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Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

D. De Grazia1,*, D. Moxey2, S. J. Sherwin1, M. A. Kravtsova3, and A. I. Ruban3

  • 1Department of Aeronautics, Imperial College London, London SW7 2AZ, United Kingdom
  • 2College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, United Kingdom
  • 3Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom

  • *d.de-grazia12@imperial.ac.uk
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Phys. Rev. Fluids 3, 024101 – Published 8 February, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.024101

Abstract

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

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References (46)

  1. L. Prandtl, Über Flüssigkeitsbewegung bei sehr kleiner Reibung, Verh. III, Intern. Math. Kongr. Heidelberg, Auch: Gesammelte Abhandlungen 2, 484 (1904).
  2. V. Y. Neiland, Theory of separation of a laminar boundary layer in a supersonic stream, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 4, 53 (1969).
  3. K. Stewartson and P. G. Williams, Self-induced separation, Proc. R. Soc. London Ser. A 312, 181 (1969).
  4. K. Stewartson, On the flow near the trailing edge of a flat plate II, Mathematika 16, 106 (1969).
  5. A. F. Messiter, Boundary-layer flow near the trailing edge of a flat plate, SIAM J. Appl. Math. 18, 241 (1970).
  6. V. V. Sychev, A. I. Ruban, and G. L. Korolev, Asymptotic Theory of Separated Flows (Cambridge University Press, Cambridge, 1998).
  7. F. T. Smith, R. I. Sykes, and P. W. Brighton, A two-dimensional boundary layer encountering a three-dimensional hump, J. Fluid Mech. 83, 163 (1977).
  8. R. I. Sykes, Stratification effects in boundary layer flows over hills, Proc. R. Soc. London Ser. A 361, 225 (1978).
  9. F. T. Smith, Pipeflows distorted by non-symmetric indentation or branching, Mathematika 23, 62 (1976).
  10. F. Smith, A three-dimensional boundary layer separation, J. Fluid Mech. 99, 185 (1980).
  11. R. I. Sykes, On three-dimensional boundary layer flows over surface irregularities, Proc. R. Soc. London Ser. A 373, 311 (1980).
  12. V. V. Bogolepov and V. Y. Neiland, Supersonic flow over a surface with local distortions, TsAGI Trans. 1363, 1 (1971).
  13. V. V. Bogolepov and V. Y. Neiland, Locally three-dimensional boundary flows, Tekh. Fiz. 1, 28 (1985).
  14. G. L. Korolev, Method for solving the equations describing the interaction of a three-dimensional boundary layer with an outer inviscid flow, Comput. Math. Math. Phys. 47, 487 (2007).
  15. M. E. Goldstein, A. Sescu, P. W. Duck, and M. Choudhari, The long range persistence of wakes behind arrow of roughness elements, J. Fluid Mech. 644, 123 (2010).
  16. M. E. Goldstein, A. Sescu, P. W. Duck, and M. Choudhari, Algebraic/transcendental disturbance growth behind a row of roughness elements, J. Fluid Mech. 668, 236 (2011).
  17. A. I. Ruban and M. A. Kravtsova, Generation of steady longitudinal vortices in hypersonic boundary layer, J. Fluid Mech. 729, 702 (2013).
  18. O. Marxen and G. Iaccarino, Numerical simulation of the effect of a roughness element on high-speed boundary-layer instability, Proceedings of the 38th Fluid Dynamics Conference (AIAA, Seattle, 2008), AIAA paper 2008-4400.
  19. G. Groskopf, M. J. Kloker, and O. Marxen, Bi-Global Secondary Stability Theory for High-Speed Boundary-Layer Flows, Center for Turbulence Research, Proceedings of the Summer Program (Stanford University, Stanford, 2008).
  20. M. Choudhari, F. Li, M. Wu, C. L. Chang, J. Edwards, M. Kegerise, and R. King, Laminar-turbulent transition behind discrete roughness elements in a high-speed boundary layer, Proceedings of the 48th AIAA Aerospace Sciences Meeting (AIAA, Orlando, 2010), AIAA Paper 2010-1575.
  21. M. Choudhari, A. Norris, F. Li, C. L. Chang, and J. Edwards, Wake instabilities behind discrete roughness elements in high speed boundary layers, Proceedings of the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition (AIAA, Texas, 2013), AIAA Paper 2013-0081.
  22. J. A. Redford, N. D. Sandham, and G. T. Roberts, Compressibility effects on boundary-layer transition induced by an isolated roughness element, AIAA J. 48, 2018 (2010).
  23. M. Bernardini, S. Pirozzoli, and P. Orlandi, Compressibility effects on roughness-induced boundary layer transition, Int. J. Heat Fluid Flow 35, 45 (2012).
  24. M. Bernardini, S. Pirozzoli, P. Orlandi, and S. K. Lele, Parameterisation of boundary-layer transition induced by isolated roughness elements, AIAA J. 52, 2261 (2014).
  25. N. De Tullio and N. D. Sandham, Direct numerical simulations of roughness receptivity and transitional shock-wave/boundary-layer interactions, NATO Report No. RTO-MP-AVT-200, 2012 (unpublished).
  26. N. De Tullio and N. D. Sandham, Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer, J. Fluid Mech. 763, 136 (2015).
  27. N. De Tullio, P. Paredes, N. D. Sandham, and V. Theofilis, Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer, J. Fluid Mech. 735, 613 (2013).
  28. J. Van den Eynde, Stability and transition of the flow behind isolated roughness elements in hypersonic boundary layers, Ph.D. thesis, University of Southampton, 2015.
  29. S. P. Schneider, Effects of roughness on hypersonic boundary-layer transition, J. Spacecr. Rockets 45, 193 (2008).
  30. B. M. Wheaton, M. D. Bartkovicz, P. K. Subbareddy, S. P. Schneider, and G. V. Candler, Proceedings of the 41st AIAA Fluid Dynamics Conference and Exhibit (AIAA, Reston, 2011), paper 2011-3248.
  31. G. Mengaldo, M. Kravtsova, A. I. Ruban, and S. J. Sherwin, Triple-deck and direct numerical simulation analyses of high-speed subsonic flow over a roughness element, J. Fluid Mech. 774, 311 (2015).
  32. G. Mengaldo, Discontinuous spectral/hp element methods: development, analysis and applications to compressible flows, Ph.D. thesis, Imperial College London, 2015.
  33. C. D. Cantwell, D. Moxey, A. Comerford, A. Bolis, G. Rocco, G. Mengaldo, D. De Grazia, S. Yakolev, J.-E. Lombard, D. Ekelshot et al., Nektar++: An open-source spectral/hp element framework, Comput. Phys. Commun. 192, 205 (2015).
  34. D. De Grazia, High order spectral/hp element methods for compressible boundary layers on hexahedral grids, Ph.D. thesis, Imperial College London, 2016.
  35. D. A. Kopriva, S. L. Woodruff, and M. Y. Hussaini, Discontinuous spectral element approximation of maxwells equations, in Discontinuous Galerkin Methods, edited by B. Cockburn, G. E. Karniadakis, and C.-W. Shu, Lecture Notes in Computational Sciences and Engineering, Vol. 11 (Springer, Berlin, 2000).
  36. D. A. Kopriva and G. Gassner, On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods, J. Sci. Comput. 44, 136 (2010).
  37. J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods—Algorithms, Analysis, and Applications (Springer, Berlin, 2008).
  38. E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd ed. (Springer, Berlin, 2009).
  39. G. Mengaldo, D. De Grazia, J. Peiro, A. Farrington, F. Witherden, P. E. Vincent, and S. J. Sherwin, Proceedings of the 7th AIAA Theoretical Fluid Mechanics Conference (AIAA, Reston, 2014).
  40. B. Cockburn and C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM J. Numer. Anal. 35, 2440 (1998).
  41. D. Moxey, M. Hazan, S. J. Sherwin, and J. Peiro, An isoparametric approach to high-order curvilinear boundary-layer meshing, Comput. Methods Appl. Mech. Eng. 283, 636 (2015).
  42. G. Mengaldo, D. De Grazia, D. Moxey, P. E. Vincent, and S. J. Sherwin, Dealiasing techniques for high-order spectral element methods on regular and irregular grids, J. Comput. Phys. 299, 56 (2015).
  43. F. M. White, Viscous Fluid Flow, 3rd ed. (McGraw-Hill, New York, 2006).
  44. B. Wasistho, Spatial direct numerical simulation of compressible boundary layer flow, Ph.D. thesis, University of Twente, 1997.
  45. G. L. Korolev, J. S. B. Gajjar, and A. I Ruban, Once again on the supersonic flow separation near a corner, J. Fluid Mech. 463, 173 (2002).
  46. P. J. Mason and B. R. Morton, Trailing vortices in the wakes of surface-mounted obstacles, J. Comput. Phys. 175, 247 (1987).

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Phys. Rev. Fluids 3, 024101– Published 8 February, 2018
  • Received 15 June 2016
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