Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows

doi:10.1007/s10483-021-2728-9

Abstract

Abstract: Many recent laboratory experiments and numerical simulations support a non-equilibrium dissipation scaling in decaying turbulence before it reaches an equilibrium state. By analyzing a direct numerical simulation (DNS) database of a transitional boundary-layer flow, we show that the transition region and the non-equilibrium turbulence region, which are located in different streamwise zones, present different non-equilibrium scalings. Moreover, in the wall-normal direction, the viscous sublayer, log layer, and outer layer show different non-equilibrium phenomena which differ from those in grid-generated turbulence and transitional channel flows. These findings are expected to shed light on the modelling of various types of non-equilibrium turbulent flows.

Key words: non-equilibrium turbulence, flat plate boundary layer, turbulence model

2010 MSC Number:

76F02

Feng LIU, Le FANG, Jian FANG. Non-equilibrium turbulent phenomena in transitional flat plate boundary-layer flows. Applied Mathematics and Mechanics (English Edition), 2021, 42(4): 567-582.

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References

[1] KOLMOGOROV, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Proceedings:Mathematical and Physical Sciences, 434, 9-13(1991)
[2] RICHARDSON, L. F. Weather Prediction by Numerical Process, Cambridge University Press, Cambridge (2007)
[3] FANG, L., ZHAO, H. K., LU, L. P., LIU, Y. W., and YAN, H. Quantitative description of non-equilibrium turbulent phenomena in compressors. Aerospace Science and Technology, 71, 78-89(2017)
[4] YAN, H., LIU, Y. W., LI, Q. S., and LU, L. P. Turbulence characteristics in corner separation in a highly loaded linear compressor cascade. Aerospace Science and Technology, 75, 139-154(2018)
[5] VASSILICOS, J. C. Dissipation in turbulent flows. Annual Review of Fluid Mechanics, 47, 95-114(2015)
[6] BOS, W. J. T. and RUBINSTEIN, R. Dissipation in unsteady turbulence. Physics Review Fluids, 2, 022601(2017)
[7] LIU, F., LU, L. P., BOS, W. J. T., and FANG, L. Assessing the non-equilibrium of decaying turbulence with reversed initial fields. Physical Review Fluids, 4, 084603(2019)
[8] HEARST, R. J. and LAVOIE, P. Velocity derivative skewness in fractal-generated, non-equilibrium grid turbulence. Physics of Fluids, 27, 071701(2015)
[9] ISAZA, J. C., SALAZAR, R., and WARHAFT, Z. On grid-generated turbulence in the near and far field regions. Journal of Fluid Mechanics, 753, 402-426(2014)
[10] FANG, L., ZHU, Y., LIU, Y. W., and LU, L. P. Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgrid-scale modeling. Physics Letters A, 379, 2331-2336(2015)
[11] VALENTE, P. C., ONISHI, R., and SILVA, C. B. D. Origin of the imbalance between energy cascade and dissipation in turbulence. Physical Review E, 90, 023003(2014)
[12] GOTO, S. and VASSILICOS, J. C. Energy dissipation and flux laws for unsteady turbulence. Physics Letters A, 379, 1144-1148(2015)
[13] SEOUD, R. E. and VASSILICOS, J. C. Dissipation and decay of fractal-generated turbulence. Physics of Fluids, 19, 105108(2007)
[14] VALENTE, P. C. and VASSILICOS, J. C. Universal dissipation scaling for nonequilibrium turbulence. Physical Review Letters, 108, 214503(2012)
[15] GOMES-FERNANDES, R., GANAPATHISUBRAMANI, B., and VASSILICOS, J. C. Particle image velocimetry study of fractal-generated turbulence. Journal of Fluid Mechanics, 711, 306-336(2012)
[16] NEDÍC, J., VASSILICOS, J. C., and GANAPATHISUBRAMANI, B. Axisymmetric turbulent wakes with new nonequilibrium similarity scalings. Physical Review Letters, 111, 144503(2013)
[17] DAIRAY, T., OBLIGADO, M., and VASSILICOS, J. C. Non-equilibrium scaling laws in axisymmetric turbulent wakes. Journal of Fluid Mechanics, 781, 166-195(2015)
[18] LAYEK, G. C. and SUNITA. Non-Kolmogorov scaling and dissipation laws in planar turbulent plume. Physics of Fluids, 30, 115105(2018)
[19] LAYEK, G. C. and SUNITA. Non-Kolmogorov dissipation in a turbulent planar jet. Physical Review Fluids, 3, 124605(2018)
[20] LESIEUR, M. Turbulence in Fluids, Kluwer Academic, Dordrecht (1997)
[21] LIU, F., LU, L. P., and FANG, L. Non-equilibrium turbulent phenomena in transitional channel flows. Journal of Turbulence, 19, 731-753(2018)
[22] KAMRUZZAMAN, M., DJENIDI, L., and ANTONIA, R. A. Behaviour of the energy dissipation coefficient in a rough wall turbulent boundary layer. Experiments in Fluids, 59, 9(2018)
[23] NEDIC, J., TAVOULARIS, S., and MARUSIC, I. Dissipation scaling in constant-pressure turbulent boundary layers. Physical Review Fluids, 2, 032601(2017)
[24] FANG, J., YAO, Y. F., LI, Z. R., and LU, L. P. Investigation of low-dissipation monotonicity-preserving scheme for direct numerical simulation of compressible turbulent flows. Computers and Fluids, 104, 55-72(2014)
[25] FANG, J., YAO, Y. F., ZHELTOVODOV, A. A., LI, Z. R., and LU, L. P. Direct numerical simulation of supersonic turbulent flows around a tandem expansion compression corner. Physics of Fluids, 27, 125104(2015)
[26] FANG, J., YAO, Y. F., ZHELTOVODOV, A. A., and LU, L. P. Investigation of three dimensional shock wave/turbulent boundary layer interaction initiated by a single-fin. AIAA Journal, 55, 509-523(2016)
[27] KELE, S. K. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103, 16-42(1992)
[28] FANG, J., GAO, F., MOULINEC, C., and EMERSON, D. R. An improved parallel compact scheme for domain-decoupled simulation of turbulence. International Journal for Numerical Methods in Fluids, 90, 479-500(2019)
[29] GAITONDE, D. V. and VISBAL, M. R. Pade-type higher-order boundary filters for the Navier-Stokes equations. AIAA Journal, 38, 2103-2112(2000)
[30] GOTTLIEB, S. and SHU, C. W. Total variation diminishing Runge-Kutta schemes. Mathematics of Computation, 67, 73-85(1998)
[31] KIM, W. and LEE, D. J. Generalized characteristic boundary conditions for computational aeroacoustics. AIAA Journal, 38, 2040-2049(2000)
[32] FASEL, H. and KONZELMANN, U. Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations. Journal of Fluid Mechanics, 221, 311-347(1990)
[33] SAYADI, T., HAMMAN, C., and MOIN, P. Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers. Journal of Fluid Mechanics, 724, 480-509(2013)
[34] SMITS, A. J., MATHESON, N., and JOUBERT, P. N. Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. Journal of Ship Research, 27, 147-157(1983)
[35] ZHANG, X. X., WATANABE, T., and NAGATA, K. Turbulent/nonturbulent interfaces in high-resolution direct numerical simulation of temporally evolving compressible turbulent boundary layers. Physical Review Fluids, 3, 094605(2018)
[36] SPALART, P. R. Direct simulation of a turbulent boundary layer up to R_θ=1410. Journal of Fluid Mechanics, 187, 61-98(1988)
[37] WU, X. H. and MOIN, P. Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. Journal of Fluid Mechanics, 630, 5-41(2009)
[38] DUCROS, F., COMTE, P., and LESIEUR, M. Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. Journal of Fluid Mechanics, 326, 1-36(1996)
[39] HINZE, J. O. Turbulence, 2nd ed., McGraw-Hill, New York (1975)
[40] WEI, T., FIFE, P., KLEWICKI, J., and MCMURTRY, P. Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. Journal of Fluid Mechanics, 522, 303-327(2005)
[41] PINTON, J. F., HOLDSWORTH, P. C. W., and LABBÉ, R. Power fluctuations in a closed turbulent shear flow. Physical Review E, 60, R2452-R2455(1999)
[42] LAUNDER, B. E. and SPALDING, D. B. Lecture in Mathematical Models of Turbulence, Academic Press, London (1972)
[43] POPE, S. Turbulent Flows, Cambridge University Press, Cambridge (2000)