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Rotation invariant constitutive relation for Reynolds stress structure parameter

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Abstract

A new Reynolds stress constitutive formula is constructed using the first-order statistics of turbulent fluctuations instead of the mean strain rate. It includes zero empirical coefficients. The formula is validated with the direet numerieal simulation (DNS) data of turbulent channel flow at Re τ =180. The Reynolds stresses given by the proposed formula agree very well with the DNS results. The good agreement persists even after the multi-angle rotation of the coordinate system, indicating the rotation invariance of the formula. The autocorrelation of the fluctuating velocity rather than the mean strain rate is close to the essence of the Reynolds stress.

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References

  1. Gatski, T. B. and Jongen, T. Nonlinear eddy viscosity and algebraic stress models for solving complex turbulent flows. Progress in Aerospace Sciences, 36(8), 655–682 (2000)

    Article  Google Scholar 

  2. Craft, T. J., Launder, B. E., and Suga, K. Development and application of a cubic eddy-viscosity model of turbulence. International Journal of Heat and Fluid Flow, 17, 108–115 (1996)

    Article  Google Scholar 

  3. Craft, T. J., Launder, B. E., and Suga, K. Prediction of turbulent transitional phenomena with a nonlinear model. International Journal of Heat and Fluid Flow, 18, 15–28 (1997)

    Article  Google Scholar 

  4. Suga, K. and Abe, K. Nonlinear eddy viscosity modelling for turbulence and heat transfer near wall and shear-free boundaries. International Journal of Heat and Fluid Flow, 21, 37–48 (2000)

    Article  Google Scholar 

  5. Abe, K., Jang, Y. J., and Leschziner, M. A. An investigation of wall-anisotropy expressions and length-scale equations for non-linear eddy-viscosity models. International Journal of Heat and Fluid Flow, 24(2), 181–198 (2003)

    Article  Google Scholar 

  6. Abe, K. An improved anisotropy-resolving subgrid-scale model with the aid of a scale-similarity modeling concept. International Journal of Heat and Fluid Flow, 39, 42–52 (2013)

    Article  Google Scholar 

  7. Ohtsuka, T. and Abe, K. On the role of an anisotropy-resolving extra term for a subgrid-scale model in near-wall turbulence. Journal of Computational Science and Technology, 7(3), 410–425 (2013)

    Article  Google Scholar 

  8. Gerolymos, G. A., Lo, C., Vallet, I., and Younis, B. A. Term-by-term analysis of near-wall second-moment closures. AIAA Journal, 50(12), 2848–2864 (2012)

    Article  Google Scholar 

  9. Wallin, S. and Johansson, A. V. An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. Journal of Fluid Mechanics, 403(1), 89–132 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Durbin, P. Separated flow computations with the k-ɛ-v 2 model. AIAA Journal, 33(4), 659–664 (1995)

    Article  Google Scholar 

  11. Gao, G. and Xu, J. L. A partial average based study of compressible turbulent flows. International Journal of Mechanic Systems Engineering, 3(1), 20–35 (2013)

    Google Scholar 

  12. Gao, G. and Yong, Y. Partial-average-based equations of incompressible turbulent flow. International Journal of Non-Linear Mechanics, 39(9), 1407–1419 (2004)

    Article  MATH  Google Scholar 

  13. Gao, G., Zhang, C. X., and Yan, W. H. Numerical study of compression corner flow field using Gao-Yong turbulence model (in Chinese). Journal of Aerospace Power, 27(1), 124–128 (2012)

    Google Scholar 

  14. Gao, G., Jiang, L., and Gao, L. Calculation of wing-body junction flow using Gao-Yong turbulence equations (in Chinese). Journal of Aerospace Power, 38(10), 1271–1274 (2012)

    MathSciNet  Google Scholar 

  15. Gao, L., Gao, G., and Jiang, L. Numerical simulation of separated turbulent flow using Gao-Yong turbulent model (in Chinese). Journal of Aerospace Power, 39(5), 1–5 (2013)

    MathSciNet  Google Scholar 

  16. She, Z. S., Hu, N., and Wu, Y. Structural ensemble dynamics based closure model for wall-bounded turbulent flow. Acta Mechanica Sinica, 25(5), 731–736 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. National Key Laboratory of Aircraft Engine, School of Energy and Power Engineering, Beihang University, Beijing, 100191, China

    Jinglei Xu

  2. The 9th Designing of China Aerospace Science Industry Corporation, Wuhan, 430000, China

    Zhengguang Tu

  3. China Academy of Aerospace Aerodynamics, Beijing, 100074, China

    Ning Hu

Authors
  1. Jinglei Xu
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  2. Zhengguang Tu
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  3. Ning Hu
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Corresponding author

Correspondence to Ning Hu.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11002014)

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Xu, J., Tu, Z. & Hu, N. Rotation invariant constitutive relation for Reynolds stress structure parameter. Appl. Math. Mech.-Engl. Ed. 36, 517–522 (2015). https://doi.org/10.1007/s10483-015-1927-9

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  • DOI: https://doi.org/10.1007/s10483-015-1927-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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