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Flat plate boundary layer accelerated by shock wave propagation

Published online by Cambridge University Press:  07 December 2022

Florian Hermet*
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
Nicolas Binder
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
Jérémie Gressier
Affiliation:
ISAE-SUPAERO, Université de Toulouse, 31400 Toulouse, France
*
Email address for correspondence: [email protected]

Abstract

The flat plate transitional boundary layer response to the acceleration induced by the shock wave propagation is studied using large-eddy simulations. The steady boundary layer global behaviour is first investigated before focusing on the transient response of a turbulent region following the shock wave propagation. It is shown that the transient response of the turbulent region exhibits strong similarities with the spatial transition process to turbulence induced by free-stream turbulence, the so-called bypass transition. The boundary layer does not evolve gradually from the initial turbulence intensity to the final turbulence intensity but undergoes a temporal transition process composed of three distinct phases. These three different phases are comparable with the three stages of a bypass transition (i.e. buffeted laminar flow, transition and fully turbulent) because they are governed by the same physical processes. On the other hand, it is highlighted that this temporal response is identical to that described by He & Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102) during the study of an incompressible boundary layer undergoing an increase of mass flow rate. The boundary layer compression by the shock propagation does not contribute to any significant change in the turbulence dynamic after an unsteady acceleration.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Andersson, P., Berggren, M. & Henningson, D.S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134150.CrossRefGoogle Scholar
Babinsky, H. & Harvey, J. (Ed.) 2011 Shock Wave–Boundary-Layer Interactions. Cambridge University Press.Google Scholar
Bermejo-Moreno, I., Campo, L., Larsson, J., Bodart, J., Helmer, D. & Eaton, J.K. 2014 Confinement effects in shock wave/turbulent boundary layer interactions through wall-modelled large-eddy simulations. J. Fluid Mech. 758, 562.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D.S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167198.Google Scholar
Brès, G.A., Ham, F.E., Nichols, J.W. & Lele, S.K. 2017 Unstructured large-eddy simulations of supersonic jets. AIAA J. 55 (4), 11641184.CrossRefGoogle Scholar
Cebeci, T. & Cousteix, J. 2005 Modeling and Computation of Boundary-Layer Flows: Laminar, Turbulent and Transitional Boundary Layers in Incompressible and Compressible Flows, 2nd edn. Horizons.Google Scholar
Fransson, J.H.M., Matsubara, M. & Alfredsson, P.H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 125.CrossRefGoogle Scholar
Guerrero, B., Lambert, M.F. & Chin, R.C. 2021 Transient dynamics of accelerating turbulent pipe flow. J. Fluid Mech. 917, A43.Google Scholar
Hack, M.J.P. & Zaki, T.A. 2014 Streak instabilities in boundary layers beneath free-stream turbulence. J. Fluid Mech. 741, 280315.CrossRefGoogle Scholar
He, S. & Jackson, J.D. 2000 A study of turbulence under conditions of transient flow in a pipe. J. Fluid Mech. 408, 138.Google Scholar
He, S. & Seddighi, M. 2013 Turbulence in transient channel flow. J. Fluid Mech. 715, 60102.CrossRefGoogle Scholar
He, S. & Seddighi, M. 2015 Transition of transient channel flow after a change in Reynolds number. J. Fluid Mech. 764, 395427.CrossRefGoogle Scholar
Heiser, W.H. & Pratt, D.T. 2002 Thermodynamic cycle analysis of pulse detonation engines. J. Propul. Power 18 (1), 6876.CrossRefGoogle Scholar
Jacobs, R.G. & Durbin, P.A. 1998 Shear sheltering and the continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10 (8), 20062011.CrossRefGoogle Scholar
Jacobs, R.G. & Durbin, P.A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185212.CrossRefGoogle Scholar
Jamme, S., Cazalbou, J.-B., Torres, F. & Chassaing, P. 2002 Direct numerical simulation of the interaction between a shock wave and various types of isotropic turbulence. Flow Turbul. Combust. 6 (3), 227268.CrossRefGoogle Scholar
Jung, S.Y. & Chung, Y.M. 2012 Large-eddy simulation of accelerated turbulent flow in a circular pipe. Intl J. Heat Fluid Flow 33 (1), 18.CrossRefGoogle Scholar
Jung, S.Y. & Kim, K. 2017 Transient behaviors of wall turbulence in temporally accelerating channel flows. Intl J. Heat Fluid Flow 67, 1326.CrossRefGoogle Scholar
Kendall, J. 1985 Experimental study of disturbances produced in a pre-transitional laminar boundary layer by weak freestream turbulence. AIAA Paper 1985-1695.Google Scholar
Klebanoff, P.S. 1971 Effect of free-stream turbulence on a laminar boundary layer. Bull. Am. Phys. Soc. 10, 1323.Google Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186 (2), 652665.CrossRefGoogle Scholar
Landahl, M.T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (02), 243.CrossRefGoogle Scholar
Larsson, J. & Lele, S. 2009 Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21, 126101.CrossRefGoogle Scholar
Launder, B.E. 1964 Laminarization of the turbulent boundary layer in a severe acceleration. Trans. ASME J. Appl. Mech. 31 (4), 707708.Google Scholar
Lee, B.H.K. 2001 Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37 (2), 147196.CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289309.CrossRefGoogle Scholar
Maruyama, T., Kuribayashi, T. & Mizushina, T. 1976 The structure of the turbulence in transient pipe flows. J. Chem. Engng Japan 9 (6), 431439.CrossRefGoogle Scholar
Mathur, A., Gorji, S., He, S., Seddighi, M., Vardy, A.E., O'Donoghue, T. & Pokrajac, D. 2018 Temporal acceleration of a turbulent channel flow. J. Fluid Mech. 835, 471490.Google Scholar
Matsubara, M. & Alfredsson, P.H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149168.CrossRefGoogle Scholar
Mayle, R.E. 1991 The role of laminar–turbulent transition in gas turbine engines. In Turbo Expo: Power for Land, Sea, and Air, vol. 5. ASME.Google Scholar
Reynolds, O. 1883 III – an experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Proc. R. Soc. Lond. A 35 (224–226), 8499.Google Scholar
Sagaut, P. 2002 Large Eddy Simulation for Incompressible Flows. Springer.CrossRefGoogle Scholar
Schlatter, P., Brandt, L., de Lange, H.C. & Henningson, D.S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20 (10), 101505.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2017 Boundary-Layer Theory. Springer.CrossRefGoogle Scholar
Sreenivasan, K.R. 1982 Laminarescent, relaminarizing and retransitional flows. Acta Mechanica 44 (1–2), 1–48.CrossRefGoogle Scholar
Touber, E. & Sandham, N.D. 2009 Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble. Theor. Comput. Fluid Dyn. 23 (2), 79107.CrossRefGoogle Scholar
Vaughan, N.J. & Zaki, T.A. 2011 Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks. J. Fluid Mech. 681, 116153.CrossRefGoogle Scholar
Vreman, A.W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 36703681.Google Scholar