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DNS Study on Vortex and Vorticity in Late Boundary Layer Transition

Part of: Turbulence Basic methods in fluid mechanics Incompressible viscous fluids

Published online by Cambridge University Press:  21 June 2017

Yiqian Wang ,
Yong Yang ,
Guang Yang  and
Chaoqun Liu
Yiqian Wang*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
Yong Yang*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Guang Yang*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA Beihang University, Beijing 100191, China
Chaoqun Liu*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
*
*Corresponding author. Email addresses:[email protected] (Y. Wang), [email protected] (Y. Yang), [email protected] (G. Yang), [email protected] (C. Liu)
*Corresponding author. Email addresses:[email protected] (Y. Wang), [email protected] (Y. Yang), [email protected] (G. Yang), [email protected] (C. Liu)
*Corresponding author. Email addresses:[email protected] (Y. Wang), [email protected] (Y. Yang), [email protected] (G. Yang), [email protected] (C. Liu)
*Corresponding author. Email addresses:[email protected] (Y. Wang), [email protected] (Y. Yang), [email protected] (G. Yang), [email protected] (C. Liu)
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Abstract

Vortex and vorticity are two correlated but fundamentally different concepts which have been the central issues in fluid mechanics research. Vorticity has rigorous mathematical definition (curl of velocity), but no clear physical meaning. Vortex has clear physical meaning (rotation) but no rigorous mathematical definition. For a long time, many people treat them as a same thing. However, based on our high-order direct numerical simulation (DNS), we found that first, “vortex” is not “vorticity tube” or “vortex tube” which is widely defined as a bundle of vorticity lines without any vorticity line leak. Actually, vortex is an open area for vorticity line penetration. Second, vortex is not necessarily congregation of vorticity lines, but dispersion in many 3-dimensional cases. Some textbooks say that vortex cannot end inside the flow field but must end on the solid wall (and/or boundaries). Our DNS observation and many other numerical results show almost all vortices are ended inside the flow field. Finally, a more theoretical study shows that neither vortex nor vorticity line can attach to the solid wall and they must be detached from the wall.

Keywords

Vortexvorticityvorticity linevorticity tube∧-vortexhairpin vortexDNSflow transitionturbulence

MSC classification

Secondary: 76F06: Transition to turbulence 76F40: Turbulent boundary layers 76M23: Vortex methods 76D17: Viscous vortex flows
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017 , pp. 441 - 459
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Wu, J., Xiong, A. and Yang, Y., Axial stretching and vortex definition, Phys. Fluids, 17 (2005), 038108.CrossRefGoogle Scholar
[2] Wu, J., Ma, H. and Zhou, M., Vorticity and Vortex Dynamics, Springer Science & Business Media, Berlin, 2007.Google Scholar
[3] Jeong, J., and Hussain, F., On the identification of a vortex, J. Fluid Mech., 285 (1995), 69–94.CrossRefGoogle Scholar
[4] Hunt, J. C. R., Wray, A. A. and Moin, P., Eddies, streams, and convergence zones in turbulent flows, Center for Turbulence Research: Proceedings of the Summer Program N89-24555, 1988.Google Scholar
[5] Adrian, R. J., Balachandar, S. and Kendall, T.M., Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech., 387 (1999), 353–396.Google Scholar
[6] Liu, C., Wang, Y., Yang, Y. and Duan, Z., New Omega vortex identification method, Sci. China Phys., Mech. Astro., 59 (2016), 1–9.CrossRefGoogle Scholar
[7] Helmholtz, H., About integrals of hydrodynamic equations related with vortical motions, J. für die reine Angewandte Mathematik, 55 (1958), 25.Google Scholar
[8] Lamb, H., Hydrodynamics, Cambridge University Press, Cambridge, 1932.Google Scholar
[9] Prandtl, L., Uber Flussigkeits bewegung bei sehr kleiner Reibung, Proccedings of Dritter Internationaler Mathematiker Kongress, (1904), 484–491.Google Scholar
[10] Durand, W. F., Aerodynamic theory: a general review of progress, J. Cell Sci., 124 (1934), 4318–4331.Google Scholar
[11] Goldstein, S., Modern Developments in Fluid Mechanics, Vol. II, Clarendon Press, Oxford, 1938.Google Scholar
[12] Küchemann, D., Report on the IUTAM symposium on concentrated vortex motions in fluids, J. Fluid Mech., 21 (1965), 1–20.CrossRefGoogle Scholar
[13] Theodorsen, T., Mechanism of turbulence, Proceedings of the Second Midwestern Conference on Fluid Mechanics, 1952.Google Scholar
[14] Kline, S. J., Reynolds, W. C., Schraub, F. A. and Runstadler, P. W., The structure of turbulent boundary layers, J. Fluid Mech., 30 (1967), 741–773.Google Scholar
[15] Corino, E. R. and Brodkey, R. S., A visual investigation of the wall region in turbulent flow, J. Fluid Mech., 37 (1969), 1–30.Google Scholar
[16] Kim, J., Moin, P. and Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177 (1987), 133–166.CrossRefGoogle Scholar
[17] Spalart, P. R., Direct simulation of a turbulent boundary layer up to Rθ =1410, J. Fluid Mech., 187 (1988), 61–98.Google Scholar
[18] Moin, P., and Mahesh, K., Direct numerical simulation: a tool in turbulence research, Annu. Rev. Fluid Mech., 30 (1998), 539–578.CrossRefGoogle Scholar
[19] Wu, X. and Moin, P., Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer, J. Fluid Mech., 630 (2009), 5–41.Google Scholar
[20] Liu, C., and Liu, Z., Multigrid mapping and box relaxation for simulation of the whole process of flow transition in 3D boundary layers, J. Comput. Phys., 119 (1995), 325–341.CrossRefGoogle Scholar
[21] Bake, S., Meyer, D. G. W. and Rist, U., Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation. J. Fluid Mech., 459 (2002), 217–243.Google Scholar
[22] Sayadi, T., Hamman, C.W. and Moin, P., Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers, J. Fluid Mech., 724 (2013), 480–509.Google Scholar
[23] Zagumennyi, Y. V. and Chashechkin, Y. D., Unsteady vortex pattern in a flow over a flat plate at zero angle of attack (two-dimensional problem), Fluid Dyn., 51 (2016), 343–359.Google Scholar
[24] Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.Google Scholar
[25] Saffman, P. G., Vortex Dynamics, Cambridge University Press, Cambridge, 1992.Google Scholar
[26] Lugt, H. J., Introduction to vortex theory, Vortex Flow Press, Potomac, 1996.Google Scholar
[27] Liu, C., Yan, Y. and Lu, P., Physics of turbulence generation and sustenance in a boundary layer, Comput. Fluids, 102 (2014), 353–384.CrossRefGoogle Scholar
[28] Smith, C. R., Walker, J. D. A., Haidari, A. H. and Sobrun, U., On the dynamics of near-wall turbulence, Philo. Trans. R. Soc. B, 336 (1991), 131–175.Google Scholar
[29] Nitsche, M., Vortex Dynamics, in Encyclopedia of Mathematics and Physics, Academic Press, New York, 2006.Google Scholar
[30] Fluid mechanics and aerodynamics (MIT lecture notes), 2009, Retrieved from http://web.mit.edu/16.unified/www/SPRING/.Google Scholar
[31] Hadamard, J., sur la Propagation des ondes et les équations de l’hydrodynamique, Hermman, Paris, 1903.Google Scholar
[32] Fuentes, O. V., On the topology of vortex lines and tubes, J. Fluid Mech., 584 (2007), 147–156.Google Scholar
[33] Lele, S. K., Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103 (1992), 16–42.Google Scholar
[34] Shu, C. W. and Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comput. Phys., 83 (1989), 32–78.Google Scholar
[35] Jiang, L., Chang, C. L., Choudhari, M. and Liu, C., Cross-validation of DNS and PSE results for instability-wave propagation in compressible boundary layers past curvilinear surfaces, 16th AIAA Computational Fluid Dynamics Conference, Orlando, 2006.Google Scholar
[36] Liu, C. and Chen, L., Parallel DNS for vortex structure of late stages of flow transition, Comput. Fluids, 45 (2011), 129–137.Google Scholar
[37] Lee, C. and Li, R., Dominant structure for turbulent production in a transitional boundary layer, J. Turbul., 8(55) (2007), 1–34.Google Scholar
[38] Moin, P., Leonard, A. and Kim, J., Evolution of a curved vortices filament into a vortices ring, Phys. Fluids, 29 (1986), 955–963.Google Scholar
[39] Hama, F. R., Boundary-layer transition induced by a vibrating ribbon on a flat plate, Proceedings of 1960 Heat Transfer and Fluid Mechanics Institute, Palo Alto, 1960.Google Scholar
[40] Hama, F. R. and Nutant, J., Detailed flow-field observations in the transition process in a thick boundary layer, Proceedings of 1963 Heat Transfer and Fluid Mechanics Institute, Pasadena, 1963.Google Scholar
[41] Tardu, S., Transport and Coherent Structures in Wall Turbulence, John Wiley & Sons, 2014.Google Scholar
[42] Head, M. and Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 107 (1981), 297–338.Google Scholar
[43] Townsend, A. A., The Structure of Turbulent Shear Flow, Cambridge University Press, Cambridge, 1976.Google Scholar
[44] Perry, A. and Chong, M., On the mechanism of wall turbulence, J. Fluid Mech., 119 (1982), 173–217.Google Scholar
[45] Adrian, R. J., Hairpin vortices organization in wall turbulence, Phys. Fluids, 19 (2007), 041301.CrossRefGoogle Scholar
[46] Zhang, W., Cheng, W., Gao, W., Qamar, A. and Samtaney, R., Geometrical effects on the airfoil flow separation and transition, Comput. Fluids, 116 (2015), 60–73.CrossRefGoogle Scholar
[47] Davidson, P. A., Turbulence: An Introduction for Scientists and Engineers, Oxford University Press, Oxford, 2004.Google Scholar