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DNS of compressible turbulent boundary layer around a sharp cone

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Abstract

Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent energy budget is studied. The computed results show that the effect of circumferential curvature on turbulence characteristics is not obvious.

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References

  1. Schneider S P. Flight data for boundary-layer transition at hypersonic and supersonic speeds. J Spacecra Rockets, 1998, 36(1): 8–20

    Article  ADS  Google Scholar 

  2. Rabb L, Simpkinson H. Free flight heat transfer measurements on two 20° cone cylinders at Mach number from 1.3 to 4.9. NACA Res Memo, 1955, NACA-RM-E55F27

  3. Rabb L, Disher J H. Boundary layer transition at high Reynolds numbers as obtained in flight of a 20° cone-cylinder with wall to local stream temperature ratios near 1.0. NACA Res Memo, 1955, NACA-RM-E55I15

  4. Chauvin L T, Speegle K C. Boundary layer transition and heat transfer measurements for flight tests of blunt and sharp 50° cones at Mach numbers from 1.7 to 4.7. NACA Res Memo, 1957, NACA-RM-L57D04

  5. Ma Y B, Zhong X L. Receptivity of a supersonic boundary layer over a flat plate (I): Wave structures and interactions, J Fluid Mech, 2003, 488: 31–78

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Zhong X L, Ma Y B. Boundary-layer receptivity of Mach 7.99 flow over a blunt cone to free-stream acoustic waves. J Fluid Mech, 2006, 556: 53–103

    Article  ADS  Google Scholar 

  7. Zhong X L. Numerical simulation of surface roughness effects on receptivity of hypersonic flow over blunt cones. AIAA Paper, 2007: 2007-0944

  8. Guarini S E, Moser R D, Shariff K, et al. Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J Fluid Mech, 2000, 414: 1–33

    Article  MATH  ADS  Google Scholar 

  9. Maeder T, Adams N A, Kleiser L. Direct simulation of turbulent supersonic boundary layer by an extended temporal approach. J Fluid Mech, 2001, 429: 187–216

    Article  MATH  ADS  Google Scholar 

  10. Rai M M, Gatski T B, Erlebacher G. Direct numerical simulation of spatially evolving compressible turbulent boundary layers. AIAA paper, 1995: 95-0583

  11. Pirozzoli S, Grasso F. Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25. Phys Fluids, 2004, 16(3): 530–545

    Article  ADS  Google Scholar 

  12. Gao H, Fu D X, Ma Y W, et al. Direct numerical simulation of supersonic boundary layer flow. Chin Phys Lett, 2005, 22(7): 1709–1712

    Article  ADS  Google Scholar 

  13. Luo J S, Wang X J, Zhou H. Inherent mechanism of breakdown in laminar-turbulent transition of plane channel flows. Sci China Ser G-Phys Mech Astron, 2005, 48(2): 228–236

    Article  ADS  Google Scholar 

  14. Li X L, Fu D X, Ma Y W. DNS of compressible turbulent boundary layer over a blunt wedge. Sci China Ser G-Phys Mech Astron, 2005, 48(2): 129–141

    Article  ADS  Google Scholar 

  15. 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, 2006, 23(6): 1519–1522

    Article  ADS  Google Scholar 

  16. Horvath T J, Berry S A, Hollis B R, et al. Boundary layer transition on slender cones in conventional and low disturbance Mach 6 wind tunnels. AIAA Paper, 2002: 2002–2743

  17. Fu D X, Ma Y W. A high order accurate different scheme for complex flow fields. Comput Phys, 1997, 134: 1–15

    Article  MATH  ADS  MathSciNet  Google Scholar 

  18. Fu D X, Ma Y W. High resolution schemes. In: Hafez M, Oshima K, eds. Computational Fluid Dynamics Review. New York: John Wiley & Sons, 1995. 234–250

    Google Scholar 

  19. Li X L, Fu D X, Ma Y W. Optimized group velocity control scheme and DNS of decaying compressible turbulence of relative high turbulent Mach number. Int Numer Mech Fluids, 48, 2005: 835–852

    Article  MATH  Google Scholar 

  20. Karlson R I, Johansson T G. LDV measurements of higher-order moments of velocity fluctuations in a turbulent boundary layer. In: Laser Anemometry in Fluid Mechanics. Lisbon Portugal: Ladoan-Instituto Superior Tecnico, 1986

    Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100080, China

    XinLiang Li, DeXun Fu & YanWen Ma

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  1. XinLiang Li
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  2. DeXun Fu
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  3. YanWen Ma
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Correspondence to XinLiang Li.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 10502052) and Informatization Construction of Knowledge Innovation Projects of the Chinese Academy of Sciences (Grant No. INF105-SCE)

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Li, X., Fu, D. & Ma, Y. DNS of compressible turbulent boundary layer around a sharp cone. Sci. China Ser. G-Phys. Mech. Astron. 51, 699–714 (2008). https://doi.org/10.1007/s11433-008-0007-8

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  • DOI: https://doi.org/10.1007/s11433-008-0007-8

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