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Recent progress in compressible turbulence

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Abstract

In this paper, we review some recent studies on compressible turbulence conducted by the authors’ group, which include fundamental studies on compressible isotropic turbulence (CIT) and applied studies on developing a constrained large eddy simulation (CLES) for wall-bounded turbulence. In the first part, we begin with a newly proposed hybrid compact–weighted essentially nonoscillatory (WENO) scheme for a CIT simulation that has been used to construct a systematic database of CIT. Using this database various fundamental properties of compressible turbulence have been examined, including the statistics and scaling of compressible modes, the shocklet–turbulence interaction, the effect of local compressibility on small scales, the kinetic energy cascade, and some preliminary results from a Lagrangian point of view. In the second part, the idea and formulas of the CLES are reviewed, followed by the validations of CLES and some applications in compressible engineering problems.

Graphical Abstract

This paper reviews some recent research on compressible turbulence from the authors’ group, including fundamental studies on compressible isotropic turbulence (left) and applied studies on developing a constrained large eddy simulation method for wall-bounded turbulence (right). These topics are two of the main directions in current turbulence research, and our results, which are new and important, fill gaps in the relevant area.

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References

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

    Book  MATH  Google Scholar 

  2. Wang, J., Wang, L.P., Xiao, Z., et al.: A hybrid approach for direct numerical simulation of isotropic compressible turbulence. J. Comp. Phys. 229, 5257–5279 (2010)

    Article  MATH  Google Scholar 

  3. Wang, J., Shi, Y., Wang, L.P., et al.: Scaling and statistics in three-dimensional compressible turbulence. Phys. Rev. Lett. 108, 214505 (2012)

    Article  Google Scholar 

  4. Wang, J., Shi, Y., Wang, L.P., et al.: Effect of shocklets on the velocity gradients in highly-compressible isotropic turbulence. Phys. Fluids 23, 125103 (2011)

    Article  Google Scholar 

  5. Wang, J., Shi, Y., Wang, L.P., et al.: Effect of compressibility on the small scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  6. Wang, J.C., Yang, Y.T., Shi, Y.P., et al.: Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505 (2013)

    Article  Google Scholar 

  7. Yang, Y.T., Wang, J.C., Shi, Y.P., et al.: Acceleration of passive tracers in compressible turbulent flow. Phys. Rev. Lett. 110, 064503 (2013)

    Article  Google Scholar 

  8. Yang, Y.T., Wang, J.C., Shi, Y.P., et al.: Interactions between inertial particles and shocklets in compressible turbulent flow. Phys. Fluids. 26, 091702 (2014)

    Article  Google Scholar 

  9. Shi, Y.P., Xiao, Z.L., Chen, S.Y.: Constrained subgrid-scale stress model for large eddy simulation. Phys. Fluids 20, 011701 (2008)

    Article  Google Scholar 

  10. Chen, S.Y., Xia, Z.H., Pei, S.Y., et al.: Reynolds-stress-constrained large eddy simulation of wall bounded turbulent flows. J. Fluid Mech. 703, 1–28 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chen, S.Y., Shi, Y.P., Xiao, Z.L., et al.: Constrained large eddy simulation of wall-bounded turbulent flows. In: Fu, S. et al. eds. Progress in Hybrid RANS-LES Modelling, NNFM 117, 121–130 (2012)

  12. Xia, Z.H., Shi, Y.P., Hong, R.K., et al.: Constrained large-eddy simulation of separated flows in a channel with streamwise-periodic constrictions. J. Turbul. 14, 1–21 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen, S.Y., Wang, M.R., Xia, Z.H.: Multiscale fluid mechanics and modeling. Procedia IUTAM. (in Press) (2013)

  14. Chen, S.Y., Chen, Y.C., Xia, Z.H., et al.: Constrained large-eddy simulation and detached eddy simulation of flow past a commercial aircraft at 14 degrees angle of attack. Sci. China Ser. G 56, 270–276 (2013)

    Article  MathSciNet  Google Scholar 

  15. Jiang, Z., Xiao, Z.L., Shi, Y.P., et al.: Constrained large-eddy simulation of wall-bounded compressible turbulent flows. Phys. Fluids 25, 106102 (2013)

    Article  Google Scholar 

  16. Hong, R.K., Xia, Z.H., Shi, Y.P., et al.: Constrained large-eddy simulation of compressible flow past a circular cylinder. Commun. Comput. Phys. 15, 388–421 (2013)

    MathSciNet  Google Scholar 

  17. Zhao, Y.M., Xia, Z.H., Shi, Y.P., et al.: Constrained large-eddy simulation of laminar-turbulent transition in channel flow. Phys. Fluids 26, 095103 (2014)

    Article  Google Scholar 

  18. Adams, N.A., Shariff, K.: A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J. Comp. Phys. 127, 27–51 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  19. Pirozzoli, S.: Conservative hybrid compact-WENO schemes for shock-turbulence interaction. J. Comp. Phys. 178, 81–117 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ren, Y.X., Liu, M., Zhang, H.: A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws. J. Comp. Phys. 192, 365–386 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Zhou, Q., Yao, Z., He, F., et al.: A new family of high-order compact upwind difference schemes with good spectral resolution. J. Comp. Phys. 227, 1306–1339 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Balsara, D.S., Shu, C.W.: Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comp. Phys. 160, 405–452 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Lele, S.K.: Compact finite difference schemes with spectral-like resolution. J. Comp. Phys. 103, 16–42 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  24. Sagaut, P., Cambon, C.: Homogeneous Turbulence Dynamics. Cambridge University Press, Cambridge (2008)

    Book  MATH  Google Scholar 

  25. She, Z.S., Lévêque, E.: Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336–339 (1994)

    Article  Google Scholar 

  26. Benzi, R., Biferale, L., Fisher, R.T., et al.: Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev. Lett. 100, 234503 (2008)

    Article  Google Scholar 

  27. Bec, J., Khanin, K.: Burgers turbulence. Phys. Rep. 447, 1–66 (2007)

    Article  MathSciNet  Google Scholar 

  28. Lee, S., Lele, S., Moin, P.: Eddy shocklets in decaying compressible turbulence. Phys. Fluids A 3, 657–664 (1991)

    Article  Google Scholar 

  29. Samtaney, R., Pullin, D.I., Kosovic, B.: Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13, 1415–1430 (2001)

    Article  Google Scholar 

  30. Larsson, J., Lele, S.K.: Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21, 126101 (2009)

    Article  Google Scholar 

  31. Meneveau, C.: Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245 (2011)

    Article  MathSciNet  Google Scholar 

  32. Ashurst, W.T., Kerstein, A.R., Kerr, R.M., et al.: Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids 30, 2343–2353 (1987)

    Article  Google Scholar 

  33. Chong, M.S., Perry, A.E., Cantwell, B.J.: A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777 (1990)

    Article  MathSciNet  Google Scholar 

  34. Pirozzoli, S., Grasso, F.: Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16, 4386–4407 (2004)

    Article  Google Scholar 

  35. Suman, S., Girimaji, S.S.: Velocity gradient invariants and local flow-field topology in compressible turbulence. J. of Turbul. 11, 1–24 (2010)

    Article  Google Scholar 

  36. Erlebacher, G., Sarkar, S.: Statistical analysis of the rate of strain tensor in compressible homogeneous turbulence. Phys. Fluids A 5, 3240–3254 (1993)

    Article  MATH  Google Scholar 

  37. Armstrong, J.W., Rickett, B.J., Spangler, S.R.: Electron density power spectrum in the local interstellar medium. Astrophys. J. 443, 209–221 (1995)

    Article  Google Scholar 

  38. Xu, H., Li, H., Collins, D.C., et al.: Evolution and distribution magnetic fields from active galactic nuclei in galaxy cluster. I. the effect of injection energy and redshift. Astrophys. J. 725, 2152–2165 (2010)

    Article  Google Scholar 

  39. Kritsuk, A.G., Norman, M.L., Padoan, P., et al.: The statistics of supersonic isothermal turbulence. Astrophys. J. 665, 416–431 (2007)

    Article  Google Scholar 

  40. Aluie, H.: Compressible turbulence: The cascade and its locality. Phys. Rev. Lett. 106, 174502 (2011)

    Article  Google Scholar 

  41. Aluie, H., Li, S., Li, H.: Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29 (2012)

    Article  Google Scholar 

  42. Miura, H., Kida, S.: Acoustic energy exchange in compressible turbulence. Phys. Fluids 7, 1732–1742 (1995)

    Article  MATH  Google Scholar 

  43. Chen, Q., Chen, S., Eyink, G., et al.: Intermittency in the joint cascade of energy and helicity. Phys. Rev. Lett. 90, 214503 (2003)

    Article  Google Scholar 

  44. Yeung, P.K.: Lagrangian investigations of turbulence. Annu. Rev. Fluid Mech. 34, 115–142 (2002)

    Article  MathSciNet  Google Scholar 

  45. Toschi, F., Bodenschatz, E.: Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404 (2009)

    Article  MathSciNet  Google Scholar 

  46. Salazar, J.P.L.C., Collins, L.R.: Two-particle dispersion in isotropic turbulent flows. Annu. Rev. Fluid Mech. 41, 405–432 (2009)

    Article  MathSciNet  Google Scholar 

  47. Sreenivasan, K.R., Schumacher, J.: Lagrangian views on turbulent mixing of passive scalars. Phil. Trans. R. Soc. A 368, 1561–1577 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  48. Parmar, M., Haselbacher, A., Balachandar, S.: Equation of motion for a sphere in non-uniform compressible flows. J. Fluid Mech. 699, 352–375 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  49. La Porta, A., Voth, G.A., Crawford, A.M., et al.: Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019 (2001)

    Article  Google Scholar 

  50. Toschi, F., Biferale, L., Boffetta, G., et al.: Acceleration and vortex filaments in turbulence. J. Turbul. 6, N15 (2005)

    Article  MathSciNet  Google Scholar 

  51. Reynolds, A.M., Mordant, N., Crawford, A.M., et al.: On the distribution of Lagrangian accelerations in turbulent flows. New J. Phys. 7, 58 (2005)

    Article  Google Scholar 

  52. Mordant, N., Crawford, A.M., Bodenschatz, E.: Three-dimensional structure of the Lagrangian acceleration in turbulent flows. Phys. Rev. Lett. 93, 214501 (2004)

    Article  Google Scholar 

  53. Chapman, D.A.: Computational aerodynamics development and outlook. AIAA J. 17, 1293–1313 (1979)

  54. Piomelli, U., Balaras, E.: Wall-layer models for large-eddy simulation. Annu. Rev. Fluid Mech. 34, 349–374 (2002)

  55. Piomelli, U.: Wall-layer models for large-eddy simulation. Prog. Aerosp. Sci. 44, 437–446 (2008)

    Article  Google Scholar 

  56. Fröhlich, J., von Terzi, D.: Hybrid LES/RANS methods for the simulation of the turbulent flows. Prog. Aerosp. Sci. 44, 349–377 (2008)

    Article  Google Scholar 

  57. Spalart, P.: Detached eddy simulation. Annu. Rev. Fluid Mech. 41, 181–202 (2009)

    Article  Google Scholar 

  58. Nikitin, N.V., Nicoud, F., Wasistho, B., et al.: An approach to wall modeling in large-eddy simulations. Phys. Fluids 12, 1629–1632 (2000)

    Article  Google Scholar 

  59. Kraichnan, R.H.: Decimated amplitude equations in turbulence dynamics. In: Dwoyer, D.L., Hussaini, M.Y., Vogit, R.G. (eds.) Theoretical approaches to turbulence, pp. 91–135. Springer, New York (1985)

    Chapter  Google Scholar 

  60. Kraichnan, R.H., Chen, S.Y.: Is there a statistical mechanics of turbulence? Phys. D. 37, 160–172 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  61. Ghosal, S., Lund, T.S., Moin, P., et al.: A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluids Mech. 286, 229–255 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  62. Coleman, G.N., Kim, J., Moser, R.D.: A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid. Mech. 305, 159–183 (1995)

    Article  MATH  Google Scholar 

  63. Brun, C., Boiarciuc, M.P., Haberkorn, M., et al.: Large eddy simulation of compressible channel flow. Theor. Comput. Fluid Dyn. 22, 189–212 (2008)

    Article  MATH  Google Scholar 

  64. Xu, C.Y., Chen, L.W., Lu, X.Y.: Large-eddy simulation of the compressible flow past a wavy cylinder. J. Fluid Mech. 665, 238–273 (2010)

    Article  MATH  Google Scholar 

  65. Rodriguez, O.: The circular cylinder in subsonic and transonic flow. AIAA J. 22, 1713–1718 (1984)

    Article  Google Scholar 

  66. Murthy, V.S., Rose, W.C.: Detailed measurements on a circular cylinder in cross flow. AIAA J. 16, 549–550 (1978)

    Article  Google Scholar 

  67. Spalart, P.R., Allmaras, S.R.: A one-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1, 5–21 (1994)

    Google Scholar 

  68. Breuer, M., Peller, N., Rapp, C., et al.: Flow over periodic hills-numerical and experimental study in a wide range of Reynolds numbers. Comput. Fluids 38, 433–457 (2009)

    Article  MATH  Google Scholar 

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Acknowledgments

This project was supported by the National Natural Science Foundation of China (Grants 11221061, 91130001, and 11302006) and the National Science Foundation for Postdoctoral Scientists of China (Grants 2011M500194 and 2012M520109).

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing, 100871, China

    Shiyi Chen, Zhenhua Xia, Jianchun Wang & Yantao Yang

  2. Physics of Fluids Group, Faculty of Science and Technology, MESA+ Research Institute, and J. M. Burgers Centre for Fluid Dynamics, University of Twente, PO Box 217, 7500, AE Enschede, The Netherlands

    Yantao Yang

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  1. Shiyi Chen
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  2. Zhenhua Xia
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  3. Jianchun Wang
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Correspondence to Shiyi Chen.

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Chen, S., Xia, Z., Wang, J. et al. Recent progress in compressible turbulence. Acta Mech Sin 31, 275–291 (2015). https://doi.org/10.1007/s10409-015-0459-9

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