Free Surface Level Research Articles

Effect of waves on the magnitude and direction of wind stress over the Ocean

Correctly estimating the wind stress at the sea surface is of the utmost importance in models for climate studies, weather forecasting, and ocean–atmosphere interaction. The wind stress is mainly obtained by drag coefficient parameterizations, which always consider the wind stress to be aligned with the wind, but this is sometimes the case. Also, during moderate to weak wind conditions, these parameterizations may lead to high estimation errors due to the presence of swell. This study measured the wind stress with a high-rate (100 Hz) sonic anemometer mounted on a spar buoy. The sea state was also characterized by obtaining the directional spectrum of the waves by six wave-staff arrays sensing the free surface level at 10 Hz. Bouy’s movement was corrected by employing an inertial motion unit. The turbulent and wave-coherent wind stress components were also estimated and analyzed. It was observed that during swell conditions with wind traveling in the same direction, the wave-coherent wind stress component has an opposite direction to the wind and dampens the total wind stress magnitude. During counter-directional wind relative to swell events, the wave boundary layer is modified; swell produces a wave-coherent wind stress in the same direction as the wind, resulting in an enhanced total wind stress magnitude. The wave age, significant wave height, and the traveling direction of the swell relative to the wind are essential to correctly estimating the wind stress in swell-dominant conditions. A set of empirical parameterizations for each wind stress component is proposed.

Bathymetry reconstruction from experimental data using PDE-constrained optimisation

Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.

Numerical modelling of flow field at shaft spillways with the marguerite-shaped inlets

By decreasing the entrained air flow discharge and improving the hydraulic characteristics of vertical shaft spillways, Marguerite-shaped inlets (MSIs) can mitigate the effects of swirling flow surrounding their inlet. The hydraulic and hydrodynamic characteristics of flow around MSIs under orifice flow regime were numerically investigated, applying different geometrical parameters. This inlet configuration can decrease the strength of swirling flow and increase the flow discharge through the shaft. The finite-volume method and the re-normalisation group k–ε turbulence model were employed to solve the governing equations of motion in a cylindrical coordinate system and a two-phase air–water flow on the water free-surface. Increasing the height and length of the blades of the MSIs was found to increase the area of the barriers against swirling flow, weaken the swirling flow strength, engender a more uniform flow and lower the water free-surface level. Extremely long or high blades, however, resulted in an intense collision of the flow with the spillway and increased the water free-surface level and the swirling flow strength at the MSI.

Research on flow field quality measurement of super high speed circulating water channel based on LDV

The flow field quality of the super high speed circulating water channel (SHSCWC) test section in the open (with a free liquid surface state) and closed (with a cavitation tunnel state) was studied. An array of flow field measuring points was established to measure the axial velocity using a laser doppler velocimeter (LDV) for both states. Meanwhile, ultrasonic sensors were used to measure the levelness of the free liquid surface in the test section. The measurement results indicated that in the open state, the non-uniformity and instability of 8 kinds of flow velocity in the flow field section are less than 1.0%, respectively, while the free liquid surface level is less than 25mm at the flow rate of 8m/s. In the closed state, the non-uniformity and instability of eight types of flow velocity in the flow field section are all below 1.0%, with turbulence being less than 0.5%. The measurement results in both states meet the requirements of technical indicators, and provide data support for the experimental research and optimal design of the SHSCWC.

Simulation of a loss of flow transient of a small Lead-Cooled reactor using a CFD-Based model

The recent development of small modular reactors needs to be followed by safety analysis using the newest available tools. This work focuses on one type of reactor, SEALER, which is a small lead cooled reactor intended for remote communities in Canada. Simulations of a loss of flow transients are performed using a CFD-based model that was specifically developed for this project. The CFD geometry includes the entire primary circuit with some simplifications. The fuel channel, steam generator and pumps use a simple geometry with momentum source and heat source/sink. Free surface level is modelled with the multiphase volume of fluid (VOF) method. The CFD part of the model is coupled to a custom code for heat transfer in the fuel rods and point kinetics for neutronics. Transient results show that core temperatures do not increase significantly and stay well below coolant boiling and fuel melting points. The CFD-based model presented here is compared against a lumped-parameter model using the same transient. It is shown that the evolution of the mass flow and temperature is significantly different and more detailed with the CFD-based model. Finally, the influence of the moment of inertia of the pump flywheel on the transient is explored.

Wave propulsion for surface vehicle by foils with active angle of attack adjustment

Extracting wave energy as propulsion for surface vehicles saves non-renewable energy. The fluid moves in a circular or elliptical trajectory in the wave, and its direction of motion varies regularly by 360°. The angle of attack of fixed-angle wave foil cannot be controlled as the direction of incoming flow changes, so the propulsion obtained from the wave is limited. This paper discusses a wave propulsion method by actively controlling the foil to follow the changing incoming current direction, thereby increasing the propulsion extracted by the foil. The wave phase at the foil position is obtained by measuring the free surface level, so as to estimate the direction of the incoming flow and adjust the foil rotation angle accordingly. The wave propulsion system was modeled and simulated in Matlab/Simulink to analyze the incoming flow and the corresponding foil angle. To take into account the foil wave interaction, STAR-CCM+ is used for numerical study. Simulation results show that the active wave foil can provide wave propulsion and has better performance than the fixed-angle wave foil.

Contribution of coastal structures to wave force attenuation: A numerical investigation of fluid-structure interaction for partially perforated caissons

Perforated caissons are increasingly used as an advanced solution for seawalls and breakwaters, even in open, rough seas. Despite their widespread implementation, challenges remain in accurately calculating wave forces acting on these structures. Furthermore, the applicability of common design formulas for determining wave forces on perforated caissons under various hydrodynamic conditions is not fully understood. In this study, the commercial CFD package FLUENT™ is employed to perform three-dimensional RANS-VOF numerical simulations of a partially perforated caisson on a rubble-mound foundation. The numerical model is evaluated from different viewpoints, including the generation of nonlinear waves, interaction between waves and common coastal structures (solid vertical walls) and finally, wave-perforated caisson interactions. A good agreement was obtained between the present model results and previous theoretical and laboratory results. The model is then utilized to qualitatively investigate wave-structure interactions through free surface levels, eddy viscosity, and spatial pressure distributions during various phases of interaction. Furthermore, the applicability of common design formulas and the perforated caisson's performance are thoroughly examined under a wide range of parameters affecting the horizontal wave force on the structure, including rubble mound height, wavelength, wave height, water depth, and berm width. The study finds that the Takahashi formula shows some discrepancies in wave force predictions, while the Tabet-Aoul method struggles to accurately predict wave forces on the front wall of the perforated caisson. The DUT's methods perform well only within the assumptions used in their developments. This research also investigates the effect of different design parameters on the forces acting on the perforated caissons and provides insights into the strengths and limitations of each design formula and discusses the conditions under which partially perforated caissons demonstrate optimal performance compared to conventional solid caissons. This information will aid engineers in determining accurate horizontal wave forces exerted on partially perforated caissons, ultimately contributing to more effective and efficient designs.

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.

Hydroelastic linearized vibrations taking into account prestressed effects due to internal liquid weight: Numerical vs. experimental results

This paper concerns the numerical simulation of the hydroelastic vibrations of an elastic tank containing a free surface liquid, around a geometrically nonlinear equilibrium configuration that takes into account the prestress effect due to the liquid weight. The computational methodology is the following. Firstly, the hydrostatic pressure on the fluid–structure interface is considered as a non-uniform follower force which depends on the liquid height. Therefore, the prestressed equilibrium at a given free-surface level, called current configuration in the paper, is computed as a geometrically nonlinear problem, in which the height of the liquid is considered as an evolution parameter. We start from an empty structure, defined as the reference configuration, which is progressively filled to reach the level of the chosen configuration. Therefore the calculation of hydroelastic vibrations of a tank filled with liquid as a function of a emptying rate is straightforward. The methodology is validated with experimental results extracted from literature.

Wave analysis based on genetic algorithms using data collected from laboratories at different scales

This paper presents the results of a comparative study of waves generated in water channels and in shaking tank systems with the aim of standardizing the use of different laboratories’ facilities and establishing scales for analyzing the evolution of waves under deep water conditions. For this purpose, experimental models are built. The experiments encompass a collection of free surface level measurements obtained from progressive waves in a hydraulic channel and from stationary waves generated by imposing controlled motion to a rectangular tank. The experimental results are also evaluated by contrasting them with analytical correlations. In addition, a model based on a genetic algorithm is proposed to extrapolate the evolution of waves under other physical conditions not measured in the laboratory. The present analysis confirms the viability of wave height comparison between waves generated in a hydraulic channel and those generated by sloshing in a rectangular tank when its natural frequency coincides with the frequency of the progressive wave. Finally, a methodology for establishing a plausible scale for wave comparisons is described and applied.

Numerical Investigation of 3D Flow Properties around Finite Emergent Vegetation by Using the Two-Phase Volume of Fluid (VOF) Modeling Technique

This study predicts how the Free Surface Level (FSL) variations around finite length vegetation affect flow structure by using a numerical simulation. The volume of fluid (VOF) technique with the Reynolds stress model (RSM) was used for the simulation. Multizone Hexahedral meshing was adopted to accurately track the free surface level with minimum numerical diffusion at the water–air interface. After the validation, finite length emergent vegetation patches were selected based on the aspect ratio (AR = vegetation width-length ratio) under constant subcritical flow conditions for an inland tsunami flow. The results showed that the generation of large vortices was predominated in wider vegetation patches (AR > 1) due to the increase and decrease in the FSL at the front and back of the vegetation compared to longer vegetation patches (AR ≤ 1), as this offered more resistance against the approaching flow. The wider vegetation patches (AR > 1) are favorable in terms of generating a large area of low velocity compared to the longer vegetation patch (AR < 1) directly downstream of the vegetation patch. On the other hand, it has a negative impact on the adjacent downstream gap region, where a 14.3–34.9% increase in velocity was observed. The longer vegetation patches (AR < 1) generate optimal conditions within the vegetation region due to great velocity reduction. Moreover, in all the AR vegetation cases, the water turbulent intensity was maximum in the vegetation region compared to the adjacent gap region and air turbulent intensity above the FSL, suggesting strong air entrainment over this region. The results of this study are important in constructing vegetation layouts based on the AR of the vegetation for tsunami mitigation.

Unsteady shallow meandering flows in rectangular reservoirs: A modal analysis of URANS modelling

Shallow flows are common in natural and human-made environments. Even for simple rectangular shallow reservoirs, recent laboratory experiments show that the developing flow fields are particularly complex, involving large-scale turbulent structures. For specific combinations of reservoir size and hydraulic conditions, a meandering jet can be observed. While some aspects of this pseudo-2D flow pattern can be reproduced using a 2D numerical model, new 3D simulations, based on the unsteady Reynolds-Averaged Navier-Stokes equations, show consistent advantages as presented herein. A Proper Orthogonal Decomposition was used to characterize the four most energetic modes of the meandering jet at the free surface level, allowing comparison against experimental data and 2D (depth-averaged) numerical results. Three different isotropic eddy viscosity models (RNG k-ε, k-ε, k-ω) were tested. The 3D models accurately predicted the frequency of the modes, whereas the amplitudes of the modes and associated energy were damped for the friction-dominant cases and augmented for non-frictional ones. The performance of the three turbulence models remained essentially similar, with slightly better predictions by RNG k-ε model in the case with the highest Reynolds number. Finally, the Q-criterion was used to identify vortices and study their dynamics, assisting on the identification of the differences between: i) the three-dimensional phenomenon (here reproduced), ii) its two-dimensional footprint in the free surface (experimental observations) and iii) the depth-averaged case (represented by 2D models).

Hunting for the correct pressure drop in a scaled reactor pool: Effect of geometry, mesh resolution, turbulence model and mass flow

The E-SCAPE (European SCAled Pool Experiment) facility at the Belgian nuclear research center SCK•CEN is a thermal hydraulic 1/6th-scale model of the MYRRHA reactor with an electrical core simulator and cooled by LBE. The E-SCAPE facility provides experimental feedback to the designers on the forced and natural flow patterns, flow mixing and stratification during operational and accidental conditions. In addition, it provides valuable data for validation of the computational techniques for their use with LBE and in the design of MYRRHA. In terms of momentum field, one of the most important integral quantity to reproduce is the pressure drop in the system which has a direct consequence on the evolution of the mass flows and determines the free-surface levels in transient scenarios. In this paper, a detailed CFD study is performed on the flow in the E-SCAPE core region with the aim on predicting the correct pressure drop. Different numerical representation of the core geometry have been modeled and subjected to validation against experimental results from E-SCAPE. Special attention has been addressed to the choice of geometric simplifications and numerical models for accurate representation of the core of the E-SCAPE pool facility.

Automated Low Investment Cost Evaporometers (ALICEs)

Evaporation is an important part of the hydrological cycle. This paper discusses the materials and methods we used to develop an evaporometer, which measures evaporation from the water surface, like a drop in water level. The main problem is that there are relatively small differences in the levels measured directly in the field. During the research, we tested conductive filament and stainless steel as measuring electrode materials. We used 3D printing in combination with low-cost open-source electronics and a hand-etched circuit board to make a device which measures the free water surface level. A 3D printed jig is used when assembling the device, and this ensures that the contact electrodes are set precisely. Another 3D printed jig is used to create the etched circuit board, which holds all the electronic devices. The device uses the low-cost open-source Arduino Uno electronics microcontroller board. Our results show that high-precision measurements can be gathered with the use of open-source electronics in 3D printed housing. The device is also durable and easy to maintain.

Analyze open channel for continuously low speed used carbon dioxide bubbles

Designing a recirculating open-channel for continuously low speed in place of a towing tank required checking on its flow characteristics. There are many methods for checking the flow characteristics such as food coloring techniques, using buoys and hydrogen gas bubbles, etc. For this research, we use carbon dioxide bubbles which are caused by the reaction between sodium bicarbonate (NaHCO3) and hydrochloric acid (HCl) that is diluted in water until the acidity is equal to pH 3. Our experiments were carried at the area near the wall and the center of the test range at depths 6, 8 and 10 centimeters from the free surface level respectively. From the experimental results, the trend of water flow patterns in the center of the channel using food coloring needles technique tends to form the fluid flow close to the computational fluid dynamics (CFD) while the results from the carbon dioxide bubble technique are different compared with the two previous techniques by less than 20 percent, and the trends of the water flow pattern results of the numerical method, the food coloring needle, and the carbon dioxide bubble techniques. The tendency of the flow pattern in the same direction.

Transverse flow-induced vibrations of a sphere in the proximity of a free surface: A numerical study

In this paper, we present a numerical study on the transverse flow-induced vibration (FIV) of an elastically mounted sphere in the vicinity of a free surface at subcritical Reynolds numbers. We assess the interaction dynamics and the vibration characteristics of fully submerged and piercing spheres that are free to vibrate in the transverse direction. We employ the recently developed three-dimensional two-phase flow–structure interaction solver to investigate fully and partially submerged configurations of an elastically mounted sphere. To begin, we examine the vortex-induced vibration (VIV) phenomenon and the vortex-shedding modes of a fully-submerged sphere vibrating freely in all three spatial directions. We systematically verify and analyze the mode transitions and the motion trajectories in the three degrees-of-freedom (3-DOF) for the Reynolds number up to 30000. We next simulate the transversely vibrating (1-DOF) full-submerged sphere over a wide range of reduced velocities 3≤U∗≤20, whereby the reduced velocity is adjusted by changing the freestream Reynolds number. The VIV response amplitude and the topology of the wake structure are compared with the measurements for the mode I and mode II response branches. We further look into the effect of the free surface on the FIV response of a transversely vibrating sphere in the proximity of a free surface. The response dynamics of the sphere is studied for three representative values of normalized immersion ratio (h∗=h∕D, where h is the distance from the top of the sphere to undisturbed free-surface level and D is the sphere diameter), at h∗=1 (fully submerged sphere with no free-surface effect), h∗=0 (where the top of the sphere touches the free surface) and h∗=−0.25 (where the sphere pierces the free surface). At the lock-in range, we observe that the amplitude response of the sphere at h∗=0 is decreased significantly compared to the case at h∗=1. It is found that the vorticity flux is diffused due to the free-surface boundary and the free surface acts as a sink of energy that leads to a reduction in the transverse force and amplitude response. When the sphere pierces the free surface at h∗=−0.25, the amplitude response at the lock-in state is found to be greater than all the submerged cases studied with the maximum peak-to-peak amplitude of ∼2D. We find that the interaction of the piercing sphere with the air–water interface causes a relatively large surface deformation and has a significant impact on the synchronization of the vortex shedding and the vibration frequency. The streamwise vorticity contours and pressure distribution are employed to understand the VIV characteristics and wake dynamics. Increased streamwise vorticity gives rise to a relatively larger transverse force to the piercing sphere at h∗=−0.25, resulting in greater positive energy transfer per cycle to sustain the large-amplitude vibration. Lastly, we study the sensitivity of large-amplitude vibration on the mass ratio, m∗, and, Froude number, Fr, at the lock-in state.

Robust estimators for free surface turbulence characterization: a stepped spillway application

Robust estimators are parameters insensitive to the presence of outliers. However, they presume the shape of the variables’ probability density function. This study exemplifies the sensitivity of turbulent quantities to the use of classic and robust estimators and the presence of outliers in turbulent flow depth time series. A wide range of turbulence quantities was analysed based upon a stepped spillway case study, using flow depths sampled with Acoustic Displacement Meters as the flow variable of interest. The studied parameters include: the expected free surface level, the expected fluctuation intensity, the depth skewness, the autocorrelation timescales, the vertical velocity fluctuation intensity, the perturbations celerity and the one-dimensional free surface turbulence spectrum. Three levels of filtering were utilised prior to applying classic and robust estimators, showing that comparable robustness can be obtained either using classic estimators together with an intermediate filtering technique or using robust estimators instead, without any filtering technique.

Solutions for Gradually Varied Flow Profiles in Prismatic and Wide Rectangular Channels by Perturbation Method

Gradually varied flow (GVF) in open channel hydraulics occurs when free water surface level gradually varies in a steady flow due to geometry alteration in the channel. Investigation of GVF profile is important because water depth along the channel should be determined when designing the channel. Mathematically, GVF profile is obtained by solution of a nonlinear ordinary differential equation. However, due to extreme nonlinearity of the equation, providing an analytical solution is practically unattainable unless under highly simplified conditions. The current study presents semi-analytical solutions for the equation in prismatic ordinary and wide rectangular channels by perturbation method (PM). At the first step, a perturbation solution is derived for wide rectangular channels using a constant Chezy coefficient. At the second step, the wide rectangular channel is investigated using Manning equation as the resistance equation. Finally, the perturbation solution is presented for an ordinary rectangular channel using Manning equation. Obtained GVF profiles using the perturbation solutions are compared with finite difference method (FDM) profiles. Results show that PM profiles are in excellent agreements with FDM ones, and therefore, PM solutions may be used to obtain GVF profiles in mentioned cases with high levels of accuracy. It was concluded that developed semi-analytical solutions may be used as reference solutions for efficiency assessment in various numerical techniques that provide solution for GVF profile in open channels.

Fundamental study on chaotic transition of two-phase flow regime and free surface instability in gas deaeration process

Deaeration is a process of eliminating aspirated air from liquid in hydraulic reservoirs to avoid cavitation in the downstream pump blades. The complex fluid dynamics associated with deaeration is investigated. The three-dimensional buoyancy driven chaotic behavior of gas-liquid interfacial two-phase flow is studied. Parametric study is executed to understand change in internal flow physics (bubble coalescence, disintegration, horizontal spread, bubble velocity etc.), strength of accelerating Rayleigh-Taylor instability, turbulent kinetic energy, amplitude of upward velocity near free surface, and rise in free surface level with the variation of parameters like incoming mixture flow rate, incoming volume fraction of air, liquid fill depth, and Atwood number. The computations show increment in cavitation, wavenumber and amplitude of upward velocity towards oscillating free surface with incoming flow rate (Re). Cavitation and free surface instability show incremental trend with volume fraction of incoming air forming a kink (cavitation reduces) due to bubble coalescence in a threshold range of volume fraction of incoming air. With the variation of Atwood number, initially cavitation reduces. But after a critical value (A*) of Atwood number, effect of bubble disintegration, and rise of cavitation become prominent, which is formulated with respect to incoming flow rate (Re). With liquid fill depth, cavitation shows a slight decrement with almost equal deaeration and constant wavelength of free surface oscillation at an increasing buoyancy driven upward velocity. Some glimpse of design solution to reduce the cavitation and enhance the deaeration is also studied and formulated to get better understanding.

A smooth polynomial shaped command for sloshing suppression of a suspended liquid container

A smooth polynomial shaped command with an adjustable command time length is proposed for eliminating the residual vibrations of a multi-mode system. The ability of eliminating jerks and vibrational modes, regardless of their number, offers the most advantage of the proposed command. A numerical simulation is conducted to test the command’s effectiveness by eliminating the residual sloshing oscillations of a liquid-filled container conveyed by an overhead crane in a rest-to-rest manoeuvre. The governing equations of the liquid free-surface level are derived by modelling the sloshing dynamics by a series of mass–spring–damper harmonics. The proposed model accounts for the coupling between the pendulum dynamics and the sloshing equivalent mechanical model. The command’s robustness to the system parameters’ uncertainties, liquid depth and cable length, are investigated as well. The ability of adjusting the command length and retaining higher sloshing modes in command-designing are also outlined.