Free Surface Model Research Articles

The impact of free surface modelling on hydrodynamic forces for ship navigating in inland waterways: water depth, drift angle, and ship speed effect

Simulations of standard manoeuvring tests require a good estimation of the hydrodynamic derivatives. These are extracted from the hydrodynamic forces applying on the ship. The present work focuses on the investigation of the importance of free surface assessment on the estimation of the hydrodynamic forces, particularly, in the presence of the ship–bottom interaction and when certain parameters are varied, including the ship’s speed and the drift angle. This investigation aims, in particular, to mark off the confidence Interval of neglecting free surface deformation hypothesis by comparing the results of static drift test with and without considering this assumption. The study was carried on a 135 m inland containership at a scale ratio of 1:25 undergoing static drift tests. In order to recreate the ship–bottom interaction, the depth to draft ratio (h/T) is varied to obtain four channel configurations. The tests are performed by numerical code under the commercial software Ansys Fluent by solving Reynolds Averaged Navier Stokes Equations(RANSE) coupled to a $$k -\omega$$ SST turbulence model. To investigate the effect of free surface modelling, the hydrodynamic forces are compared when the free surface separating air and water is considered, using Volume Of Fluid (VOF) method, and when the free surface is neglected. The simulations are carried out for various ship speeds and various drift angles.

Bank effects for KVLCC2

A study is presented on ship–bank interaction effects in which viscous-flow solvers are used to predict the hydrodynamic forces and moments on the ship. The ship under consideration is the KRISO Very Large Crude Carrier (KVLCC2). For this hull form, Flanders Hydraulics Research (FHR) has conducted shallow water model tests in their towing tank equipped with surface-piercing banks and a vertical quay wall. The forces and moments on the KVLCC2 model were obtained for various water depths and lateral distances to the banks. Additionally, the wave elevation was measured between the quay wall and the ship model. In this study, two different CFD codes are used to predict the loads on the KVLCC2 as a function of the water depth and lateral position in the channel. The effect of propeller suction and free surface modelling on the results is quantified. Furthermore, comparisons will be made with CFD results from literature and potential flow computations to highlight the benefits of each approach. It will be shown that with careful setup of the computations, reliable predictions of the ship–bank interaction effects can be obtained.

Capillary-driven flows along curved interior corners

In the absence of gravity, spontaneous capillary flow along an interior corner is a significant portion of liquid behavior in spacecraft. To effectively control the space liquid, the design of fluids management processes in the low-gravity environment of space requires a rapid and accurate prediction of capillary flow in interior corners. So far, the previous studies have been focused on the capillary flow along the straight interior corner. However, the curved interior corner is far more common. A comprehensive theoretical model is established to study the curved corner effects based on previous studies. By analysis, the centrifugal force caused by the curve motion is the decisive factor which makes the capillary flow in curved interior corners different from that in straight interior corners. The influences of centrifugal force on the free surface and friction factor are discussed, and high-precision approximation modeling method is used in free surface modeling to speed up the solving process. To validate the theoretical model, a series of microgravity drop tower experiments are conducted. By comparison, the theoretical results agree well with the experimental results. The results show that the liquid rises faster as the channel curvature increases. This feature can be used to transport and manage liquid better in spacecraft. A modified Suratman number Su is introduced to judge the curved corner effects. When Su=3, the relative error e caused by neglecting the curved corner effects is up to 36% which means the curved corner effects have a great influence on the capillary flow. When Su ≪ 1, the relative error e is close to 0 which means the curved corner effects can be neglected.

Numerical analysis of wave-induced poro-elastic seabed response around a hexagonal gravity-based offshore foundation

In order to prevent the future risk of soil and structural failures for the offshore foundations, it is essential to evaluate the seabed soil behaviors in the vicinity of the foundation under dynamic wave loadings. The objective of this paper is to investigate the wave-induced soil response and liquefaction risk around a hexagonal gravity-based offshore foundation. Three-dimensional (3D) numerical analysis is performed by applying an integrated multiphysics model developed in the finite volume method (FVM) based OpenFOAM framework. The integrated model incorporates solvers of the nonlinear waves, the linear elastic structure and the anisotropic poro-elastic seabed soil. The free surface model and soil model are verified by grid convergence studies. The wave-induced soil response model is validated by reproducing a laboratory experiment and a good agreement is obtained.Distributions of wave-induced shear stress, pore pressure, vertical displacement and seepage flow structure in the seabed are investigated. It is found that the presence of the foundation significantly amplifies the wave-induced shearing effect and vertical displacement in the underlying seabed soil. Seabed consolidation state in the presence of the structure is evaluated. Since the foundation is embedded in the seabed at a depth, the vertices of the hexagonal foundation cause the stress concentration in the nearby soil during the consolidation process. Therefore, the momentary liquefaction at the vertices is not as significant as that at the edges due to the high initial effective stress. A parametric study with different wave heights is conducted to examine the changes of soil response and momentary liquefaction depth around the hexagonal foundation. Effects of isotropic and anisotropic soil permeability on the pore pressure distribution are investigated. It shows that the effect of anisotropic permeability should be considered for the medium sand that is modelled in the present study.

Elastic 3D PS converted-wave Gaussian beam migration

Elastic-wave migration is a desirable technique because it can image the structure of the earth more accurately. We develop a new elastic Gaussian beam migration method with 3D three component (3D-3C) seismic data that focuses on a complex PS-converted wave. Based on the elastic-wave equations and complete boundary conditions, we derive effective work formulas for an accurate multimode wave downward continuation for the free-space, ocean-bottom, and free-surface models. We separate the PS-wave into linear-polarized P-S1 and P-S2 waves to simplify the expression and derivation of the migration. To image the vectorial wave directly and solve the reverse-polarity issue, we use the crosscorrelations of P-wave divergence and PS-wave curl operators as the 3D P- and PS-imaging conditions, and we develop a unit vector to define the rotation direction of the PS-wave. With our approach, 3D-3C multimode waves are automatically decomposed to P- and PS-waves during the migration without the need for prior data separation, which not only reduces the crosstalk noise caused by inaccurate multimode wave decomposition but also decreases the processing cost. Applications of this method to two 3D-3C synthetic examples indicate successful PS-wave migration. Also, confirming that the PS-image can be constructed by summing the P-S1 and P-S2 images and is independent of the choice of the ray-centered local coordinates validates this method.

An axisymmetric non-hydrostatic model for double-diffusive water systems

Abstract. The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model set-up. This article applies the Reynolds-averaged Navier–Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature- and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to double-diffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required.

Effect of the end sill angle on the hydrodynamic parameters of a stilling basin

In this study, the effect of an end sill angle on the hydrodynamic parameters of a stilling basin, such as pressure, velocity, turbulence intensity, vorticity and energy dissipation, is investigated numerically. Simulations are performed using RNG and VOF for turbulence and free surface models, respectively. After verifying the numerical results with the experimental data, the effect of four end sill angles of \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\) and \( 90^{\circ}\) on the flow parameters in the stilling basin is analyzed. Results show that the stilling basin with triangle end sill with angle of \(60^{\circ}\) has the best performance by dissipating 62% of energy.

MATEC Web of Conferences – General and efficient algorithms for handling intricate situations in trimmed surface rendering

Trimmed surfaces have been widely used in complicated product design in mechanical engineering especially in complex free form surface models of CAD/CAM/CAE. Focusing on the deficiencies of the algorithms available in published literatures when handling some intricate situations, this paper proposes a more general and efficient algorithm of trimmed surface rendering (ATSR). The ATSR is a general algorithm that can deal with most intricate situations, which frequently occur in practical engineering that no special attention has been paid to in references at hand, as well as common situations. Furthermore, this paper presents a new algorithm for the nodes of polygon connecting into elements (ANCE). The ANCE can handle most tricky polygons appearing in the process of rendering and achieve successful triangulation for the to-be-rendered surface. Preferable results are obtained in the case studies, which indicate that the algorithms (ATSR and ANCE) are efficient and effective in handling complicated as well as common trimmed surface models in real engineering industry.

Theoretical analysis and of three dimensional free surface of electrospinning

Electrospinning is a new type of free-end spinning built on the electric field. The electric force of PAN polymer solution overcomes the surface tension of the solution, and then it causes wave and forms jet flow. In the process of injection, the solution is evaporated or solidified, and eventually forming a fiber on the receiving device. Different from ordinary single needle head, in this study, a new type of three-dimension free surface nozzle is used to produce multiple jets at the same time, this will greatly improve production efficiency. In this paper the model of three-dimension free surface is analyzed by the theory of fluid mechanics, the relationship among the wave length and surface tension and the electric field is obtained. Through the experiment, the conclusion is verified, and the formula is correct.

Numerical visualization of air intake induced by free surface vortex

Free surface vortex control is vital in a pump sump system because the air absorbed by free surface vortex induces noise, vibration, and cavitation corrosion on the pumping system. In this study, the change of free surface vortex and air absorption in a pump intake has been investigated by the Volume of Fraction (VOF) method with steady multiphase flow model in order to represent the behavior of the free surface vortex exactly. The homogeneous free surface model is used to apply interactions of air and water. The results show that air intake by the free surface vortex motion can be visualized using the iso-surface of air volume fraction. The vortices make an air column from the free surface to the pump intake. Also, it was found that the free surface vortex can be controlled by installing curtain walls.

Experimental investigation of ventilated partial cavitating flows with special emphasis on flow pattern regime and unsteady shedding behavior around an axisymmetric body at different angles of attack

The objective of this paper is mainly to investigate the ventilated partial cavitating flow structure at different angles of attack with experimental methods. A high-speed camera technique is used to record cavity evolution patterns. The numerical simulation is performed by CFX Solver with a free surface model and filter-based turbulence model. Three flow pattern maps are constructed to depict the flow pattern and structures at different angles of attack α, i.e. the range of Froude number Fr and gas entrainment coefficient CQ. The maps show that the angle of attack α has a significant effect on ventilated cavitating flow structures. With the increasing value of α, the asymmetry of ventilated cavity becomes obvious and the angle between the axis of the body and the closure line θ is decreased. The value of the included angle θ is found to vary with Fr number and CQ. The cavity break-off may be mainly determined by the momentum and the direction of re-entrant jet flow.

PRESSURE GRADIENT PREDICTION FOR DIFFERENT FLOW PATTERNS OF HEAVY OIL AND NATURAL GAS IN A HORIZONTAL PIPE USING CFD TECHNIQUES AND EMPIRICAL CORRELATIONS

Two-phase flows are of fundamental importance in the petroleum industry, considering that most petroleum reservoirs produce oil and gas simultaneously. Because system pressure gradient is a result of the frictional effects between fluids and pipe wall, and the interfacial effects between the fluids themselves, the precise determination of this parameter is complex. Many authors have sought to predict pressure gradient by using computational fluid dynamic techniques and empirical correlations. The present work aims to compare heavy oil and natural gas mixture pressure gradients in a horizontal pipe for different flow patterns using the application ANSYS CFX 13.0, Lockhart and Martinelli, and Beggs and Brill correlations. The analysis investigated the results for bubbly, plug, and stratified flows. The results showed that Beggs and Brill over predicted pressure gradient values. It was also observed a good agreement between numerical and Lockhart and Martinelli correlation for bubbly and plug flows, with root-mean-square deviations (RMSD) of 5.78 and 19.55 percent, respectively. As for the stratified flow cases, the numerical results presented a poor agreement, with a RMSD greater than 90 percent. The high percent deviation for this flow regime is due to the increase in the gas input content. To compute the high gas velocity effects and, hence, improve the agreement, we suggest the use of turbulence and free surface models as well as different values of drag coefficient in the numerical setup.

Explicit representation and parametrised impacts of under ice shelf seas in the <i>z</i><sup>∗</sup> coordinate ocean model NEMO 3.6

Abstract. Ice-shelf–ocean interactions are a major source of freshwater on the Antarctic continental shelf and have a strong impact on ocean properties, ocean circulation and sea ice. However, climate models based on the ocean–sea ice model NEMO (Nucleus for European Modelling of the Ocean) currently do not include these interactions in any detail. The capability of explicitly simulating the circulation beneath ice shelves is introduced in the non-linear free surface model NEMO. Its implementation into the NEMO framework and its assessment in an idealised and realistic circum-Antarctic configuration is described in this study. Compared with the current prescription of ice shelf melting (i.e. at the surface), inclusion of open sub-ice-shelf cavities leads to a decrease in sea ice thickness along the coast, a weakening of the ocean stratification on the shelf, a decrease in salinity of high-salinity shelf water on the Ross and Weddell sea shelves and an increase in the strength of the gyres that circulate within the over-deepened basins on the West Antarctic continental shelf. Mimicking the overturning circulation under the ice shelves by introducing a prescribed meltwater flux over the depth range of the ice shelf base, rather than at the surface, is also assessed. It yields similar improvements in the simulated ocean properties and circulation over the Antarctic continental shelf to those from the explicit ice shelf cavity representation. With the ice shelf cavities opened, the widely used three equation ice shelf melting formulation, which enables an interactive computation of melting, is tested. Comparison with observational estimates of ice shelf melting indicates realistic results for most ice shelves. However, melting rates for the Amery, Getz and George VI ice shelves are considerably overestimated.

Numerical simulation of bubble formation and condensation of steam air mixture injected in subcooled pool

Bubble formation and condensation of steam-air mixture vertically injected in a subcooled water pool was simulated, combining thermal phase change model into the two continuous phase free surface model of ANSYS CFX 17.1. Continuous surface force model was used to calculate surface tension force and the influence of non-condensable gas was accounted for by component transportation equation and assumption of interface temperature equal to saturation temperature at local partial steam pressure. The thermal phase change model includes an experimental correlation for liquid side sensible heat transfer. Based on available experiment data from literatures, singular pure steam bubble and steam-mixture bubble in a pool were first simulated to see the predictability of the proposed method and then, the same method was applied to the bubble formation, detachment and condensation process of injected steam air mixture from a nozzle. Bubble dimeter, water subcooling and non-condensable gas concentration studied range from 4.9mm to 50mm, 12K to 40K, and 0 to 31.5% respectively. The results of the computations indicate that the present method can predict very well the bubble formation and condensation both for pure steam case and with non-condensable gas.

A (non-)hydrostatic free-surface numerical model for two-layer flows

A semi-implicit (non-)hydrostatic free-surface numerical model for two layer flows is derived from the Navier–Stokes equations by applying kinematic boundary conditions at moving interfaces and by decomposing the pressure into the hydrostatic and the hydrodynamic part. When the latter is ignored, the algorithm conveniently transforms into a solver for a hydrostatic flow. In addition, when the vertical grid spacing is larger than the layer depths, the algorithm naturally degenerates into a solver for the shallow water equations. In this paper, the presented numerical model is developed for the horizontal centrifugal casting, a metallurgical process, in which a liquid metal is poured into a horizontally rotating cylindrical mold. The centrifugal force pushes the liquid metal toward the mold wall resulting in a formation of a sleeve with a uniform thickness. The mold gradually extracts the sensible and the latent heat from the sleeve, which eventually becomes solid. Often a second layer of another material is introduced during the solidification of the first layer. The proposed free-surface model is therefore coupled with the heat advection-diffusion equation with a stiff latent heat source term representing the solidification. The numerical results show a good agreement with measurements of temperatures performed in the plant. A validation of the proposed model is also provided with the help of using other numerical techniques such as the approximate Riemann solver for the two layer shallow water equations and the volume of fluid method.

A study of energy transfer during water entry of solids using incompressible SPH simulations

Cavity formation during water entry of a solid corresponds to the deceleration experienced by the solid. Several experimental studies in the past have facilitated qualitative understanding of the relation between flow and impact properties and the type of cavity formed. The types of cavities formed are classified primarily based on the nature of the seal, such as (a) surface seal, (b) deep seal, (c) shallow seal and (d) quasi-static seal. The flow mechanism behind these features and their effects on the speed of the impacting solid require further quantitative understanding. A study of such phenomenon is difficult using the existing CFD techniques owing to the fact that the high density ratios between the two phases, namely water and air, bring in issues with respect to the convergence of the linear system used to solve for the pressure field for a divergence-free velocity field. Based on a free surface modeling method, we present Incompressible Smoothed Particle Hydrodynamics (ISPH) simulations of water entry of two-dimensional solids of different shapes, densities and initial angular momenta. From the velocity field of the fluid and shape of the cavity, we relate the transfer of kinetic energy from the solid to the fluid through different phases of the cavity formation. Finally, we present a three-dimensional simulation of water entry to assert the utility of the method for analysis of real life water entry scenarios.

Using pseudo-spectral method on curved grids for SH-wave modeling of irregular free-surface

This paper uses curved grids in the context of a pseudo-spectral method to model 2-D SH-wave propagation in a medium with an irregular free-surface. A technique originally developed for computational fluid dynamics (CFD) is first used to generate curved grids following the irregular free-surface. Then the SH-wave equations in curved coordinates are derived, together with numerical boundary conditions at a free-surface are presented. Finally, a Fourier-Chebyshev pseudo-spectral method is used to simulate SH-wave propagation in curved coordinates and solutions in Cartesian coordinates are obtained. This numerical scheme is tested against the analytical solution for Lamb's problem in a uniform elastic half space with a sloping surface. An excellent agreement is found, which confirms the accuracy of the method present here. In addition, the scheme is applied to the model of topography with discontinuous derivative, and the results are compared with those obtained from the modeling on conventional curved grids by algebraic transform. It shows that the new scheme is more accurate than that on algebraic grids.

Efficient spectral methods for a class of unsteady-state free-surface ship models using wavelets

A mathematical model of the transient free-surface model of unsteady ship motions is discussed. In this paper, the two reliable wavelet methods are proposed for the numerical solutions of the transient free-surface model. Mathematical derivations show that in fact the horizontal and vertical derivatives can be expressed by TFSGF. Additionally, the wavelet-based computational methods have been applied to solve the radiation problem of a floating hemisphere at zero speed. The approximation results of hydrodynamic coefficients show good agreement with the analytical solutions. Some numerical examples are presented to demonstrate the validity and applicability of the proposed method.

Experimental and numerical evaluation of discharge capacity of sharp-crested triangular plan form weirs

Weirs are those structures used extensively for flood passage, flow measurement, flow deviation and controlling the water level in dams, rivers and open channels. In this study, the numerical model was simulated using flow-3D software and the results from experimental and numerical model were compared. Investigations have shown that the results of RNG turbulence model are better compared to k-e and LES models. Then, to model the turbulence, and to determine the location of free-surface profile, RNG model and VOF method were used respectively. Experimental results show proper coordination with estimated results of numerical model. For similar low values of h/p, the performance of 30 degree sharp crested triangular plan form weir for discharging of overflow was more suitable than other sharp-crested triangular plan form weirs.

A free surface modelling method in SPH simulation of ultrasonic atomization

A free surface modelling method in SPH simulation of ultrasonic atomization