Investment casting is a near-net-shape route for stainless steel components with complex flow passages, thin blades, and pressure-boundary geometry that would be difficult or impossible to machine. The process sequence—wax pattern, ceramic shell, dewaxing, shell firing, pouring, knockout, and finishing—offers dimensional accuracy and surface quality, but it also creates thermal conditions that are difficult to reproduce in a numerical model. In impellers and valve bodies, the same massive features that make casting attractive—hubs, seal rings, flanges, and internal ribs—become hot spots that must remain connected to liquid feed metal until solidification is complete.
Shrinkage porosity is therefore a central yield-limiting defect rather than an incidental one. A shrinkage cavity forms when a hot spot solidifies without sufficient liquid metal replenishment; dispersed porosity forms when a wide freezing range isolates small pockets of liquid between growing dendrites. Both mechanisms are sensitive to pouring temperature, shell temperature, pouring rate, local modulus, and the heat-transfer path from the shell to the surroundings.
| Alloy | C (wt.%) | Cr (wt.%) | Ni (wt.%) | Mo (wt.%) | Other (wt.%) | Liquidus (°C) | Solidus (°C) |
|---|---|---|---|---|---|---|---|
| 2205 duplex stainless steel | 0.02 | 22 | 6 | 3.1 | N 0.17; Fe balance | 1465 | 1348 |
| CF8M austenitic stainless steel | 0.08 | 19 | 10 | 2.5 | Mn 1.5; Si 1.5; Fe balance | 1435 | 1319 |
A six-month production Pareto analysis at a precision casting plant concentrated attention on a small set of recurring defects. Open impellers failed mainly through hub shrinkage and hub sand holes; closed impellers through hub and seal-ring shrinkage; valve bodies through internal-rib and flange-root shrinkage. These locations are consistent with the thermal structure of the parts: the hub and seal ring in an impeller, and the flange and internal rib in a valve body, are locally massive relative to the surrounding sections and therefore solidify late.
Calibrating the shell-to-air heat-transfer coefficient
The first simulation models used boundary conditions taken from typical process cards and literature values. The metal-to-shell interfacial heat-transfer coefficient was set to 500 W/m²K, within the 300–660 W/m²K range obtained by linear extrapolation for investment casting and close to the 482 W/m²K average reported for aluminum alloy castings. With the shell-to-air coefficient left at the software default of 10 W/m²K, the predicted shrinkage was retained almost entirely in the riser, and the impeller casting appeared sound. Production cut sections showed the opposite: shrinkage in the hub of open impellers and in the hub and seal ring of closed impellers.
The discrepancy was traced to the external boundary condition. Heat transfer from the shell to the workshop air can be written as
$$ \Delta Q=h_1(T-T_a)+\sigma\varepsilon\left(T^4-T_a^4\right) $$
where h1 is the shell-to-air heat-transfer coefficient, T is the shell temperature, Ta is the ambient temperature, ε is the radiation emissivity, and σ is the Stefan–Boltzmann constant. In the calibration runs, radiation was not varied, so h1 acted as an effective convective coefficient representing the workshop environment. The plant ambient temperature was approximately 10–20 °C; the model used 15 °C. Free-air convection is commonly 5–25 W/m²K and forced convection 10–500 W/m²K, so the plant environment could not be represented by a single default value without verification.
Simulations were therefore run with h1 = 10, 20, 30, 40, 50, and 60 W/m²K. For the open impeller, the predicted shrinkage remained in the riser at 10 W/m²K, decreased inside the riser at 20–30 W/m²K, and appeared in the hub at 40–60 W/m²K. For the closed impeller, seal-ring shrinkage grew and moved downward as h1 increased; hub shrinkage appeared at 40 W/m²K and reached its largest predicted extent at 60 W/m²K. The trend was consistent: stronger shell cooling shortened the effective feeding period and transferred shrinkage from the riser into the casting.
Comparison with production cut sections placed the effective plant range at h1 = 40–50 W/m²K. A value of 45 W/m²K was then tested on a second open impeller and a second closed impeller. The open-impeller model reproduced the hub shrinkage seen after sectioning. The closed-impeller model reproduced four shrinkage locations above the seal ring while leaving the hub sound, again matching the machined production part. This established 45 W/m²K as the working shell-to-air coefficient for subsequent simulations under the same shell system and workshop conditions.
Robust parameter selection for 2205 impellers
Calibrating the boundary condition improved the match between simulation and production, but it did not by itself define a process window that would remain stable when the workshop environment changed. A Taguchi L9(33) design was used to separate control factors from environmental noise. Pouring temperature, pouring rate, and shell temperature were treated as control factors; the shell-to-air heat-transfer coefficient was treated as the noise factor at 40, 45, and 50 W/m²K. Each of the nine orthogonal runs was therefore simulated three times, giving 27 results.
| Factor | Range | Level 1 | Level 2 | Level 3 |
|---|---|---|---|---|
| A. Pouring temperature (°C) | 1580–1620 | 1580 | 1600 | 1620 |
| B. Pouring rate (kg/s) | 5–7 | 5 | 6 | 7 |
| C. Shell temperature (°C) | 650–850 | 650 | 750 | 850 |
The response was the predicted shrinkage volume in cm³. Because smaller shrinkage is better, the signal-to-noise ratio was calculated using the smaller-is-better form:
$$ \eta=-10\log_{10}\left(\frac{1}{n}\sum_{i=1}^{n}y_i^2\right) $$
where η is the signal-to-noise ratio, yi is the shrinkage volume for one noise condition, and n = 3. Averaged across the nine orthogonal runs, the predicted shrinkage volume increased from 1.145 cm³ at h1 = 40 W/m²K to 2.163 cm³ at 45 W/m²K and 2.990 cm³ at 50 W/m²K. Within each noise level, increasing the pouring temperature or decreasing the shell temperature reduced the shrinkage volume. The effect of pouring rate was weaker and its direction varied with the heat-transfer condition.
The highest mean signal-to-noise ratio occurred at 1620 °C pouring temperature, 650 °C shell temperature, and 7 kg/s pouring rate. The contribution analysis confirmed the ranking. Pouring temperature contributed 64.126% of the variance in signal-to-noise response, shell temperature 34.874%, and pouring rate about 1%. Pouring rate was therefore not an effective lever for shrinkage control in this process window, whereas pouring temperature and shell temperature were the two variables that determined whether the casting remained sound when the shell-to-air coefficient drifted.
| Factor | Degrees of freedom | Sum of squares | Contribution |
|---|---|---|---|
| A. Pouring temperature | 2 | 41.448 | 64.126% |
| B. Pouring rate | 2 | 0.646 | 1% |
| C. Shell temperature | 2 | 22.540 | 34.874% |
| Total | 6 | 64.634 | 100% |
The optimized combination was checked against simulation. At 1620 °C, 650 °C, and 7 kg/s, the measured signal-to-noise ratios at the three noise levels were calculated from shrinkage volumes of 0, 1.116, and 2.013 cm³, giving η = −2.4696. The predicted value was −2.458, an error of 0.0116. The same parameter set also produced the smallest shrinkage volumes among all orthogonal runs at each noise level. Production batches using these settings yielded stable impeller castings.
Closed impeller: restoring feed paths and avoiding impingement
The large closed impeller used for the next stage was a single-suction, six-passage component weighing 122 kg and measuring 611 × 611 × 285 mm. Its maximum wall thickness was 175 mm, its minimum wall thickness 8.5 mm, and its blade thickness 8.5–10 mm. The hub diameter was 110 mm, the seal-ring diameter 495 mm, and the passage width 110 mm. The alloy was ASTM A890 3A duplex stainless steel, cast with a shell designed for a 1620 °C pouring temperature, 650 °C shell temperature, 7 kg/s pouring rate, 500 W/m²K metal-to-shell coefficient, and 45 W/m²K shell-to-air coefficient. The finite-element mesh used 8 mm elements on the casting and 20 mm elements on the shell, producing 93,990 two-dimensional elements and 883,390 three-dimensional elements.
The initial design placed the seal ring upward, fed the hub through a central main ingate, and used a cup-shaped riser. Three side ingates with pads were placed around the seal ring to feed its local hot spots. The simulation predicted shrinkage at both the hub and the seal ring. The seal-ring defects arose because three side ingates could not cover every seal-ring-to-blade junction; isolated liquid remained outside the reach of the side feed. The hub defect had a different cause. The riser root had a large exposed area to the surrounding air, so it cooled faster than the lower hub and began to freeze before the hub had been fed. The result was a “necked” feed path between the riser and the hub.
Two geometry changes were made. The number of side ingates was increased from three to six, so that each seal-ring hot spot had a local feed path, and the riser bottom diameter was increased from 150 mm to 170 mm to raise its modulus. The riser top was changed to a hexagonal shape for easier wax assembly. The revised simulation removed the seal-ring shrinkage, but a small hub defect remained. The solidification pattern showed that the riser was feeding in a V-shaped mode while the lower hub remained liquid, indicating a persistent hot spot at the bottom of the hub.
The hot spot was caused by the pouring method rather than by the riser size. In the original top-pour arrangement, the metal stream entered through the center of the cup and impinged directly on the hub bottom. Temperature fields at 4.5, 22, and 32 s showed that the hub bottom remained hot while the surrounding shell cooled. The pour was therefore changed from center pouring to side pouring along the cup wall. The metal entered without direct impingement, which reduced the local heat concentration and also limited mechanical disturbance of the shell. The revised simulation eliminated the hub shrinkage. Production castings were sectioned after machining; both the seal ring and the hub were sound.
Valve body: when the sand core controls solidification
The valve body was a DN40 CF8M casting weighing 13.7 kg and measuring 214 × 164.5 × 158 mm. Its flange diameter was 158 mm and its flange thickness 25.5 mm, making the flange the thickest section. The initial gating design placed the two flanges vertically. Wax-formed ingates of 20 × 50 × 20 mm fed the body, and additional 25 × 55 × 20 mm pads were placed above the flanges. Two internal runners of 30 × 60 × 40 mm were intended to feed the internal ribs, and a 60 × 60 × 225 mm cross-runner connected the ingates and flange pads. A cup of Φ65 × Φ130 × 120 mm introduced the metal, and 10 × 15 mm tie bars provided wax drainage, venting, and slag collection. The simulation used 4 mm elements on the casting and a 6 mm shell, producing 79,476 two-dimensional elements and 666,314 three-dimensional elements.
The initial simulation predicted shrinkage at the flange roots. The cross-runner sides froze early and cut the feed path from the flange pads, leaving isolated liquid at the upper flange roots. The first design change—removing the two central ingates, extending the flange pads toward the back of the flange, and enlarging the cross-runner—produced a simulation in which the shrinkage appeared only in the gating system. That result was misleading. Production castings made with the revised design showed gas holes on the top surface, shrinkage at both flange roots, and pronounced shrinkage in the internal ribs.
The discrepancy came from a shell feature that had not been modeled. During shell making, the internal cavity was sand-plugged; after shell consolidation, the sand acted as an internal core. The first simulation treated the cavity as empty. The sand core slowed heat extraction from the internal ribs and changed the solidification sequence. A corrected model included the sand core and used 77,586 two-dimensional elements and 692,249 three-dimensional elements. When the revised gating design was re-simulated with the core, the model reproduced the top-surface gas and slag entrapment, the slow cooling of the internal ribs, and the flange-root shrinkage. The corrected result matched the production defect map.
| Design / model | Principal change | Result |
|---|---|---|
| Initial design, no sand core | Two central ingates, two flange pads, 60 × 60 × 225 mm cross-runner | Simulated flange-root shrinkage; early freezing of cross-runner sides cut the feed path. |
| Option 2, no sand core | Central ingates removed; flange pads extended; cross-runner enlarged | Simulation showed defects only in the gating system, but production showed top gas holes, flange-root shrinkage, and rib shrinkage. |
| Option 2, corrected model | Internal sand core added to the model | Simulation reproduced top gas/slag entrapment, rib shrinkage, and flange-root shrinkage; matched production. |
| Option 3, corrected model | Central gate 50 × 50 × 95 mm above the rib; flange pads 95 mm wide × 50 mm thick; cross-runner 70 × 70 × 255 mm | Simulation showed shrinkage only in the cross-runner; production castings were sound and passed hydrostatic and pneumatic leak tests. |
Option 3 restored a central gate, but placed it above the internal rib rather than at the original position. The 50 × 50 × 95 mm gate served three functions: it fed the rib, provided a vent path for gas and slag, and reduced the tendency for the top surface to entrap gas. The flange pads were increased to 95 mm wide and 50 mm thick, and the cross-runner to 70 × 70 × 255 mm, so that the feed path remained open even though the sand core slowed internal cooling. In the final simulation, the casting solidified without isolated liquid in the flange or rib, and the last shrinkage was confined to the cross-runner. Production parts showed no flange or internal defects after cleaning and passed both hydrostatic and pneumatic tests.
Design implications and limits
The cases show that simulation accuracy in investment casting depends less on the solver than on the effective boundary conditions and mold details. The shell-to-air coefficient is not a material constant. At 10 W/m²K, the model placed shrinkage in the riser and predicted a sound casting; at 40–60 W/m²K, it placed shrinkage in the hub and seal ring, where production found it. The 40–50 W/m²K range, with 45 W/m²K used for validation, was specific to the shell system, workshop air movement, and ambient temperature of the plant. A different shell thickness or foundry environment would require a new inverse calibration.
For the 2205 impeller family, the robust process window was 1620 °C pouring temperature, 650 °C shell temperature, and 7 kg/s pouring rate. The value of this combination is not simply that it produced the smallest predicted shrinkage under one condition; it produced the smallest shrinkage across the 40–50 W/m²K noise range. Pouring temperature and shell temperature accounted for almost all of the signal-to-noise response, while pouring rate contributed about 1%. This makes pouring temperature and shell temperature the variables to control tightly during production, and pouring rate a secondary setting.
Feeding design must address both modulus and sequence. In the large closed impeller, increasing the riser diameter and adding side ingates removed the seal-ring defects, but the hub defect persisted until the central pour was changed to side pouring. The impingement had created a hot spot below the riser that no reasonable riser enlargement could compensate for. In the valve body, the opposite lesson applied: removing the central ingate improved the simulation only because the model omitted the sand core. Once the core was included, the central gate was necessary for rib feeding and venting, and the flange pads and cross-runner had to be enlarged to maintain the feed path.
These results apply to the specific alloys, shell systems, and geometries examined: 2205 impellers in the 72–122 kg range, and a 13.7 kg DN40 CF8M valve body. The Taguchi design used three levels and a three-level noise factor, so it resolves main effects rather than complex interactions. The shell-to-air calibration treated radiation as part of an effective coefficient rather than as a separately varied term. Within those limits, the sequence—inverse calibration, robust parameter selection, and mold-feature-aware gating design—provides a practical route from simulated solidification to production castings with reduced shrinkage and higher yield.