Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

doi:10.1007/s10483-019-2500-8

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (7): 1041-1052.doi: https://doi.org/10.1007/s10483-019-2500-8

• 论文 • 上一篇

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

Qingxiang LI¹, Ming PAN¹, Quan ZHOU^1,2, Yuhong DONG^1,2

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

收稿日期:2018-06-12 修回日期:2018-12-12 出版日期:2019-07-01 发布日期:2019-07-01
通讯作者: Yuhong DONG E-mail:dongyh@staff.shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11572183, 91852111, and 11825204) and the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

Qingxiang LI¹, Ming PAN¹, Quan ZHOU^1,2, Yuhong DONG^1,2

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

Received:2018-06-12 Revised:2018-12-12 Online:2019-07-01 Published:2019-07-01
Contact: Yuhong DONG E-mail:dongyh@staff.shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11572183, 91852111, and 11825204) and the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)

摘要/Abstract

摘要： The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.

关键词: torsion of cracked cylinder, singular integral equations, boundary element method, stress intensity factor, direct numerical simulation (DNS), drag reduction, anisotropic porous medium, turbulent open channel flow

Abstract: The direct numerical simulation (DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.

Key words: torsion of cracked cylinder, singular integral equations, boundary element method, stress intensity factor, drag reduction, anisotropic porous medium, direct numerical simulation (DNS), turbulent open channel flow

中图分类号:

76T20

Qingxiang LI, Ming PAN, Quan ZHOU, Yuhong DONG. Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 1041-1052.

参考文献

[1] ZAGNI, A. F. E. and SMITH, K. V. H. Channel flow over permeable beds of graded spheres. Journal of the Hydraulics Division, 102, 207-222(1976)
[2] BREUGEM, W. P., BOERSMA, B. J., and UITTENBOGAARD, R. E. The influence of wall permeability on turbulent channel flow. Journal of Fluid Mechanics, 562, 35-72(2006)
[3] SUGA, K., MATSUMURA, Y., ASHITAKA, Y., TOMINAGA, S., and KANEDA, M. Effects of wall permeability on turbulence. International Journal of Heat and Fluid Flow, 31, 974-984(2010)
[4] TILTON, N. and CORTELEZZI, L. The destabilizing effects of wall permeability in channel flows:a linear stability analysis. Physics of Fluids, 18, 051702(2006)
[5] TILTON, N. and CORTELEZZI, L. Linear stability analysis of pressure-driven flows in channels with porous walls. Journal of Fluid Mechanics, 604, 411-445(2008)
[6] ROSTI, M. E., LUCA, C., and MAURIZIO, Q. Direct numerical simulation of turbulent channel flow over porous walls. Journal of Fluid Mechanics, 784, 396-442(2015)
[7] KUWATA, Y. and SUGA, K. Direct numerical simulation of turbulence over anisotropic porous media. Journal of Fluid Mechanics, 784, 41-71(2017)
[8] ROSTI, M. E., BRANDT, L., and PINELLI, A. Turbulent channel flow over an anisotropic porous wall-drag increase and reduction. Journal of Fluid Mechanics, 842, 381-394(2018)
[9] LUO, L. S. Unified theory of lattice Boltzmann models for nonideal gases. Physical Review Letters, 81(8), 1618-1621(1998)
[10] MARTYS, N. S. Improved approximation of the Brinkman equation using a lattice Boltzmann method. Physics of Fluids, 13, 1807-1810(2001)
[11] NITHIARASU, P., SEETHARAMU, K. N., and SUNDARARAJAN, T. Natural convective heat transfer in a fluid saturated variable porosity medium. International Journal of Heat and Mass Transfer, 40, 3955-3967(1997)
[12] TANG, Z., LIU, N. S., and DONG, Y. H. Lattice Boltzmann simulations of turbulent shear flow between parallel porous walls. Applied Mathematics and Mechanics (English Edition), 35, 1479-1494(2014) https://doi.org/10.1007/s10483-014-1885-6
[13] YADAV, P. K., JAISWAL, S., and SHARMA, B. D. Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel. Applied Mathematics and Mechanics (English Edition), 39, 993-1006(2018) https://doi.org/10.1007/s10483-018-2351-8
[14] LIU, Q., HE, Y. L., LI, Q., and TAO, W. Q. A multiple-relaxation-time lattice Boltzmann model for convection heat transfer in porous media. International Journal of Heat and Mass Transfer, 73, 761-775(2014)
[15] REES, D. A. S. and STORESLETTEN, L. The effect of anisotropic permeability on free convective boundary layer flow in porous media. Transport in Porous Media, 19, 79-92(1995)
[16] KRISHNA, D. J., BASAK, T., and DAS, S. K. Natural convection in a heat generating hydrodynamically and thermally anisotropic non-Darcy porous medium. International Journal of Heat and Mass Transfer, 51, 4691-4703(2008)
[17] ERGUN, S. Fluid flow through packed columns. Chemical Engineering Progress, 48, 89-94(1952)
[18] GUO, Z. and ZHAO, T. S. Lattice Boltzmann model for incompressible flows through porous media. Physical Review E, 66, 036304(2002)
[19] KIM, J. and MOIN, P. Application of a frational-step method to incompressible Navier-Stokes equations. Journal of Computational Physics, 59, 308-323(1985)
[20] VERZICCO, R. and ORLANDI, P. A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. Journal of Computational Physics, 123, 402-414(1996)
[21] MOIN, P. and KIM, J. Numerical investigation of turbulent channel flow. Journal of Fluid Mechanics, 118, 341-377(1982)
[22] HANDLER, R. A., SAYLOR, J. R., LEIGHTON, R. I., and ROVELSTAD, A. L. Transport of a passive scalar at a shear-free boundary in fully developed turbulent open channel flow. Physics of Fluids, 11, 2607-2625(1999)
[23] WANG, L., DONG, Y. H., and LU, X. Y. An investigation of turbulent open channel flow with heat transfer by large eddy simulation. Computers and Fluids, 34, 23-47(2005)
[24] KOMORI, S., NAGAOSA, R., MURAKAMI, Y., CHIBA, S., ISHⅡ, K., and KUWAHARA, K. Direct numerical simulation of three-dimensional open-channel flow with zero-shear gas-liquid interface. Physics of Fluids A:Fluid Dynamics, 5, 115-125(1993)
[25] MORINISHI, Y., LUND, T. S., VASILYEV, O. V., and MOIN, P. Fully conservative higher order finite difference schemes for incompressible flow. Journal of Computational Physics, 19, 90-124(1998)
[26] DONG, Y. H. and LU, X. Y. Direct numerical simulation of stably and unstably stratified turbulent open channel flows. Acta Mechanica, 177, 115-136(2005)
[27] LIU, C., TANG, S., DONG, Y. H., and SHEN, L. Heat transfer modulation by inertial particles in particle-laden turbulent channel flow. Journal of Heat Transfer, 140, 112003(2018)
[28] RAUPACH, M. R., ANTONIA, R. A., and RAJAGOPALAN, S. Rough-wall turbulent boundary layers. Applied Mechanics Reviews, 44, 1-25(1991)
[29] WU, W. T., HONG, Y. J., and FAN, B. C. Numerical investigation of turbulent channel flow controlled by spatially oscillating spanwise Lorentz force. Applied Mathematics and Mechanics (English Edition), 36, 1113-1120(2015) https://doi.org/10.1007/s10483-015-1972-6
[30] NIKURADSE, J. Strömungswiderstand in rauhen Rohren. Journal of Applied Mathematics and Mechanics, 11, 409-411(1931)
[31] EL-SAMNI, O. A., CHUN, H. H., and YOON, H. S. Drag reduction of turbulent flow over thin rectangular riblets. International Journal of Engineering Science, 45, 436-454(2007)
[32] GARCÍA-MAYORAL, R. and JIMÉNEZ, J. Drag reduction by riblets. Philosophical Transactions of the Royal Society of London A:Mathematical, Physical and Engineering Sciences, 369, 1412- 1427(2011)
[33] CHOI, K. S. Smart flow control with riblets. Advanced Materials Research, 745, 27-40(2013)
[34] FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14, L73-L76(2002)
[35] CHOI, H., MOIN, P., and KIM, J. Direct numerical simulation of turbulent flow over riblets. Journal of Fluid Mechanics, 255, 503-539(1993)
[36] LUO, H. X. and BEWLEY, T. R. Design, modeling, and optimization of compliant tensegrity fabrics for the reduction of turbulent skin friction. Smart Structures and Materials 2003:Modeling, Signal Processing, and Control, 5049, 460-470(2003)
[37] JIMENEZ, J., UHLMANN, M., PINELLI, A., and KAWAHARA, G. Turbulent shear flow over active and passive porous surfaces. Journal of Fluid Mechanics, 442, 89-117(2001)
[38] PEROT, B. and MOIN, P. Shear-free turbulent boundary layers I:physical insights into near-wall turbulence. Journal of Fluid Mechanics, 295, 199-227(1995)
[39] BERNARD, P. S., THOMAS, J. M., and HANDLER, R. A. Vortex dynamics and the production of Reynolds stress. Journal of Fluid Mechanics, 253, 385-419(1993)
[40] KASAGI, N., SUMITANI, Y., SUZUKI, Y., and ⅡDA, O. Kinematics of the quasi-coherent vortical structure in near-wall turbulence. Experimental Heat Transfer Fluid Mechanics and Thermodynamics, 16, 2-10(1995)
[41] PAN, M., LI, Q. X., TANG, S., and DONG, Y. H. Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method. Applied Mathematics and Mechanics (English Edition), 39, 1-12(2018) https://doi.org/10.1007/s10483-018-2316-8
[42] CHOI, K. S. Near-wall structure of a turbulent boundary layer with riblets. Journal of Fluid Mechanics, 208, 417-458(1989)
[43] WILLMARTH, W. W. and LU, S. S. Structure of the Reynolds stress near the wall. Journal of Fluid Mechanics, 55, 65-92(1972)
[44] LIU, C. X., TANG, S., and DONG, Y. H. Effect of inertial particles with different specific heat capacities on heat transfer in particle-laden turbulent flow. Applied Mathematics and Mechanics (English Edition), 38, 1-10(2017) https://doi.org/10.1007/s10483-017-2224-9

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Haoyang LI, Weijian LIU, Yuhong DONG. A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1597-1612.
[2]	Huayang DANG, Dongpei QI, Minghao ZHAO, Cuiying FAN, C.S. LU. Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 841-856.
[3]	Yansong WANG, Baolin WANG, Youjiang CUI, Kaifa WANG. Anti-plane pull-out of a rigid line inclusion from an elastic medium[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 809-822.
[4]	Chenxue JIA, Zihao WANG, Donghui ZHANG, Taihua ZHANG, Xianhong MENG. Fracture of films caused by uniaxial tensions: a numerical model[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2093-2108.
[5]	Juan PENG, Dengke LI, Zaixing HUANG, Guangjian PENG, Peijian CHEN, Shaohua CHEN. Interfacial behavior of a thermoelectric film bonded to a graded substrate[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1853-1870.
[6]	Zheng HONG, Zhengyin YE, Kangling WU, Kun YE. Effect of anisotropic resistance characteristic on boundary-layer transitional flow[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1935-1950.
[7]	Bofu WANG, Qiang WANG, Quan ZHOU, Yulu LIU. Active control of flow past an elliptic cylinder using an artificial neural network trained by deep reinforcement learning[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1921-1934.
[8]	Xin ZHANG, Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1901-1920.
[9]	Hongxiao YAO, Weian YAO, Chong ZUO, Xiaofei HU. Radial integral boundary element method for simulating phase change problem with mushy zone[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1155-1170.
[10]	A. T. TRAN, H. LE QUANG, Q. C. HE, D. H. NGUYEN. Mathematical modeling and numerical computation of the effective interfacial conditions for Stokes flow on an arbitrarily rough solid surface[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 721-746.
[11]	Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1633-1648.
[12]	W. T. ANG, X. WANG. A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(4): 551-566.
[13]	Xing ZHAO, Zhenghua QIAN, Jinxi LIU, Cunfa GAO. Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 139-156.
[14]	M. KARIMI, A. GHASSEMI, A. ATRIAN, M. VAHABI. Compensation of stress intensity factors in hollow cylinders containing several cracks under torsion by electro-elastic coating[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1335-1360.
[15]	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.