Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-17T07:23:39.676Z Has data issue: false hasContentIssue false
  • English
  • Français

An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound

Published online by Cambridge University Press:  19 August 2019

Henrique Raposo Open the ORCID record for Henrique Raposo [Opens in a new window] ,
Shahid Mughal Open the ORCID record for Shahid Mughal [Opens in a new window]  and
Richard Ashworth Open the ORCID record for Richard Ashworth [Opens in a new window]
Henrique Raposo*
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK Central Research and Technology, Airbus, Bristol BS34 7PA, UK
Shahid Mughal
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Richard Ashworth
Affiliation:
Central Research and Technology, Airbus, Bristol BS34 7PA, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The generation of the first-mode instability through scattering of an acoustic wave by localised surface roughness, suction or heating is studied with a time-harmonic compressible adjoint linearised Navier–Stokes (AHLNS) approach for subsonic flow conditions. High Strouhal number analytical solutions to the compressible Stokes layer problem are deduced and shown to be in better agreement with numerical solutions compared to previous works. The adjoint methodology of Hill in the context of acoustic receptivity is extended to the compressible flow regime and an alternative formulation to predict sensitivity to the angle of incidence of an acoustic wave is proposed. Good agreement of the acoustic AHLNS receptivity model is found with published direct numerical simulations and the simpler finite Reynolds number approach. Parametric investigations of the influence of the acoustic wave angle on receptivity amplitudes reveal that the linearised unsteady boundary layer equations are a valid model of the acoustic signature for a large range of acoustic wave obliqueness values, failing only where the wave is highly oblique and travels upstream. An extensive parametric study of the influence of frequency, spanwise wavenumber, local Reynolds number and free-stream Mach number over the efficiency function for the different types of wall perturbation mechanisms is undertaken.

JFM classification

Boundary Layers: Boundary layer receptivity Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 105 - 129
Copyright
© 2019 Cambridge University Press 

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

Ackerberg, R. C. & Phillips, J. H. 1972 The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity. J. Fluid Mech. 51 (01), 137–157.10.1017/S0022112072001119Google Scholar
Airiau, C. 2000 Non-parallel acoustic receptivity of a Blasius boundary layer using an adjoint approach. Flow Turbul. Combust. 65 (3), 347–367.10.1023/A:1011472831831Google Scholar
Arnal, D. & Casalis, G. 2000 Laminar-turbulent transition prediction in three-dimensional flows. Prog. Aerosp. Sci. 36 (2), 173–191.10.1016/S0376-0421(00)00002-6Google Scholar
Bernots, T.2014 Receptivity of the boundary layer in transonic flow past an aircraft wing. PhD thesis, Imperial College London.Google Scholar
Bertolotti, F. P.1991 Linear and nonlinear stability of boundary layers with streamwise varying properties. PhD thesis, The Ohio State University, Columbus, OH.Google Scholar
Bertolotti, F. P., Herbert, T. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474.10.1017/S0022112092002453Google Scholar
Brand, R. S. & Nagel, R. T. 1982 Reflection of sound by a boundary layer. J. Sound Vib. 85 (1), 31–38.Google Scholar
Carpenter, M., Choudhari, M., Li, F., Streett, C. & Chang, C. 2010 Excitation of crossflow instabilities in a swept wing boundary layer. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. AIAA Paper 2010-378.Google Scholar
Choudhari, M.1994 Acoustic receptivity of compressible boundary layers: receptivity by way of surface-temperature variations. NASA Tech. Rep. 4599, Langley Research Center.Google Scholar
Choudhari, M. & Streett, C. L. 1992 A finite Reynolds-number approach for the prediction of boundary-layer receptivity in localized regions. Phys. Fluids A 4 (11), 2495–2514.10.1063/1.858437Google Scholar
Crouch, J. & Bertolotti, F. P. 1992 Nonlocalized receptivity of boundary layers to three-dimensional disturbances. In 30th Aerospace Sciences Meeting and Exhibit. AIAA Paper 1992-0740.Google Scholar
Crouch, J. D. 1992a Localized receptivity of boundary layers. Phys. Fluids A 4 (7), 1408–1414.10.1063/1.858416Google Scholar
Crouch, J. D. 1992b Non-localized receptivity of boundary layers. J. Fluid Mech. 244, 567–581.10.1017/S0022112092003197Google Scholar
Crouch, J. D. & Spalart, P. R. 1995 A study of non-parallel and nonlinear effects on the localized receptivity of boundary layers. J. Fluid Mech. 290, 29–37.10.1017/S0022112095002400Google Scholar
De Tullio, N. & Ruban, A. I. 2015 A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers. J. Fluid Mech. 771, 520–546.10.1017/jfm.2015.196Google Scholar
Dobrinsky, A. Y.2003 Adjoint analysis for receptivity prediction. PhD thesis, Rice University, Houston, TX.Google Scholar
Duck, P. W. 1990 The response of a laminar boundary layer in supersonic flow to small-amplitude progressive waves. J. Fluid Mech. 219, 423–448.10.1017/S0022112090003019Google Scholar
El-Hady, N. M. 1991 Nonparallel instability of supersonic and hypersonic boundary layers. Phys. Fluids A 3 (9), 2164–2178.10.1063/1.857898Google Scholar
Goldstein, M. E. 1983 The evolution of Tollmien–Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.10.1017/S002211208300261XGoogle Scholar
Goldstein, M. E. 1985 Scattering of acoustic waves into Tollmien–Schlichting waves by small streamwise variations in surface geometry. J. Fluid Mech. 154, 509–529.10.1017/S0022112085001641Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Dyn. 29 (1), 245–283.10.1146/annurev.fluid.29.1.245Google Scholar
Hill, D. C. 1995 Adjoint systems and their role in the receptivity problem for boundary layers. J. Fluid Mech. 292, 183–204.10.1017/S0022112095001480Google Scholar
Hosseinverdi, S. & Fasel, H. F. 2019 Numerical investigation of laminar-turbulent transition in laminar separation bubbles: the effect of free-stream turbulence. J. Fluid Mech. 858, 714–759.10.1017/jfm.2018.809Google Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Dyn. 26 (1), 411–482.10.1146/annurev.fl.26.010194.002211Google Scholar
Mack, L. M.1984 Boundary-layer linear stability theory. Tech. Rep. California Institute of Technology, Jet Propulsion Laboratory.Google Scholar
Moore, F. K.1951 Unsteady laminar boundary-layer flow. NACA Tech. Mem. Tech. Rep. 2471.Google Scholar
Mughal, M. S. & Ashworth, R. M. 2013 Uncertainty quantification based receptivity modelling of crossflow instabilities induced by distributed surface roughness in swept wing boundary layers. In 43rd AIAA Fluid Dynamics Conference. AIAA Paper 2013-3106.Google Scholar
Nayfeh, A. H. & Ashour, O. N. 1994 Acoustic receptivity of a boundary layer to Tollmien–Schlichting waves resulting from a finite-height hump at finite Reynolds numbers. Phys. Fluids 6 (11), 3705–3716.10.1063/1.868361Google Scholar
Pralits, J. O., Airiau, C., Hanifi, A. & Henningson, D. S. 2000 Sensitivity analysis using adjoint parabolized stability equations for compressible flows. Flow Turbul. Combust. 65 (3–4), 321–346.10.1023/A:1011434805046Google Scholar
Raposo, H., Mughal, S. & Ashworth, R. 2018a Acoustic receptivity and transition modeling of Tollmien–Schlichting disturbances induced by distributed surface roughness. Phys. Fluids 30 (4), 044105.10.1063/1.5024909Google Scholar
Raposo, H., Mughal, S. & Ashworth, R. 2018 Acoustic receptivity of compressible Tollmien–Schlichting waves with an efficient time-harmonic linearized Navier–Stokes method. In 2018 Fluid Dynamics Conference. AIAA Paper 2018-3379.Google Scholar
Reed, H. L. & Saric, W. S. 2015 Receptivity: the inspiration of mark morkovin. In 45th AIAA Fluid Dynamics Conference. AIAA Paper 2015-2471.Google Scholar
Ruban, A. I. 1985 On Tollmien–Schlichting wave generation by sound. In Laminar–Turbulent Transition (ed. Kozlov, V. V.), pp. 313–320. Springer.10.1007/978-3-642-82462-3_39Google Scholar
Ruban, A. I., Bernots, T. & Kravtsova, M. A. 2016 Linear and nonlinear receptivity of the boundary layer in transonic flows. J. Fluid Mech. 786, 154–189.10.1017/jfm.2015.587Google Scholar
Salwen, H. & Grosch, C. E. 1981 The continuous spectrum of the Orr–Sommerfeld equation. Part 2. Eigenfunction expansions. J. Fluid Mech. 104, 445–465.10.1017/S0022112081002991Google Scholar
Saric, W. S. 1994 Physical description of boundary-layer transition: experimental evidence. In Special Course on Progress in Transition Modelling. AGARD Rep. 793, p. 51. AGARD.Google Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34 (1), 291–319.10.1146/annurev.fluid.34.082701.161921Google Scholar
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35 (1), 413–440.10.1146/annurev.fluid.35.101101.161045Google Scholar
Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129–162.10.1146/annurev.fluid.38.050304.092139Google Scholar
Stewartson, K. 1951 On the impulsive motion of a flat plate in a viscous fluid. Q. J. Mech. Appl. Maths 4 (2), 182–198.10.1093/qjmam/4.2.182Google Scholar
Streett, C. L.1998 Direct harmonic linear Navier–Stokes methods for efficient simulation of wave packets. AIAA Paper 98-0784.10.2514/6.1998-784Google Scholar
Tempelmann, D., Hanifi, A. & Henningson, D. S. 2012 Swept-wing boundary-layer receptivity. J. Fluid Mech. 700, 490–501.10.1017/jfm.2012.152Google Scholar
Thomas, C., Mughal, S. & Ashworth, R. 2017 On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer. Phys. Fluids 29 (3), 034102.10.1063/1.4977092Google Scholar
Tumin, A. 2007 Three-dimensional spatial normal modes in compressible boundary layers. J. Fluid Mech. 586, 295–322.10.1017/S002211200700691XGoogle Scholar
Tumin, A. M. & Fedorov, A. V. 1983 Spatial growth of disturbances in a compressible boundary layer. J. Appl. Mech. Tech. Phys. 24 (4), 548–554.10.1007/BF00907906Google Scholar
Wiegel, M. & Wlezien, R. 1993 Acoustic receptivity of laminar boundary layers over wavy walls. In 3rd Shear Flow Conference. AIAA Paper 1993-3280.Google Scholar
Zhigulev, V. N. & Fedorov, A. V. 1987 Boundary-layer receptivity to acoustic disturbances. J. Appl. Mech. Tech. Phys. 28 (1), 28–34.10.1007/BF00918768Google Scholar
Zuccher, S. & Luchini, P. 2014 Boundary-layer receptivity to external disturbances using multiple scales. Meccanica 49 (2), 441–467.10.1007/s11012-013-9804-xGoogle Scholar
Supplementary material: File

Raposo et al. supplementary material

Raposo et al. supplementary material 1

Download Raposo et al. supplementary material(File)
File 332.6 KB