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DNS of a turbulent Couette flow at constant wall transpiration up to $Re_{\unicode[STIX]{x1D70F}}=1000$

  • S. Kraheberger (a1) (a2), S. Hoyas (a3) and M. Oberlack (a1) (a2)


We present a new set of direct numerical simulation data of a turbulent plane Couette flow with constant wall-normal transpiration velocity $V_{0}$ , i.e. permeable boundary conditions, such that there is blowing on the lower side and suction on the upper side. Hence, there is no net change in flux to preserve periodic boundary conditions in the streamwise direction. Simulations were performed at $Re_{\unicode[STIX]{x1D70F}}=250,500,1000$ with varying transpiration rates in the range $V_{0}^{+}\approx 0.03$ to 0.085. Additionally, a classical Couette flow case at $Re_{\unicode[STIX]{x1D70F}}=1000$ is presented for comparison. As a first key result we found a considerably extended logarithmic region of the mean velocity profile, with constant indicator function $\unicode[STIX]{x1D705}=0.77$ as transpiration increases. Further, turbulent intensities are observed to decrease with increasing transpiration rate. Mean velocities and intensities collapse only in the cases where the transpiration rate is kept constant, while they are largely insensitive to friction Reynolds number variations. The long and wide characteristic stationary rolls of classical turbulent Couette flow are still present for all present DNS runs. The rolls are affected by wall transpiration, but they are not destroyed even for the largest transpiration velocity case. Spectral information indicates the prevalence of the rolls and the existence of wide structures near the blowing wall. The statistics of all simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.


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del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.
Avsarkisov, V., Hoyas, S., Oberlack, M. & García-Galache, J. P. 2014a Turbulent plane Couette flow at moderately high Reynolds number. J. Fluid Mech. 751, R1.
Avsarkisov, V., Oberlack, M. & Hoyas, S. 2014b New scaling laws for turbulent Poiseuille flow with wall transpiration. J. Fluid Mech. 746, 99122.
Bech, K., Tillmark, N., Alfredsson, P. & Andersson, H. 1995 An investigation of turbulent plane Couette flow at low Reynolds numbers. J. Fluid Mech. 286, 291325.
Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to Re 𝜏 = 4000. J. Fluid Mech. 758, 327343.
Bobke, A., Örlü, R. & Schlatter, P. 2015 Simulations of turbulent asymptotic suction boundary layers. J. Turbul. 17 (2), 157180.
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189214.
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. J. Phys. A 2 (5), 765777.
Del Alamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20 (10), 101511.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergent zones in turbulent flows. In Proceedings of the 1988 Summer Program, Center for Turbulence Research. Stanford University.
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647664.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jiménez, J., Uhlman, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89117.
Kametani, Y., Fukagata, K., Örlü, R. & Schlatter, P. 2015 Effect of uniform blowing suction in a turbulent boundary layer at moderate Reynolds number. Intl J. Heat Fluid Flow 55, 132142.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channels flows at low Reynolds number. J. Fluid Mech. 177, 133166.
Kitoh, O., Nakabyashi, K. & Nishimura, F. 2005 Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structure. J. Fluid Mech. 539, 199227.
Kitoh, O. & Umeki, M. 2008 Experimental study on large-scale streak structure in the core region of turbulent plane Couette flow. Phys. Fluids 20 (2), 025107.
Komminaho, J., Lundbladh, A. & Johansson, A. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259–258.
Lam, K. & Banerjee, S. 1992 On teh condition of streak formation in a bounded turbulent flow. Phys. Fluids 4, 306320.
Lee, M. & Moser, R. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395415.
Lee, M. & Moser, R. 2017 Extreme-scale motions in turbulent plane Couette flows. J. Fluid Mech.; (under consideration for publication),
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 1642.
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re 𝜏 = 590. Phys. Fluids 11 (4), 943945.
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2011 Large-scale motions and inner/outer layer interactions in turbulent Couette–Poiseuille flows. J. Fluid Mech. 680, 534563.
Pirozzoli, S., Bernardini, M. & Orlandi, P. 2014 Turbulence statistics in Couette flow at high Reynolds number. J. Fluid Mech. 758, 323343.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Schlatter, P. & Örlü, R. 2011 Turbulent asymptotic suction boundary layers studied by simulation. J. Phys. Conf. Ser. 318, 022020.
Spalart, P. R. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297324.
Sumitani, Y. & Kasagi, N. 1995 Direct numerical simulation of turbulent transport with uniform wall injection and suction. AIAA J. 33, 12201228.
Tillmark, N.1995 Experiments on transition and turbulence in plane Couette flow. PhD thesis, KTH, Royal Institute of Technology.
Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7, 116.
Zhapbasbaev, U. K. & Isakhanova, G. Z. 1998 Developed turbulent flow in a plane channel with simultaneous injection through one porous wall and suction through the other. J. Appl. Mech. Tech. Phys. 39, 53.
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