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Direct Numerical Simulation on Mach Number and Wall Temperature Effects in the Turbulent Flows of Flat-Plate Boundary Layer

Published online by Cambridge University Press:  28 November 2014

Xian Liang  and
Xinliang Li
Xian Liang
Affiliation:
School of Mathematics and Information Science, Beifang University for Nationalities, Yinchuan 750021, China
Xinliang Li*
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuanxi Road, Beijing 100190, China
*
*Email addresses:liangxian@imech.ac.cn(X. Liang), lixl@imech.ac.cn(X. L. Li)
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Abstract

In this paper, direct numerical simulation (DNS) is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate at Ma∞ = 2.25,5,6,8. When Ma∞ = 8, two cases with the ratio of wall-to-reference temperature Tω/T∞ = 1.9 and 10.03 are considered respectively. The wall temperature approaches recovery temperatures for other cases. The characteristics of compressible turbulent boundary layer (CTBL) affected by freestream Mach number and wall temperature are investigated. It focuses on assessing compressibility effects and the validity of Morkovin's hypothesis through computing and analyzing the mean velocity profile, turbulent intensity, the strong Reynolds analogy (SRA) and possibility density function of dilatation term. The results show that, when the wall temperature approaches recovery temperature, the effects of Mach number on compressibility is insignificant. As a result, the compressibility effect is very weak and the Morkovin's hypothesis is still valid for Mach number even up to 8. However, when Mach number equal to 8, the wall temperature effect on the compressibility is sensitive. In this case, when Tω/T∞ = 1.9, the Morkovin's hypothesis is not fully valid. The validity of classical SRA depends on wall temperature directly. A new modified SRA is proposed to eliminate such negative factor in near wall region. Finally the effects of Mach number and wall temperature on streaks are also studied.

Keywords

47.27.E-47.27.nb47.40.KiHypersonicdirectly numerical simulationcompressibility effectsturbulent boundary layerstrong Reynolds analogy
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 1 , January 2015 , pp. 189 - 212
Copyright
Copyright © Global Science Press Limited 2015 

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References

[1]Spina, E. F., The physics of supersonic turbulent boundary layers, Annu. Rev. Fluid Mech., 26(1994), 287–319.CrossRefGoogle Scholar
[2]Schlatter, P. and Örlü, , Assessment of direct numerical simulation data of turbulent boundary layers, J. Fluid Mech., 659(2010), 116–126.CrossRefGoogle Scholar
[3]Lele, S. K., Compact Finite Difference Schemes with Spectral-like Resoution, J. Comput. Phys., 103(1992), 16–42.Google Scholar
[4]Fu, D. X. and Ma, Y. W., A high-order accurate difference scheme for complex flow fields, J. Comput. Phys., 134(1997), 1–15.CrossRefGoogle Scholar
[5]Tian, Z. F. and Dai, S. Q., High-order compact exponential finite difference methods for convection-diffusion type problems, J. Comput. Phys., 220(2007), 952–974.Google Scholar
[6]Deng, X. G., Mao, M. L., Tu, G. H., Zhang, H. X. and Zhang, Y. F.High-order and high accurate CFD methods and their applications for complex grid problems, Commun. Comput. Phys., 11(2012), 1081–1102.Google Scholar
[7]van Leer, B., Upwind and high-resolution methods for compressible flow: From donor cell to residual-distribution schemes, Commun. Comput. Phys., 1(2006), 192–206.Google Scholar
[8]Shu, C. W., Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE/NASA Tech. CR(1997), Technical Report 206253.Google Scholar
[9]Jiang, G. S. and Shu, C. W., Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126(1996), 202–228.CrossRefGoogle Scholar
[10]Balsara, D. and Shu, C. W., Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order accuracy, J. Comput. Phys., 160(2000), 405–452.Google Scholar
[11]Ren, Y. X., Liu, M. and Zhang, H., A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws, J. Comput. Phys., 192(2003), 365–386.CrossRefGoogle Scholar
[12]Pirozzoli, S., Conservative hybrid compact-WENO schemes for shock-turbulence interaction, J. Comput. Phys., 178(2002), 81–117.Google Scholar
[13]Marcos, C., Bruno, C. and Wai, S. D., High order weighted essentially non-oscillatory WENOZ schemes for hyperbolic conservation laws, J. Comput. Phys., 230(2011), 1766–1792.Google Scholar
[14]Martin, M. P., Taylor, E. M., Wu, M. and Weirs, V. G., A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence, J. Comput. Phys., 220(2006), 270–289.CrossRefGoogle Scholar
[15]Zhu, J. and Qiu, J. X., Trigonometric WENO schemes for hyperbolic conservation laws and highly oscillatory Problems, Commun. Comput. Phys., 8(2010), 1242–1263.Google Scholar
[16]Pirozzoli, S., Numerical methods for high-speed flows, Annu. Rev. Fluid Mech., 43(2011), 163–194.CrossRefGoogle Scholar
[17]Morkovin, M. V., Effects of compressibility on turbulent flows, In Favre, A., editor, Macutee canique de la Turbulence, CNRS (1962), 367–380.Google Scholar
[18]Rai, M. M., Gatski, T. B. and Erlebacher, G., Direct simulation of spatially evolving compressible turbulent boundary layers, AIAA Paper, 1995-0583(1995).CrossRefGoogle Scholar
[19]Pirozzoli, S. and Grasso, F., Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25, Phys. Fluids, 16(2004), 530–545.Google Scholar
[20]Gatski, T.B. and Erlebacher, G., Numerical simulation of a spatially evolving supersonic turbulent boundary layer, NASA Tech. TM(2002), 211934.Google Scholar
[21]Li, X. L., Fu, D. X., Ma, Y. W., Direct numerical simulation of a spatially evolving supersonic turbulent boundary layer at Ma=6, Chin. Phys. Lett., 23(2006), 1519–1522.Google Scholar
[22]Pirozzoli, S. and Bernardini, M., Turbulence in supersonic boundary layers at moderate Reynolds number, J. Fluid Mech., 688(2011), 120–168.CrossRefGoogle Scholar
[23]Maeder, T., Adams, N. A. and Kleiser, L.. Direct simulation of turbulent supersonic boundary layers by an extended temporal approach, J. Fluid Mech., 429(2001), 187–216.Google Scholar
[24]Martin, M. P., DNS of hypersonic turbulent boundary layers, AIAA Paper(2004), 2004–2337.Google Scholar
[25]Duan, L., Beekman, I. and Martin, M. P., Direct numerical simulation of hypersonic turbulent boundary layers. part 2. effect of wall temperature, J. Fluid Mech., 655(2010), 419–445.CrossRefGoogle Scholar
[26]Duan, L., Beekman, I. and Martin, M. P., Direct numerical simulation of hypersonic turbulent boundary layers. part 3. effect of Mach number, J. Fluid Mech., 672(2011), 245–267.CrossRefGoogle Scholar
[27]Duan, L. and Martin, M. P., Direct numerical simulation of hypersonic turbulent boundary layers. part 4. effect of high enthalpy, J. Fluid Mech., 684(2011), 25–59.Google Scholar
[28]Lagha, M., Kim, J. and Eldradge, J. D., et al., A numerical study of compressible turbulent boundary layers, Phys. Fluids, 23(2011), 015106.Google Scholar
[29]Lagha, M., Kim, J. and Eldradge, J. D., et al.Near-wall dynamics of compressible boundary layers, Phys. Fluids, 23(2011), 065109.CrossRefGoogle Scholar
[30]Liang, X., Li, X. L. and Fu, D. X., Ma, Y. W., DNS and analysis of a spatially evolving hypersonic turbulent boundary layer over a flat plate at Mach 8. Sci. Sin-Phys. Mech. Astron., 42(2012), 282–293.Google Scholar
[31]Liang, X. and Li, X. L., DNS of a spatially evolving hypersonic turbulent boundary layer at Mach 8, Sci. China-Phys. Mech. Astron., 56(2013), 1408–1418.Google Scholar
[32]He, Z. W., Li, X. L. and Liang, X., Nonlinear spectral-like schemes for hybrid schemes, Sci. China-Phys. Mech. Astron., 57(2014), 753–763.Google Scholar
[33]Li, X. L. and Yan, L.. Optimized Sixth-order Monotonicity-Preserving Scheme by Nonlinear Spectral Analysis, Int. J. Numer. Methods Fluids, 73(2013), 560–577.Google Scholar
[34]Liang, X., Li, X. L. and Fu, D. X., Ma, Y. W., Complex transition of double-diffusive convection in a rectangular enclosure with height-to-length ratio equal to 4, part 1. Commun. Comput. Phys., 6(2009), 247–268.Google Scholar
[35]White, F. M., Viscous fluid flow. McGraw-Hill, (1974), pages 367–380.Google Scholar
[36]Coleman, G. N., Kim, J. and Moser, R. D., A numerical study of turbulent supersonic isothermal-wall channel flow, J. Fluid Mech., 305(1995), 159–183.CrossRefGoogle Scholar
[37]Bradshaw, P., Compressible turbulent shear layers, Annu. Rev. Fluid Mech., 9(1977), 33–54.CrossRefGoogle Scholar
[38]Cebeci, T. and Smith, A. M. O., Analysis of Turbulent Boundary Layers, Academic Press Inc, New York (1974).Google Scholar
[39]Gaviglio, J., Reynolds analogies and experimental study of heat transfer in the supersonic boundary layer, Int. J. Heat Mass Transfer, 30(1987), 911–926.Google Scholar
[40]Rubesin, M. W., Extra compressibility terms for favre-averaged two-equation models of in-homogeneous turbulent flows, NASA Tech. CR(1990), Technical Report 177556.Google Scholar
[41]Huang, P. G., Coleman, G. N. and Bradshaw, P., Compressible turbulent channel flows, DNS results and modeling, J. Fluid Mech., 305(1995), 185–218.CrossRefGoogle Scholar
[42]Lele, S. K., Compressibility effects on turbulence, Annu. Rev. Fluid Mech., 26(1994), 211–254.CrossRefGoogle Scholar
[43]Fu, D. X., Ma, Y. W., Li, X. L. and Wang, Q., Direct Numerical Simulation of Compressible Turbulence, Science Press, Beijing(2010).Google Scholar
[44]Townsend, A. A., The Structure of Turbulent Shear Flow, Cambridge University Press, London(1976).Google Scholar
[45]Kline, S. J., Reynolds, W. C. and Scheaub, F. A., et al., The structure of turbulent boundary layers, J. Fluid Mech., 30(1967), 741–773.Google Scholar
[46]Bakewell, H. P. and Lumley, J. L.. Viscous sub-layer and adjacent wall region in turbulent pipe flow, Pyhs. Fluids, 10(1967), 1880–1889.Google Scholar