Credible computational fluid dynamic (CFD) simulations of aortic dissection are challenging, because the defining parallel flow channels-the true and the false lumen-are separated from each other by a more or less mobile dissection membrane, which is made up of a delaminated portion of the elastic aortic wall. We present a comprehensive numerical framework for CFD simulations of aortic dissection, which captures the complex interplay between physiologic deformation, flow, pressures, and time-averaged wall shear stress (TAWSS) in a patient-specific model. Our numerical model includes (1) two-way fluid-structure interaction (FSI) to describe the dynamic deformation of the vessel wall and dissection flap; (2) prestress and (3) external tissue support of the structural domain to avoid unphysiologic dilation of the aortic wall and stretching of the dissection flap; (4) tethering of the aorta by intercostal and lumbar arteries to restrict translatory motion of the aorta; and a (5) independently defined elastic modulus for the dissection flap and the outer vessel wall to account for their different material properties. The patient-specific aortic geometry is derived from computed tomography angiography (CTA). Three-dimensional phase contrast magnetic resonance imaging (4D flow MRI) and the patient's blood pressure are used to inform physiologically realistic, patient-specific boundary conditions. Our simulations closely capture the cyclical deformation of the dissection membrane, with flow simulations in good agreement with 4D flow MRI. We demonstrate that decreasing flap stiffness from [Formula: see text] to [Formula: see text] kPa (a) increases the displacement of the dissection flap from 1.4 to 13.4 mm, (b) decreases the surface area of TAWSS by a factor of 2.3, (c) decreases the mean pressure difference between true lumen and false lumen by a factor of 0.63, and (d) decreases the true lumen flow rate by up to 20% in the abdominal aorta. We conclude that the mobility of the dissection flap substantially influences local hemodynamics and therefore needs to be accounted for in patient-specific simulations of aortic dissection. Further research to accurately measure flap stiffness and its local variations could help advance future CFD applications.

Fluid–structure interaction simulations of patient-specific aortic dissection

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with , drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above , the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of , the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ( ), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

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High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

Superhydrophobic surfaces can entrap gas pockets within their grooves when submerged in water. Such a mixed-phase boundary is shown to result in an effective slip velocity on the surface, and has promising potential for drag reduction and energy-saving in hydrodynamic applications. The target flow regime, in most such applications, is a turbulent flow. Previous analyses of this problem involved direct numerical simulations of turbulence with the superhydrophobic surface modelled as a flat boundary, but with a heterogeneous mix of slip and no-slip boundary conditions corresponding to the surface texture. Analysis of the kinematic data from these simulations has helped to establish the magnitude of drag reduction for various texture topologies. The present work is the first investigation that, alongside a kinematic investigation, addresses the robustness of superhydrophobic surfaces by studying the load fields obtain from data from direct numerical simulations (DNS). The key questions at the focus of this work are: does a superhydrophobic surface induce a different pressure field compared to a flat surface? If so, how does this difference scale with system parameters, and when does it become significant that it can deform the air-water interface and potentially rapture the entrapped gas pockets? To this end, we have performed DNS of turbulent channel flows subject to superhydrophobic surfaces over a wide range of texture sizes spanning values from to when expressed in terms of viscous units. The pressure statistics at the wall are decomposed into two contributions: one coherent, caused by the stagnation of slipping flow hitting solid posts, and one time-dependent, caused by overlying turbulence. The results show that the larger texture size intensifies the contribution of stagnation pressure, while the contribution from turbulence is essentially insensitive to . 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 . The scaling of the induced pressure and the consequent deformations of the air-water interface are analysed. Based on our results, 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. Our results indicate that when the system parameters are expressed in terms of viscous units, the main parameters controlling the problem are and a Weber number based on inner dimensions; We obtain good collapse when all our results are expressed in wall units, independently of the Reynolds number.

Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces

Underwater Superhydrophobicity: Stability, Design and Regulation, and Applications

In this review, we discuss how superhydrophobic surfaces (SHSs) can provide friction drag reduction in turbulent flow. Whereas biomimetic SHSs are known to reduce drag in laminar flow, turbulence adds many new challenges. We first provide an overview on designing SHSs, and how these surfaces can cause slip in the laminar regime. We then discuss recent studies evaluating drag on SHSs in turbulent flow, both computationally and experimentally. The effects of streamwise and spanwise slip for canonical, structured surfaces are well characterized by direct numerical simulations, and several experimental studies have validated these results. However, the complex and hierarchical textures of scalable SHSs that can be applied over large areas generate additional complications. Many studies on such surfaces have measured no drag reduction, or even a drag increase in turbulent flow. We discuss how surface wettability, roughness effects and some newly found scaling laws can help explain these varied results. Overall, we discuss how, to effectively reduce drag in turbulent flow, an SHS should have: preferentially streamwise-aligned features to enhance favourable slip, a capillary resistance of the order of megapascals, and a roughness no larger than 0.5, when non-dimensionalized by the viscous length scale.This article is part of the themed issue 'Bioinspired hierarchically structured surfaces for green science'.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2016.0189

Bioinspired surfaces for turbulent drag reduction.

Superhydrophobic surfaces can significantly reduce hydrodynamic skin drag by accommodating large slip velocity near the surface due to entrapment of air bubbles within their micro-scale roughness elements. While there are many Stokes flow solutions for flows near superhydrophobic surfaces that describe the relation between effective slip length and surface geometry, such relations are not fully known in the turbulent flow limit. In this work, we present a phenomenological model for the kinematics of flow near a superhydrophobic surface 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 reported scaling in the Stokes flow limit. 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 direct numerical simulations of turbulent flows over superhydrophobic posts over a wide range of texture sizes from L+ ≈ 6 to 310 and solid fractions from ϕs = 1/9 to 1/64. Our report also embarks on the extension of friction laws of turbulent wall-bounded flows to superhydrophobic surfaces. To this end, we present a review of a simplified model for the mean velocity profile, which we call the shifted-turbulent boundary layer model, and address two previous shortcomings regarding the closure and accuracy of this model. Furthermore, we address the process of homogenization of the texture effect to an effective slip length by investigating correlations between slip velocity and shear over pattern-averaged data for streamwise and spanwise directions. 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.

On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces

Superhydrophobic surfaces can retain gas pockets within their microscale textures when submerged in water. This property reduces direct contact between water and solid surfaces and presents opportunities for improving hydrodynamic performance by decreasing viscous drag. In most realistic applications, however, the flow regime is turbulent and retaining the gas pockets is a challenge. In order to overcome this challenge, it is crucial to develop an understanding of physical mechanisms that can lead to the failure of superhydrophobic surfaces in retaining gas pockets when the overlying liquid flow is turbulent. We present a study of the onset of failure in gas retention by analysing direct numerical simulations (DNS) of turbulent flows over superhydrophobic surfaces coupled with the deformation of air–water interfaces that hold the gas pockets. The superhydrophobic surfaces are modelled as periodic textures with patterned slip and no-slip boundary conditions on the overlying water flow. The liquid–gas interface is modelled via a linearized Young–Laplace equation, which is solved coupled with the overlying turbulent flow. A wide range of texture sizes and interfacial Weber numbers are considered in this study. Our analysis identifies flow-induced upstream-travelling capillary waves that are coherent in the spanwise direction as one mechanism for failure in retention of gas pockets. To confirm physical understanding of these waves, a semianalytical inviscid linear analysis is developed; the wave speeds obtained from the space–time correlations in the DNS data were found to match with the predictions of the semianalytical model. The magnitude of the pressure fluctuations due to these waves was found to increase with decreasing surface tension, and increase with a much stronger dependence on the slip velocity, when all numbers are reported in wall units. Based on a fitted scaling, a threshold criterion for the failure of superhydrophobic surfaces is developed that is based on estimates of the onset condition required for the motion of contact lines. The second contribution of this work is the development of boundary maps that identify stable and unstable zones in a parameter space consisting of working parameter and design parameters including texture size and material contact angle. We provide a brief description of previously identified failure modes of superhydrophobic surfaces, namely the stagnation pressure and shear-driven drainage mechanisms. In an overlay map, the stable and unstable zones due to each mechanism are presented. For various input conditions, we provide scaling laws that identify the most critical mechanism limiting the stability of gas retention by superhydrophobic surfaces.

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Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces

Drag reduction and interfacial robustness of turbulent flows over superhydrophobic surfaces with randomly distributed textures are investigated using direct numerical simulations. Slip length, pressure fluctuations, and interface deformations are analyzed and compared against aligned textures.

Jongmin Seo

Papers

Fluid–structure interaction simulations of patient-specific aortic dissection

Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces

On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces

Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces

Effect of texture randomization on the slip and interfacial robustness in turbulent flows over superhydrophobic surfaces