Skip to main content
×
Home
    • Aa
    • Aa

Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers

  • SHIVSAI AJIT DIXIT (a1) and O. N. RAMESH (a1)
Abstract

Experiments were done on sink flow turbulent boundary layers over a wide range of streamwise pressure gradients in order to investigate the effects on the mean velocity profiles. Measurements revealed the existence of non-universal logarithmic laws, in both inner and defect coordinates, even when the mean velocity descriptions departed strongly from the universal logarithmic law (with universal values of the Kármán constant and the inner law intercept). Systematic dependences of slope and intercepts for inner and outer logarithmic laws on the strength of the pressure gradient were observed. A theory based on the method of matched asymptotic expansions was developed in order to explain the experimentally observed variations of log-law constants with the non-dimensional pressure gradient parameter (Δp=(ν/ρU3τ)dp/dx). Towards this end, the system of partial differential equations governing the mean flow was reduced to inner and outer ordinary differential equations in self-preserving form, valid for sink flow conditions. Asymptotic matching of the inner and outer mean velocity expansions, extended to higher orders, clearly revealed the dependence of slope and intercepts on pressure gradient in the logarithmic laws.

Copyright
References
Hide All
Afzal N. 1976 Millikan's argument at moderately large Reynolds number. Phys. Fluids 19 (4), 600602.
Afzal N. & Narasimha R. 1976 Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure. J. Fluid Mech. 74, 113128.
Bradshaw P. & Ferriss D. H. 1965 The response of a retarded equilibrium turbulent boundary layer to the sudden removal of pressure gradient. NPL Aero. Report 1145.
Bradshaw P. & Gregory N. 1959 The determination of local turbulent skin-friction from observations in the viscous sublayer. ARC London R&M 3202.
Buschmann M. H. & Gad-el-Hak M. 2003 Generalized logarithmic law and its consequences. AIAA J. 41 (1), 4048.
Clauser F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91108.
Clauser F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 151.
Coles D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191226.
Coles D. E. 1957 Remarks on the equilibrium turbulent boundary layer. J. Aero. Sci. 24, 495506.
Fernholz H. H. 2006 The role of skin-friction measurements in boundary layers with variable pressure gradients. In IUTAM Symposium on One Hundred Years of Boundary Layer Research (ed. Meier G. E. A. & Sreenivasan K. R.), pp. 231240. Springer.
Fernholz H. H., Janke G., Schober M., Wagner P. M. & Warnack D. 1996 New developments and applications of skin-friction measuring techniques. Meas. Sci. Technol. 7, 13961409.
Fernholz H. H. & Warnack D. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329356.
George W. K. & Castillo L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50 (12), 689729.
Gill A. E. 1968 The Reynolds number similarity argument. J. Math. Phys. 47, 437441.
Herring H. J. & Norbury J. F. 1967 Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients. J. Fluid Mech. 27, 541549.
Jones M. B., Marusic I. & Perry A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 127.
Jones W. P. & Launder B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337351.
Kim H. T., Kline S. J. & Reynolds W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133160.
Kline S. J., Reynolds W. C., Schraub F. A. & Runstadler P. W. 1967 The structure turbulent boundary layers. J. Fluid Mech. 30, 741773.
Launder B. E. & Jones W. P. 1969 Sink flow turbulent boundary layers. J. Fluid Mech. 38, 817831.
MacMillan F. A. 1956 Experiments on Pitot-tubes in shear flow. ARC London R&M 3028.
Mellor G. L. & Gibson D. M. 1966 Equilibrium turbulent boundary layers. J. Fluid Mech. 24, 225253.
Millikan C. B. 1938 A critical discussion of turbulent flows in channels and circular tubes. In Proc. 5th Intl Cong. Appl. Mech. (ed. den Hartog J. P. & Peters H.), pp. 386392. Wiley/Chapman & Hall.
Narasimha R. & Sreenivasan K. R. 1973 Relaminarization in highly accelerated turbulent boundary layers. J. Fluid Mech. 61, 417447.
Nickels T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217239.
Panton R. L. 2007 Composite asymptotic expansions and scaling wall turbulence. Phil. Trans. R. Soc. Lond. A365, 733754.
Patel V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185208.
Patel V. C. & Head M. R. 1968 Reversion of turbulent to laminar flow. J. Fluid Mech. 34, 371392.
Perry A. E., Marusic I. & Jones M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 6191.
Perry A. E., Marusic I. & Li J. D. 1994 Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis. Phys. Fluids 6, 10241035.
Rotta J. C. 1962 Turbulent boundary layers in incompressible flow. Prog. Aeronaut. Sci. 2, 1220.
Schlichting H. & Gersten K. 2000 Boundary-Layer Theory, 8th edn.Springer.
Spalart P. R. 1986 Numerical study of sink flow boundary layers. J. Fluid Mech. 172, 307328.
Spalart P. R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 6198.
Spalart P. R. & Leonard A. 1986 Direct numerical simulation of equilibrium turbulent boundary layers. In Turbulent Shear Flows 5 (ed. Durst F. J. et al. ), pp. 232252. Springer.
Townsend A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn.Cambridge University Press.
Townsend A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn.Cambridge University Press.
Van Dyke M. 1975 Perturbation Methods in Fluid Mechanics. Stanford, CA: Parabolic Press.
Warnack D. & Fernholz H. H. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 2. The boundary layer with relaminarization. J. Fluid Mech. 359, 357381.
Yajnik K. S. 1970 Asymptotic theory of turbulent shear flows. J. Fluid Mech. 42, 411427.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 32 *
Loading metrics...

Abstract views

Total abstract views: 91 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.