Abstract
A full momentum integral-based method for determining wall shear stress is presented. The method is mathematically exact and has the advantage of having no explicit streamwise gradient terms. It is applicable for flows that change rapidly in the streamwise direction and, in particular, to flows with ill-defined outer boundary conditions or when the measurement grid does not extend over the whole boundary layer thickness. The method is applied to two different experimental plane turbulent wall jet data sets for which independent estimates of wall shear stress were known, and the different results compare favorably. Complications owing to experimental limitations and measurement error in determining wall shear stress from the proposed method are presented, and mitigating strategies are described.
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Notes
In order to convert the given viscous units to physical dimensions, ρ = 1.18 kg/m3, ν = 1.57 × 10−5 m2/s and u τ = 0.1 m/s are used.
References
Curd EF (1981) Possible applications of wall jets in controlling air contaminants. Ann Occup Hyg 24(1):133–146. doi:10.1093/annhyg/24.1.133
Fernholz HH, Janke G, Schober M, Wagner PM, Warnack D (1996) New developments and applications of skin-friction measuring techniques. Meas Sci Technol 7:1396–1409. doi:10.1088/0957-0233/7/10/010
Fukagata K, Iwamotu K, Kasagi N (2002) Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys Fluids 14(11):L73–L76. doi:10.1063/1.1516779
George WK, Abrahamsson H, Eriksson J, Karlsson RI, Löfdahl L, Wosnik M (2000) A similarity theory for the turbulent plane wall jet without external stream. J Fluid Mech 425:367–411. doi:10.1017/S002211200000224X
Gupta AK, Kaplan RE (1972) Statistical characteristics of Reynolds stress in a turbulent boundary layer. Phys Fluids 15(6):981–985. doi:10.1063/1.1694060
Johansson TG, Castillo L (2002) Near-wall measurements in turbulent boundary layers using laser doppler anemometry. In Joint US ASME-European fluids engineering summer conference. Jul 14–18, Montreal, Quebec, Canada, FEDSM 2002-31070
Johansson TG, Mehdi F, Naughton JW (2006) Some problems with near-wall measurements and the determination of the wall shear stress. In 25th AIAA aerodynamic measurement technology and ground testing conference. 5–8 June, San Francisco, AIAA 2006-3833 (invited)
Karlsson R, Eriksson J, Persson J (1993) An experimental study of a two-dimensional plane turbulent wall jet. Technical report, Vattenfall Utveckling AB, Älvkarleby Laboratory, Sweden, VU-S93-B36
Karlsson RI, Johansson TG (1986) LDV measurements of higher order moments of velocity fluctuations in a turbulent boundary layer. In International Symposium on Applications of Laser Anemometry to Fluid Mechanics III. 7–9 July, Lisbon, Portugal, A87-40701, pp 17-35
Klewicki JC (2007) Handbook of experimental fluid mechanics, chapter 12.2: Measurement of wall shear stress. In Tropea C, Yarin J, Foss A (eds) Cambridge University Press. Cambridge, pp 876–886
Launder BE, Rodi W (1983) The turbulent wall jet—measurements and modeling. Ann Rev Fluid Mech 15:429–459. doi:10.1146/annurev.fl.15.010183.002241
Mehdi F (2006) Skin-friction measurements in a wall jet. Master’s thesis, Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden
Mehdi F, Klewicki JC, White CM (2010) Mean momentum balance analysis of rough-wall turbulent boundary layers. Phys D 239(14):1329–1337. doi:10.1016/j.physd.2009.06.008
Mehdi F, White CM (2011) Integral form of the skin friction coefficient suitable for experimental data. Exp Fluids 50:43–51. doi:10.1007/s00348-010-0893-1
Mehdi F, Klewicki JC, White CM (2013) Mean force structure and its scaling in rough-wall turbulent boundary layers. J Fluid Mech 731:682–712. doi:10.1017/jfm.2013.385
Naughton JW, Sheplak M (2002) Modern developments in shear-stress measurements. Prog Aerosp Sci 38(6–7):515–570. doi:10.1016/S0376-0421(02)00031-3
Naughton JW, Viken SA, Greenblatt D (2006) Skin friction measurements on the NASA hump model. AIAA J 44(6):1255–1265. doi:10.2514/1.14192
Örlü R, Fransson JHM, Alfredsson PH (2010) On near wall measurements of wall bounded flows—the necessity of an accurate determination of the wall position. Prog Aerosp Sci 46(8):353–387. doi:10.1016/j.paerosci.2010.04.002
Schlatter P, Örlü R (2010) Assessment of direct numerical simulation data of turbulent boundary layers. J Fluid Mech 659:116–126. doi:10.1017/S0022112010003113
Spalart PR (1988) Direct simulation of a turbulent boundary layer up to R θ = 1410. J Fluid Mech 187:61–98. doi:10.1017/S0022112088000345
Tavoularis S (2005) Measurement in fluid mechanics. Cambridge University Press, Cambridge, pp 328–341
Tomkins CD, Adrian RJ (2003) Spanwise structure and scale growth in turbulent boundary layers. J Fluid Mech 490:37–74. doi:10.1017/S0022112003005251
Winter KG (1977) An outline of the techniques available for the measurement of skin friction in turbulent boundary layers. Prog Aerosp Sci 18:1–57. doi:10.1016/0376-0421(77)90002-1
Wygnanski I, Katz Y, Horev E (1992) On the applicability of various scaling laws to the turbulent wall jet. J Fluid Mech 234:669–690. doi:10.1017/S002211209200096X
Acknowledgments
The data of Karlsson et al. (1993) were obtained from the ERCOFTAC “Classic Collection” Database. The authors are thankful to the CFD and Turbulence Mechanics research group at the University of Manchester— cfd.mace.manchester.ac.uk/ercoftac—for hosting the database.
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Mehdi, F., Johansson, T.G., White, C.M. et al. On determining wall shear stress in spatially developing two-dimensional wall-bounded flows. Exp Fluids 55, 1656 (2014). https://doi.org/10.1007/s00348-013-1656-6
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DOI: https://doi.org/10.1007/s00348-013-1656-6