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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 Transaction of the Royal Socirty A, 336, pp. 131–175, 1991. [Crossref]
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Theodorsen, T., Mechanism of turbulence. Proceeding of Second Midwestern Confer- ence on Fluid Mechanics Bulls, Ohio State University: Columbus, Ohio, 149, 1952.
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Lee, C.B. & Wu, J.Z., Transition in wall-bounded flows. Applied Mechanics Reviews,
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Robinson, S.K., Coherent motions in the turbulent boundary layer. Annual Reviews Fluid Mechanics, 23(601), pp. 601–639, 1991. [Crossref]
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Robinson, S.K., The kinematics of turbulent boundary layer structure. NASA TM
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Panton, R., Overview of the self-sustaining mechanisms of wall turbulence. Progress in Aerospace Sciences, 37, pp. 341–383, 2001.
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Adrian, R.J., Hairpin vortex organization in wall turbulence. Physics of Fluids, 19, 041301, 2007.
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Dennis, D.J.C., Coherent structures in wall-bounded turbulence. Annals of the Brazilian Academy of Sciences, 87(2), pp. 1161–1193, 2015.
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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.
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Acarlar, M. & Smith, C., A study of hairpin vortices in a laminar boundary layer. Part I. Hairpin vortices generated by a hemisphere protuberance. Journal of Fluid Mechanics, 175, pp. 1–41, 1987.
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Hon, T.L. & Walker, J.D.A., Evolution of hairpin vortices in a shear flow. Computers and Fluids, 20(3), pp. 343–358, 1991.
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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. [Crossref]
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Zhou, J., Adrian, R.J. & Balachander, S., Autogeneration of near-wall vortical struc- tures in channel flow. Physics of Fluids, 8(1), pp. 288–290, 1996. [Crossref]
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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.
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Liu, C. & Chen, L., Parallel DNS for vortex structure of late stages of flow transition. Computers & Fluids, 45, pp. 129–137, 2011. [Crossref]
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Duguet, Y., Schlatter, P., Henningson, D. & Eckhardt, B., Self-sustained localized struc- tures in a boundary-layer flow. Physics Revised Letters, 108, 044501, 2012. [Crossref]
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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.
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Eitel-Amor, G., Örlu, R., Schlatter, P. & Flores, O., Hairpin vortices in turbulent bound- ary layers. Physics of Fluids, 27, 025108, 2015.
19.
Sabatino, D.R. & Maharjan, R., Characterizing the formation and regeneration of hairpin vortices in a laminar boundary layer. Physics of Fluids, 27, 124104, 2015.
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Moore, D.W., Finite amplitude waves on aircraft trailing vortices. Aeronautical Quarterly, 23, pp. 307–314, 1972.
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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. [Crossref]
22.
Cebechi, T. & Smith, A.M.O., Analysis of Turbulent Boundary Layer, Academic Press: New York, 1974.
23.
Matsuura, K., Numerical simulation of a straight vortex tube in the shear of a laminar boundary-layer flow. Proceeding of AsiaSim, pp. 1–2, 2015.
24.
Chassaing, P., Antonia, R.A., Anselmet, F., Joly, L. & Sarkar, S., Variable Density Fluid Turbulence, Kluwer Academic Publishers, 2010.
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Malik, M.R., Numerical methods for hypersonic boundary layer stability. Journal of Computational Physics, 86(2), pp. 376–413, 1990.
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Open Access
Research article

Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow

k. matsuura
Graduate School of Science and Engineering, Ehime University, Japan
International Journal of Computational Methods and Experimental Measurements
|
Volume 4, Issue 4, 2016
|
Pages 474-483
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

Effects of circulation on the evolution of vortex tubes and the associated response of near-wall flows in the shear of laminar boundary-layer flows are investigated using a model proposed by Hon and Walker (Hon, T.L. & Walker, J.D.A, Computers & Fluids, 20(3), pp. 343–358, 1991). Direct numerical simula- tions with freestream Mach number of 0.5 are conducted. Firstly, the dynamics of single hairpin vortex is investigated. Numerous secondary hairpin vortices, much more than previously reported, which are regularly aligned in the streamwise direction are allowed to be newly generated according to the shear-layer instability of the legs of an initial hairpin vortex. Small-scale turbulence is then produced when the circulation is sufficiently large. Secondly, a straight vortex tube model is investigated. Sinu- ous deformation of a shear layer, which leads to the generation of discrete hairpin vortices, becomes obvious especially near the upper region of the vortex tube. In order to quantify the initial instability triggering the generation of the secondary hairpin vortices, quasi-linear stability analysis is conducted. While only one unstable mode appears when the circulation is small, two modes, that is, off-wall mode and near-wall mode, appear when the circulation is large. The cases of circulation where the two modes appear correspond to those of circulation where the production of small-scale turbulence is observed in the simulations of the single hairpin vortex.

Keywords: Boundary layer, Direct numerical simulation, Hairpin vortex, Laminar-turbulent transition, Stability, Turbulence, Vortex tube

1. Introduction

2. Computational Details

3. Results and Discussion

4. Conclusions

Acknowledgments

This work was supported by Grant for Basic Science Research Projects from the Sumitomo Foundation and the Institute of Statistical Mathematics (ISM) Cooperative Research Program 2016 ISM-CRP2019. Computational resources are provided by ISM and Japan Aerospace Exploration Agency (JAXA).

References
1.
Smith, C.R., Walker, J.D.A., Haidari, A.H. & Sobrun, U., On the dynamics of near-wall turbulence. Philosophical Transaction of the Royal Socirty A, 336, pp. 131–175, 1991. [Crossref]
2.
Theodorsen, T., Mechanism of turbulence. Proceeding of Second Midwestern Confer- ence on Fluid Mechanics Bulls, Ohio State University: Columbus, Ohio, 149, 1952.
3.
Lee, C.B. & Wu, J.Z., Transition in wall-bounded flows. Applied Mechanics Reviews,
4.
Robinson, S.K., Coherent motions in the turbulent boundary layer. Annual Reviews Fluid Mechanics, 23(601), pp. 601–639, 1991. [Crossref]
5.
Robinson, S.K., The kinematics of turbulent boundary layer structure. NASA TM
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, 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.
10.
Acarlar, M. & Smith, C., A study of hairpin vortices in a laminar boundary layer. Part I. Hairpin vortices generated by a hemisphere protuberance. Journal of Fluid Mechanics, 175, pp. 1–41, 1987.
11.
Hon, T.L. & Walker, J.D.A., Evolution of hairpin vortices in a shear flow. Computers and Fluids, 20(3), pp. 343–358, 1991.
12.
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. [Crossref]
13.
Zhou, J., Adrian, R.J. & Balachander, S., Autogeneration of near-wall vortical struc- tures in channel flow. Physics of Fluids, 8(1), pp. 288–290, 1996. [Crossref]
14.
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.
15.
Liu, C. & Chen, L., Parallel DNS for vortex structure of late stages of flow transition. Computers & Fluids, 45, pp. 129–137, 2011. [Crossref]
16.
Duguet, Y., Schlatter, P., Henningson, D. & Eckhardt, B., Self-sustained localized struc- tures in a boundary-layer flow. Physics Revised Letters, 108, 044501, 2012. [Crossref]
17.
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.
18.
Eitel-Amor, G., Örlu, R., Schlatter, P. & Flores, O., Hairpin vortices in turbulent bound- ary layers. Physics of Fluids, 27, 025108, 2015.
19.
Sabatino, D.R. & Maharjan, R., Characterizing the formation and regeneration of hairpin vortices in a laminar boundary layer. Physics of Fluids, 27, 124104, 2015.
20.
Moore, D.W., Finite amplitude waves on aircraft trailing vortices. Aeronautical Quarterly, 23, pp. 307–314, 1972.
21.
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. [Crossref]
22.
Cebechi, T. & Smith, A.M.O., Analysis of Turbulent Boundary Layer, Academic Press: New York, 1974.
23.
Matsuura, K., Numerical simulation of a straight vortex tube in the shear of a laminar boundary-layer flow. Proceeding of AsiaSim, pp. 1–2, 2015.
24.
Chassaing, P., Antonia, R.A., Anselmet, F., Joly, L. & Sarkar, S., Variable Density Fluid Turbulence, Kluwer Academic Publishers, 2010.
25.
Malik, M.R., Numerical methods for hypersonic boundary layer stability. Journal of Computational Physics, 86(2), pp. 376–413, 1990.
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Matsuura, K. (2016). Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow. Int. J. Comput. Methods Exp. Meas., 4(4), 474-483. https://doi.org/10.2495/CMEM-V4-N4-474-483
K. Matsuura, "Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow," Int. J. Comput. Methods Exp. Meas., vol. 4, no. 4, pp. 474-483, 2016. https://doi.org/10.2495/CMEM-V4-N4-474-483
@research-article{Matsuura2016DirectNS,
title={Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow},
author={K. Matsuura},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2016},
page={474-483},
doi={https://doi.org/10.2495/CMEM-V4-N4-474-483}
}
K. Matsuura, et al. "Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow." International Journal of Computational Methods and Experimental Measurements, v 4, pp 474-483. doi: https://doi.org/10.2495/CMEM-V4-N4-474-483
K. Matsuura. "Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow." International Journal of Computational Methods and Experimental Measurements, 4, (2016): 474-483. doi: https://doi.org/10.2495/CMEM-V4-N4-474-483
MATSUURA K. Direct Numerical Simulation of A Straight Vortex Tube in A Laminar Boundary-Layer Flow[J]. International Journal of Computational Methods and Experimental Measurements， 2016， 4(4)： 474-483. https://doi.org/10.2495/CMEM-V4-N4-474-483