Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier–Stokes (RANS) equations. In the past few years, with the availability of large and diverse data sets, researchers have begun to explore methods to systematically inform turbulence models with data, with the goal of quantifying and reducing model uncertainties. This review surveys recent developments in bounding uncertainties in RANS models via physical constraints, in adopting statistical inference to characterize model coefficients and estimate discrepancy, and in using machine learning to improve turbulence models. Key principles, achievements, and challenges are discussed. A central perspective advocated in this review is that by exploiting foundational knowledge in turbulence modeling and physical constraints, researchers can use data-driven approaches to yield useful predictive models.

Turbulence Modeling in the Age of Data

Data from experiments and direct simulations of turbulence have historically been used to calibrate simple engineering models such as those based on the Reynolds-averaged Navier--Stokes (RANS) equations. In the past few years, with the availability of large and diverse datasets, researchers have begun to explore methods to systematically inform turbulence models with data, with the goal of quantifying and reducing model uncertainties. This review surveys recent developments in bounding uncertainties in RANS models via physical constraints, in adopting statistical inference to characterize model coefficients and estimate discrepancy, and in using machine learning to improve turbulence models. Key principles, achievements and challenges are discussed. A central perspective advocated in this review is that by exploiting foundational knowledge in turbulence modeling and physical constraints, data-driven approaches can yield useful predictive models.

Results on turbulent skin friction reduction over air- and liquid-impregnated surfaces are presented for aqueous Taylor-Couette flow. The surfaces are fabricated by mechanically texturing the inner cylinder and chemically modifying the features to make them either non-wetting with respect to water (air-infused, or superhydrophobic case), or wetting with respect to an oil that is immiscible with water (liquid-infused case). The drag reduction, which remains fairly constant over the Reynolds number range tested (100 ≤ Reτ ≤ 140), is approximately 10% for the superhydrophobic surface and 14% for the best liquid-infused surface. Our results suggest that liquid-infused surfaces may enable robust drag reduction in high Reynolds number turbulent flows without the shortcomings associated with conventional superhydrophobic surfaces, namely, failure under conditions of high hydrodynamic pressure and turbulent flow fluctuations.

Turbulent drag reduction over air- and liquid- impregnated surfaces

Biomimetic multifunctional surfaces inspired from animals.

The mechanism of turbulent drag reduction (DR) with super-hydrophobic (SH) surfaces is investigated by direct numerical simulation (DNS) and analysis of the governing equations in channel flow. The DNS studies were performed using lattice Boltzmann methods in channels with ‘idealized’ SH surfaces on both walls, comprised of longitudinal micro-grooves (MG), transverse MG, or micro-posts. DRs of to , to , and to were realized in DNS with longitudinal MG, transverse MG, and micro-posts, respectively. By mathematical analysis of the governing equations, it is shown that, in SH channel flows with any periodic SH micro-pattern on the walls, the magnitude of DR can be expressed as , where the first term represents the DR resulting from the effective slip on the walls, and the second term represents the DR or drag increase (DI) resulting from modifications to the turbulence dynamics and any secondary mean flows established in the SH channel compared to a channel flow with no-slip walls at the same bulk Reynolds number as the SH channel. Comparison of this expression to DNS results shows that, with all SH surface micro-patterns studied, between 80 % and 100 % of the DR in turbulent flow arises from the effective slip on the walls. Modifications to the turbulence dynamics contribute no more than 20 % of the total DR with longitudinal MG or micro-posts of high shear-free fraction (SFF), and a DI with transverse MG or micro-posts of moderate SFF. The effect of the SH surface on the normalized dynamics of turbulence is found to be small in all cases, and confined to additional production of turbulence kinetic energy (TKE) within a thin ‘surface layer’ of thickness of the order of the width of surface micro-indentations. Outside of this ‘surface layer’, the normalized dynamics of turbulence proceeds as in a turbulent channel flow with no-slip walls at the friction Reynolds number of the SH channel flow.

On the mechanism of turbulent drag reduction with super-hydrophobic surfaces

Turbulent skin-friction drag reduction with superhydrophobic (SH) longitudinal microgrooves and riblets is investigated by direct numerical simulation (DNS), using lattice Boltzmann methods, in channel flow. The liquid/gas interfaces in the SH longitudinal microgrooves were modelled as stationary, curved, shear-free boundaries, with the meniscus shape determined from the solution of the Young–Laplace equation. Interface protrusion angles of were investigated. For comparison, the same geometries as those formed by the SH interfaces were also studied as riblets. Drag reductions of up to 61 % and up to 5 % were realized in DNS with SH longitudinal microgrooves and riblets, respectively, in turbulent channel flows at bulk Reynolds numbers of ( ) and ( ), with arrays of SH longitudinal microgrooves or riblets of size and on both walls, where and denote the widths and spacings of the microgrooves in base flow wall units, respectively. An exact analytical expression is derived which allows the net drag reduction in laminar or turbulent channel flow with any SH or no-slip wall micro-texture to be decomposed into contributions from: (i) the effective slip velocity at the wall, (ii) modifications to the normalized structure of turbulent Reynolds shear stresses due to the presence of this effective slip velocity at the wall, (iii) other modifications to the normalized structure of turbulent Reynolds shear stresses due to the presence of the wall micro-texture, (iv) modifications to the normalized structure of mean flow shear stresses due to the presence of the wall micro-texture and (v) the fraction of the flow rate through the wall micro-texture. Comparison to DNS results shows that SH longitudinal microgrooves and riblets share a common mechanism of drag reduction in which of the drag reduction arises from effects (i) and (ii). The contributions from (iii)–(v) were always drag enhancing, and followed a common scaling with SH longitudinal microgrooves and riblets when expressed as a function of the square root of the microgroove cross-sectional area in wall units. Extrapolation of drag reduction data from DNS to high Reynolds number flows of practical interest is discussed. It is shown that, for a given geometry and size of the surface micro-texture in wall units, the drag reduction performance of micro-textured surfaces degrades with increasing bulk Reynolds number of the flow. Curved SH interfaces at low protrusion angle ( ) were found to enhance the drag reduction by up to 3.6 % compared to flat interfaces, while reducing the instantaneous pressure fluctuations on the SH interfaces by up to a factor of two. This suggests that the longevity of SH interfaces in turbulent flow may be improved by embedding the SH surface within the microgrooves of shallow, scalloped riblets.

The common mechanism of turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves and riblets

The drag reduction characteristics and sustainability bounds of superhydrophobic (SH) surfaces in high Reynolds number turbulent flows are investigated using results from direct numerical simulation (DNS) and scaling-law analysis. The DNS studies were performed, using lattice Boltzmann methods, in turbulent channel flows at bulk Reynolds numbers of , allow for a priori prediction of the magnitude of drag reduction with SH or LI surfaces in turbulent flow at any Reynolds number. For the most stable of these SH surface microtextures, namely, longitudinal microgrooves, the pressure stability bounds of the SH surface under the pressure loads of turbulent flow are investigated. It is shown that the pressure stability bounds of SH surfaces are also significantly curtailed with increasing Reynolds number of the flow. Using these scaling laws, the narrow range of SH surface geometrical parameters which can yield large drag reduction as well as sustainability in high Reynolds number turbulent flows is identified.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/00F4EE9CA23AB316267936A665DC8FDF/S0022112018010273a.pdf/div-class-title-on-drag-reduction-scaling-and-sustainability-bounds-of-superhydrophobic-surfaces-in-high-reynolds-number-turbulent-flows-div.pdf

On drag reduction scaling and sustainability bounds of superhydrophobic surfaces in high Reynolds number turbulent flows

http://absimage.aps.org/image/DFD16/MWS_DFD16-2016-001581.pdf

The Common Mechanism of Turbulent Skin-Friction Drag Reduction with Super-Hydrophobic Micro-Grooves and Riblets

The structure and dynamics of turbulence in turbulent channel flow with super-hydrophobic (SH) walls has been investigated using DNS with Lattice Boltzmann methods. The channel walls consisted of longitudinal arrays of SH microgrooves of width g, separated by distances of w. The liquid/gas interfaces in the SH walls were modeled as idealized, flat, shear-free surfaces. Simulations were performed at a bulk Reynolds number of \(Re_b = U_{bulk} h/\nu = 3600\), corresponding to \(Re_{\tau _0} = u_{\tau _0} h / \nu \approx 223\). Drag reductions (DR) of 5–47 % and 51–83 % were obtained with \(g/w=1\), and \(g/w = 7\) and \(g/w = 15\), respectively. DR was found to be primarily due to surface slip. Mathematical analysis shows that the magnitude of DR in both laminar and turbulent flow is given by \(DR = U_{slip}/U_{bulk} + O(\varepsilon )\). In laminar flow, where DR is purely due to surface slip, \(\varepsilon \) is zero. In turbulent flow, \(\varepsilon \) attains a small nonzero value at high DR, reflecting additional DR effects resulting from modification of the turbulence dynamics in the interior of the flow due to the presence of the SH surface. Analysis of the turbulence statistics and kinetic energy budgets in the drag-reduced flow reveals that the influence of the SH surface remains confined to a surface layer of thickness on the order of the SH microgrooves width, g. Outside of this layer, the ‘normalized’ turbulence dynamics proceeds as in regular turbulent channel flow. Within the surface layer, the presence of the pattern of longitudinal microgrooves on the SH surfaces gives rise to spanwise variations in all Reynolds-averaged turbulence quantities, leading to development of a mean secondary flow and additional turbulence production and Reynolds shear stresses within the surface layer of the SH channel.

Amirreza Rastegari

Papers

On the mechanism of turbulent drag reduction with super-hydrophobic surfaces

The common mechanism of turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves and riblets

On drag reduction scaling and sustainability bounds of superhydrophobic surfaces in high Reynolds number turbulent flows

The Common Mechanism of Turbulent Skin-Friction Drag Reduction with Super-Hydrophobic Micro-Grooves and Riblets

Structure and Dynamics of Turbulence in Super-Hydrophobic Channel Flow