Potential Flow Theory Research Articles

Three-dimensional elastic Rayleigh–Taylor instability at the cylindrical interface

This paper presents a linear analysis of elastic Rayleigh–Taylor instability at both cylindrical column and cylindrical shell interfaces. By considering the rotational part of the disturbance flow field, an exact solution is derived, revealing that the most unstable mode is two-dimensional in the cross section. As the column radius decreases, the maximum growth rate increases, while the corresponding azimuthal wave number decreases incrementally until it reaches 1. Thinning the cylindrical shell is found to be a destabilizing effect, leading to an increase in both the cutoff wave number and the most unstable azimuthal wave number. The maximum growth rate usually increases as the shell becomes thinner, except in cases with small radii where feedthrough effects occur. For thin shells with small radii, the cutoff axial wave number is determined by the radius rather than the shell thickness. Comparisons between the growth rates derived from the potential flow theory and the exact solution show significant discrepancies in cylindrical shells, mainly due to substantial deviations in the cutoff wave number.

Dynamic responses of non-isolated and isolated liquid storage tanks under mainshock-aftershock sequences

After the mainshock earthquake, aftershocks often occur frequently, and the destructive effect of aftershocks on structures cannot be ignored. Based on the potential flow theory, the mechanical behavior of liquid is simulated. Considering liquid-solid coupling, material nonlinearity, and liquid sloshing, a three-dimensional numerical calculation model of liquid storage tank is established. No pulse-like and pulse-like mainshock-aftershock sequences are selected, and the seismic responses of non-isolated and isolated liquid storage tanks is compared and studied. The results show that the mainshock-aftershock sequence has a significant impact on the dynamic responses of the liquid storage tank, and the maximum increase rate reaches to 195.4 %. The effect of the mainshock-aftershock sequence on the dynamic responses of non-isolated liquid storage tanks is greater than on the dynamic response of isolated liquid storage tanks. Compared with the pulse-like mainshock-aftershock sequences, the no pulse-like mainshock-aftershock sequences generally have a greater impact on the dynamic responses of the liquid storage tanks. Overall, isolation significantly reduce the impact of mainshock-aftershock sequences on the dynamic responses of liquid storage tanks, and effectively enhance the seismic performance of liquid storage tanks under mainshock-aftershock sequences.

Research on the aero-hydro coupling characteristics of the floating twin-rotor wind turbine system

The concept of installing two wind turbines on a floating platform, known as a floating twin-rotor wind turbine system, has recently garnered significant interest. This configuration can harness greater wind energy resources, reduce installation and mooring costs by sharing mooring lines, and minimize losses due to wake effects between turbines through yaw control. However, previous research has not sufficiently addressed the dynamic performance analysis of such systems. This study focuses on a high-capacity floating twin-rotor wind turbine system and develops an aero-hydrodynamic coupled analysis method based on the free vortex wake method and potential flow theory, specifically tailored for the twin-rotor configuration. This method facilitates real-time iterative calculations of wind and wave loads acting on the system and suggests optimization strategies for its design. Our findings indicate that the design of high-capacity floating twin-rotor systems can significantly reduce costs. Furthermore, the twin-rotor floating system design enhances wake recovery and achieves optimal comprehensive performance when the rotor spacing ratio (S/D) is 1.2 for the IEA 15 MW turbine. The coupled interactions induce periodic variations in aerodynamic performance, with the amplitude of these variations increasing with turbulence intensity. This research lays a theoretical foundation for advancing the design, platform optimization, and coupled computational analyses of large-capacity, large-scale floating twin-rotor wind turbine systems.

Predictive Modeling of Semi-Submersible Floater Motion Using Bi-LSTM Model

Abstract Floating offshore wind turbines (FOWTs) are emerging as a promising renewable energy solution, tapping into the vast wind resources in deep-sea locations. Accurate predictions of heave, pitch, sway, roll, yaw, and surge are essential to ensuring the structural integrity and power generation efficiency of FOWTs. Traditional methods relying on potential flow theory to predict FOWTs’ hydrodynamic responses involve simplifications that may not capture real-world complexities. Although computational fluid dynamics (CFD) simulations offer accuracy, they are computationally expensive. This study explores the use of Bi-directional long-short-term memory (Bi-LSTM) neural networks as an alternative to address computational challenges in predicting FOWTs’ hydrodynamic responses. These networks excel at handling time series data, capturing temporal correlations crucial for understanding FOWT floater motion dynamics. They also effectively capture bidirectional dependencies, enhancing their suitability for this application. The model considers various input parameters, including wave amplitudes, periods, steepness, directions, and floater design characteristics such as stifness, pre-tension, and the free length of mooring lines. The Bi-LSTM model is trained using a subset of the CFD dataset generated for the scaled OC5 semi-submersible platform with mooring, reserving the remainder for validation and testing. The comparison between simulated and predicted motion demonstrated a strong correlation in surge but noticeable discrepancies in heave and pitch. FFT analysis highlighted consistent frequency components but variations in magnitude, suggesting areas for model sensitivity improvement and further investigation into wave interaction dynamics. The correlation coefficients revealed a strong positive correlation for the surge motion, while the heave and pitch motions showed slightly lower correlation coefficients, suggesting better performance in predicting the surge.

Water wave radiation by an array of bottom-mounted surface-piercing concentric cylinders

This paper develops a wave radiation analysis model in horizontal oscillation mode for concentric cylindrical arrays with arbitrary numbers and arrangements within the framework of linear potential flow theory. The concentric cylinders have solid inner cylinders and porous outer cylinders, and they are both bottom-mounted and surface-piercing. The porous boundary conditions of the outer cylinders are treated using Darcy's law, and the flow field is divided into one outer region and N (number of cylinders) inner regions with the outer cylinders as the boundary. Employing eigenfunction expansion and region-matching methods, expressions for the radiation velocity potential of each region are obtained, and then expressions of the added mass and damping coefficient of each cylinder are obtained. Following a rigorous verification of the results against published literature, this paper proceeds to analyze the impact of various parameters, including oscillation modes, outer cylinder permeability, radius ratio, spacing, and the number of cylinders, on the wave radiation characteristics of tandem-arranged cylindrical arrays. The research reveals that when the oscillation direction of the structure is parallel with its arrangement direction, the hydrodynamic coefficient curves exhibit significant spikes, attributed to the influence of the Dirichlet trapped mode. Outside the peak regions, the hydrodynamic coefficient curves display regular fluctuations, which are attributed to the alternating occurrence of constructive and destructive interference effects within the wave field.

Numerical investigation of the effects of short-crested irregular waves on the performance of a floating power capture platform

This paper presents a novel power capture platform concept consisting of a semi-submersible platform and multiple point-absorber wave energy converters (WECs). The primary objective of the current study is to investigate the dynamic behavior of the power capture platform under short-crested irregular wave conditions. A spreading function is used to modify the JONSWAP spectrum into a wave spectrum that accounts for both frequency and direction. To ensure the reliability of the numerical analysis, three-dimensional potential flow theory and boundary element method (BEM) are utilized to perform mesh convergence analysis and hydrodynamic validation of the platform and WEC models. Time-domain simulations are conducted to evaluate the effects of wave directionality on the platform motion, mooring line tension, and power absorption of the WEC array. In addition, three models, “single WEC”, “WEC array” and “fixed power capture platform” are defined. The influence of hydrodynamic interactions and platform motion are predicted by comparing the power absorption of individual WEC, WEC row, and WEC array among these models. The results show that the effects of wave directionality on the performance of the floating power capture platform cannot be ignored. The findings of this study may provide some insights into the design of power capture platforms. Meanwhile, it is recommended to determine the wave characteristics of the target operational area in advance, in order to find out the optimal design for system stability and power absorption.

Global Responses Analysis of Submerged Floating Tunnel Considering Hydroelasticity Effects

To investigate the applicability and differences in wave loads and the dynamic response calculation principles for SFT on an entire-length scale, two numerical models of entire-length SFT with identical dimensions and parameters were established. These models are employed by a 3D diffraction method based on rigid-body assumptions, the potential flow theory and the Dummy-Connection-Mass (DCM) method based on the lumped mass method and Morison equation while considering hydroelasticity effects. The applicability of the potential flow theory and Morison equation for wave load calculation of SFT is presented along with the differences in their dynamic response calculation, which aim to explore the impact on SFT dynamic responses considering hydroelasticity by comparing the numerical calculation results. Furthermore, a comparison between free-end boundary and fixed-end boundary models, established using the DCM method, is conducted to examine the reasonableness of the commonly adopted free-end boundary condition.

Wave-to-wire modelling and hydraulic PTO optimization of a dense point absorber WEC array

We investigate the hydrodynamic interactions and power extraction efficiency of a dense array of Point Absorber (PA) Wave Energy Converters (WECs) clustered around the fixed pillar of a wind turbine –the Ocean Grazer device– with a standard hydraulic Power Take-Off (PTO) system. Using potential flow theory, a detailed wave-to-wire model is developed in WEC-Sim with four distinct hydraulic PTO designs: i) Multi PTO-with individual hydraulic PTO systems for each buoy, ii) Shared PTO V1-with a unified PTO system for the entire array, iii) Shared PTO V2-with the accumulator volume split into two segments, and iv) Shared PTO V3-with four strategically distributed segments. Key parameters such as the diameter of the hydraulic pistons, volume and pre-charged pressure of the high-pressure accumulators, hydraulic motor displacement and the speed of the electric generator are optimized with a genetic algorithm and a parametric analysis across various sea states. The results highlight that strategically allocating the accumulators across the floaters of a dense WEC array can yield significantly higher power production and should be considered at the early design stages.

Investigation of motion response suppression characteristics in floating platforms equipped with novel spiral side plates

AbstractTo enhance the stability of floating wind turbine platforms, this study combines the structural characteristics of helical side plates and proposes the installation of serrated helical side plates on Spar wind turbine platforms. Based on potential flow theory, the present study employs blade element momentum theory and radiation‐diffraction theory. Upon establishing a dynamic data link library, wind‐wave coupling was implemented, and the dynamic response characteristics of platforms with different helical side plates were compared. The results indicate that in the frequency domain analysis, the platform with serrated helical side plates demonstrates reduced sensitivity to waves, with a particularly notable increase in added mass in the heave direction, suggesting excellent hydrodynamic performance. In the time domain analysis, improvements in the platform's surge and heave stability performances were observed, measuring 10.99% and 10.64%, respectively, in extreme conditions. Owing to the unique features of the serrated structure, the tension in the mooring chains on the wave‐facing side is reduced, thereby effectively lowering the fatigue load on the mooring chains.

An Experimental and Numerical Study of Motion Responses of Multi-Body Arrays with Hinge Connections

Hinged multi-body systems are gaining popularity in the field of ocean engineering. Their performance is commonly evaluated using numerical simulations, but comparisons with experimental data are required to ensure the accuracy of the computational tools. However, there is a dearth of experimental studies on the motion performance of hinged multi-body systems, particularly those involving more than two hinged floating bodies. This study aims to fill this gap in experimental data for hinged multi-body systems beyond two bodies. The rectangular box was chosen as the test model due to its stable hydrodynamic properties and ease of numerical modelling. Five identical boxes were prefabricated and subsequently tested in the pool in a sequence ranging from one to five boxes to capture the motion performance. Additionally, a numerical programme based on potential flow theory was developed for mutual validation with the experimental data. Firstly, the physical properties of each box were determined through equations calculation and a free decay test, enabling the acquisition of all parameters for conducting numerical simulations. Then, the response amplitude operator (RAO) curves for the heave and pitch motion of a single box were depicted, and the results indicated that the resonant frequency in pitch direction obtained from the regular wave test was consistent with that obtained from the free decay test. Finally, the motion RAO curves of hinged multi-body systems were presented and analysed. The agreement between the measured and computed results confirms the suitability of the experimental data presented in this study as benchmark data for validating numerical simulations.

Hydrodynamic performance characteristics of small-scale in-situ buoys with critical motion requirements

As the accuracy of high-precision oceanographic measurement instruments increases, the operational requirements for buoy motion become critical. This study focuses on the small-scale in-situ buoy, optimizing buoy configuration to ensure stability and performance. Aiming at the special structure which consists of a large floating column and several small tube connectors, a method for evaluating the hydrodynamic performance is proposed which combines potential flow theory with Morison equation. And the method validity is confirmed using experimental data. The performances analysis of different type buoy with catenary or taut mooring system are developed. According to the critical motion requirements for the long-term stability, the cylindrical type buoy equipped with a catenary mooring system is regarded as the most stable and economical choice, exhibiting a surge motion response of 4.07 m, a heave motion response of 2.89 m, and a pitch motion response of 9.37°. Furthermore, the anchor chain acts as an elastic damper which can mitigate the transient impact of the environmental loads, greatly limiting the amplitude of the longitudinal and heaving motions. And the maximum mooring line tension is 249.28 kN, which is significantly lower than other schemes. The evaluation method offers a technical support for engineering applications.

Rayleigh–Taylor instability in a Casson fluid layer with heat and mass transfer

This study investigates the stability of the interface between two fluids, a Casson fluid on top and a viscous fluid below, with heat and mass transfer occurring between them. We used the potential flow theory, which simplifies the problem by ignoring tangential stresses and focusing on normal stress balance. We did not consider no-slip conditions at the boundaries, assuming zero normal velocity at these rigid boundaries instead. A second-order polynomial equation was developed to calculate the growth rate of instabilities and solved numerically using the Newton–Raphson method. The results showed that heat and mass transfer improved the stability of the interface, even though the Atwood number, a measure of instability, remained high.

Layout Optimization of Wave Energy Park Based on Multi-Objective Optimization Algorithm

Abstract In this paper, both semi-analytical method and numerical simulation is applied to investigate the hydrodynamic behavior of large arrays of point-absorber wave energy converters (WECs). To analyze wave interactions among multiple WECs within an array, a semi-analytical model is developed based on the potential flow theory and the matched eigen-function expansions method. The fluid domain is divided into two kinds of regions: interior regions underneath the cylinders and an exterior region surrounding all the cylinders. The matched eigenfunction expansions method is employed to solve the radiation potential problem in each domain, and the hydrodynamic coefficients and motion response of the cylinders in the array are evaluated. To validate the accuracy of the semi-analytical method, WAMIT is adopted to simulate the wave energy park numerically and compared with the results by the semi-analytical model. The hydrodynamic characteristics and power absorption performance of the WECs within the wave energy park are analyzed. The power performance of a wave energy park is studied as functions of layout geometry, incident wave direction and separation distance between WECs respectively. Finally, MOPSO based on a surrogate model is used to optimize the layout of wave energy array.

Performance assessment of a Triple Coaxial-Cylinder Wave-Energy Converter (TCWEC)

We propose a novel Triple Coaxial-cylinder Wave-Energy Converter (TCWEC) system, as an evolution of the commonly deployed dual-coaxial cylinder WEC (DCWEC). TCWEC consists of one inner cylinder and two concentric outer cylinders, characterized by two coupled resonant frequencies, improving wave power absorption. A semi-analytical model, based on potential flow theory and matched eigenfunction expansions, is developed to analyze the 3-Degrees of Freedom (DOF) system. The viscous drag coefficients are determined by Computational Fluid Dynamics (CFD) simulations and employed as equivalent linear damping. Analysis of impact of the viscous flow-separation factor fvis on the capture width indicates that the higher energy-absorption capability of TCWEC is not merely attributed to a smaller fvis value, but rather a planned split of the outer cylinder in DCWEC design into two cylinders in TCWEC, so as to produce an effectively broader resonance property. Under identical sea conditions, it is found that, compared to DCWEC, the optimal capture width of TCWEC is increased by as much as 77% in regular waves. In irregular waves, the optimal capture width is increased up to 40% across the entire frequency range. These findings suggest that the energy absorption efficiency of TCWEC is promising and its potential for real-world applications.

Analysis and research on the hydrodynamic performance of offshore floating photovoltaic systems under large tidal variations

Abstract This paper focuses on the multi-module connected offshore floating photovoltaic system, designing a mooring system with buoys, considering the effects of buoy size, position on the motion response of the photovoltaic system, mooring cable tension, and photovoltaic air gap. Based on the three-dimensional potential flow theory, optimal parameters for buoys were selected using regular waves at an average depth of 10 meters. Subsequently, factors such as tidal differences, randomness of waves, wind, and currents were taken into account, and the motion response, mooring tension, and photovoltaic air gap were calculated separately at water depths of 8 m, 10 m, and 12 m. The analysis results indicate that the offshore floating photovoltaic system with a buoy mooring system, under the influence of tidal differences, does not show significant differences in the minimum air-gap height of the photovoltaic system, ensuring safe and stable operation.

Comparative study of analytical models with linear and quadratic pressure drop conditions on a perforated plate in water waves

Proper pressure drop conditions are essential in predicting hydrodynamic performance of perforated structures in the framework of a potential flow theory. In this study, we investigate water waves passing through a perforated plate with various pressure drop models to examine how pressure drop conditions affect the hydrodynamic performance of perforated structures. We derive the analytical solutions of waves across the perforated plate by adopting three commonly pressure drop conditions, including one linear pressure drop condition (LPDC), and two quadratic pressure drop conditions (QPDCs). A series of laboratory experiments are conducted to validate the present theoretical results. We compare the hydrodynamic performance between the experimental data and the theoretical solutions with the three different pressure drop models, typically for wave reflection coefficients, dynamic pressures, and velocity fields measured by the technique of particle image velocimetry in the experiments. It is found that the existing pressure drop models can predict well wave reflection coefficients, dynamic pressure, and velocity profiles at certain conditions. However, the linear wave solutions associated with LPDC or QPDCs generally underpredict the amplitude of particle velocity near the free surface on the perforated plate. This underestimation increases largely as the wave steepness increases. The LPDC performance relies much on the selection of empirical coefficients. For the QPDCs, the analytical models show deviated results from the experimental data for wave reflection coefficients when the wave steepness is relatively low.

Omnidirectional control of the wake of a circular cylinder with spinning rods subject to a turbulent flow

We numerically investigate the attribute of omnidirectionality of the flow-control system comprised of a large circular cylinder equipped with eight spinning rods of smaller diameter, subject to an incoming flow that adopts different angles of attack. Detached-eddy simulations are employed to compute hydrodynamic loads and to provide flow topology at a Reynolds number of 1000. Two cases are assessed regarding the rods angular velocities. In case 0, all rods spun with the same angular velocity. In case 1, velocities were inspired by potential-flow theory. The two systems have the same input kinetic energy in common. To assess the system response, the velocities were increased proportionally. Both cases succeeded in reducing the mean drag. However, while case 1 proved to become ever “more omnidirectional” with increasing angular velocities, case 0 demonstrated to be prone to the angle of attack as it was unable to suppress vortex shedding for sufficiently large slopes of the incoming flow, and in such circumstances, unable to reduce hydrodynamic forces. We verify that the lift is mitigated in case 1, in contrast to case 0. Even for a vortex-free downstream flow resulting from configurations of high velocities and high angle of attack, the latter produces asymmetric recirculation regions downstream of the system that drive a pressure imbalance. The different outcomes of the two systems are also explored from the viewpoint of power consumption, and it is revealed that the omnidirectionality of case 1 is intrinsically related to the emphasis imposed on rotation rates of a subset of the eight rods.

Струйный эффект при возникновении присоединенной каверны от системы импульсивных давлений

We consider the plane problem of the emergence of an attached cavity caused by the sudden action of impulsive pressures at some initial time. It is assumed that these pressures are distributed on the upper part of the boundary of a stationary circular cylinder immersed in liquid. A problem with unilateral constraints is formulated, on the basis of which the flow of liquid at the initial moment of time and the initial zone of separation of liquid particles are determined. At the next moments of time, an attached cavity is formed, the shape of which is determined based on the solution of the dynamic initial-boundary value problem of the theory of potential flows of an ideal incompressible fluid with free boundaries. The main unknowns in it are the velocity potential, the shape of the cavity, the dynamics of the separation points, and the perturbation of the external free boundary of the liquid. It is required to study the posed problem at short times, focusing on the behavior of the internal free boundary of the liquid near the separation points. When studying this problem, pressure in the cavern, which is created artificially, plays an important role. At low pressures, the internal free boundary of the liquid near the separation point is located on opposite sides of this point. In this case, the end part of the cavity resembles a stream of gas directed along the boundary of the cylinder towards the liquid.

On modeling added mass and circulation terms with fast potential-flow methods for oscillating-foil propulsors

The design of cycloidal thrusters and other oscillating foil propulsors requires fast tools that provide accurate estimates of propulsor hydrodynamic performance and mechanical loads. Potential-flow theory coupled with empirical formulae that account for viscous effects is the best choice for fast multi-parameter optimization. Within this context, oscillating foils are usually approximated as thin wings with flow solutions derived from small-disturbance theory. Added mass (non-circulatory) effects may be relevant even under such assumptions. They can be easily included in the flow equations assuming that the foil is a flat plate heaving and pitching. However, for blade motions involving complex trajectories like those in Voith Schneider propellers, the foils describe cycloidal loops, and the assumption of small pitch angles is no longer valid. Therefore, a more accurate modeling of added mass and circulatory terms is required.This paper presents extensions to a previous model, which allows for a more precise representation of the added mass terms in the potential flow equations, combining low computational cost and accurate modeling. The results show clear improvement in the evolution foil forces in time when the new approach is used. The extensions are especially needed for the simulations of foils describing complex paths with large variations of pitch angle. Applications to transverse-axis cycloidal propulsors are presented as well as to unconventional counter-flapping propulsors that have recently appeared in the scientific literature. Validation of the method with RANS computations is provided.

A frequency domain analysis method for the dynamic response of a submerged floating tunnel under wave action

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism.