Mean Parameters of an Incompressible Turbulent Boundary Layer on the Wind Tunnel Wall at Very High Reynolds Numbers
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Mean Parameters of an Incompressible Turbulent Boundary Layer on the Wind Tunnel Wall at Very High Reynolds Numbers Anton Gorbushin1,2 · Svetlana Osipova1,2 · Vladimir Zametaev1,2,3 Received: 21 June 2020 / Accepted: 9 November 2020 © Springer Nature B.V. 2020
Abstract The mean parameters of a two-dimensional incompressible turbulent boundary layer with zero pressure gradient were measured on the smooth wall of the TsAGI T-128 transonic wind tunnel in the range Reθ = 5.3 × 104–2.9 × 105 velocity profiles, skin friction coefficient, and shape factor. Novel data were obtained in the range Reθ ≈ 2.35 × 105–2.9 × 105. At the maximum Reynolds number, the record value of the von Kármán number Reτ ∼1 × 105 was reached and the logarithmic law was maintained up to y+ ≈ 1.3 × 104. The equilibrium state of the boundary layer was estimated using Clauser’s equilibrium parameter, which was G = 6.4–6.8 for high Reynolds numbers. The results of the investigation confirm the conclusions of other studies on the universality of dimensionless velocity profile in the boundary layer outer region. The results were compared with semi-empirical dependencies, direct numerical simulation (DNS) results and the results of other studies performed both on wind tunnel walls and on a flat plate. At high Reynolds numbers the agreement between the shape factor was within ΔH = ± 0.012 (± 1%), with a skin friction coefficient—Δcf= ± 0.00006 (± 3.7%).
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Vol.:(0123456789)
Flow, Turbulence and Combustion
Graphic Abstract
0.004
Cf
0.003
0.002
0.001
0 1 000
Re θ 10 000
100 000
1/5 law 1/7 law Clauser, 1956 Coles-Fernholz Prandtl-Karman Nikuradse Schlich ng Karman-Schoenherr Schultz-Grunow Winter and Gaudet, 1973 Pirozzoli, 2014 Winter and Gaudet, 1973 Fernholz, 1995 Osterlund, 1999 Kornilov, 2001 Oweis et al, 2010 Valikivi et al (Pitot), 2015 Valikivi et al (NSTAP), 2015 Alizard et al (SDNS), 2015 Wenzel (SDNS), 2019 T-128
1 000 000
Keywords Turbulent boundary layer · Wind tunnel · Very high Reynolds numbers
1 Introduction Experimental studies of zero pressure gradient (ZPG) turbulent boundary layers (TBLs) on smooth walls have been conducted for more than a hundred years. Despite the large number of available results, this type of research is still of particular interest: Smits et al. (2011), and Marusic et al. (2013) highlight the importance of further investigations of the boundary layer at very high Reynolds numbers. One of the recommended approaches is to conduct experiments at facilities with thick TBLs—in their opinion, this could allow us to identify all the time and length characteristic scales. The turbulent boundary layers at very large Reynolds numbers draw attention for two reasons: (i) practical interest in the design of large aircraft and ships; (ii) researchers have always wondered: what would happen to the TBL at Re → ∞? The greatest interest is caused by an incompressible ZPG TBL— many articles are focused on this canonical case. These pape
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