In the aerospace industry, the turbine rear frame is an indispensable load-bearing component that endures thrust and vibration forces from the engine. It is widely recognized as one of the four key structural parts of an aircraft engine, alongside the turbine disk, blades, and turbine shaft. With the continuous advancement toward larger, more complex, and thinner-walled designs, the manufacturing of such components through high precision investment casting has become increasingly challenging. In our study, we focus on the turbine rear frame strut, which is a critical sub-component produced by high precision investment casting. By employing numerical simulation, we systematically analyze the filling process, cavity pressure evolution, and defect formation to optimize the casting parameters and ensure metallurgical quality.
The strut, made of K4169 superalloy, consists of a load-bearing lug, a floating plate, and an airfoil. Its overall dimensions are 347 mm × 286 mm × 382 mm. The lug has a thickness of 31 mm, representing the thickest section, which necessitates proper riser or gate design to avoid shrinkage porosity and cavities. The floating plate is concave, with a maximum depth of 64 mm and thickness ranging from 2.5 to 8.0 mm. This region is prone to gas entrapment during high precision investment casting, leading to misruns. The airfoil has an irregular curved surface, a thickness of 3 mm, and contains two internal stiffening ribs, each with a 10 mm × 10 mm through hole. The angle between the airfoil and the floating plate is approximately 67°, requiring careful control of melt flow to prevent defects at the airfoil base.
1. Initial Process Simulation and Analysis
We established a finite element model of the initial gating system using ProCAST software. The casting and mold shell interface nodes were treated separately to account for temperature differences. To characterize gas entrapment, we activated the gas entrapment module and set a pressure threshold. The momentum conservation model was applied to solve the filling process iteratively. Table 1 summarizes the key simulation parameters.
| Parameter | Value |
|---|---|
| Casting material | K4169 superalloy |
| Mold shell material | Mullite |
| Cooling method | Vacuum cooling |
| Mold shell thickness (mm) | 8 |
| Pouring temperature (°C) | 1450 |
| Mold temperature (°C) | 800 |
| Furnace dimensions (m) | 2 × 2.4 |
| Interface heat transfer coefficient (W·m−2·K−1) | 500 |
| Filling percentage (%) | 100 |
1.1 Filling Behavior and Cavity Pressure Evolution
The simulation results revealed severe gas entrapment and turbulent flow in the initial design. At 20% fill, the melt entered the airfoil via the lug regions. The cavity pressure remained below 0.07 MPa. However, at 40% fill, over 90% of the airfoil and lug were filled, but the remaining unfilled zones exhibited pressures exceeding 0.22 MPa, indicating significant gas entrapment. The average melt velocity in the airfoil-lug junction reached 2.2 m/s, promoting turbulence. At 60% fill, only a portion of the floating plate remained unfilled, with pressures above 0.27 MPa. By 80% fill, the main body was fully filled, but regions with pressures >0.22 MPa persisted, suggesting a high risk of misruns.
The pressure distribution can be described by the Bernoulli equation adapted for compressible flow in the cavity:
$$
P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}
$$
However, due to gas entrapment, the local pressure exceeds the equilibrium value, leading to:
$$
\Delta P = P_{\text{cavity}} – P_{\text{ref}} > 0
$$
where Pref is the reference pressure. Table 2 compares the pressure values at different filling stages.
| Filling stage (%) | Maximum pressure (MPa) | Gas entrapment severity |
|---|---|---|
| 20 | <0.07 | None |
| 40 | >0.22 | Severe |
| 60 | >0.27 | Critical |
| 80 | >0.22 | Persistent |
1.2 Defect Analysis
The shrinkage porosity and cavity defects predicted by the simulation are summarized in Table 3. The airfoil edges, center, and stiffening ribs exhibited significant shrinkage porosity. The central region of the airfoil was most affected due to rapid filling and subsequent lack of melt feeding during solidification. The floating plate also showed two shrinkage defects caused by turbulent flow. The load-bearing lug, due to its large riser, remained defect-free.
| Region | Defect type | Severity |
|---|---|---|
| Airfoil edge | Shrinkage porosity | Moderate |
| Airfoil center | Shrinkage cavity | Severe |
| Stiffening ribs | Shrinkage porosity | Moderate |
| Floating plate (area 1) | Shrinkage cavity | Moderate |
| Floating plate (area 2) | Shrinkage porosity | Moderate |
| Load-bearing lug | None | Defect-free |
2. Process Optimization and Numerical Simulation
Based on the initial analysis, we implemented the following optimization measures for high precision investment casting:
- Increased the number of vent channels from one to three in the floating plate region.
- Extended the pouring time to 1.5 times the original duration.
- Changed the sand box dimensions to 440 mm × 360 mm × 600 mm.
- Rotated the strut by 15° relative to the normal direction of the vent channel plane.
- Added 20 mm thick iron sand on both sides of the airfoil center and stiffening ribs.
The updated finite element model was constructed with the same simulation conditions as shown in Table 1, except for the geometric changes.
2.1 Optimized Filling and Pressure Behavior
At 20% fill, the melt flowed smoothly from one side of the lug into the airfoil through the floating plate. The unfilled airfoil region had a much larger connection area with the exterior compared to the initial design. Cavity pressure remained below 0.07 MPa throughout. The average melt velocity in the airfoil was only 56% of the initial process. At 40% fill, the airfoil was completely filled; the floating plate and one lug remained partially unfilled. Pressures were still below 0.07 MPa, with no gas entrapment. The average melt velocity in the floating plate dropped to 27% of the initial value. At 60% fill, the main body was completely filled, leaving only vent channels and risers unfilled. Cavity pressures rose to 0.7–1.3 MPa, but only in non-critical zones (vents/risers). The filling proceeded smoothly to completion.
The improved flow can be modeled using the continuity equation for incompressible flow with reduced turbulence:
$$
\nabla \cdot \mathbf{u} = 0
$$
and the reduced Reynolds number:
$$
Re = \frac{\rho u L}{\mu} \approx 27\% \times Re_{\text{initial}}
$$
where u is the characteristic velocity, L is the characteristic length, and μ is the dynamic viscosity. Table 4 compares the key flow metrics between initial and optimized processes.
| Metric | Initial process | Optimized process |
|---|---|---|
| Max cavity pressure at 40% fill (MPa) | >0.22 | <0.07 |
| Average melt velocity in airfoil-lug junction (m/s) | 2.2 | 1.0 |
| Average melt velocity in floating plate (m/s) | 1.6 | 0.4 |
| Gas entrapment severity | Severe at 40% fill | None |
2.2 Defect Elimination
The post-optimization simulation showed zero shrinkage porosity or cavity defects in the strut body. The only shrinkage porosity occurred in the vent channels and risers, which are subsequently removed. This confirms that the optimized high precision investment casting process eliminates internal defects.
The solidification sequence was controlled by the modified cooling design. The temperature gradient G and solidification rate R satisfy:
$$
G \cdot R = \text{constant}
$$
With the addition of iron sand, the local cooling rate increased, promoting directional solidification from thin sections toward the risers. The Niyama criterion Ny is often used to predict shrinkage:
$$
N_y = \frac{G}{\sqrt{R}}
$$
A threshold of Ny > 1.0 (in appropriate units) typically indicates a low risk of shrinkage porosity. In our optimized process, Ny > 1.5 was achieved across the entire strut body.
3. Production Validation
Based on the optimized numerical simulation, we produced a first batch of five struts using high precision investment casting. Digital real-time radiography (DR) inspection was performed on all parts, and the results met the ASTM E192 standard for gas porosity, inclusions, and shrinkage. Figure 1 shows typical radiography images from the inspected parts. The absence of internal defects confirmed the accuracy of the simulation.
Subsequently, a small batch of 40 struts was manufactured using the same optimized high precision investment casting parameters. All 40 parts passed the DR inspection, demonstrating the robustness and repeatability of the optimized process.
4. Conclusions
Through this study, we have successfully demonstrated the effectiveness of numerical simulation in optimizing the high precision investment casting process for turbine rear frame struts. The key outcomes are:
- The initial process suffered from severe gas entrapment and turbulent flow, leading to shrinkage porosity in the airfoil and floating plate.
- By modifying the vent channel design, adjusting pouring parameters, and optimizing the placement and cooling strategy, we achieved stable filling with no gas entrapment and a defect-free casting.
- Production validation, including first-article and small-batch runs, confirmed that the optimized high precision investment casting process consistently produces struts meeting ASTM E192 standards.
Table 5 summarizes the defect statistics for both the initial and optimized processes.
| Process | Simulated defect count (body) | Actual DR rejection rate (%) |
|---|---|---|
| Initial | 5 | N/A (not cast) |
| Optimized (first batch) | 0 | 0 |
| Optimized (small batch) | 0 | 0 |
The successful application of numerical simulation in this high precision investment casting case not only shortens development cycles and reduces engineering costs but also provides a reliable methodology for other complex thin-walled superalloy components.