logo

SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 62, Issue 4: 044711(2019) https://doi.org/10.1007/s11433-018-9310-4

Numerical investigation of plane Couette flow with weak spanwise rotation

More info
  • ReceivedJun 29, 2018
  • AcceptedOct 8, 2018
  • PublishedDec 7, 2018
PACS numbers

Abstract

Direct numerical simulation of rotating plane Couette flow (RPCF) at $Re_w=1300$ and $Ro=0.02$ was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with $\Delta~x^+=8.51,~\Delta~z^+=4.26$, $\Delta~y^+|_{\text{min}}=0.0873$ and $\Delta~y^+|_{\text{max}}=3.89$ is fine enough to simulate the problem at the present parameters. The streamwise length $L_x$ and spanwise length $L_z$ of the computational box have different impacts on the flow statistics, where the statistics were converged if $L_x$ is longer than $8\pi~h$, while no converged results were obtained for different $L_z$. More importantly, our results with very long simulation time showed that a state transition would happen if $L_x\geq~8\pi~h$, from a state with four pairs of roll cells to a state with three pairs of roll cells with $L_z=6\pi~h$. Each state could survive for more than $1500h/U_w$, and the flow statistics were different.


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11822208, 11772297, 11672123, and 91752201). The simulations were run on the TH-2A super computer in Guangzhou and the supercomputer in Southern University of Science and Technology of China.


References

[1] Lezius D. K., Johnston J. P.. 1976, 77: 153 CrossRef Google Scholar

[2] Alfredsson P. H., Persson H.. 1989, 202: 543-557 CrossRef ADS Google Scholar

[3] N. Tillmark, and P. H. Alfredsson, in Advances in Turbulence VI, edited by S. Gavrilakis, L. Machiels, and P. A. Monkewitz (Kluwer, The Netherlands, 1996), pp. 391--394. Google Scholar

[4] H. Alfredsson, and N. Tillmark, in IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions, edited by T. Mullin, and R. Kerswell (Springer Netherlands, Dordrecht, 2005), pp. 173--193. Google Scholar

[5] Hiwatashi K., Alfredsson P. H., Tillmark N., Nagata M.. 2007, 19: 048103 CrossRef ADS Google Scholar

[6] Tsukahara T., Tillmark N., Alfredsson P. H.. 2010, 648: 5 CrossRef Google Scholar

[7] Suryadi A., Tillmark N., Alfredsson P. H.. 2013, 54: 1617 CrossRef ADS Google Scholar

[8] Suryadi A., Segalini A., Alfredsson P. H.. 2014, 89: 033003 CrossRef PubMed ADS Google Scholar

[9] Kawata T., Alfredsson P. H.. 2016, 791: 191-213 CrossRef ADS Google Scholar

[10] Kawata T., Alfredsson P. H.. 2016, 1: 034402 CrossRef Google Scholar

[11] K. H. Bech, and H. I. Andersson, in Advances in Turbulence VI, edited by S. Gavrilakis, L. Machiels, and P. A. Monkewitz (Kluwer, The Netherlands, 1996), pp. 91--94. Google Scholar

[12] Bech K. H., Andersson H. I.. 1996, 317: 195-214 CrossRef ADS Google Scholar

[13] Komminaho J., Lundbladh A., Johansson A. V.. 1996, 320: 259 CrossRef Google Scholar

[14] Bech K. H., Andersson H. I.. 1997, 347: 289-314 CrossRef ADS Google Scholar

[15] Nagata M.. 1998, 358: 357-378 CrossRef Google Scholar

[16] M. Barri, and H. I. Andersson, in Advances in Turbulence XI, edited by J. M. L. M. Palma, and A. Silva Lopes (Springer-Verlag, Berlin Heidelberg, 2007), pp. 100--102. Google Scholar

[17] Barri M., Andersson H. I.. 2009, CrossRef Google Scholar

[18] Tsukahara T.. 2011, 318: 022024 CrossRef ADS Google Scholar

[19] Salewski M., Eckhardt B.. 2015, 27: 045109 CrossRef Google Scholar

[20] Gai J., Xia Z., Cai Q., Chen S.. 2016, 1: 054401 CrossRef Google Scholar

[21] Cai Q., Gai J., Sun Z., Xia Z.. 2016, 17 CrossRef Google Scholar

[22] J. Gai, Z. Liu, J. Luo, Q. Cai, and Z. Xia, Acta. Phys. Sin. 65, 244703 (2016). Google Scholar

[23] Kim J., Moin P., Moser R.. 1987, 177: 133-166 CrossRef ADS Google Scholar

[24] Lee M., Moser R. D.. 2015, 774: 395-415 CrossRef ADS arXiv Google Scholar

[25] K. H. Bech, and H. I. Andersson, in Direct and Large-Eddy Simulation I: Selected papers from the First ERCOFTAC Workshop on Direct and Large-Eddy Simulation, edited by P. R Voke, L. Kleiser, and J.-P. Chollet (Springer, Dordrecht, 1994), pp. 13--24. Google Scholar

[26] Yang Z., Wang B. C.. 2018, 838: 658-689 CrossRef ADS Google Scholar

[27] Dai Y. J., Huang W. X., Xu C. X.. 2016, 28: 115104 CrossRef ADS Google Scholar

[28] Xia Z., Shi Y., Chen S.. 2016, 788: 42-56 CrossRef ADS Google Scholar

[29] Guo Y., Finlay W. H.. 1991, 228: 661 CrossRef Google Scholar

[30] Huisman S. G., van der Veen R. C. A., Sun C., Lohse D.. 2014, 5: 3820 CrossRef PubMed ADS arXiv Google Scholar

[31] Xia Z., Shi Y., Cai Q., Wan M., Chen S.. 2018, 837: 477-490 CrossRef ADS Google Scholar

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1