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Subgrid-scale model based on the vorticity gradient tensor for rotating turbulent flows

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Abstract

A new subgrid-scale (SGS) stress model is proposed for rotating turbulent flows, and the new model is based on the traceless symmetric part of the square of the velocity gradient tensor and the symmetric part of the vorticity gradient tensor (or the so-called vorticity strain rate tensor). The new subgrid-scale stress model is taken into account the effect of the vortex motions in turbulence, which is reflected on the anti-symmetric part of the velocity gradient tensor. In addition, the eddy viscosity of the new model reproduces the proper scaling as O(y3) near the wall. Then, the new SGS model is applied in large-eddy simulation of the spanwise rotating turbulent channel flow. Different simulating cases are selected to test the new model. The results demonstrate that the present model can well predict the mean velocity profiles, the turbulence intensities, and the rotating turbulence structures. In addition, it needs no a second filter, and is convenient to be used in the engineering rotational flows.

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References

  1. Smagorinsky, J.: General circulation experiments with the primitive equations: i the basic experiment. Mon. Weather Rev. 91, 99–164 (1963)

    Article  Google Scholar 

  2. Deardorff, J.W.: A numerical study of three-dimensional turbulent channel flow at large reynolds numbers. J. Fluid Mech. 41, 453–480 (1970)

    Article  Google Scholar 

  3. Chollet, J.P., Lesieur, M.: Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. J. Atmos. Sci. 38(12), 2747–2757 (1981)

    Article  Google Scholar 

  4. Cui, G.X., Xu, C.X., Fang, L., et al.: New subgrid eddy-viscosity model for large-eddy simulation of anisotropy turbulence. J. Fluid Mech. 582, 377–397 (2007)

    Article  MathSciNet  Google Scholar 

  5. Vreman, A.: An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16, 3670–3681 (2004)

    Article  Google Scholar 

  6. Nicoud, F., Toda, H.B., Cabrit, O., et al.: Using singular valuesto build a subgrid-scale model for large-eddy simulations. Phys. Fluids 23, 085106 (2011)

    Article  Google Scholar 

  7. Yu, C., Hong, R., Xiao, Z., et al.: Subgrid-scale eddy viscosity model for helical turbulence. Phys. Fluids 25(9), 095101 (2013)

    Article  Google Scholar 

  8. Germano, M., Piomelli, U., Moin, P., et al.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7), 1760–1765 (1991)

    Article  Google Scholar 

  9. Lilly, D.K.: A proposed modification of the germano subgrid-scale closure method. Phys. Fluids A 4(3), 633–635 (1992)

    Article  Google Scholar 

  10. Piomelli, U.: High reynolds number calculations using the dynamic subgrid-scale stress model. Phys. Fluids A 5(6), 1484–1490 (1993)

    Article  Google Scholar 

  11. Meneveau, C., Lund, T.S., Cabot, W.H.: A lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385 (1996)

    Article  Google Scholar 

  12. Yu, C., Xiao, Z., Li, X.: Dynamic optimization methodology based on subgrid-scale dissipation for large-eddy simulation. Phys. Fluids 28(1), 015113 (2016)

    Article  Google Scholar 

  13. Tafti, D.K., Vanka, S.P.: A numerical study of the effects of spanwise rotation on turbulent channel flow. Phys. Fluids A 3, 642–656 (1990)

    Article  Google Scholar 

  14. Jiang, Z., Xia, Z., Shi, Y., et al.: Large-eddy simulation of spanwise rotating turbulent channel flow with dynamic variants of eddy viscosity model. Phys. Fluids 30(4), 040909 (2018)

    Article  Google Scholar 

  15. Kobayashi, H.: The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys. Fluids 17(4), 045104 (2005)

    Article  Google Scholar 

  16. Yang, Z.X., Cui, G.X., Zhang, Z.S., et al.: A modified nonlinear sub-grid scale model for large-eddy simulation with application to rotating turbulent channel flows. Phys. Fluids 24(7), 075113 (2012)

    Article  Google Scholar 

  17. Yang, Z.X., Cui, G.X., Xu, C.X., et al.: Large-eddy simulation of rotating turbulent channel flow with a new dynamic global-coefficient nonlinear subgrid stress model. J. Turbul. 13, N48 (2012)

    Article  MathSciNet  Google Scholar 

  18. Silvis, M.H., Verstappen, R.: Nonlinear subgrid-scale models for large-eddy simulation of rotating turbulent flows. In Direct and large-eddy simulation XI, pp. 129–134. Springer, Cham (2019)

    Chapter  Google Scholar 

  19. Teitelbaum, T., Mininni, P.D.: Effect of helicity and rotation on the free decay of turbulent flows. Phys. Rev. Lett. 103(1), 014501 (2009)

    Article  Google Scholar 

  20. Borue, V., Orszag, S.A.: Spectra in helical three-dimensional homogeneous isotropic turbulen-ce. Phys. Rev. 55, 7005 (1997)

    Article  MathSciNet  Google Scholar 

  21. Johnston, J.P., Halleen, R.M., Lezius, D.K.: Effects of spanwise rotationon the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533–559 (1972)

    Article  Google Scholar 

  22. Cale, B., Wang, B.C.: Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow. Int. J. Heat Fluid Flow 80, 108480 (2019)

    Article  Google Scholar 

  23. Dai, Y.J., Huang, W.X., Xu, C.X.: Coherent structures in streamwise rotating channel flow. Phys. Fluids 31, 021204 (2019)

    Article  Google Scholar 

  24. Cheng, Q., Ng, C.O.: Rotating electroosmotic flow of an Eyring fluid. Acta. Mech. Sin. 33(2), 295–315 (2017)

    Article  MathSciNet  Google Scholar 

  25. Yang, Z.X., Wang, B.C.: Capturing Taylor–Görtler vortices in a streamwise-rotating channel at very high rotation numbers. J. Fluid Mech. 838, 658–689 (2018)

    Article  MathSciNet  Google Scholar 

  26. Yang, Z.X., Deng, B.Q., Wang, B.C., et al.: The effects of streamwise system rotation on pressure fluctuations in a turbulent channel flow. Phys. Fluids 30, 091701 (2018)

    Article  Google Scholar 

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grants 91852203 and 11472278), the National Key Research and Development Program of China (Grant 2016YFA04-01200), Science Challenge Project (Grant TZ2016001), and Strategic Priority Research Program of Chinese Academy of Sciences (Grants XDA17030100 and XDC01000000). The authors thank the National Supercomputer Center in Tianjin (NSCC-TJ) and the National Supercomputer Center in Guangzhou (NSCC-GZ) for providing computer time.

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Authors and Affiliations

  1. LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Han Qi, Xinliang Li & Changping Yu

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Han Qi & Xinliang Li

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  1. Han Qi
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  2. Xinliang Li
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  3. Changping Yu
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Correspondence to Changping Yu.

Appendix: the grid independence

Appendix: the grid independence

We choose different grid resolutions for each case and then obtain a better grid resolution. Nx× Ny× Nz = 32 × 33 × 32, 32 × 49 × 32, 32 × 57 × 32 are used in case1 (Reτ= 180, Roτ= 22), Nx× Ny× Nz= 32 × 33 × 32, 32 × 49 × 32, 32 × 57 × 32 are used in case 2 (Reτ= 180, Roτ= 40), Nx× Ny× Nz= 32 × 33 × 32, 32 × 57 × 32, 32 × 65 × 32 are used in case 3 (Reτ= 180, Roτ= 80), and Nx× Ny× Nz= 48 × 49 × 48, 64 × 65 × 64, 64 × 73 × 64 are used in case 4 (Reτ= 435, Roτ= 10.3).

In Fig. 8, we show the mean velocity profiles from different grid resolutions of different cases. From Fig. 8a, we found all the resolutions are close to each other. In Fig. 8b, the results from grid resolutions 32 × 49 × 32, 32 × 57 × 32 are close to the DNS result. In Fig. 8c, grid resolutions 32 × 33 × 32 under-predicts the mean velocity profile, and the results of grid resolutions 32 × 57 × 32, 32 × 65 × 32 have a better agreement with the DNS result. In Fig. 8d, the results of grid resolutions 64 × 65 × 64, 64 × 73 × 64 are close to each other and are higher than the results of grid resolution 48 × 49 × 48. Thus, we use the grid resolution 32 × 33 × 32, 32 × 49 × 32, 32 × 57 × 32, 64 × 65 × 64 for case 1, 2, 3, and 4.

Fig. 8
figure 8

Mean velocity profiles from different grid resolutions a at Reτ= 180, Roτ= 22, b at Reτ= 180, Roτ= 40, c at Reτ= 180, Roτ= 80, d at Reτ= 435, Roτ= 10.3

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Qi, H., Li, X. & Yu, C. Subgrid-scale model based on the vorticity gradient tensor for rotating turbulent flows. Acta Mech. Sin. 36, 692–700 (2020). https://doi.org/10.1007/s10409-020-00960-5

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