Abstract
The momentum integral-based method developed by Mehdi and White (Exp Fluids 50(1):43–51. https://doi.org/10.1007/s00348-010-0893-1, 2011) for determining wall skin friction in turbulent wall-bounded flow is evaluated in separated flows in which independent estimates of wall skin friction are known. Owing to flow complexities, a direct measurement of the wall skin friction in separated flow is experimentally challenging. In this pursuit, the momentum integral-based method is particularly attractive as the method is mathematically exact and determination of the wall skin friction only requires measurement of the wall-normal profile of mean velocity and Reynolds shear stress. The present analysis uses existing experimental particle image velocimetry and direct numerical simulation data of flow over a backward-facing step as well as DNS over a smooth hump to demonstrate that the method is viable. The method is also shown to be viable in estimating the wall skin friction in flows over non-flat geometries.
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References
Adrian RJ (2007) Hairpin vortex organization in wall turbulence. Phys Fluids 19(4):041301. https://doi.org/10.1063/1.2717527
Alving AE, Fernholz H (1996) Turbulence measurements around a mild separation bubble and downstream of reattachment. J Fluid Mech 322:297–328. https://doi.org/10.1017/s0022112096002807
Bagnold R (1946) Motion of waves in shallow water, interaction between waves and sand bottoms. In: The physics of sediment transport by wind and water. ASCE, pp 91–110. https://doi.org/10.1098/rspa.1946.0062
Brzek B, Cal RB, Johansson G, Castillo L (2007) Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers. Phys Fluids 19(6):065101. https://doi.org/10.1063/1.2732439
Dean B, Bhushan B (2010) Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review. Philos Trans R Soc A Math Phys Eng Sci 368(1929):4775–4806. https://doi.org/10.1098/rsta.2010.0201
Dejoan A, Leschziner M (2004) Large eddy simulation of periodically perturbed separated flow over a backward-facing step. Int J Heat Fluid Flow 25(4):581–592. https://doi.org/10.1016/j.ijheatfluidflow.2004.03.004
Dengel P, Fernholz H (1990) An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation. J Fluid Mech 212:615–636. https://doi.org/10.1017/s0022112090002117
Dixit SA, Ramesh O (2009) Determination of skin friction in strong pressure-gradient equilibrium and near-equilibrium turbulent boundary layers. Exp Fluids 47(6):1045. https://doi.org/10.1007/s00348-009-0698-2
Fukagata K, Iwamoto K, Kasagi N (2002) Contribution of reynolds stress distribution to the skin friction in wall-bounded flows. Phys Fluids 14(11):L73–L76. https://doi.org/10.1063/1.1516779
Haritonidis JH (1989) The measurement of wall shear stress. In: Advances in fluid mechanics measurements. Springer, pp 229–261
Klewicki J, Fife P, Wei T, McMurtry P (2007) A physical model of the turbulent boundary layer consonant with mean momentum balance structure. Philos Trans R Soc A Math Phys Eng Sci 365(1852):823–840. https://doi.org/10.1098/rsta.2006.1944
Le H, Moin P, Kim J (1997) Direct numerical simulation of turbulent flow over a backward-facing step. PJ Fluid Mech 330:349–374. https://doi.org/10.1017/s0022112096003941
Marquillie M, Laval J-P, Dolganov R (2008) Direct numerical simulation of a separated channel flow with a smooth profile. J Turbul 9:N1. https://doi.org/10.1029/jc092ic07p07017
McPhee MG, Maykut GA, Morison JH (1987) Dynamics and thermodynamics of the ice/upper ocean system in the marginal ice zone of the greenland sea. J Geophys Res Oceans 92(C7):7017–7031. https://doi.org/10.1029/jc092ic07p07017
Mehdi F, White CM (2011) Integral form of the skin friction coefficient suitable for experimental data. Exp Fluids 50(1):43–51. https://doi.org/10.1007/s00348-010-0893-1
Mehdi F, Johansson TG, White CM, Naughton JW (2014) On determining wall shear stress in spatially developing two-dimensional wall-bounded flows. Exp Fluids 55(1):1656. https://doi.org/10.1007/s00348-013-1656-6
Nagib HM, Chauhan KA (2008) Variations of von kármán coefficient in canonical flows. Phys Fluids 20(10):101518. https://doi.org/10.1063/1.3006423
Naughton JW, Sheplak M (2002) Modern developments in shear-stress measurement. Prog Aerosp Sci 38(6–7):515–570. https://doi.org/10.1016/s0376-0421(02)00031-3
Niegodajew P, Dróżdż A, Elsner W (2019) A new approach for estimation of the skin friction in turbulent boundary layer under the adverse pressure gradient conditions. Int J Heat Fluid Flow 79:108456. https://doi.org/10.1016/j.ijheatfluidflow.2019.108456
Pond I, Ebadi A, Dubief Y, White CM (2017) An integral validation technique of rans turbulence models. Comput Fluids 149:150–159. https://doi.org/10.1016/j.compfluid.2017.02.016
Prandtl L, Tietjens OG (1934) Fundamentals of hydro- and aeromechanics. General Publishing Company, North York
Saric S (2007) Turbulent flow separation control by boundary-layer forcing. Ph.D. thesis Technische Universität. http://elib.tu-darmstadt.de/diss/000873. Accessed June 2020
Simpson RL (1989) Turbulent boundary-layer separation. Annu Rev Fluid Mech 21(1):205–232. https://doi.org/10.1146/annurev.fl.21.010189.001225
Song S, DeGraaff DB, Eaton JK (2000) Experimental study of a separating, reattaching, and redeveloping flow over a smoothly contoured ramp. Int J Heat Fluid Flow 21(5):512–519. https://doi.org/10.1016/s0142-727x(00)00039-4
Volino RJ, Schultz MP (2018) Determination of wall shear stress from mean velocity and Reynolds shear stress profiles. Phys Rev Fluids 3(3):034606. https://doi.org/10.1103/physrevfluids.3.034606
White CM, Mungal MG (2008) Mechanics and prediction of turbulent drag reduction with polymer additives. Annu Rev Fluid Mech 40:235–256. https://doi.org/10.1146/annurev.fluid.40.111406.102156
Yoshioka S, Obi S, Masuda S (2001) Turbulence statistics of periodically perturbed separated flow over backward-facing step. Int J Heat Fluid Flow 22(4):393–401. https://doi.org/10.1016/s0142-727x(01)00079-0
Acknowledgements
The authors are thankful to Hung Le (Stanford University), M. Marquillie (Laboratoire de Mecanique de Lille) and Shuya Yoshioka (Keio University), and their teams for providing access to their data. MEW is grateful for financial support by the Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. CMW is grateful for financial support from the National Science Foundation through Grant no. NSF CBET-1437851 and the Office of Naval Research through Grant no. N000141712307.
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Wengrove, M.E., Ebadi, A., White, C.M. et al. Evaluation of the momentum integral method to determine the wall skin friction in separated flows. Exp Fluids 61, 250 (2020). https://doi.org/10.1007/s00348-020-03065-8
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DOI: https://doi.org/10.1007/s00348-020-03065-8