Skip to main content

Advertisement

Log in

Computational aerodynamic optimization of wing-design concept at supersonic conditions by means of the response surface method

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

In this paper, by means of computational fluid dynamics, a significant study has been made on the effects of geometric parameters of wing with capability of flying efficiently and cost-effectively at supersonic condition. Multi-objective optimization has been performed for the aerodynamic shape optimization of the wing configuration. The three-dimensional wing shape defined by four design variables is optimized. For achieving the most desirable aerodynamic efficiency (lift-to-drag ratio), Response Surface Method and Genetic Algorithm is utilized. To ensure the reliability of the solution and validating the numerical evaluation, flow around a delta wing is simulated and results are compared with credible numerical works. Furthermore, the particular design variables, which have serious effects on the objective functions, are found. Wing sweep angle along with aspect ratio has strong effects on the main outputs. Given that the current flow regime is supersonic, counteracting the negative effects of shock waves is one the most important design points. Among the studied parameters, leading edge sweep angle has the greatest impact on the main objectives of this research and it is the primary factor for delaying the formation of shock waves over the wing surface. Lift and drag coefficients, as primary objective functions, have higher sensitivity to changes in aspect ratio. By comparison to best geometry among initial cases, aerodynamic efficiency is increased by approximately 15% as a result of optimization study of this supersonic wing geometry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27

Similar content being viewed by others

References

  1. Anderson JD (1997) A history of aerodynamics and its impact on flying machines. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  2. Secanell M, Suleman A, Gamboa P (2006) Design of a morphing airfoil using aerodynamic shape optimization. AIAA J 44:1550–1562. https://doi.org/10.2514/1.18109

    Article  Google Scholar 

  3. Lock RC, Bridgewater J (1967) Theory of aerodynamic design for swept-winged aircraft at transonic and supersonic speeds. Prog Aerosp Sci 8:139–228. https://doi.org/10.1016/0376-0421(67)90004-8

    Article  MATH  Google Scholar 

  4. Sadraey M (2012) Aircraft design: a systems engineering approach. Wiley, Amsterdam

    Book  Google Scholar 

  5. Talay TA (2012) Introduction to the aerodynamics of flight. NASA, New York

    Google Scholar 

  6. Yoshida K (2009) Supersonic drag reduction technology in the scaled supersonic experimental airplane project by JAXA. Prog Aerosp Sci 45:124–146. https://doi.org/10.1016/j.paerosci.2009.05.002

    Article  Google Scholar 

  7. Yuhara T, Rinoie K, Makino Y (2014) Conceptual design study on LH2 fueled supersonic transport considering performance and environmental impacts. AIAA SciTech Forum. https://doi.org/10.2514/6.2014-0028

    Google Scholar 

  8. Hitchens F (2015) The encyclopedia of aerodynamics. Andrews UK Limited, London

    Google Scholar 

  9. Ueda Y, Yoshida K, Matsushima K, Ishikawa H (2014) Supersonic natural-laminar-flow wing-design concept at high-reynolds-number conditions. AIAA J 52:1294–1306. https://doi.org/10.2514/1.J052555

    Article  Google Scholar 

  10. Fu Z, Bai J, Liu N, Zhang Y, Xu J (2017) Planform parameter study and wing twist distribution optimization of a supersonic transport configuration. AIAA Meeting Papers. https://doi.org/10.2514/6.2017-2198

    Google Scholar 

  11. Li P, Sobieczky H, Seebass R (1995) A design method for supersonic transport wings. AIAA Meet Pap. https://doi.org/10.2514/6.1995-1819

    Google Scholar 

  12. Aerion Corporation Press Conference (2014) Aerion AS2 poised to become first supersonic business jet. http://www.aerionsupersonic.com/press-center/. Accessed 01 June 2017

  13. Elmer K, Welge H, Salamone J, Cowart R (2013) SCAMP: supersonic passenger transport transonic acceleration flight profiles with considerations of focused sonic boom. AIAA Meet Pap. https://doi.org/10.2514/6.2013-1065

    Google Scholar 

  14. Liebhardt B, Gollnick V, Luetjens K (2011) Estimation of the market potential for supersonic airliners via analysis of the global premium ticket market. AIAA ATIO Conf. https://doi.org/10.2514/6.2011-6806

    Google Scholar 

  15. Mavris DN, Hayden WT (1996) Formulation of an IPPD methodology for the design of a supersonic business jet. Georgia Institute of Technology. http://hdl.handle.net/1853/6329. Accessed 07 June 2017

  16. Chudoba B, Coleman G, Huang X, Huizenga A, Czysz P, Butler C (2006) A feasibility study of a supersonic business jet (SSBJ) based on the Learjet airframe. AIAA Meet Pap. https://doi.org/10.2514/6.2006-28

    Google Scholar 

  17. Sturdza P (2007) Extensive supersonic natural laminar flow on the Aerion business jet. AIAA Meeting Papers. https://doi.org/10.2514/6.2007-685

    Google Scholar 

  18. Kim Y, Jeon Y, Lee D (2006) Multi-objective and multidisciplinary design optimization of supersonic fighter wing. J Aircraft. https://doi.org/10.2514/1.13864

    Google Scholar 

  19. Reuther J, Alonso JJ, Rimlinger MJ, Jameson A (1999) Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers. J Comput Fluid 28:675–700. https://doi.org/10.2514/6.2002-2838

    Article  MATH  Google Scholar 

  20. Kiyici F, Aradag S (2015) Design and optimization of a supersonic business jet. AIAA AVIATION Forum. https://doi.org/10.2514/6.2015-3064

    Google Scholar 

  21. Parashar S, Bloebaum C (2006) Multi-objective genetic algorithm concurrent subspace optimization (MOGACSSO) for multidisciplinary design. AIAA Meet Pap. https://doi.org/10.2514/6.2006-2047

    Google Scholar 

  22. Kenway GKW, Martins JRRA (2015) Multipoint aerodynamic shape optimization investigations of the common research model wing. AIAA J 10(2514/1):J054154

    Google Scholar 

  23. Lyu Z, Xu Z, Martins J R R A (2014) Benchmarking optimization algorithms for wing aerodynamic design optimization. In: the 8th International conference on computational fluid dynamics (ICCFD8). Chengdu, Sichuan

  24. Holland J (1992) Adaption in natural and artificial systems. MIT Press, Cambridge

    Google Scholar 

  25. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Wesley Longman Publishing, Boston

    MATH  Google Scholar 

  26. Sforza P (2014) Commercial airplane design principles, 1st edn. Butterworth-Heinemann, Oxford, pp 119–212

    Book  Google Scholar 

  27. Wu Z, Zhang Q, Bao T, Li L, Deng J, Hu Z (2016) Experimental and numerical study on ethanol and dimethyl ether lifted flames in a hot vitiated co-flow. J Fuel 184:620–628. https://doi.org/10.1016/j.fuel.2016.07.064

    Article  Google Scholar 

  28. Spalart P, Allmaras S (1992) A one-equation turbulence model for aerodynamic flows. AIAA Meet Pap. https://doi.org/10.2514/6.1992-439

    Google Scholar 

  29. Dehghan Manshadi M, Jamalinasab M (2016) Optimizing a two-element wing model with morphing flap by means of the Response Surface Method. Iran J Sci Technol Trans Mech Eng. https://doi.org/10.1007/s40997-016-0067-8

    Google Scholar 

  30. Catalano P, Amato M (2003) An evaluation of RANS turbulence modelling for aerodynamic applications. J Aerosp Sci Technol 7:493–509. https://doi.org/10.1016/S1270-9638(03)00061-0

    Article  MATH  Google Scholar 

  31. Weiss JM, Maruszewski JP, Smith WA (1997) Implicit solution of the Navier–Stokes equations on unstructured meshes. AIAA Meet Pap. https://doi.org/10.2514/6.1997-2103

    Google Scholar 

  32. Kalitzin G, Medic G, Laccarino G, Durbin P (2005) Near-wall behavior of RANS turbulence models and implications for wall functions. J Comput Phys 204:265–291. https://doi.org/10.1016/j.jcp.2004.10.018

    Article  MATH  Google Scholar 

  33. Oyama A, Imai G, Ogawa A, Fujii K (2008) Aerodynamic characteristics of a delta wing at high angles of attack. AIAA Meet Pap. https://doi.org/10.2514/6.2008-2563

    Google Scholar 

  34. Ma D, Zhao Y, Qiao Y, Li G (2015) Effects of relative thickness on aerodynamic characteristics of airfoil at a low Reynolds number. Chin J Aeronaut 28:1003–1015. https://doi.org/10.1016/j.cja.2015.05.012

    Article  Google Scholar 

  35. Roelof V, Farokhi S (2015) Introduction to transonic aerodynamics. Springer, New York

    MATH  Google Scholar 

  36. Dehghan Manshadi M, Rabani R (2016) Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall. Acta Mech Sin 32:792. https://doi.org/10.1007/s10409-016-0586-y

    Article  Google Scholar 

  37. Sartor F, Timme S (2015) Reynolds averaged Navier–Stokes simulations of shock buffet on half wing body configuration. AIAA SciTech Forum. https://doi.org/10.2514/6.2015-1939

    Google Scholar 

  38. Monotgormery D (2008) Design and analysis of experimental. Wiley, Amsterdam

    Google Scholar 

  39. Reh S, Beley J, Mukherjee S, Khor EH (2006) Probabilistic finite element analysis using ANSYS. J Struct Safe 28:17–43. https://doi.org/10.1016/j.strusafe.2005.03.010

    Article  Google Scholar 

  40. Myers RH, Montgomery DC, Anderson-Cook CM (2009) Response surface methodology: process and product optimization using designed experiments. Wiley, Amsterdam

    MATH  Google Scholar 

  41. Taguchi G (1986) Introduction to quality engineering: designing quality into products and processes. 1st edn, Quality Resources

  42. Plackett RL, Burman JP (1946) The design of optimum multifactorial experiments, 1st edn. Oxford University Press, Biometrika

    MATH  Google Scholar 

  43. Chiba K, Makino Y, Takatoya T (2007) Multidisciplinary design exploration of wing shape for Silent supersonic technology demonstrator. AIAA Meet Pap. https://doi.org/10.2514/6.2007-4167

    Google Scholar 

  44. ANSYS® Academic Research, Release 16.0, Help System, Workbench Guide, ANSYS®, Inc

  45. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197. https://doi.org/10.1109/4235.996017

    Article  Google Scholar 

  46. Lahuta M, Patek Z, Szollos A (2014) Computational aerodynamic optimization of low-speed wing. Acta Polytech 54:420–425. https://doi.org/10.14311/AP.2014.54.0420

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mojtaba Dehghan Manshadi.

Additional information

Technical Editor: Márcio Bacci da Silva.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manshadi, M.D., Aghajanian, S. Computational aerodynamic optimization of wing-design concept at supersonic conditions by means of the response surface method. J Braz. Soc. Mech. Sci. Eng. 40, 254 (2018). https://doi.org/10.1007/s40430-018-1150-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-018-1150-4

Keywords

Navigation