Free Surface Oscillations Research Articles

Coupling analysis between wave resonance in the moonpool and heave motion of the twin hulls with mooring effect

Fluid resonance in the moonpool formed by two identical rectangular hulls in water waves is investigated by employing the Computational Fluid Dynamics (CFD) package OpenFOAMⓇ. The influence of vertical stiffness on the behavior of moonpool resonance coupling with the heave motion response is presented. Numerical simulations show that the free surface oscillation in the moonpool exhibits a two-peak variation with the incident wave frequency, defined as the first and second peak frequencies. A local Keulegan–Carpenter (KC) number is introduced for describing the influence of fluid viscosity and flow rotation on the fluid resonance and heave motion resonance. At the first peak frequency, the free surface oscillation and heave motion response show an in-phase relationship, where increase in the vertical stiffness can increase the relative motion between them. This finally leads to an increase in the KC number, indicating the increased effect of energy dissipation with increase in the vertical stiffness. At the second peak frequency with an out-of-phase relationship between the free surface oscillation and heave motion response, the variation of the KC number is not sensitive to the vertical stiffness. Correspondingly, the influence of energy dissipation is not strongly dependent on the vertical stiffness.

Defining and Mitigating Flow Instabilities in Open Channels Subjected to Hydropower Operation: Formulations and Experiments

A thorough literature review was conducted on the effects of free surface oscillation in open channels, highlighting the risks of the occurrence of positive and negative surge waves that can lead to overtopping. Experimental analyses were developed to focus on the instability of the flow due to constrictions, gate blockages, and the start-up and shutdown of hydropower plants. A forebay at the downstream end of a tunnel or canal provides the right conditions for the penstock inlet and regulates the temporary demand of the turbines. In tests with a flow of 60 to 100 m3/h, the effects of a gradually and rapidly varying flow in the free surface profile were analyzed. The specific energy and total momentum are used in the mathematical characterization of the boundaries along the free surface water profile. A sudden turbine stoppage or a sudden gate or valve closure can lead to hydraulic drilling and overtopping of the infrastructure wall. At the same time, a PID controller, if programmed appropriately, can reduce flooding by 20–40%. Flooding is limited to 0.8 m from an initial amplitude of 2 m, with a dissipation wave time of between 25 and 5 s, depending on the flow conditions and the parameters of the PID characteristics.

Free surface oscillation driven by rotating stirrer

To gain insights into the mechanisms of free surface oscillation in a rotating mixing container, we observe the free surface deformation and measure the torque acting on the bar. The container was half-filled with liquids. Periodic surface oscillation occurs. At the rotational speed where the amplitude of the oscillation reaches its maximum, the time-averaged torque also takes the local maximum values. To account for the sloshing mechanism, an equation of motion is derived using the Lagrangian mechanics; we found that the sloshing occurs when the collision frequency of bar on the surface is consistent with the natural frequency of the system and the damping coefficient is sufficiently smaller than unity. The time-averaged torque increases when the sloshing becomes violent. We conclude that the hydrodynamics of oscillation is successfully modeled using point-mass mechanics, and thus we can reasonably capture the rotation speed at which violent oscillation occurs.Graphical Free surface deformation driven by the rotating arm in the cylindrical container which is half-filled with liquids

Multiple moonpools within a vessel free to heave and pitch: An experimental study

Moonpools in marine vessels and offshore platforms are vertical openings through the structure used to support underwater operations. Experimental investigations of multiple moonpool resonant responses coupled with vessel heave and pitch motions are presented in this study. For three moonpools at forward, central, and aft locations of a rectangular vessel, the simultaneous location-dependent free surface response amplitudes and oscillation phases are compared for a range of incident wave frequencies in the piston mode range. For the vessel free to heave and pitch, the central moonpool has the highest response amplitude; whereas, a previous study with fixed vessel (Garad et al. 2023) showed that the largest free surface responses are observed in the forward moonpool. Due to coupled hydrodynamic interactions between the moonpool oscillations and the vessel motions, the moonpool resonance frequency is linked with the vessel heave response. Multiple response amplitudes peaks are observed in the forward and aft moonpools due to body motions. The non-dimensional response amplitude increases nonlinearly with decreasing wave steepness close to the resonance frequency. The multiple moonpool oscillations show distinct phase differences from one another and with the outer wave, the individual values depending on the incident wave frequency. Considering the vessel motions, comparison with experiments without moonpools shows that the pitch response is increased due to multiple moonpool oscillations. The hydrodynamic interactions between multiple moonpools and a floating vessel have prospective applications in the case of marine platforms, where the resonant motions can be used for wave energy conversion through oscillating water column devices.

Nonlinear behavior of wave resonances in moonpool with a recess under wave actions

Nonlinear wave resonance in moonpool with a recess under wave actions is studied by using CFD simulations based on OpenFOAM® package. Compared to the rectangular moonpool, the influence of free surface nonlinearity plays an important role in the wave resonance in the recess moonpool. Harmonic analysis indicates that the higher-order harmonic induced sloshing-mode resonance even approaches the same magnitude as the first-order harmonic induced piston-mode motion. The superposition between them also leads to extreme free surface oscillation in the recess moonpool. A peak appears in the total horizontal wave forces by the higher-order harmonic induced sloshing resonance due to the anti-symmetric mode. In a word, the free surface nonlinearity is an indispensable factor in the response of fluid resonance in moonpool with recess configurations.

Revealing the effects of laser beam shaping on melt pool behaviour in conduction-mode laser melting

Laser beam shaping offers remarkable possibilities to control and optimise process stability and tailor material properties and structure in laser-based welding and additive manufacturing. However, little is known about the influence of laser beam shaping on the complex melt-pool behaviour, solidified melt-track bead profile and microstructural grain morphology in laser material processing. A simulation-based approach is utilised in the present work to study the effects of laser beam intensity profile and angle of incidence on the melt-pool behaviour in conduction-mode laser melting of stainless steel 316L plates. The present high-fidelity physics-based computational model accounts for crucial physical phenomena in laser material processing such as complex laser–matter interaction, solidification and melting, heat and fluid flow dynamics, and free-surface oscillations. Experiments were carried out using different laser beam shapes and the validity of the numerical predictions is demonstrated. The results indicate that for identical processing parameters, reshaping the laser beam leads to notable changes in the thermal and fluid flow fields in the melt pool, affecting the melt-track bead profile and solidification microstructure. The columnar-to-equiaxed transition is discussed for different laser-intensity profiles.

Resonant Oscillations within Multiple Moonpools for a Fixed Rectangular Vessel

_ We present experimental results of resonant free surface oscillations within three circular moonpools arranged in tandem at forward, central, and aft positions of a fixed rectangular vessel in head waves. The piston mode resonance frequency is primarily captured, which decreases with the increase in the vessel draft. The aim is to study the effect of body diffraction on the free surface amplitude and phase of the oscillating water columns at the three locations. The results indicate that, in general, the forward moonpool has the highest response amplitude, whereas the relative amplitudes of the central and aft moonpools depend on the wave frequency. It is observed that the nondimensional response amplitude increases nonlinearly with decreasing wave steepness close to the resonance frequency, while the effect diminishes at lower wave frequencies. The oscillation phase differences between the moonpools show effects of wave-body interaction, a phenomenon dependent on the vessel draft and wave frequency. Finally, the study includes a comparison of the responses at the three moonpool locations between multiple and single configurations. Introduction A moonpool is a vertical opening through the ship deck and open to the sea at the bottom, which is installed in vessels specialized in certain offshore operations. Resonant water column oscillations are encountered in moonpools (Aalbers 1984) due to vessel operations in waves. On the other hand, oscillating water columns (OWCs) have been extensively researched, primarily due to their potential for ocean wave energy conversion (Evans 1978; Heath 2012; Falcão & Henriques 2016). Now, considering design perspectives, the focus of the studies on water column resonance in waves depends on the specific marine application. For example, wave energy converters would require maximized OWC responses for efficient energy capture (Evans & Porter 1995; Morris-Thomas et al. 2007), while large free surface oscillations within moonpools of drillships have adverse effects on the vessel dynamics (Fakuda 1977).

Efficacious slosh suppression technique in road tankers to enhance the effectiveness of drinking water distribution

During summer months, many parts of the world experience the water crisis and water tankers transport fresh drinking water from rivers and other reservoirs and distribute to communities often located at far off places. Effectiveness of this distribution is adversely affected by the instability of tankers due to the phenomenon called liquid sloshing, the oscillation of free liquid surface subjected to external excitation. The liquid within the tank moves along the side walls back and forth creating an oscillation which becomes dangerously worse at certain situations. Sloshing makes the tanker unstable when the operating frequency and the tanker frequency coincides which may even cause the tanker to roll over. Hence, quite often, the tankers have to be operated on roads only at its maximum capacity and the water left in the tank may have to be spilled and wasted if the storage facility at the destination is less than the tanker capacity. In this work we are proposing an optimum design of water tankers to minimize the effect of sloshing and thereby enabling trouble-free operation of the tankers even in partially filled conditions. Sloshing parameters such as slosh height and dynamic wall pressures are experimentally and numerically analyzed for various tank geometries with and without baffles. A numerical model for analyzing slosh parameters is also developed and validated using experimental results. Based on the study an optimized tanker configuration is proposed.

A numerical approach for hydrodynamic performance evaluation of multi-degree-of-freedom floating oscillating water column (OWC) devices

A numerical approach has been developed in this study for hydrodynamic analysis of complex-shaped oscillating water column (OWC) converters. Physically, in the circumstance when the device is free to move or moored in waves, the airflow movement inside the chamber is coupled tightly with the changing of the internal fluid surface and the hydrodynamic response of the device. By taking these coupling effects into account, appropriate boundary integral equations are formulated with supplemental theoretical relations. The boundary value problem is then solved using a higher-order boundary element method (HOBEM). After obtaining the wave force and dynamic air force, the coupled motions and hydrodynamic efficiency are evaluated by integration. In particular, unlike conventional methods limited to fixed OWCs, the proposed method is proved applicable to those floating with coupled rigid-body motions. An optimal turbine parameter is hence mathematically derived to maximise the wave power absorption. Besides the linear quantities, nonlinear wave drift loads are evaluated via a newly derived formulation that accounts for the far-field contribution and the oscillating air pressure over the internal fluid surface. Based on the above methodology and the resulting tool, numerical studies are carried out for three cylindrical OWC scenarios that are floating in waves, attached by a reflector and connected to a submerged caisson, respectively. Different modes of body motion and typical free-surface oscillation modes in the chamber are analysed and discussed. It is found that, for an OWC with an attached arc-shaped reflector or connected to a submerged caisson, its wave power absorption can be characterised by a series of apparent peaks which are associated with the resonant internal fluid and in close proximity to the resonance frequencies of body motions involving surge, heave or pitch. Numerical results also indicate the benefits of floating OWCs from the coupled rigid-body motion modes and OWC’s resonance, expanding the frequency range of efficient conversion and improving the device’s adaptability to variable oceanic environments.

Hydrodynamic response of moored ships to seismic-induced harbor oscillations

Free-surface oscillations induced by seismic waves were observed in many harbors. These free-surface fluctuations could lead to damage in a wide range of forms, such as breakage of mooring systems due to excessive ship motions. The damage to moored ships and mooring systems will remarkably reduce their emergency capability to incoming tsunamis, probably further leading to property losses and casualties. However, investigation of floating bodies under seismic-induced free-surface oscillations is rare. Particularly, the hydrodynamic response of moored ships to seismic-induced harbor oscillations has not yet been studied. In this article, the transient hydrodynamic characteristics of moored ships under seismic-induced harbor oscillations are investigated by a hybrid Boussinesq-panel model where the free-surface oscillations are modeled by a fully nonlinear Boussinesq wave model and are further used to drive the ship motions. Results reveal that seismic-induced harbor oscillations can trigger long-period movements of moored ships, consistent with the existing observations. The long-period ship motions consist of the natural modes of the mooring system and the forced modes relating to long-period harbor oscillations. Notably, the ship's maximum displacement can be amplified remarkably when the periods of natural modes coincide with those of the forced modes. The effects of modal shapes of seismic-induced multi-mode harbor oscillations on the ship motions are analyzed. Finally, a brief discussion on studying the countermeasures against ship motions triggered by seismic-induced harbor oscillations is presented. • The hydrodynamic response of moored ships to seismic-induced harbor oscillations is first investigated using a hybrid Boussinesq-panel model. • The capacity of seismic-induced harbor oscillations to trigger long-period movements of moored ships is revealed, especially reproducing a typical process of this phenomenon. • The transient hydrodynamic characteristics of moored ships under seismic-induced harbor oscillations are analyzed, especially considering the resonant case when the natural periods of the ship motions are close to that of harbor oscillations. • The effects of modal shapes of seismic-induced multi-mode harbor oscillations on the ship motions are examined.

Study of Free Oscillations of Bays in the Northwestern Part of Posyet Bay

To study the specific features of free surface oscillations in the northwestern part of Posyet Bay (the Sea of Japan), a series of experimental works using an installation with a laser meter for measuring hydrosphere pressure variations were carried out in 2012 and 2014. In the course of the joint analysis, measurement results for oscillations with periods of 10–30 min and the results of calculations using a numerical model of shallow water with a difference approximation on an irregular triangular space grid, datasets of the space–time parameters for the resonance oscillations of the studied water area were obtained. The results of the numerical simulations confirm the manifestation of the resonance properties of Novgorodskaya, Expedicii, and Reyd Pallada Bays water areas on the oscillations singled out during the experimental studies. The positions of the peaks on the model resonance curves are consistent with the positions of the clearly pronounced peaks of the energy spectrum in the field data.

Wave-like motion and secondary currents in arrays of emergent cylinders induced by large scale eddying motion

Free-surface flows with riparian corridors are known to develop large eddies resulting from the instability associated to the inflectional profile of the longitudinal velocity in the spanwise direction. They periodically generate strong momentum exchanges inside the vegetation corridor, triggering a wave-like motion, detectable as free-surface oscillations and out-of-phase velocity components. We propose a characterization of the flow inside the vegetation corridor, focusing on the wave-like motion and its influence on secondary currents. We conditionally sample the fluid motion to highlight the structure of the phase-averaged coherent structure. Quadrant analysis shows that there is a strong variation of Reynolds stress anisotropy in the spanwise direction, which is one of the key generation mechanisms of secondary currents. Spectrograms of longitudinal and lateral velocity fluctuations reveal that the oscillatory motion is imposed on the whole of the vegetated layer, because of continuity. The analysis of the phase-averaged 2D vertical-longitudinal flow reveals that there is a complex 3D pattern of mass fluxes associated to each large eddy. In particular there is an anti-symmetric net mass imbalance which, by mass conservation, generates a mass flux directed outwards, to the main channel, near the bottom of the channel. The Eulerian expression of this motion is obtained as the spatial average of the flow over the length of the large eddy, resulting in the pattern of the secondary current in the vertical-spanwise plane. It is shown that the secondary motion is a necessary feature of free-surface turbulent flows that develop large-scale inflectional instabilities.

Onset of axisymmetric sloshing in a food processor.

We report on the axisymmetric oscillation at the air-water interface in a food processor and Taylor-Couette systems. To gain insights into the mechanisms of free-surface oscillation, we conduct a series of experiments on the visual observations of free-surface deformation and the velocity measurements. At relatively low rotation speeds, the surface height at the rotating object surface decreases but remains stationary. As the rotation speed increases in small increments, oscillation begins when the deformed free surface detaches from the rotating object, and its onset depends strongly on the initial surface height. To account for the similarity mechanism of the onset, a scaled surface deformation based on the bulk Froude number is introduced herein; we find that the oscillation occurs at the scaled surface deformation beyond unity. These findings explain the causal relationship between the surface deformation and the oscillation onset and help to predict its occurrence to avoid mechanical damage to an apparatus with rotating components.

ABOUT STABILITY OF THE MOVEMENT OF THE REFUELING VEHICLE EQUIPED WITH DIGITAL SYSTEM OF BRAKE FORCES DISTRIBUTION DURING THE EMERGENCY BRAKING

The impact of enforced oscillations of the free surface of fuel in the car tank on the stability area of a closed digital brake force distribution system is considered. The object of the study is the process of stabilized movement of the tanker during the emergency braking. The subject of the study is a large tanker with a gross weight (3-3.5) *104 kg, equipped with a tank with a volume of (17-20) m3 and a system of direction stability. The goal of the work is investigation of the impact of transported fuel fluctuations on the stability of the refueling vehicle during the emergency braking and introducing of methods for selecting values of variable parameters of the electronic brake force distribution system to minimize it. Conclusion. Considering the oscillations of the free surface of the liquid in the mathematical model of disturbed movement of a closed system of stability significantly reduces the stability area of the system in the low frequency range due to the loop, the size and position of which depend on the filling level of the tank. Need to choose an envelope loop that according to different levels of tank filling.

Sloshing of Fluid Between Rotating Inner Vertical Shaft and Stationary Outer Casing

Abstract Unsteady behaviors of free surface around a rotating vertical shaft in cylindrical stationary casing were investigated. Experiments were carried out with various rotating frequency of the shaft at two initial water levels. An axi-symmetrical free surface oscillation took place when the rotational speed of the shaft became larger than a certain value. The frequency of the free surface oscillation decreased as the rotating frequency increased. A theoretical model was developed, and the mechanisms of the free surface oscillation were clarified. The oscillation was found to be a sloshing mode excited by the change of fluid angular velocity, caused by the change of wetted areas on the inner rotating shaft and outer stationary casing, associated with the change in free surface height.

Oscillating water column behaviour at forward, central, and aft locations within a fixed vessel

The oscillating water column (OWC) responses within forward, central and aft located moonpools for a fixed vessel are studied experimentally under regular head wave conditions. A potential theory-based solver (WAMIT) is used to determine the resonant frequencies of the water column which decrease with the increase in draft. The free surface elevation of the confined water inside the OWC for the piston mode frequencies are studied independently for the forward, central and aft OWCs, showing a strong dependence on location, draft, and wave frequency. For the vessel of 2 m length and OWC diameter of 0.19 m, maximum amplification factors of 1.71 (forward), 1.4 (central) and 1.51 (aft) are observed around the resonant frequencies for 0.15 m, 0.30 m, and 0.25 m vessel drafts respectively. The relative response is largely magnified for wave frequencies around the resonant range at lower wave steepness where wave-induced oscillations are non-linear. The understanding of location-dependent responses can be useful in the context of wave energy harvesting from OWC installed in a vessel where the free-surface oscillations are used to generate energy.

ABOUT THE INFLUENCE OF VIBRATIONS OF THE CONVEYED LIQUID ON THE AREA OF STABILITY OF A CLOSED SYSTEM AUTOMATIC VEHICLE COURSE CONTROL

The existing publications that investigate vehicle course stability optimization were analyzed. A mathematical model, which describes the disturbed movement of a car with a tank, was compiled. This model allows to consider the liquid free surface oscillations and determine their effect on the car course stability during constant motion or emergency braking. There was described the main information regarding the car that was used to perform mathematical calculations. An algorithm was developed for deriving the characteristic equation for a complex system of differential equations describing dynamic changes in the movement parameters of a car, oscillations of partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit system for ensuring course stability. Based on the developed mathematical model, the influence of forced oscillations of the fluid on the stability area of the system built in the plane of variable parameters of the controller is investigated. It is shown that low-frequency oscillations of the free surface of a liquid lead to a significant reduction in the stability area, which indicates the need to consider such oscillations when solving problems of analysis and synthesis of this system. It was found that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by a redistribution of mass and disturb the movement, an increase of the speed unambiguously leads to a deterioration in directional stability. That enables exclusion of speed from the number of variable parameters and significantly simplify the problem being solved. The calculations for cases with different loading levels were performed. It was found out that the level of liquid in the tank, considering its relationship with the speed, has an ambiguous effect on the car course stability, and it is unacceptable to limit the research calculations to the case with 50 % load. Instead of this, it is necessary to find a line that bends from above the stability boundaries that correspond to many liquid levels.
 Keywords: fluid vibrations; exchange rate stability system; area of stability; tank; PID-controller; parameters.

The influence of flexible fluid structure interactions on sway induced tank sloshing dynamics

The analysis of liquid sloshing remains a challenging computational mechanics topic due to its complex underlying physics. The rapid simulation of sloshing problems requires accurate modelling of two-phase fluid dynamics and sloshing impacts on solid tank boundaries by suitable Flexible Fluid Structure Interaction (FFSI) models. This paper presents a hydroelastic model for the prediction of sway induced sloshing loads on flexible trapezoidal and rectangular tanks. Tank walls and a vertical baffle in way of the mid span of the tank bottom are idealized by Timoshenko beam structural dynamics. Hydroelastic analysis is enabled by a Boundary Element Method (BEM) that couples tank wall and baffle structural dynamics with free surface hydrodynamics to evaluate excitation forces and peak hydrodynamic pressures in way of the tank perimeter. Results show that for the case study presented accounting for the influence of hydroelasticity in a rectangular tank may lead to decrease of free surface oscillations and peak pressure by 20%. This is because the dynamics of tank flexibility are coupled with the angular frequency of the sway motion. These benefits amplify further for the case of trapezoidal tank designs for which the free surface and pressure of the trapezoidal tank with lateral angle θ=80° are decreased relative to the rectangular one by about 80% and 65%, respectively.

Experimental investigation of a free surface oscillation in a model pump-turbine

Hydro power plants provide balancing services to the power grid and the amount is expected to increase in the near future. One of these services is the compensation of reactive power and the regulation of the power factor. Therefore, hydro power units equipped with synchronous machines are operated in so called synchronous condenser mode. During this operation the runner is dewatered and rotates in air above a free surface at the draft tube cone. As a result, a free surface oscillation is excited under some conditions. This paper deals with the experimental investigation of this flow phenomenon. Therefore, model tests are conducted at the hydraulic laboratory of the Institute of Energy Systems and Thermodynamics at TU Wien. The investigated model pump-turbine is equipped with a draft tube cone made of acrylic glass for optical investigations. In addition to the standard instrumentation, fast response pressure transducers are installed at different planes and positions. The machine setup and measurement conditions aim at the investigation of the free surface oscillation and shall prevent other influences. The experiments are performed for both runner rotation directions, different initial water levels at the draft tube and different densimetric Froude numbers. High speed camera recordings are conducted and the amplitude of the water formation is determined by post processing the captured images. In periodic state the frequency of the free surface oscillation is extracted out of the pressure signals. Finally general trends and dependencies are deduced from the acquired data.

Experimental investigation of transient harbor resonance induced by solitary waves

Free-surface oscillations within a square harbor subjected to solitary waves are investigated through physical experiments. The effects of various wave heights and water depths on the resonance within the harbor are examined. In this study, the technique of wavelet-based bicoherence spectra is employed for the first time to investigate the nonlinear wave–wave interaction of the transient harbor resonance induced by solitary waves. The results show that the relation between the maximum surface elevation, ηmax, within the harbor and the incident wave height of a solitary wave can be regarded as approximately linear. Moreover, for the same incident solitary wave height, the larger the water depth is, the greater the value of ηmax becomes. The analyses of the wavelet-based bicoherence indicate that the natural modes of the harbor are generated in the following two ways: (1) direct generation from the energy transfer of the solitary waves, and (2) the subsequent generation from the nonlinear interaction between various wave components. The first mechanism plays a decisive role in the generations of low-order natural modes, while the second mechanism also has a vital catalytic role in triggering higher-order modes. Finally, it is examined that the duration of harbor oscillations changes obviously with incident wave heights and water depths.