Free Surface Effects Research Articles

Prediction of flow around a sharp-nosed bridge pier: influence of the Froude number and free-surface variation on the flow field

This study investigates the influence of free-surface variation on the velocity field using numerical simulations of flow around a sharp-nosed pier that is representative of a typical masonry bridge pier. The study evaluates the assumption that free-surface effects are negligible at small Froude numbers by comparing the change in flow field predictions due to the use of a free-surface model (i.e. multi-phase simulation with a volume of fluid (VOF) model in place of a rigid-lid approximation (i.e. single phase simulation). Results show that simulations using the VOF model are in better agreement with experimental data than those using the rigid-lid approximation. Importantly, results show that even though the change in free-surface height near the pier is small comparative to the approach flow, it still has a significant effect on velocities in front of the pier and in the wake region, and including at low Froude numbers.

The free surface effect on a chemotaxis–diffusion–convection coupling system

Suspension of an oxytactic bacteria (e.g. the species Bacillus subtilis) placed in a container with its upper surface open to the atmosphere results in the formation of complex bioconvection patterns. The bacteria consume the oxygen diluted in the water, thereby causing the decrease of oxygen concentration everywhere except on the free surface. Through the free surface, which is in direct contact with the air, oxygen diffuses into the water. Slightly denser than water, the oxytactic bacteria are able to swim towards the higher concentration of oxygen (i.e. upwards) and they concentrate in a thin layer below the free surface. This causes the change of the suspension density and Rayleigh–Taylor type instabilities to occur. The chemotaxis phenomenon has been successfully modeled within continuum mechanics approach under certain simplifications. The set of (non-linearly) coupled equations describing the process involves the Boussinesq approximation of the Navier–Stokes equations governing the fluid motion and two convection–diffusion type equations governing the bacteria and oxygen concentrations. One of the simplifications that might significantly influence numerical simulations is the boundary condition for fluid equation on the free surface. This condition ensures that the vertical component of the velocity is zero, thus keeping the position of free surface fixed. This assumption significantly simplifies numerical procedure since the non-linearly coupled system can then be solved on stationary grid. However, allowing the motion of the free surface and completing the system with appropriate boundary conditions on contact line (liquid–solid–gas interface), a more realistic model is derived and new insights on nonlinear dynamics of the chemotaxis phenomenon are obtained. Our aims in this paper are to upgrade the currently available model into a more realistic one in both two and three dimensions, to propose a numerical procedure to deal with the new system (now posed on time-dependent domain) and, finally, to show the difference between this new model and the previous simplified one.

Surface, Interface, and Temperature Effects on the Phase Separation and Nanoparticle Self Assembly of Bi-Metallic Ni0.5Ag0.5: A Molecular Dynamics Study.

Classical molecular dynamics (MD) simulations were used to investigate how free surfaces, as well as supporting substrates, affect phase separation in a NiAg alloy. Bulk samples, droplets, and droplets deposited on a graphene substrate were investigated at temperatures that spanned regions of interest in the bulk NiAg phase diagram, i.e., miscible and immiscible liquid, liquid-crystal, and crystal-crystal regions. Using MD simulations to cool down a bulk sample from 3000 K to 800 K, it was found that phase separation below 2400 K takes place in agreement with the phase diagram. When free surface effects were introduced, phase separation was accompanied by a core-shell transformation: spherical droplets created from the bulk samples became core-shell nanoparticles with a shell made mostly of Ag atoms and a core made of Ni atoms. When such droplets were deposited on a graphene substrate, the phase separation was accompanied by Ni layering at the graphene interface and Ag at the vacuum interface. Thus, it should be possible to create NiAg core-shell and layer-like nanostructures by quenching liquid NiAg samples on tailored substrates. Furthermore, interesting bimetallic nanoparticle morphologies might be tuned via control of the surface and interface energies and chemical instabilities of the system.

The deformation dynamics of Twinning-like Lattice Reorientation in magnesium nanowires

Twinning-like Lattice Reorientation (TLR) is a newly reported unconventional plasticity mechanism in magnesium, producing a crystalline grain with 90° rotated lattice relative to the parent. In this paper the deformation dynamics of TLR are investigated using molecular dynamics. The sensitivities of TLR nucleation and growth to temperatures and strain rates manifest the thermal activation of TLR. The free surface effect is also revealed on TLR formation at sub-micron lengthscale.

A local Lagrangian gradient smoothing method for fluids and fluid-like solids: A novel particle-like method

The Lagrangian Gradient Smoothing Method (L-GSM) proposed in our earlier work overcomes effectively the ‘tensile instability’ problem inherently existed in the widely used smoothed particle hydrodynamics (SPH) method. However, the employment of background grid in L-GSM for the construction of gradient smoothing domains leads some drawbacks to the L-GSM framework: low computational efficiency, complex implementation procedure and technical challenges for parallel computing algorithm development. Accordingly, this study proposes a novel particle-like method, termed as local L-GSM (LL-GSM), through constructing gradient smoothing domains locally for LL-GSM particles. The present LL-GSM consists of three unique ingredients: (1) Only locally constructed gradient smoothing domains are used; (2) an efficient localized neighbor-searching algorithm is developed for the search of supporting particles; (3) a simple and effective free surface technique is adopted for accurate application of free surface effect. The accuracy, stability and efficiency of the newly proposed LL-GSM framework are then investigated comprehensively by conducting thorough theoretical and numerical analyses. At last, benchmark problems including two incompressible flows and two free surface flows are used to verify the capability of LL-GSM in handling large deformation of fluids and fluid-like solids. The LL-GSM results are evaluated carefully by comparing with experimental results, theoretical solutions, and numerical solutions. Results comparison demonstrates that the proposed LL-GSM method can give very accurate numerical solutions in all these problems with a much better computational efficiency and easier implementation. It is also evidenced that, same to L-GSM, the LL-GSM is free from the ‘tensile instability’ issue.

Diffusional mass flux accommodating two-dimensional grain boundary sliding in ODS ferritic steel

The interplay between grain boundary sliding (GBS) and atomic diffusion was studied for understanding the fundamental mechanisms of superplasticity and diffusion creep. Two-dimensional GBS was achieved during shear deformation at 900 °C with strain rates of 1.1 × 10−5–3.3 × 10−5 s−1 in oxide dispersion strengthened ferritic steel with an anisotropic grain structure, which was designed to minimize the free surface effects including floating grains. Microstructural development during the deformation was observed via electron backscatter diffraction and surface fiducial markers drawn by Ga+ focused ion beam. The plastic flow was predominantly mediated by the cooperative process of GBS and grain boundary diffusion, while other mechanisms including intragranular deformation was hardly recognized. The diffusional flux was typically triggered by local principal stress induced at grain boundaries; the matters flew from overlapping (compressive) to splitting (tensile) grain boundaries. In addition, grain boundary morphology changed from wavy to flat patterns via mass flux from convex to concave sides of grain boundaries to minimize the grain boundary energy. Two distinct interplays between GBS and atomic diffusion were confirmed; the most predominant mode was GBS along the shear strain (i.e. Rachinger sliding) and diffusional accommodation via grain boundaries, while a less amount of Coble diffusion creep along macroscopic principal stress was confirmed with GBS accommodation uncorrelated with the shear strain (i.e. Lifshitz sliding).

2-D poroelastic wave modelling with a topographic free surface by the curvilinear grid finite-difference method

The curvilinear grid finite-difference method, which is suitable for accurate modelling of seismic waves in the presence of topographic free surfaces, is applied in this study to model poroelastic waves. Poroelastic wave equations of Biot’s theory are expressed in curvilinear coordinates and solved on a collocated grid by utilizing the fourth-order Runge–Kutta time integral scheme with alternative applications of forward and backward MacCormack finite differences. Discretization of the irregular free surface with the curvilinear coordinate grid enables a good fit of the topographic surface, and this good fit results in higher numerical accuracy in comparison with stair-case approximation. The formulas of the free-surface boundary conditions for poroelastic media are also derived for the curvilinear coordinates and subsequently implemented with the traction-imaging method, which is a generalization of the stress-imaging method and can maintain high accuracy in curvilinear coordinates. To verify the performance of the proposed algorithm and determine its accuracy, we conduct numerical simulations on several different models, and compare our numerical solutions with other solutions that are calculated by analytical expressions, generalized reflection/tranmission method and spectral-element method. Besides, the fluid–solid dynamic compatibility of porous media is demonstrated using a three-layered half-space model, and effects of the irregular free-surface on poroelastic waves are investigated for a four-layered model with strong irregular free-surface topography. The good performance of the proposed algorithm suggests that the curvilinear grid finite-differece method is a useful tool for the study of poroelastic wave propagation.

Numerical Prediction of Propeller-Hull Interaction Characteristics Using RANS Method

Abstract The paper presents the results of computational evaluation of the hull-propeller interaction coefficients, also referred to propulsive coefficients, based on the unsteady RANS flow model. To obtain the propulsive coefficients, the ship resistance, the open-water characteristics of the propeller, and the flow past the hull with working propeller were computed. For numerical evaluation of propeller open-water characteristics, the rotating reference frame approach was used, while for self-propulsion simulation, the rigid body motion method was applied. The rotating propeller was modelled with the sliding mesh technique. The dynamic sinkage and trim of the vessel were considered. The free surface effects were included by employing the volume of fluid method (VOF) for multi-phase flows. The self-propulsion point was obtained by performing two runs at constant speed with different revolutions. The well-known Japan Bulk Carrier (JBC) test cases were used to verify and validate the accuracy of the case studies. The solver used in the study was the commercial package Star-CCM+ from SIEMENS.

Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier–Stokes equations

To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes equations. The explicit particle method is based on a penalty problem, which converges theoretically to the incompressible Navier--Stokes equations, and is discretized in space by generalized approximate operators defined as a wider class of approximate operators than those of the smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods. By considering an analytical derivation of the explicit particle method and truncation error estimates of the generalized approximate operators, sufficient conditions of convergence are conjectured.Under these conditions, the convergence of the explicit particle method is confirmed by numerically comparing errors between exact and approximate solutions. Moreover, by focusing on the truncation errors of the generalized approximate operators, an optimal weight function is derived by reducing the truncation errors over general particle distributions. The effectiveness of the generalized approximate operators with the optimal weight functions is confirmed using numerical results of truncation errors and driven cavity flow. As an application for flow problems with free surface effects, the explicit particle method is applied to a dam break flow.

Experiment and numerical simulation of Taylor–Couette flow controlled by oscillations of inner cylinder cross section

An experimental and numerical study of the controlled Taylor–Couette flow with free surface is presented in this work. It is aimed to carry out a controlling strategy based upon a combination of free surface effect and an inner cylinder cross section oscillation. Numerical simulations are performed using FLUENT software package for three-dimensional incompressible flows. The basic system geometry is characterized by a height H = 170 mm, an inner and outer cylinders with, respectively, R1 = 31.5 mm and R2 = 35 mm, a ratio of the inner to outer cylinder radii ɳ = 0.9, an aspect ratio Γ = 28.5 and a ratio of the gap to the inner cylinder radius, δ = 0.1. It is established that the first and the second instabilities are delayed. The Taylor vortices and Ekman cells can be destroyed throughout a process applicable for all the flow regimes encountered in the Taylor–Couette flow. The Taylor vortices show a particular sensitivity and can be easily destroyed using low deforming frequencies (f 20 Hz) are required for the complete disappearance.

The Effect of Internal Free Surfaces on Void Swelling of Irradiated Pure Iron Containing Subsurface Trenches

We studied the effects of internal free surfaces on the evolution of ion-induced void swelling in pure iron. The study was initially driven by the motivation to introduce a planar free-surface defect sink at depths that would remove the injected interstitial effect from ion irradiation, possibly enhancing swelling. Using the focused ion beam technique, deep trenches were created on a cross section of pure iron at various depths, so as to create bridges of thickness ranging from 0.88 μm to 1.70 μm. Samples were then irradiated with 3.5 MeV Fe2+ ions at 475 °C to a fluence corresponding to a peak displacement per atom dose of 150 dpa. The projected range of 3.5 MeV Fe2+ ions is about 1.2 μm so the chosen bridge thicknesses involved fractions of the ion range, thicknesses comparable to the mean ion range (peak of injected interstitial distribution), and thicknesses beyond the full range. It was found that introduction of such surfaces did not enhance swelling but actually decreased it, primarily because there were now two denuded zones with a combined stronger influence than that of the injected interstitial. The study suggests that such strong surface effects must be considered for ion irradiation studies of thin films or bridge-like structures.

Numerical investigation of scale effect of nominal wake of four-screw ship

An experimental investigation is conducted to obtain the nominal wake of a four-screw ship in a towing tank using a particle image velocimetry (PIV) measurement system. A computational study on the viscous flow fields of the ship at different scales is carried out using the Reynolds-averaged Navier–Stokes (RANS) method, without considering the free surface effect. The scale effect for the axial nominal wake field of the inside and outside propeller discs is analyzed in detail. The results show that the CFD results and PIV data are in good agreement. Different circumferential distribution patterns of the axial nominal wake field exist between the inside and outside propeller discs, especially in the zone behind the brackets. The mean wake fraction of the inside propeller is generally larger than that of the outside propeller when different radii are considered. For both the inside and outside propellers, the mean axial wake fraction is relatively large in the inner radius area (0.3 ≦ r/R ≦ 0.6), whereas it is relatively small and almost coincident in the outer radius area (0.7 ≦ r/R) at different scales. ωx (Axial wake fraction) decreases nonlinearly with the increase in Reynolds number for both the inside and outside propeller discs, whereas Δωx (wake fraction difference) increases linearly with the increase in the Reynolds number. With the increase of the model scale, the harmonics components decreases gradually.

A screw dislocation near a damaged arbitrary inhomogeneity–matrix interface

In the literature, the analytical solutions concerned with the interaction between screw dislocation and surfaces/interfaces have been mainly limited to simple geometries and perfect interfaces. The focus of the current work is to provide an approach based on a rigorous semi-analytical theory suitable for treatment of such surfaces/interfaces that concurrently have complex geometry and imperfect bonding. The proposed approach captures the singularity of the elastic fields exactly. A vast variety of the pertinent interaction problems such as dislocation near a multi-inhomogeneity with arbitrary geometry bonded imperfectly to a matrix, dislocation near the free boundaries of a finite elastic medium of arbitrary geometry, and so on is considered. In the present approach the out-of-plane component of the displacement in each domain is decomposed as the displacement corresponding to a screw dislocation in a homogeneous elastic body of infinite extent and the disturbance displacement due to the interaction. Subsequently, the disturbance displacement in each medium is expressed in terms of eigenfunction expansion. Damaged interfaces are modeled by a spring layer of vanishing thickness, and the amount of damage is controlled via the stiffness of the spring. For the illustration of the robustness of the proposed methodology a variety of examples including the interaction of a screw dislocation with a circular as well as a star-shaped inhomogeneities, two interacting inhomogeneities, imperfectly bonded to an unbounded medium are given. Also, examples for highlighting the effect of free surfaces in the case of finite domains are provided. It is revealed that in the cases where matrix is stiffer than the inhomogeneity and the dislocation is inside the inhomogeneity, or the other way around, then the amount of interface damage can change the sign of the image force.

EBSD, XRD and SRS characterization of a casting Al-7wt%Si alloy processed by equal channel angular extrusion: Dislocation density evaluation

Aluminum‑silicon (AlSi) alloys of high silicon contents are composite materials; they are used whenever high casting properties are required. They are slightly ductile below 8wt%Si. An increase in ductility can be obtained by refining Si-crystals in elaboration or by a further hot working. In the present work, an Al-7wt%Si alloy was processed by Equal Channel Angular Extrusion (ECAE) at temperatures 20 °C and 160 °C up to three passes. The die was formed by two cylindrical channels with characteristic angles Φ = 110° and Ψ = 0. EBSD, X ray diffraction (XRD) and Strain Rate Sensitivity (SRS) were used to characterize the microstructure and the mechanical properties. High levels of strain were introduced at both temperatures. The activation volume was lowered to 125b3 and 210b3 at 20 °C and 160 °C respectively and was considered to be dislocation density dependent. The remaining dislocation densities calculated from EBSD, XRD and SRS experiments are quite different. This was explained by the scale difference and by the sensitivities of the methods to the free surface effect.

Evaluation of the Viscous Drag for a Domed Cylindrical Moored Wave Energy Converter

Viscous drag, nonlinear in nature, is an important aspect of the fluid–structure interaction modelling and is usually not taken into account when the fluid is assumed to be inviscid. Potential flow solvers can competently compute radiation damping, which is related to the radiated wave field. However, the drag damping primarily related to the viscous effects is usually neglected in the radiation/diffraction problems solved by the boundary element method (BEM), also known as the boundary integral element method (BIEM). This drag force can have a significant impact in the case of structures extending much deeper below the free surface, or for those that are completely submerged. In this paper, the drag coefficient C d was quantified for the heave and surge response of a structure which consists of a moored horizontally oriented domed cylinder with two surface piercing square columns located at the top surface. The domed cylinder is the primary part and is submerged. The drag coefficient is estimated using the experimental measurements related to harmonic monochromatic wave–structure interaction. Finally, this estimated drag coefficient was used in the modified time domain model, which includes the nonlinear viscous correction term, and the resulting device response in heave and surge directions is presented for an irregular incoming wave field. The comparison of the numerical model and the experiments validates the estimated C d values obtained earlier. Prior to the time domain model, frequency-dependent parameters such as added mass, radiation damping, and excitation force were computed using three mainstream potential flow packages (that is, ANSYS AQWA, WAMIT, and NEMOH), and a comparison is presented. The effect of free surface on the drag coefficient is investigated through differences in C d values between heave and surge modes.

Experimental study on the combined damage of liquid cabin structure subjected to charge explosion with preset fragments

As an important part of multicompartment protective structure in naval vessels, the structure of liquid cabin plays a major role in resisting blast wave and high-speed fragments. The aim of this study was to evaluate the damage of a liquid cabin structure under combined blast wave and fragment loading created by charge explosion with preset fragments. A series of experiments were conducted to investigate the effects of free surface inside liquid cabin and fragment type on structural damage. Moreover, to facilitate the evaluation of failure modes of structure under combined loading, the liquid cabin under bare blast loading was also assessed. The experimental tests were analyzed using pressure sensors and residual displacement of structure walls. It is shown that free surface can decrease the intensity of pressure pulse and reduce the deformation of liquid cabin. A large nummular fragment caused a stronger shock wave and more severe structural damage than a dense fragment cluster. The deformation direction of front plate of liquid cabin induced by the blast wave is opposite to that of fragment loading. Therefore, the superposed or enhanced damage of combined loading on front plate is not shown, and fragment loading is the main factor causing the damage of liquid cabin structure.

The Glass-Transition Temperature of Supported PMMA Thin Films with Hydrogen Bond/Plasmonic Interface.

The interfacial effect is one of the significant factors in the glass-transition temperature (Tg) of the polymeric thin film system, competing against the free surface effect. Herein, the Tgs of poly (methyl methacrylate) (PMMA) films with different thicknesses and substrates are studied by fluorescence measurements, focusing on the influence of interfacial effects on the Tgs. The strong interaction between PMMA and quartz substrate leads to increased Tgs with the decreased thickness of the film. The plasmonic silver substrate causes enhanced fluorescence intensity near the interface, resulting in the delayed reduction of the Tgs with the increasing film thickness. Moreover, as a proof of the interface-dependent Tgs, hydrogen bonds of PMMA/quartz and molecules orientation of PMMA/silver are explored by the Raman spectroscopy, and the interfacial interaction energy is calculated by the molecular dynamics simulation. In this study, we probe the inter-relationship between the interfacial interactions arising from the different substrates and the Tg behavior of polymer thin films.

Modeling rock destruction under blasting of closely spaced borehole charges

The design scheme is developed, and simulation of radial cracks growth under blasting of closely spaced borehole charges is carried out. The case studies of confined explosion of two charges located in neighboring boreholes are considered. Blasting of decoupled charges in neighboring boreholes is investigated. The free surface effect on a shape and size of radial cracks under explosion of two closely spaced boreholes rising to the surface is simulated. The blast pattern to gain the maximum size of the destruction zone is determined.

Theoretical and numerical analysis of vertical distribution of active particles in a free-surface wetland flow

Presented in this paper is a theoretical and numerical analysis for active particles in a fully developed steady wetland flow dominated by the free-surface effect. An ecological risk assessment model for the concentration distribution of active particles is devised as an extension of the general form of concentration transport equation for passive particles in wetland flows. The vorticity in the free-surface wetland flow is found to depend on the dimensionless parameter α, which reflects the combined action of vertical momentum dispersion, microscopic curvature of flow passages, friction of vegetation and water depth. The large α results in the decrease of vorticity at the free surface and the increase at the bed bottom. The analytical solution of stable concentration distribution is rigorously derived for the active particles in both weak and strong vortical flows, under the combined action of the effective mass dispersion by the ambient flow, as well as the translational diffusion and vertical swimming by the active particles. It is found that the strong vorticity weakens the concentration of active particles in the free-surface wetland flow, while the strong diffusion, by the wetland flow and active particles, enhances the concentration. The large α results in the increase of concentration near the free surface and the decrease of concentration near the bed bottom. The time scale for active particles to reach the stable concentration distribution is mainly dependent on the dimensionless parameter, Pe, which reflects the relative strength of the vertical swimming and the total diffusion due to the wetland flow and the active particles.

Linear wave response of a 2D closed flexible fish cage

Closed flexible fish cages (CFFC) are proposed as a new concept in marine aquaculture, replacing the conventional net cages in order to meet ecological challenges related to fish lice and escapes. A linear mathematical model of a freely floating 2D CFFC in waves have been developed. It was found that the wave induced rigid body motion responses of a flexible CFFC in sway, heave and roll are significantly different from the responses of a rigid CFFC. Large ratios between free-surface elevation amplitudes and incident wave amplitude are predicted inside the tank at the first and third natural sloshing frequencies. It implies that non-linear free surface effects must be accounted for inside the tank in realistic sea conditions. The dynamic tension in the membrane of the CFFC must be smaller than the static tension in the applied structural method. For the analysed case with 25 m between the centre of the floaters, the most probable largest dynamic tension is larger than the static tension, for significant wave heights larger than 0.5 meter. The effect of scaling of elasticity on the rigid body motion have also been investigated. The non-dimensional response of the CFFC versus non-dimensional frequency, and based on Froude scaling using an elasticity available in model scale have been compared to the response of the CFFC using the elasticity for full scale. These responses were found to deviate to a large extent, showing limitations of model tests of a CFFC.