Numerical and analytical modeling of the propulsive wing and fuselage of an air taxi

The problem of creating propulsive airfoils is considered. Such airfoils have a slit through which the boundary layer is sucked out. Located just behind this gap, a specially profiled section of the airfoil creates a propulsive thrust. The thrust is created due to an abrupt change in the pressure profile on the slit through which the boundary layer is sucked. In the last 15–20 years, the concept of a so-called propulsive wing with reduced or zero aerodynamic drag due to the suction of the boundary layer from its upper surface has been actively studied in the world. Such a wing makes it possible to reduce the aerodynamic drag of the aircraft by several times due to boundary layer laminarization and minimizing the velocity defect associated with viscous friction in the boundary layer, in the wake of the aircraft. The paper proposes a method for numerical modeling of airfoils for a propulsive wing constructed by solving the inverse problem of aerodynamics. The designed airfoils have a maximum construction height, an optimal combination of the lifting force coefficient Cl and the thrust coefficient CT, created by air suction from the wing surface. The developed technique correctly predicts the point of the laminar-turbulent transition, since the characteristics of the airfoils directly depend on the length of the laminar section. The layout of an aircraft built according to the scheme of a propulsive flying wing of ultra-small aspect ratio using the developed airfoils has been studied. The design of aerodynamic profiles was carried out by solving the inverse problem of aerodynamics with subsequent refinement of geometry using global optimization algorithms. Calculations were carried out using the Langtry−Menter turbulence γ-ReΘ Transition Shear Stress Transport model, in which there are relations for the intermittency criterion, makes it possible to simulate a laminar-turbulent transition. Calculations have shown that the developed airfoils make it possible to create an aircraft airframe with a maximum lift coefficient Clmax which exceeds the Clmax of a mechanized wing with a flap released during takeoff and landing. In horizontal flight, the Cl is three times larger than that of a typical wing. The wing with the developed profiles has a high propulsive efficiency due to the proximity of pressure and velocity in the thrust section of the airfoils and external flow. At the same time, the thrust surface of the propulsive wing exceeds the nozzle area or the total coverage of aircraft propellers by several times. The developed airfoils and integrated aerodynamic layout of the aircraft are well combined with the principles of building a distributed power plant, and allow you to combine immunity to increased atmospheric turbulence during vertical takeoff and landing with economical horizontal flight. Airfoils have an important advantage over traditional wing mechanization because they have no moving parts, and the increase or decrease in lift is regulated by changing the flow rate of the sucked air.

1. Felder J.L., Tong M.T., Chu J. sensitivity of mission energy consumption to turboelectric distributed propulsion design assumptions on the N3-X hybrid wing body aircraft. Proc. of the 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2012. https://doi.org/10.2514/6.2012-3701

2. Bradley M., Droney C. Subsonic Ultra Green Aircraft Research. Phase I Final Report. NASA/CR2011-216847. 2011, 193 p.

3. Felder J.L., Kim H.D., Brown G. An examination of the effect of boundary layer ingestion on turboelectric distributed propulsion systems. Proc. of the 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2011. https:// doi.org/10.2514/6.2011-300

4. Alrashed M., Nicoladis T., Pilidis P., Jafari S. Utilisation of turboelectric distribution propulsion in commercial aviation: A review on NASA’s TeDP concept. Chinese Journal of Aeronautics, 2021, vol. 34, no. 11, pp. 48–65. https://doi.org/10.1016/j.cja.2021.03.014

5. Chen Z., Zhang M., Chen Y., Sang W., Tan Z., Li D., Zhang B. Assessment on critical technologies for conceptual design of blendedwing-body civil aircraft. Chinese Journal of Aeronautics, 2019, vol. 32, no. 8, pp. 1797–1827. https://doi.org/10.1016/j.cja.2019.06.006

6. Yaros S.F., Sexstone M.G., Huebner L.D., Lamar J.E., McKinley R.E., Jr., Torres A.O., Burley C.L., Scott R.C., Small W.J. Synergistic Airframe-Propulsion Interactions and Integrations. A White Paper Prepared by the 1996-1997 Langley Aeronautics Technical Committee. NASA/TM-1998-207644, 1998, 122 p.

7. Burston M., Ranasinghe K., Gardi A., Parezanovic V., Ajaj R., Sabatini R. Design principles and digital control of advanced distributed propulsion systems. Energy, 2022, vol. 241, pp. 122788. https://doi.org/10.1016/j.energy.2021.122788

8. Richards E.J., Walker W.S., Greening J.R. Tests of a Griffith Aerofoil in the 13 ft x 9 ft Wind Tunnel. Part 1, Part 2, Part 3, Part 4. ARC R&M-2148 ARC-7464 ARC-7561 ARC-8054 ARC-8055. 1944.

9. Goldschmied F. Fuselage self-propulsion by static-pressure thrust: Wind-tunnel verification. Proc. of the Aircraft Design, Systems and Operations Meeting, 1987. https://doi.org/10.2514/6.1987-2935

10. Goldschmied F. Airfoil static-pressure thrust: flight test verification. Proc. of the Aircraft Design, Systems and Operations Conference, 1990. https://doi.org/10.2514/6.1990-3286

11. Goldschmied F. Thick-wing spanloader all-freighter: design concept for tomorrow’s air cargo. Proc. of the Aircraft Design, Systems and Operations Conference, 1990. https://doi.org/10.2514/6.1990-3198

12. Cella U., Quagliarella D., Donelli R. Imperatore B. Design and test of the UW-5006 transonic natural-laminar-flow wing. Journal of Aircraft, 2010, vol. 47, no. 3, pp. 783–795. https://doi.org/10.2514/1.40932

13. Bulat P.V., Kurnukhin A.A., Prodan N.V. Numerical simulation of propulsive aerodynamic profiles. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2022, vol. 22, no. 5, pp. 1007–1015. (in Russian). https://doi.org/10.17586/2226-1494-2022-22-5-1007-1015

14. Bulat P.V., Dudnikov S.Iu., Kuznetcov P.N. Fundamental Aerodynamics of the Unmanned Aerial Vehicles. Tutorial. Moscow, “Sputnik+” Publ., 2021, 273 p. (in Russian)

15. Tamaki T., Nagano S. Effects of inlet distortions on a multi-stage compressor. Proc. of the 4th International Symposium on Air Breathing Engines, 1979. https://doi.org/10.2514/6.1979-7003

16. Sandercock D.M., Sanger N.L. Some observations of the effects of radial distortions on performance of a transonic rotating blade row. NASA TN D-7824, 1974, 48 p.

17. Hancock J.P. Test of a high efficiency transverse fan. Proc. of the 16th Joint Propulsion Conference, 1980. https://doi.org/10.2514/6.1980-1243

18. Harloff G.J., Wilson D.R. Cross-flow propulsion fan experimental development and finite-element modeling. Journal of Aircraft, 1981, vol. 18, no. 4, pp. 310–317. https://doi.org/10.2514/3.57494

19. Dygert R.K., Dang T.Q. Experimental investigation of embedded cross-flow fan for airfoil propulsion/circulation control. Proc. of the 45th AIAA Aerospace Sciences Meeting and Exhibit, 2007. https://doi.org/10.2514/6.2007-368

20. Gologan C., Mores S., Steiner H., Seitz A. Potential of the cross-flow fan for powered-lift regional aircraft applications. Proc. of the 9th AIAA Aviation Technology, Integration, and Operations Conference (ATIO), 2009. https://doi.org/10.2514/6.2009-7098

21. Langel C.M., Chow R., Van Dam C.P., Maniaci D.C., Erhmann R.S., White E.B. A computational approach to simulating the effects of realistic surface roughness on boundary layer transition. Proc. of the 52nd Aerospace Sciences Meeting, 2014. https://doi.org/10.2514/6.2014-0234

22. Doll U., Migliorini M., Baikie J., Zachos K.P., Röhle I., Melnikov S., Steinbock J., Dues M., Kapulla R., MacManus D.G., Lawson N.J. Non-intrusive flow diagnostics for unsteady inlet flow distortion measurements in novel aircraft architectures. Progress in Aerospace Sciences, 2022, vol. 130, pp. 100810. https://doi.org/10.1016/j.paerosci.2022.100810

23. Dang T.Q., Bushnell P.P. Aerodynamics of cross-flow fans and their application to aircraft propulsion and flow control. Progress in Aerospace Sciences, 2009, vol. 45, no. 1-3, pp. 1–29. https://doi.org/10.1016/j.paerosci.2008.10.002

24. Karpuk S.V., Kazarin P., Gudmundsson S., Golubev V.V. Preliminary feasibility study of a multi-purpose aircraft concept with a leadingedge embedded cross-flow fan. Proc. of the 2018 AIAA Aerospace Sciences Meeting, 2018. https://doi.org/10.2514/6.2018-1744

25. Kulkarni A.R., La Rocca G., Veldhuis L.L.M., Eitelberg G. Sub-scale flight test model design: Developments, challenges and opportunities. Progress in Aerospace Sciences, 2022, vol. 130, pp. 100798. https:// doi.org/10.1016/j.paerosci.2021.100798

26. Perry A.T., Ansell P.J., Kerho M., Ananda G., D’Urso S. Design, analysis, and evaluation of a propulsive wing concept. Proc. of the 34th AIAA Applied Aerodynamics Conference, 2016. https://doi.org/10.2514/6.2016-4178

27. Prodan N.V., Kurnukhin A.A. Application of mathematical optimization methods for designing airfoil considering viscosity. Russian Aeronautics, 2021, vol. 64, no. 4, pp. 670–677. https://doi. org/10.3103/S1068799821040115

28. Kramer B., Ansell Ph., D’Urso S., Ananda G., Perry A. Design, Analysis, and Evaluation of a Novel Propulsive Wing Concept. LEARN Phase I. Final Report. Contract Number NNX15AE39A. June 30th, 2016, 80 p.

29. Bulat P.V., Prodan N.V., Kurnukhin A.A. On the influence of the laminar-turbulent transition in the numerical modeling of the wing airfoil. Russian Aeronautics, 2021, vol. 64, no. 3, pp. 455–465. https:// doi.org/10.3103/S1068799821030120

30. Abzalilov D.F., Mardanov R.F. Calculation and optimization of aerodynamic characteristics of airfoils with jet blowing in the presence of vortex in the flow. Russian Aeronautics, 2016, vol. 59, no. 3, pp. 358–363. https://doi.org/10.3103/S1068799816030107

31. Drela M. XFOIL: An analysis and design system for low Reynolds number airfoils. Lecture Notes in Engineering, 1989, vol. 54, pp. 1–12. https://doi.org/10.1007/978-3-642-84010-4_1

32. Langtry R.B., Menter F.R. Transition modeling for general CFD applications in aeronautics. Proc. of the 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005. https://doi.org/10.2514/6.2005-522

33. Malan P., Suluksna K., Juntasaro E. Calibrating the γ-Reθ transition model for commercial CFD. Proc. of the 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, 2009. https://doi.org/10.2514/6.2009-1142

34. Liu K., Wang Y., Song W.-P., Han Z.-H. A two-equation localcorrelation-based laminar-turbulent transition modeling scheme for external aerodynamics. Aerospace Science and Technology, 2020, vol. 106, pp. 106128. https://doi.org/10.1016/j.ast.2020.106128

35. Solomatin R.S., Semenov I.V., Men’shov I.S. Towards calculating turbulent flows with the Spalart-Allmaras model by using the LUSGS-GMRES algorithm. Keldysh Institute Preprints, 2018, no. 119, pp. 1–30. (in Russian)

36. Dudnikov S.Y., Kuznetsov P.N., Mel’nikova A.I., Vokin L.O. Simulation of flows at low Reynolds numbers as applied to the design of aerodynamic surfaces for unmanned aerial vehicles. Russian Aeronautics, 2021, vol. 64, no. 4, pp. 620–629. https://doi.org/10.3103/S1068799821040061

37. Bulat P.V., Prodan N.V., Dudnikov S.YU., Kurnukhin A.A. Investigation of the characteristics of airfoils with air suction from the upper surface and a given pressure distribution. Izvestiya vysshikh uchebnykh zavedenii, 2022, no. 3. (in Russian)