Modelling turbulent skin-friction control using linearized Navier–Stokes equations

• Published in: Journal of fluid mechanics 2012-07, Vol.702, p.403-414
• Main Authors: Duque-Daza, C. A., Baig, M. F., Lockerby, D. A., Chernyshenko, S. I., Davies, C.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Correlation; Exact sciences and technology; Fluid dynamics; Fluid flow; Fluid mechanics; Friction; Fundamental areas of phenomenology (including applications); Mathematical models; Navier-Stokes equations; Physics; Reynolds number; Streak; Turbulence; Turbulence control; Turbulent flow; Turbulent flows, convection, and heat transfer
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2012.189

Linearized Navier–Stokes equations are solved to investigate the impact on the growth of near-wall turbulent streaks that arises from streamwise-travelling waves of spanwise wall velocity. The percentage change in streak amplification due to the travelling waves, over a range of wave parameters, is compared to published direct numerical simulation (DNS) predictions of turbulent skin-friction reduction; a clear correlation between the two is observed. Linearized simulations at a much higher Reynolds number, more relevant to aerospace applications, produce results that show no marked differences to those obtained at low Reynolds number. It is also observed that there is a close correlation between DNS data of drag reduction and a very simple characteristic of the ‘generalized’ Stokes layer generated by the streamwise-travelling waves.