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[1] Smith, C.R., Walker, J.D.A., Haidari, A.H. & Sobrun, U., On the dynamics of near-wall turbulence. Philosophical Transactions of the Royal Society A, 336, pp. 131–175, 1991.
[2] Theodorsen, T., Mechanism of turbulence. Proceeding of Second Midwestern Confer-ence on Fluid Mech., Bull., 149, Ohio State Univ., Columbus, Ohio, 1952.
[3] Lee, C.B. & Wu, J.Z., Transition in wall-bounded flows. Applied Mechanics Reviews, 61, pp. 030802-1-21, 2008.
[4] Robinson, S.K., Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics, 23(601), pp. 601-639, 1991.
[5] Robinson, S.K., The kinematics of turbulent boundary layer structure. NASA TM 103859, 1991.
[6] Panton, R., Overview of the self-sustaining mechanisms of wall turbulence. Progress in Aerospace Sciences, 37, pp. 341–383, 2001.
[7] Adrian, R.J., Hairpin vortex organization in wall turbulence. Physics of Fluids, 19, pp. 041301, 2007.
[8] Dennis, D.J.C, Coherent structures in wall-bounded turbulence. Annals of the Brazilian Academy of Sciences, 87(2), pp. 1161–1193, 2015.
[9] Moin, P., Leonard, A. & Kim, J., Evolution of a curved vortex filament into a vortex ring. Physics of Fluids, 29(4), pp. 955–963, 1986. 41.
[10] Hon, T.L. & Walker, J.D.A, Evolution of hairpin vortices in a shear flow. Computers and Fluids, 20(3), pp. 343–358, 1991.
[11] Singer, B.A. & Joslin, R.D., Metamorphosis of a hairpin vortex into a young turbulent spot. Physics of Fluids, 6(11), pp. 3724–3736, 1994.
[12] Zhou, J., Adrian, R.J. & Balachander, S, Autogeneration of near-wall vortical structures in channel flow. Physics of Fluids, 8(1), pp. 288–290, 1996.
[13] Zhou, J., Adrian, R.J. & Balachandar, S., Mechanisms for generating coherent packets of hairpin vortices in channel flow. Journal of Fluid Mechanics, 387, pp. 353–396, 1999.
[14] Liu, C. & Chen, L., Parallel DNS for vortex structure of late stages of flow transition. Computers & Fluids, 45, pp. 129–137, 2011.
[15] Cohen, J., Karp, M. & Mehta, V., A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows. Journal of Fluid Mechanics, 747, pp. 30–43, 2014.
[16] Eitel-Amor, G., Örlu, R., Schlatter, P. & Flores, O., Hairpin vortices in turbulent bound-ary layers. Physics of Fluids. 27, pp. 025108, 2015.
[17] Kim, K., Sung, H. J. & Adrian, R.J., Effects of background noise on generating coher-ent packets of hairpin vorticies. Physics of Fluids. 20(105107), pp. 1–10, 2008.
[18] Jiang, M., Machiraju, R. & Thompson, D., Detection and Visualization of Vortices, The Visualization Handbook, Academic Press, 2005.
[19] Günther, T. & Theisel, H., The state of the art in vortex extraction, Computer Graphics Forum, 37(6), pp. 149–173, 2018.
[20] Sujudi, D. & Haimes, R., Identification of swirling flow in 3-D vector fields, AIAA-95-1715-CP, 1995.
[21] Kida, S. & Miura, H., Identification and analysis of vortical structures. European Jour-nal of Mechanics – B/Fluids, 17(4), pp. 471–488, 1998.
[22] Peikert, R. & Roth, M., The “Parallel Vectors” operator – a vector field visualization primitive, Proceedings of IEEE Visualization ’99, pp. 263-270, 1999.
[23] Gelder, A.V. & Pang, A., Using PVsolve to analyse and locate positions of parallel vec-tors. IEEE Transactions on Visualization and Computer Graphics, 15(4), pp. 682–695, 2009.
[24] Schafhitzel, T., Vollrath, J.E., Gois, J.P., Weiskopf, D., Castelo, A. & Ertl, T., Topology-preserving λ2-based vortex core line detection for flow visualization, Computer Graph-ics Forum (Eurovis 2008), 27(3), pp. 1023–1030, 2008.
[25] Liu, C., et al., Third generation of vortex identification methods: Omega and Liutex/Rortex based systems. Journal of Hydrodynamics, 31(2), pp. 205–223, 2019.
[26] Gao, Y., Liu, J., Yu, Y. & Liu, C., A Liutex based definition and identification of vortex core center lines. Journal of Hydrodynamics, 31(3), pp. 445–454, 2019.
[27] Matsuura, K. & Kato, C., Large-eddy simulation of compressible transitional flows in a low-pressure turbine cascade. AIAA Journal, 45(2), pp. 442–457, 2007.
[28] Matsuura, K. & Nakano, M., A throttling mechanism sustaining a hole tone feedback system at very low Mach numbers, Journal of Fluid Mechanics, 710, pp. 569–605, 2012.
[29] Cebechi, T. & Smith, A.M.O, Analysis of Turbulent Boundary Layer, Academic Press: New York, 1974.
[30] Matsuura, K., DNS investigation into the effect of free-stream turbulence on hairpin-vortex evolution, WIT Transactions on Engineering Sciences, 120, pp. 149–159, 2018.
[31] Huang, H., Wu, S., Cohen-Or, D., Gong, M., Zhang, H., Li, G. & Chen, B., L1-medial skeleton of point cloud. ACM Transactions on Graphics, 32(4), pp. 1–8, 2013.
[32] Hirsch, C., Numerical Computation of Internal & External Flows, Second Edition, Butterworth-Heinemann, 2007.
[33] Matsuura, K., Hairpin vortex generation around a straight vortex tube in a laminar boundary-layer flow, arXiv: 1808.06510v1, pp. 1–41, 2018.
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Open Access
Research article

Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence

Kazuo Matsuura*
Graduate School of Science and Engineering, Ehime University, Japan
International Journal of Environmental Impacts
|
Volume 3, Issue 1, 2020
|
Pages 69-83
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: 01-21-2020
View Full Article|Download PDF

Abstract:

A new method that evaluates dominant local dynamics by skeletonization, mathematical term decom- position and the re-combination of a reduced number of dominant terms around the skeleton points is proposed to clarify the dynamics of hairpin vortices generated during the boundary-layer transition under free-stream turbulence (FST). The development of the method is based on the results of direct numerical simulations conducted for the laminar-turbulent transition on a flat plate with FST intensities of 0–6% and a free-stream Mach number of 0.5. Regarding the skeletonization, a new algorithm for extracting the interior points of vortex structures represented by enclosed iso-surfaces is developed. To identify the dominant terms, governing equations are decomposed into non-further-decomposable (NFD) terms. The proposed method is also extended to time series flow field data to reveal the variation of the combination set of dominant NFD terms during the evolution of vortex structures. The present method enables the automatic finding and categorization of the variations of the sets of dominant terms that govern local dynamics during the evolution of hairpin vortices.

Keywords: Boundary Layer, Direct Numerical Simulation, Hairpin Vortex, Laminar-Turbulent Transition, Stability, Turbulence
Acknowledgments

The present study was benefited from the outcome of a collaborative research project between Ehime University, Japan, and IHI Corporation. Computations were partly conducted using a supercomputer system at the Japan Aerospace Exploration Agency (JAXA-JSS2). This work was supported by a Grant for Basic Science Research Projects from the Sumitomo Founda-tion and the Institute of Statistical Mathematics (ISM) Cooperative Research Program 2016 ISM-CRP2019. Computational resources were provided by ISM and JAXA.

References
[1] Smith, C.R., Walker, J.D.A., Haidari, A.H. & Sobrun, U., On the dynamics of near-wall turbulence. Philosophical Transactions of the Royal Society A, 336, pp. 131–175, 1991.
[2] Theodorsen, T., Mechanism of turbulence. Proceeding of Second Midwestern Confer-ence on Fluid Mech., Bull., 149, Ohio State Univ., Columbus, Ohio, 1952.
[3] Lee, C.B. & Wu, J.Z., Transition in wall-bounded flows. Applied Mechanics Reviews, 61, pp. 030802-1-21, 2008.
[4] Robinson, S.K., Coherent motions in the turbulent boundary layer. Annual Review of Fluid Mechanics, 23(601), pp. 601-639, 1991.
[5] Robinson, S.K., The kinematics of turbulent boundary layer structure. NASA TM 103859, 1991.
[6] Panton, R., Overview of the self-sustaining mechanisms of wall turbulence. Progress in Aerospace Sciences, 37, pp. 341–383, 2001.
[7] Adrian, R.J., Hairpin vortex organization in wall turbulence. Physics of Fluids, 19, pp. 041301, 2007.
[8] Dennis, D.J.C, Coherent structures in wall-bounded turbulence. Annals of the Brazilian Academy of Sciences, 87(2), pp. 1161–1193, 2015.
[9] Moin, P., Leonard, A. & Kim, J., Evolution of a curved vortex filament into a vortex ring. Physics of Fluids, 29(4), pp. 955–963, 1986. 41.
[10] Hon, T.L. & Walker, J.D.A, Evolution of hairpin vortices in a shear flow. Computers and Fluids, 20(3), pp. 343–358, 1991.
[11] Singer, B.A. & Joslin, R.D., Metamorphosis of a hairpin vortex into a young turbulent spot. Physics of Fluids, 6(11), pp. 3724–3736, 1994.
[12] Zhou, J., Adrian, R.J. & Balachander, S, Autogeneration of near-wall vortical structures in channel flow. Physics of Fluids, 8(1), pp. 288–290, 1996.
[13] Zhou, J., Adrian, R.J. & Balachandar, S., Mechanisms for generating coherent packets of hairpin vortices in channel flow. Journal of Fluid Mechanics, 387, pp. 353–396, 1999.
[14] Liu, C. & Chen, L., Parallel DNS for vortex structure of late stages of flow transition. Computers & Fluids, 45, pp. 129–137, 2011.
[15] Cohen, J., Karp, M. & Mehta, V., A minimal flow-elements model for the generation of packets of hairpin vortices in shear flows. Journal of Fluid Mechanics, 747, pp. 30–43, 2014.
[16] Eitel-Amor, G., Örlu, R., Schlatter, P. & Flores, O., Hairpin vortices in turbulent bound-ary layers. Physics of Fluids. 27, pp. 025108, 2015.
[17] Kim, K., Sung, H. J. & Adrian, R.J., Effects of background noise on generating coher-ent packets of hairpin vorticies. Physics of Fluids. 20(105107), pp. 1–10, 2008.
[18] Jiang, M., Machiraju, R. & Thompson, D., Detection and Visualization of Vortices, The Visualization Handbook, Academic Press, 2005.
[19] Günther, T. & Theisel, H., The state of the art in vortex extraction, Computer Graphics Forum, 37(6), pp. 149–173, 2018.
[20] Sujudi, D. & Haimes, R., Identification of swirling flow in 3-D vector fields, AIAA-95-1715-CP, 1995.
[21] Kida, S. & Miura, H., Identification and analysis of vortical structures. European Jour-nal of Mechanics – B/Fluids, 17(4), pp. 471–488, 1998.
[22] Peikert, R. & Roth, M., The “Parallel Vectors” operator – a vector field visualization primitive, Proceedings of IEEE Visualization ’99, pp. 263-270, 1999.
[23] Gelder, A.V. & Pang, A., Using PVsolve to analyse and locate positions of parallel vec-tors. IEEE Transactions on Visualization and Computer Graphics, 15(4), pp. 682–695, 2009.
[24] Schafhitzel, T., Vollrath, J.E., Gois, J.P., Weiskopf, D., Castelo, A. & Ertl, T., Topology-preserving λ2-based vortex core line detection for flow visualization, Computer Graph-ics Forum (Eurovis 2008), 27(3), pp. 1023–1030, 2008.
[25] Liu, C., et al., Third generation of vortex identification methods: Omega and Liutex/Rortex based systems. Journal of Hydrodynamics, 31(2), pp. 205–223, 2019.
[26] Gao, Y., Liu, J., Yu, Y. & Liu, C., A Liutex based definition and identification of vortex core center lines. Journal of Hydrodynamics, 31(3), pp. 445–454, 2019.
[27] Matsuura, K. & Kato, C., Large-eddy simulation of compressible transitional flows in a low-pressure turbine cascade. AIAA Journal, 45(2), pp. 442–457, 2007.
[28] Matsuura, K. & Nakano, M., A throttling mechanism sustaining a hole tone feedback system at very low Mach numbers, Journal of Fluid Mechanics, 710, pp. 569–605, 2012.
[29] Cebechi, T. & Smith, A.M.O, Analysis of Turbulent Boundary Layer, Academic Press: New York, 1974.
[30] Matsuura, K., DNS investigation into the effect of free-stream turbulence on hairpin-vortex evolution, WIT Transactions on Engineering Sciences, 120, pp. 149–159, 2018.
[31] Huang, H., Wu, S., Cohen-Or, D., Gong, M., Zhang, H., Li, G. & Chen, B., L1-medial skeleton of point cloud. ACM Transactions on Graphics, 32(4), pp. 1–8, 2013.
[32] Hirsch, C., Numerical Computation of Internal & External Flows, Second Edition, Butterworth-Heinemann, 2007.
[33] Matsuura, K., Hairpin vortex generation around a straight vortex tube in a laminar boundary-layer flow, arXiv: 1808.06510v1, pp. 1–41, 2018.
Cite this:
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BibTex Style
MLA Style
Chicago Style
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Matsuura, K. (2020). Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence. Int. J. Environ. Impacts., 3(1), 69-83. https://doi.org/10.2495/EI-V3-N1-69-83
K. Matsuura, "Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence," Int. J. Environ. Impacts., vol. 3, no. 1, pp. 69-83, 2020. https://doi.org/10.2495/EI-V3-N1-69-83
@research-article{Matsuura2020AlgorithmicEO,
title={Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence},
author={Kazuo Matsuura},
journal={International Journal of Environmental Impacts},
year={2020},
page={69-83},
doi={https://doi.org/10.2495/EI-V3-N1-69-83}
}
Kazuo Matsuura, et al. "Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence." International Journal of Environmental Impacts, v 3, pp 69-83. doi: https://doi.org/10.2495/EI-V3-N1-69-83
Kazuo Matsuura. "Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence." International Journal of Environmental Impacts, 3, (2020): 69-83. doi: https://doi.org/10.2495/EI-V3-N1-69-83
Matsuura K.. Algorithmic Exploration of Dominant Terms Around Hairpin Vortices Generated During Boundary-Layer Transition Under Free-Stream Turbulence[J]. International Journal of Environmental Impacts， 2020， 3(1)： 69-83. https://doi.org/10.2495/EI-V3-N1-69-83