Potential Flow Theory Research Articles

The hydrodynamic pressure analysis and simplified calculation method of added mass of oscillating horizontal cylinder in finite water depth

Based on the potential flow theory, the hydrodynamic pressure governing equation of an incompressible and ideal fluid acting on a single oscillating horizontal cylinder in finite water depth is derived, solved using the variable separation method. Analytical solutions for the hydrodynamic pressure of the oscillating horizontal cylinder in both sway and heave directions are established via the multipole expansion method and verified against numerical solutions. Using these analytical solutions, the hydrodynamic pressure distributions of the horizontal cylinder under sway and heave motions, varying with dimensionless parameters immersion ratio H (H=h0/h) and diameter-depth ratio L (L=2a/h), are studied. It is found that at the distance of the cylinder from the free surface and seabed is the key factor influencing hydrodynamic pressure distribution. Additionally, the added mass was calculated through integration of hydrodynamic pressure, and the variation of added mass coefficients with L‾ (L‾=2a/h0) and H‾(H‾=2a/(h−h0)) is analyzed. It is observed that, in both sway and heave motions, added mass coefficients increase with decreasing L‾ and increasing H‾. Simplified calculation formulas for added mass coefficients of the horizontal cylinder under sway and heave motions are developed using a two-step fitting method. Finally, errors in calculating the added mass coefficients are compared between the simplified calculation formulas and the analytical solution, showing errors of less than 5%, indicating high accuracy of the proposed simplified calculation formulas for added mass coefficients.

Visualization of Potential Flow: Dealing with the Branch Cuts

The theory of potential flow is important in several application fields, in particular: in aero dynamics, fluid dynamics, electrostatics, porous media flow. In the classical approach flow is described by a potential function of the complex plane into the complex plane. Using potential function contouring the visualizing of streamlines in flow nets can reveal important characteristics of the flow in question, for which alternative methods fail. However, branch cuts of important potential functions pose a problem for the visual representation. Here methods are outlined how to deal with the problem: (1) to be aware that equalities, common in real number algebra, may not hold in the complex number space; (2) to partition the complex plane into sub-domains on which the functions are evaluated sequentially. The description of the methods uses superpositions of complex logarithms as examples, but the ideas can be adopted for the visualisation to other potentials as well.

Freak wave generation modulated by high wind and linear shear flow in finite water depth

In finite water depths, the effects of high winds and linear shear flow (LSF), encompassing both uniform flow and constant vorticity shear flow on freak wave generation are explored. A nonlinear Schrödinger equation, adjusted for high wind and LSF conditions, is derived using potential flow theory and the multiscale method. This equation accounts for the modulational instability (MI) of water waves and the evolution of freak wave amplitudes. MI analysis reveals that for waves to maintain MI, high tail winds (moving in the same direction as the wave) require less vorticity and deeper water, while adverse winds (moving in the opposite direction) necessitate more vorticity and shallower water depths compared to conditions without wind. Uniform up-flows (down-flows), positive (negative) vorticity, and high tail (adverse) winds, which inhibit (promote) wave propagation, increase (decrease) the MI growth rate and amplify (diminish) freak wave heights. It is through this MI that the generation of freak waves is either promoted or inhibited.

A hybrid modeling approach: dynamic simulation of two-phase fluid flow in compacting gas condensate reservoirs using potential flow theory

Simulating the flow processes of complex hydrocarbon mixtures, such as gas condensate mixtures and volatile oils, in deep reservoirs is one of the most challenging problems in reservoir hydrodynamics. The challenge lies in meeting three requirements simultaneously when creating a simulator: high accuracy, low computational cost, and high reliability. These metrics determine the performance of the simulation. Meeting all these requirements at the same time necessitates a hybrid approach to solving the problem and optimizing the computational algorithm in terms of CPU time. A new technique has been developed for hybrid modeling of the development of deposits of complex hydrocarbon mixtures. This technique integrates the theory of potential flow, the Binary Flow Model (which accounts for rock compaction, PVT properties of reservoir fluids, phase transformation, and mass transfer between phases), and the material balance equations of the hydrocarbon system using time discretization. In this case, to linearize nonlinear differential equations for the flow of a gascondensate mixture, the method of averaging reservoir pressure along the radial coordinate was used. By introducing the Khrestianovich function, an algorithm was obtained to determine the rate of inflow of the gas-condensate mixture to the well. Using material balance equations for gas and condensate, it was possible to obtain differential equations that describe changes in reservoir pressure and condensate saturation over time. Based on this technique, a simulator for a gas condensate reservoir was created, enabling computer studies to be conducted. The results demonstrated the proposed technique's good accuracy compared with the results of the semi-analytical solution. Keywords: dynamic modeling; simulation; monitoring; streamline; hybrid modeling; binary model.

AN EVALUATION OF WAVE ENERGY GENERATION AND COST OF ENERGY IN THE BLACK SEA

The performance of several axisymmetric wave energy converters is studied by evaluating the yearly energy capture and the expense of energy in two sites in the Black Sea. The added mass, hydrodynamic damping, and wave forces exerted on the floats are calculated by a 3D panel method based on potential flow theory. The oscillations of the floats are calculated in the time domain by employing a family of Runge-Kutta Methods at various levels of accuracy and the yearly energy generated is calculated by taking into account the occurrence of sea states in a year. The expense of energy captured by each wave energy converter is evaluated by calculating the Levelized Cost of Energy. The results show that the WECs with Berkeley Wedge-Shaped floats generate the maximum amount of energy in Sinop and Hopa. The most economical wave energy converters are those with a cone float and with a Berkeley Wedge-Shaped float in Sinop and Hopa, respectively.

Study on the performance and efficiency of multi-objective evolutionary algorithms for trimaran outrigger layout seakeeping optimization problem

Trimaran as a high-performance vessel, possesses excellent characteristics such as high speed, low wave-making resistance, and good seakeeping performance. Different from conventional monohull ship, the design of a trimaran requires additional consideration of the outrigger layout, as the position of two outriggers can affect its hydrodynamic performance. In this study, high-speed slender body potential flow theory (also named the 2D+t theory or the 2.5D method) was employed to calculate the heave and pitch motion in order to evaluate the seakeeping performance of trimarans with different outrigger layouts at varying speeds. Model experiments were subsequently conducted to validate the effectiveness of the 2.5D method in simulating the motion of trimarans under different outrigger layouts. Three multi-objective evolutionary algorithms, including Non-dominated sorting genetic algorithm II (NSGA-II), Non-dominated sorting genetic algorithm III (NSGA-III), and Multi-objective evolutionary algorithm based on decomposition (MOEA/D), as well as their applications in the optimization of trimaran outrigger layouts were introduced. Utilizing the 2.5D method based computational program as the solver, the efficiency and performance of these multi-objective evolutionary algorithms were compared. Discuss the advantages and disadvantages of three multi-objective evolutionary algorithms in solving trimaran outrigger layout optimization problem by comparing the optimization results from two aspects: optimization efficiency, and optimal solution performance. The results indicate that for optimization efficiency, the weighted sum approach based MOEA/D exhibits best optimization efficiency. NSGA-II and NSGA-III show a good advantage in terms of optimal solution performance, and compared to NSGA-II, NSGA-III can obtain more Pareto solutions.

Hydrodynamic performance of multi-chamber oscillating water columns in a caisson array

A theoretical model based on the linear potential flow theory and eigenfunction expansion-matching method is developed to analyze the interaction between water waves and multi-chamber oscillating water columns (OWCs) embedded in a caisson array. The semi-analytical solution consists of the diffraction and radiation components of periodic OWCs. The velocity singularity at the tip of the OWC chamber walls is resolved by implementing a Chebyshev polynomial expansion. The unknown expansion coefficients are determined by the continuity equations of velocity and pressure at the interface of subdomains. The semi-analytical solution is verified using the Haskind relation and the conservation law of wave energy flux. It is found that multi-chamber OWCs have higher hydrodynamic efficiency over a broader frequency bandwidth than traditional single- and dual-chamber OWCs. The maximum hydrodynamic efficiency η increases with increasing of chamber number (J), from 0.5 (J = 1) to nearly 1.0 (J = 8 and 12). It is also found that a larger incident wave angle leads to a narrower frequency bandwidth for energy capturing. Increasing the incident wave angle from π/3 to 5π/12 results in a decrease of the first cutoff frequency kc from 2.41 to 2.02, and therefore results in the energy capture bandwidth narrowing accordingly. Both constructive and destructive hydrodynamic interactions between caissons array and OWCs are observed over the tested frequency range. Interestingly, when configuration of the OWC chambers is reversed, the transmission coefficient remains unchanged.

Spatially variable seismic underground motions in layered porous seabed medium induced plane wave

In ocean engineering anti-seismic filed, the marine environment is usually regarded as the coupling field of seawater-layered porous seabed-elastic bedrock. This paper presents a theoretical method to study the spatially variable seismic underground motions in stratified seabed system. Based on the potential flow theory, Biot's porous model and random vibration theory, the transfer function and coherence function model of the underground seismic motions in the marine coupling field are derived. On the basis of the above theoretical derivation, the program of the spatial variability seismic underground motions of the coupling field is simulated and developed, and its accuracy and effectiveness are verified. Moreover, the effects of soil stiffness and overlying seawater level on the seismic response are also analyzed. Numerical results show that spatially variable seismic underground motions are significantly different from those on the ocean bottom. The simulation of spatially variable seismic underground motions for layered seabed field is significant for both theoretical study and ocean engineering application.

Theoretical investigation on a heaving wave energy converter-dual-arc breakwater integration system array

The hydrodynamic performance of an array of heaving wave energy converter (WEC)-dual-arc breakwater integration systems was investigated using a theoretical model in the present paper based on the potential flow theory, with each dual-arc breakwater consisting of a bottom-mounted inner solid and outer perforated arc-shaped cylinder. The multiple scattering problem was solved using a hybrid iterative method. The mean transmission coefficient was introduced to quantify the wave attenuation performance. After successfully validating the theoretical model, the array effect and the hydrodynamic characteristics of the proposed integration system array are investigated. Focusing on the layout of a linear equidistant column, the calculation results indicate that the WEC and dual-arc breakwater array have mutual benefits in enhancing the wave energy extraction and wave attenuation performance. Compared to an array of bottom-mounted solid and porous cylinders, the proposed integration system array provides much better protection to the leeward region except at a very low wave frequency. In the considered frequency region, a closely arranged integration system array under the perpendicular incident waves has a very constructive array effect on the overall performance. For two staggered columns of integration systems, the wave energy absorption of the leeward column is improved and the sheltering effect to the leeward region is better at a high frequency as compared to the one-column layout; in contrast, the overall performance for two aligned columns is better at a low frequency.

Response of an Oscillating Water Column spanning a circle sector and embedded in a circular platform

This paper develops a semi-analytical solution of a water waves problem concerning the interaction between linear waves and an Oscillating Water Column (OWC) embedded into a circular platform. Unlike similar studies available in the literature, the proposed investigation concerns a realistic situation involving the use of an OWC having limited angular width. Such a configuration is likely to be employed in the arrangement of platforms in which the use of a large OWC is neither efficient nor feasible.The proposed solution is developed in the framework of the linear potential flow theory. The solution relies on the use of a domain decomposition approach involving eigen-function expansions of velocity potentials with unknown coefficients, which are calculated via a matching technique. The solution is utilized for conducting relevant parameter studies concerning the effects of the main geometrical parameters on the overall system performance and on the system hydrodynamic parameters.

Hydrodynamic Characteristics Analysis and Mooring System Optimization of an Innovative Deep-Sea Aquaculture Platform

As nearshore aquaculture spaces become saturated, the development of fisheries aquaculture for deep sea has become an inevitable trend. This paper proposes an innovative deep-sea aquaculture platform that incorporates a vessel-shaped main structure and a single-point mooring system. The potential flow theory and the Morison equation are utilized to calculate the hydrodynamic loads on the main structure and the netting and mooring systems, respectively. The deformation and force of the netting in current are simulated, and the accuracy of the analytical methods used is validated based on experimental results. The influences of the netting system on the hydrodynamic characteristics of the platform are analyzed. Optimization on the single-point mooring system is conducted under static and dynamic conditions, considering the influences of various mooring parameters, including mooring line length, buoyancy of buoys, and mass of sinkers. The patterns of changes in motion response, mooring line tension, and minimum touchdown length under different mooring parameters are calculated and analyzed. The results indicate that changes in mooring line length have minimal impact on the dynamic response of the platform and mooring system. The addition of appropriate buoys or sinkers can reduce the motion response of the platform and the tension in the mooring lines. Moreover, compared to adding buoys, incorporating sinkers more effectively enhances the overall safety and stability of the platform system.

Numerical Calibration of the Mooring System for a Semi-Submersible Floating Wind Turbine Model

Abstract Numerical modeling of the floating offshore wind turbine (FOWT) dynamics plays a critical role at the design stage of a floating wind project. Still, there exist challenges for verification of efficient engineering models against experimental results. Recently, an experimental campaign was carried out for a 1:96 downscaled model of the OC4-DeepCWind semi-submersible platform with mooring lines made of fiber ropes and chains. Leveraging the results of this campaign, this paper focuses on the development and calibration of a numerical model for the semi-submersible platform with a focus on the dynamic responses under bichromatic waves. In the numerical model, the hydrodynamic loads are modeled based on the potential flow theory with Morison drag. The lumped mass method is applied to model the mooring system. Both free decay tests and bichromatic wave conditions are considered in the model calibration process, and key uncertain parameters (e.g., mooring line length) that affect the response have been identified and discussed. Using the proposed calibration procedure, we establish a reasonably good numerical model for prediction of the platform motion and mooring dynamics. The low-frequency responses of the platform under bichromatic waves are well-captured. These outcomes contribute to the development of efficient numerical FOWT models under experimental uncertainty.

Swirling Capillary Instability of Rivlin–Ericksen Liquid with Heat Transfer and Axial Electric Field

The mutual influences of the electric field, rotation, and heat transmission find applications in controlled drug delivery systems, precise microfluidic manipulation, and advanced materials’ processing techniques due to their ability to tailor fluid behavior and surface morphology with enhanced precision and efficiency. Capillary instability has widespread relevance in various natural and industrial processes, ranging from the breakup of liquid jets and the formation of droplets in inkjet printing to the dynamics of thin liquid films and the behavior of liquid bridges in microgravity environments. This study examines the swirling impact on the instability arising from the capillary effects at the boundary of Rivlin–Ericksen and viscous liquids, influenced by an axial electric field, heat, and mass transmission. Capillary instability arises when the cohesive forces at the interface between two fluids are disrupted by perturbations, leading to the formation of characteristic patterns such as waves or droplets. The influence of gravity and fluid flow velocity is disregarded in the context of capillary instability analyses. The annular region is formed by two cylinders: one containing a viscous fluid and the other a Rivlin–Ericksen viscoelastic fluid. The Rivlin–Ericksen model is pivotal for comprehending the characteristics of viscoelastic fluids, widely utilized in industrial and biological contexts. It precisely characterizes their rheological complexities, encompassing elasticity and viscosity, critical for forecasting flow dynamics in polymer processing, food production, and drug delivery. Moreover, its applications extend to biomedical engineering, offering insights crucial for medical device design and understanding biological phenomena like blood flow. The inside cylinder remains stationary, and the outside cylinder rotates at a steady pace. A numerically analyzed quadratic growth rate is obtained from perturbed equations using potential flow theory and the Rivlin–Ericksen fluid model. The findings demonstrate enhanced stability due to the heat and mass transfer and increased stability from swirling. Notably, the heat transfer stabilizes the interface, while the density ratio and centrifuge number also impact stability. An axial electric field exhibits a dual effect, with certain permittivity and conductivity ratios causing perturbation growth decay or expansion.

Floating wind turbine response in uni- and multi-directional nonlinear waves by numerical and experimental investigations

Natural sea waves are typically multi-directional. However, the existing studies on the interaction of waves and structures mostly concentrate on uni-directional waves. In this study, using a higher-order boundary element method based on the nonlinear potential flow theory and the perturbation expansion technique, a numerical model is developed to investigate the hydrodynamic performance of a semi-submersible wind turbine foundation in uni- and multi-directional waves. Comprehensive validations with the wave-tank experiment are conducted. It is found that the significant platform response increases with the peak wave period in uni-directional irregular waves, while the high-frequency “energy” ratio changes little. The significant wave height hardly influences motion responses from either the time- or the frequency-domain perspective. In multi-directional irregular waves, the translational motions exhibit monotonicity with wave directionality. The energy concentration around the primary direction leads to a dominant wave-frequency motion and an increase in the high-frequency “energy” ratio. Although the individual modal motion responses are variable functions of wave nonlinearity, their averaged translational and rotational motions are nearly constant, indicating an energy transition or a trade-off relationship among the modal motions. In addition, unlike the uni-directional wave case, the low- and high-frequency “energy” ratios increase quadratically and decrease linearly with the significant wave height in multi-directional waves, respectively. All these findings demonstrate that wave directionality can change the wave–structure interaction properties and therefore needs to be adequately considered in engineering applications.

A discrete-module-beam hydroelasticity method with finite element theory in analyzing VLFS in different engineering scenarios

A numerical tool is developed in the framework of the Discrete-Module-Beam method to analyze hydroelasticity of very large floating structures (VLFS) such as floating offshore photovoltaic platforms (FOPV). The proposed method utilizes finite element theory to perform structural analysis. The 3D potential flow theory is used to perform a hydrodynamic analysis after macro-submodule division. For the structural analysis part, the platform is divided into macro-submodules and each macro-submodule is represented by a beam, which is then further discretized into micro beam elements with the nodes categorized into three groups, that is, the lumped mass, the boundary nodes and the inner nodes. Derivation of the lumped-mass stiffness matrix and recovery of the displacement distribution are given. Procedures to deal with interconnections, complex boundary conditions and unsteady loads are elaborated. Good agreement is obtained in different loading scenarios to the numerical and experimental results.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

Multi-fidelity CFD for obtaining the runner blade profile parameters of a Francis turbine for optimum hydrodynamic performance

The high fidelity Navier Stokes equations based CFD codes precisely take care of the turbulent and viscous effects of complex flows passing through the hydraulic turbines. However, for preliminary design synthesis and analysis purposes, this full 3D flow can be assumed as a combination of two 2D flows (meridional axi-symmetric flow and blade-to-blade or cascade flow) which is the basis of low fidelity potential flow theory for hydraulic turbines. This paper presents the utilities of high as well as low fidelity CFD analyses for obtaining a runner blade design which yields an optimum hydrodynamic performance of a prototype Francis Turbine. The complete flow domain of the Francis turbine has been considered for the high-fidelity analysis which is carried out by using ANSYS CFX 16.0 for different operating conditions. Whereas, for the low fidelity investigations, full three-dimensional flow domains of different blade rows (i.e., stay vanes, guide vanes and runner) of the Francis turbine is divided into two 2D flow domains (i.e., an axisymmetric annulus of the turbine space for meridional flow analysis and cascades at different sections from hub to shroud for blade-to-blade analysis). By using the low fidelity analysis, runner blade design parameters have been adequately varied in order to obtain a population of different promising runner blade designs. Performances of these promising designs are evaluated, and the obtained results are thoroughly analysed through the response surface analysis. An optimized hydrodynamic performance design of the runner is obtained for the target values of responses (here, swirl velocity at trailing edge of the runner (Cu2) and stagnation pressure at trailing edge of the runner (P02/ρ)) at different sections from hub to shroud by determining the design parameters of blade profiles at different sections. The adopted multi-fidelity CFD approach is found very effective and has the potential to yield reasonably accurate hydraulic designs of the Francis turbine in considerably lesser time and cost.

A frequency-domain hydroelastic analysis of a membrane-based offshore floating photovoltaic platform in regular waves

This study presents an approach for analyzing the hydroelastic response of membrane-based floating photovoltaic (PV) platforms. The structural deformation of the platform’s main components, including a floater and a membrane, is further described through a comprehensive set of in-plane and out-of-plane modes. This analysis employs potential flow theory and 3D hydroelasticity theory to evaluate the hydrodynamic loads. Additionally, the Morison equation is utilized to express the drag term associated with the floater’s in-plane motion. Addressing the connection between the floater and the membrane is achieved through the Lagrange multiplier method. Ultimately, this study establishes a frequency-domain coupled dynamic equation for the platform. The response results provide modal amplitudes and displacement data for test points, revealing that under low-frequency conditions, the flexible floater and the membrane conform to wave profiles. As the frequency increases, the impact of the floater’s stiffness becomes prominent, resulting in a substantial three-dimensional interaction effect. In addition, this study examines various structural parameters, specifically the membrane pretension, elastic modulus, and the bending stiffness of the floater, to illustrate their influence on the motion and deformation of the platform. This work contributes to a deeper comprehension of membrane-based floating PV systems and their practical applications.

Wave attenuation by three-dimensional circular floating sea ice: Regular and irregular waves

The evolution of ice conditions and wave patterns in polar water areas is complex, and studying the hydrodynamic response between sea ice and waves is crucial. In this study, the hydrodynamic response of sea ice in infinitely deep water is investigated by a sea ice scattering model based on linear potential flow and thin plate approximation theory. Building upon regular wave and sea ice scattering models, an irregular wave model was established and analyzed. This paper discusses the factors that influence sea ice resonance in a three-dimensional scattering model. It categorizes resonance phenomena into strong and weak based on mass and elasticity coefficients and provides a predictive function for identifying strong resonance points. Additionally, the study examines sea ice attenuation from an energy perspective. Research on sea ice in irregular waves indicates a negative correlation between the directional spreading parameter and wave attenuation. An increase in directional spreading parameter weakens the inhibitory effect on the high-frequency part of the waves. Increasing sea ice thickness enhances wave attenuation, exerting an inhibitory effect on waves in the high-frequency region.

Evolution of wind-induced wave groups in water of finite depth

The generation of water waves by wind is a fundamental and much-studied problem of scientific and operational concern. One mechanism that has obtained a wide degree of acceptance and use is the Miles air shear flow instability theory in which water waves grow due to energy transfer from the air at a critical level where the wave phase speed matches the wind speed. In this paper we revisit and extend this theory by examining how the predicted wave growth rate depends on the water depth and the wind shear parameters. At the same time we include frictional effects due to water bottom stress and at the water surface, and add an additional driving term due to wave stress in the air near the sea surface, using a turbulent parametrisation. The theory is developed using a frictional modification of the usual potential flow theory for water waves, the modified Euler equations, coupled to linearised air-flow equations. To assist our analysis we develop a long-wave approximation for the key Miles growth parameter, which explicitly shows how this depends on the water depth and the wind shear parameters. Since our focus is on the development of wave groups, we present a forced nonlinear Schrödinger equation in which the forcing term describes wave growth or decay. For very shallow water the modified Euler equations are reduced to their shallow-water counterpart, which are briefly discussed using Riemann invariants.