Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T22:25:02.906Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition induced by an egg-crate roughness on a flat plate in supersonic flow

Published online by Cambridge University Press:  09 September 2022

Amanda Chou Open the ORCID record for Amanda Chou [Opens in a new window] ,
Pedro Paredes Open the ORCID record for Pedro Paredes [Opens in a new window] ,
Michael A. Kegerise ,
Rudolph A. King Open the ORCID record for Rudolph A. King [Opens in a new window] ,
Meelan Choudhari Open the ORCID record for Meelan Choudhari [Opens in a new window]  and
Fei Li
Amanda Chou*
Affiliation:
Flow Physics and Control Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Pedro Paredes
Affiliation:
National Institute of Aerospace, Hampton, VA 23666, USA Computational Aerosciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Michael A. Kegerise
Affiliation:
Flow Physics and Control Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Rudolph A. King
Affiliation:
Flow Physics and Control Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Meelan Choudhari
Affiliation:
Computational Aerosciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
Fei Li
Affiliation:
Computational Aerosciences Branch, NASA Langley Research Center, Hampton, VA 23681, USA
*
†Email address for correspondence: amanda.chou@nasa.gov
Get access Rights & Permissions [Opens in a new window]

Abstract

Hot-wire measurements in a Mach 3.5 quiet tunnel were made in the wake of a roughness patch on a flat plate. These measurements were used to determine mode shapes and frequencies of the dominant instabilities leading to boundary-layer transition. The egg-crate roughness pattern is an analytic function described by a sinusoidal equation, similar to an array of discrete elements that are positioned in a spanwise and streamwise grid, but containing both protuberances and dimples. This is an intermediate configuration towards understanding the underlying physics of a pseudorandom distributed roughness, and ultimately, the underlying physics of roughness-induced boundary-layer transition. The roughness pattern had a wavelength of 6.25 mm, with a nominal amplitude of 272 ${\rm \mu}{\rm m}$ (0.49 times the boundary layer thickness at the first row of protuberances). The roughness was positioned near the leading edge of the flat plate and contained 3.5 wavelengths in the streamwise direction and 7.5 wavelengths in the spanwise direction. The dominant instability was centred near 74 kHz at a free stream unit Reynolds number of $12.9\times 10^{6}\,{\rm m}^{-1}$ and resembled an antisymmetric mode downstream of each of the protuberances in the roughness patch. Computations using linear stability analysis based on the plane-marching parabolized stability equations (PSE) showed limited agreement with measurements when comparing the growth of the wake instability. Better agreement with the measurements was observed when considering the modification of first mode waves by the egg-crate roughness patch and the solution of the three-dimensional harmonic linearized Navier–Stokes equations was used as the in-flow to the PSE. The agreement confirms the significance of disturbance growth both upstream of and above a finite length roughness patch and the effect on the growth of instabilities in the wake.

JFM classification

Compressible Flows: Compressible boundary layers Instability: Transition to turbulence Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 948 , 10 October 2022 , A27
Check for updates
Creative Commons
To the extent this is a work of the US Government, it is not subject to copyright protection within the United States. Published by Cambridge University Press
Copyright
© National Aeronautics and Space Administration, 2022.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

van Albada, G.D., van Leer, B. & Robers, W.W. 1982 A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108, 76–84.Google Scholar
Balakumar, P. & Kegerise, M.A. 2016 Roughness-induced transition in a supersonic boundary layer. AIAA J. 54 (8), 2322–2337.CrossRefGoogle Scholar
Baurle, R.A., White, J.A., Drozda, T.G. & Norris, A.T. 2020 VULCAN-CFD user manual: Ver. 7.1.0. NASA Tech. Memo. TM-2020-5000767.Google Scholar
Beckwith, I.E., Creel, T.R. Jr, Chen, F.-J. & Kendall, J.M. 1983 Free stream noise and transition measurementes in a Mach 3.5 pilot quiet tunnel. In 21st AIAA Aerospace Sciences Meeting. AIAA Paper 1983-42.CrossRefGoogle Scholar
Berry, S.A. & Horvath, T.J. 2008 Discrete-roughness transition for hypersonic flight vehicles. J. Spacecr. Rockets 45 (2), 216–227.CrossRefGoogle Scholar
Carmichael, B.H. 1958 Critical Reynolds numbers for multiple three dimensional roughness elements. Report number NAI-58-589 (BLC-112). Northrop Aircraft, Inc., Hawthorne, CA, USA.Google Scholar
Carpenter, M., Choudhari, M., Li, F., Streett, C. & Chang, C.-L. 2010 Excitation of crossflow instabilities in a swept wing boundary layer. In 48th AIAA Aerospace Sciences Meeting. AIAA Paper 2010-378.CrossRefGoogle Scholar
Chen, F.J., Malik, M.R. & Beckwith, I.E. 1989 Boundary-layer transition on a cone and flat plate at Mach 3.5. AIAA J. 27 (6), 687–693.CrossRefGoogle Scholar
Chou, A., Kegerise, M.A. & King, R.A. 2020 a Transition induced by an egg-crate roughness on a flat plate in supersonic flow. In AIAA Aviation 2020 Forum. AIAA Paper 2020-3045.CrossRefGoogle Scholar
Chou, A., Kegerise, M.A. & King, R.A. 2020 b Transition induced by streamwise arrays of roughness elements on a flat plate in Mach 3.5 flow. J. Fluid Mech. 888, A21.CrossRefGoogle ScholarPubMed
Choudhari, M., Li, F., Chang, C.-L., Norris, A. & Edwards, J. 2013 Wake instabilities behind discrete roughness elements in high speed boundary layers. In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. AIAA Paper 2013-0081.CrossRefGoogle Scholar
Choudhari, M., Li, F. & Edwards, J. 2009 Stability analysis of roughness array wake in a high-speed boundary layer. In 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA Paper 2009-170.CrossRefGoogle Scholar
Choudhari, M., Li, F. & Paredes, P. 2018 Effect of distributed patch of smooth roughness elements on transition in a high-speed boundary layer. AIAA Paper 2018-3532.CrossRefGoogle Scholar
Choudhari, M., Li, F., Paredes, P. & Duan, L. 2019 Effect of 3D roughness patch on instability amplification in a supersonic boundary layer. In AIAA Scitech 2019 Forum. AIAA Paper 2019-0877.CrossRefGoogle Scholar
Choudhari, M., Li, F., Wu, M., Chang, C.-L., Edwards, J., Kegerise, M. & King, R. 2010 Laminar-turbulent transition behind discrete roughness elements in a high-speed boundary layer. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA Paper 2010-1575.CrossRefGoogle Scholar
De Tullio, N., Paredes, P., Sandham, N.D. & Theofilis, V. 2013 Laminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layer. J. Fluid Mech. 735, 613–646.CrossRefGoogle Scholar
De Tullio, N. & Sandham, N.D. 2015 Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer. J. Fluid Mech. 763, 136–165.CrossRefGoogle Scholar
Downs, R.S., White, E.B. & Denissen, N.A. 2008 Transient growth and transition induced by random distributed roughness. AIAA J. 46 (2), 451–462.CrossRefGoogle Scholar
Drews, S.D., Downs III, R.S., Doolittle, C.J., Goldstein, D.B. & White, E.B. 2011 Direct numerical simulations of flow past random distributed roughness. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. AIAA Paper 2011-564.CrossRefGoogle Scholar
Edwards, J.R. 1997 A low-diffusion flux-splitting scheme for Navier–Stokes calculations. Comput. Fluids 26 (6), 635–659.CrossRefGoogle Scholar
Hermanns, M. & Hernández, J.A. 2008 Stable high-order finite-difference methods based on non-uniform grid point distributions. Intl J. Numer. Meth. Fluids 56, 233–255.CrossRefGoogle Scholar
Jiang, G.S. & Shu, C.W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202–228.CrossRefGoogle Scholar
Kegerise, M.A., King, R.A., Choudhari, M., Li, F. & Norris, A. 2014 An experimental study of roughness-induced instabilities in a supersonic boundary layer. In 7th AIAA Theoretical Fluid Mechanics Conference. AIAA Paper 2014-2501.CrossRefGoogle Scholar
Kegerise, M.A., King, R.A., Owens, L.R., Choudhari, M., Norris, A., Li, F. & Chang, C.-L. 2012 An experimental and numerical study of roughness-induced instabilities in a Mach 3.5 boundary layer. In RTO-AVT-200/RSM-030, pp. 1–14. NATO RTO.Google Scholar
Kegerise, M.A., Owens, L.R. & King, R.A. 2010 High-speed boundary-layer transition induced by an isolated roughness element. In 40th Fluid Dynamics Conference and Exhibit. AIAA Paper 2010-4999.CrossRefGoogle Scholar
Kim, Y.C. & Powers, E.J. 1979 Digital bispectral analysis and its applications to nonlinear wave interactions. IEEE Trans. Plasma Sci. PS-7 (2), 120–131.CrossRefGoogle Scholar
King, R.A., Kegerise, M.A. & Berry, S.A. 2009 Version 2 of the protuberance correlations for the shuttle-orbiter boundary layer transition tool. NASA Tech. Paper TP-2009-215951.Google Scholar
Kuester, M.S., White, E.B., Sharma, A., Goldstein, D.B. & Brown, G. 2014 Distributed roughness shielding in a blasius boundary layer. In 44th AIAA Fluid Dynamics Conference. AIAA Paper 2014-2888.CrossRefGoogle Scholar
Muppidi, S. & Mahesh, K. 2012 Direct numerical simulations of roughness-induced transition in supersonic boundary layers. J. Fluid Mech. 693, 28–56.CrossRefGoogle Scholar
Padilla Montero, I. & Pinna, F. 2021 Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer. J. Fluid Mech. 915, A90.CrossRefGoogle Scholar
Paredes, P., Choudhari, M. & Li, F. 2017 Instability wave-streak interactions in a supersonic boundary layer. J. Fluid Mech. 831, 524–553.CrossRefGoogle Scholar
Paredes, P., Choudhari, M., Li, F., Jewell, J., Kimmel, R., Marineau, E. & Grossir, G. 2019 Nosetip bluntness effects on transition at hypersonic speeds: experimental and numerical analysis. J. Spacecr. Rockets 56 (2), 369–387.CrossRefGoogle Scholar
Paredes, P., Hermanns, M., Le Clainche, S. & Theofilis, V. 2013 Order $10^{4}$ speedup in global linear instability analysis using matrix formation. Comput. Meth. Appl. Mech. Engng 253, 287–304.CrossRefGoogle Scholar
Reda, D.C. 2002 Review and synthesis of roughness-dominated transition correlations for reentry applications. J. Spacecr. Rockets 39 (2), 161–167.CrossRefGoogle Scholar
Saric, W.S., Reed, H.L. & White, E.B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.CrossRefGoogle Scholar
Schneider, S.P. 2008 Effects of roughness on hypersonic boundary-layer transition. J. Spacecr. Rockets 45 (2), 193–209.CrossRefGoogle Scholar
Sharma, A., Drews, S.D., Kuester, M., Goldstein, D.B. & White, E.B. 2014 Evolution of disturbances due to discrete and distributed surface roughness in initially laminar boundary layers. In 52nd Aerospace Sciences Meeting. AIAA Paper 2014-0235.CrossRefGoogle Scholar
Suryanarayanan, S., Goldstein, D.B., Brown, G.L., Berger, A.R. & White, E.B. 2017 On the mechanics and control of boundary layer transition induced by discrete roughness elements. In 55th AIAA Aerospace Sciences Meeting. AIAA Paper 2017-307.CrossRefGoogle Scholar
Wheaton, B.M. & Schneider, S.P. 2012 Roughness-induced instability in a hypersonic laminar boundary layer. AIAA J. 50 (6), 1245–1256.CrossRefGoogle Scholar
Wheaton, B.M. & Schneider, S.P. 2014 Hypersonic boundary-layer instabilities due to near-critical roughness. J. Spacecr. Rockets 51 (1), 327–342.CrossRefGoogle Scholar
Williamson, J. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 48–56.CrossRefGoogle Scholar
Wu, M. & Martin, M.P. 2007 Direct numerical simulation of supersonic boundary layer over a compression ramp. AIAA J. 45 (4), 879–889.CrossRefGoogle Scholar