Hydrodynamic forces on blocks and vertical wall on a step bottom

In the present study, the problems of diffraction and radiation of water waves by a cylindrical heaving wave energy converter (WEC) placed in front of a reflecting V-shaped vertical breakwater are formulated. The idea conceived is based on the possible exploitation of amplified scattered and reflected wave potentials originating from the presence of V-shaped breakwater, towards increasing the WEC’s wave power absorption due to the wave reflections. An analytical solution based on the method of images is developed in the context of linear water wave theory, taking into account the hydrodynamic interaction phenomena between the converter and the vertical wall. Numerical results are presented and discussed concerning the hydrodynamic forces on the absorber and its wave power efficiency for various examined parameters, namely, the breakwaters’ forming angle, the distance between the converter and the vertical walls and the wave heading angle. The results show that the amount of the harvested wave power by the WEC in front of the walls is amplified compared to the wave power absorbed by the same WEC in the open sea.

Interactions between fully nonlinear water waves and cylinder arrays in a wave tank

A variational formulation of water waves is developed, based on the Hamiltonian theory of surface waves. An exact and unified description of the two-dimensional problem in the vertical plane is obtained in the form of a Hamiltonian functional, expressed in terms of surface quantities as canonical variables. The stability of the corresponding canonical equations can be ensured by using positive definite approximate energy functionals. While preserving full linear dispersion, the method distinguishes between short-wave nonlinearity, allowing the description of Stokes waves in deep water, and long-wave nonlinearity, applying to long waves in shallow water. Both types of nonlinearity are found necessary to describe accurately large-amplitude solitary waves.

Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This work presents a direct time domain methodology for Fluid-Structure Interaction analysis between linearized fluids and rigid bodies. To this end, a direct time domain Boundary Element formulation pertaining to 3-D wave propagation in acoustic media is developed. The method is based on higher order B-Spline fundamental solutions developed for scalar wave propagation in 3-D infinite media and uses higher order spatial discretization. Integration of singularities appearing in the fundamental solutions is treated numerically through triangle coordinates and a successive mapping technique. This method is used within the B-Spline Impulse Response framework for the calculation of the time history of the response of the acoustic medium and the calculation of the hydrodynamic forces on the wetted surface of the fluid-structure interface. The proposed B-Spline BEM is stable as compared to the relevant Retarded Potential formulations reported in the literature. Although this method is non-local in time, only a relatively small number of time steps are required in the B-Spline Response functions, making the method very efficient especially for prolonged external excitations. Fluid-Structure interaction models are proposed for the dynamics of rigid bodies submerged in, or floating on, semi-infinite fluid domains. Validation of the BEM is presented in the application examples. The accuracy stability and efficiency of the proposed models are also demonstrated.

The diffraction of waves by three bottom fixed vertical circular cylinders is investigated by using the boundary element method. This method has been successfully applied to the isolated vertical circular cylinder and now is used to study the interaction between waves and multiple vertical cylinders. In this paper, a numerical analysis by the boundary element method is developed by the linear potential theory. The numerical analysis by the boundary element method is based on Green's second theorem and introduced to an integral equation for the fluid velocity potential around the vertical circular cylinders. To verify this method, the results obtained in present study are compared with the results computed by the multiple scattering method. The results of the comparisons show strong agreement. Also in this paper, several numerical examples are given to illustrate the effects of various parameters on the wave exciting force such are the separation distance, the wave number and the incident wave angle. This numerical computation method might be used broadly for the design of various offshore structures to be constructed in the future.

The hydrodynamic response of a porous flexible circular-cylinder in regular waves was analytically studied. To simplify the problem, the cover and the bottom of the cylinder were ignored. Small amplitude water wave theory and structural responses were assumed. The velocity potentials were solved using the Fourier-Bessel series expansion method and the least squares approximation method. The convergence of the series was numerically tested to determine the number of terms in the series expansion. Two types of installations were considered for deformation, hydrodynamic forces, structural flexibility, drafts, and porosity. The present study represented a preliminary step in the study of the fish cage.

ObjectivesSonic toothbrushes generate hydrodynamic shear forces for oral biofilm removal on tooth surfaces, but the effective thresholds for biofilm removal remain unexplored. This in vitro study aimed to investigate various threshold values for hydrodynamic biofilm removal in vitro.Materials and methodsA specialized test bench was designed with a known water flow field within a gap, ensuring that hydrodynamic shear forces on the wall were solely dependent on the volume flow, which was quantifiable using an integrated flow meter and proven by a computational fluid dynamics simulation. A young 20 h supragingival six-species biofilm was developed on hydroxyapatite disks (∅ 5 mm) and applied into the test bench, subjecting them to ascending force levels ranging from 0 to 135 Pa. The remaining biofilms were quantified using colony forming units (CFU) and subjected to statistical analysis through one-way ANOVA.ResultsVolume flow measures < 0.1 l/s: Error 1% of reading were established with the test bench. Untreated biofilms (0 Pa, no hydrodynamic shear forces) reached 7.7E7 CFU/harvest and differed significantly from all treated biofilm groups. CFU reductions of up to 2.3E6 were detected using 20 Pa, and reductions of two orders of magnitude were reached above wall shear forces of 45 Pa (6.9E5).ConclusionsCritical hydrodynamic force levels of at least 20 Pa appear to be necessary to have a discernible impact on initial biofilm removal.Clinical relevancePure hydrodynamic forces alone are insufficient for adequate biofilm removal. The addition of antiseptics is essential to penetrate and disrupt hydrodynamically loosened biofilm structures effectively.

A novel boundary element method based on series expansion is developed for wave diffraction by a vertical circular cylinder in the time domain. Unlike traditional potential flow boundary element methods in which velocity potentials are evaluated on each panel, both the velocity potential and its normal derivative are expanded by Laguerre functions in the vertical direction and Fourier series along the circumference of cylinder, respectively. A boundary integral equation is therefore established associated with expansion coefficients in the sense of Galerkin collocation. Free-surface Green function in the time domain is no longer explicitly computed but its integration involving Fourier-Laguerre basis functions on the whole cylindrical surface is evaluated. Incoming waves are transient with wavefronts, which are more general than steady-state plane progressive waves. Results obtained by using the present method are compared with those from existing time-domain analysing method.

Liquid sloshing is a common phenomenon in the transporting of liquid tanks. Liquid waves lead to fluctuating forces on the tank wall. If these fluctuations are not predicted or controlled, they can lead to large forces and momentum. Baffles can control liquid sloshing fluctuations. One numerical method, widely used to model the liquid sloshing phenomena is Smoothed Particle Hydrodynamics (SPH). Because of its Lagrangian nature, SPH is suitable for simulating free surface flow. In the present study, a relatively accurate Incompressible SPH (ISPH) method improved by kernel gradient correction tensors, particle shifting algorithms, turbulence viscosity calculations, and free surface particle detectors is applied for the free surface flow modeling. In comparison to the other SPH Simulations and experimental data, these results show that the present algorithm is effective for simulating free surface problems. The present algorithm has been applied to simulate liquid sloshing phenomena, while the aim of this study is the investigation of vertical and horizontal baffle effects on the control and damping of liquid sloshing. Results show that for vertical baffles, baffle size has a major role in sloshing fluctuation damping. For horizontal baffles, also including size, the baffle base position has a significant role in liquid sloshing fluctuation damping. When horizontal baffle is near the free surface, sloshing fluctuation-damping increases.

The scattering of linear water waves by an infinitely long rectangular structure parallel to a vertical wall in oblique seas is investigated. Analytical expressions for the diffracted potentials are derived using the method of separation of variables. The unknown coefficients in the expressions are determined through the application of the eigenfunction expansion matching method. The expressions for wave forces on the structure are given. The calculated results are compared with those obtained by the boundary element method. In addition, the influences of the wall, the angle of wave incidence, the width of the structure, and the distance between the structure and the wall on wave forces are discussed. The method presented here can be easily extended to the study of the diffraction of obliquely incident waves by multiple rectangular structures.

This study uses numerical simulations to investigate the complex fluid dynamics around two adjacent rotating cylinders arranged side by side. The primary focus is on understanding the influence of Reynolds number (Re), rotational speed ([Formula: see text]), gap spacing ([Formula: see text]), and compressibility effects at different Mach numbers ([Formula: see text]). Simulations were performed using ANSYS Fluent 19.0, employing a finite volume-based solver and the shear stress transport (SST) [Formula: see text]–[Formula: see text] turbulence model. The numerical methodology is validated against experimental results for flow over a single rotating cylinder and numerical studies for the two-cylinder configuration. The analysis encompasses velocity magnitude contours, pressure distributions, vorticity patterns, and drag coefficients to elucidate the intricate flow interactions over two vertically placed side-by-side cylinders. Across Reynolds numbers ranging from 50 to 200, the flow exhibits distinct transitions from laminar to turbulent regimes, characterized by forming vortices and emerging flow separation zones. Higher Reynolds numbers generally lead to more turbulent and asymmetric flow patterns, increasing drag coefficients due to intensified wake formation and vortex shedding. The cylinders’ rotational speed significantly influences flow dynamics: lower speeds favor symmetric vortex formations, while higher speeds induce complex turbulent flows with enhanced vortex shedding. Outward rotation of the cylinders accelerates flow between them, increasing velocities and drag coefficients, whereas inward rotation reduces velocities and drag coefficients due to reduced flow interactions. Alterations in the gap spacing ([Formula: see text]) between cylinders reveal critical insights: smaller gaps intensify rotational effects, enhancing vortex shedding and increasing drag coefficients, whereas larger gaps promote stable flows with reduced vortex-shedding tendencies and lower drag coefficients. Compressibility effects at Mach numbers ranging from 0.2 to 0.8 amplify wake elongation, flow compression, and asymmetric vortex shedding, contributing to higher drag coefficients in transonic and supersonic regimes. This study advances understanding of fluid dynamics around cylindrical configurations, providing insights essential for optimizing engineering designs and performance across various applications. Future research directions may involve refining models, exploring additional parameters, and advancing predictive capabilities further to enhance practical insights into similar fluid flow phenomena.

Pressures and forces due to directional waves on a vertical wall fronted by wave screens

In the design of a salt-water intake system which is connected to the ocean, a numerical model is developed to simulate the hydraulic and structural dynamic responses to the ocean's wave action. On the basis of available data, the design wave height is determined from the condition for breaking. For such a complex system, wherein several natural periods are contributing to the total response, a range of wave periods is considered. The standing wave system resulting from the reflection of a progressive wave train from a vertical wall (clapotis) is modelled and the hydrodynamic response of the system is computed. To limit water level fluctuations in the well, a strong damping of the water column is provided by constricting the flow through an orifice plate installed at the bottom of the pump well. The hydrodynamic force on the suspended pumps due to nearby submerged turbulent jet flow is described. A damped single-degree-of-freedom oscillator is employed to represent the structural dynamics of the pumps. Extensive experiments are required to supplement this work in order to describe the complex system fully. Keywords: dynamic analysis, salt-water intake, waves, hydrodynamic force, suspended pump, submerged jet, oscillator.

The process of the bubble growth and detachment from a wall with uniform up°ow parallel to the wall has been studied in this thesis. Experiments have been designed and performed in such a way that the assumptions of an existing analytical model were met. The aim of this study was to validate the predictions and to quantify the hydrodynamic lift force on a boiling bubble. This kind of detailed modeling of detachment can in principle be combined with numerical modeling of °ow with heat transfer in evaporator tubes, e.g. ri°ed tubes, with the aid of commercially available packages. The ¯ndings can be used to predict boiling characteristics in complicated geometries, such as ri°ed tubes, for conditions that occur during di®erent operation regimes of conventionally ¯red power plants. In the corresponding EC-project, all major European electricity companies join e®orts to design a power plant operating under high-temperature steam conditions to achieve 5% increase of the net e±ciency. The model presented yields analytical expressions for the forces acting on the bub- ble. A fully closed solution of the added mass forces involved in motion and growth of bubbles footed on the wall was obtained. Validation and quanti¯cation experiments corresponding to this model are described in this thesis. Nucleate boiling experiments were performed using demineralized water at near- saturated °ow boiling conditions. Both the thermal boundary condition and the approaching °ow (inlet) condition have been prescribed. The bubble substrate tem- perature and approach velocity were both constant. A microscale heater and a Wheat- stone bridge were used to maintain a constant wall temperature around an arti¯cial cavity. This cavity was used as the nucleation site where bubble would appear on a vertical part of the wall. This bubble generator has been given a special shape to minimize the velocity boundary layer thickness at the location of the arti¯cial cavity. The bubble generator intrudes a pipe and positions the arti¯cial site at the center of the pipe. As a result, a (nearly) homogeneous liquid velocity pro¯le approaches the bubble at the boiling site. Extensive image processing analysis enabled the determination of bubble geometrical parameters and to make a 3D reconstruction of the bubble volume history. The main non-hydrodynamic force components in the direction perpendicular to the vertical wall were determined from the measured quantities. The sum of these forces should equal the hydrodynamic force that is independently assessed using model predictions and measured geometrical parameter histories. This comparison was made, and used to draw conclusions on how much the deformations in°uence comparison with the model predictions and how the model should be ex- tended. In addition to model validation, temperature and power measurements have been used in a heat transfer analysis. It is shown that a signi¯cant part (60-70%) of the heat needed to make a bubble of certain volume in °ow boiling experiments arises from the superheated liquid layer in front of the heating element in respect to the heat delivered through the micro layer beneath the bubble foot from the electrical heater. These ¯ndings are con¯rmed by comparing the heater area and e®ective area, and by investigating the area of the bubble in°uence. The main conclusion drawn is that the assumption of a truncated sphere shape of the bubble does not correspond to actual bubble shapes at early times of bubble growth. The bubble is °attened parallel to the wall in this stage of growth. Therefore the volume equivalent radius does not yield an accurate representation of the actual frontal area of the bubble. That is the reason why the prediction of the hydrodynamic lift force is not good for this case. In the second half of the growth time the bubble becomes elongated away from the wall. It is not growing any more, but it moves away from the wall and pushes the surrounding liquid. This results in the negative hydrodynamic force. Before the de- tachment the neck is formed and this phenomenon is not considered by the model. Deformations should be accounted for by introducing more than one geometrical pa- rameter to describe the shape. Other recommendations given in this thesis consider the improvement of the experimental set-up and using some other measuring tech- niques. A brief description of how the model can be combined with commercially available packages has been provided. Boiling is the most e±cient, yet least understood, phase change process. The work presented in this thesis leads to an increased understanding of the physical phe- nomenon of the bubble growing and detaching in °ow boiling. The obtained knowl- edge should be used to improve modeling of this process and to be applied in industry.