Potential Flow Solver Research Articles

Experimental decomposition of nonlinear hydrodynamic loads and hydroelastic responses in wave–structure interactions of monopile wind turbines

This study explores the nonlinear effects of hydrodynamic loads and hydroelastic responses in monopile-supported offshore wind turbines, with a focus on their harmonic structures. High-quality experimental data were collected in a shallow water basin across various irregular waves. Their harmonic components up to the fourth order were successfully isolated using a novel four-phase decomposition technique, which effectively extracts harmonics from random time series. The results highlight significant contributions of higher-order harmonics across various sea states. Specifically, two physical models were employed: a flexible monopile to capture structural hydroelastic deformations during large wave events and a rigid monopile to accurately estimate hydrodynamic loads without hydroelastic effects. Additionally, numerical results from fully nonlinear potential-flow calculations were compared, revealing that while the potential-flow solver underestimates total wave loading, especially for higher harmonics. In terms of the free-surface elevations and hydrodynamic forces, this study confirms that their higher-order harmonics align well with the scaling of their corresponding linear components in both amplitude and phase. This enables the prediction of higher-order profiles based solely on their linear components. However, this efficient model is inadequate for accurately estimating the higher-order harmonics of monopile's hydroelastic responses during these extreme wave events, highlighting the need for further refinement.

Self-propulsion performance prediction in calm water based on RANS/TEBEM coupling method

This paper proposes a hybrid RANS/TEBEM method to conduct self-propulsion prediction in calm water with accuracy and improve its efficiency by means of larger time step. In the coupling procedure, the rotating propeller is represented by time-averaged, spatial inhomogeneous body force field obtained from the potential flow solver based on Taylor Expansion Boundary Element Method (TEBEM) in RANS simulation. Effective wake is evaluated by subtracting induced velocities computed by potential solver from total velocities in RANS solver at a coupling plane upstream of propeller plane. The influence of coupling plane position and grid density on the numerical results is also investigated. Through KCS and KVLCC2 cases, it is shown that the predicted value of propeller revolution speed is within 4% of the experimental value, verifying the robustness and reliability of this method.

Hydrodynamic analysis of an oscillating water column array in presence of variable bathymetry

In this study, hydrodynamic analysis of an oscillating water column (OWC) array in the presence of the variable bathymetry (seafloor depth) is performed by using a semi-analytical potential-flow solver. Within the framework of linear theory, the boundary-value problem associated with wave diffraction and radiation by an OWC array with variable bathymetry is formulated and the semi-analytical hydrodynamic model is developed using the matched eigenfunction expansion method. The fluid domain above variable bathymetry is mathematically discretized into multiple subdomains using the boundary approximation method. The Haskind relation and the energy flux conservation law are used to verify the semi-analytical model. The hydrodynamic performance of the OWC array in the presence of the ripple and coral reef bathymetries are investigated in further. Pronounced oscillations are observed for the curve of reflection coefficient Cr and hydrodynamic efficiency η for cases with ripple and coral reef bathymetries. Bragg resonance is identified as the triggering of the strong oscillations in Cr and η for case of ripple bathymetry. The primary frequency of Bragg resonance and the peaked value of Cr converge as the ripple number increases (i.e., Ns > 3). Particularly, for cases with coral reef bathymetry, the wave resonance modal in open-ended basins results in a significant wave amplification at the weather side of the OWC array.

BIMBAMBUM: A potential flow solver for single cavitation bubble dynamics

In the absence of analytical solutions for the dynamics of non-spherical cavitation bubbles, we have implemented a numerical simulation solver based on the boundary integral method (BIM) that models the behavior of a single bubble near an interface between two fluids. The density ratio between the two media can be adjusted to represent different types of boundaries, such as a rigid boundary or a free surface. The solver allows not only the computation of the dynamics of the bubble and the fluid-fluid interface, but also, in a secondary processing phase, the computation of the surrounding flow field quantities. We present here the detailed implementation of this solver and validate its capabilities using theoretical solutions, experimental observations, and results from other simulation softwares. This solver is called BIMBAMBUM which stands for Boundary Integral Method for Bubble Analysis and Modeling in Bounded and Unbounded Media. Program summaryProgram Title: BIMBAMBUMCPC Library link to program files:https://doi.org/10.17632/89vv35pmhr.1Licensing provisions: GPLv3Programming language: C++ and PythonNature of problem: The code solves the axisymmetric dynamics of single cavitation bubble in the vicinity of different types of boundaries. The boundaries are treated as an interface between two fluids, where the fluids can have different density ratios. The two fluids are considered inviscid and incompressible and the associated flows irrotational so that Laplace's equation is valid everywhere.Solution method: A boundary integral method is used to calculate the velocities on the discretized bubble surface and the fluid-fluid interface. The position of these boundaries can then be updated in time using a Lagrangian approach. In the fluid domain surrounding the bubble, the velocities and pressure are estimated using a combination of the boundary integral method and finite differences.Additional comments including restrictions and unusual features: The code solves the bubble dynamics as long as its surface remains simply connected.

High-Order Spectral Irregular Wave Generation Procedure in Experimental and Computational Fluid Dynamics Numerical Wave Tanks, with Application in a Physical Wave Tank and in Open-Source Field Operation and Manipulation

The accurate generation of a target sea state in numerical or experimental wave tanks is a fundamental line of research for the ocean engineering community. It guarantees the quality and relevance of wave–structure interaction tests. This study presents a reproducible irregular wave generation and qualification procedure, accounting for the nonlinear aspects of wave propagation. It can be used for both numerical simulation and experiments. The presented numerical and experimental results are obtained from the OpenFOAM solver and the Ecole Centrale Nantes wave tank facilities, respectively. The procedure comprises two steps: First, the wavemaker motion is calibrated numerically to generate the target wave spectrum at the position of interest. This is achieved with a wavemaker-equipped nonlinear potential flow solver. The open-source HOS-NWT solver, based on the high-order spectral method, was employed in this study. Then, the corrected wavemaker motion is used directly in the experimental wave tank. OpenFOAM simulations were performed to generate waves with the relaxation method, using wave elevation and velocity field data from HOS-NWT. The procedure was finally tested for mild and extreme breaking sea states. The waves generated by the HOS-NWT solver, the experiment, and the OpenFOAM simulation were compared from both stochastic and deterministic perspectives.

Comparison of Unsteady Low- and Mid-Fidelity Propeller Aerodynamic Methods for Whirl Flutter Applications

Aircraft configurations with propellers have been drawing more attention in recent times, partly due to new propulsion concepts based on hydrogen fuel cells and electric motors. These configurations are prone to whirl flutter, which is an aeroelastic instability affecting airframes with elastically supported propellers. It commonly needs to be mitigated already during the design phase of such configurations, requiring, among other things, unsteady aerodynamic transfer functions for the propeller. However, no comprehensive assessment of unsteady propeller aerodynamics for aeroelastic analysis is available in the literature. This paper provides a detailed comparison of nine different low- to mid-fidelity aerodynamic methods, demonstrating their impact on linear, unsteady aerodynamics, as well as whirl flutter stability prediction. Quasi-steady and unsteady methods for blade lift with or without coupling to blade element momentum theory are evaluated and compared to mid-fidelity potential flow solvers (UPM and DUST) and classical, derivative-based methods. Time-domain identification of frequency-domain transfer functions for the unsteady propeller hub loads is used to compare the different methods. Predictions of the minimum required pylon stiffness for stability show good agreement among the mid-fidelity methods. The differences in the stability predictions for the low-fidelity methods are higher. Most methods studied yield a more unstable system than classical, derivative-based whirl flutter analysis, indicating that the use of more sophisticated aerodynamic modeling techniques might be required for accurate whirl flutter prediction.

Performance of a Raft-Type Wave Energy Converter with Diverse Mooring Configurations

The development and utilization of wave energy, heralded as a potential leading source of clean energy worldwide, have garnered considerable attention from the global research community. Among the diverse array of wave energy converters (WECs), the raft-type WEC stands out for its potential to efficiently harness and utilize wave energy, offering high energy conversion rates and a broad frequency response range. This paper delves into the evaluation of a raft-type WEC’s performance in various mooring configurations under different wave conditions. Our analysis primarily focuses on the dynamics of the two-body WEC using a weakly nonlinear three-dimensional potential flow solver. The considered device comprises two interconnected floating barges, incorporating a power take-off system at the hinged connection point. This investigation involves the use of equivalent linear damping to model the power take-off (PTO) system. To validate the numerical simulations, we conduct physical model experiments with WECs. Additionally, the coupling of the raft-type WEC’s dynamics and its mooring dynamics was examined, highlighting the performance differences between various mooring systems through a comparative analysis.

Comparing the Utility of Coupled Aero-Hydrodynamic Analysis Using a CFD Solver versus a Potential Flow Solver for Floating Offshore Wind Turbines

There has been a great effort towards development of renewable energy systems to combat global warming with significant interest towards research and development of floating offshore wind turbines (FOWTs). With commercial projects such as Hywind Scotland, Hywind Tampen and others, there is a shift of industry attention from bottom-fixed offshore turbines to FOWTs. In this work, we focus on comparing industry standard Potential Flow (PF) methods versus Computational Fluid Dynamics (CFD) solvers for a scaled version of the IEA 15 MW turbine and associated FOWT system. The results from the two solvers are compared/validated using experimental thrust values for the fixed turbine. The motions and the thrust for the FOWT system are then compared for the two solvers along with hydrodynamic properties of the floater hull. The wake features downstream of the turbine are analyzed for the fixed and floating turbine using the CFD solver. The wake from the CFD solver is also compared with a simplified PF model. Finally, a simplified cost-benefit analysis is presented for the two solvers to compare the usefulness and utility of a CFD solver as compared to presently used industry-standard PF methods.

Analysis of the Wave Attenuating and Dynamic Behaviour of a Floating Breakwater Integrating a Hydro-Pneumatic Energy Storage System

Floating breakwaters have recently been generating increasing interest as a vital means to provide shelter and protect the ever-increasing number of structures deployed at sea. Notwithstanding the novel ideas being put forward, to date, floating breakwater deployment has been limited to inshore and shallow water areas. The scale of such structures has been restricted to the smaller spectrum. Furthermore, whilst some concepts to integrate floating breakwaters with other offshore systems have been proposed to benefit from cost-sharing strategies, studies related to floating breakwaters integrating energy storage are lacking in the open literature. The present research investigates the wave attenuating and dynamic performance of a large-scale floating breakwater in deep seas with a hydro-pneumatic energy storage system also integrated within the structure. This article highlights the arising need for floating breakwaters and sheds light on the present-day technological status of floating wave breakers. It then lays the ground for the proposed, novel floating breakwater concept that aims to address the current knowledge gaps in this field of study. The simulation results generated from numerical modelling via the potential flow solver ANSYS® AQWA™ have been promising, connoting that the addition of hydro-pneumatic energy storage to a floating breakwater will not lead to a degradation in the dynamic performance or wave breaking efficiency of the floating structure.

Hydrodynamic analysis of a novel multi-buoy wind-wave energy system

Hybrid wind-wave systems combining the wave energy converters (WECs) with offshore wind turbines (OWTs) is a promising way to enhance the power production and improve the sea space utilization. In this paper, a novel hybrid wind-wave conceptual system, in which a multi-buoy WEC is integrated with a fixed monopile OWT, is proposed. This is the first concept utilizing multi-buoy WECs and is distinguished from existing hybrid wind-wave systems with a fixed monopile OWT, which integrate a single oscillating water column or a heaving point absorber. To characterize the hydrodynamics associated with the proposed system in operational wave conditions with different directionalities, a potential flow solver with an appropriate power take-off (PTO) model is applied. The results demonstrate a significant buoy-buoy and buoy-monopile hydrodynamic interaction, suggesting that the existing hydrodynamic characteristics for the wind-wave system with a single buoy WEC may not be applicable to the new system. More importantly, the power performance of the present system is proven to be better than the corresponding single-buoy wind-wave system, as being quantitatively assessed by the newly-defined evaluation index within the range of the consideration of this paper.

A semi-analytical hydrodynamic model for floating offshore wind turbines (FOWT) with application to a FOWT heave plate tuned mass damper

This paper proposes a semi-analytical MacCamy–Fuchs–Morison (MFM) hybrid hydrodynamic model for very efficient simulations of FOWT responses without resorting to potential flow solvers. First, closed-form expressions of the 6-by-6 added mass matrix and 6-dimensional complex wave load transfer function are derived based on the Morison equation. Comparison of the wave load models show that the pure Morison model over predicts high-frequency wave loads above the diffraction limit, while the pure MacCamy–Fuchs model performed poorly at low frequencies due to the existence of heave plates. The MFM hybrid model resolves both issues and gives good agreement with the potential flow theory at all frequencies. The proposed MFM hybrid model is then employed to a representative application case, i.e. a semi-submersible FOWT installed with heave plate tuned mass dampers (HPTMDs). It is shown that implementing a deep installation of the HPTMDs effectively suppresses foundation roll, heave responses and tower side–side vibrations.

Numerical investigation of bottom slamming using one and two way coupled methods of S175 hull

Numerical simulations of bottom slamming are conducted for a S175 container ship hull using two-phase computational fluid dynamics (CFD) and potential flow solvers. Suitable combinations of these two different models are used for two different coupling strategies named one and two way coupling methods. Various parameters such as the incident wave steepness, wavelength and the forward speed (specified using the Froude number) in a head sea over a range are considered to investigate the slamming phenomenon based on the one way and the two way coupling methods. The overall analysis shows that for most of the cases, the prediction of the bottom slamming pressure from the one-way coupling method maintains a nearly steady difference with respect to that of the two way coupling method over the range of the input parameters and thus forms basis for a new empirical formulation to estimate the peak slamming pressure for a range forward speeds. The performance of this empirical formula is qualitatively discussed with respect to the prediction from the two way coupling method. It is observed that the derived analytical formulation gives reliable results and may be used for efficient estimation of bow slamming pressures at a relatively low computational cost.

Numerical study of the effect of central platform motion on the wave energy converter array

Placing multiple wave energy converters (WECs) on a central floating platform has become a popular approach of ocean energy conversion in recent years. The strong interaction between the WECs and the platform brings a number of technical challenges for the design of such devices. The present study investigates the effect of the platform motion on the WEC array of a typical ocean energy harvesting device, consisting of a central support platform and eight point-absorber WECs arranged in a circular array. The numerical studies are performed in four stages based on the potential flow solver ANSYS-AQWA. The power absorption of each WEC in isolation and of eight WECs operating simultaneously is evaluated and compared in the first and second stages respectively, revealing the interaction among the WECs. The effect of a fixed and a floating platform on the power absorption of the WEC array is investigated in the next two stages. The systematic studies demonstrates that the heave motion of the platform improves the power absorption of the WEC array for most wave frequencies tested, due to the increase in the wave-surface elevations around the WECs and the phase differences of the heave motion between the WECs and the platform. The opposite is true for the pitch motion of the platform. Furthermore, the WEC dimension, the platform dimension, and the distance between the WECs and the platform should be optimized based on the actual operating sea conditions to increase the wave-surface elevations and the phase differences. Otherwise, the motion of the platform should be restricted as much as possible.

A unified steady and unsteady formulation for hydrodynamic potential flow simulations with fully nonlinear free surface boundary conditions

This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a mathematical formulation and a numerical treatment that can be used both to carry out transient simulations, and to compute steady solutions — for any flow admitting them. In the literature on numerical towing tank in fact, steady and unsteady fully nonlinear potential flow solvers are characterized by different mathematical formulations. The kinematic and dynamic fully nonlinear free surface boundary conditions are discussed, and in particular it is proven that the kinematic free surface boundary condition, written in semi-Lagrangian form, can be manipulated to derive an alternative non penetration boundary condition by all means identical to the one used on the surface of floating bodies or on the basin bottom. The simplified mathematical problem obtained is discretized over space and time via Boundary Element Method (BEM) and Implicit Backward Difference Formula (BDF) scheme, respectively. The results confirm that the solver implemented is able to solve steady potential flow problems just by eliminating null time derivatives in the unsteady formulation. Numerical results obtained confirm that the solver implemented is able to accurately reproduce results of classical steady flow solvers available in the literature.

Review of vortex lattice method for supersonic aircraft design

AbstractThere has been a renewed interest in developing environmentally friendly, economically viable, and technologically feasible supersonic transport aircraft and reduced order modeling methods can play an important contribution in accelerating the design process of these future aircraft. This paper reviews the use of the vortex lattice method (VLM) in modeling the general aerodynamics of subsonic and supersonic aircraft. The historical overview of the vortex lattice method is reviewed which indicates the use of this method for over a century for development and advancements in the aerodynamic analysis of subsonic and supersonic aircraft. The preference of VLM over other potential flow-solvers is because of its low order highly efficient computational analysis which is quick and efficient. Developments in VLM covering steady, unsteady state, linear and non-linear aerodynamic characteristics for different wing planform for the purpose of several different types of design optimisation is reviewed. For over a decade classical vortex lattice method has been used for multi-objective optimisation studies for commercial aircraft and unmanned aerial vehicle’s aerodynamic performance optimisation. VLM was one of the major potential flow solvers for studying the aerodynamic and aeroelastic characteristics of many wings and aircraft for NASA’s supersonic transport mission (SST). VLM is a preferred means for solving large numbers of computational design parameters in less time, more efficiently, and cheaper when compared to conventional CFD analysis which lends itself more to detailed study and solving the more challenging configuration and aerodynamic features of civil supersonic transport.

A high-order finite difference method with immersed-boundary treatment for fully-nonlinear wave–structure interaction

In order to predict nonlinear wave loading on marine structures, a fully nonlinear higher-order finite difference based potential flow solver with all boundary conditions treated by an immersed boundary method has been developed in this paper. The solver adopts high-order finite difference schemes for the spatial derivatives and a 4th order Runge–Kutta method for time stepping. Test cases of forced oscillation of a cylinder in an infinite fluid domain are first studied, which reveal the advantage of the acceleration potential method in terms of wave load computation. Then a wave generation problem using a piston type wave maker is tested. Special attention is paid to the intersection point between the free surface and the body surface, and a scheme which best meets the accuracy and stability requirements is suggested from several proposals. A novel hyperviscosity filter, which works for both uniform and non-uniform grids, is introduced to stabilize the time-domain solution of the wave maker problem. Finally, a forced heaving cylinder on the free surface is considered, and the nonlinear wave loads on the cylinder are analyzed and compared to benchmark results.

Comparative Study of Potential Flow and CFD in the Assessment of Seakeeping and Added Resistance of Ships

The need for maritime freight transport of various goods has never been greater. Consequently, ships are designed with ever-increasing dimensions, with the emphasis, of course, on length. One of the many challenges in the design of large ships is the prediction of their behavior in waves, i.e., motions, and consequently, added resistance. In this paper, a comparative study of two numerical tools for estimating ship motions and added resistance is presented. The first tool is the well-established DNV’s commercial seakeeping code Wasim, a weakly nonlinear potential flow (PF) solver based on a Rankine panel method. The other is the increasingly recognized open-source Computational Fluid Dynamic (CFD) toolkit OpenFOAM®, a viscous flow solver with a turbulence model; it is based on the finite volume method (FVM) combined with a volume-of-fluid (VOF) technique for sea-surface evolution. The study is carried out for two ship seakeeping cases in head-sea regular waves, respectively, without and with ship forward speed. The first case refers to a 6750 TEU containership scale model developed at the LHEEA laboratory in Nantes for a benchmark study, providing experimental data for all test cases. Pitch and heave response is calculated and compared with the experimental values. The second case refers to a KRISO container ship, an extensively researched hull model in ship hydrodynamics. In addition to the pitch and heave, added resistance is also calculated and compared with the experimental values. Hence, it provides a comprehensive basis for a comparative analysis between the selected solvers. The results are systematically analyzed and discussed in detail. For both cases, deterioration of the PF solution with increasing wave steepness is observed, thus suggesting limitations in the modeled nonlinear effects as a possible reason. The accuracy of the CFD solver greatly depends on the spatial discretization characteristics, thus suggesting the need for grid independence studies, as such tools are crucial for accurate results of the examined wave–body interaction scenarios.

An Aero-Structural Model for Ram-Air Kite Simulations

Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around the wing and the deformation of the membrane structure. In this paper, we introduce a staggered coupling scheme combining a structural finite element solver using a dynamic relaxation technique with a potential flow solver. The developed method proved numerically stable for determining the equilibrium shape of the wing under aerodynamic load and is thus suitable for performance measurement and load estimation. The method was validated with flight data provided by SkySails Power. Measured forces on the tether and steering belt of the robotic kite control pod showed good resemblance with the simulation results. As expected for a potential flow solver, the kite’s glide ratio was overestimated by 10–15%, and the measured tether elevation angle in a neutral flight scenario matched the simulations within 2 degrees. Based on the obtained results, it can be concluded that the proposed aero-structural model can be used for initial designs of ram-air kites with application to airborne wind energy.

Multi-fidelity hydrodynamic analysis of an autonomous surface vehicle at surveying speed in deep water subject to variable payload

Autonomous surface vehicles (ASV) allow the investigation of coastal areas, ports, and harbors as well as harsh and dangerous environments such as the arctic regions. In the past decade, several studies addressed the shape optimization, control and stability, and seakeeping of ASVs. Nevertheless, the hydrodynamic analysis of ASV performance subject to variable operational parameters lacks a thorough investigation. In this context, this paper presents a multi-fidelity (MF) hydrodynamic analysis of a catamaran ASV, namely the shallow water autonomous multipurpose platform (SWAMP), at surveying speed in calm water and subject to variable payload and location of the center of mass, accounting for the variety of equipment that the vehicle can carry. The analysis is conducted in deep water, which is the condition mostly encountered by the ASV during surveys of coastal and harbor areas. The objective of the analysis is the investigation of the effects of the payload and its arrangement on the variations of the resistance, the vehicle attitude, and the wave generated in the region between the catamaran hulls. These are assessed using an unsteady Reynolds–averaged Navier–Stokes equation (URANSE) code and a linear potential flow (PF) solver. The latter also includes variable grid refinement and coupling between hydrodynamic loads and rigid body equations of motion. Furthermore, the limitation of a PF analysis in the current context is investigated. Finally, a multi-fidelity Gaussian process (MF-GP) model is obtained combining high- (URANSE) and low-fidelity (PF) solutions following an additive correction approach of the latter. The MF-GP model is iteratively refined using an active learning approach based on the maximum prediction uncertainty and the computational cost of the numerical simulations. Numerical results show that the MF-GP is effective in producing response surfaces of the SWAMP performance with a limited computational cost. It is highlighted how the SWAMP performance is significantly affected not only by the payload, but also by the location of the center of mass. The latter can be therefore properly calibrated to minimize the resistance and allow for longer-range operations.

OrcaFlex Modelling of a Multi-Body Floating Solar Island Subjected to Waves

Floating solar energy is an industry with great potential. As the industry matures, floating solar farms are considered in more challenging environments, where the presence of waves must be accounted for in mismatch studies and fatigue and mechanical considerations regarding electrical cables and mooring lines. Computational modelling of floating solar islands is now a critical step. The representation of such islands on industry-validated software is very complex, as it includes a large number of elements, each interacting with its neighbours. This study focuses on conditions with small waves (amplitude of <1 m) that are relevant to sheltered areas where generic float technologies can be utilized. A multi-body island composed of 3 × 3 floats is modelled in OrcaFlex. A solution to model the kinematic constraint chain between floats is presented. Three different modelling solutions are compared in terms of results and computation time. The most accurate model includes a multi-body computation of float responses in a potential flow solver (OrcaWave). However, solving the equations for a single float and applying the results to each float individually also gives accurate results and reduces the computation time by a factor of 3. These results represent a basis for further works in which larger and more realistic floating islands can be modelled.