Numerical Study of Unsteady Flow Separation on Small Scale Wings Using Vortex Identification Methods
Main Article Content
Abstract
The goal of this work is to develop vortex identification methods for better understanding the unsteady separation using particle-based direct numerical simulation for the unsteady incompressible flow past small wings. It is shown that in flows with Reynolds number 1000, the first vortex identification method, vorticity contour, is used to capture the vortical region behind the surface in which the package of unsteady votex bubbles is observed in different angle of attacks. The second vortex identification method, Q-criterion, has shown the advantages in order to capture the vortical region and track the near-wall separation by recording the vortex strengths of leading edge vortex and trailing edge vortex at high angle of attacks. The time history of the strengths has shown a good agreement to the time history of drag coefficient. The third vortex identification method, Lagrangian coherent structure, has shown its strength to record the most stretching, attracting, and shearing material surfaces that form the skeletons of Lagrangian particle dynamics in the far-field wake region. Accordingly, the tracking of particles in high shear surfaces, which is very important to determine the roadmap of unsteadiness, is well captured
Keywords
Unsteady Laminar Separation, Vortex Method, Vortex Identification, Lagrangian Coherent Structure
Article Details
References
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[3] Ellington, C., The novel aerodynamics of insect flight: Applications to micro-air vehicles, Journal of Experimental Biology, Vol. 202, pp. 3439-3448, 1999. https://doi.org/10.1242/jeb.202.23.3439
[4] Diwan, S. S., & Ramesh, O. N., Laminar separation bubbles: Dynamics and control, Sadhana, Vol. 32, pp. 103-109, 2007. https://doi.org/10.1007/s12046-007-0009-7
[5] Dickinson, M. H., & Gotz, K. G., Unsteady aerodynamic performance of model wings at low Reynolds numbers, Journal of Experimental Biology, Vol. 174, pp. 45-64, 1993. https://doi.org/10.1242/jeb.174.1.45
[6] Dung, D. V., Lavi, R. Z., & Muhammad, H., Two-dimensional fast Lagrangian vortex method for simulating flows around a moving boundary, Journal of Mechanical Engineering, Vol. 12, No. 1, pp. 31-46, 2015.
[7] Green, M. A., Rowley, C. W., & Haller, G., Detection of Lagrangian coherent structures in three-dimensional turbulence, Journal of Fluid Mechanics, Vol. 572, pp. 111-120, 2007. https://doi.org/10.1017/S0022112006003648
[8] Jakobsson, J., Investigation of Lagrangian coherent structures-To understand and identify turbulence, Dissertation, Chalmers University of Technology, Sweden, 2012.
[9] Haller, G., Lagrangian coherent structures from approximate velocity data, Physics of Fluids, Vol. 14, No. 6, pp. 1851-1861, 2002. https://doi.org/10.1063/1.1477449
[10] Lipinski, D., Cardwell, B., & Mohseni, K., A Lagrangian analysis of a two-dimensional airfoil with vortex shedding, Journal of Physics A: Mathematical and Theoretical, Vol. 41, No. 34, 2008. https://doi.org/10.1088/1751-8113/41/34/344011
[11] Ploumhans, P., & Winckelmans, G. S., Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry, Journal of Computational Physics, Vol. 165, No. 2, pp. 354-406, 2000. https://doi.org/10.1006/jcph.2000.6614
[12] Hunt, J. C. R., Wray, A., & Moin, P., Eddies, stream, and convergence zones in turbulent flows, Center for turbulence research report CTR-S88, pp. 193-208, 1988.
[13] Chakraborty, P., Balachandar, S., & Adrian, R. J., On the relationships between local vortex identification schemes, Journal of Fluid Mechanics, Vol. 535, pp. 189-214, 2005. https://doi.org/10.1017/S0022112005004726
[14] Germer, T., Lagrangian coherent structures with guaranteed material separation, Computer Graphics Forum, Vol. 30, No. 3, 2011. https://doi.org/10.1111/j.1467-8659.2011.01925.x
[15] Brunton, S. L., & Rowley, C. W., Fast computation of FTLE fields for unsteady flows: a comparison of methods, Chaos, Vol. 20, No. 1, 2010. https://doi.org/10.1063/1.3270044