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Related turbulent momentum and passive scalar transfer in a turbulent channel flow

槽道湍流中动量和被动标量输运特性及其相关性研究

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Abstract

Direct numerical simulation was carried out to investigate the correlation between the momentum and passive scalar transfer in a turbulent channel flow with Reτ= uτδ/ν = 180 and Pr = 0.71, where uτ is the friction velocity, δ is the channel half width, and ν is the kinematic viscosity. The one-point and two-point energy transfer and the corresponding scalar transfer are of particular interest. There is a significant positive correlation between the one-point energy and scalar transfer, particularly near the wall, and the correlation between the two production terms is always larger than that between the other terms. By resorting to the Karman-Howarth-Monin-Hill equation and the scale-by-scale scalar transfer budget equation, we explored the two-point energy and scalar transfer at two different vertical locations (i.e., one location close to the wall y+ = 10 and the other location slightly away from the wall y+ = 60). An inverse interscale transfer phenomenon of the energy and scalar is observed in the spanwise direction at y+ = 10, which is caused by the corresponding streak stretching, whereas along the streamwise and the vertical directions a forward interscale energy and scalar transfer phenomenon is observed. The physical mechanisms (e.g., production, dissipation, and viscous diffusion terms) contributing to the two-point energy transfer closely resemble those in the two-point scalar transfer. The intrinsic correlation between both the two-point energy and scalar transfer can find its roots in the similarity between the momentum and scalar streaks.

摘要

对雷诺数Reτ = uτδ/ν = 180 (uτ为摩擦速度, δ为槽道半宽, ν为运动黏度)及普朗特数Pr = 0.71 的槽道湍流开展直接数值以研究槽道湍流中动量和被动标量的输运特性及两者间的相关性. 研究结果表明单点能量和标量输运之间存在明显的正相关性, 并且生产项之间的相关性总是大于其他项之间的相关性. 通过计算Karman-Howarth-Monin-Hill方程和尺度间标量输运方程, 研究了法向方向两个距离壁面不同位置处两点间能量和标量输运特性(靠近壁面的位置y+ = 10, 另一个远离壁面的位置y+ = 60). 在y+ = 10处, 在展向方向观察到由动量条带及标量条带拉伸引起的能量和标量的反向传递现象, 而在流向和垂直方向观察到尺度间正向能量和标量传递现象. 两点间能量输运的物理机制(例如, 能量产生、 耗散和黏性扩散)与两点间标量输运的物理机制非常相似. 能量及标量输运机制的相关性与动量条带和标量条带之间的相似性密不可分.

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References

  1. R. D. Moser, J. Kim, and N. N. Mansour, Direct numerical simulation of turbulent channel flow up to Reτ = 590, Phys. Fluids 11, 943 (1999).

    Article  Google Scholar 

  2. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).

    Book  Google Scholar 

  3. B. A. Kader, Temperature and concentration profiles in fully turbulent boundary layers, Int. J. Heat Mass Transf. 24, 1541 (1981).

    Article  Google Scholar 

  4. H. Kawamura, H. Abe, and K. Shingai, DNS of turbulence and heat transport in a channel flow with different Reynolds and Prandtl numbers and boundary conditions, Int. Symp. Turbul. Heat Mass Transf. 3, 15 (2000).

    Google Scholar 

  5. J. Kim, and P. Moin, Transport of passive scalars in a turbulent channel flow, in: Turbulent Shear Flows (Springer, Berlin, 1989).

    Book  Google Scholar 

  6. N. Kasagi, Y. Tomita, and A. Kuroda, Direct numerical simulation of passive scalar field in a turbulent channel flow, J. Heat Transf. 114, 598 (1992).

    Article  Google Scholar 

  7. N. Kasagi, and Y. Ohtsubo, Direct numerical simulation of low Prandtl number temperature field in a turbulent channel flow, in: Turbulent Shear Flows 8 (Springer-Verlag, Berlin, 1993).

    MATH  Google Scholar 

  8. H. Abe, H. Kawamura, and Y. Matsuo, Surface heat-flux fluctuations in a turbulent channel flow up to Reτ = 1020 with Pr = 0.025 and 0.71, Int. J. Heat Fluid Flow 25, 404 (2004).

    Article  Google Scholar 

  9. H. Abe, and R. A. Antonia, Near-wall similarity between velocity and scalar fluctuations in a turbulent channel flow, Phys. Fluids 21, 025109 (2009).

    Article  Google Scholar 

  10. Y. Iritani, N. Kasagi, and M. Hirata, Heat transfer mechanism and associated turbulence structure in the near-wall region of a turbulent boundary layer, in: Turbulent Shear Flows 4, L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw, eds. (Springer-Verlag, Berlin, 1985).

    Google Scholar 

  11. R. A. Antonia, L. V. Krishnamoorthy, and L. Fulachier, Correlation between the longitudinal velocity fluctuation and temperature fluctuation in the near-wall region of a turbulent boundary layer, Int. J. Heat Mass Transf. 31, 723 (1988).

    Article  Google Scholar 

  12. H. Kong, H. Choi, and J. S. Lee, Dissimilarity between the velocity and temperature fields in a perturbed turbulent thermal boundary layer, Phys. Fluids 13, 1466 (2001).

    Article  Google Scholar 

  13. R. J. Hill, Exact second-order structure-function relationships, J. Fluid Mech. 468, 317 (2002), arXiv: physics/0209027.

    Article  MathSciNet  Google Scholar 

  14. N. Marati, C. M. Casciola, and R. Piva, Energy cascade and spatial fluxes in wall turbulence, J. Fluid Mech. 521, 191 (2004).

    Article  MathSciNet  Google Scholar 

  15. A. Cimarelli, E. De Angelis, J. Jiménez, and C. M. Casciola, Cascades and wall-normal fluxes in turbulent channel flows, J. Fluid Mech. 796, 417 (2016).

    Article  MathSciNet  Google Scholar 

  16. F. Hamba, Inverse energy cascade and vortical structure in the near-wall region of turbulent channel flow, Phys. Rev. Fluids 4, 114609 (2019).

    Article  Google Scholar 

  17. P. C. Valente, and J. C. Vassilicos, The energy cascade in grid-generated non-equilibrium decaying turbulence, Phys. Fluids 27, 045103 (2015).

    Article  Google Scholar 

  18. R. Gomes-Fernandes, B. Ganapathisubramani, and J. C. Vassilicos, The energy cascade in near-field non-homogeneous non-isotropic turbulence, J. Fluid Mech. 771, 676 (2015).

    Article  Google Scholar 

  19. Y. Zhou, K. Nagata, Y. Sakai, T. Watanabe, Y. Ito, and T. Hayase, Energy transfer in turbulent flows behind two side-by-side square cylinders, J. Fluid Mech. 903, A4 (2020).

    Article  MathSciNet  Google Scholar 

  20. F. Alves Portela, G. Papadakis, and J. C. Vassilicos, The turbulence cascade in the near wake of a square prism, J. Fluid Mech. 825, 315 (2017).

    Article  MathSciNet  Google Scholar 

  21. F. Hamba, Turbulent energy density and its transport equation in scale space, Phys. Fluids 27, 085108 (2015).

    Article  Google Scholar 

  22. F. Hamba, Turbulent energy density in scale space for inhomogeneous turbulence, J. Fluid Mech. 842, 532 (2018).

    Article  MathSciNet  Google Scholar 

  23. H. Suzuki, K. Nagata, Y. Sakai, T. Hayase, Y. Hasegawa, and T. Ushijima, An attempt to improve accuracy of higher-order statistics and spectra in direct numerical simulation of incompressible wall turbulence by using the compact schemes for viscous terms, Int. J. Numer. Meth. Fluids 73, 509 (2013).

    Article  MathSciNet  Google Scholar 

  24. H. Kawamura, H. Abe, and Y. Matsuo, DNS of turbulent heat transfer in channel flow with respect to Reynolds and Prandtl number effects, Int. J. Heat Fluid Flow 20, 196 (1999).

    Article  Google Scholar 

  25. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16 (1992).

    Article  MathSciNet  Google Scholar 

  26. Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 143, 90 (1998).

    Article  MathSciNet  Google Scholar 

  27. P. A. Davidson, Turbulence: An Introduction for Scientist and Engineers (Oxford University Press, Oxford, 2004).

    MATH  Google Scholar 

  28. H. Tennekes, and J. L. Lumley, A First Course in Turbulence (Massachusetts Institute of Technology Press, Cambridge, 1972).

    Book  Google Scholar 

  29. Y. Guezennec, D. Stretch, and J. Kim, in The structure of turbulent channel flow with passive scalar transport: Proceedings of the Summer Program (Stanford University, Palo Alto, 1990).

    Google Scholar 

  30. N. Marati, A Scale by Scale Budget in Wall Turbulence, Dissertation for Doctoral Degree (Università di Roma La Sapienza, Roma, 2005).

    Google Scholar 

  31. K. L. Hao, Numerical Investigation on the Characteristics of the Energy Transfer Processes and the Small-scale Motions in a Dual-plane Jet Flow (in Chinese), Dissertation for Doctoral Degree (Nanjing University of Science and Technology, Nanjing, 2021).

    Google Scholar 

  32. K. Hao, K. Nagata, and Y. Zhou, Scale-by-scale energy transfer in a dual-plane jet flow, Phys. Fluids 32, 105107 (2020).

    Article  Google Scholar 

  33. Y. Zhou, and J. C. Vassilicos, Energy cascade at the turbulent/nonturbulent interface, Phys. Rev. Fluids 5, 064604 (2020), arXiv: 2004.02221.

    Article  Google Scholar 

  34. J. H. Xie, and O. Bühler, Exact third-order structure functions for two-dimensional turbulence, J. Fluid Mech. 851, 672 (2018).

    Article  MathSciNet  Google Scholar 

  35. J. H. Xie, C. de Silva, R. Baidya, X. I. Yang, and R. Hu, Third-order structure function in the logarithmic layer of boundary-layer turbulence, Phys. Rev. Fluids 6, 074602 (2021).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 91952105, 11802133 and 12002318), the Six Talent Peaks Project in Jiangsu Province (Grant No. 2019-SZCY-005), and the Fundamental Research Funds for Central University (Grant No. 30918011325).

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Authors and Affiliations

  1. School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Ahui Tian  (田阿慧), Feng Liu  (刘锋) & Yi Zhou  (周毅)

  2. School of Energy and Power Engineering, North University of China, Taiyuan, 030051, China

    Feng Liu  (刘锋)

Authors
  1. Ahui Tian  (田阿慧)
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  2. Feng Liu  (刘锋)
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  3. Yi Zhou  (周毅)
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Contributions

Author contributions Ahui Tian validated the simulation results, processed the simulation data, and wrote the first draft of the manuscript. Feng Liu helped process the simulation data and provided financial support. Yi Zhou designed the research, performed the numerical simulation, completed the formal analysis, helped organize the manuscript and revised the final version, and provided financial support.

Corresponding author

Correspondence to Yi Zhou  (周毅).

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Tian, A., Liu, F. & Zhou, Y. Related turbulent momentum and passive scalar transfer in a turbulent channel flow. Acta Mech. Sin. 38, 322242 (2022). https://doi.org/10.1007/s10409-022-22242-x

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