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When a laser beam induces surface tension gradient at the free surface of a liquid, a weak surface depression is expected and has been observed. Here we report giant depression and rupture in “optothermocapillary fluids” under the illumination of laser and sunlight. Computational fluid dynamics models were developed to understand the surface deformation and provided desirable physical parameters of the fluid for maximum deformation. New optothermocapillary fluids were created by mixing transparent lamp oil with different candle dyes. They can be cut open by sunlight and be patterned to different shapes and sizes using an ordinary laser show projector or a common laser pointer. Laser driving and elevation of optothermocapillary fluids, in addition to the manipulation of different droplets on their surface, were demonstrated as an efficient controlling method and platform for optofluidic operations. The fundamental understanding of light-induced giant depression and creation of new optothermocapillary fluids encourage the fundamental research and applications of optofluidics.

International audience; We report on the development and validation of a new Numerical Wave Tank (NWT) solving fully nonlinear potential flow (FNPF) equations, as a more efficient variation of Grilli et al.'s NWT [Grilli et al., A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom, International Journal for Numerical Methods in Fluids 35 (2001) 829-867], which was successful at modeling many wave phenomena, including landslide-generated tsunamis, rogue waves, and the initiation

In this paper, a multiphase moving particle semi-implicit (MPS) method is developed by introduction of various multiphase models into the original MPS method for single-phase flows, and is then applied to the numerical simulations of two-layer-liquid and three-layer-liquid sloshing in a 2-D rectangular tank under different external excitations. To validate the accuracy of the present multiphase MPS method, the qualitative and quantitative results, including wave profiles, interface elevations and impact pressures, are compared with experimental data and other numerical results, which show a good agreement. In particular, the evolutions of free surface and phase interfaces are compared and an obvious discrepancy is found, indicating that the phase interfaces may suffer from complex deformations while the free surface keeps relatively quiet. Moreover, the different modes of phase interface are observed under different excitation frequencies. Then, the violent sloshing of a three-layer-liquid system is simulated and the phenomenon of internal wave breaking is well captured, which mainly benefitted from the Lagrangian basis of MPS method and its advantage in multiphase flows with complex interfaces. Finally, the three-layer-liquid sloshing with a vertical baffle are simulated to investigate the suppressing effect of baffle on multi-layer-liquid sloshing.

The dynamic behaviors of weld pool and fusion hole are mutually coupled in tungsten inert gas (TIG) welding with reserved gap. This simulation has important significance for revealing the effect of fusion hole on weld pool and in enriching the knowledge of TIG welding process with gap. A combined heat distribution model that is adaptive to the free surface deformation of weld pool was established in the article. The interface of the fusion hole was tracked by using volume of fluid (VOF) method. The heat and fluid flow fields of weld pool and the dynamic evolution of fusion hole were simulated numerically. Simulated results show that the appearance of fusion hole intensifies the internal flow, which facilitates the downward flow of liquid metal and promotes penetration. Under the 1.5-mm gap, the fusion hole reaches the critical unstable state with 2.78-mm width after undergoing the growth stage. The overall fluid flow trends on the top surface of the weld pool are consistent under three different gaps. The fluid on the top surface flows most intensely with the gap of 1.3 mm after the formation of fusion hole. And the initial formation time of fusion hole is advanced with the increase of gap width. The computed results agree well with experimental data.

The present study investigated the influence of hot isostatic pressing (HIPing) on the fatigue life of Al–Si–Cu–Mg 354-T6 casting alloy. Surface porosity revealed the major impact on the fatigue life of non-hot isostatic pressed (non-HIPed) C354-T6 samples, where all non-HIPed samples fractured because surface porosity acted as crack initiation sites (CIS). It was found that as the pore size/perimeter increases, the sample fatigue life decreases and vice versa. HIPing technology revealed a positive impact on the fatigue life of C354-T6 casting alloy through eliminating porosity and/or reducing the size of the pores such that the specimens’ fatigue life was significantly increased. The hot isostatic pressed (HIPed) samples revealed crack initiation sites (CIS) at structure irregularities such as slip bands and oxide films. These structure irregularities, however, displayed less effect on the samples’ fatigue life, as compared to porosity. With regard to all fatigue-tested samples either HIPed or non-HIPed, the fatigue crack was observed to initiate at the sample free surface, regardless of the type of structure irregularities acted as CIS. The maximum stress concentration was attained at this point of the sample surface.

The reflection of three-dimensional (3D) plane waves in a highly anisotropic (triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag (TPL), dual-phase-lag (DPL), Green-Naghdi-III (GN-III), Lord-Shulman (LS), and classical coupled (CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.

In this study experiments in a laboratory tank to examine the effect of bed with vegetation on the motion of gravity currents between fresh and salt water with high salinity were performed. The shape of the tank was composite (trapezoidal at the bottom and rectangular at the top). The tank was separated into two reservoirs with a vertical gate. One of the reservoirs was filled with salt water (sw) with various densities from 1050 till 1090 kg/m3. These values of densities simulates and represents the spread of liquid waste. The release of pollutants into rivers and wetlands, the spread of an oil spill into the ocean are examples of gravity currents that have detrimental environmental consequences. The second reservoir was filled with fresh water (w) and vegetation at the bed. When the gate is opened, the heavier liquid propagates towards the tank with the lightest liquid which is displaced along the free surface in the opposite direction. The results showed that the shape of the valley plays a very important role on the front velocity of gravity currents. The low water height and the presence of trapezoidal shape decreases the velocity of the gravity current. The increase of the initial height (for fresh and high salinity water) also produces gravity currents with higher velocity.

The performance and flow field of hydropower turbine in shallow water can be affected by the presence of free surface. Therefore, the influence of free surface on the turbine performance was studied through transient computational fluid dynamics (CFD) analysis. The turbine included three blades made of NACA0018 hydrofoil. Submerged depths and different tip speed ratio (TSR) were two main variables in this numerical simulation. A comprehensive simulation of quantities was performed for submerged depths ranging from h / R = 1.2 to 2.0, and tip speed ratio from λ = 1.0 to 30. The results revealed that the presence of the free surface decreased the power coefficient by 19.05% for the closest submerged depth of h / R = 1.2 at optimal tip speed ratio of λ = 2.5. The wave breaking also occurred when the submerged depth was smaller than h / R = 2.0. In the case of variable pitch, the top speeds for free-to-spin cases were investigated by 6DOF method. The top speed had a 4.24% drop by comparing the largest and the smallest submerged depths. Variable pitch also improved the power coefficient by 28.09% when the free surface was far from the hydropower turbine. However, the power coefficient improvement became significantly small when the hydropower turbine was placed close to the free surface.

To enable a virtual design and optimization process of partially filled coolant tanks a reliable numerical approach is needed to predict the liquid and gas two phase flow inside the tanks. In this study numerical results are validated by experimental data to examine the suitability of the method for the tank design process. The liquid motion inside the tanks can be described as sloshing with high amplitude, off-resonant roll excitation and was examined using a homogeneous multiphase model and VOF interface capturing approach as well as an experimental setup including piezoelectric pressure sensors and qualitative observation of the free surface. The effect of two vertical baffles on the maximum pressure and the position of phase interface was determined. The comparison between the computational and experimental results reveals that the numerical model tends to under predict the experimental peak pressures but resolves the liquid surface in close agreement with the experiments.

In this article, we introduce the Free surface Quasi-Newton method with Least-Squares and Surrogate (FreQ-LeSS) to solve steady free surface flows, as encountered in, for example, marine applications. The method has two important advantages over other methods. First of all it is fast thanks to the efficient iterative scheme based on quasi-Newton iterations that make use of an advanced surrogate model. Second, it has good compatibility because it poses no special requirements on the flow solver that is called in the algorithm. The excellent convergence speed of the FreQ-LeSS method is demonstrated for a shallowly submerged submarine: good quality wave patterns are obtained in few iterations. These results match with ISIS-CFD, validating the FreQ-LeSS method. The total cost of solving this steady free surface problem is only a few times that of solving a steady single-phase flow with fixed free surface position. We conclude that FreQ-LeSS promises to be much faster than the two-phase time-stepping methods typically used to solve these problems, and provides a sharper interface at the same time thanks to the fitting approach. In the present work, we restrict ourselves to problems without surface-penetrating objects, to avoid the associated complications related to the contact-line motion.

In this paper, we extend the long-wave theory for the free surface dynamics of the thin non-Newtonian second-grade fluid (ANZIAM J 60(2): 249–268, 2018) over the stretching sheet by the inclusion of thermo-capillarity and the variable fluid properties effect in the systematic long-wave theory framework. The two-dimensional flow of non-Newtonian fluid over a non-porous heated stretching sheet is described by the conservation of mass, momentum, and energy equations with free surface and no-slip boundary conditions. From standard long-wave theory expansion technique in terms of the small aspect ratio of the fluid layer, we derive the transient equation systematically to describe the free surface dynamics of the thin-liquid film. We apply the finite volume method with implicit flux discretization for numerical investigation of the effects of thermocapillary forces, non-Newtonian parameter, and variable fluid properties. The investigation reveals that the Newtonian fluid with variable viscosity property exhibits faster thinning in comparison to the second-grade non-Newtonian fluid concerning the prescribed temperature at the sheet and the stretching rate. Furthermore, under constant fluid properties assumptions, the derived non-Newtonian thin-film model decouples from the thermal problem and reduces to the isothermal viscous model of Santra and Dandapat (Z Angew Math Phys 60(4): 688–700, 2009).

In engineering blasting, the determination of the range of rock blasting fracture zone has important guiding significance for blasting construction. This paper proposes a method that can accurately and directly obtain the range of rock blasting fracture zone. Based on the theory of elastic wave propagation, test rods which are made of appropriate material are selected and prepared. A certain number of boreholes are drilled for subsequent insertion of the test rods along the direction perpendicular to the free surface of the excavation at a certain distance from the blast hole. Based on the field blasting test results, the deepest fracture position of the test rod is used as the boundary of the blasting fracture zone, and the range of the rock blasting fracture zone is obtained. A numerical analysis model is established according to the Mohr–Coulomb constitutive relationship and the Von Mises yield criterion. Then, the range of the fracture zone and the maximum horizontal radius of the fracture zone are analyzed and obtained. The numerical analysis results are compared with the field measured data. It is demonstrated that the range of the fracture zone obtained by the numerical simulation is in good agreement with the blasting test results of the pre-embedded test rods. The research results can provide references for the safety control of blasting and excavation of rock slopes.

This paper proposes a 3-D non-hydrostatic free surface flow model with a newly proposed general boundary-fitted grid system to simulate the nonlinear interactions of the bi-chromatic deep-water gravity waves. First, the monochromatic bidirectional and bi-chromatic bidirectional waves of small wave steepness are successively simulated to verify the abilities of the numerical model. Then, a series of bi-chromatic progressive waves of moderate wave steepness and different crossing angles are simulated and analyzed in detail. It is found that if the crossing angle is close to or smaller than the resonant angle, apparent discrepancies are observed among the numerical results, the linear wave theory, and the steady third-order theory. Otherwise, the three solutions coincide well. Through analysis, it is concluded that the discrepancies are caused by the third-order quasi-resonant interactions between the bi-chromatic progressive waves. Such interactions not only could modify the wave spectrum, but could also change the wave shape patterns.

Liquid sloshing under coupled surge and heave excitations in a rectangular tank has been numerically investigated by applying a Navier–Stokes solver. Fieriest coupled sloshing was further considered, and the internal baffle was expected to suppress the violent sloshing wave. After getting fully validated against available results from the literatures, the numerical model was applied to research coupled sloshing, and both vertical baffle and horizontal baffle have been considered. Due to the strong vortexes created by the sharper corners of the baffles and the reduction of the effective water bulk climbing through the tank walls, the sloshing was dramatically reduced. The increase of the baffle distance away from the tank bottom led to a decrease in the sloshing wave. It was noted that the baffle near the free surface caused the maximal dissipation. The frequency response of the sloshing wave was accordingly illustrated.

The behavior of third gradient materials is analyzed. They possess stress tensor fields of second, third and fourth order. Starting from the principle of virtual power, we derive the admissible boundary conditions. Those on free surfaces can only be obtained by the application of the divergence theorem of surfaces. On the other hand, such an application to fictitious internal cuts makes no sense although it is usually practiced. We prove that some of the boundary conditions on a free surface may be interpreted as the equilibrium conditions of a shell. So a crust shell exists on such a surface and a beam exists where patches of the surface meet. On the other hand, no such shells or beams can be found with fictitious surfaces in the interior of a continuum. Our finding does not depend on any specific constitutive assumption.

A numerical scrutiny was performed to analyze the effect of driving forces on molten pool in gas metal arc welding. In addition to the basic governing equations required for a general heat and mass transfer analysis by computational fluid dynamics, a volume-of-fluid equation for free surface tracking and additional conservation equations for calculating the distribution of alloy elements were used. Driving forces—buoyancy, drag force, arc pressure, electromagnetic force, Marangoni pressure, and droplet impingement—and the arc heat source were mathematically modeled and applied to the simulation. In order to examine the effect of driving forces, a two-dimensional axisymmetric simulation was performed, and the effect of each driving force was analyzed using the velocity components. In the radial velocity component, the effect of droplet impingement and the Marangoni force was large, and in the vertical velocity component, the droplet impingement effect was dominant. A three-dimensional simulation was also performed considering all the driving forces together, and the result was verified by comparison with experimental results. Relatively high alloying element contents were found at the bottom of the fusion zone, which was due to the droplet impingement generating a high vertical velocity.

This paper determines the elastic fields in a positive half-space embedded with a spherical inhomogeneity under the context of Steigmann–Ogden surface/interface mechanical model. The half-space is loaded by an equal-biaxial far-field tension applied at infinity. While bulk domains are treated as linearly isotropic elastic solids, both the half-space plane boundary and the matrix/inhomogeneity interface are modeled by the Steigmann–Ogden theory. The well-developed method of Boussinesq displacement potentials is used to solve the elastostatic Navier’s equations of equilibrium. In view of the geometry and loading configurations, four sets of cylindrical and spherical harmonic potentials are carefully proposed to solve the problem. Implementation of the nonclassical Steigmann–Ogden boundary conditions at both the half-space free surface and the spherical interface results in a semianalytical solution in the form of infinite Legendre series. Extensive parametric studies are performed with respect to the surface and interface Steigmann–Ogden material parameters, shear moduli ratio between the spherical inhomogeneity and its surrounding matrix, and the inhomogeneity radius-to-depth ratio. Comparison and contrast with the well known Gurtin–Murdoch model reveals the significance of surface flexural rigidities at both boundaries of the considered mechanical model. When compared with the effects of matrix/inhomogeneity interface, the surface tension, Lame constants and flexural rigidities at the half-space plane boundary are of secondary importance. This work is able to shed some lights on the modeling of self-organized adatoms and islands that is essential in the semiconductor industry.

In this work, a resolved CFD–DEM coupling model for the simulation of gas-liquid-solid flows is developed: the interface capturing method based on the colour function is employed for fluids (i.e. a gas and liquid) whilst Discrete Element Method (DEM) is used for particles. The Volume Penalisation (VP) method is adopted to consider the hydrodynamic interactions between fluids and particles along with the Immersed Free Surface (IFS) method, which artificially extends the gas-liquid interface into the interior of the particle to account for the wettability. The unique point of the proposed model is that the thickness of the gas-liquid interface can be controlled by using both interface compression and diffuse interface techniques simultaneously. From the simulation results, it is presented that the accurate evaluation of the surface tension force as well as the capillary force can be achieved by appropriately controlling the interface thickness. Moreover, the major two methods in the literature to calculate the capillary force are compared in this work. The validity of the proposed model is presented for both static and dynamic cases. The behaviour of two colliding particles with a dynamic liquid bridge is then simulated to demonstrate the applicability of the proposed model to a complex three-phase system.

When waves from two weather systems converge at a certain sea area, cross waves can be produced. It is important to have a better understanding of the motion characteristics of ship in cross sea to ensure its navigation safety. In this paper, the motion responses of a S175 container ship hull in cross sea is first analyzed based on CFD technique using RANS method. VOF method is used to model and capture the free surface and overset grid technique is adopted to simulate ship motions in waves. Verifications on ship motion by the numerical method have been conducted for time step- and grid-independent studies. According to the motion results by numerical simulation, typical conditions are chosen for further investigation of slamming pressure on bow area and green water on deck. It is found that vertical motion responses of ship induced by cross waves can be quite large and the ship experienced obvious roll–pitch-coupled motion. Severe bow slamming and green water under cross sea state are also observed. The bow flare slamming pressure on the baseline can be quite large in symmetric cross wave. Asymmetrical slamming impacts occurred when the ship sails in an asymmetric cross wave field.

The purpose of this study is to apply the cumulant lattice Boltzmann method (LBM) to simulate high Reynolds number free surface flows. The single-phase cumulant LBM is extended to solve the free surface flows by using the phase-field method as the interface capturing scheme. Numerical simulations are performed on an experimental problem of dam break flow impact on a vertical cylinder. Important numerical aspects such as collision model, grid resolution, time step and interface mobility parameter are investigated. It is found that the severe impact pressure oscillation in the simulation by the conventional SRT model, can be significantly suppressed by the cumulant model. Good agreement between the cumulant LBM numerical simulation and the experiment has been obtained on both the free surface profiles and the impact pressures. The numerical results obtained by the present study demonstrate that the cumulant LBM can be a powerful numerical tool for simulations of violent free surface flow problems.

A novel numerical method combining Eigenfunction matching method (EMM) and 3D Rankine source method is developed to investigate wave-body interaction over a sloping bottom. The extended EMM is proposed to create an incident wave model over the sloping bottom, thereby obtaining the Froude-Krylov force and Neumann data on wet surfaces of the floating body for the diffraction problem. A 3D Rankine source method concerning the sloping bottom is developed, in which the free surface and seabed are both divided into the inner domain and outer domain. Source panels are placed in an exponential manner in the latter domain, by which the far field radiation condition is well satisfied. To verify the proposed method, comparisons with other mathematical models involving added mass and damping coefficients, wave exciting forces and motion RAOs by a floating hemisphere and a LNG carrier are carried out.

The formation and removal of exogenous inclusions in a real-size two-strand tundish is simulated by the proposed unsteady 3D comprehensive numerical model of the respective fluid-structure interaction, which takes into account the impacting and washing effects on the refractory wear. A large eddy simulation is employed to describe the molten steel vortex flow. Thus, the thermal profiles of the molten steel and refractory lining are constructed. One-way coupled unsteady Euler-Lagrange approach is adopted to estimate the detachment and motion of the exogenous inclusion. The inclusion’s Reynolds number is utilized for evaluating the inclusion separation at the refractory lining after formation and at the upper surface of the molten steel. At a 1.2 m/min casting speed, 49 and 38 pct of exogenous inclusions are created at the turbulent inhibitor inner bottom and long nozzle inner wall, respectively. In contrast, only 13 pct of new inclusions are produced at all other inner walls. About 80 pct of newly generated inclusions are then trapped by free surfaces, 78 pct of which are removed at the first free surface. The initial diameter of exogenous inclusions ranges from 13 to 48 μm. The removal ratio of exogenous inclusions in the tundish first grows from 61 to 80 pct, with the casting speed rising from 1.0 to 1.2 m/min and then drops to 63 pct after the further casting speed rise to 1.4 m/min.

Numerical simulation of dam-break water flow over a horizontal dry bed has been performed. We have modified and verified computational techniques, including methods for determining the position of the interface and the continuum model for the surface tension force implemented in the PIFI code, as well as the OpenFOAM software with the interFoam solver and various cases of the two-parameter ( $$k{-}\varepsilon$$ ) model with corrections made taking into account the behavior of flows in regions of low Reynolds numbers. Calculated integral characteristics of dam-break flow were analyzed and compared with measured data. It is shown that taking into account surface tension and using an adequate turbulence model leads to deceleration of water flow and hence to a decrease in the velocity of the wave front, resulting in better agreement between the results of calculations and laboratory experiments.

This paper proposes an analytical solution for the calculation of vibrations from a twin tunnel embedded in a half-space to assess the influence of a neighbouring tunnel on the ground-borne vibrations due to underground railway traffic. Using the wave function method, the total wave field in a half-space containing two cavities is expanded as the combination of down-going plane waves from the free surface and outgoing cylindrical waves from each cavity. The two tunnels are modelled as hollow cylinders, and the wave field inside them can be represented as the superposition of outgoing and regular cylindrical waves. To solve this multiple scattering problem, three sets of coordinate system defined at the scattering surfaces are used to describe the cylindrical waves in polar coordinates and the plane waves in rectangular coordinates. The application of transformation and translation properties between plane and cylindrical waves makes it possible to represent the waves emanating from one scattering surface in terms of the coordinates defined at the other two surfaces. The boundary conditions at the free surface and two tunnels can then be applied to solve for the expansion coefficients for the vector wave functions of plane and cylindrical waves. The present approach is also valid for a multi-layered ground, and in the layer with the tunnels, the field is composed of outgoing waves from the tunnels, down-going waves from the upper interface of the layer and up-going waves from the lower interface. Numerical results show that there is one critical velocity around shear wave speed of soils for a single/twin tunnel in a homogeneous half-space. For a multi-layered geometry, two global critical velocities may exist for the twin tunnel case, and they are determined by the properties of the soil layer where the twin tunnel is located in and the layer below the tunnels.

Azimuthal gyroscopic waves in a floatation fluid forming a centrifuged layer on the solid wall of a cylindrical cavity of the rotor are studied. The exact solution of the linearized hydrodynamic problem with a nonclassical boundary condition on the free surface is obtained. The dispersion equation is derived. The influence of the inertial surface of the fluid on the stability of quasi-solid-body rotation of the centrifuged layer is studied.

Sloshing is associated with the structural safety of liquid storage vessel. Installing the baffles inside the containers would be beneficial for the mitigating the damage due to the severe sloshing. In this study, an innovative type of double-side curved baffle was proposed to evaluate its effect on reducing sloshing in a rectangular tank under surge and pitch excitation. For comparison with conventional baffles, effects of the vertical baffle and the T-type baffle on mitigating sloshing were also studied experimentally and numerically by analyzing the free surface wave elevation as well as the hydrodynamic pressure on the tank wall. The effective stress at the double-side curved baffle along the height direction of the baffle is much smaller than that at the T-type baffle although they have the same mitigation effect on sloshing wave heights. The sloshing-induced effective stress on the double-side curved baffles was analyzed by varying their radian. Findings show that the effective stress on the baffle tends to decrease with the increase in the radian. The velocity field was presented to observe effect of the baffles on sloshing with the aid of ADINA and laboratory experiments conducted on a hexapod motion platform.

International audience; Control of macrosegregation phenomena and deformation-related defects is a main issue in steel continuous casting. Numerical simulation could help industrial engineers to master these defects. However, as a first step, it is essential to achieve a concurrent computation of fluid flow in the bulk liquid and stress-strain evolution in the already solidified regions. With this aim in view, a new specific partitioned solver has been developed to model the liquid flow, essentially induced by the inlet jet distributed by the submerged nozzle, as well as the thermal deformation of the solid shell. The solver procedure allows simulating the transient regime, up to convergence to the steady-state regime. For this purpose, the computational finite element mesh moves and grows continuously. Within this evolving mesh, three different zones are defined: the solid shell as a pure Lagrangian zone, the liquid nozzle region as a pure Eulerian zone, and an intermediate Eulerian-Lagrangian zone. Conservation equations (energy, mass, and momentum) are solved in a general arbitrary Lagrangian-Eulerian framework, with a level-set formulation to track the free surface evolution at the meniscus. The article is composed of two parts. In the first part, the model is detailed with the resolution steps involved in the coupled resolution approach. In the second part, a simple verification test case is firstly proposed, followed by a more relevant and practical application to model an industrial pilot continuous casting process.

The drag and side force coefficients of a half-submerged cylinder in a free-surface flow were calculated through numerical simulations, with the aim of supporting the numerical modelling of log transport in rivers. The variability of these coefficients with the yaw angle with respect to the flow direction and with the ratio between the flow depth and the diameter of the cylinder were investigated. Simulations were performed with the three-dimensional code ANSYS/CFX, employing the volume of fluid multiphase technique to reproduce the critical interaction between the free surface and the cylinder. The numerical tests, showing the rise of the drag force coefficient for increasing yaw angles passing from flow-parallel to flow-perpendicular cylinder and the peak of the side force coefficient for flow-oblique cylinder, were validated by comparison with the results of laboratory experiments. The simulations were then extended to conditions with significant blockage in the vertical direction which had not been previously experimented, revealing a strong increase in the force coefficients for decreasing ratios between the flow depth and the cylinder diameter. A detailed description of the reproduced flow features in the proximity of the cylinder for the different cases was furthermore obtained. Such report, in addition to the analysis of the force coefficients, could serve a much wider range than that of log transport, i.e., any case in which a floating cylinder interacts with free-surface flow.

Imperfect mechanical or dielectric interfaces in piezoelectric sensors/actuators reduce the electromechanical efficiency of the system. The major drawback of an imperfect interface in a system is its disability to transfer stress or potential across the surface effectively. This leads to imperfect signal communication and thereby affecting its performance. The present study encapsulates the shear wave (Love wave in low velocity layer and B-G wave) propagation characteristics in an imperfectly bonded piezoelectric layered structure, also subjected to material gradients. The imperfect bonding interface is considered to be mechanically compliant and dielectrically weak (or high) conducting. With help of admissible, but non-traditional, boundary conditions at the interface, the dispersion equations of waves are derived by method of infinite determinants for both electrically open and shorted conditions at the free surface. Phase velocity, electromechanical coupling factor and mass loading sensitivity of shear waves are sketched graphically with special concern on the influence of interface imperfection on them. The results reported can serve to overcome the deficit in the performance of Love wave sensors due to mechanically/dielectrically imperfect interfacial surface.

Shallow-water sloshing motions in a three-dimensional rectangular tank are investigated. The Boussinesq-type equations in terms of velocity potential and the finite-difference scheme are applied for the solutions of numerical model. Through linking the rate of decay of the wave amplitudes to the energy dissipation due to the friction at the tank walls, a linear damping term is proposed and added into the free surface boundary condition. Taking the tank under excited frequencies near the lowest natural frequency, the maximum transient wave amplitudes and steady-state wave amplitudes of sloshing motions at the tank wall are presented and verified by the experimental results given in the literature. The characteristics of sloshing motions in tank under different coupled excitations are studied. The results indicate that coupled surge-sway excitations lead to the weaker nonlinear sloshing motions in tank than the single degree of freedom excitations. The intersection of sloshing wave crest lines finally tend to the diagonal line of the tank under the coupled surge-sway excitations with different amplitudes. And the irregular free surface oscillations appear at the corners of the tank excited by the coupled surge-sway-roll-pitch-yaw harmonic motions.

A numerical method for solving 3D unsteady potential flow problem of ship advancing in waves is put forward. The flow field is divided into an inner and an outer domain by introducing an artificial matching surface. The inner domain is surrounded by ship wetted surface and matching surface as well as part of the free surface. The free surface condition for the inner domain is formulated by perturbation about the double-body flow or uniform incoming flow assumption. The outer domain is surrounded by matching surface and the rest free surface as well as infinite far-field radiation boundary. The free surface condition for the outer domain is formulated by perturbation about uniform incoming flow. The simple Green function and transient free surface Green function are used to form the boundary integral equation (BIE) for the inner and outer domains, respectively. Taylor Expansion Boundary Element Method (TEBEM) is utilized to solve the double-body flow and inner domain and outer domain unsteady flow BIE. Matching conditions for the inner domain flow and outer domain flow are enforced by the continuity of velocity potential and normal velocity on the matching surface. Direct pressure integration on ship wetted surface is used to obtain the first-order and second-order wave forces (moments). The numerical predictions on the displacement, added resistance, sway mean drift force and yaw mean drift moment of the modified KVLCC2 ship at different forward speeds are investigated by the proposed TEBEM method. It is also compared with the other numerical results. The physical tank experiment results are also developed to validate the accuracy of numerical tank results. Compared with the experiment solutions, a good agreement can be obtained by TEBEM method.

The paper starts with a detailed investigation of the boundary conditions at free and fixed boundaries of any second gradient material and clarifies whether a surface tension is to be expected. The classical approach to the reaction stresses of higher gradient materials leaves a vast indeterminacy in most boundary value problems. An advanced approach is presented that yields much more definite distributions of the reaction stresses and consequently also of the surface tension. It starts from a compressible fluid the stiffness and bulk viscosity of which tend to infinity. Furthermore, the complete set of restrictions on the material parameters of linear incompressible second gradient fluids is derived from the postulate of nonnegative dissipation. Finally, a stirring process with a free surface is studied as an example. The results are based on the numerical solution of the boundary value problems of three partial differential equations of second, fourth and sixth order, respectively.

The viscoplastic fluid flow initiated in a circular pipe/plane channel during its filling in the gravity field at the flow rate specified at the inlet section is investigated. A mathematical formulation of the problem is stated based on complete equations of motion, the continuity equation, the natural boundary conditions on a free surface, and no-slip boundary condition on the solid wall. The rheological behavior of the medium is described by the Schwedoff–Bingham law, which presupposes the existence of quasi-solid motion zones (unyielded zones) in regions of low strain rates. The numerical solution of the problem is based on the finite-difference approach including the finite volume method and SIMPLE algorithm for calculating velocity and pressure fields at the internal nodes of a staggered grid. The method of invariants is used to satisfy the boundary conditions on the free surface. To provide a through computation of the flow with unyielded regions, regularization of the rheological equation is implemented. The behavior of a free boundary, flow structure, and flow characteristics as a function of the main parameters is investigated. It is found that in the course of time the initially flat free boundary acquires a stationary convex shape, which remains invariant while moving through the pipe/channel at the rate-average velocity. In the flow near and far away from the free boundary, one can distinguish fountain flow zones and one-dimensional flow regions, respectively. The typical flow structures with different numbers and various locations of unyielded regions in the flow are shown. The topograms of the above-mentioned flow structures as functions of the ratio of viscous and gravity forces and plasticity in the fluid flow are plotted. The stable and unstable behavior of the free boundary shape is shown to be related to the values of the constitutive parameters.

The research presented in this paper focusses on the underwater blast resilience of a hybrid composite sandwich panel, consisting of both glass-fibre and carbon-fibre. The hybrid fibres were selected to optimise strength and stiffness during blast loading by promoting fibre interactions. In the blast experiment, the aim was to capture full-field panel deflection during large-scale underwater blast using high-speed 3D Digital Image Correlation (DIC). The composite sandwich panel was partially submerged and subjected to a 1 kg PE7 charge at 1 m stand-off. The charge was aligned with the centre of the panel at a depth of 275 mm and mimicked the effect of a near-field subsurface mine. The DIC deflection data shows that the horizontal cross-section of the panel deforms in a parabolic shape until excessive deflection causes core shear cracking. The panel then forms the commonly observed “bathtub” deformation shape. DIC data highlighted the expected differences in initial conditions compared to air-blast experiments, including the pre-strains caused by the mass of water (hydrostatic pressure). Furthermore, water depth was shown to significantly influence panel deflection, strain and hence damage sustained under these conditions. Panel deformations and damage after blast was progressively more severe in regions deeper underwater, as pressures were higher and decayed slower compared to regions near the free surface. An identical hybrid composite sandwich panel was subjected to air blast; one panel underwent two 8 kg PE7 charges in succession at 8 m stand-off. DIC was also implemented to record the panel deformations during air blast. The air and underwater blast tests represent two different regimes of blast loading: one far-field in air and one near-field underwater. The difference in deflection development, caused by the differing fluid mediums and stand-off distances, is apparent from the full-field results. During underwater blast the panel underwent peak pressure loading of approximately 52.6 MPa whilst during air blast the panel was subjected to 67.7 kPa followed by 68.9 kPa peak pressure loads in succession. The two experiments demonstrate the response of the same hybrid composite sandwich panel under two differing blast regimes. The post-blast damage and strength of the hybrid panels following air and underwater blasts were evaluated. Post-blast testing revealed that the underwater blast causes significantly more damage compared to air blast, particularly debonding between the skins and core. The air blast panel sustains no visible rear skin/core debonding, whereas 13 regions of rear-face debonds are identified on the underwater blast panel. Sustaining no front-skin breakage was advantageous for retaining a high proportion of the compressive modulus for this hybrid layup following underwater blast. Damage mechanisms were interrelated. Determining the most detrimental type is not straightforward in real explosive and non-idealised experiments, however debonding was understandably shown to be significant. A further study to isolate failure modes and improve in situ instrumentation is ongoing.

Abstract The precipitation of supersaturated solutes at free surfaces in ternary Fe–3Au–4W and binary Fe–3Au and Fe–4W alloys (composition in weight percentage) for different ageing times was investigated at a temperature of 700 °C. The time evolution of the surface precipitation is compared among the three alloys to investigate the interplay between the Au and W solutes in the ternary system. The Au-rich grain-interior surface precipitates show a similar size and kinetics in the Fe–Au–W and Fe–Au alloys, while the W-rich grain-interior surface precipitates show a smaller size and a higher number density in the Fe–Au–W alloy compared to the Fe–W alloy. The kinetics of the precipitation on the external free surface for the ternary Fe–Au–W alloy is compared to the previously studied precipitation on the internal surfaces of the grain-boundary cavities during creep loading of the same alloy. Graphical abstract

HIGHLIGHTS • Efficient calculation method is developed for elastic boundary load of film-substrate system. • Three types of imperfect interface models are developed and verified. ABSTRACT In this paper, an efficient calculation method based on discrete Fourier transformation is developed for evaluating elastic load induced elastic deformation fields of film-substrate system. Making use of 2D discrete Fourier transformation, the elastic fields induced by Hertz load is harvested in frequency domain, and the displacement and stress fields across the interface are enforced to satisfy the elasticity conditions for each Fourier modes. Given arbitrary distributed stress field at free surface plane of the three types of film-substrate systems, unique resultant elastic field within the can be harvested. Hertz load of half space, elastic film on elastic substrate, elastic film on rigid substrate system and elastic film-substrate system with three types of imperfect interface models are investigated: ( 1 ) the spring-like imperfect interface model which can be described as: u k f | z f = − h − u k f | z s = 0 = K T σ k z a n d u k f | z f = − h − u z s | z s = 0 = K N σ z z ; ( 2 ) the dislocation-like interface model, where interface displacement and stress components relation can be described as: u i f | z f = 0 = k i j u u i s | z s = 0 a n d σ i z f | z f = 0 = σ i z s | z f = 0 ; ( 3 ) the force-like interface model, where interface displacement and stress components relation can be described as: u i f | z f = 0 = u i s | z s = 0 a n d σ i z f | z f = 0 = k i j t σ i z s | z s = 0 respectively. Finally, several simulation examples are performed for verification of the reliability and efficiency of the proposed semi-analytical methods.

A mesoscopic model was established to investigate thermo-fluid dynamic behavior in selective laser melting of 316L stainless steel. A powder packing model, including particle size distribution based on the discrete element method, was developed to describe the relative density variation of the powder bed with different layer thicknesses. A finite element method model with Gaussian laser beam was established to predict the dynamic thermal behavior and flow mechanism of the particles for a single-line scanning. The level-set method was used to trace the free surface of the molten metal with temperature-dependent surface tension. A function to describe the relative density of the powder bed with its thickness was obtained. An evaporation model considering the influence of mass, energy loss, and evaporation on the surface morphology of the molten pool was established. According to the temperature and velocity field in the molten pool, a vortex formed by the Marangoni effect might decrease the depth and increase the width of the molten pool. The molten pool was not disconnected by Plateau–Rayleigh instability due to the small length/diameter ratio at low scanning speeds. The model assuming regularly arranged powder bed underestimates the maximum temperature as compared to the model considering a randomly packed powder bed because a higher relative density of the former facilitates heat conduction. The simulated results are consistent with experimental results, including porosity, material loss, and surface defects.

An experimental study to investigate various features of subsurface vortices and their evolutions inside a closed pump intake under different pressure conditions at free surface, and to analyze the influence of a pipe bell with different mean axial velocities at the same water level on flow patterns is presented. For all cases, three different flow regimes are closely observed: various side-wall attached, back-wall attached and submerged vortices structures, and their evolutions are subject to the free-surface pressure for a critical flow rate, the number and strength of all these vortex rise as the absolute value of the pressure increases for a higher flow rate, for a lower flow rate, whether the side-wall vortices occur or not is related closely to the pressure magnitude, and there are no vortices for lower absolute pressure values, the number and the strength of the side-wall vortices increase as the absolute pressure values increase. Besides, based on statistical analyses, the side-wall vortex probability on the right side along the stream-wise direction is much higher than that on the opposite side for all operation cases, particularly single vortex probability, and the back-wall vortex probabilities are quite higher with values of more than 90%, meanwhile, the multi-vortices probability is much higher than that of the single-vortex. The captured vortices have been qualitatively classified into different “vortex zones”: no vortex zones and vortex zones including transition, single- and multi-vortex. The Reynolds number and the absolute value pressure are the most important parameters which influence the existence and the number of these vortices, and the increase of the two parameters reduces the no vortex transition zone and causes bigger difference in the back-wall and side-wall vortex zones.

In this paper, the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model. The numerical model is verified and validated by experimental data. Then, two factors are considered, the global wave steepness and the frequency bandwidth of the wave groups, in the studies of the in-line wave forces and the wave run-up around a cylinder. It is found that both the in-line wave forces and the wave run-up are remarkably increased with the increase of the global wave steepness, whereas the effect of the frequency bandwidth on the in-line wave forces is relatively weak in comparison with its effect on the wave run-up. The minimum and maximum wave run-ups are located in the directions of 22.5° and 180° with respect to the direction of the incident waves, respectively. Additionally, a new empirical formula is proposed for predicting the in-line wave forces by using only the free surface elevations around the cylinder. The results of the formula agree well with the simulation results.

As the global warming, the Arctic Shipping Routes are gradually opened. The icebreakers are still in need to ensure the safe navigation of ships. During the voyage from East Asia to North-western Europe, the icebreaker will experience a long-distance voyage where over 60% of the distance is open water. As the bow of the icebreaker is full and the length-beam ratio is relatively high, it is quite important to study added resistance of the icebreaker. The results of added resistance, heave and pitch motion in regular waves are consistent with the variation trend using two methods. For computational efficiency, the nonlinear potential method was used to predict added resistance and vertical movement of the icebreaker at five wind directions. The added resistance in head waves is higher than in other wave directions. The maximum value was obtained at the wave length-ship length ratio of 1.2. The relationship between the phase of motion and resistance can be easily obtained. Meanwhile, the free surface around the hull can also be easily obtained. Moreover, compared to the CFD method, the nonlinear potential method can save more computing resources and time. It has important application value in the early design of the icebreaker.

The study of the deformation and damage evolution behaviour of surrounding rock under excavation unloading conditions is of vital importance for a deep understanding of the mechanism of roadway failure. In this study, unloading testing using a partially hollow thick-walled cylinder cement mortar specimen with dimensions of 280 mm (height) × 200 mm (outer diameter) × 60 mm (inner diameter) and a solid height of 60 mm at the bottom was performed to investigate the deformation response and damage failure evolution characteristics of the surrounding rock. The experimental results showed that the higher deviatoric stress level accelerated the damage development caused by the unloading effect and improved the expansion rate of the internal cracks, which led to a higher radial strain rate, total strain, and acoustic emission hits. When deviatoric stress increased to a relatively higher level, the radial strain rates were highly unstable, and the surrounding rock near or at the opening free surface was damaged locally and regionally. During the failure process of the specimen, the generation of the deformation and damage in the unloading stage was more alive (as indicated by the growth rate). Nevertheless, the main deformation and damage to the surrounding rock were generated and accumulated in the maintaining stage after unloading.

The kinematic and dynamic boundary conditions on the free surface of a fluid should be posed for water wave problems. In the framework of potential theory for an inviscid and incompressible fluid with an irrotational motion, the combined boundary condition, which involves the velocity potential only, is often used by eliminating the elevation terms mathematically. Such a combination is correct for the solutions in the frequency domain, and is not feasible for an initial-boundary-value problem in the time domain since it leads to a totally different physical formulation. The correct initial conditions for pure gravity waves and hydroelastic waves are presented.

In this work, we apply lubricated squeezing to perform planar extension of styrene-butadiene rubbers (SBRs) and illustrate how large step-strained SBR undergo chain relaxation. When the imposed step strain is moderate or the stepwise planar extension is imposed sufficiently slowly, the stress relaxation is spatially uniform. Upon a large stepwise extension imposed over a period much shorter than the overall chain relaxation time, the strained SBR undergo spatially inhomogeneous molecular relaxation, plausibly due to localized chain disentanglement that results from the molecular force imbalance. As a manifestation of localized elastic yielding, the SBR specimen appears wrinkled upon unloading in the middle of stress relaxation. In situ birefringence measurements confirm that uneven chain relaxation is ongoing during stress relaxation that involves keeping the sample height H fixed after squeezing from the initial height H0 to H. Thus, localized chain relaxation is shown to take place even in the presence of geometrical constraint, i.e., the absence of any free surface or meniscus. In comparison, homogenous stepwise deformation was found to result in nonquiescent relaxation for simple shear and filament breakup for uniaxial melt stretching.

PurposeThe purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature.Design/methodology/approachA two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB.FindingsThe problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material.Originality/valueThe modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

A new method was presented to inhibit bulging deformation and fluctuation of free surface by magnetic pressure. A research combined with numerical and experimental methods was conducted to investigate the feasibility and inhibition efficiency. The parameters including magnetic flux density, frequency and action area of magnetic pressure were analyzed. The results show that the method is feasible, and the bulged free surface is fully inhibited by the proper magnetic pressure. The inhibition efficiency increases as the increase in magnetic flux density and frequency, which shows a linear relationship with the magnetic flux density. The frequency has a great influence on the inhibition efficiency when the frequency is changed from 0.15 to 5.00 kHz. However, the frequency more than 5.00 kHz has little influence on the inhibition efficiency and is recommended in application process. When the ratio of the action area to the area of bulged free surface is 0.8, the best inhibition is achieved. However, when the ratio is more than 1.2, a distinct W-shaped free surface is observed. The surficial and internal flow is strengthened with proper magnetic pressure imposed. Moreover, under the action of magnetic pressure, the fluctuation amplitude of free surface decreases from 4.0 to 1.2 mm and the main fluctuation with frequency of 2.34 Hz is dispersed into several minor fluctuations with frequency of 0.4–4.3 Hz.