The Role of PDE in Transonic Aerodynamics and Morphing Wing Design : A Systematic Literature Review

Hamdi Akhsan, Amanda Asti Vania, Widia Ermalia, Zanne Anggelina

Abstract


Fluid dynamics and aerodynamic design of aircraft wings play a crucial role in improving flight efficiency, especially in the transonic regime. This research aims to analyze the application of partial differential equations (PDE) in aircraft design optimization and explore technical solutions to challenges that arise in Computational Fluid Dynamics (CFD). Our research method is Literature Review (SLR) using systematic steps such as database search, screening and thematic analysis based on references from recent scientific journals from 2020 to present (2025) through ScienceDirect, Google Scholar, arXiv,MDPI, DOAJ dan Academia . An initial search yielded 234,939 journals on PDEs, but after selection, 36 journals met the inclusion criteria and were thematically analyzed. The main findings show that the Navier-Stokes, Continuity, and Bernouli Equations are the cornerstones in understanding the fluid flow behavior around an Aircraft wing. Advances in CFD technology have led to innovations, such as the application of morphing wings and winglets, which can improve aerodynamic efficiency and reduce fuel consumption. However, challenges such as CFD solver robustness, design complexity with many variables, and geometry constraints are still an obstacle in aerodynamic optimization. It can be concluded that utilizing PDE in CFD contributes significantly to the development of higher efficiency aircraft and supports design innovations that are more adaptive to modern aerodynamic demands, especially in the transonic regime.


Full Text:

PDF

References


S. S. Wang, F. Z., Animasaun, I. L., Muhammad, T., & Okoya, “Recent advancements in fluid dynamics: Drag reduction, lift generation, computational fluid dynamics, turbulence modelling, and multiphase flow,” Arab. J. Sci. Eng., vol. 49, no. 8, pp. 10237–10249., 2024, doi: https://doi.org/10.1007/s13369-024-08945-3.

S. Zhang, Z., Wang, Q., & Zhang, “Review of computational fluid dynamics analysis in biomimetic applications for underwater vehicles.,” Biomimetics, vol. 9, no. 2, p. 79, 2024, doi: https://doi.org/10.3390/biomimetics9020079.

R. K. Telaumbanua, M. F. E., & Zebua, “Analisis aplikasi mekanika fluida dalam industri penerbangan.,” J. Ilmu Ekon. Pendidik. dan Tek., vol. 1, no. 2, pp. 63–69, 2024, doi: https://doi.org/10.70134/identik.v1i2.93.

P. Jemitola, P., & Okonkwo, “An analysis of aerodynamic design issues of box-wing aircraft.,” J. Aviat. Technol. Eng., vol. 12, no. 2, p. 2, 2023, doi: https://doi.org/10.7771/2159-6670.1253.

H. Zhang, J., & Wei, “A review on configuration optimization of hybrid energy system based on renewable energy,” Heat Transf. data centers, vol. 61, p. 16648714, 2023, doi: https://doi.org/10.3389/fenrg.2022.977925.

V. Kumar, S. K., Narayanaswamy, I., & Ramesh, “In Design and development of aerospace vehicles and propulsion systems: Proceedings of SAROD 2018,” Springer Singapore, pp. 253–265, 2021, doi: https://doi.org/10.1007/978-981-15-9601-8_19.

A. V. Rao, K. S., Sivapragasam, M., Narahari, H. K., & Bharadwaj, “Aerodynamic optimization of transonic wing for light jet aircraft. In Design and development of aerospace vehicles and propulsion systems: Proceedings of SAROD 2018,” Springer Singapore., pp. 253–265, 2021, doi: https://doi.org/10.1007/978-981-15-9601-8_19.

W. J. Broadley, P., Nabawy, M. R., Quinn, M. K., & Crowther, “Dynamic experimental rigs for investigation of insect wing aerodynamics.,” J. R. Soc. Interface, vol. 19, no. 191, p. 20210909, 2020, doi: https://doi.org/10.1098/rsif.2021.0909.

A. Stelmasiak and M. Zalewska, “Computational Fluid Dynamics Simulation of Thermal Processes in Food Technology and Their Applications in the Food Industry,” pp. 1–33, 2025.

V. R. Aleksandr, N. E. T. K. A. C. H. E. V., & Kamireddi, “An overview on basics of computational fluid dynamics.,” J. Artif. Intell. Fluid Dyn., vol. 1, no. 1, pp. 21–30, 2022, doi: https://orcid.org/0000-0003-2710-8743.

G. Shah, A. Singhal, R. Apte, and R. Dupetawalla, “An Assessment of the Application of Bernoulli ’ s Theorem in the Generation of Lift Force,” vol. 10, no. 3, pp. 1–7, 2021.

M. L. Pinindriya, S. T., Soemaryanto, A. R., Fajar, M., Hidayat, K., Hamonangan, J. A., & Ramadiansyah, “Impact of airfoil section on winglet design for enhancing aerodynamics performance of aircraft using CFD analysis.,” Indones. J. Aerospace, vol. 5, no. 2, 2023, doi: https://doi.org/10.55981/ijoa.2023.900.

M. M. Dong, C., & Arief, “Morphing wing designs in commercial aviation,” arXiv Prepr. arXiv, p. 2502.07182, 2025, doi: https://arxiv.org/abs/2502.07182.

F. K. Akhter, M. Z., Ali, A. R., & Omar, “Aerodynamics of a three-dimensional bionic morphing flap.,” Sustain. Energy Technol. Assessments, vol. 52, p. 102286, 2022, doi: https://doi.org/10.1016/j.seta.2022.102286.

D. W. Yazdi, R. R., Reist, T. A., & Zingg, “Aerodynamic optimization of a Flying V aircraft based on the Reynolds-averaged Navier–Stokes equations.,” AIAA SCITECH 2024 Forum, vol. 19, no. 9, 2024, doi: https://doi.org/10.2514/6.2024-1909.

A. Petrocchi, M. Mauriello, and G. Barakos, “Transonic buffet alleviation via virtual control surfaces,” Aerosp. Sci. Technol., vol. 140, p. 108478, 2023, doi: 10.1016/j.ast.2023.108478.

Y. Wei, X., & Li, “Study on a rapid aerodynamic optimization method of flying wing aircraft for conceptual design.,” Int. J. Aerosp. Eng., pp. 1–12, 2022, doi: https://doi.org/10.1155/2022/5775355.

Z. Shi, D., Pan, T., Zhu, X., & Li, “A strategy for predicting transonic compressor performance at low Reynolds number,” Aerosp. Sci. Technol., vol. 12, no. 4, p. 349, 2025, doi: https://doi.org/10.3390/aerospace12040349.

J. Deng, Z., Wang, Y., Pan, X., Wu, J., Yang, F., Zhao, Y., Bai, X., & Liu, “Design and experimental verification of a large-scale coupled morphing-wing mechanism for hypersonic vehicles,” Def. Technol. Adv. online Publ., 2025, doi: https://doi.org/10.1016/j.dt.2025.10.031.

D. A. Hoffmann, J., & Weiss, “Compressible and viscous effects in transonic planar flow around a circular cylinder—A numerical analysis based on a commercially available CFD tool,” Fluids, vol. 8, no. 6, p. 182, 2023, doi: https://doi.org/10.3390/fluids8060182.

J. Niu, X., & Li, “Investigation and design of the transonic laminar flow characteristics in a laminar aircraft.,” Appl. Sci., vol. 12, no. 22, p. 11820, 2022, doi: https://doi.org/10.3390/app122211820.

D. W. Chau, T., & Zingg, “Aerodynamic design optimization of a transonic strut-braced-wing regional aircraft.,” J. Aircr., vol. 59, no. 1, pp. 253–271, 2022, doi: https://doi.org/10.2514/1.C036389.

D. E. Beckers, F. M., Schollenberger, M., Lutz, T., Bongen, D., Radespiel, R., Florenciano, J. L., & Funes-Sebastian, “CFD investigation of high-lift propeller positions for a distributed propulsion system,” AIAA Aviat. 2022 Forum, p. 3217, 2022, doi: https://doi.org/10.2514/6.2022-3217.

L. A. Gallani, M. A., Góes, L. C., & Nerosky, “Effects of distributed electric propulsion on the performance of a general aviation aircraft.,” AIAA/IEEE Electr. Aircr. Technol. Symp., vol. 1, no. 6, 2020.

S. Karahan, K., & Cadirci, “Investigation of fluid dynamics in various aircraft wing tank designs using 1D and CFD simulations,” Aerospace, vol. 11, no. 7, p. 519, 2024, doi: https://doi.org/10.3390/aerospace11070519.

N. R. Bombardieri, R., Cavallaro, R., Sanchez, R., & Gauger, “Aerostructural wing shape optimization assisted by algorithmic differentiation.,” Struct. Multidiscip. Optim., 2020, doi: https://doi.org/10.1007/s00158-021-02884-5.

S. Champasak, P., Buaphet, P., & Bureerat, “Aeroelastic multi-objective optimisation of an aircraft wing taking into account gust alleviation,” SciTech Res. J., vol. 13, no. 2, pp. 1–10., 2021, doi: https://ph02.tci-thaijo.org/index.php/jstrmu/article/view/247300.

C. Gutierrez-Castillo, P., Aguilar-Cabello, J., Alcalde-Morales, S., Parras, L., & del Pino, “On the lift curve slope for rectangular flat plate wings at moderate Reynolds number,” J. Wind Eng. Ind. Aerodyn., vol. 208, p. 104459., 2021, doi: https://doi.org/10.1016/j.jweia.2020.104459.

J. R. Martins, “Aerodynamic design optimization: Challenges and perspectives,” Comput. Fluids, vol. 239, p. 105391, 2022, doi: https://doi.org/10.1016/j.compfluid.2022.105391.

J. R. Yildirim, A., Kenway, G. K., Mader, C. A., & Martins, “A Jacobian-free approximate Newton–Krylov startup strategy for RANS simulations.,” J. Comput. Phys., vol. 397, p. 108741, 2019, doi: https://doi.org/10.1016/j.jcp.2019.06.018.

J. R. Li, J., He, S., & Martins, “Data-driven constraint approach to ensure low-speed performance in transonic aerodynamic shape optimization,” Aerosp. Sci. Technol., vol. 92, pp. 536–550, 2019, doi: https://doi.org/10.1016/j.ast.2019.06.008.

G. Petrocchi, A., Mauriello, M., & Barakos, “Experimental and numerical investigation of transonic buffet and control-surface response,” Aerosp. Sci. Technol., 2023, doi: https://eprints.gla.ac.uk/301258/1/301258.

L. L. Van Arnhem, N., de Vries, R., Sinnige, T., Vos, R., Eitelberg, G., & Veldhuis, “Engineering method to estimate the blade loading of propellers in nonuniform flow,” AIAA J., vol. 58, no. 12, pp. 5332–5346, 2020, doi: https://doi.org/10.2514/1.J059485.

& F. Robby, M., Karudin, A., Refdinal, “Aerodynamic analysis of NACA 2412 airfoil on UAV aircraft wing using Ansys Fluent software.,” Int. J. Innov. Mech. Constr. Energy, vol. 1, no. 3, 2023, doi: https://doi.org/10.24036/ijimce.v1i3.49.

D. Rubin, R. L., & Zhao, “New development of classical actuator disk model for propellers at incidence,” AIAA J., vol. 59, no. 3, pp. 1040–1054, 2021, doi: https://doi.org/10.2514/1.J059734.

M. Wei, N. I. U., Zhang, Y., Chen, H. C. H., & Zhang, “Numerical study of a supercritical airfoil/wing with variable-camber technology,” Chinese J. Aeronaut., vol. 33, no. 7, pp. 1850–1866, 2020, doi: https://doi.org/10.1016/j.cja.2020.01.008.




DOI: https://doi.org/10.24198/jiif.v10i2.69625

Refbacks

  • There are currently no refbacks.


Journal Indexed By:
Visit Statistics: