Skip to main content
×
Home

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

  • Shengli Cao (a1), Wei Wang (a1), Jiazhong Zhang (a1) and Yan Liu (a2)
Abstract
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.

Copyright
Corresponding author
*Corresponding author. Email addresses: csl1993@stu.xjtu.edu.cn (S. L. Cao), weiwwang@foxmail.com (W. Wang), jzzhang@mail.xjtu.edu.cn (J. Z. Zhang), liuyan@nwpu.edu.cn (Y. Liu)
References
Hide All
[1] Horton H. P.. Laminar separation bubbles in two and three dimensional incompressible flow. PhD thesis, 1968.
[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):457463, 1982.
[3] O’meara M. and Mueller T. J.. Laminar separation bubble characteristics on an airfoil at low Reynolds numbers. AIAA journal, 25(8):10331041, 1987.
[4] Gaster M.. The structure and behaviour of laminar separation bubbles. Citeseer, 1969.
[5] Lin J. C. M. and Pauley L. L.. Low-Reynolds-number separation on an airfoil. AIAA journal, 34(8):15701577, 1996.
[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, 632:245271, 2009.
[7] Egambaravel J. and Mukherjee R.. Linear stability analysis of laminar separation bubble over NACA0012 airfoil at low Reynolds numbers.
[8] Hammond D. A. and Redekopp L. G.. Local and global instability properties of separation bubbles. European Journal of Mechanics-B/Fluids, 17(2):145164, 1998.
[9] Rist U. and Maucher U.. Investigations of time-growing instabilities in laminar separation bubbles. European Journal of Mechanics-B/Fluids, 21(5):495509, 2002.
[10] Schmidt G. S. and Mueller T. J.. Analysis of low Reynolds number separation bubbles using semiempirical methods. AIAA journal, 27(8):9931001, 1989.
[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):414426, 2010.
[12] Shum Y.K. and Marsden D.J.. Separation bubble model for low Reynolds number airfoil applications. Journal of aircraft, 31(4):761766, 1994.
[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, 210:593626, 1990.
[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, 28:613646, 1991.
[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):125136, 1997.
[16] Haller G.. Finding finite-time invariant manifolds in two-dimensional velocity fields. Chaos: An Interdisciplinary Journal of Nonlinear Science, 10(1):99108, 2000.
[17] Haller G.. Lagrangian coherent structures from approximate velocity data. Physics of Fluids (1994-present), 14(6):18511861, 2002.
[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):271304, 2005.
[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):953963, 2015.
[20] Haller G.. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512:257311, 2004.
[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):15071529, 2008.
[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.
[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.
[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, 258:4760, 2013.
[25] Haller G. and Yuan G.. Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D: Nonlinear Phenomena, 147(3):352370, 2000.
[26] Haller G.. A variational theory of hyperbolic Lagrangian coherent structures. Physica D: Nonlinear Phenomena, 240(7):574598, 2011.
[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.
[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):188222, 2003.
[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):401456, 1998.
[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):18151845, 2003.
[31] Kunz P. J.. Aerodynamics and design for ultra-low Reynolds number flight. PhD thesis, Stanford University, 2003.
[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.
[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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 31 *
Loading metrics...

Abstract views

Total abstract views: 122 *
Loading metrics...

* Views captured on Cambridge Core between 3rd May 2017 - 14th December 2017. This data will be updated every 24 hours.