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Various approaches to determine active regions in an unstable global mode: application to transonic buffet

Published online by Cambridge University Press:  25 October 2019

Edoardo Paladini Open the ORCID record for Edoardo Paladini [Opens in a new window] ,
Olivier Marquet Open the ORCID record for Olivier Marquet [Opens in a new window] ,
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window] ,
Jean-Christophe Robinet Open the ORCID record for Jean-Christophe Robinet [Opens in a new window]  and
Julien Dandois Open the ORCID record for Julien Dandois [Opens in a new window]
Edoardo Paladini*
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Olivier Marquet
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Denis Sipp
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
Jean-Christophe Robinet
Affiliation:
DynFluid Laboratory, Arts et Métiers ParisTech, 75013 Paris, France
Julien Dandois
Affiliation:
DAAA, ONERA, Université Paris Saclay, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: edoardo.paladini89@gmail.com
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Abstract

The transonic flow field around a supercritical airfoil is investigated. The objective of the present paper is to enhance the understanding of the physical mechanics behind two-dimensional transonic buffet. The paper is composed of two parts. In the first part, a global stability analysis based on the linearized Reynolds-averaged Navier–Stokes equations is performed. A recently developed technique, based on the direct and adjoint unstable global modes, is used to compute the local contribution of the flow to the growth rate and angular frequency of the unstable global mode. The results allow us to identify which zones are directly responsible for the existence of the instability. The technique is firstly used for the vortex-shedding cylinder mode, as a validating case. In the second part, in order to confirm the results of the first part, a selective frequency damping method is locally used in some regions of the flow field. This method consists of applying a low-pass filter on selected zones of the computational domain in order to damp the fluctuations. It allows us to identify which zones are necessary for the persistence of the instability. The two different approaches give the same results: the shock foot is identified as the core of the instability; the shock and the boundary layer downstream of the shock are also necessary zones while damping the fluctuations on the lower surface of the airfoil; and outside the boundary layer between the shock and the trailing edge or above the supersonic zone does not suppress the shock oscillation. A discussion on the several physical models, proposed until now for the buffet phenomenon, and a new model are finally offered in the last section.

JFM classification

Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 617 - 647
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Copyright
© 2019 Cambridge University Press 

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References

Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.Google Scholar
Barakos, G. & Drikakis, D. 2000 Numerical simulation of transonic buffet flows using various turbulence closures. Intl J. Heat Fluid Flow 21 (5), 620–626.Google Scholar
Beneddine, S., Sipp, D., Arnault, A., Dandois, J. & Lesshafft, L. 2016 Conditions for validity of mean flow stability analysis. J. Fluid Mech. 798, 485–504.Google Scholar
Brunet, V.2003 Computational study of buffet phenomenon with unsteady RANS equations. AIAA Paper 2003–3679.Google Scholar
Cambier, L., Heib, S. & Plot, S. 2013 The Onera elsA CFD software: input from research and feedback from industry. Mech. Industry 14 (3), 159–174.Google Scholar
Chomaz, J. M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.Google Scholar
Chomaz, J. M., Huerre, P. & Redekopp, L. G. 1988 Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 60 (1), 25–28.Google Scholar
Crouch, J. D., Garbaruk, A. & Magidov, D. 2007 Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224 (2), 924–940.Google Scholar
Crouch, J. D., Garbaruk, A., Magidov, D. & Jacquin, L. 2009a Global structure of buffeting flow on transonic airfoils. In IUTAM Symposium on Unsteady Separated Flows and their Control, pp. 297–306.; Springer.Google Scholar
Crouch, J. D., Garbaruk, A., Magidov, D. & Travin, A. 2009b Origin of transonic buffet on aerofoils. J. Fluid Mech. 628, 357–369.Google Scholar
Cunha, G., Passaggia, P.-Y. & Lazareff, M. 2015 Optimization of the selective frequency damping parameters using model reduction. Phys. Fluids 27 (9), 094103.Google Scholar
Deck, S. 2005 Numerical simulation of transonic buffet over a supercritical airfoil. AIAA J. 43 (7), 1556–1566.Google Scholar
Edwards, J. R. & Chandra, S. 1996 Comparison of eddy viscosity-transport turbulence models for three-dimensional, shock-separated flowfields. AIAA J. 34 (4), 756–763.Google Scholar
Edwards, J. R. & Liou, M.-S. 1998 Low-diffusion flux-splitting methods for flows at all speeds. AIAA J. 36 (9), 1610–1617.Google Scholar
Feldhusen, A., Hartmann, A., Klaas, M. & Schröder, W. 2014 High-speed tomographic PIV measurements of buffet flow over a supercritical airfoil. In 17th International Symposium on Appl. of Laser Techniques to Fluid Mechanics, Lisbon, Portugal. Springer.Google Scholar
Garnier, E. & Deck, S. 2010 Large-eddy simulation of transonic buffet over a supercritical airfoil. In Direct and Large-Eddy Simulation VII (ed. Armenio, V., Geurts, B. & Fröhlich, J.), ERCOFTAC Series, vol. 13. Springer.Google Scholar
Giannelis, N. F., Vio, G. A. & Levinski, O. 2017 A review of recent developments in the understanding of transonic shock buffet. Prog. Aerosp. Sci. 92, 39–84.Google Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.Google Scholar
Grossi, F., Braza, M. & Hoarau, Y. 2014 Prediction of transonic buffet by delayed detached-eddy simulation. AIAA J. 52 (10), 2300–2312.Google Scholar
Guiho, F.2015 Analyse de stabilité linéaire globale d’écoulements compressibles: application aux interactions onde de choc/couche limite (in French). PhD thesis, ENSAM.Google Scholar
Guiho, F., Alizard, F. & Robinet, J-C. 2016 Instabilities in oblique shock wave/laminar boundary-layer interactions. J. Fluid Mech. 789, 1–35.Google Scholar
Harten, A. & Hyman, J. M. 1983 Self adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comp. Phys. 50 (2), 235–269.Google Scholar
Hartmann, A., Feldhusen, A. & Schröder, W. 2013 On the interaction of shock waves and sound waves in transonic buffet flow. Phys. Fluids 25 (2), 026101.Google Scholar
Hecht, F. 2012 New development in freefem++. J. Numer. Math. 20 (3-4), 251–265.Google Scholar
Hilton, W. F. & Fowler, R. G.1947 Photographs of shock wave movement. NPL R&M no. 2692, National Physical Laboratories.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22 (1), 473–537.Google Scholar
Iorio, M. C.2015 Global stability analysis of turbulent transonic flows on airfoil geometries. PhD thesis, Technical University of Madrid.Google Scholar
Iorio, M. C., Gonzalez, L. M. & Ferrer, E. 2014 Direct and adjoint global stability analysis of turbulent transonic flows over a naca0012 profile. Intl J. Numer. Meth. Fluids 76 (3), 147–168.Google Scholar
Jackson, C. P.1987 A finite-element study of the onset of vortex shedding in flow past variously shaped bodies. 182, 23–45.Google Scholar
Jacquin, L., Molton, P., Deck, S., Maury, B. & Soulevant, D. 2009 Experimental study of shock oscillation over a transonic supercritical profile. AIAA J. 47 (9), 1985–1994.Google Scholar
Jordi, B. E., Cotter, C. J. & Sherwin, S. J. 2014 Encapsulated formulation of the selective frequency damping method. Phys. Fluids 26 (3), 034101.Google Scholar
Jordi, B. E., Cotter, C. J. & Sherwin, S. J. 2015 An adaptive selective frequency damping method. Phys. Fluids 27 (9), 094104.Google Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self-excited wake flows. J. Sound Vib. 99 (1), 53–83.Google Scholar
Lee, B. H. K. 1990 Oscillatory shock motion caused by transonic shock boundary-layer interaction. AIAA J. 28 (5), 942–944.Google Scholar
Lee, B. H. K. 2001 Self-sustained shock oscillations on airfoils at transonic speeds. Prog. Aerosp. Sci. 37 (2), 147–196.Google Scholar
Lee, B. H. K., Murty, H. & Jiang, H. 1994 Role of Kutta waves on oscillatory shock motion on an airfoil. AIAA J. 32 (4), 789–796.Google Scholar
Luchini, P., Giannetti, F. & Pralits, J.2008 Structural sensitivity of linear and nonlinear global modes. AIAA Paper 2008–4227.Google Scholar
Marquet, O. & Lesshafft, L.2015 Identifying the active flow regions that drive linear and nonlinear instabilities. arXiv:1508.07620.Google Scholar
Marquet, O., Sipp, D. & Jacquin, L. 2008 Sensitivity analysis and passive control of cylinder flow. J. Fluid Mech. 615, 221–252.Google Scholar
Memmolo, A., Bernardini, M. & Pirozzoli, S. 2018 Scrutinity of buffet mechanism in transonic flow. Intl J. Heat Fluid Flow 28 (5), 1031–1046.Google Scholar
Nitzsche, J. 2009 A numerical study on aerodynamic resonance in transonic separated flow. In International Forum on Aeroelasticity and Structural Dynamics, Seattle, WA. IFASD.Google Scholar
Pearcey, H. H.1958 A method for the prediction of the onset of buffeting and other separation effects from wind tunnel tests on rigid models. AGARD TR 223. ARC Report no. 20631.Google Scholar
Pearcey, H. H. & Holder, D. W.1962 Simple methods for the prediction of wing buffeting resulting from bubble type separation. NPL AERO-REP 1024. ARC Report no. 23884.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.Google Scholar
Sartor, F., Mettot, C. & Sipp, D. 2015 Stability, receptivity, and sensitivity analyses of buffeting transonic flow over a profile. AIAA J. 53 (7), 1980–1993.Google Scholar
Schmid, P. J. & Brandt, L. 2014 Analysis of fluid systems: Stability, receptivity, sensitivity: lecture notes from the FLOW-NORDITA summer school on advanced instability methods for complex flows, Stockholm, Sweden, 2013. Appl. Mech. Rev. 66 (2), 024803.Google Scholar
Sipp, D. & Lebedev, A.2007 Global stability of base and mean flows: a general approach and its applications to cylinder and open cavity flows. 593, 333–358.Google Scholar
Sipp, D., Marquet, O., Meliga, P. & Barbagallo, A. 2010 Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 63 (3), 030801.Google Scholar
Spalart, P. R. & Allmaras, S. R.1992 A one equation turbulence model for aerodynamic flows. AIAA Paper 1992-0439.Google Scholar
Spee, B. M.1966 Wave propagation in transonic flow past two-dimensional aerofoils. Tech. Rep. NLR-NT T.123. Nationaal Lucht-en Ruimtevaartlaboratorium.Google Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39 (4), 249–315.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.Google Scholar
Thierry, M. & Coustols, E. 2006 Numerical prediction of shock induced oscillations over a 2D airfoil: influence of turbulence modelling and test section walls. Intl J. Heat Fluid Flow 27 (4), 661–670.Google Scholar
Xiao, Q., Tsai, H.-M. & Liu, F. 2006 Numerical study of transonic buffet on a supercritical airfoil. AIAA J. 44 (3), 620–628.Google Scholar