Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T08:37:45.717Z Has data issue: false hasContentIssue false

Enhancement of disturbance wave amplification due to the intrinsic three-dimensionalisation of laminar separation bubbles

Published online by Cambridge University Press:  17 October 2018

D. Rodríguez*
Affiliation:
Laboratory of Theoretical and Applied Mechanics (LMTA)Graduate Program in Mechanical Engineering (PGMEC)Department of Mechanical EngineeringUniversidade Federal Fluminense NiteróiRJ, Brazil
E. M. Gennaro*
Affiliation:
São Paulo State University (UNESP)Campus São João da Boa VistaSão João da Boa VistaSP, Brazil

Abstract

Previous studies demonstrated that laminar separation bubbles (LSBs) in the absence of external disturbances or forcing are intrinsically unstable with respect to a three-dimensional instability of centrifugal nature. This instability produces topological modifications of the recirculation region with the introduction of streamwise vorticity in an otherwise purely two-dimensional time-averaged flows. Concurrently, the existence of spanwise inhomogeneities in LSBs have been reported in experiments in which the amplification of convective instability waves dominates the physics. The co-existence of the two instability mechanisms is investigated herein by means of three-dimensional parabolised stability equations. The spanwise waviness of the LSB on account of the primary instability is found to modify the amplification of incoming disturbance waves in the linear regime, resulting in a remarkable enhancement of the amplitude growth and a three-dimensional arrangement of the disturbance waves in the aft portion of the bubble. Present findings suggest that the oblique transition scenario should be expected in LSBs dominated by the convective instability, unless high-amplitude disturbances are imposed.

Type
Research Article
Copyright
© Royal Aeronautical Society 2018 

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.)

Footnotes

A version of this paper first appeared at the ICAS 2018 Conference held in Belo Horizonte, Brazil, September 2018.

References

REFERENCES

Gault, D.E. Boundary-layer and stalling characteristics of the naca 63-009 airfoil section, NACA TN 1894, 1949.Google Scholar
McCullough, G.B. and Gault, D.E. Examples of three representative types of airfoil-section stall at low speed, NACA TN 2502, 1951.Google Scholar
Alam, M. and Sandham, N.D. Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment, J Fluid Mechanics, 2000, 410, pp 128.CrossRefGoogle Scholar
Diwan, S.S. and Ramesh, O.N. On the origin of the inflectional instability of a laminar separation bubble, J Fluid Mechanics, 2009, 629, pp 263298.CrossRefGoogle Scholar
Dovgal, A.V., Kozlov, V.V. and Michalke, A. Laminar boundary layer separation: instability and associated phenomena, Progress in Aerosp Sciences, 1994, 3, pp 6194.CrossRefGoogle Scholar
Marxen, O., Lang, M. and Rist, U. Vortex formation and vortex breakup in laminar separation bubbles, J Fluid Mechanics, 2013, 728, pp 5890.CrossRefGoogle Scholar
Rist, U. and Maucher, U. Investigations of time-growing instabilities in laminar separation bubbles, European J Mechanics – B/Fluids, 2002, 21, pp 495509.CrossRefGoogle Scholar
Rist, U. and Maucher, U. Direct numerical simulation of 2-d and 3-d instability waves in a laminar separation bubble. In B. Cantwell, editor, AGARD-CP-551 Application of Direct and Large Eddy Simulation to Transition and Turbulence, pp 34–1, 34–7, 1994.Google Scholar
Rodríguez, D., Gennaro, E.M. and Juniper, M.P. The two classes of primary modal instability in laminar separation bubbles, J Fluid Mechanics, 2013, 734, pp R4.CrossRefGoogle Scholar
Theofilis, V., Hein, S. and Dallmann, U. On the origins of unsteadiness and three-dimensionality in a laminar separation bubble, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 2000, 358, pp 32293246.CrossRefGoogle Scholar
Rodríguez, D., Gennaro, E.M. and Souza, L.F. Self-excited primary and secondary instability on laminar separation bubbles, J Fluid Mechanics, to be submitted, 2018.Google Scholar
Rodríguez, D. and Theofilis, V. Structural changes of laminar separation bubbles induced by global linear instability, J Fluid Mechanics, 2010, 655, pp 280305.CrossRefGoogle Scholar
Kawahara, G., Jimémez, J., Uhlmann, M. and Pinelli, A. Linear instability of a corrugated vortex sheet – a model for streak instability, J Fluid Mechanics, 2003, 483, pp 315342.CrossRefGoogle Scholar
Saxena, V., Leibovich, S. and Berkooz, G. Enhancement of three-dimensional instability of free shear layers, J Fluid Mechanics, 1999, 379, pp 2338.CrossRefGoogle Scholar
Spalart, P.R. and Strelets, M.K. Mechanisms of transition and heat transfer in a separation bubble, J Fluid Mechanics, 2000, 403, pp 329349.CrossRefGoogle Scholar
Watmuff, J.H. Evolution of a wave packet into vortex loops in a laminar separation bubble, J Fluid Mechanics, 1999, 397, pp 119169.CrossRefGoogle Scholar
Broadhurst, M. and Sherwin, S. The parabolised stability equations for 3d-flows: implementation and numerical stability, Applied Numerical Mathematics, 2008, 58, (7): 10171029.CrossRefGoogle Scholar
Herbert, T. Parabolized stability equations, Annual Review of Fluid Mechanics, 1997, 29, pp 245283.CrossRefGoogle Scholar
Bertolotti, F.P., Herbert, Th. and Spalart, P.R. Linear and nonlinear stability of the Blasius boundary layer, J Fluid Mechanics, 1992, 242, pp 441474.CrossRefGoogle Scholar
Chang, C.-L., Malik, M.R., Erlenbacher, G. and Hussaini, M.Y. Linear and nonlinear PSE for compressible boundary layers, ICASE Report No. 93-70, 1993.Google Scholar
Rodríguez, D., Sinha, A., Brès, G. and Colonius, T. Inlet conditions for wave packet models in turbulent jets based on eigenmode decomposition of large eddy simulation data, Physics of Fluids, 2013, 25, pp 105107.CrossRefGoogle Scholar
Mack, L.M. Boundary layer linear stability theory. AGARD-R-709 Special course on stability and transition of laminar flow, 1984, pp 3.1–3.81.Google Scholar
Tumin, A. Multimode decomposition of spatially growing perturbations in a two-dimensional boundary layer, Physics of Fluids, 2003, 15, pp 25252540.CrossRefGoogle Scholar
Rodríguez, D. and Theofilis, V. Massively parallel numerical solution of the biglobal linear instability eigenvalue problem using dense linear algebra, AIAA J, 2009, 47, (10): 24492459.CrossRefGoogle Scholar
Gennaro, E.M., Rodríguez, D., Medeiros, M.A.F. and Theofilis, V. Sparse techniques in global flow instability with application to compressible leading-edge flow, AIAA J, 2013, 51, (9): 22952303.CrossRefGoogle Scholar
Rodríguez, D. and Gennaro, E.M. Three-dimensional flow stability analysis based on the matrix-forming approach made affordable. In J. S. Hesthaven, editor, International Conference on Spectral and High-Order Methods 2016, Lecture Notes in Computational Science and Engineering. Springer, 2017.CrossRefGoogle Scholar
Arnoldi, W.E. The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quarterly of Applied Mathematics, 1951, 9, pp 1729.CrossRefGoogle Scholar
Amestoy, P.R., Duff, I.S., L’Excellent, J.-Y. and Koster, J. A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J Matrix Analysis and Applications, 2001, 23, (1): 1541.CrossRefGoogle Scholar
Li, F. and Malik, M.R. Spectral analysis of parabolized stability equations, Computers & Fluids, 1997, 26, (3): 279297.CrossRefGoogle Scholar
Andersson, P., Henningson, D.S. and Hanifi, A. On a stabilization procedure for the parabolic stability equations, J Engineering Mathematics, 1998, 33, pp 311332.CrossRefGoogle Scholar
Huerre, P. and Monkewitz, P.A. Absolute and convective instabilities in free shear layers, J Fluid Mechanics, 1985, 159, pp 151168.CrossRefGoogle Scholar
Michelis, T., Yarusevych, S. and Kotsonis, M. On the origin of spanwise vortex deformations in laminar separation bubbles, J Fluid Mechanics, 2018, 841, pp 81108.CrossRefGoogle Scholar
Kurelek, J.W., Lambert, A.R. and Yarusevych, S. Coherent structures in the transition process of a laminar separation bubble, AIAA J, 2016, 54, (8): 22952309.CrossRefGoogle Scholar
Pauley, L.P., Moin, P. and Reynolds, W.C. The structure of two-dimensional separation, J Fluid Mechanics, 1990, 220, pp 397411.CrossRefGoogle Scholar
Henk, R.W., Reynolds, W.C. and Reed, H.L. An experimental investigation of the fluid mechanics of an unsteady, three-dimensional separation. Technical Rep. TF-49, Department of Mechanical Engineering, Stanford University, 1990.Google Scholar
Serna, J. and Lázaro, B.J. The final stages of transition and the reattachment region in transitional separation bubbles, Experiments in Fluids, 2017, 55, pp 1695.CrossRefGoogle Scholar
Serna, J. and Lázaro, B.J. On the bursting condition for transitional separation bubbles, Aerosp Science and Technology, 2015, 44, pp 4350.CrossRefGoogle Scholar