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Study on Mass Transports in Evolution of Separation Bubbles Using LCSs and Lobe Dynamics

Part of: General aerodynamics and subsonic flows Equations of mathematical physics and other areas of application Stability

Published online by Cambridge University Press:  03 May 2017

Shengli Cao ,
Wei Wang ,
Jiazhong Zhang  and
Yan Liu
Shengli Cao*
Affiliation:
School of Power and Energy Engineering, Xi'an Jiaotong University, Xi'an, 710049, P.R. China
Wei Wang*
Affiliation:
School of Power and Energy Engineering, Xi'an Jiaotong University, Xi'an, 710049, P.R. China
Jiazhong Zhang*
Affiliation:
School of Power and Energy Engineering, Xi'an Jiaotong University, Xi'an, 710049, P.R. China
Yan Liu*
Affiliation:
School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, 710072, P.R. China
*
*Corresponding author. Email addresses:[email protected] (S. L. Cao), [email protected] (W. Wang), [email protected] (J. Z. Zhang), [email protected] (Y. Liu)
*Corresponding author. Email addresses:[email protected] (S. L. Cao), [email protected] (W. Wang), [email protected] (J. Z. Zhang), [email protected] (Y. Liu)
*Corresponding author. Email addresses:[email protected] (S. L. Cao), [email protected] (W. Wang), [email protected] (J. Z. Zhang), [email protected] (Y. Liu)
*Corresponding author. Email addresses:[email protected] (S. L. Cao), [email protected] (W. Wang), [email protected] (J. Z. Zhang), [email protected] (Y. Liu)
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Abstract

The lobe dynamics andmass transport between separation bubble and main flow in flow over airfoil are studied in detail, using Lagrangian coherent structures (LCSs), in order to understand the nature of evolution of the separation bubble. For this problem, the transient flow over NACA0012 airfoil with low Reynolds number is simulated numerically by characteristic based split (CBS) scheme, in combination with dual time stepping. Then, LCSs and lobe dynamics are introduced and developed to investigate themass transport between separation bubble and main flow, from viewpoint of nonlinear dynamics. The results show that stable manifolds and unstable manifolds could be tangled with each other as time evolution, and the lobes are formed periodically to induce mass transport between main flow and separation bubble, with dynamic behaviors. Moreover, the evolution of the separation bubble depends essentially on the mass transport which is induced by lobes, ensuing energy and momentum transfers. As the results, it can be drawn that the dynamics of flow separation could be studied using LCSs and lobe dynamics, and could be controlled feasibly if an appropriate control is applied to the upstream boundary layer with high momentum.

Keywords

Mass transportseparation bubbleLagrangian coherent structureslobe dynamics

MSC classification

Secondary: 35Q35: PDEs in connection with fluid mechanics 35Q30: Navier-Stokes equations 76G25: General aerodynamics and subsonic flows 93D05: Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.) 86-08: Computational methods
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017 , pp. 285 - 302
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Horton, H. P.. Laminar separation bubbles in two and three dimensional incompressible flow. PhD thesis, 1968.Google Scholar
[2] Mueller, T. J. and Batil, S.M.. Experimental studies of separation on a two-dimensional airfoil at low Reynolds numbers. AIAA journal, 20(4):457–463, 1982.Google Scholar
[3] O’meara, M. and Mueller, T. J.. Laminar separation bubble characteristics on an airfoil at low Reynolds numbers. AIAA journal, 25(8):1033–1041, 1987.Google Scholar
[4] Gaster, M.. The structure and behaviour of laminar separation bubbles. Citeseer, 1969.Google Scholar
[5] Lin, J. C. M. and Pauley, L. L.. Low-Reynolds-number separation on an airfoil. AIAA journal, 34(8):1570–1577, 1996.Google Scholar
[6] Yarusevych, S., Sullivan, P. E., and Kawall, J. G.. On vortex shedding from an airfoil in low-Reynolds-number flows. Journal of Fluid Mechanics, 632:245–271, 2009.Google Scholar
[7] Egambaravel, J. and Mukherjee, R.. Linear stability analysis of laminar separation bubble over NACA0012 airfoil at low Reynolds numbers.Google Scholar
[8] Hammond, D. A. and Redekopp, L. G.. Local and global instability properties of separation bubbles. European Journal of Mechanics-B/Fluids, 17(2):145–164, 1998.Google Scholar
[9] Rist, U. and Maucher, U.. Investigations of time-growing instabilities in laminar separation bubbles. European Journal of Mechanics-B/Fluids, 21(5):495–509, 2002.Google Scholar
[10] Schmidt, G. S. and Mueller, T. J.. Analysis of low Reynolds number separation bubbles using semiempirical methods. AIAA journal, 27(8):993–1001, 1989.Google Scholar
[11] Almutairi, J.H., Jones, L. E., and Sandham, N.D.. Intermittent bursting of a laminar separation bubble on an airfoil. AIAA journal, 48(2):414–426, 2010.Google Scholar
[12] Shum, Y.K. and Marsden, D.J.. Separation bubble model for low Reynolds number airfoil applications. Journal of aircraft, 31(4):761–766, 1994.Google Scholar
[13] Van Dommelen, L. L. and Cowley, S. J.. On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory. Journal of Fluid Mechanics, 210:593–626, 1990.Google Scholar
[14] Shariff, K., Pulliam, T. H., and Ottino, J.M.. A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder. Lect. Appl. Math, 28:613–646, 1991.Google Scholar
[15] Duan, J. and Wiggins, S.. Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics. Nonlinear Processes in Geophysics, 4(3):125–136, 1997.Google Scholar
[16] Haller, G.. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos: An Interdisciplinary Journal of Nonlinear Science, 10(1):99–108, 2000.Google Scholar
[17] Haller, G.. Lagrangian coherent structures from approximate velocity data. Physics of Fluids (1994-present), 14(6):1851–1861, 2002.CrossRefGoogle Scholar
[18] Shadden, S. C., Lekien, F., and Marsden, J. E.. Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D: Nonlinear Phenomena, 212(3):271–304, 2005.Google Scholar
[19] Lei, P., Zhang, J., Li, K., and Wei, D.. Study on the transports in transient flow over impulsively started circular cylinder using Lagrangian coherent structures. Communications in Nonlinear Science and Numerical Simulation, 22(1):953–963, 2015.Google Scholar
[20] Haller, G.. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512:257–311, 2004.Google Scholar
[21] Surana, A. and Haller, G.. Ghost manifolds in slow-fast systems, with applications to unsteady fluid flow separation. Physica D: Nonlinear Phenomena, 237(10):1507–1529, 2008.Google Scholar
[22] Beron-Vera, F. J., Olascoaga, M. J., and Goni, G. J.. Oceanic mesoscale eddies as revealed by Lagrangian coherent structures. Geophysical Research Letters, 35(12), 2008.Google Scholar
[23] Mathur, M., Haller, G., Peacock, T., Ruppert-Felsot, J. E., and Swinney, H. L.. Uncovering the Lagrangian skeleton of turbulence. Physical Review Letters, 98(14):144502, 2007.Google Scholar
[24] BozorgMagham, A. E., Ross, S. D., and Schmale, D. G.. Real-time prediction of atmospheric Lagrangian coherent structures based on forecast data: an application and error analysis. Physica D: Nonlinear Phenomena, 258:47–60, 2013.Google Scholar
[25] Haller, G. and Yuan, G.. Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D: Nonlinear Phenomena, 147(3):352–370, 2000.Google Scholar
[26] Haller, G.. A variational theory of hyperbolic Lagrangian coherent structures. Physica D: Nonlinear Phenomena, 240(7):574–598, 2011.Google Scholar
[27] Lipinski, D. and Mohseni, K.. A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures. Chaos: An Interdisciplinary Journal of Nonlinear Science, 20(1):017504, 2010.Google Scholar
[28] Mancho, A. M., Small, D., Wiggins, S., and Ide, K.. Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields. Physica D: Nonlinear Phenomena, 182(3):188–222, 2003.Google Scholar
[29] Malhotra, N. and Wiggins, S.. Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to rossby wave flow. Journal of nonlinear science, 8(4):401–456, 1998.Google Scholar
[30] Nithiarasu, P.. An efficient artificial compressibility (AC) scheme based on the characteristic based split (CBS) method for incompressible flows. International Journal for Numerical Methods in Engineering, 56(13):1815–1845, 2003.Google Scholar
[31] Kunz, P. J.. Aerodynamics and design for ultra-low Reynolds number flight. PhD thesis, Stanford University, 2003.Google Scholar
[32] Lipinski, D., Cardwell, B., and Mohseni, K.. A Lagrangian analysis of a two-dimensional airfoil with vortex shedding. Journal of Physics A: Mathematical and Theoretical, 41(34):344011, 2008.Google Scholar
[33] Yarusevych, S., Sullivan, P. E., and Kawall, J. G.. Coherent structures in an airfoil boundary layer and wake at low Reynolds numbers. Physics of Fluids (1994-present), 18(4):044101, 2006.Google Scholar