Direct numerical simulations of turbulent flows over superhydrophobic surfaces [electronic resource]
Keywords: Mechanical Engineering.

Superhydrophobic surfaces can effectively capture gas pockets within their micro-scale structures when submerged in water. A thin layer of gas pockets forms slippery boundaries for the overlaying liquid flow leading to reduced skin friction. Therefore, superhydrophobic surfaces present opportunities for improving hydrodynamic performance over a wide range of systems such as those in naval applications. In most realistic applications, the flow regime is turbulent. However, in such regimes the key physical phenomenon controlling drag reduction, and stability of gas pockets are not well understood. In this work direct numerical simulations of turbulent channel flows with superhydrophobic walls are used to analyze the kinematics as well as interfacial robustness of superhydrophobic surfaces. Superhydrophobic surfaces are modeled as heterogeneous mix of slip and no-slip boundary conditions corresponding to the surface texture. The gas-liquid interface is first assumed to be perfectly flat with infinite surface tension. Then we introduced deformability of the gas-liquid interface with finite surface tension. A wide range of texture and interfacial parameters are considered in this study, including texture size spanning from $L^+=6$ to $L^+=310$, solid fractions from $\phi_s$=1/4 to 1/64, and Weber number from $We_L=10^{-3}$ to $We_L=8\times 10^{-3}$. This thesis consists of four studies contributing towards understanding of interactions between turbulent flows and superhydrophobic surfaces. First, we presents a phenomenological model for the kinematics of flow near superhydrophobic surfaces with periodic post patterns at high Reynolds numbers. The model predicts an inverse square root scaling with solid fraction, and a cube root scaling of the slip length with pattern size, which is different from the previously reported scaling in the Stokes flow limit in the literature. A mixed model is then proposed that recovers both Stokes flow solution and the presented scaling respectively in the small and large texture size limits. This model is validated using DNS data over a wide range of texture sizes and solid fractions. Current study embarks on a review of a simplified model for the mean velocity profile and address two previous shortcomings regarding the closure and accuracy of this model. The process of homogenization of the texture effect to an effective slip length showed that for $L^+$ of up to $O(10)$, shear stress and slip velocity are perfectly correlated and well described by a homogenized slip length consistent with Stokes flow solutions. In contrast, in the limit of large $L^+$, the pattern-averaged shear stress and slip velocity become uncorrelated and thus the homogenized boundary condition is unable to capture the bulk behavior of the patterned surface. Second, the present work addresses the robustness of superhydrophobic surfaces by studying the load fields obtained from DNS data. This part focuses on how the textured surfaces create different pressure fields on the wall. For SHS with isotropic posts, effects of stagnation pressure formed by slip flow is mainly investigated. The pressure statistics at the wall are decomposed into two contributions, a coherent field, caused by the stagnation of slipping flow hitting solid posts, and a time-dependent field, caused by overlaying turbulence. The results show that the larger texture size intensifies the stagnation pressure contribution, while the turbulence contribution is essentially insensitive to $L^+$. The two-dimensional stagnation pressure distribution at the wall and the pressure statistics in the wall-normal direction are found to be self-similar for different $L^+$. The scaling of the induced pressure and the consequent deformations of the air-water interface are analyzed. Based on the results and considering finite contact angle, an upper bound on the texture wavelength is quantified that limits the range of robust operation of superhydrophobic surfaces when exposed to high speed flows. Results indicate that when the system parameters are in terms of viscous units, the main parameter controlling the stagnation pressure is $L^+$. However, when analyzing failure, two additional parameters, the Weber number and surface contact angle, play a role in determining the onset of failure. %Furthermore, the current work studies the dynamics associated with the deformability of the air-water interface when superhydrophobic surfaces are exposed to turbulent flows. The stagnation pressure effects are investigated in one-way coupled analyses where the effect of interface deformation on the flow is ignored. In the third study, we address this shortcoming by investigating fully coupled flow and interface phenomenon. Our results suggest that the deformability of the interface, characterized by a finite Weber number, contributes to the intensification of the turbulent pressure fluctuations near the surface. We demonstrate that the additional pressure field is due to a capillary wave that is energized by turbulence, and travels upstream. For SHSs with textures with textures a arrays of posts, we found that the deformability of interface intensifies the pressure fluctuations near the surface in spanwise-coherent modes, on top of stagnation pressure and pressure fluctuations from overlaying turbulence. The spatio-temporal characteristics of this pressure are quantified, and analyzed by a semi-analytical model. The nature and scaling of theses capillary waves are shown to be consistent between direct numerical simulations and semi-analytical models. The results suggest that the capillary waves are but are energized by the overlying turbulent flow developed as the normal modes of oscillation of the interface as a membrane. Results indicate that when the system parameters are in terms of viscous units, the main parameters controlling the dynamics of capillary wave is Weber number based on slip velocity and texture size, $We_s=\rho U_s^2 L/\sigma$ as well as $L^+$. Lastly, this work examines how the randomness of texture patterns can affect the drag reduction effectiveness and interfacial robustness when these surfaces are in contact with an overlaying turbulent flow. For fixed texture size and solid fraction, randomness of the feature distribution decreases the stability of the gas pocket when compared to surfaces with aligned features. Slip lengths of randomly distributed textures under turbulent flows are also indicate less drag reduction than those of surfaces with aligned features. Our results present a predictive quantification of the effect of texture randomness on both drag reduction and robustness.