Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F13: Boundary Layer: Superhydrophobic Surfaces IBoundary Layers FSI

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Chair: Rayhaneh Akhava, University of Michigan Room: 506 
Monday, November 20, 2017 8:00AM  8:13AM 
F13.00001: A numerical framework for the simulation of flows with soluble surfactant: application to superhydrophobic drag reduction Fernando TempranoColeto, Charles Cleret de Langavant, Arthur Guittet, Maxime Theillard, Francois Peaudecerf, Julien Landel, Paolo LuzzattoFegiz, Frederic Gibou The study of flow over superhydrophobic surfaces (SHS) is an area in which the role of surfactants has recently been proven as potentially critical (Peaudecerf et al., PNAS 2017). Traces of surfactants adsorb onto the plastron and are redistributed by the flow, triggering adverse Marangoni stresses that can negate drag reduction. This effect is crucially dependent on seven dimensionless groups describing momentum and surfactant transport, as well as on texture geometry, and is governed by six strongly coupled PDEs in a complex domain. To investigate this problem, as well as other flows with surfactants, we describe a new computational approach for the transport of soluble surfactant in an incompressible fluid (de Langavant et al., JCP 2017 and Guittet et al., JCP 2015). The interface is represented with a levelset approach, and the governing equations are discretized combining finitedifference and finitevolume techniques in Cartesian nonuniform Quad/Octree grids, which allow for an efficient treatment of the multiple scales involved. This research is intended to be the first building block towards direct numerical simulations of realistic turbulent flows over SHS inclusive of surfactants, which are unavoidable in largescale applications. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F13.00002: Thermal transport due to liquid jet impingement on superhydrophobic surfaces with isotropic slip: isoflux wall Matthew Searle, Julie Crockett, Daniel Maynes Thermal transport due to a liquid water jet impinging at an isoflux superhydrophobic surface with isotropic slip was modeled analytically by means of an integral analysis of the transport equations. The resulting system of ordinary differential equations was solved numerically. Impingement on superhydrophobic surfaces greatly reduces the heat transfer that occurs. Local and average Nusselt numbers are presented as a function of radial position (0 to 45 jet radii), jet Reynolds number ($3\times10^3$ to $1.5\times10^4$), liquid Prandtl number (2 to 11), normalized slip length (0 to 0.2), and normalized temperature jump length (0 to 0.2) and these results are all compared to classical behavior. The noslip and no temperature jump Nusselt numbers for the isoflux scenario are greater than the corresponding isothermal case. The difference in Nusselt number between these two heating conditions becomes negligible as the temperature jump length increases to quantities realizable on superhydrophobic surfaces undergoing jet impingement. [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F13.00003: Degradation of turbulent skinfriction drag reduction with superhydrophobic, liquidinfused and riblet surfaces with increasing Reynolds number Rayhaneh Akhavan, Amirreza Rastegari It is shown that the magnitude of Drag Reduction (DR) with SuperHydrophobic (SH), liquidinfused, or riblet surfaces can be parameterized in terms of the shift, $\Delta B$, in the intercept of a loglaw representation of the mean velocity profile and the friction coefficient of the base flow. Available DNS data shows $\Delta B$ to be Reynolds number independent and only a function of the geometrical parameters of the surface microtexture in viscous wall units. This allows the DR results from DNS to be extrapolated to higher Reynolds numbers. It is shown that for a given geometry and size of the wall microtexture in viscous wall units, the magnitude of DR degrades by factors of $\sim 2  3$ as the friction Reynolds number of the base flow increases from $Re_{\tau_0} \sim 200$ of DNS to $Re_{\tau_0} \sim 10^5 10^6$ of practical applications. Extrapolation of DNS results in turbulent channel flow at $Re_{\tau_0} \approx 222$ and $442$ with SH longitudinal microgrooves of width $15 \le g^{+0} \le 60$ and shearfreefractions of $0.8750.985$ shows that the maximum DRs which can be sustained with SH longitudinal microgrooves of size $g^{+0} \le 2030$ in practical applications is limited to DRs of $2535\%$ at $Re_{\tau_0} \sim 10^5$ and $2025\%$ at $Re_{\tau_0} \sim 10^6$. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F13.00004: Stability limits of superhydrophobic longitudinal microgrooves in high Reynolds number turbulent flows Amirreza Rastegari, Rayhaneh Akhavan 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 $Re_{\tau_0} \approx 222$ and 442 with SH LMGs at protrusion angle of $\theta=30^o$. Given that the magnitude of pressure fluctuations in turbulent channel flow scales as $p_{rms}^+ \sim \sqrt{\ln(Re_{\tau})}$, 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 $Re_{\tau_0} \sim 200$ of DNS to $Re_{\tau_0} \sim 10^5  10^6$ of practical applications. For SH LMGs operating at Weber numbers of $We^{+0} \equiv \mu u_{\tau_0}/\sigma \approx 3 \times 10^{3}  1.5 \times 10^{2}$, corresponding to friction velocities of $u_{\tau_0}\approx 0.2  1$ m/s, this limits the size of stable LMGs to $g^{+0}\approx 5  30$ at $Re_{\tau_0}\approx 10^5$ and $g^{+0}\approx 420$ at $Re_{\tau_0}\approx 10^6$, and the maximum drag reductions to $DR_{max} \sim 20 30\%$ at $Re_{\tau_0} \sim 10^5$ and $DR_{max} \sim 10  20\%$ at $Re_{\tau_0} \sim 10^6$. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F13.00005: Direct Numerical Simulation of Multiphase flow over Realistic Superhydrophobic Surfaces Karim Alame, Krishnan Mahesh Direct numerical simulations are performed using the volume of fluid methodology, for turbulent channel flow of water over a realistic superhydrophobic surface, which traps air. The surface is obtained from scanned data of the real sprayed surface. Multiphase laminar Couette flow and turbulent channel cases are examined. Drag reduction for different interface heights are shown, and the effect of turbulence on multiphase flow over rough surfaces is discussed. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F13.00006: Multiphase unsteady Stokes flow over longitudinal grooved surface: an analytical study Krishnan Mahesh, Yixuan Li, Karim Alame Motivated by recent interest in superhydrophobic technology, we study the effect of grooved multiphase textures exposed to turbulent channel flow of one fluid, while being infused with a second fluid. An analytical solution of unsteady Stokes flow in the presence of spanwise periodic grooves is derived. Comparison with volume of fluid (VOF) simulation data shows good agreement. The solution scales with $\omega L^2/\nu$, where $\omega$ is the frequency of the oscillatory slip velocity, $L$ is the characteristic length of the groove, and $\nu$ is the kinematic viscosity of the external fluid. A parametric study of the viscosity ratio between the two types of fluid, the penetration of the outside flow, and the frequency of the oscillatory slip velocity is presented. Our theoretical analysis shows that the multiphase grooved surface produces a highpass filter effect on turbulent flow. [Preview Abstract] 
Monday, November 20, 2017 9:18AM  9:31AM 
F13.00007: Drag penalty due to the asperities in the substrate of superhydrophobic and liquid infused surfaces Edgardo J. Garcia Cartagena, Isnardo Arenas, Stefano Leonardi Direct numerical simulations of two superposed fluids in a turbulent channel with a textured surface made of pinnacles of random height have been performed. The viscosity ratio between the two fluids are $N=\mu_o/\mu_i=50$ ($\mu_o$ and $\mu_i$ are the viscosities of outer and inner fluid respectively) mimicking a superhydrophobic surface (water over air) and N=2.5 (water over heptane) resembling a liquid infused surface. Two set of simulations have been performed varying the Reynolds number, $Re_\tau=180$ and $Re_\tau=390$. The interface between the two fluids is flat simulating infinite surface tension. The position of the interface between the two fluids has been varied in the vertical direction from the base of the substrate (what would be a rough wall) to the highest point of the roughness. Drag reduction is very sensitive to the position of the interface between the two fluids. Asperities above the interface induce a large form drag and diminish considerably the drag reduction. When the mean height of the surface measured from the interface in the outer fluid is greater than one wall unit, $k^+>1$, the drag increases with respect to a smooth wall. Present results provide a guideline to the accuracy required in manufacturing superhydrophobic and liquid infused surfaces. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F13.00008: Coherent structures over Super Hydrophobic and Liquid Infused Surfaces Isnardo Arenas, Matteo Bernardini, Stefano Leonardi Numerical Simulations of two superposed fluids in a turbulent channel have been performed. Both walls of the channel are made of longitudinal riblets with a gas fractions of $0.5$ and several pitch values $p^+=18, 36, 72, 144$. For Liquid Infused Surfaces, LIS, with a viscosity ratio $m = \mu_1/\mu_2 = 0.4$ (where the subscripts $1$ and $2$ indicate the fluid in the cavities and the overlying fluid respectively) two cases have been considered varying the Weber number: $We = 0$, implying an interface sustained by the surface tension and $We = 1000$ with the dynamics of the interface between the two fluids modeled with a Level Set Approach. Results are compared to the case mimicking water over air (Super hydrophobic Surface SHS $m = 0.02$) and $We=0$. A smooth channel with one fluid only at $Re_{\tau}=180$ is used as reference and to assess how the LIS and SHS modify coherent structures near the wall. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F13.00009: The application of slip length models to larger textures in turbulent flows over superhydrophobic surfaces Chris Fairhall, Ricardo GarciaMayoral We present results from direct numerical simulations of turbulent flows over superhydrophobic surfaces. We assess the validity of simulations where the surface is modelled as homogeneous slip lengths, comparing them to simulations where the surface texture is resolved. Our results show that once the coherent flow induced by the texture is removed from the velocity fields, the remaining flow sees the surface as homogeneous. We then investigate how the overlying turbulence is modified by the presence of surface texture. For small textures, we show that turbulence is shifted closer to the wall due to the presence of slip, but otherwise remains essentially unmodified. For larger textures, the texture interacts with the turbulent lengthscales, thereby modifying the overlying turbulence. We also show that the saturation of the effect of the spanwise slip length (Fukagata et al. 2006, Busse & Sandham 2012, Seo & Mani 2016), which is drag increasing, is caused by the impermeability imposed at the surface. [Preview Abstract] 
Monday, November 20, 2017 9:57AM  10:10AM 
F13.00010: Effect of angle of obliquely aligned superhydrophobic surface on dragreducing performance in turbulent channel flow Hiroya Mamori, Sho Watanabe, Koji Fukagata Direct numerical simulation of a turbulent channel flow with superhydrophobic surfaces is performed to investigate friction drag reduction effect. All simulations are performed under a constant pressure gradient and the friction Reynolds number is set to be 180. Especially, we focus on the influence of the angle of microridge structure to flow direction. The gas area fraction on the surface is kept at 50\% and the groove width is kept constant at 33.75 wall units. When the microridge is parallel to the flow, the bulk mean velocity is increased about 15\% which corresponds the skinfriction drag reduction effect. As increasing the microridge angle, the drag reduction effect is found to deteriorate rapidly due to a decrease in the slip velocity. We also perform the analysis for the Reynolds stress budgets and found that the modification in each physical effect is qualitatively similar for different angle cases, but it is more pronounced if the microridge is aligned with the stream. [Preview Abstract] 
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