Free Surface Motion Research Articles

Numerical Study on the Characteristic of Temperature Drop of Crude Oil in a Model Oil Tanker Subjected to Oscillating Motion

During tanker transportation, crude oil is heated occasionally to ensure its good flowability. Whether the heating scheme is scientific or not directly influences the safety and economy of the tanker transportation. The determination of a scientific heating scheme requires fully understanding of the characteristic of oil temperature drop during tanker transportation. However, the oscillation caused by the marine environment leads to totally different thermal and hydraulic characteristic from that of the static cases. Therefore, a systematic investigation of thermal and hydraulic process of the motion system is more than necessary. Since the marine is subjected to rotational and/or translational motion, the essence of the temperature drop process is an unsteady mixed convection process accompanied with free liquid surface movement. In this study, the movement of the free liquid surface and the characteristic of the temperature drop of the crude oil in the cargo when the tanker is subjected to rotational motion were investigated using ANSYS FLUENT (15.0, Ansys, Inc., Canonsburg, PA, USA) with user defined functions. The research result shows that the oscillating motion leads to the motion of the free surface, converting the natural convection for the static case to forced convection, and thus significantly enhancing the temperature drop rate. It is found that the temperature drop rate is positively related to the rotational angular velocity.

An adaptive variational procedure for the conservative and positivity preserving Allen–Cahn phase-field model

In this paper, we present an adaptive variational procedure for unstructured meshes to capture fluid–fluid interfaces in two-phase flows. The two phases are modeled by the phase-field finite element formulation, which involves the conservative Allen–Cahn equation coupled with the incompressible Navier–Stokes equations. The positivity preserving variational formulation is designed to maintain the bounded and stable solution of the Allen–Cahn equation. For the adaptivity procedure, we consider the residual-based error estimates for the underlying differential equations of the two-phase system. In particular, the adaptive refinement/coarsening is carried out by the newest vertex bisection algorithm by evaluating the residual error indicators based on the error estimates of the Allen–Cahn equation. The coarsening algorithm avoids the storage of the tree data structures for the hierarchical mesh, thus providing the ease of numerical implementation. Furthermore, the proposed nonlinear adaptive partitioned procedure aims at reducing the amount of coarsening while maintaining the convergence properties of the underlying nonlinear coupled differential equations. We investigate the adaptive phase-field finite element scheme through the spinodal decomposition in a complex curved geometry and the volume-conserved interface motion driven by the mean curvature flow for two circles in a square domain. We then assess the accuracy and efficiency of the proposed procedure by modeling the free-surface motion in a sloshing tank. In contrast to the non-adaptive Eulerian grid counterpart, we demonstrate that the mesh adaptivity remarkably reduces the degrees of freedom and the computational cost by nearly half for similar accuracy. The mass loss in the Allen–Cahn equation via adaptivity process is also reduced by nearly three times compared to the non-adaptive mesh. Finally, we apply the adaptive numerical framework to solve the application of a dam-breaking problem with topological changes.

Numerical study on interaction of a solitary wave with the submerged obstacle

The extremely nonlinear interaction between waves and marine structures is one of most challenging problems in ocean engineering. In this study, the propagation of a solitary wave over a submerged vertical obstacle is investigated by a developed two-dimensional multi-phase viscous model. The constrained interpolation profile (CIP) based on Cartesian grid method is introduced to solve the Navier-Stokes equations, and free surface is captured accurately by the Tangent of Hyperbola for INterface Capturing (THINC) scheme. First, the free surface motions and velocity fields of a solitary wave interacting with a submerged obstacle are simulated. The present calculations fit fairly well with the measurements through whole wave propagation over the submerged obstacle. Second, the corresponding vorticity fields are calculated to illustrate characteristics of vortex generation and evolution. Third, wave forces acting on the submerged obstacle are calculated, and the results agree well with existing computations. Finally, the effectiveness of the submerged obstacle as a targeted breakwater is estimated by evaluating the reflection and transmission coefficients. The presented computations confirm that the CIP-based Cartesian grid method is capable of reproducing strongly nonlinear interaction of a solitary wave with the submerged obstacle and performing predictions of comprehensive flow-field information accurately.

Fluid sloshing in rectangular vessels with side-wall baffles using conformal mappings of multiply-connected domains

This paper focuses on the problem of inviscid, irrotational, incompressible fluid sloshing in a rectangular vessel with rigid, impermeable side-wall baffles, and investigates the feasibility of using time-dependent conformal mappings to numerically simulate the evolution of the unknown free-surface in fully-dynamic simulations. An algorithm which uses conformal mappings of a multiply-connected domain to relate the conjugate harmonic functions along the free-surface is documented, and kinematic results presented for a prescribed free-surface motion. The results show that the specific mapping for an infinite depth fluid has one free, within specific bounds, mapping parameter, while the mapping for finite depth fluids has two free mapping parameters. It is shown that having two free parameters gives a wider range of situations under which the conformal mapping can be computed, and it is concluded that the finite depth mapping should be used (in the appropriate limit) even for infinite depth simulations. Overall it is found that a computationally efficient algorithm can be devised to relate the conjugate harmonic functions along the free-surface of the flow domain.

Thermocapillary flow and free-surface deformation of liquid bridge under different magnetic fields

The effects of transverse and cusp magnetic fields have been conducted on the thermocapillary flow and free-surface deformation in a silicon liquid bridge. The volume of fluid (VOF) method is adopted to track the free-surface movement. Based on our numerical results, both the transverse and cusp magnetic fields have a remarkable suppressing effect on the thermocapillary flow and free-surface deformation. The suppressing effect is directional in the case of the transverse magnetic field. At θ = 0° plane, the transverse magnetic field evidently suppresses the surface deformation near z = 0.225 cm region when BT0 ≤ 0.1 T and starts to have the suppression effect near z = 0.921 cm region when 0.1 T < BT0 ≤ 0.3 T. The deformation suppression performances at θ = 90° plane are opposite to that at θ = 0° plane. The critical Hartmann numbers for deformation damping on the θ = 0° and θ = 90° planes are 230.12 and 240.22, respectively. The cusp magnetic field causes concentration of the convection vortexes near the interface. Deformation suppression capability of cusp magnetic field is stronger than that of the transverse magnetic field. The critical Hartmann numbers for deformation damping on the θ = 0° and θ = 90° planes have the same value of 98.36 under the cusp magnetic field.

Estimation of gap resonance relevant to side-by-side offloading

Side-by-side offloading is becoming a more and more important offshore operation, where one vessel is moored alongside another one, forming a narrow gap between them. Using different types of incident waves, i.e. white noise waves, transient wave groups and regular waves, we investigated both the transient and steady-state resonant responses of the fluid in narrow gaps at model scale. The nonlinearity and uncertainties in obtaining the response amplitude operators (RAOs) of resonant fluid motions in narrow gaps are addressed. It appears that transient wave group testing is a promising approach for the investigation of gap resonance problem, because it avoids unwanted wave reflection induced by the limitation in the size of wave basins. To predict the gap resonant RAOs numerically, artificial damping is introduced into three different potential flow solvers to damp the otherwise over-estimated free surface motions in narrow gaps. The predicted RAOs, which are based on the potential flow solvers with the addition of calibrated damping, then show satisfactory agreement with the experimental data for a series of narrow gaps. This result confirms the reliability of the potential flow solvers in predicting gap resonant response (at model scale) for narrow gap widths that are relevant to engineering practice.

Numerical Analysis of Free Surface Movement around the Artificial Reef of Overflow Type

Numerical Analysis of Free Surface Movement around the Artificial Reef of Overflow Type

Numerical investigation of cavity formation mechanism for micron-waterdrop impact on deep pool

As one of the most fundamental and iconic fluid motion, droplet impact exists widely in scientific technologies and natural environment, and the phenomenon has been studied both for fundamental mechanism and for industrial applications in aerospace engineering, inkjet printing, agricultural irrigation and hydraulic structure erosion. Therefore, it is of great significance to study such basic movements for understanding the interfacial deformation of gas and liquid flow and improving the applications of droplet impact movement in engineering. Droplet impacting on a deep liquid pool has been extensively investigated for droplets with millimeter diameter. In this article, focusing on the cavity formation mechanism during a Micron-sized waterdrop impact on a deep pool, we perform systematic numerical simulations with adaptive mesh refinement technique and volume of fluid method to study the impact of a 290 μm water droplet on a deep water pool at velocities in a range of 2.5-6.5 m/s. The free surface motion, geometric variation of the cavity, local pressure field and vorticity field at selected times are presented to identify the pool-drop water mixing, capillary wave propagation, cavity formation, vortex ring generation and bubble entrapment phenomenon, and the dynamic mechanism of cavity motion is further explored. It is found that under the premise of neglecting the surface tension effects on the cavity whose depth is in a range of h∈(D, hmax), where D is the radius of initial droplet and hmax is the maximum depth, the cavity growth time to reach its maximum depth still scales as t∝h5/2, where t is time, but in the end, the formation of the bottom of the cavity is driven by capillary waves. There are two types of the initial cavity shapes: one is U-shape and the other is hemispherical shape, the former one generally changes into V-shape, and in the latter case, the bottom of the cavity will gradually transform into cylindrical shape, resulting in a thin jet and possible bubble entrapment. Cavity collapse is closely related to capillary wave propagation. When the impact velocity is low (Fr=567.1, Re=1595, We=121.8), the low-pressure zone is initially generated at the junction between the cavity sidewall and the bottom, a large vortex ring is then generated near the free surface and the bottom of the cavity, respectively. Under high impact velocities (Fr=792.1, Re=1885, We=170.2), the thin jet is observed, the generation of the vortex ring is suppressed. The low-pressure zone is first generated at the junction between the wave bottom and the cavity sidewall, after the cavity becomes cylindrical, the cavity collapses before the capillary wave arrives at the bottom, causing a bubble entrapment.

The 3D Numerical Study on Flow and Sediment Properties of a River with Grouped Spur Dikes

A 3D numerical model named NEWTANK is employed to investigate the flow motion and sediment transport in grouped spur dikes system. This model is based on the Navier-Stokes equations, adopting the Volume of Fluid (VOF) method to track the free surface motion, while the solid is described by using the Porous Media Method (PMM). The Large Eddy Simulation (LES) is applied to capture turbulence. In sediment calculation parts, the suspended load and bedload are treated separately but combined together to update bed variation eventually. The finite difference form and Two-step Projection Method are employed in the process of discretizing the governing equation. Several carefully selected flume experiments are introduced to verify this model's reliability before its application on the simulation of grouped spur dike case, and detailed flow characteristics and sediment properties are analyzed afterwards.

Verification of a Total Lagrangian ANCF Solution Procedure for Fluid–Structure Interaction Problems

The objective of this investigation is to verify a new total Lagrangian continuum-based fluid model that can be used to solve two- and three-dimensional fluid–structure interaction problems. Large rotations and deformations experienced by the fluid can be captured effectively using the finite element (FE) absolute nodal coordinate formulation (ANCF). ANCF elements can describe arbitrarily complex fluid shapes without imposing any restriction on the amount of rotation and deformation within the finite element, ensure continuity of the time-rate of position vector gradients at the nodal points, and lead to a constant mass matrix regardless of the magnitude of the fluid displacement. Fluid inertia forces are computed, considering the change in the fluid geometry as the result of the large displacements. In order to verify the ANCF solution, the dam-break benchmark problem is solved in the two- and three-dimensional cases. The motion of the fluid free surface is recorded before and after the impact on a vertical wall placed at the end of the dam dry deck. The results are in good agreement with those obtained by other numerical methods. The results obtained in this investigation show that the number of degrees-of-freedom (DOF) required for ANCF convergence is around one order of magnitude less than what is required by other existing methods. Limitations and advantages of the verified ANCF fluid model are discussed.

Numerical study on transient harbor oscillations induced by successive solitary waves

Tsunamis are traveling waves which are characterized by long wavelengths and large amplitudes close to the shore. Due to the transformation of tsunamis, undular bores have been frequently observed in the coastal zone and can be viewed as a sequence of solitary waves with different wave heights and different separation distances among them. In this article, transient harbor oscillations induced by incident successive solitary waves are first investigated. The transient oscillations are simulated by a fully nonlinear Boussinesq model, FUNWAVE-TVD. The incident successive solitary waves include double solitary waves and triple solitary waves. This paper mainly focuses on the effects of different waveform parameters of the incident successive solitary waves on the relative wave energy distribution inside the harbor. These wave parameters include the incident wave height, the relative separation distance between adjacent crests, and the number of elementary solitary waves in the incident wave train. The relative separation distance between adjacent crests is defined as the ratio of the distance between adjacent crests in the incident wave train to the effective wavelength of the single solitary wave. Maximum oscillations inside the harbor excited by various incident waves are also discussed. For comparison, the transient oscillation excited by the single solitary wave is also considered. The harbor used in this paper is assumed to be long and narrow and has constant depth; the free surface movement inside the harbor is essentially one-dimensional. This study reveals that, for the given harbor and for the variation ranges of all the waveform parameters of the incident successive solitary waves studied in this paper, the larger incident wave heights and the smaller number of elementary solitary waves in the incident tsunami lead to a more uniform relative wave energy distribution inside the harbor. For the successive solitary waves, the larger relative separation distance between adjacent crests can cause more obvious fluctuations of the relative wave energy distribution over different resonant modes. When the wave height of the elementary solitary wave in the successive solitary waves equals to that of the single solitary wave and the relative separation distance between adjacent crests is equal to or greater than 0.6, the maximum oscillation inside the harbor induced by the successive solitary waves is almost identical to that excited by the single solitary wave.

Propagation of Solitary Waves over Double Submerged Barriers

Protection of nearshore area by means of artificial structure is an important issue for coastal engineering community. In this study, we aim to investigate wave hydrodynamics and hydrodynamic performance due to solitary waves interacting with double submerged barriers. Double barriers, put bottom-mounted vertically on the flat seafloor and also paralleled to each other, are considered as a wave absorber. New experiments are carried out to provide measured data for model validation. Numerical simulations are performed using a depth- and phase-resolving model, based on the Reynolds-Averaged Navier–Stokes equations with a non-linear k-ɛ turbulence closure model. Model–data comparisons show good agreements in terms of free surface fluctuations in time histories and error analyses are performed. Numerical results are then used to study the variations of the free surface motions of breaking waves and the flow fields. In particular, the model results reveal that the optimal horizontal distance, judged as minimum wave transmission, between two submerged barriers is approximately 2.5 times the still water depth for present wave conditions and obstacle geometries. Furthermore, numerical model is extended to evaluate the functional efficiency of a dual-slotted-barrier system with different obstacle configurations under various conditions of solitary waves by means of energy reflection, transmission and dissipation coefficients.

Three dimensional modeling of free surface flow and sediment transport with bed deformation using automatic mesh motion

This study presents the development of a 3D numerical code for flow-sediment interactions with associated bed changes in free surface flows. To capture the water-air interface, a novel volume of fluid (VOF) formulation is implemented using the ghost fluid method with one-side extrapolation for dynamic pressure. Equations for fluid flow and free surface motion are decoupled due to separation of time scales. Accordingly, time step size can be increased by a factor of 3-orders of magnitude and still preserve numerical stability and computational efficiency. A novel finite area method (FAM) is utilized to discretize Exner equation on irregular bed surface providing a 3D finite volume-like discretization on curved surfaces. The evolution of the water-sediment interface is captured by a novel vertex-based unstructured mesh dynamic motion solve using Laplace operator with variable diffusivity. The code is implemented in foam-extend and tested against two classical experiments. Good results are obtained with correct trends and lower absolute error compared to previous mobile bed models. This shows that the developed code has a good potential of being applied to mobile-bed hydraulic real problems.

Wave motion in internal water of a floating logistics terminal

Recently a concept of floating logistic terminal (FLT) is proposed for accelerating exploration or improving productivity of offshore oil and gas. The present study focuses on the characteristics of free surface motion in the internal water of a floating logistics terminal. For the sake of simplicity of the analysis, it is assumed that the FLT has infinite number of small bodies which are located symmetrically at an equal distance from the big floating body. The problem is solved by the eigenfunction expansion method. Utilizing this method, some important near resonance phenomena are found. Plots of the free surface deformation show that the combined modes which occur at certain ratios of $$b/\beta$$ have a large deformation, while other near resonance modes are not severe. It is concluded that to avoid certain $$b/\beta$$ ratios which have combined resonance mode it is important that we design the FLT.

Interaction between motion of free fluid surfaces and ship motions

This scientific research presents very important aspects of the liquefying process of bulk cargo carried on board merchant ship which may lead to loss of the intact stability of bulk carriers, with serious consequences for the safety of ships and their crew.We are going to present an analytical modelling, modal analysis and finite elements analysis applied in the hydrodynamics of the ship in the water environment, when realising a complex model 3D of the ship’s bulkheads by modelling with finite volumes with the purpose of emphasising these walls’ behaviour when on board the bulk carrier there is a sloshing effect due to free liquid surfaces in the ship’s cargo holds and we also performed a complex study regarding the structural answer of transverse bulkheads of the cargo holds due to the impact of free liquid surfaces.

Wave scattering by a fixed submerged platform over a step bottom

This study deals with oblique and normal water wave scattering by a fixed submerged body of rectangular cross section which is infinite in length and finite in width. The fluid domain is considered as infinite as well as semi-infinite in nature. The study is carried out under the assumption of small amplitude linear water wave theory. It is considered that the bottom has a step and the submerged body is considered in shallower water depth region. The velocity potential is derived using the eigenfunction expansion method. The unknown constants, which appear in the expansion formulae, are obtained using orthogonal relation along with the boundary conditions at the interfaces. The wave-induced hydrodynamic forces acting on the submerged body and vertical wall are computed for different geometrical parameters. The wave reflection coefficient and the free surface motion are also calculated to see the wave phenomena around the submerged body.

Liquid Sloshing in a Rotating, Laterally Oscillating Cylindrical Container

Free surface movement of water in a rotating, laterally oscillating cylindrical container was qualitatively investigated. Time-dependent dynamic pressure was measured instead of free surface displacement. The swirling direction was determined by forcing the frequency and rotating direction of the cylindrical container. The swirling direction was opposite to that of the rotating cylindrical container when the forcing frequency was low, whereas the crest of the free surface swirled in the same direction as that of the rotating cylindrical container when the forcing frequency greatly increased. Unstable swirling occurred when swirling direction changes, but it disappeared as the rotating frequency increased.

Tracking free surface and estimating sloshing force using image processing

Ultrasonic level sensors are commonly used to measure the motion of the free surface in fluid sloshing. They are used to measure the elevation of the free surface at a single point. The sloshing forces are generally measured with load sensors, which require two sets of measurements, with and without the fluid in the tank. This paper develops a method, which tracks the free surface motion during sloshing with a camera and uses the captured images to estimate the forces due to sloshing in a rectangular tank. One of the major assumptions is that the displacement input which causes sloshing is one dimensional and the resulting sloshing motion is two dimensional. For the method to correctly estimate the sloshing forces along the displacement input direction, sloshing should be around the resonant sloshing frequency. This new method can track the motion of the complete free surface rather than a single point. It estimates the sloshing forces using image processing and potential flow theory, without the need for a load cell measurement. Free surface shapes and sloshing force estimates obtained by image processing are compared with those measured by the sensors. Good agreement is observed for low amplitude sloshing around fundamental resonance frequency.

Surfing surface gravity waves

A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497–503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

Towards non-intrusive reduced order 3D free surface flow modelling

In this article, we describe a novel non-intrusive reduction model for three-dimensional (3D) free surface flows. However, in this work we limit the vertical resolution to be a single element. So, although it does resolve some non-hydrostatic effects, it does not examine the application of reduced modelling to full 3D free surface flows, but it is an important step towards 3D modelling. A newly developed non-intrusive reduced order model (NIROM) (Xiao et al., 2015a) has been used in this work. Rather than taking the standard POD approach using the Galerkin projection, a Smolyak sparse grid interpolation method is employed to generate the NIROM. A set of interpolation functions is constructed to calculate the POD coefficients, where the POD coefficients at previous time steps are the inputs of the interpolation function. Therefore, this model is non-intrusive and does not require modifications to the code of the full system and is easy to implement.By using this new NIROM, we have developed a robust and efficient reduced order model for free surface flows within a 3D unstructured mesh finite element ocean model. What distinguishes the reduced order model developed here from other existing reduced order ocean models is (1) the inclusion of 3D dynamics with a free surface (the 3D computational domain and meshes are changed with the movement of the free surface); (2) the incorporation of wetting-drying; and (3) the first implementation of non-intrusive reduced order method in ocean modelling. Most importantly, the change of the computational domain with the free surface movement is taken into account in reduced order modelling. The accuracy and predictive capability of the new non-intrusive free surface flow ROM have been evaluated in Balzano and Okushiri tsunami test cases. This is the first step towards 3D reduced order modelling in realistic ocean cases. Results obtained show that the accuracy of free surface problems relative to the high fidelity model is maintained in ROM whilst the CPU time is reduced by several orders of magnitude.