Abstract
We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient for two Reynolds numbers \(Re_\theta =6200\) and \(Re_\theta =8000\). We perform detailed multi-resolution measurements by combining large-scale and long-range microscopic particle imaging. We investigate scaling laws for the mean velocity and for the total shear stress in the inner layer. In the inner part of the inner layer the mean velocity can be fitted by a log-law. In the outer part a modified log-law provides a good fit, which depends on the pressure gradient parameter and on a parameter for the mean inertial effects. Emphasis is on the Reynolds number effects on the mean velocity and shear stress.
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References
A.E. Alving, H.H. Fernholz, Mean-velocity scaling in and around a mild, turbulent separation bubble. Phys. Fluids 7, 1956–1969 (1995)
K.C. Brown, P.N. Joubert, The measurement of skin friction in turbulent boundary layers with adverse pressure gradients. J. Fluid Mech. 35, 737–757 (1969)
K.A. Chauhan, P.A. Monkewitz, H.M. Nagib, Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41, 021404 (2009)
C. Cierpka, S. Scharnowski, C.J. Kähler, Parallax correction for precise near-wall flow investigations using particle imaging. Appl. Opt. 52, 2923–2931 (2013)
C.M. de Silva, E.G. Gnanamanickam, C. Atkinson, N.A. Buchmann, N. Hutchins, J. Soria, I. Marusic, High spatial range velocity measurements in a high Reynolds number turbulent boundary layer. Phys. Fluids 26:025117–1–19 (2014)
S.A. Dixit, O.N. Ramesh, Determination of skin friction in strong pressure-gradient equilibrium and near-equilibrium turbulent boundary layers. Exp. Fluids 47, 1045–1058 (2009)
K. Gersten, H. Herwig, Strömungsmechanik. Grundlagen der Impuls-, Wärme- und Stoffübertragung aus asymptotischer Sicht. Vieweg, 1992
A.G. Gungor, Y. Maciel, M.P. Simens, J. Soria, Analysis of a turbulent boundary layer subjected to a strong adverse pressure gradient. J. Phys.: Conf. Ser. 506, 012007 (2014)
S. Herpin, C.Y. Wong, M. Stanislas, J. Soria, Stereoscopic PIV measurements of a turbulent boundary layer with a large spatial dynamic range. Exp. Fluids 45, 745–763 (2008)
C.J. Kähler, S. Scharnowski, C. Cierpka, On the uncertainty of digital PIV and PTV near walls. Exp. Fluids 52, 1641–1656 (2012)
T. Knopp, N.A. Buchmann, D. Schanz, B. Eisfeld, C. Cierpka, R. Hain, A. Schröder,C.J. Kähler, Investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using PIV. J Turbul 16, 250–272 (2015)
T. Knopp, D. Schanz, A. Schröder, M. Dumitra, R. Hain, C.J. Kähler, Experimental investigation of the log-law for an adverse pressure gradient turbulent boundary layer flow at \(Re_\theta \) up to 10000. Flow Turbul. Combust. 92, 451–471 (2014)
H. McDonald, The effect of pressure gradient on the law of the wall in turbulent flow. J. Fluid Mech. 35, 311–336 (1969)
H. Nagib. Personal communication. 2013
H.M. Nagib and K.A. Chauhan. Variations of von Karman coefficient in canonical flows. Phys. Fluids, 20:101518–1–10, 2008
T.B. Nickels, Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217–239 (2004)
P.E. Skare, P.A. Krogstad, A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319–348 (1994)
W. Szablewski, Turbulente Strömungen in divergenten Kanälen. Ing.-Arch. 22, 268–281 (1954)
T. Wei, R. Schmidt, P. McMurtry, Comment on the clauser chart method for determining the friction velocity. Exp. Fluids 38, 695–699 (2005)
Acknowledgments
The authors are grateful to Prof. Skare for providing his data. The authors are also grateful to Profs. Rossow, Radespiel, Nagib and Herwig and to Drs. B. Eisfeld, A. Krumbein and D. Schwamborn for valuable discussions and suggestions.
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Knopp, T. et al. (2016). Experimental Investigation of a Turbulent Boundary Layer Subject to an Adverse Pressure Gradient at \(Re_{\theta }\) up to 10000 Using Large-Scale and Long-Range Microscopic Particle Imaging. In: Stanislas, M., Jimenez, J., Marusic, I. (eds) Progress in Wall Turbulence 2. ERCOFTAC Series, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-20388-1_24
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DOI: https://doi.org/10.1007/978-3-319-20388-1_24
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