Development a computationally efficient method to solve direct and inverse aerodynamic problems related to turbomachines

Authors

DOI:

https://doi.org/10.15587/1729-4061.2026.365474

Keywords:

inverse problem, flow function, Euler equation, quasi-three-dimensional flow, flow section, aerodynamic design

Abstract

This study investigates aerodynamic processes in interblade, axial annular, and radial-axial channels in turbomachines. The task addressed relates to the need to improve the computational efficiency in solving direct and inverse aerodynamic problems when analyzing and designing flow parts of turbomachines.

A computationally efficient method for solving direct and inverse aerodynamic problems has been proposed, which provides acceptable accuracy for engineering practice at significantly lower computational costs compared to conventional CFD approaches. The results include a devised single mathematical formulation based on Euler equations for a compressible fluid, written in terms of the flow function.

The proposed method makes it possible to consider direct and inverse problems within a common mathematical structure. The system of equations is reduced to a single differential equation and a set of algebraic relations while the global flow problem is decomposed into a set of independent problems for individual cross-sections. The inverse problem is stated as a nonlinear optimization problem based on the mass flow rate agreement condition derived from the energy equation. The computational complexity is reduced by using the flow function and the decomposition of the computational domain.

The method combines the capabilities of direct analysis and reconstruction of the flow channel geometry based on the predefined aerodynamic characteristics. Verification by experimental data and direct calculation results demonstrated good agreement between the velocity distributions and the reconstructed geometry; the maximum deviations did not exceed 0.3%.

The results could be practically applied to preliminary design, parametric optimization, as well as inverse design of the flow parts in turbomachines

Author Biographies

Valery Subotovich, Anatolii Pidhornyi Institute of Power Machines and Systems of the National Academy of Sciences of Ukraine

Doctor of Technical Sciences, Senior Researcher

Department of Thermogasdynamics of Power Machines No. 33

Oleksandr Yudin, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Technical Sciences

Department of Turbine Construction

Artem Babaiev, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Technical Sciences

Department of Turbine Construction

Valentyn Barannik, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Technical Sciences

Department of Turbine Construction

Olena Avdieieva, National Technical University «Kharkiv Polytechnic Institute»

Candidate of Technical Sciences, Associate Professor

Department of Computer Modeling of Processes and Systems

Department of Turbine Construction

References

  1. Denton, J. D. (1983). An Improved Time-Marching Method for Turbomachinery Flow Calculation. Journal of Engineering for Power, 105 (3), 514–521. https://doi.org/10.1115/1.3227444
  2. Denton, J. D. (1993). The 1993 IGTI Scholar Lecture: Loss Mechanisms in Turbomachines. Journal of Turbomachinery, 115 (4), 621–656. https://doi.org/10.1115/1.2929299
  3. Dawes, W. N. (1993). The Extension of a Solution-Adaptive Three-Dimensional Navier–Stokes Solver Toward Geometries of Arbitrary Complexity. Journal of Turbomachinery, 115 (2), 283–295. https://doi.org/10.1115/1.2929234
  4. Denton, J. D., Dawes, W. N. (1998). Computational fluid dynamics for turbomachinery design. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 213 (2), 107–124. https://doi.org/10.1243/0954406991522211
  5. Dawes, W. N. (2007). Turbomachinery computational fluid dynamics: asymptotes and paradigm shifts. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 365 (1859), 2553–2585. https://doi.org/10.1098/rsta.2007.2021
  6. Sandberg, R. D., Michelassi, V. (2019). The Current State of High-Fidelity Simulations for Main Gas Path Turbomachinery Components and Their Industrial Impact. Flow, Turbulence and Combustion, 102 (4), 797–848. https://doi.org/10.1007/s10494-019-00013-3
  7. Sandberg, R. D., Michelassi, V. (2022). Fluid Dynamics of Axial Turbomachinery: Blade- and Stage-Level Simulations and Models. Annual Review of Fluid Mechanics, 54 (1), 255–285. https://doi.org/10.1146/annurev-fluid-031221-105530
  8. Slotnick, J., Khodadoust, A., Alonso, J., Darmofal, D., Gropp, W., Lurie, E., Mavriplis, D. J (2014). CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences. NASA Technical Report. Available at: https://ntrs.nasa.gov/citations/20140003093
  9. Wheeler, A. P. S. (2024). High fidelity simulation of dense vapours with thermodynamic consistent modelling. Computers & Fluids, 268, 106088. https://doi.org/10.1016/j.compfluid.2023.106088
  10. Zhang, E., Watanabe, T., Lai, Z., Bai, B. (2024). A compressible flow solver for turbomachinery of the real gases with strongly variable properties. Energy, 290, 129915. https://doi.org/10.1016/j.energy.2023.129915
  11. Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32 (8), 1598–1605. https://doi.org/10.2514/3.12149
  12. Pope, S. B. (2000). Turbulent Flows. Cambridge University Press. https://doi.org/10.1017/cbo9780511840531
  13. Hammond, J., Pepper, N., Montomoli, F., Michelassi, V. (2022). Machine Learning Methods in CFD for Turbomachinery: A Review. International Journal of Turbomachinery, Propulsion and Power, 7 (2), 16. https://doi.org/10.3390/ijtpp7020016
  14. Waschkowski, F., Zhao, Y., Sandberg, R., Klewicki, J. (2022). Multi-objective CFD-driven development of coupled turbulence closure models. Journal of Computational Physics, 452, 110922. https://doi.org/10.1016/j.jcp.2021.110922
  15. Spalart, P. R. (2021). Hybrid RANS-LES Methods. Advanced Approaches in Turbulence, 133–159. https://doi.org/10.1016/b978-0-12-820774-1.00010-0
  16. Jameson, A. (1988). Aerodynamic design via control theory. Journal of Scientific Computing, 3 (3), 233–260. https://doi.org/10.1007/bf01061285
  17. Giles, M. B., Pierce, N. A. (2000). An Introduction to the Adjoint Approach to Design. Flow, Turbulence and Combustion, 65 (3-4), 393–415. https://doi.org/10.1023/a:1011430410075
  18. Shahpar, S. (2010). Optimisation Strategies Used in Turbomachinery Design from an Industrial Perspective. In book: INTRODUCTION TO OPTIMIZATION AND MULTIDISCIPLINARY DESIGN IN AERONAUTICS AND TURBOMACHINERY. Vol. 1. Chap. 7. Publisher: Von-Karmaan Institute (VKI). Available at: https://www.researchgate.net/publication/267763601_Optimisation_strategies_used_in_turbomachinery_design_from_an_industrial_perspective
  19. Li, Z., Zheng, X. (2017). Review of design optimization methods for turbomachinery aerodynamics. Progress in Aerospace Sciences, 93, 1–23. https://doi.org/10.1016/j.paerosci.2017.05.003
  20. Lavimi, R., Benchikh Le Hocine, A. E., Poncet, S., Marcos, B., Panneton, R. (2024). A review on aerodynamic optimization of turbomachinery using adjoint method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 238 (13), 6405–6441. https://doi.org/10.1177/09544062231221625
  21. Wu, C.-H. (1952). A General Theory of Three-Dimensional Flow in Subsonic and Supersonic Turbomachines of Axial, Radial, and Mixed-Flow Types. Journal of Fluids Engineering, 74 (8), 1363–1380. https://doi.org/10.1115/1.4016114
  22. Novak, R. A., Hearsey, R. M. (1977). A Nearly Three-Dimensional Intrablade Computing System for Turbomachinery. Journal of Fluids Engineering, 99 (1), 154–166. https://doi.org/10.1115/1.3448517
  23. Davis, W. R., Millar, D. A. J. (1975). A Comparison of the Matrix and Streamline Curvature Methods of Axial Flow Turbomachinery Analysis, From a User’s Point of View. Journal of Engineering for Power, 97 (4), 549–558. https://doi.org/10.1115/1.3446059
  24. Denton, J. D. (1978). Throughflow Calculations for Transonic Axial Flow Turbines. Journal of Engineering for Power, 100 (2), 212–218. https://doi.org/10.1115/1.3446336
  25. Li, Z., Liu, Y. (2023). An Aerodynamic Loss Model for Axial Turbine Design. Journal of Turbomachinery, 145 (9). https://doi.org/10.1115/1.4062804
  26. Subbotovich, V. P., Yudin, A. Yu. (2004). Zadacha rascheta skorosti na poverhnosti lopatki turbomashiny kak zadacha optimizacii. Vestnik Nacionalnogo tehnicheskogo universiteta «HPI», 12, 101–106.
  27. Subbotovich, V. P., Yudin, A. Yu., Fan, K. T. (2008). Obtekanie trehmernym potokom reshetki profilej turbomashiny na poverhnosti vrasheniya. Vestnik Nacionalnogo tehnicheskogo universiteta «HPI», 6, 41–46. Available at: https://repository.kpi.kharkov.ua/handle/KhPI-Press/18786
  28. Subbotovich, V. P., Yudin, A. Yu., Temchenko, S. A. (2011). Metod rascheta techeniya v oseradialnyh kolcevyh kanalah. Visnyk Natsionalnoho tekhnichnoho universytetu «KhPI». Seriya: Enerhetychni ta teplotekhnichni protsesy y ustatkuvannia, 6, 24–27. Available at: https://library.kpi.kharkov.ua/files/Vestniki/2011_6.pdf
  29. Subbotovich, V. P. (2013). Potok cherez vrashayushuyusya reshetku osevoy turbomashiny na proizvolnoy poverhnosti S1. Visnyk Natsionalnoho tekhnichnoho universytetu «KhPI». Seriya: Enerhetychni ta teplotekhnichni protsesy y ustatkuvannia, 14 (987), 43–48. Available at: https://repository.kpi.kharkov.ua/handle/KhPI-Press/3813
  30. Subbotovich, V. P. (2013). Kompleksnoe teoreticheskoe i eksperimentalnoe reshenie zadach aerodinamiki protochnyh chastey turbin. Kharkiv: NTU «KhPI», 355.
  31. Kopelev, S. Z., Slitenko, A. F. (1994). Konstrukcii i raschet sistem ohlazhdeniya GTD. Kharkiv: Osnova, 240.
  32. Tarasov, A. I., Gurinov, A. A., Rassohin, E. V. (2005). O modelirovanii teploobmena na profilyah turbiny lopatok s pomoshyu CFD programm. Vestnik Nacionalnogo tehnicheskogo universiteta «HPI», 6, 81–84.
  33. Temchenko, S. A. (2015). Obratnaya aerodinamicheskaya zadacha dlya optimalnogo proektirovaniya kolcevyh diffuzornyh kanalov turbomashin. Kharkiv: NTU «KhPI», 147.
  34. Subbotovich, V. P., Yudin, A. Yu., Temchenko, S. A. (2014). Raschet turbinnoy stupeni po zazoram kak reshenie obratnyh aerodinamicheskih zadach v svobodnyh kolcevyh kanalah. Vestnik Nacionalnogo tehnicheskogo universiteta «HPI», 13, 35–38. Available at: https://repository.kpi.kharkov.ua/items/88c0b411-ad9f-4a63-b64f-2d8cf0208ae7
Devising a computationally efficient method to solve direct and inverse aerodynamic problems related to turbomachines

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Published

2026-06-29

How to Cite

Subotovich, V., Yudin, O., Babaiev, A., Barannik, V., & Avdieieva, O. (2026). Development a computationally efficient method to solve direct and inverse aerodynamic problems related to turbomachines. Eastern-European Journal of Enterprise Technologies, 3(7 (141), 71–82. https://doi.org/10.15587/1729-4061.2026.365474

Issue

Vol. 3 No. 7 (141) (2026): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2026 Valery Subotovich, Oleksandr Yudin, Artem Babaiev, Valentyn Barannik, Olena Avdieieva

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