Evolution Of Free Surface Research Articles

Free surface lump wave dynamics of a saturated superfluid 4He film with nontrivial boundary condition at the substrate surface

In this article, the free surface wave dynamics of a saturated (∼10−6 cm) superfluid 4He film is considered under the condition that there exists a very weak downward localized superfluid flow into the substrate. For saturated film, the effect of surface tension plays a decisive role in the surface wave evolution dynamics of the system. The free surface evolution is shown to be governed by forced Kadomtsev Petviashvili-I equation, with the forcing function depending on downward superfluid velocity at the substrate surface. Exact as well as perturbative free surface lump wave solutions of the (2 + 1) dimensional nonlinear evolution equation are obtained and the effect of the leakage velocity function on the lump wave solutions are shown.

Numerical analysis of the influence of molten pool instability on the weld formation during the high speed fiber laser welding

The dynamic behaviors of the molten pool play a critical role in determining the weld bead formation process and the welded joints quality. A numerical simulation modeling method is proposed to investigate the instability of the molten pool and understand its influence on the formation process of the weld and the related welding defects during the high speed fiber laser welding. In the modeling, the molten metal flowing dynamic behaviors and free surface evolution of molten pool are coupling taken into account. The instable phenomena including the profiles variation of the molten pool surface in the vertical direction and edges oscillation in the horizontal direction are demonstrated and discussed in the simulation results in details. The Rayleigh instability of the molten pool is numerically approved and the relationship between the molten pool profile and Rayleigh instability is revealed, which is kept consistent with the experiment and literature results. It is found that the welding defects formation process in the weld is greatly affected by the instable phenomena in the molten pool. The oscillation and fluctuation of the molten pool surface in the horizontal direction and vertical direction during the cooling process can directly result in the defects formation in the weld.

Ship hull slamming analysis with smoothed particle hydrodynamics method

In the marine and ocean engineering area, the water-entry process is a typical problem of fluid-solid interaction, which involves complex phenomenon such as the large deformation of free surface and considerable structure movement. In this process, the predicting impact load and summarizing the evolution law of the free surface deformation have important reference significance for the hull structure design. To address this issue, numerical simulations are carried out using a robust Smoothed Particle Hydrodynamics (SPH) model. The accuracy of the present SPH model is firstly validated by simulating the water entry of bow-flare section in two and three dimensions, respectively. Then, we investigate the variation characteristics of impact load and the evolution of free surface during the entry of the bow-flare ship section with different roll angles (θ=0∘∼20.3∘). Attention is focused on the flow separating phenomenon and the spray jet on the free surface. Finally, the water entry of a three dimensional ship hull is simulated. The velocity and pressure of flow field are analyzed and some conclusions are drawn.

Role of impinging powder particles on melt pool hydrodynamics, thermal behaviour and microstructure in laser-assisted DED process: A particle-scale DEM – CFD – CA approach

High speed imaging of molten pool free-surface hydrodynamics in laser-assisted directed energy deposition process clearly revealed a highly oscillatory and dynamic melt flow due to impinging powder particles. Surprisingly, most of the reported computational work exclude the injection of powder particles and rather adopt a homogeneous mass and energy addition approach, and therefore provides less accurate predictions. In this work, we develop a coupled multi-physics particle-scale approach utilizing the discrete element method for particle trajectory prediction, the computational fluid dynamics for free-surface thermo-fluidic modelling and the cellular automata method for grain growth evolution. In the model, the governing physical phenomena, such as laser-powder interaction, in-flight particle heating, phase change (melting, vaporization and solidification), free-surface evolution, molten pool hydrodynamics and impinging particles-melt interaction have been considered. Experiments for the deposition of Inconel-625 on an Inconel-625 substrate are carried out, and the model predictions are validated with the experimental measurements. For the first time, the predicted thermo-fluidic simulation results reveal highly oscillatory, chaotic and random melt flow attributed to the impinging powder particles. During the deposition, it is found that the role of the Marangoni convection is less significant as compared to the momentum imparted by the impinging powder particles in the melt pool. Using the simulated thermal undercooling data, cellular automata-based grain growth simulation predicts elongated columnar dendrites in the melt pool that grows epitaxially from the melt pool interface and stretches towards the centre. Using the Kurz-Fisher model, the effect of local thermodynamic solidification conditions on the size of dendritic microstructure is also described. The predicted melt pool geometry, temperature field and grain structure compare well with the experimental measurements.

Three-dimensional numerical simulation of violent free surface deformation based on a coupled level set and volume of fluid method

The purpose of this study is to evaluate the ability of the coupled level set and volume of fluid (CLSVOF) method to reproduce violent three-dimensional (3D) free surface deformation induced by different types of dambreak problems. A 3D CLSVOF-based numerical solver is developed, and the finite difference method is adopted to discretize the fluid domain. By applying these methods, the VOF advection equation is solved under the tangent of hyperbola framework to capture the interactions with the weighted linear interface calculation scheme (THINC/WLIC). The OCRWENO scheme is employed to accurately handle the LS advection equation, and the Navier–Stokes equations are discretized by a projection method. For dealing with fluid–structure interactions, the direct forcing immersed boundary method is employed. The developed numerical solver is applied to model free surface evolution in a variety of dambreak experiments. Good agreement is obtained between the numerical simulation and experimental results for each case, thus proving the suitability of the proposed numerical approach for the simulation of violent free surface deformation. The numerical solver developed in this paper has potential for reproducing strongly nonlinear free surface phenomena in other ocean engineering applications.

Gravitational Effects in the Collision of Elasto-Viscoplastic Drops on a Vertical Plane

The collision of drops in a solid substrate is an interesting problem with several practical applications. When the drop is made of a complex fluid the problem presents numerical challenges due to the interaction of the mechanical properties and the free surface approach. In the present work, we solve the numerical problem of elasto-viscoplastic drops colliding in vertical plane. The free surface evolution is handled by a Marker-And-Cell method combined with a Front-Tracking interface representation. Special emphasis is given to the gravitational effects by means of exploring the Froude number. We were able to find a rich variety of outputs that can be classified as sticking, sliding, bouncing, detaching, and slithering.

Wilton Ripples in Weakly Nonlinear Dispersive Models of Water Waves: Existence and Analyticity of Solution Branches

Traveling waves on the surface of the ocean play an important role in many oceanographic processes which necessitates a detailed quantitative understanding of their properties. The water wave equations, which govern the free-surface evolution of an ideal fluid, are the most successful model for this phenomena, but are exceedingly difficult to analyze due to their strongly nonlinear character and the fact that they are posed on a domain with moving boundary. For this reason, weakly nonlinear dispersive models are an essential tool for practitioners, and in this contribution, we study traveling wave solutions of a broad class of such models. The simplest family of traveling wave solutions are the Stokes waves which can be characterized as simple bifurcation (one-dimensional null space of the linearized operator) from the trivial (flat-water) branch of solutions. We focus our analysis on the much less studied non-simple case of Wilton ripples which have linear behavior characterized by two co-propagating harmonics (a two-dimensional null space of the linearized operator). More specifically, we show that such branches of solutions exist for a class of nonlinear dispersive model equations, and that they are analytic with respect to a natural wave height/slope parameter.

Stability of thin film flowing down the outer surface of a rotating non-uniformly heated vertical cylinder

We investigated an incompressible viscous liquid film flow over a rotating vertical cylinder of radius R and of infinite length rotating with a uniform angular velocity $$\varvec{\Omega }$$ about its axis. The surface of the vertical cylinder is non-uniformly heated where the temperature varies linearly in the downstream direction. The flow is assumed to be axisymmetric, and the component of the velocity along the azimuthal direction is assumed to be constant. The surface tension of the liquid is assumed to vary linearly with temperature such that as the temperature increases, the surface tension decreases. This gives rise to Marangoni stress over the free surface of the thin film. Using the long-wave approximation method, we derived a free surface evolution equation. For linear stability analysis, we used a normal mode approach and found that the Marangoni number plays a double role. There exists a critical Marangoni number $$\left( \mathrm{Mn}^{*}\right) $$ such that for $$\mathrm{Mn} \mathrm{Mn}^{*}$$ it plays a destabilizing role. We also found that as the rotation number $$\mathrm{Ro}$$ increases, the destabilizing zone increases but it decreases with the increment of the radius R of the cylinder. We further performed a weakly nonlinear analysis of the flow using the method of multiple scales. The study reveals that the Marangoni number Mn, the radius R and the rotation number $$\mathrm{Ro}$$ have substantial effects on different stability zones. The study also reveals that in the supercritical stable (subcritical unstable) zone, the threshold amplitude of the nonlinear disturbance increases (decreases) with the increment of Mn and $$\mathrm{Ro}$$ but decreases (increases) with the increment of R. The nonlinear wave speed in the supercritical stable zone decreases with the increment of Mn and $$\mathrm{Ro}$$, whereas it increases with the increment of R. We also examined the effect of thermocapillarity and rotation on the profile of the steady travelling wave solutions of the leading order part of the evolution equation.

Linear analysis of the dispersion relation of surface waves of a magnetic fluid in a square container under an external oblique magnetic field

In this study, free surface evolution of a magnetic fluid in a finite size tank which is subjected to an external magnetic field was investigated. The physical problem and equations governing fluid motion and magnetic field were given with boundary conditions. Using proper selection of variables, dimensionless equation system governing magnetic fluid sloshing were written. Resolution method based on multiple scale variables was presented and solution of the linear problem was given. The dispersion relation obtained in the finite depth case was compared with that corresponding to an infinite depth calculated with the same assumptions. Direction and magnitude of the external magnetic field, magnetic permeability ratio and surface tension effects on magnetic fluid free surface stability were analysed and important results were discussed.

Effect of strain path on roughness evolution of free surface during plastic deformation

The purpose of this study is to quantitatively analyze the effect of strain path on roughness evolution of free surface during plastic deformation. Firstly, the crystal plastic finite element model for a representative volume element (RVE) of polycrystalline is established, including the polycrystalline geometric model and initial topography model. Next, based on two groups of strain path including five typical strain paths, i.e., uniaxial tension (UT), biaxial tension (BT), plane strain tension (PST), plane strain compression (PSC) and in-plane pure shear (PPS), the 3D surface roughness of free surface after the plastic deformation is presented quantitatively. The total change of surface topography can be divided into two parts, which relate to the homogenous deformation and inhomogeneous deformation. In a simple manner, the homogenous deformation and inhomogeneous deformation can correspond with the elastic deformation and plastic deformation respectively. As in the elastic deformation, the effect of the misorientation of the adjacent grains and strain localization in the polycrystalline material on the surface topography has no chance to exert on the very small strain. So the inhomogeneity of polycrystalline material has been ignored in the elastic deformation. For the effect of homogeneous deformation, the relationship between the surface roughness of the deformed surface, initial roughness and strain path is analytically derived. For the contribution of the inhomogeneous deformation to surface roughening, the quantitative relationship between surface roughness of the deformed surface and the strain path is acquired by the mathematical fitting based on hundreds of crystal plasticity finite element simulations. The final surface roughness of the deformed surface is obtained by combining these two parts. Then the experiment of biaxial tension on 6061 aluminum alloy sheet is taken as an example to verify the accuracy of surface roughness calculation. The comparison of experimental results and calculated results shows good consistency. Thereafter the surface roughening phenomena in the plastic deformation are observed at three different scales. The homogeneous deformation does not form additional peaks and valleys but changes the spacing and height of peaks and valleys of the initial surface topography, which brings about the surface roughening at macroscale level. In inhomogeneous deformation, the misorientation of the adjacent grains in the polycrystalline material is taken into consideration, which leads to the grain rotation and generates the additional peaks and valleys of the initial surface topography. The surface roughening due to this part can be seen at the mesoscopic scale. And the step phenomenon caused by slip bands inner the grains is the microscopic scale roughening behavior. This work is beneficial to understand the roughness evolution of free surface quantitatively with the effect of strain path and make out the surface roughening phenomena at different scales.

Effects of spatially-varying substrate anchoring on instabilities and dewetting of thin nematic liquid crystal films.

Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destabilizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, such as emerging wavelengths, may not be influenced by the imposed substrate anchoring. Going further into the nonlinear regime, considered via large-scale GPU-based simulations, shows however that nonlinear effects may play an important role, in particular in the case of strong substrate anchoring anisotropy. Our simulations show that instability of the film develops in two stages: the first stage involves formation of ridges that are perpendicular to the local anchoring direction; and the second involves breakup of these ridges and formation of drops, whose final distribution is influenced by the anisotropy imposed by the substrate. Finally, we show that imposing more complex substrate anisotropy patterns allows us to reach basic understanding of the influence of substrate-imposed defects in director orientation on the instability evolution.

Cusped solitary wave with algebraic decay governed by the equation for surface waves of moderate amplitude

The existence of a new type of cusped solitary wave, which decays algebraically at infinity, for a nonlinear equation modeling the free surface evolution of moderate amplitude waves in shallow water is established by employing qualitative analysis for differential equations. Furthermore, the exact parametric representation as well as its planar graph for such type of wave is also given.

Experimental and analytical investigation of the response of a mud layer to solitary waves

Although the different aspects of wave-mud interaction have been studied by many researchers, few studies have been conducted on the effect of solitary wave on the particle velocities formed in the layers of cohesive sediments. The main objective of the present study is to investigate different features of the mud mechanical responses to the solitary wave loadings. This paper describes a comprehensive study of solitary wave-mud interaction by means of sets of laboratory tests, in which time series of the velocity in the water and mud layers, as well as free-surface evolutions, were measured. Wave damping and several aspects of the mechanical response of the mud layer to solitary wave loadings, e.g. mud particle velocities, the ratio between positive and negative peak velocities, time shift between peak velocities in the mud and water layer and the mud movement period, were studied through nondimensional parameters. It was shown that, at higher values of the mud water content ratio, the time shifts between the peak velocities in the mud and water layers decrease, whereas the mud movement period and the ratio of the positive to the negative peaks increase. Similar trends were observed as the height of the solitary wave was increased. A viscous analytical two-layered model has been developed. Comparing to the measurements, the present model and the model of Liu and Chan (J Fluid Mech 579:467–480, 2007) presented a similar behaviour for simulating the mechanical response of mud under the action of a solitary wave and both models performed better than the model of Jiang and Zhao (J Waterw Port Coast Ocean Eng 115:345–362, 1989).

Porosity and liquation cracking of dissimilar Nd:YAG laser welding of SUS304 stainless steel to T2 copper

In this study, we present experimental laser welding SUS304 stainless steel to T2 copper. The forming mechanism of fusion zone polygonal porosity and heat affected zone (HAZ) liquation cracking were systemically investigated and possible solutions to the welding process were also proposed. We deemed that the generation of HAZ liquation cracking mainly underwent three stages: crack incubation, crack initiation and crack growth. Formation of HAZ liquation cracking was closely related to precipitation of Cu-Fe compounds at grain boundaries and grain boundary liquation. The occurrence of porosity was determined by the keyhole instability correlated with fluid flow, keyhole free surface evolutions and composition segregation in a welding process. The susceptibility to HAZ liquation cracking can be effectively lowered by controlling the heat input during laser welding. In addition, the porosity in the fusion zone can be eliminated by reasonably adjusting laser deflection angle in the experiments, which greatly improved the microstructure and mechanical properties of welded joints.

Numerical study of pore formation in thermal spray coating process by investigating dynamics of air entrapment

When a liquid droplet impacts onto a solid surface, a thin air film is generally entrapped between the droplet and the substrate at the central portion which eventually evolves into a spherical air bubble for minimizing the surface energy. It leads to the formation of pores in the thermal spray coatings. This interesting phenomenon during the impact of molten metal droplets in thermal spray deposition that involves freezing is not clearly understood because of opaque nature of the metal droplet. Earlier works have focused on hydrodynamics of air entrapment without considering the phase change. Without considering heat transfer and phase change, the actual conditions of thermal spray deposition were not represented. The current study numerically analyzes pore formation by investigating the entrapped air film dynamics during the high-speed impact of a micron-sized molten metal droplet onto a solid substrate for thermal spray conditions by considering fluid flow, heat transfer, solidification phase change and free surface evolution. The volume of fluid surface tracking method (VOF) coupled with the solidification and heat transfer model within a continuum formulation is utilized. Results show that initially a thin circular film of air was entrapped in the impacting droplet which subsequently grew into an air bubble. The formation of the air bubble from the entrapped air film involves a complicated evolutionary process consisting of retraction, contraction and toroid formation of the air film. The analysis of heat transfer shows that wall heat flux distribution has a strong relation with dynamic feature of the trapped air. Further, it is shown that wettability of the substrate affects the detachment of the air bubble, which suggests a method for air bubble elimination from the solidifying droplet. Trapped air film tends to detach easily from the surface for low contact angle.

A comprehensive study on dam-break flow over dry and wet beds

This paper presents a comparative study of the influence of the initial and geometrical conditions on dam-break flow. The conditions are including the reservoir still water level, length and width as well as tail-water depth on dry and wet beds, respectively. The free surface evolution is analyzed through the volume of fluid (VOF) method. The sensitivity to mesh resolution and turbulence closure models are evaluated in three cell sizes and four models, respectively. Likewise, the turbulence closure models namely Reynolds averaged Navier-Stokes (RANS) and large eddies simulation (LES) are compared with the previous experimental data. The LES showed relatively better agreement than other ones on the free surface evolution. The results declared the crucial role of the initial and geometrical conditions on the free surface progression, flow energy, outflow and inflow hydrographs and the resultant forces.

Stability analysis of split-explicit free surface ocean models: Implication of the depth-independent barotropic mode approximation

The evolution of the oceanic free-surface is responsible for the propagation of fast surface gravity waves, which approximatively propagate at speed gH (with g the gravity and H the local water depth). In the deep ocean, this phase speed is roughly two orders of magnitude faster than the fastest internal gravity waves. The very strong stability constraint imposed by those fast surface waves on the time-step of numerical models is handled using a mode splitting between slow (internal/baroclinic) and fast (external/barotropic) motions to allow the possibility to adopt specific numerical treatments in each component. The barotropic mode is traditionally approximated by the vertically integrated flow because it has only slight vertical variations. However the implications of this assumption on the stability of the splitting are not well documented. In this paper, we describe a stability analysis of the mode splitting technique based on an eigenvector decomposition using the true (depth-dependent) barotropic mode. This allows us to quantify the amount of dissipation required to stabilize the approximative splitting. We show that, to achieve stable integrations, the dissipation usually applied through averaging filters can be drastically reduced when incorporated at the level of the barotropic time stepping. The benefits are illustrated by numerical experiments. In addition, the formulation of a new mode splitting algorithm using the depth-dependent barotropic mode is introduced.

Electromagnetic vortex suppression to prevent air core phenomenon for draining of electrically conducting liquids

The air core phenomenon observed during liquid suction or drainage through a narrow drain port can be reproduced artificially by starting the draining after rotating the cylindrical tank containing the liquid. Because the entrainment of gas-phase fluids during pump suction or liquid draining generates a breakdown of the machinery or defects in the product, various studies have been conducted to retard or prevent the air core phenomenon. Instead of utilizing an artificial structure such as a mesh or vane, as applied in previous studies, the present study introduces a new approach in which a magnetic field is applied to the container. First, the magnetic field applied induces an electric current through a reciprocal action with the liquid flow in the container. Next, the induced current and applied magnetic field create a Lorentz force, which is an electromagnetic body force. The Lorentz force helps with the suppression of existing flows. To couple the flow and electromagnetic fields, we solve the Poisson’s equation for the electric potential along with the momentum conservation. As the draining progresses, a volume-of-fluid (VOF) free surface capturing method is applied to track the free surface evolution, including the air core generation. For various Hartmann number (Ha) conditions, the internal velocities, vorticities, and Lorentz forces are comparatively presented. Finally, the effects of suppressing the air core phenomenon through the application of a magnetic field are discussed.

Research on dam-break induced tsunami bore acting on the triangular breakwater based on high order 3D CLSVOF-THINC/WLIC-IBM approaching

In present study, high order three dimensional coupled level set and volume of fluid (CLSVOF) based simulations about dam-break induced tsunami bore interacting with the stationary triangular breakwater was numerically investigated. Under our CLSVOF approaching, VOF advection equation is solved by tangent of hyperbola for interface capturing (THINC) with weighed linear interface calculation (WLIC) scheme, and level set advection equation is solved directly by the high-resolution optimized compact reconstruction weighted essentially non-oscillatory (WENO) scheme. Navier-Stokes equations is solved by a projection method on a fixed staggered Cartesian finite difference mesh. The pressure Poisson equation is solved by the point successive over-relaxation (PSOR) method. The direct forcing immersed boundary method (IBM) was implemented for breakwater-tsunami bore interface treatment. Numerical experiments based on our high order 3D CLSVOF-THINC/WLIC-IBM method were carried out in a rectangular water channel with a stationary typical triangular breakwater. The numerical results were compared with corresponding laboratory experimental results and reasonable agreements were obtained with satisfied accuracy. Numerical cases with different shape of triangular breakwater are carried out then in order to investigate the free surface evolution and energy dissipation due to the breakwater and useful conclusion is obtained.

Effect of an Oblique Magnetic Field Applied to the Sloshing of Free Surface Waves in the Magnetic Fluid

In this paper, linear theory of magnetic fluid sloshing in a rectangular tank subjected to an external oblique magnetic field was studied. Historic of subject as well his importance for fluid mechanics, technology and industrial applications. Magnetic fluid was considered perfect, incompressible and irrotational. Surface tension, gravity and magnetic permeability were taken into account. Linear equations are solved with linear boundary conditions. In the framework of the linear theory, variable separation method makes it possible to construct solutions and obtain eigenfrequencies and the eigen modes. The linear theory is still valid for a very small amplitude of sloshing. The direction and amplitude effects of the external oblique magnetic field on the free surface evolution were analyzed and main results were synthesized. The stability criteria are discussed theoretically and graphically illustrated.