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

Qingxiang LI, Ming PAN, Quan ZHOU, Yuhong DONG

doi:10.1007/s10483-019-2500-8

Applied Mathematics and Mechanics >

2019 , Vol. 40 >Issue 7: 1041 - 1052

DOI: https://doi.org/10.1007/s10483-019-2500-8

Articles

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

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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 date: 2018-06-12

Revised date: 2018-12-12

Online published: 2019-07-01

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)

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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

Cite this article

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, 2019 , 40(7) : 1041 -1052 . DOI: 10.1007/s10483-019-2500-8

References

[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

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