Free Surface Disturbance Research Articles

Water entry of a sphere moving along a circular path at a constant speed

When a marine propeller rotates in partially submerged conditions, air is entrained from above the undisturbed free-surface, which is called the reference surface, and the ventilated air surrounds the propeller blades, causing thrust loss and excessive vibration, all of which seriously damage the durability of the propeller shaft system of a ship. In the present study, the entry of a propeller blade is simplified by the water entry problem of a sphere moving along a circular path at a constant speed. A high-speed camera was employed to capture the rapidly changing flow structures in detail. Above the reference surface, we focused on the free-surface disturbances, including splash and dome formation. Beneath the reference surface, the development and collapse of ventilated cavities, followed by the line-vortex cavity and cavity undulation, were observed. The ventilated cavity of the present study appears to be more elongated than those of the free-falling sphere's water entry experiments. Two parallel vortical structures appeared after the cavity pinch-off, and bubbles were entrained into these structures to form the line-vortex cavity. The sphere's drag was directly measured via the torque meter attached to the sphere's rotating axis. The relation between the measured drag and the flow around the sphere was identified.

RUNUP OF A SURFACE SOLITARY WAVE ON A THIN VERTICAL SEMI-SUBMERSED SCREEN

Global climate changes lead to an increase in the number and intensity of extreme events in the seas and oceans (tsunamis, floods, storm surges, etc.). This can have catastrophic consequences involving the destruction of civil infrastructure, the flooding of large areas of recreational land, the loss of life, and can also adversely affect water quality, sediment transport, and habitats for living organisms. The creation of artificial berms on the seabed and breakwater piers changes significantly the parameters of wave processes, reducing destructive effect of waves in the coastal zone. But the use of traditional coastal protection structures (dams, piers, breakwaters) is not always efficient and economically reasonable. Thin permeable barriers are increasingly being considered as an alternative option in providing economic and ecological protection of coastal areas. The purpose of this research is to substantiate the effectiveness of vertical semi-submerged walls for protection the shores of natural reservoirs from the destructive energy of surface waves. Such a structure is non-permeable near the free surfacer, and is supported by piles at some distance from the bottom, which allows the flow of water and sediments. The physical simulation of the interaction of a nonlinear solitary wave, which is considered as a tsunami model, with a semi-submerged thin vertical barrier is performed in the experimental channel to evaluate the effectiveness of vertical wave barriers against the destructive energy of long waves. It was found that interaction of a solitary wave with an overhanging vertical wall leads to generation both of the reflected wave, due to roll of the incident wave on the structure, and the transmitted wave, which is formed after the liquid mass passes through the gap between the bottom and the wall. Quantitative characteristics of the interaction of the wave with the obstacle were obtained with the help of capacitive sensors, which were installed along the main axis of the laboratory channel to record the free surface disturbances caused by the propagation of the wave in the channel, its reflection from the wave screen and its transmission downstream. The processing of the received data made it possible to estimate the parameters of a solitary wave, which was formed in the channel by the impact of a heavy body on the water surface, those are the amplitude, length, and velocity of wave propagation. The energy attenuation of a solitary wave is estimated, which is an important characteristic of the channel and makes it possible to obtain more accurate values of reflection and transmission coefficients. Evaluations of wave reflection and transmission coefficients show that thin partially submerged vertical barriers are sufficiently effective in reducing the energy of nonlinear solitary waves although they do not suppress the waves completely. The depth of the screen-type permeable obstacle immersion relative to the free surface has a significant influence on the reflection/transmission coefficients and its effectiveness, accordingly. It has been established that semi-submerged obstacles can dissipate up to 60% of the incident wave energy.

PIV Measurements of Open-Channel Turbulent Flow under Unconstrained Conditions

Many open-channel turbulent flow studies have been focused on highly constrained conditions. Thus, it is rather conventional to note such flows as being fully developed, fully turbulent, and unaffected by sidewalls and free surface disturbances. However, many real-life flow phenomena in natural water bodies and artificially installed drain channels are not as ideal. This work is aimed at studying some of these unconstrained conditions. This is achieved by using particle image velocimetry measurements of a developing turbulent open-channel flow over a smooth wall. The tested flow effects are low values of the Reynolds number based on the momentum thickness Reθ (ranging from 165 to 930), low aspect ratio AR (ranging from 1.1 to 1.5), and Froude number Fr (ranging from 0.1 to 0.8). The results show that the mean flow has an inner region with a logarithmic layer with a von Kármán constant of 0.40–0.41, and a log law constant ranging from 5.0 to 6.0. The friction velocity and coefficient of skin friction are predictable using the formulations of Fr and Reθ presented in this work. The outer region is also characterized by a dip location, which is predictable using an equation associated with Reθ. The higher-order turbulence statistics, on the other hand, show distinguishing traits, such as correlation coefficients ranging from −0.1 to 0.5. Overall, this work demonstrates that for the unconstrained conditions studied, friction evaluations associated with Reynolds shear stress and some notable turbulence modelling functions used in conventional open-channel flows are inapplicable.

Modeling of the Initial Stage of Wave Generation by a Suddenly Rising or Falling Seabed

In this study, a three-dimensional entirely nonlinear model was used for simulating the wave generation problem caused by seabed movement. This study focuses on the waveform of the initial stage of wave generation. The numerical model was verified by comparing the simulated results with existing experimental results. Satisfactory results of the waveforms and flow fields were obtained. The simulations of the free surface disturbances and flow field velocities caused by the sudden rising or falling of a circular cylinder with the dimensionless radius ([Formula: see text]) and height ([Formula: see text]) normalized by still-water depth are discussed. We considered the combinations of [Formula: see text]–10 and [Formula: see text]–0.3. For the moving cylinder with a moderate height (e.g. [Formula: see text] and [Formula: see text]) and [Formula: see text], it is found that the water-surface shape is closer to the shape of the terrain. The central water level ([Formula: see text]) varying with time is also focused herein. For the rising cylinder, when [Formula: see text], the maximum [Formula: see text] is always less than its corresponding [Formula: see text] for any [Formula: see text]. For the falling cylinder, if [Formula: see text] is larger than five times the still water depth, then the maximum [Formula: see text] will exceed its corresponding [Formula: see text]. This result provides a further understanding of the basic phenomenon of the initial waves caused by the movement of the seabed topography.

Numerical Simulation for One-Dimensional (1D) Wave Propagation by Solving the Shallow Water Equations using the Preissmann Implicit Scheme

This research simulated one-dimensional wave propagation by solving the shallow water equations using the Preissman implicit numerical scheme due to its ability to maintain simplicity and stability at a larger time step value. This numerical model was fundamentally developed to satisfy the shallow water condition, where the water depth or horizontal-length scale is much smaller than the free-surface disturbance wavelength or vertical-length scale, and to comprehensively test the accuracy of the model. Consequently, three different types of waves were considered and these include (1) tidal, (2) roll, and (3) solitary. In the first case, the model was proven to be robust and accurate due to its relatively-small errors for both water-surface elevation and velocity indicating that the Preismann scheme is suitable for longwave simulations. In the second case, it was fairly accurate in capturing the periodic permanent roll waves despite showing a higher water-surface elevation than the one observed and this discrepancy is due to the neglect of the turbulent Reynold stress in the model. Meanwhile, the last case showed remarkable discrepancies in the water-surface elevation because the dispersion effect is quite significant during the wave propagation. This indicates that the Preismann scheme underestimated the wave crest along with time when the dispersion term was neglected. All simulations were performed using the tridiagonal matrix algorithm, thereby eliminating the need for iterations for the solution of the Preismann scheme. The findings of this study are beneficial to the next generation of the Preissmann-scheme models which can be designed to include turbulence and dispersion terms.

Effect of free surface perturbation on fully developed smooth open channel flow

Light floater boards are commonly used in open channel flow studies to reduce free surface disturbances. However, the shear layer generated from the surface of the floaters, which has not been considered in previous research, may have unintended effects, and can alter the downstream flow characteristics. This aspect is investigated using particle image velocimetry at Reynolds number of 35,100 by varying the perturbation caused by the floaters. With the perturbation, the mean velocity profiles show a dip and the Reynolds shear stress becomes negative near the free surface. It is shown that, due to perturbations caused by ejections and sweeps of the inverted shear layer at the floater bottom surface, the joint probability density function of velocity fluctuations near the free surface shifts from ejections and sweeps to outward and inward interactions. The data indicate that the shear penetrates deeper into the flow towards the bed with increase in perturbation.

Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate

Gravity induced film flow over a rigid smoothly corrugated substrate heated uniformly from below, is explored. This is achieved by reducing the governing equations of motion and energy conservation to a manageable form within the mathematical framework of the well-known long-wave approximation; leading to an asymptotic model of reduced dimensionality. A key feature of the approach and to solving the problem of interest, is proof that the leading approximation of the temperature field inside the film must be nonlinear to accurately resolve the thermodynamics beyond the trivial case of ‘a flat film flowing down a planar uniformly heated incline.’ Superior predictions are obtained compared with earlier work and reinforced via a series of corresponding solutions to the full governing equations using a purpose written finite element analogue, enabling comparisons to be made between free-surface disturbance and temperature predictions, as well as the streamline pattern and temperature contours inside the film. In particular, the free-surface temperature is captured extremely well at moderate Prandtl numbers. The stability characteristics of the problem are examined using Floquet theory, with the interaction between the substrate topography and thermo-capillary instability modes investigated as a set of neutral stability curves. Although there are no relevant experimental data currently available for the heated film problem, recent existing predictions and experimental data concerning the behaviour of corresponding isothermal flow cases are taken as a reference point from which to explore the effect of both heating and cooling.

Free-surface disturbances due to the submersion of a cylindrical obstacle

We explore the initial perturbations that form on a liquid free surface as a result of the submersion of a circular cylinder beneath the surface, a scenario that arises in a number of diverse applications. The behaviour of the free surface is determined by transforming the equations of motion of the system via the Wehausen scheme, to variables for the free surface. A small-time series expansion is utilized to construct a recursive scheme that can be implemented numerically, and the time frame over which this approximation is valid is analysed. The resulting numerical model allows one to extend the results in the literature to study arbitrary cylinder sizes, including those where the cylinder is close to the free surface, and arbitrary cylinder motions. Of particular interest in this study was identifying the conditions under which strong jets would appear, and those were the free surface exhibited gravity waves. The formation of a central jet is found to be related to the growth of secondary, nonlinear waves, which rapidly merge as the obstacle is submerged. Classification maps are presented as a function of obstacle size and submersion speed, to identify the conditions which lead to jetting. Furthermore, the acceleration profile of the cylinder is shown to significantly affect the conditions under which jets form, which we argue is due to the rate at which energy is injected into the system.

Free-surface effects induced by internal solitons forced by shearing currents

Free-surface effects induced by internal solitary waves (ISWs) propagating through a background shear current are theoretically investigated in a shallow water framework. Following the Hamiltonian approach, we implement a mathematical formulation valid for a free surface, two-layer stratified system in the presence of mobile layers. Associated to the undisturbed condition characterized by the background fluid at rest, solitons with both positive and negative polarities are considered. To reproduce the typical oceanic conditions, we focus on theoretical predictions for a density ratio set to 0.99. Although under Boussinesq conditions a rigid-lid at the top of the theoretical domain is considered a good approximation, our analysis shows that main ISWs features may change when the fluid system, forced by shear currents, is modeled with a free surface. Signs assumed by three dimensionless quantities, i.e., the deformation parameter, the background velocity, and the undisturbed amplitude, allowed us to uniquely predict how the undisturbed solitons modify their interfacial profiles and change their celerity, in response to the background forcing. Our results show that waves celerity predicted by the rigid-lid model can be lower than the one resulting from the Hamiltonian formulation, although this never occurs in the absence of mobile layers. Theoretical predictions reveal that shearing current can induce deviations from the standard ISWs free-surface profile. We discuss the role of nonhydrostatic pressures in inducing free-surface short disturbances, in the form of undulated or multihumped profiles. The typical phase-opposition between interfacial and surface displacements can be lost as the free-surface displacements assume multihumped configurations.

Laboratory Experiments on Tsunamigenic Discrete Subaqueous Volcanic Eruptions. Part 1: Free Surface Disturbances

AbstractA submarine volcanic eruption has the potential to generate a dangerous local tsunami. To better understand the free surface disturbance generated by an underwater volcanic eruption, which will form the initial condition for any subsequent wave generation, we conducted a series of laboratory experiments. In these experiments, compressed air was injected into a tank filled with water to simulate an underwater eruption. The experiments were repeated over a range of different pressures and water depths. Each eruption can be divided into three phases: A momentum‐driven jet, a buoyancy‐driven plume, and a fountain‐generation regime. Our experiments exhibit two fountain regimes (a dome regime and a finger regime), with a transition between them. These fountain regimes have been observed in several real submarine volcanic eruptions. This paper proposes a Froude number criterion to combine the water depths and source conditions together with the aspect ratios of fountains to quantify different fountain regimes. This quantitative relationship holds for two real subaqueous volcanic eruption cases (Myojin‐Sho eruption in 1952 and 1996 eruption in Karymskoye Lake). The fountain of the Myojin‐Sho shallow submarine eruption on September 23,1952 appears to have been in the dome regime, which means it was a relatively weak eruption. Unlike other eruptions from this volcano, which did generate tsunamis, no tsunami waves were detected on September 23 . This study contributes to an enhanced understanding of the usually unseen mechanism of free surface disturbances by volcanic gas injection during submarine eruptions.

Virtual Replica of a Towing Tank Experiment to Determine the Kelvin Half-Angle of a Ship in Restricted Water

The numerical simulation of ship flows has evolved into a highly practical approach in naval architecture. In typical virtual towing tanks, the principle of Galilean relativity is invoked to maintain the ship as fixed, while the surrounding water is prescribed to flow past it. This assumption may be identified, at least partly, as being responsible for the wide-scale adoption of computational solutions within practitioners’ toolkits. However, it carries several assumptions, such as the levels of inlet turbulence and their effect on flow properties. This study presents an alternative virtual towing tank, where the ship is simulated to advance over a stationary fluid. To supplement the present work, the free surface disturbance is processed into Fourier space to determine the Kelvin half-angle for an example case. The results suggest that it is possible to construct a fully unsteady virtual towing tank using the overset method, without relying on Galilean relativity. Differences between theoretical and numerical predictions for the Kelvin half-angle are predominantly attributed to the assumptions used by the theoretical method. The methods presented in this work can potentially be used to validate free-surface flows, even when one does not have access to experimental wave elevation data.

A Potential Field Description for Gravity-Driven Film Flow over Piece-Wise Planar Topography

Models based on a potential field description and corresponding first integral formulation, embodying a reduction of the associated dynamic boundary condition at a free surface to one of a standard Dirichlet-Neumann type, are used to explore the problem of continuous gravity-driven film flow down an inclined piece-wise planar substrate in the absence of inertia. Numerical solutions of the first integral equations are compared with analytical ones from a linearised form of a reduced equation set resulting from application of the long-wave approximation. The results obtained are shown to: (i) be in very close agreement with existing, comparable experimental data and complementary numerical predictions for isolated step-like topography available in the open literature; (ii) exhibit the same qualitative behaviour for a range of Capillary numbers and step heights/depths, becoming quantitively similar when both are small. A novel outcome of the formulation adopted is identification of an analytic criteria enabling a simple classification procedure for specifying the characteristic nature of the free surface disturbance formed; leading subsequently to the generation of a related, practically relevant, characteristic parameter map in terms of the substrate inclination angle and the Capillary number of the associated flow.

Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g., see Lamb’s Treatise, 1879). With traces back to Russell’s experimental observations of the Great Wave of Translation in 1834, Korteweg and de Vries (1895), and others, derived an unforced equation to describe the balance between nonlinearity and dispersion required to model the solitary wave. More recently, Akylas (1984) derived a forced KdV equation to model a pressure distribution on the free-surface (e.g., a ship). Since then, the forced KdV equation has been shown to be a useful model approximation for two-dimensional flow past disturbances in an open channel. In this paper, we review the stationary solutions of the forced KdV equation for four types of localised disturbances: (i) a flat plate separating two free surfaces; (ii) a compact bump, or dip in the channel bottom topography; (iii) a compact distribution of pressure on the free surface and (iv) a step-wise change in the otherwise constant horizontal level of the channel bottom topography. Moreover, Dias and Vanden-Broeck (2002) developed a phase plane method to analyse flow over a bump, and this general approach has also been applied to the three other types of forcing (see Binder et al., 2005–2015, and others). In this study, we use eleven basic flow types to classify the steady solutions of the forced KdV equation using the phase plane method. Additionally, considering solutions that are wave-free both far upstream and far downstream, we compare KdV model approximations of the uniform flow conditions in the far-field with exact solutions of the full problem. In particular, we derive a new KdV model approximation for the upstream dimensionless flow-rate which is conveniently given in terms of the known downstream dimensionless flow-rate.

Nonlinear simulation of resonant sloshing in wedged tanks using boundary element method

Nonlinear sloshing problems in wedged tanks are simulated based on the paralleled boundary element method. An improved semi-Lagrangian procedure is introduced for the free-surface updating near non-vertical tank walls. Two types of resonances are mainly considered. One is the classical resonance, which is induced by a lateral excitation on the tank. Featured sloshing phenomena in wedged tanks are observed compared with those in rectangular tanks. The other type is the Faraday waves due to the forced tank oscillation perpendicular to the undisturbed free-surface plane. Effects of the excitation frequency, acceleration amplitude, instability regions and initial free-surface disturbance on behaviours of the resonant sloshing in wedged tanks are investigated.

Free-surface film flow over topography: Full three-dimensional finite element solutions

An efficient Bubnov–Galerkin finite element formulation is employed to solve the Navier–Stokes and continuity equations in three-dimensions for the case of surface-tension dominated film flow over substrate topography, with the free-surface location obtained using the method of spines. The computational challenges encountered are overcome by employing a direct parallel multi-frontal method in conjunction with memory-efficient out-of-core storage of matrix co-factors. Comparison is drawn with complementary computational and experimental results for low Reynolds number flow where they exist, and a range of new benchmark solutions provided. These, in turn, are compared with corresponding solutions, for non-zero Reynolds number, from a simplified model based on the long-wave approximation; the latter is shown to produce comparatively acceptable results for the free-surface disturbance experienced, when the underpinning formal restrictions on geometry and capillary number are not exceeded.

Describing dynamics of nonlinear axisymmetric waves in dispersive media with new equation

A single nonlinear partial differential equation of the wave type for an axisymmetric case is obtained by the introduction of special auxiliary function. In contrast to cylindrical Korteweg–de Vries equation, new equation describes centrifugal and centripetal waves not only far from the center, but in its vicinity as well. With the use of this equation a number of specific problems on the evolution of the free surface disturbances are numerically solved for the cases of a horizontal bottom and a drowned concave. The research also demonstrates the difference between the results of calculations on the base of the complete equation and on the basis of the linearized equation.

Study on Bow Shape Optimization of Ultra Large Block Coefficient Ship and CFD Simulations of Initial and Optimized Hull Forms

The present paper describes a hull form improvement of innovative low-speed Ultra Large Block coefficient Ship (ULBS). A hull form optimization method for reducing wave-making resistance and wave-breaking at the bow using nonlinear programming method (NLP) based on the Rankine source method is discussed. In the optimization process, wave-making resistance coefficient,surface integrals of the square of free surface elevations and free surface disturbance function D(x,y)-values are selected as the objective functions. Bow-body shape is optimized under the prescribed design constraints based on the present method. Numerical examples are given for unconventional ULBS. The three improved hull forms for the corresponding objective functions are obtained by optimal designs which indicate that the objective functions are reduced distinctly. In order to verify the present optimization method based on the potential solver, the flow characteristics around the initial and bow optimized hull forms are analyzed by using Computational Fluid Dynamics (CFD) analysis based on the Navier-Stokes (NS) solver. Comparisons of the computed resistance coefficients, pressure and velocity distributions of the initial and bow optimized hull forms are presented. It is confirmed that simulation results based on the viscous flow solver show reasonable agreements with the numerical results based on the Rankine source method for the bow optimized hull forms.

Study on bow wave breaking around ultra large block coefficient ship

Due to the increase of maritime transportation volume day by day it is necessary to design a ship hull having large carrying capacity with low resistance. In case of slow moving ships, usually wave breaking occurs in front of bow. A considerable portion of resistance occurs due to the energy dissipation of such wave breaking in case of Ultra Large Block coefficient Ship (ULBS) suggested by the authors. The key objective of this research work is to investigate the relationship between bow wave breaking and free surface disturbance function that may be used as a parameter for numerical prediction of bow wave breaking. In this regard, the experiments and numerical calculations have been carried out for six models of ULBS. From the results, it can be concluded that the wave breaking area in front of bow increases with the increase of surface integral of the square of free surface disturbance function, Froude number and block coefficient.DOI: http://dx.doi.org/10.3329/jname.v10i2.16104

Effect of an applied magnetic field on sloshing pressure in a magnetic fluid

Sloshing of a magnetic fluid can be controlled through altering the sloshing natural frequency by applying magnetic fields. The magnetic field is applied by two permanent magnets. The intensity of the applied magnetic field is changed by varying the position of the magnets and the magnet type. The dynamic pressure responses on the inner wall surface were used to gain an understanding of the sloshing phenomenon in this investigation. Several frequency response spectra are obtained in each experimental condition. These results indicated that the free surface disturbance caused by the sloshing was suppressed by the applied magnetic field.

超肥型船型の提案と船首砕波に関する基礎的研究

Due to the increase of maritime transportation volume day by day it is necessary to design a ship hull having large carrying capacity with low resistance. For this purpose, the authors propose innovative concepts of Ultra Large Block coefficient Ship (ULBS). In this paper, its concepts and study plans are shown, and its bow wave breaking phenomena are investigated as one of the fundamental studies on ULBS hull form. As experimental studies, wave breaking surface areas caused by ULBS models are measured. As theoretical ones, wave making resistance coefficients and distributions of free surface elevation are evaluated by means of Rankine source method, and distributions of free surface disturbance function D(x,y) are evaluated by means of Baba's low speed theory. Various parameters related to the wave breaking phenomena are investigated in comparisons between experimental and theoretical results. Under these investigations, it can be concluded that theoretical results based on wave making resistance coefficients, surface integrals of the square of free surface elevation and surface integrals of the square of free surface disturbance function have strong elations to wave breaking surface areas.