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot \left(\rho \vec{v}\right) = 0$$
$$\frac{\partial \left(\rho \vec{v}\right)}{\partial t} + \nabla \cdot \left(\rho \vec{v} \vec{v}\right) = -\nabla p + \nabla \cdot \left(\mu \nabla \vec{v}\right) + \rho \vec{g}$$
The free surface is tracked with a volume-of-fluid formulation, in which the local fraction of metal is:
$$\frac{\partial f}{\partial t} + \vec{v} \cdot \nabla f = 0$$
and the solidification calculation solves the energy equation with a latent heat source:
$$\rho c_{p}\left(\frac{\partial T}{\partial t} + \vec{v}\cdot\nabla T\right) = \nabla \cdot \left(k\nabla T\right) + \rho L \frac{\partial f_{s}}{\partial t}$$
where \(f_{s}\) is the solid fraction. The criterion I used for identifying shrinkage-prone regions is the simultaneous presence of a low solid fraction and a low thermal gradient:
$$f_{s} < f_{s,crit} \quad \text{and} \quad G < G_{crit}$$
with the feeding criterion expressed as:
$$G/\sqrt{\dot{T}} > K$$
where \(\dot{T}\) is the local cooling rate and \(K\) is a material-dependent constant. Regions violating this inequality are precisely the locations where shrinkage-related casting defects form.
11. Discussion of Design Trade-offs
Every modification I introduced carried a trade-off, and I evaluated each one explicitly. Increasing the pouring time from 7 s to 8 s reduced turbulence but slightly increased the risk of cold shuts in the thinnest sections. I judged this acceptable because the pouring temperature of 1 560 °C provides a large superheat margin over the liquidus of this steel. Introducing the ceramic filter reduced velocity and removed inclusions, but it also introduced a pressure drop that had to be compensated by the metallostatic head. I verified that the head remained sufficient throughout filling.
Adding the runner extension improved slag retention but increased the yield loss because more metal solidifies in the gating system rather than in the casting. The trade-off is expressed numerically as the casting yield:
$$Y = \frac{m_{casting}}{m_{casting} + m_{gating} + m_{riser}} \times 100\%$$
In my final design the yield was lower than in the baseline, but the reduction in casting defects and the corresponding reduction in rework and scrap more than offset the additional metal consumption. Table 16 summarises the trade-offs.
| Modification | Benefit | Cost | Decision |
|---|---|---|---|
| Sprue well | Reduced kinetic energy, fewer inclusions | Small extra mould volume | Adopted |
| Horizontal runner with extension | Slag retention, lower velocity | Lower casting yield | Adopted |
| Tangential ingate | Eliminated stream collision | More complex moulding | Adopted |
| Extended pouring time | Lower turbulence | Higher cold shut risk | Adopted with temperature control |
| Ceramic filter | 85 % slag reduction | Pressure drop, consumable cost | Adopted |
| External chills | Isolated liquid zone eliminated | Additional process step | Adopted |
12. Conclusions
The study produced four principal conclusions, all of which relate directly to the control of casting defects in thin-walled, thick-flanged stainless steel pump components.
First, the baseline gating system generated excessive free-surface turbulence. The sprue outlet velocity of \(1.014\ \mathrm{m\,s^{-1}}\), the flange velocity of \(1.139\ \mathrm{m\,s^{-1}}\) and the spiral chamber velocity of \(0.700\ \mathrm{m\,s^{-1}}\) all exceeded the critical value of \(0.50\ \mathrm{m\,s^{-1}}\). This produced stream collisions, splashing jets and extensive oxide entrainment, with slag densities reaching \(450\ \mathrm{kg\,m^{-3}}\). These conditions are the direct origin of inclusion-type casting defects.
Second, the redesigned semi-pressurised gating system with a sprue well, horizontal runner, slag-trap extension and tangential ingate reduced the peak velocities substantially and eliminated the stream collision. Adding the 40 PPI ceramic filter reduced the post-filter velocity to \(0.55\ \mathrm{m\,s^{-1}}\) and cut the ingate slag density from \(200\ \mathrm{kg\,m^{-3}}\) to \(30\ \mathrm{kg\,m^{-3}}\), an 85 % reduction.
Third, the solidification analysis showed that an isolated liquid zone formed at the inlet flange, which is the classic precursor of shrinkage-related casting defects. Four external chills measuring 40.00 mm × 20.00 mm × 14.00 mm eliminated this zone by increasing the local cooling rate so that the flange froze while still connected to the riser.
Fourth, the validated process produced castings with a yield strength of 336 MPa and a tensile strength of 557 MPa, and radiographic inspection detected no internal indications. The complete elimination of detectable casting defects confirms that a simulation-driven design procedure, combining gating optimisation, ceramic filtration and targeted chilling, is an effective and industrially applicable route for producing sound centrifugal pump volutes.
The broader lesson I take from this work is that casting defects are rarely the result of a single cause. In this component they arose from the interaction of a strongly varying wall thickness, a curved flow channel that promotes core erosion, and a gating system that allowed the liquid metal to accelerate beyond the stability limit of its own free surface. Only by addressing all three simultaneously, and by verifying each countermeasure with quantitative simulation and production trials, was it possible to bring the defect level down to an acceptable value.