Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

doi:10.1007/s10483-019-2442-8

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (3): 331-342.doi: https://doi.org/10.1007/s10483-019-2442-8

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

Yitong FAN¹, Cheng CHENG¹, Weipeng LI^1,2

1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China;
2. Engineering Research Center of Gas Turbine and Civil Aero Engine, Shanghai 200240, China

收稿日期:2018-09-05 修回日期:2018-11-02 出版日期:2019-03-01 发布日期:2019-03-01
通讯作者: Weipeng LI E-mail:liweipeng@sjtu.edu.cn
基金资助:
Project supported by the National Basic Research Program of China (973 Program) (No. 2014CB744802) and the National Natural Science Foundation of China (No. 11772194)

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

Yitong FAN¹, Cheng CHENG¹, Weipeng LI^1,2

1. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China;
2. Engineering Research Center of Gas Turbine and Civil Aero Engine, Shanghai 200240, China

Received:2018-09-05 Revised:2018-11-02 Online:2019-03-01 Published:2019-03-01
Contact: Weipeng LI E-mail:liweipeng@sjtu.edu.cn
Supported by:
Project supported by the National Basic Research Program of China (973 Program) (No. 2014CB744802) and the National Natural Science Foundation of China (No. 11772194)

摘要/Abstract

摘要： As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Re_τ=5 200 are investigated based on two different methods, i.e., the FukagataIwamoto-Kasagi (FIK) identity (FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73-L76 (2002)) and the Renard-Deck (RD) identity (DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. É. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Re_θ=13 650. Journal of Fluid Mechanics, 743, 202-248 (2014)). The direct numerical simulation (DNS) data provided by Lee and Moser (LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Re_τ ≈ 5 200. Journal of Fluid Mechanics, 774, 395-415 (2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers. The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

关键词: hemodynamics, arteria coronaria sinistra, atherosis, mean skin friction, turbulent channel flow, Reynolds number effect, drag decomposition

Abstract: As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Re_τ=5 200 are investigated based on two different methods, i.e., the FukagataIwamoto-Kasagi (FIK) identity (FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73-L76 (2002)) and the Renard-Deck (RD) identity (DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. É. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Re_θ=13 650. Journal of Fluid Mechanics, 743, 202-248 (2014)). The direct numerical simulation (DNS) data provided by Lee and Moser (LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Re_τ ≈ 5 200. Journal of Fluid Mechanics, 774, 395-415 (2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers. The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

Key words: hemodynamics, arteria coronaria sinistra, atherosis, drag decomposition, turbulent channel flow, mean skin friction, Reynolds number effect

中图分类号:

76F40

Yitong FAN, Cheng CHENG, Weipeng LI. Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(3): 331-342.

参考文献

[1] GARIÉPY, M., TRÉPANIER, J. Y., and MALOUIN, B. Generalization of the far-field drag decomposition method to unsteady flows. AIAA Journal, 51(6), 1309-1319(2013)
[2] GAD-EL-HAK, M. Interactive control of turbulent boundary layers:a futuristic overview. AIAA Journal, 32(9), 1753-1765(1994)
[3] DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. É. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Re_θ=13650. Journal of Fluid Mechanics, 743, 202-248(2014)
[4] FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73-L76(2002)
[5] GOMEZ, T., FLUTET, V., and SAGAUT, P. Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Physical Review E, 79(3), 035301(2009)
[6] BANNIER, A., GARNIER, É., and SAGAUT, P. Riblet flow model based on an extended FIK identity. Flow, Turbulence and Combustion, 95, 351-376(2015)
[7] PEET, Y. and SAGAUT, P. Theoretical prediction of turbulent skin friction on geometrically complex surfaces. Physics of Fluids, 21(10), 105105(2009)
[8] MEHDI, F. and WHITE, C. M. Integral form of the skin friction coefficient suitable for experimental data. Experiments in Fluids, 50(1), 43-51(2011)
[9] MEHDI, F., JOHANSSON, T. G., WHITE, C. M., and NAUGHTON, J. W. On determining wall shear stress in spatially developing two-dimensional wall-bounded flows. Experiments in Fluids, 55, 1656(2014)
[10] LI, F. C., KAWAGUCHI, Y., SEGAWA, T., and HISHIDA, K. Reynolds-number dependence of turbulence structures in a drag-reducing surfactant solution channel flow investigated by particle image velocimetry. Physics of Fluids, 17(7), 075104(2005)
[11] DE GIOVANETTI, M., HWANG, Y., and CHOI, H. Skin-friction generation by attached eddies in turbulent channel flow. Journal of Fluid Mechanics, 808, 511-538(2016)
[12] YOON, M., AHN, J., HWANG, J., and SUNG, H. J. Contribution of velocity-vorticity correlations to the frictional drag in wall-bounded turbulent flows. Physics of Fluids, 28(8), 081702(2016)
[13] RENARD, N. and DECK, S. A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer. Journal of Fluid Mechanics, 790, 339-367(2016)
[14] KIM, J. Control of turbulent boundary layers. Physics of Fluids, 15(5), 1093-1105(2003)
[15] WHITE, C. M. and MUNGAL, M. G. Mechanics and prediction of turbulent drag reduction with polymer additives. Annual Review Fluid Mechanics, 40, 235-256(2008)
[16] TOUBER, E. and LESCHZINER, M. A. Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. Journal of Fluid Mechanics, 693, 150-200(2012)
[17] KAMETANI, Y. and FUKAGATA, K. Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction. Journal of Fluid Mechanics, 681, 154-172(2011)
[18] BHUSHAN, B. Shark-skin surface for fluid-drag reduction in turbulent flow. Biomimetics, Springer, Cham, 227-265(2016)
[19] CHOI, H., MOIN, P., and KIM, J. Direct numerical simulation of turbulent flow over riblets. Journal of Fluid Mechanics, 255, 503-539(1993)
[20] GATTI, D., QUADRIO, M., and FROHNAPFEL, B. Reynolds number effect on turbulent drag reduction. 5th European Turbulence Conference, University of Delft, Delft (2015)
[21] ROBINSON, S. K. The Kinematics of Turbulent Boundary Layer Structure, National Aeronautics and Space Administration, Washington, D. C. (1991)
[22] ABBASSI, M. R., BAARS, W. J., HUTCHINS, N., and MARUSIC, I. Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures. International Journal of Heat and Fluid Flow, 67, 30-41(2017)
[23] HWANG, Y. Near-wall turbulent fluctuations in the absence of wide outer motions. Journal of Fluid Mechanics, 723, 264-288(2013)
[24] LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Re_τ ≈ 5200. Journal of Fluid Mechanics, 774, 395-415(2015)
[25] KIM, J., MOIN, P., and MOSER, R. Turbulence statistics in fully developed channel flow at low Reynolds number. Journal of Fluid Mechanics, 177, 133-166(1987)
[26] LEE, M., MALAYA, N., and MOSER, R. D. Petascale direct numerical simulation of turbulent channel flow on up to 786 K cores. Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, Association for Computing Machinery, New York (2013)
[27] LEE, M., ULERICH, R., MALAYA, N., and MOSER, R. D. Experiences from leadership computing in simulations of turbulent fluid flows. Computing in Science & Engineering, 16(5), 24-31(2014)
[28] OLIVER, T. A., MALAYA, N., ULERICH, R., and MOSER, R. D. Estimating uncertainties in statistics computed from direct numerical simulation. Physics of Fluids, 26(3), 035101(2014)
[29] DEAN, R. B. Reynolds number dependence of skin friction and other bulk flow variables in twodimensional rectangular duct flow. Journal of Fluids Engineering, 100(2), 215-223(1978)
[30] ABE, H. and ANTONIA, R. A. Relationship between the energy dissipation function and the skin friction law in a turbulent channel flow. Journal of Fluid Mechanics, 798, 140-164(2016)
[31] LAADHARI, F. Reynolds number effect on the dissipation function in wall-bounded flows. Physics of Fluids, 19(3), 038101(2007)
[32] HINZE, J. O. Turbulence, McGraw-Hill, New York (1975)
[33] KIM, K. C. and ADRIAN, R. J. Very large-scale motion in the outer layer. Physics of Fluids, 11(2), 417-422(1999)
[34] LIU, Z., ADRIAN, R. J., and HANRATTY, T. J. Large-scale modes of turbulent channel flow:transport and structure. Journal of Fluid Mechanics, 448, 53-80(2001)
[35] HWANG, J. and SUNG, H. J. Influence of large-scale motions on the frictional drag in a turbulent boundary layer. Journal of Fluid Mechanics, 829, 751-779(2017)
[36] BALAKUMAR, B. J. and ADRIAN, R. J. Large- and very-large-scale motions in channel and boundary-layer flows. Philosophical Transactions of the Royal Society of London A:Mathematical, Physical and Engineering Sciences, 365(1852), 665-681(2007)
[37] IWAMOTO, K., FUKAGATA, K., KASAGI, N., and SUZUKI, Y. Friction drag reduction achievable by near-wall turbulence manipulation at high Reynolds numbers. Physics of Fluids, 17(1), 011702(2005)
[38] DENG, B. Q. Research on Mechanism of Drag-Reduction Control Based on Coherent Structures in Wall-Turbulence (in Chinese), Ph. D. dissertation, Tsinghua University (2014)

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 10

编辑推荐

Metrics

本文评价

[1]	Kunpeng WANG, Qingxiang LI, Yuhong DONG. Transport of dissolved oxygen at the sediment-water interface in the spanwise oscillating flow[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(4): 527-540.
[2]	Erhui WANG, Xuelan ZHANG, Liancun ZHENG, Chang SHU. Machine learning of synaptic structure with neurons to promote tumor growth[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(11): 1697-1706.
[3]	Daiwen JIANG, Hui ZHANG, Baochun FAN, Zijie ZHAO, Jian LI, Mingyue GUI. Numerical study of the turbulent channel flow under space-dependent electromagnetic force control at different Reynolds numbers[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(4): 435-448.
[4]	Zhaosheng YU, Chenlin ZHU, Yu WANG, Xueming SHAO. Effects of finite-size neutrally buoyant particles on the turbulent channel flow at a Reynolds number of 395[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(2): 293-304.
[5]	Zhaoyu SHI, Jincai CHEN, Guodong JIN. Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(11): 1605-1616.
[6]	Mingwei GE, Guodong JIN. Response of turbulent enstrophy to sudden implementation of spanwise wall oscillation in channel flow[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(8): 1159-1170.
[7]	Wentang WU, Yanji HONG, Baochun FAN. Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1113-1120.
[8]	K. GAYATHRI K. SHAILENDHRA. Pulsatile blood flow in large arteries: comparative study of Burton’s and McDonald’s models[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(5): 575-590.
[9]	葛铭纬许春晓黄伟希崔桂香. Transient response of enstrophy transport to opposition control in turbulent channel flow[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(2): 127-138.
[10]	黄景泉;李竞梅. AN ANALYSIS OF HEMODYNAMICS OF THE ANTERIOR DESCENDING BRANCH OF THE ARTERIA CORONARIA SINISTRA[J]. Applied Mathematics and Mechanics (English Edition), 1993, 14(9): 853-858.