Multi-Disciplinary Optimization of Mixed-Flow Turbine for Additive Manufacturing †
Abstract
1. Introduction
2. Optimization Problem
2.1. Parametrization
- Meridional contours at hub and shroud: Thirty-one parameters dictate the position of the control points of the b−spline curves. Critical points at the inlet and outlet should respect AM manufacturing constraints, limiting the construction angles to below 55 degrees. Angle and distance with respect to the neighboring point are therefore used as parameters instead of the x-y coordinates.
- Blade angle distribution at hub and shroud: Fourteen parameters control the blade angles. The design space is selected within the acceptable range regarding the maximum absolute angle of .
- Azimuthal angle variations at mid-span: Five parameters control the deviation from the linear interpolation between hub and shroud azimuthal angles. They dictate the local bowing of the blade, deviating it from a ruled surface, as would be a limitation imposed by manufacturing through flank milling.
- Thickness distribution at hub, mid-span and shroud: Eighteen parameters control the thickness distribution. Rounded trailing edges are considered. However, as a rule of thumb, there should be at least three passes of the laser for the skin of the printed component, with an overall thickness not smaller than 0.8 mm. Therefore, a control point is located for each section close to the trailing edge, and its value is maintained above 1 mm.
2.2. Mesh and Solver Setup
2.3. Problem Definition
2.4. Optimization Algorithm
2.5. Mesh Independence Study
3. Results and Discussion
3.1. Optimization History and Optimal Geometry
- 1.
- The inlet blade section has been increased by moving the first blade shroud control point upward without inducing any sweep.
- 2.
- The inlet rake angle and azimuthal angle variations are reduced, particularly near the trailing edge. This induces a blade with smaller bowing, leading to a more radially fibered design with less bending stress.
- 3.
- The hub fillet radius has increased from 2.8 mm to 2.97 mm.
- 4.
- The overall thickness at the shroud has been reduced. The thickness of the intermediate section at mid-span has been decreased, starting from the second half of the chord. This tapering reduces stresses, as less mass is positioned at a higher radius, whereas the cross-sectional area increases towards the hub, distributing the reduced centrifugal load over a larger area.
- 5.
- The solid blade angle at the inlet is now slightly negative.
3.2. Structural Analysis
- On the pressure side near the trailing edge (A). By reducing the blade bowing midway between leading and trailing edges, the geometry is closer to a radially fibered blade, known for its higher stress resistance. The reduced thickness at the shroud and intermediate sections also contributes to relieving the stress.
- On the suction side at the intersection with the hub (B). The stress is reduced mostly by increasing the hub fillet radius and hub thickness.
- On the suction side around (C). The stress is decreased by reducing the inlet rake angle and the blade bowing near the leading edge. Modifications of the hub’s solid angle distribution contribute favorably but to a lesser extent.
- In the rotor center, aligned with the inlet (D). Stresses in this region are generated by centrifugal force due to mass located at a large radius. The backplate has been designed to partially relieve the stress there. The presence of a center hole has not been considered in this study but is very likely to increase the circumferential stress in this region.
3.3. Flow Analysis
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AM | Additive Manufacturing |
CFD | Computational Fluid Dynamics |
CSM | Computational Structural Mechanics |
SQP | Sequential Quadratic Programming |
Nomenclature | |
p | Static pressure [Pa] |
P | Power [W] |
J | Objective function |
Equivalent sand grain size [m] | |
Hydraulic diameter [m] | |
Reynolds number [-] | |
Hub | |
Shroud | |
Inlet | |
Outlet | |
Von Mises | |
p-Norm value | |
Design parameter | |
Solid blade angle [-] | |
Efficiency [-] | |
Adjoint variable | |
Stress [Pa] | |
Rotor angular velocity [s−1] | |
Azimuthal angle [-] | |
Meridional contour angle [-] | |
Rake angle [-] |
References
- Bartolo, P. Stereolithographic Processes. In Stereolitography: Materials, Processes and Applications; Bartolo, P., Ed.; Springer: Boston, MA, USA, 2011; pp. 1–36. [Google Scholar]
- Gao, W.; Zhang, Y.; Ramanujan, D.; Ramani, K.; Chen, Y.; Williams, C.; Shin, Y.; Zhang, S.; Zavattieri, P. The Status, Challenges, and Future of Additive Manufacturing in Engineering. Comput. Aided Des. 2015, 69, 65–89. [Google Scholar] [CrossRef]
- Mercado, F.; Rojas, A.A. Additive Manufacturing Methods: Techniques, Materials, and Closed-loop Control Applications. J. Adv. Manuf. Technol. 2020, 109, 17–31. [Google Scholar] [CrossRef]
- Dinita, A.; Neacsa, A.; Portoaca, A.I.; Tanase, M.; Ilinca, C.N.; Ramadan, I.N. Additive Manufacturing Post-Processing Treatments, a Review with Emphasis on Mechanical Characteristics. Materials 2023, 16, 4610. [Google Scholar] [CrossRef] [PubMed]
- Bello, K.A.; Kanakan-Katumba, M.G.; Maladzhi, R.W. A Review of Additive Manufacturing Post-Treatment Techniques for Surface Quality Enhancement. Proc. CIRP 2023, 120, 404–409. [Google Scholar] [CrossRef]
- Prakash, P.; Jothilakshmi, P. Additive Manufacturing in Turbomachineries. Int. J. Eng. Tech. Mgmt. Res. 2019, 9, 31–47. [Google Scholar]
- Magerramova, L.; Volkow, M.; Svinareva, M.; Siversky, A. The Use of Additive Technologies to Create Lightweight Parts for Gas Turbine Engine Compressors. In Proceedings of the Name of the AMSE Turbo Expo, Oslo, Norway, 11–15 June 2018. [Google Scholar]
- 3D Systems. Available online: https://www.3dsystems.com/turbomachinery (accessed on 18 August 2024).
- Pietropaoli, M.; Ahlfeld, R.; Montomoli, F.; Ciani, A.; d’Ercole, M. Design for Additive Manufacturing: Internal Channel Optimization. J. Eng. Gas Turbines Power 2017, 139, 102101. [Google Scholar] [CrossRef]
- Palman, M.; Abraham, Y.; Agapovichev, A.; Yildrim, A.; Acarer, S.; Verstraete, T.; Saracoglu, B.H.; Cukurel, B. Conceptualizing a Pre-Assembled Additively Manufactured Gas Turbine Engine: Technological Feasibility. In Proceedings of the AIAA SCITECH 2024, Orlando, FL, USA, 8–12 January 2024. [Google Scholar]
- Additively Manufactured Pre-Assembled Engine (APE). Available online: https://bcukurel.net.technion.ac.il/ape/ (accessed on 29 July 2024).
- Ergin, C.; Verstraete, T.; Saracoglu, B.H. The Design and Optimization of Additively Manufactured Radial Compressor of a Miniature Gas Turbine Engine. J. Fluids Eng. 2024, 146, 071108. [Google Scholar] [CrossRef]
- Agromayor, R.; Anand, N.; Muller, J.D.; Pini, M.; Nord, L.O. A Unified Geometry Parametrization Method for Turbomachinery Blades. Comput. Aided Des. 2021, 133, 102987. [Google Scholar] [CrossRef]
- Chatel, A.; Verstraete, T. Aerodynamic Optimization of the SRV2 Radial Compressor Using an Adjoint-Based Optimization Method. In Proceedings of the ASME Turbo Expo 2022, Rotterdam, The Netherlands, 13–17 June 2022. [Google Scholar]
- Verstraete, T.; Muller, L.; Mueller, J.D. CAD-Based Adjoint Optimization of the Stresses in a Radial Turbine. In Proceedings of the ASME Turbo Expo 2017, Charlotte, NC, USA, 26–30 June 2017. [Google Scholar]
- Spalart, P.R.; Allmaras, S.R. A One-Equation Turbulence Model for Aerodynamic Flows. La Rech. Aerosp. 1994, 1, 5–21. [Google Scholar]
- Balbaa, M.; Mekhiel, S.; Elbestawi, M.; McIsaac, J. On Selective Laser melting of Inconel 718: Densification, Surface Roughness, and Residual Stresses. Mater. Des. 2020, 193, 108818. [Google Scholar] [CrossRef]
- Jia, Q.; Gu, D. Selective Laser Melting Additive Manufacturing of Inconel 718 Superalloy Parts: Densification, Microstructure and Properties. J. Alloys Compd. 2014, 585, 713–721. [Google Scholar] [CrossRef]
- Sharma, S.; Panaiappan, K.; Mishra, V.D.; Vedantam, S.; Murthy, H.; Rao, B.C. Mechanical Characterization of Near-Isotropic Inconel 718 Fabricated by Laser Powder-Bed Fusion. Metall. Mater. Trans. A 2023, 54, 270–285. [Google Scholar] [CrossRef]
- Gruber, K.; Stopyra, W.; Kobiela, K.; Madejski, B.; Malicki, M.; Kurzynowski, T. Mechanical Properties of Inconel 718 Additively Manufactured by Laser Powder Bed Fusion after Industrial High-Temperature Heat Treatment. J. Manuf. Process. 2022, 73, 642–659. [Google Scholar] [CrossRef]
- Muduli, S.K.; Mishra, R.K.; Satapathy, R.K.; Chandel, S. Effect of Operating Variables on the Performance of a Highly Loaded Annular Combustor. Int. J. Turbo Jet Engines 2014, 32, 85–95. [Google Scholar] [CrossRef]
- High Temp Metals. Available online: https://www.hightempmetals.com/techdata/hitempInconel718data.php/ (accessed on 5 August 2024).
- Kambampati, S.; Gray, J.S.; Kim, H.A. Level Set Topology Optimization of Structures under Stress and Temperature Constraints. Comput. Struct. 2020, 235, 106265. [Google Scholar] [CrossRef]
- Xu, S.; Radford, D.; Meyer, M.; Mueller, J.D. Stabilisation of Discrete Steady Adjoint Solvers. J. Comput. Phys. 2015, 299, 175–195. [Google Scholar] [CrossRef]
- Nielsen, E.J.; Lu, J.; Park, M.A.; Darmofal, D.L. An Implicit, Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids. Comput. Fluids 2004, 33, 1131–1155. [Google Scholar] [CrossRef]
- Dwight, R.P.; Brezillon, J. Efficient and Robust Algorithms for Solution of the Adjoint Compressible Navier-Stokes Equations with Applications. Int. J. Numer. Methods Fluids 2009, 60, 365–389. [Google Scholar] [CrossRef]
- Muller, L.; Verstraete, T. Adjoint-based Multi-Point and Multi-Objective Optimization of a Turbocharger Radial Turbine. Int. J. Turbomach. Propuls. Power 2019, 4, 10. [Google Scholar] [CrossRef]
- Hottois, R.; Chatel, A.; Coussement, G.; Debruyn, T.; Verstraete, T. Comparing Gradient-Free and Gradient-Based Multi-Objective Optimization Methodologies on the VKI-LS89 Turbine Vane Test Case. J. Turbomach. Propuls. Power 2022, 145, 1–30. [Google Scholar]
- Muller, L.; Verstraete, T. CAD Integrated Multipoint Adjoint-Based Optimization of a Turbocharger Radial Turbine. J. Turbomach. Propuls. Power 2017, 2, 14. [Google Scholar] [CrossRef]
- Meng, F.; Zheng, Q.; Zhang, J. Effects of Blade Fillet Structures on Flow Field and Surface Heat Transfer in a Large Meridional Expansion Turbine. Energies 2019, 12, 3035. [Google Scholar] [CrossRef]
- Kienzle, N.; Hoang, D.H.N.; Waesker, M.; Buelten, B.; di Mare, F.; Doetsch, C. Influence of Fillet Radius on the Flow and Strength Behaviour of a Shrouded Centrifugal Compressor Impeller. In Proceedings of the 14th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics, Gdansk, Poland, 12–16 April 2021. [Google Scholar]
- Loir, V.; Saracoglu, B.H.; Verstraete, T. Mixed-flow turbine multi-disciplinary optimization for additive manufacturing. In Proceedings of the 16th European Turbomachinery Conference, Hannover, Germany, 24–28 March 2025. paper n. ETC2025-183. [Google Scholar]
Boundary | Quantity | Value | Units |
---|---|---|---|
357,000 | [Pa] | ||
Inlet | 1100 | [K] | |
61 | [°] | ||
Outlet | 100,000 | [Pa] | |
Rotating walls | 58,000 | [rpm] |
Quantity | Target Value | Acceptable Range |
---|---|---|
1.898 kg/s | ±1% | |
P | 341 kW | ±3% |
Quantity | Bound(s) | Initial | Optimal | Units |
---|---|---|---|---|
P | <351.84 >331.34 | 336.76 | 351.76 | [kW] |
<1.917 >1.879 | 1.919 | 1.916 | [kg/s] | |
<580 | 680.25 | 574.80 | [MPa] | |
<830 | 861.29 | 696.30 | [MPa] | |
/ | 87.33 | 89.61 | [%] |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the authors. Published by MDPI on behalf of the EUROTURBO. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).
Share and Cite
Loir, V.; Saracoglu, B.H.; Verstraete, T. Multi-Disciplinary Optimization of Mixed-Flow Turbine for Additive Manufacturing. Int. J. Turbomach. Propuls. Power 2025, 10, 26. https://doi.org/10.3390/ijtpp10030026
Loir V, Saracoglu BH, Verstraete T. Multi-Disciplinary Optimization of Mixed-Flow Turbine for Additive Manufacturing. International Journal of Turbomachinery, Propulsion and Power. 2025; 10(3):26. https://doi.org/10.3390/ijtpp10030026
Chicago/Turabian StyleLoir, Victor, Bayindir H. Saracoglu, and Tom Verstraete. 2025. "Multi-Disciplinary Optimization of Mixed-Flow Turbine for Additive Manufacturing" International Journal of Turbomachinery, Propulsion and Power 10, no. 3: 26. https://doi.org/10.3390/ijtpp10030026
APA StyleLoir, V., Saracoglu, B. H., & Verstraete, T. (2025). Multi-Disciplinary Optimization of Mixed-Flow Turbine for Additive Manufacturing. International Journal of Turbomachinery, Propulsion and Power, 10(3), 26. https://doi.org/10.3390/ijtpp10030026