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Direct numerical simulation of high-speed transition due to roughness elements

Published online by Cambridge University Press:  17 April 2019

Prakash Shrestha Open the ORCID record for Prakash Shrestha [Opens in a new window]  and
Graham V. Candler
Prakash Shrestha*
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street SE, MN 55455, USA
Graham V. Candler
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street SE, MN 55455, USA
*
†Email address for correspondence: shres048@umn.edu
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Abstract

We study and compare instability mechanisms of a Mach 5.65 laminar boundary layer tripped by an isolated diamond-shaped trip and by an array of diamond-shaped trips using direct numerical simulations. A low-Reynolds-number experiment, consisting of the trip array (Semper & Bowersox, AIAA J., vol. 55 (3), 2017, pp. 808–817), is used to validate our simulations. Three dynamically prominent flow structures are observed in both trip configurations. These flow structures are the upstream vortex system, the shock system, and the downstream shear layers/counter-rotating streamwise vortices that originate from the top and sides of the trips. Analysis of the power spectral density of pressure reveals the source of instability to be an interaction between the shear layers and the counter-rotating streamwise vortices downstream of both trip configurations. The interaction leads to the formation of hairpin-like structures that eventually break down to turbulent flow. This finding contrasts with that of an isolated cylindrical trip (Subbareddy et al., J. Fluid Mech., vol. 748, 2014, pp. 848–878) where the upstream vortex system is found to be the source of instability. Therefore, the shape of a trip plays an important role in the instability mechanism. Furthermore, dynamic mode decomposition (Rowley et al., J. Fluid Mech., vol. 641, 2009, pp. 115–127; Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28) of three-dimensional snapshots of pressure fluctuations unveil globally dominant modes consistent with the power spectral density analysis in both diamond-shaped trip configurations.

JFM classification

Boundary Layers: Boundary layer stability Compressible Flows: Compressible boundary layers Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , pp. 762 - 788
Copyright
© 2019 Cambridge University Press 

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References

Acarlar, M. S. & Smith, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.Google Scholar
Baker, C. J. 1979 The laminar horseshoe vortex. J. Fluid Mech. 95, 347–367.Google Scholar
Berry, S. A., Auslender, A. H., Dilley, A. D. & Calleja, J. F. 2001 Hypersonic boundary layer trip development for Hyper-X. J. Spacecr. Rockets 38 (6), 853–864.Google Scholar
Borg, M. P., Schneider, S. P. & Juliano, T. J. 2008 Effect of freestream noise on roughness-induced transition for the X-51A forebody. J. Spacecr. Rockets 45 (6), 1106–1116.Google Scholar
Boyd, S. & Vandenberghe, L. 2004 Convex Optimization. Cambridge University Press.Google Scholar
Brandt, L. 2014 The lift-up effect: the linear mechanism behind transition and turbulence in shear flows. Eur. J. Mech. (B/Fluids) 47, 80–96.Google Scholar
Candes, E. J., Wakin, M. B. & Boyd, S. P. 2008 Enhancing sparsity by reweighted l 1 minimization. J. Fourier Anal. Applics. 14, 877–905.Google Scholar
Candler, G. V., Johnson, H. B., Nompelis, I., Subbareddy, P. K., Drayna, T. W., Gidzak, V. & Barnhardt, M. D.2015 Development of the US3D code for advanced compressible and reacting flow simulations. AIAA Paper 2015-1893.Google Scholar
Choudhari, M., Li, F., Wu, M., Chang, C., Edwards, J., Kegerise, M. & King, R.2010 Laminar–turbulent transition behind discrete roughness elements in a high-speed boundary layer. AIAA Paper 2010-1575.Google Scholar
Chu, B.-T. 1965 On the energy transfer to small disturbances in fluid flow (part I). Acta Mechanica 1 (3), 215–234.Google Scholar
Danehy, P. M., Bathel, B., Ivey, C., Inman, J. A. & Jones, S. B.2009 NO PLIF study of hypersonic transition over a discrete hemispherical roughness element. AIAA Paper 2009-394.Google Scholar
Danehy, P. M., Ivey, C. B., Inman, J. A., Bathel, B. F., Jones, S. B., Jiang, N., Webster, M., Lempert, W., Miller, J. & Meyer, T.2010 High-speed PLIF imaging of hypersonic transition over discrete cylindrical roughness. AIAA Paper 2010-703.Google Scholar
Donoho, D. L. 2006 Compressed sensing. IEEE Trans. Inf. Theory 52 (4), 1289–1306.Google Scholar
Drayna, T. W., Haag, C. J. W., Bartkowicz, M. D. & Gidzak, V. M.(2016) LINK3D, Software Package, Ver 0.9.0, GoHypersonic, Inc., Minneapolis, MN.Google Scholar
van Driest, E. R. 1956 On turbulent flow near a wall. J. Aeronaut. Sci. 23 (11), 1007–1011.Google Scholar
van Driest, E. R. & Blumer, C. B. 1962 Boundary-layer transition at supersonic speeds – three-dimensional roughness effects (spheres). J. Aeronaut. Sci. 29 (8), 909–916.Google Scholar
Duan, Z. & Xiao, Z. 2017 Hypersonic transition induced by three isolated roughness elements on a flat plate. Comput. Fluids 157, 1–13.Google Scholar
Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T. 1999 Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152 (2), 517–549.Google Scholar
Ergin, F. G. & White, E. B. 2006 Unsteady and transitional flows behind roughness elements. AIAA J. 40 (11), 2504–2514.Google Scholar
Hanifi, A., Schmid, P. J. & Henningson, D. S. 1996 Transient growth in compressible boundary layer flow. Phys. Fluids. 8 (3), 826–837.Google Scholar
Harris, F. J. 1978 On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66 (1), 53–83.Google Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88, Center for Turbulence Research, Stanford University.Google Scholar
Iyer, P. S. & Mahesh, K. 2013 High-speed boundary-layer transition induced by a discrete roughness element. J. Fluid Mech. 729, 524–562.Google Scholar
Jovanović, M. R., Schmid, P. J. & Nichols, J. W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 024103.Google Scholar
Klebanoff, P. S., Cleveland, W. G. & Tidstrom, K. D. 1992 On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element. J. Fluid Mech. 237, 101–187.Google Scholar
Klebanoff, P. S. & Tidstrom, K. D. 1972 Mechanism by which a two-dimensional roughness element induces boundary layer transition. Phys. Fluids 15 (7), 1173–1188.Google Scholar
Laufer, J. 2012 Aerodynamics noise in supersonic wind tunnels. J. Aerosp. Sci. 28 (9), 685–692.Google Scholar
Muppidi, S. & Mahesh, K. 2012 Direct numerical simulations of roughness-induced transition in supersonic boundary layers. J. Fluid Mech. 693, 28–56.Google Scholar
Nichols, J. W., Larsson, J. & Bernardini, M. 2017 Stability and modal analysis of shock/boundary layer interactions. Theor. Comput. Fluid Dyn. 31, 33–50.Google Scholar
Redford, J. A., Sandham, N. D. & Roberts, G. T. 2010 Compressibility effects on boundary-layer transition induced by an isolated roughness element. AIAA J. 48 (12), 2818–2830.Google Scholar
Rowley, C. W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.Google Scholar
Sayadi, T. & Schmid, P. J. 2016 Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers. Theor. Comput. Fluid Dyn. 30, 415–428.Google Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.Google Scholar
Schneider, S. P. 2008 Effects of roughness on hypersonic boundary-layer transition. J. Spacecr. Rockets 45 (2), 193–209.Google Scholar
Semper, M. T. & Bowersox, R. D. W. 2017 Tripping of a hypersonic low-Reynolds-number boundary layer. AIAA J. 55 (3), 808–817.Google Scholar
Shrestha, P. & Candler, G. V.2016a Direct numerical simulation of trip induced transition. AIAA Paper 2016-4380.Google Scholar
Shrestha, P. & Candler, G. V.2016b Study of transition mechanisms induced by an array of roughness elements. APS Meeting Abstracts.Google Scholar
Shrestha, P. & Candler, G. V.2018a Numerical study of trip spacing in hypersonic boundary layer transition. AIAA Paper 2018-1098.Google Scholar
Shrestha, P. & Candler, G. V.2018b Effects of freestream Reynolds number and trip height on high-speed transition. AIAA Paper 2018-3533.Google Scholar
Shrestha, P., Nichols, J. W., Jovanović, M. R. & Candler, G. V.2017 Study of trip-induced hypersonic boundary layer transition. AIAA Paper 2017-4513.Google Scholar
Subbareddy, P. K., Bartkowicz, M. D. & Candler, G. V. 2014 Direct numerical simulation of high-speed transition due to an isolated roughness element. J. Fluid Mech. 748, 848–878.Google Scholar
Subbareddy, P. K. & Candler, G. V. 2009 A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows. J. Comput. Phys. 228 (5), 1347–1364.Google Scholar
Tani, I. & Sato, H. 1956 Boundary-layer transition by roughness element. J. Phys. Soc. Japan 11 (12), 1284–1291.Google Scholar
Tullio, N. D., Parades, 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.Google Scholar
Whitehead, A. H. Jr 1969 Flow-field and drag characteristics of several boundary layer tripping elements in hypersonic flow. NASA Tech. Rep. D-5454. NASA.Google Scholar
Williams, O. J. H. & Smits, A. J. 2017 Effect of tripping on hypersonic turbulent boundary-layer statistics. AIAA J. 55 (9), 3051–3058.Google Scholar
Wright, M. J., Candler, G. V. & Prampolini, M. 1996 Data parallel lower–upper relaxation method for the Navier–Stokes equations. AIAA J. 34 (7), 1371–1377.Google Scholar