APS -70th Annual Meeting of the APS Division of Fluid Dynamics- Event - Stability limits of superhydrophobic longitudinal microgrooves in high Reynolds number turbulent flows

摘要

The stability of the liquid/gas interfaces on SuperHydrophobic (SH) Longitudinal MicroGrooves (LMGs) in high Reynolds number turbulent flows of practical interest is investigated by analytical extrapolation of DNS results in turbulent channel flow at $Re_{au_0} approx 222$ and 442 with SH LMGs at protrusion angle of $heta=-30^o$.Given that the magnitude of pressure fluctuations in turbulent channel flow scales as $p_{rms}^+ sim sqrt{ln(Re_{au})}$, it is found that the stability limits of SH LMGs diminishes by factors of $sim 4$ when the Reynolds number of the base flow increases from $Re_{au_0} sim 200$ of DNS to $Re_{au_0} sim 10^5 - 10^6$ of practical applications. For SH LMGs operating at Weber numbers of $We^{+0} equiv mu u_{au_0}/sigma approx 3 imes 10^{-3} - 1.5 imes 10^{-2}$, corresponding to friction velocities of $u_{au_0}approx 0.2 - 1$ m/s, this limits the size of stable LMGs to $g^{+0}approx 5 - 30$ at $Re_{au_0}approx 10^5$ and $g^{+0}approx 4-20$ at $Re_{au_0}approx 10^6$, and the maximum drag reductions to $DR_{max} sim 20- 30%$ at $Re_{au_0} sim 10^5$ and $DR_{max} sim 10 - 20%$ at $Re_{au_0} sim 10^6$.