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arXiv2021

Optimizing wave-generation and wave-damping in 3D-flow simulations with implicit relaxation-zones

In finite-volume-based flow-simulations with free-surface waves, wave reflections at the domain boundaries can cause substantial errors in the results and must therefore be minimized. This can be achieved via `implicit relaxation zones', but only if the relaxation zone's case-dependent parameters are optimized. This work proposes an analytical approach for optimizing these parameters. The analytical predictions are compared against results from 2D-flow simulations for different water depths, flow solvers, and relaxation functions, and against results from 3D-flow simulations with strongly wave-reflecting bodies subjected to nonlinear free-surface waves. The present results demonstrate that the proposed approach satisfactorily predicts both the optimum parameter settings and the upper-limit for the corresponding reflection coefficients $C_{\mathrm{R}}$. Simulation results for $C_{\mathrm{R}}$ were mostly below or equal to the analytical predictions, but never more than $3.4\%$ larger. Therefore, the proposed approach can be recommended for engineering practice. Furthermore, it is shown that implicit relaxation zones can be considered as a special-case of forcing zones, a family of approaches which includes among others absorbing layers, damping zones and sponge layers. The commonalities and differences between these approaches are discussed, including to what extend the present findings are applicable to these other approaches and vice versa.

physics.flu-dyn↗
arXiv2018

Mixed modeling for large-eddy simulation: the minimum-dissipation-bardina model

The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES) approach. The current work applies a volume filtering procedure according to Schumann (1975). To demonstrate the procedure the Schumann filter is first applied to a convection-diffusion equation. The Schumann filter results in volume-averaged equations, which are not closed. To close these equations a model is introduced, which represents the interaction between the resolved scales and the small subgrid scales. Here, the anisotropic minimum-dissipation model of Rozema et al. (2015) is considered. The interpolation scheme necessary to evaluate the convective flux at the cell faces can be viewed as a second filter. Thus, the convection term of the filtered convection-diffusion equation can be interpreted as a double-filtered term. This term is approximated by the scale similarity model of Bardina et al. (1983). Thus, a mixed minimum-dissipation-Bardina model is obtained. Secondly, the mathematical methodology is extended to the Navier-Stokes equations. Here, the pressure term is analyzed separately and added to the convection-diffusion equation as a sink term. Finally, spatially filtered Navier-Stokes equations that depend on both the anisotropic minimum-dissipation (AMD) model proposed by Rozema et al. (2015) and the scale similarity model of Bardina et al. (1983) are obtained. Hence, a mathematically consistent method of mixing the AMD model and the Bardina model is achieved.

physics.flu-dyn↗
arXiv2018

Reducing water entry impact forces

The forces on an object impacting the water are extreme in the early moments of water entry and can cause structural damage to biological and man-made bodies alike. These early-time forces arise primarily from added mass, peaking when the submergence is much less than one body length. We experimentally investigate a means of reducing impact forces on rigid spheres by making a jet of water strike the quiescent water surface prior to the object impacting. The water jet accelerates the pool liquid and forms a cavity into which a sphere falls. Through on-board accelerometer measurements and high speed imaging, we quantify the force reduction compared to the case of a sphere entering a quiescent pool. Finally, we find the emergence of a critical jet volume required to maximize force reduction; the critical volume is rationalized using scaling arguments informed by near-surface particle image velocimetry (PIV) data.

physics.flu-dyn↗
arXiv2018

An adaptive solver for viscoelastic incompressible two-phase problems applied to the study of the splashing of slightly viscoelastic droplets

We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal & Kupferman (2004,2005} combined with the time-split scheme proposed by Hao & Pan (2007}. The use of this time-split scheme has been proven to increase the stability of the numerical computation of two-phase flows. We show that the adaptive computational technique can be used to simulate viscoelastic flows efficiently. The solver is coded using the open-source libraries provided by the \basilisk \cite{Basilisk} platform. In particular, the method is implemented for Oldroyd-B type viscoelastic fluids and related models (FENE-P and FENE-CR). The numerical scheme is then used to study the splashing of weakly viscoelastic drops. The solvers and tests of this work are freely available on the Basilisk web site

physics.flu-dyn↗
arXiv2019

Theoretical justification and error analysis for slender body theory

Slender body theory facilitates computational simulations of thin fibers immersed in a viscous fluid by approximating each fiber using only the geometry of the fiber centerline curve and the line force density along it. However, it has been unclear how well slender body theory actually approximates Stokes flow about a thin but truly three-dimensional fiber, in part due to the fact that simply prescribing data along a one-dimensional curve does not result in a well-posed boundary value problem for the Stokes equations in $\mathbb{R}^3$. Here, we introduce a PDE problem to which slender body theory (SBT) provides an approximation, thereby placing SBT on firm theoretical footing. The slender body PDE is a new type of boundary value problem for Stokes flow where partial Dirichlet and partial Neumann conditions are specified everywhere along the fiber surface. Given only a 1D force density along a closed fiber, we show that the flow field exterior to the thin fiber is uniquely determined by imposing a fiber integrity condition: the surface velocity field on the fiber must be constant along cross sections orthogonal to the fiber centerline. Furthermore, a careful estimation of the residual, together with stability estimates provided by the PDE well-posedness framework, allow us to establish error estimates between the slender body approximation and the exact solution to the above problem. The error is bounded by an expression proportional to the fiber radius (up to logarithmic corrections) under mild regularity assumptions on the 1D force density and fiber centerline geometry.

math.AP↗
arXiv2018

Structure and Persistence of Ship Wakes and the Role of Langmuir-Type Circulations

Surface ships operating in ocean waves are shown to generate transverse surface currents which persist long after the initial ship-induced currents have decayed. These surface currents are due to the formation of large-scale Langmuir-type circulations and are suggested to be the mechanism for the concentration of surface-active substance into streaks or bands, which are regularly seen in synthetic aperture radar imagery of the ocean surface. These circulations are generated by the Craik-Leibovich vortex force, which results from interaction of ship-induced current with ambient surface waves. Once generated, the circulations persist due to their large-scale nearly-inviscid nature. Numerical simulations of the wake behind a surface ship in calm, head, and following seas are presented and show good agreement with radar imagery from at-sea experiments. It is demonstrated that surface currents do not persist in the absence of surface waves, but can persist for tens of kilometers through the formation of Langmuir-type circulations. Since the circulations are driven by the cross product of the Stokes drift and the wake vorticity, the structure of the persistent wake is a function of relative heading of the ship with respect to the direction of surface-wave propagation.

physics.flu-dyn↗
arXiv2018

Numerical investigations of the fluid-structure interaction of a NACA0012 airfoil based on large-eddy simulations

The purpose of this work is to expand the work of Streher (2017) in order to investigate the aeroelastic instabilities generated by the flow around a moving NACA0012 airfoil. The profile has a chord length of $c=0.1 m and is exposed to a flow at a Reynolds number of Re=30,000. The airfoil has only two degrees of freedom: Translation in relation to the vertical direction and a rotation around the span-wise axis. A partitioned approach based on two separate solvers and a fluid-structure interaction (FSI) coupling scheme is applied. The in-house CFD solver FASTEST-3D computes the fluid sub-problem according to the wall-resolved large-eddy simulation (LES) combined with the Smagorinsky model (1963). The structural sub-problem is solved by a rigid movement solver implemented by Viets (2013), which is based on the equations of motion for rigid bodies. The FSI coupling exchanges information between both solvers based on loose or strong coupling algorithms. A thorough analysis of the problem is primarily performed in order to acquire a computational setup that provides the best compromise between accuracy and CPU-time requirements. Three system configurations are then tested and thoroughly investigated: One leads to an oscillatory behavior of the airfoil characterized by limited small amplitudes. The other is characterized by the presence of the torsional divergence aeroelastic instability. Finally, a configuration aimed at the flutter phenomenon is established. However, not enough data are currently available and therefore this dynamic aeroelastic instability can not be thoroughly investigated in the present work. In the near future, this study will serve as a base for the flutter experiments and computations performed at the Department of Fluid Mechanics located of the Helmut-Schmidt-University.

physics.flu-dyn↗
arXiv2018

Large-eddy simulations of the flow around a NACA0012 airfoil at different angles of attack

The purpose of this work is to investigate the flow around a fixed NACA0012 airfoil profile at different angles of attack using wall-resolved LES. The profile has a chord length of c=0.1 m and is exposed to a flow at a Reynolds number of Re=100,000. The background is that in the next step the coupled problem should be considered, dealing with the flutter problem. The software ANSYS ICEM CFD is utilized in order to generate the meshes, which are then applied for the simulation with the in-house software FASTEST-3D. This is based on a finite-volume approach and a three sub-steps predictor-corrector scheme as spatial and temporal discretizations, respectively. The turbulence is modeled by the large-eddy simulation technique and the subgrid-scales are modeled according to Smagorinsky. An analysis of the meshes concerning the dimensionless wall distances is performed based on the spatial and time-averaged results of the velocities, the spatial and time-averaged streamlines, the instantaneous velocities, the spatial and time-averaged Reynolds stresses and the aerodynamic coefficients. A selection of the less computational time demanding grids that can correctly approximate the solutions of the test case is made. In a near future these will be applied to investigate the fluid-structure interaction and particularly the flutter phenomenon of the NACA0012 profile within a turbulent flow.

physics.flu-dyn↗
arXiv2018

Numerical simulations of emulsions in shear flows

We present a modification of a recently developed volume of fluid method for multiphase problems, so that it can be used in conjunction with a fractional step-method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity on the volume-fraction (from 10% to 30%) and the Capillary number (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibits a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them.

physics.flu-dyn↗
arXiv2018

Nonlinear dynamo in obliquely rotating stratified electroconductive fluid in an uniformly magnetic field

We study a new type of large-scale instability, which arises in obliquely rotating stratified electroconductive fluid with an external uniform magnetic field and a small-scale external force having zero helicity. This force gives rise to small-scale oscillations of the velocity with a small Reynolds number. Using the method of multi-scale asymptotic expansions there are obtained nonlinear equations for vortex and magnetic perturbations in the third order in Reynolds number. Studied is the linear stage of magneto-vortex dynamo caused by instabilities of $α$-effect type. Stationary solutions for the equations of nonlinear magneto-vortex dynamo are found by numerical methods in the form of localized chaotic structures.

physics.flu-dyn↗
arXiv2018

Assessment of the impact of two-dimensional wall deformations' shape on high-speed boundary layer disturbances

Previous experimental and numerical studies showed that two-dimensional roughness elements can stabilize disturbances inside a hypersonic boundary layer, and eventually delay the transition onset. The objective of this paper is to evaluate the response of disturbances propagating inside a high-speed boundary layer to various two-dimensional surface deformations of different shapes. We perform an assessment of the impact of various two-dimensional surface non-uniformities, such as backward or forward steps, combinations of backward and forward steps, wavy surfaces, surface dips, and surface humps. Disturbances inside a Mach 5.92 flat-plate boundary layer are excited using periodic wall blowing and suction at an upstream location. The numerical tools consist of a high-accurate numerical algorithm solving for the unsteady, compressible form of the Navier-Stokes equations in curvilinear coordinates. Results show that all types of surface non-uniformities are able to reduce the amplitude of boundary layer disturbances to a certain degree. The amount of disturbance energy reduction is related to the type of pressure gradients that are posed by the deformation (adverse or favorable). A possible cause (among others) of the disturbance energy reduction inside the boundary layer is presumed to be the result of a partial deviation of the kinetic energy to the external flow, along the discontinuity that is generated by the wall deformation.

physics.flu-dyn↗
arXiv2018

Self-sorting of Bi-dispersed Colloidal Particles near Contact Line of an Evaporating Sessile Droplet

We investigate deposit patterns and associated morphology formed after the evaporation of an aqueous droplet containing mono- and bi-dispersed colloidal particles. In particular, the combined effect of substrate heating and particle diameter is investigated. We employ high-speed visualization, optical microscopy and scanning electron microscopy to characterize the evaporating droplets, particle motion, and deposit morphology, respectively. In the context of mono-dispersed colloidal particles, an inner deposit and a typical ring form for smaller and larger particles, respectively, on a nonheated surface. At larger substrate temperature, a thin ring with inner deposit forms, explained by the self-pinning of the contact line and advection of the particles from the contact line to the center of the droplet due to Marangoni flow. In the context of bi-dispersed colloidal particles, self-sorting of the colloidal particles within the ring occurs at larger substrate temperature. The smaller particles deposit at the outermost edge as compared to the larger diameter particles and this preferential deposition in a stagnation region near the contact line is due to the spatially-varying height of the liquid-gas interface above the substrate. The sorting occurs at a smaller ratio of the diameter of the smaller and larger particle. At the larger substrate temperature and a larger ratio, the particles do not get sorted and mix into each other. Our measurements show that there exists a critical substrate temperature as well as a diameter ratio in order to achieve the sorting. We propose regime maps on substrate temperature-particle diameter and substrate temperature-diameter ratio plane for mono- and bi-dispersed solutions, respectively.

physics.flu-dyn↗
arXiv2018

Analysis of an Evaporating Sessile Droplet on a Non-Wetted Surface

We investigate evaporation of a sessile droplet on a non-wetted surface in the framework of diffusion-limited and quasi-steady evaporation. We extend previous models and numerically solve Laplace equation for the diffusion of liquid vapor in ambient. We propose a unified, simple and accurate expression of the evaporation mass flux valid for 90^o < theta < 180^o, where theta is the equilibrium contact angle. In addition, using the derived expression of the evaporation mass flux, we propose a simple and accurate expression of the evaporation mass rate for a non-wetted surface, which does not exhibit singularity at theta = 180^o. Finally, using the scaling analysis, the expression of the evaporation mass flux is utilized to estimate the direction and magnitude of the characteristic evaporation-driven flow velocity inside the droplet on a non-wetted surface. The predicted flow direction is found to be consistent with the previous measurements.

physics.flu-dyn↗
arXiv2018

Competitive electrohydrodynamic and electrosolutal advection arrests evaporation kinetics of droplets

The present article reports the hitherto unreported phenomenon of arrested evaporation dynamics in pendent droplets in an electric field ambience. The evaporation kinetics of pendant droplets of electrically conducting saline solutions in the presence of a transverse, alternating electric field is investigated experimentally. It has been observed that while increase of field strength arrests the evaporation, increment in field frequency has the opposite effect. The same has been explained on the solvation kinetics of the ions in the polar water. Theoretical analysis reveals that change in surface tension and diffusion driven evaporation model cannot predict the arrested or decelerated evaporation. With the aid of Particle Image Velocimetry, suppression of internal circulation velocity within the droplet is observed under electric field stimulus, and this affects the evaporation rate directly. A mathematical scaling model is proposed to quantify the effects of electrohydrodynamic circulation, electrothermal and electro-solutal advection on the evaporation kinetics of the droplet. The analysis encompasses major governing parameters, viz. the thermal and solutal Marangoni numbers, the Electrohydrodynamic number, the electro Prandtl and electro Schmidt numbers and their respective contributions. It has been shown that the electrothermal Marangoni effect is supressed by the electric field, leading to deteriorated evaporation rates. Additionally, the electrosolutal Marangoni effect further supresses the internal advection, which again arrests the evaporation rate by a larger proportion. Stability analysis reveals that the electric body force retards the stable internal circulation within such droplets and arrests advection.

physics.flu-dyn↗
arXiv2018

Variational Lagrangian formulation of the Euler equations for incompressible flow: A simple derivation

In 1966, Arnold [1] showed that the Lagrangian flow of ideal incompressible fluids (described by Euler equations) coincide with the geodesic flow on the manifold of volume preserving diffeomorphisms of the fluid domain. Arnold's proof and the subsequent work on this topic rely heavily on the properties of Lie groups and Lie algebras which remain unfamiliar to most fluid dynamicists. In this note, we provide a simple derivation of Arnold's result which only uses the classical methods of calculus of variations. In particular, we show that the Lagrangian flow maps generated by the solutions of the incompressible Euler equations coincide with the stationary curves of an appropriate energy functional when the extremization is carried out over the set of volume-preserving diffeomorphisms.

physics.flu-dyn↗
arXiv2019

Helicity dynamics, inverse and bi-directional cascades in fluid and MHD turbulence: A brief review

We briefly review helicity dynamics, inverse and bi-directional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the non-dissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two-dimensional fluid, energy cascades instead to larger scales, and so does magnetic helicity in three-dimensional MHD. However, evidence obtained recently indicates that in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including with quasi-geostrophic forcing. Such bi-directional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due for example to imposed rotation, stratification or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly-resolved data sets stemming from large laboratory experiments, high-performance computing and in-situ satellite observations, machine-learning tools are bringing novel perspectives to turbulence research, e.g. in helping devise new explicit sub-grid scale parameterizations, which may lead to enhanced physical insight, including in the future in the case of these new bi-directional cascades.

physics.flu-dyn↗
arXiv2018

The Surprising Transition in Atmospheric Boundary Layer Turbulence Structure from Neutral to Moderately Convective Stability States and Mechanisms Underlying Large-scale Rolls

The vectoral wind structure of daytime atmospheric boundary layer (ABL) turbulence is strongly dependent on the balance between shear-driven turbulence production of horizontal fluctuations (driven by winds at the mesoscale), and buoyancy-driven turbulence production of vertical velocity fluctuations (driven by solar heating), characterized by the global instability state parameter $-z_i/L > 0$. In the fully shear-driven neutral limit $-z_i/L \rightarrow 0$, the surface layer is dominated by coherent streamwise-elongated concentrations of negative streamwise fluctuating velocity (low-speed streaks), while in the moderately convective state ($z_i/L \sim 10$ ) buoyancy generates streamwise-elongated thermal updraft sheets of concentrated vertical velocity fluctuations. Using large-eddy simulation (LES), we study the transition between the neutral and moderately convective states by quantifying correlations and integral scales as a function of $-z_i/L$ created by systematically increasing surface heat flux with fixed geostrophic wind. We discover a surprising sudden transition in ABL turbulence structure at $-z_i/L \approx 0.40$ with dramatic enhancement of streamwise coherence, particularly in the mixed layer, and a sudden change in ABL dynamic response to further increase in surface heating. In the supercritical ABL, continued increase in surface heat flux leads to a maximal coherence state at ($z_i/L \sim 1.0-1.5$) associated with helical large-scale roll structure and exceptionally coherent thermal updrafts, a process driven by two key dynamical effects: (a) a surprising continual increase in streamwise coherence of streamwise velocity fluctuations and shear-driven low-speed streaks and (b) increasing spatial correlation between the coherent low-speed streaks in the surface layer below and in the coherent thermal updrafts with in the mixed layer above.

physics.flu-dyn↗