Determination of skin friction in strong pressure-gradient equilibrium and near-equilibrium turbulent boundary layers

The conventional Clauser-chart method for determination of local skin friction in zero or weak pressure-gradient turbulent boundary layer flows fails entirely in strong pressure-gradient situations. This failure occurs due to the large departure of the mean velocity profile from the universal logarithmic law upon which the conventional Clauser-chart method is based. It is possible to extend this method, even for strong pressure-gradient situations involving equilibrium or near-equilibrium turbulent boundary layers by making use of the so-called non-universal logarithmic laws. These non-universal log laws depend on the local strength of the pressure gradient and may be regarded as perturbations of the universal log law. The present paper shows that the modified Clauser-chart method, so developed, yields quite satisfactory results in terms of estimation of local skin friction in strongly accelerated or retarded equilibrium and near-equilibrium turbulent boundary layers that are not very close to relaminarization or separation.

[1]  John K. Eaton,et al.  Turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient , 2005, Journal of Fluid Mechanics.

[2]  D. E. Coles,et al.  PROCEEDINGS: COMPUTATION OF TURBULENT BOUNDARY LAYERS - 1968 AFOSR-IFP-STANFORD CONFERENCE, STANFORD UNIV., CALIF., 19-24 AUGUST 1968. VOLUME II. COMPILED DATA, , 1969 .

[3]  Alexander Smits,et al.  Further observations on the mean velocity distribution in fully developed pipe flow , 2004, Journal of Fluid Mechanics.

[4]  R. Henkes,et al.  Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients , 1998 .

[5]  A. Townsend The Structure of Turbulent Shear Flow , 1975 .

[6]  Mohamed Gad-el-Hak,et al.  Generalized Logarithmic Law and Its Consequences , 2003 .

[7]  J. Norbury,et al.  Some experiments on equilibrium turbulent boundary layers in favourable pressure gradients , 1967, Journal of Fluid Mechanics.

[8]  P. Monkewitz,et al.  Evidence on Non-Universality of Kármán Constant , 2007 .

[9]  H. H. Fernholz,et al.  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 , 1998 .

[10]  A. Kendall,et al.  A method for estimating wall friction in turbulent wall-bounded flows , 2008 .

[11]  A. Leonard,et al.  Direct Numerical Simulation of Equilibrium Turbulent Boundary Layers , 1987 .

[12]  Tie Wei,et al.  Comment on the Clauser chart method for determining the friction velocity , 2005 .

[13]  Jens M. Österlund,et al.  Experimental studies of zero pressure-gradient turbulent boundary layer flow , 1999 .

[14]  F. Clauser Turbulent Boundary Layers in Adverse Pressure Gradients , 1954 .

[15]  H. Fernholz The Role of Skin-Friction Measurements in Boundary Layers with Variable Pressure Gradients , 2006 .

[16]  Donald Coles,et al.  THE YOUNG PERSON'S GUIDE TO THE DATA , 1968 .

[17]  F. Clauser The Turbulent Boundary Layer , 1956 .

[18]  Arne V. Johansson,et al.  A note on the overlap region in turbulent boundary layers , 2000 .

[19]  M. R. Head,et al.  Reversion of turbulent to laminar flow , 1968, Journal of Fluid Mechanics.

[20]  Peter N. Joubert,et al.  Low-Reynolds-number turbulent boundary layers , 1991, Journal of Fluid Mechanics.

[21]  J. C. Rotta,et al.  Turbulent boundary layers in incompressible flow , 1962 .

[22]  V. C. Patel Calibration of the Preston tube and limitations on its use in pressure gradients , 1965, Journal of Fluid Mechanics.

[23]  Hassan M. Nagib,et al.  Variations of von Kármán coefficient in canonical flows , 2008 .

[24]  T. B. Nickels,et al.  Inner scaling for wall-bounded flows subject to large pressure gradients , 2004, Journal of Fluid Mechanics.

[25]  H. H. Fernholz,et al.  New developments and applications of skin-friction measuring techniques , 1996 .

[26]  Per Egil Skåre,et al.  A turbulent equilibrium boundary layer near separation , 1994, Journal of Fluid Mechanics.

[27]  O. N. Ramesh,et al.  Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers , 2008, Journal of Fluid Mechanics.

[28]  Ivan Marusic,et al.  Evolution and structure of sink-flow turbulent boundary layers , 2001, Journal of Fluid Mechanics.

[29]  A. Musker,et al.  Explicit Expression for the Smooth Wall Velocity Distribution in a Turbulent Boundary Layer , 1979 .

[30]  Philippe R. Spalart,et al.  Experimental and numerical study of a turbulent boundary layer with pressure gradients , 1993, Journal of Fluid Mechanics.