Free Surface Variation Research Articles

Hydrodynamic characteristics of a seven blade highly-skewed propeller operating underneath a free surface

The performance of a highly-skewed seven-blade propeller operating underneath a free surface was simulated with different loading conditions using detached-eddy simulation and volume of fluid method. The presentation includes the hydrodynamic loads and distribution of the velocity, followed by a discussion of the vortex structure and free surface variation. Finally, the analysis delves into the power spectra of pressure and turbulence kinetic energy. The results suggest that there a decrease in the thrust, torque, and efficiency of the propeller. The blade tip vortex is observed to be distorted and delayed in merging in free surface condition. The shaft frequency, three times the shaft frequency, and blade frequency still make contributions in the far wake at J = 0.71 for free surface condition.

A Fast Algorithm for the Prediction of Distance at Closest Point of Approach in the Maneuvering of Two Ships

Abstract The situation of two ships maneuvering in the vicinity is not so rare, and the significant hydrodynamic interaction effect always poses a threat to navigation safety in these conditions. The assessment of the Distance at Closest Point of Approach (DCPA) is necessary for ship collision avoidance decision-making. In this study, an efficient ship maneuvering model for close-distance maneuvering is developed to predict DCPA rapidly, where the hydrodynamic interaction between ships is accounted for. The Maneuvering Modeling Group (MMG) standard model is used to predict ship motion, and the hydrodynamic interaction effect is estimated in real-time by a code based on the potential flow theory where the variation of free surface is neglected. The ship maneuvering model is validated by the comparison between simulation and experiment in turning and zig-zag maneuvering; furthermore, the validated maneuvering model is used to predict the trajectory under the ship hydrodynamic effect. The characteristic of ship maneuvering under the ship hydrodynamic interaction between two ships is described and illustrated, and the influence of the velocity and lateral distance on the ship trajectory is revealed. A sensitivity analysis of the maneuvering model is performed to determine whether the hydrodynamic interaction effect is necessary to be evaluated exactly for an accurate predicted trajectory and DCPA. The DCPA in different situations is calculated, which represents the ship collision risk.

Influence of cylinder rotation in close to a free surface on flow characteristics

This study investigates the numerical simulation of unsteady flow over a rotating circular cylinder near a free surface using the Volume of Fluid (VOF) method. The hydrodynamic characteristics and flow pattern are analyzed for various Froude numbers (0.3, 0.55, and 1), submergence depths (0.4, 0.6, and 1), and rotation rates (±0.5, ±1, and ±2). The results indicate that both the rotation direction and rate significantly influence flow instability. Counterclockwise rotation reduces free surface instability and drag coefficient. At a rotation rate of 2, the average drag coefficient decreases by 93% compared to a stationary cylinder at Froude number 0.3. Clockwise rotation induces free surface instability and increases the lift and drag coefficients. Higher Froude numbers result in more significant free surface variations, and increased submergence depth leads to stretched vortices.

Numerical simulations of Phan-Thien-Tanner viscoelastic fluid flows based on the SPH method

Numerical simulations of viscoelastic fluid flows are always a hot issue in the field of computational fluid dynamics and the study of their complex rheological properties has important academic and engineering application value. In the present work, we develop a smoothed particle hydrodynamics (SPH) method for simulating transient viscoelastic fluid flows governed by the Phan-Thien-Tanner (PTT) constitutive equation. To improve the computational accuracy of the SPH method, the mixed symmetric correction algorithm of kernel gradient is implemented. To remove the particle clustering and unphysical fracture in fluid stretching which is named as the tensile instability, the artificial stress model is added into the momentum equation. We firstly apply the proposed SPH method to solve the plane Poiseuille flow of a PTT viscoelastic fluid, in which the effectiveness and advantage of the method are verified by comparing the SPH solution with those obtained by the finite volume method (FVM) and analyzing the l2 norm error of different SPH solutions to the FVM solution. Then, the method is employed to simulate the impact behavior of a PTT viscoelastic droplet with a rigid plate. In particular, we not only investigate the spreading behavior of PTT viscoelastic droplet after impacting the rigid plate, but also for the first time capture and analyze the bouncing behavior of droplet by decreasing the Reynolds number. The influences of the Reynolds number, the Weissenberg number, the solvent viscosity ratio, and the PTT elongational parameter on the droplet dynamics behavior are further deeply studied. Numerical results demonstrate that the SPH method proposed in this paper is a powerful computation tool for simulating PTT viscoelastic fluid flows and is capable of effectively describing their complex rheological properties and free surface variation characteristics.

Simulation of solidification microstructure evolution of 316L stainless steel fabricated by selective laser melting using a coupled model of smooth particle hydrodynamics and cellular automata

Selective Laser Melting (SLM) is an efficient and advanced manufacturing technology that utilizes lasers to melt and solidify metal or alloy powders, layer by layer, to form the desired object shape. This study aims to investigate the evolution behavior of the solidification microstructure during the SLM process and presents a novel numerical simulation method based on the Smoothed Particle Hydrodynamics-Cellular Automaton (SPH-CA) coupling model. The SPH-CA coupling model combines the particle information, such as position and temperature, from Smoothed Particle Hydrodynamics (SPH) with the Cellular Automaton (CA) method in a one-way coupling manner, enabling simultaneous computation of multiple physical fields, including heat transfer, melting, solidification, and morphology. This model addresses challenges that are difficult to handle in grid-based computations, such as free surface variations, boundary deformations, interfacial motion, and large deformations. Additionally, it effectively simulates the morphology of the solidification microstructure. Furthermore, the coupling process performs kernel function weighted calculations at the same scale, which results in higher accuracy compared to the grid-based multiscale mapping. The simulation results demonstrate that different processing parameters influence the morphology of the molten pool and the thermal undercooling, thereby affecting the growth characteristics of the grains. A higher laser scanning speed leads to smaller molten pool size, finer grain sizes in the solidification microstructure, larger laser grain angles, and a higher content of columnar grains. These findings are consistent with experimental observations and existing conclusions, providing evidence for the feasibility and effectiveness of the proposed model in the context of SLM.

Rayleigh–Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

Rayleigh–Taylor (RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considered as a quadratic function of temperature. The long wave hypothesis is used to derive a nonlinear free surface evolution equation of the thin viscoelastic film. Linear stability analysis shows that for a prescribed the viscoelastic coefficient, substrate cooling products instability, while substrate heating remains stability. Furthermore, we analyze the influence of viscoelastic coefficient on RT instability. Results show that the viscoelastic coefficient reinforces the RT instability whether the substrate is heated or cooled. Moreover, we use the line method to numerically simulate the nonlinear evolution equation and systematically examine the space-time variation of the film free surface. The numerical results illustrate that increasing the viscoelastic coefficient can enhance the disturbance amplitude and wave frequency. This means that the viscoelastic coefficient makes the system unstable, which is consistent with result of the linear stability analysis. In addition, the oscillation tends to accumulate downstream of the inclined substrate when the evolution time is long enough. Finally, the variation of film thickness with related parameters for different viscoelastic coefficients is investigated.

Experimental and multiphase modeling of small vertical-axis hydrokinetic turbine with free-surface variations

Vertical-axis hydrokinetic turbines are promising option to harness the low velocity currents. However, limited investigations have been carried out considering the interactions between the turbine rotor and the channel section, including the free-surface. Thus, a vertical-axis turbine model has been designed and manufactured, to be tested in an open channel. Also, a three-dimensional multiphase simulation has been carried out, using the volume of fluid (VOF) model, to capture the air–water interface and to investigate the free-surface variations effects on the turbine output. Experimentally, the turbine model has been characterized under different flow conditions and free-surface levels. The peak power coefficients are found to increase with the upstream velocity. This effect is directly linked to the blockage ratio and the Froude number. A reasonably good match has been found between the experimental and the numerical results. The VOF model is able to simulate the free-surface longitudinal variations, and the effect of the turbine blockage of the channel. The velocity field and the pressure coefficient distribution, around the turbine rotor, have been studied and correlated with the free-surface variations from upstream to downstream of the turbine. Finally, the vortex street generated by the blade–plate interaction has been analyzed.

Improved smoothed particle dynamics simulation of eXtended Pom-Pom viscoelastic fluid

Viscoelastic fluids widely exist in nature and industrial production, and the study of their complex rheological properties has important academic value and application significance. In this work, an improved smoothed particle hydrodynamics (SPH) method is proposed to numerically simulate the viscoelastic flow based on the eXtended Pom-Pom (XPP) model. In order to improve the accuracy of the calculation, a kernel gradient correction discrete format without kernel derivative calculation is adopted. In order to prevent fluid particles from penetrating the solid wall, an enhanced boundary processing technology is proposed. To eliminate the tensile instability, an artificial stress is coupled into the momentum equation of conservation. Based on the XPP model, the viscoelastic Poiseuille flow and the viscoelastic droplet impacting solid wall problem are simulated by using the improved SPH method. The effectiveness and advantages of the improved SPH method are verified by comparing the SPH solutions with the solutions from the analytical method or finite difference method. The convergence of the improved SPH method is further evaluated by using several different particle sizes. On this basis, the influences of rheological parameters such as Reyonlds number <i>Re</i>, Weissenberg number <i>Wi</i>, solvent viscosity ratio <i>β</i>, anisotropy parameter <i>α</i>, relaxation time ratio <i>γ</i> and molecular chain arm number <i>Q</i> on the flow process are analyzed in depth. For the viscoelastic Poiseuille flow, the bigger the value of <i>Re</i>, <i>Wi</i>, and <i>α</i>, the larger the steady-state velocity is; the larger the value of <i>γ</i> and <i>Q</i>, the smaller the steady-state velocity is; the larger the value of<i> β</i>, the weaker the velocity overshoot is, but it does not affect the steady-state velocity. For the viscoelastic droplet problem, the larger the value of <i>Re</i> and <i>Wi</i>, the faster the droplet spreads; the larger the value of <i>β</i>, the weaker the droplet shrinkage behavior is, but it does not affect the final spreading width of droplet; the larger the value of <i>α</i>, the larger the droplet’s spreading width is; the larger the value of<i> γ</i> is, the stronger the droplet shrinkage behavior is; the larger the value of <i>Q</i>, the weaker its influence on the droplet’s spread width is. The improved SPH method in this paper can effectively describe the complex rheological properties and the free surface variation characteristics of viscoelastic fluid based on XPP model.

Numerical modeling of sloshing flow interaction with an elastic baffle using SPHinXsys

Sloshing is a complex fluid motion with high non-linearity. Violent sloshing results in large impact pressure on the tank that may lead to structural damage. Sloshing suppression using anti-sloshing baffles and interaction mechanisms between structure and fluid attract attention increasingly among engineering applications. In this paper, the sloshing flow interaction with an elastic baffle is investigated both numerically and experimentally. SPHinXsys, an open-source library in the entire smoothed particle hydrodynamic (SPH) framework, is applied to study sloshing interaction with an elastic baffle. To validate SPHinXsys model, a series of experiments are performed in a rectangular tank. The quantitative comparisons between numerical results and experimental measurements on the time variation of free surface, pressure and baffle deformation are conducted. The diffusion process of the dye around the baffle in the experiment is recorded and simulated by the FSI solver coupled with the diffusion model. Then the velocity field for varying filling depths is investigated numerically. The total dynamic force acting on the baffle for different water depths is also discussed.

Numerical simulation of mould filling process using ansys

ABSTRACT Filling of moulds with molten metal and solidifying it affects the cycle time, casting’s interior quality and the amount of material required throughout the process. Blow holes, slag inclusions, cold shut, shrinkage, and other casting faults are all linked to the mould filling process. Industry demands the simulation of filling and solidification process before the actual operation begins. The simulation helps to examine the molten metal’s free surface variations, temperature distribution, and gas pouring problems to reduce filling-related defects and benefited to the industrial sector by eliminating the wastage of raw resources, money, labour and time. CFD analysis was carried out to investigate the impact of VOF and air entrapment in the casting part at subjected velocities to uncover pouring flaws of the casting part generated in response to the applied velocities.

Two-dimensional continuum modelling granular column collapse by non-local peridynamics in a mesh-free method with rheology

Abstract

A Three-Dimensional Numerical Study of Wave Induced Currents in the Cetraro Harbour Coastal Area (Italy)

In this paper we propose a three-dimensional numerical study of the coastal currents produced by the wave motion in the area opposite the Cetraro harbour (Italy), during the most significant wave event for the coastal sediment transport. The aim of the present study is the characterization of the current patterns responsible for the siltation that affects the harbour entrance area and the assessment of a project solution designed to limit this phenomenon. The numerical simulations are carried out by a three-dimensional non-hydrostatic model that is based on the Navier–Stokes equations expressed in integral and contravariant form on a time-dependent curvilinear coordinate system, in which the vertical coordinate moves in order to follow the free surface variations. The numerical simulations are carried out in two different geometric configurations: a present configuration, that reproduces the geometry of the coastal defence structures currently present in the harbour area and a project configuration, which reproduces the presence of a breakwater designed to modify the coastal currents in the area opposite the harbour entrance.

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

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

A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion.

A variational principle is derived for two-dimensional incompressible rotational fluid flow with a free surface in a moving vessel when both the vessel and fluid motion are to be determined. The fluid is represented by a stream function and the vessel motion is represented by a path in the planar Euclidean group. Novelties in the formulation include how the pressure boundary condition is treated, the introduction of a stream function into the Euler–Poincaré variations, the derivation of free surface variations and how the equations for the vessel path in the Euclidean group, coupled to the fluid motion, are generated automatically.

Numerical investigation of flow pattern around a T-shaped spur dike in the vicinity of attractive and repelling protective structures

This piece of research simulated the flow pattern around a T-shaped spur dike in the vicinity of attractive and repelling protective structures in a 90° bend using computational fluid dynamic (CFD) model. This CFD analysis has utilized RNG turbulence model to simulate turbulent flow field, and free surface variations were modeled through finite volume of fluid. A comparison between mean velocities in the main spur dike field was indicative of an acceptable precision of CFD model in simulating flow pattern along river bends in the presence of a spur dike. This numerical model mainly aimed at a scrutinizing study of the process of flow pattern around the T-shaped spur dike, the maximum velocity variations, the secondary flow strength, and the maximum stresses along the bend and the main spur dike field. Results demonstrated an increase in the maximum shear stress in attractive and repelling modes of the protective structure by 23.5 and 17.6%, respectively, in comparison with the vertical mode.

On force consideration in coupled ISPH framework for sediment transport in presence of free-surface flow

A coupled divergence-free Incompressible Smoothed Particle Hydrodynamics (ISPH) framework for sediment transport is extended for application in generalized free-surface flow situations. The computation of interaction force pair between pure fluid and sediment modules makes the model flexible enough to be applicable for diverse scenarios with variable resolutions. Three scenarios are included to quantify the contribution of individual components in the force pair. First two scenarios with rapid free-surface variation highlight the effect of fluid pressure gradient on granular flow. The third scenario with minimal free-surface variation considers bed movement under a horizontal marine pipeline for a prolonged time period. The framework can simulate sediment transport for generalized problems with slowly/rapidly varying free-surface flow conditions.

Study on Green Water of Tumblehome Hull Using Dam-Break Flow and Ranse Models

Abstract The tumblehome hull adopts some novelty designs such as low-tumblehome freeboard and wave-piercing bow. The new form design makes the ship have many special hydrodynamic performances. Especially the green water of tumblehome hull is different from that of hulls with flare free board. Green water is a strong nonlinear phenomenon of ship-wave interaction, the variation of free surface of liquid is complicated, and there are still some difficulties to solve green water problems well with numerical simulation method. In this paper firstly the motion responses of the tumblehome hull was calculated based on 3D potential theory, and then the dam-break flow model was used to calculate green water height and pressure distribution. According to the result of numerical simulation, some typical working conditions are chosen for 3D CFD simulation using RANS method. The results of numerical simulation methods are compared with the experimental results measured in towing tank. The influence of different ship form parameters and wave parameters to the green water of tumblehome hull is analyzed, and some regularities of green water on tumblehome hull in regular waves are summarized.

A Semi-Analytical Model for the Hydraulic Resistance Due to Macro-Roughnesses of Varying Shapes and Densities

A friction model resulting from investigations into macro-roughness elements in fishways has been compared with a broad range of studies in the literature under very different bed configurations. In the context of flood modelling or aquatic habitats, the aim of the study is to show that the formulation is applicable to both emergent or submerged obstacles with either low or high obstacle concentrations. In the emergent case, the model takes into account free surface variations at large Froude numbers. In the submerged case, a vegetation model based on the double-averaging concept is used with a specific turbulence closure model. Calculation of the flow in the roughness elements gives the total hydraulic resistance uniquely as a function of the obstacles’ drag coefficient. The results show that the model is highly robust for all the rough beds tested. The averaged accuracy of the model is about 20% for the discharge calculation. In particular, we obtain the known values for the limiting cases of low confinement, as in the case of sandy beds.

New asymptotic heat transfer model in thin liquid films

In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution should be explained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.

A sharp‐interface elliptic numerical model of laminar two‐phase gas‐liquid downward flow in a vertical parallel plate channel

AbstractA sharp‐interface two‐phase numerical analysis is performed for co‐current downward laminar flow of a liquid film and a gas. A complete two‐phase model based on the two‐dimensional elliptic governing equations is presented. The numerical model implements a dynamically moving non‐orthogonal computational mesh that tracks the phase interface precisely. The capability of this new model is demonstrated by comparisons with two previous free surface falling film studies and one experiment. New results are presented on the effect of independent variation of the Reynolds and Froude numbers on the axial variation of the film free surface. Finally, the effects of the velocity of the gas phase on the liquid film development are examined for flow in a parallel‐plate channel. An analytical solution for the fully‐developed velocity profiles for the two‐phase flow is also presented.