Browsing by Subject "theoretical"

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    A numerical and theoretical study of drag reduction using superhydrophobic surfaces
    (2018-09) Li, Yixuan
    Motivated by the potential drag reduction benefits of superhydrophobic surfaces (SHS), direct numerical simulation (DNS) and theoretical analyses are used to explore the interaction between SHS and turbulent channel flow. First, DNS is used to study the drag reduction by SHS in laminar channel flow. Resolved multi-phase simulations using the volume of fluid (VOF) methodology are performed to study the effects of groove geometry, interface shear rate and meniscus penetration independently. An analytical solution for the flow in a laminar channel with grooved surface with gas-pocket within is obtained. The solution accounts for both the groove geometry and the trapped fluid properties, and shows good agreement with simulation results. The solution is used to propose a scaling law that collapses data across fully wetted to fully gas-filled regimes. The trapped gas is simulated as both flat and meniscal interfaces. The drag reduction initially increases with interface deflection into the groove and then decreases for large deflections as the interface velocity approaches zero due to the proximity to the bottom of the groove. Next, the geometric effect of SHS in turbulent flow is studied by performing DNS at friction Reynolds number $\Rey_\tau = 400$ over longitudinal grooves whose size is comparable to the viscous sublayer thickness. It is found that despite the bulk flow being close to that of a flat-wall channel, the slip effect of the grooves causes some differences within the viscous sublayer. Spectral analysis of the velocity transfer function between the interior and the exterior regions of the grooves shows that the grooves suppress the energy at low frequencies. The DNS reveals negligible Reynolds shear stress near the grooves, which motivates an unsteady Stokes flow model. It is assumed that the flow in the vicinity of the grooves is governed by the unsteady Stokes equations, forced by an oscillating external flow. The effects of streamwise, spanwise and vertical velocity, freestream wavenumber and the height of freestream perturbation above the groove are studied. The non-dimensional parameter $\omega L^2/\nu$ obtained from this model problem ($L$ is half of the groove span, $\omega$ is the frequency of the external turbulent signal and $\nu$ is the kinematic viscosity) is used to relate the model to the current DNS. Good agreement is seen with DNS at low frequencies. It is suggested that higher frequency disturbances are produced by smaller spanwise structures near the wall, and when this effect is accounted for, good agreement is also observed at higher frequencies. Finally, we study multiphase flow within grooved textures exposed to external unsteadiness. We derive analytical expressions for multiphase unsteady Stokes flow within periodic grooves driven by oscillating streamwise/spanwise freestream velocity. Good agreement is obtained between the analytical solution and DNS performed with the VOF method. The effect of oscillation frequency, Reynolds number, and the multiphase interface location on the transfer function between the input signal external to the groove and output near the interface, is examined. Also, the effective slip length and the shear stress over the grooved plane are studied.