Froude Scaling Research Articles

Three-dimensional discrete element simulations on pressure ridge formation

Abstract. This study presents the first three-dimensional discrete element method simulations of pressure ridge formation. Pressure ridges are an important feature of the sea-ice cover, as they contribute to the mechanical thickening of ice and likely limit the strength of sea ice at large scales. We validate the simulations against laboratory-scale experiments, confirming their accuracy in predicting ridging forces and ridge geometries. Then we demonstrate that Cauchy–Froude scaling applies for translating laboratory-scale results on ridging to full-scale scenarios. We show that non-simultaneous failure, where an ice floe fails at distinct locations across the ridge length, is required for an accurate representation of the ridging process. This process cannot be described by two-dimensional simulations. We also find a linear relationship between the ridging forces and the ice thickness, contrasting with earlier results in the literature obtained by two-dimensional simulations.

Experimental Study on the Spring-like Effect on the Hydrodynamic Performance of an Oscillating Water Column Wave Energy Converter

The oscillating water column (OWC) wave energy converter has demonstrated significant potential for converting ocean wave energy. The spring-like effect of air compressibility can significantly affect the hydrodynamic behavior of the device, but it has rarely been investigated through experimental studies. In this study, an experimental test on a model-scaled OWC device was carried out in a wave flume using a series of regular and irregular waves. The spring-like effect was taken into account by the combination of the air chamber with an additional air reservoir of appropriate volume, where the total volume was scaled according to the square of the Froude scale. The hydrodynamic performance was compared with the results obtained without considering the spring-like effect. A phase difference between the air pressure and airflow rate was observed when employing the additional air reservoir. The amplitudes of free surface elevation and airflow rate increased, while the air pressure was reduced when the spring-like effect was considered. The results demonstrate that failure to consider the spring-like effect can lead to overestimation of the hydrodynamic efficiencies, and the errors were mainly affected by the incident wave frequency.

A true double-body method based on porous media model for simulation and froude scaling verification of an aquaculture vessel resistance

A blueprint of a novel aquaculture vessel composed of rectangular cylinders, pontoons, and nets with the capacity for self-propulsion was drawn. However, when completely different flow features are caused by non-stream shapes, resistance prediction cannot be accurately performed through conventional ship model experiments as the existing scale rules may be invalid. Besides, the existence of nets creates obstacles not only in model tests but also in numerical simulations. Therefore, resistance evaluation of the vessel with nets is very challenging. Porous media model for nets is one of feasible solutions and was validated by previously published experimental results, although a control volume was required. However, porous media model is incompatible with volume of fluid multiphase, which makes the double-body method adopted inevitably. A literally true double-body method based on porous media model was proposed. The comparison of vessels with and without a net exhibited a beneficial interaction between the net and the vessel hull, especially for nets with higher solidity. Furthermore, the Froude scaling law was adopted based on the hypothesis of Reynolds number invariance. All the full-scale resistances predicted by it in seven scale ratios demonstrated satisfactory consistency, and the relative errors grew with the increase of the scale ratios.

Flow Patterns Modeling over Spillway: Review Study

A spillway dam, constructed concurrently with concrete or masonry, is a vital infrastructure designed to provide the controlled release of surplus water that surpasses the dam's storage capacity. Since the Ogee spillway is among the best and most well-known worldwide, it deserves study. Weir flow, inertia, and gravity are crucial in many open-channel applications. Consequently, hydraulic performance data between model and prototype structures are commonly scaled using Froude similitude. As the upstream head decreases in a weir flow, the surface tension and viscosity forces become more important, perhaps to the point where Froude scaling fails to achieve complete model-prototype similarity. Size-scale effects are responsible for various alterations to the head-discharge connection, the nappe trajectory, and air entrainment. Hydraulic parameters were explored in this work utilizing Flow3D software to find weir geometry optimization using the CFD method. In addition, this study attempted to evaluate flow on various parts of crested weirs in three different models.

Physical Modelling Of A Caisson Breakwater Under Impulsive Cyclonic Waves : Case Of Port East (Reunion Island)

The GPMDLR (Port Authority of La Réunion Island, France) has requested ARTELIA to carry out the preliminary studies for the enlargement of the containers terminal in Port East. In this context, the laboratory of ARTELIA has performed 2D physical model testing to evaluate the behavior of caissons exposed to cyclonic conditions. The solution based on a vertical breakwater has been proposed as an alternative to a rubble mound breakwater given the lack of quarries suitable to provide big quantities of large rocks. Main objectives of the study were: the evaluation of overtopping rates (mean and max), the verification of the stability of foot protection blocks and stones, and the recording of wave pressures (gauges) and loads (scale) on the caissons. Given the fact that most of the waves broke violently upon the caisson, the nature of efforts was impulsive and the scaling to prototype by classical Froude similarity principles was not appropriate. Results were therefore amended following Cuomo’s correction factors for the Froude scaling law (Cuomo et al. 2010). Times series of efforts (forces and pressures) were used to feed numerical models (static and dynamic) allowing for the verification of caissons’ geotechnical stability and the design of concrete parts. This article collects the concerns, feedback and further questioning related to the conducted experiment.

Scaling of wave energy converters for optimum performance in the Adriatic Sea

The wave energy potential in the Adriatic Sea is investigated at seven offshore locations, and the mean annual energy, average electric power production, operating hours, as well as the coefficient of variation of the monthly power production are determined for three wave energy converters. Since wave energy converters are commonly designed and optimized to extract energy from ocean waves, they have low capacity factors in low-energy seas or bays such as the Adriatic Sea, where the sea states are slight to moderate. The scaling of the wave energy converters is performed on the basis of the Froude scaling law for AquaBuoy and Pelamis devices. The results of WECs at eleven scales are compared with those obtained for a Lysekil WEC. The obtained results show that the capacity factors of the downscaled WECs increase significantly at their optimum scales, reaching about 29 % and 42 % for the AquaBuoy and Pelamis, respectively, depending on the location. By comparing the results obtained for the AquaBuoy and Pelamis at a scale of 0.7 with the results of a full-scale Lysekil WEC, it may be concluded that the downscaled WECs may be more suitable for the considered locations in the Adriatic Sea while keeping their economic viability.

Performance and limits of a geotechnical centrifuge: DEM-LBM simulations of saturated granular column collapse

This study investigates the dynamics of granular flows in geotechnical centrifuge models, focusing on the effects of centrifugal and Coriolis accelerations. While conventional laboratory-scale investigations often rely on Froude scaling, geotechnical centrifuge modelling offers a unique advantage in incorporating stress-dependent processes that fundamentally shape flow rheology and dynamics. Using the Discrete Element Method (DEM) and the Lattice-Boltzmann Method (LBM), we simulate the collapse of a just-saturated granular column within a rotating reference frame. The model’s accuracy is validated against expected trends and physical experiments, demonstrating its strong performance in replicating idealised collapse behaviour. Acceleration effects on both macro- and grain-scale dynamics are examined through phase front and coordination number analysis, providing insight on how centrifugal and Coriolis accelerations influence flow structure and mobility. This work enhances our understanding of granular flow dynamics in geotechnical centrifuge models by introducing an interstitial pore fluid and considering multiple factors that influence flow behaviour over a wide parameter space.Graphical abstract

Procedure for evaluation of LNG CCS with reference vessel using nonlinear dynamic analysis

This paper presents a procedure for evaluating the structural safety of Liquefied Natural Gas (LNG) Cargo Containment System (CCS) against sloshing load by comparing the results of linear and nonlinear dynamic structural strength analysis with those of verified reference vessels. This comparative procedure indirectly considers (1) limitation of implementing real physical phenomena in model experiments including the Froude scaling method, density ratio, etc., (2) assumptions in statistical analysis for calculating design loads, and (3) complicated effects not implemented in nonlinear dynamic analysis such as phase transition between liquid and gas, hull deflection, and the detailed geometry of the CCS, among others. The uncertainties in sloshing model experiments and statistical analysis can be addressed by introducing the pressure correction factors, which make the linear design loads of the reference vessel satisfy the CCS’s capacity. Finally, the structural nonlinearity, which was not accounted for in the nonlinear dynamic analysis, can be taken into consideration through a comparison of the usage factors from nonlinear dynamic analysis. To apply the proposed structural assessment procedure, the GTT NO96 series were selected and applied to two failure modes. In the application of this procedure, the Triangular Impulse Response Function (TIRF) method was adopted, to efficiently calculate numerous linear dynamic structural strength analyses required for Dynamic Amplification Factor (DAF). Through this application applying larger sloshing loads to the reinforced NO96 CCS of the target vessel compared to the reference vessel, the feasibility of this procedure was shown.

Interception performance of intake structures with a flow diversion barrier under supercritical flow conditions

Intake structures are commonly used in drainage systems to redirect surface rainfall runoff into underground tunnels. The Hong Kong West Drainage Tunnel (HKWDT) system is designed to capture stormwater from steep upland catchments during periods of heavy rainfall, concurrently maintaining a minimal environmental flow downstream during dry weather. However, during heavy rainfall events, excess rainfall water is often directed into the drainage system, presenting a significant challenge to the urban drainage system. Undistorted Froude scale physical models and computational fluid dynamics (CFD) models are developed to investigate the flow performance. In this study, effects of various design parameters on water diversion performance are examined across a wide range of inflow conditions. Steeper channel bottom slopes leading to a larger proportion of water being directed downstream. Extending the length of the bottom rack effectively reduces adhering flow. Introducing a transverse barrier generates a hydraulic jump, which increases flow diversion into the LFC. With higher barrier heights, the hydraulic jump becomes stronger, facilitating greater water diversion into the downstream sewage system. The results indicate potential solutions to these challenges and provide valuable insights into optimizing flow diversion performance in intake structures, particularly in areas characterized by steep terrains and varying flow conditions.

M4 WEC development and wave basin Froude testing

The M4 wave energy converter (WEC) is a moored, multi-float, multi-PTO (power takeoff), multi-mode, attenuator-type system designed to be capable of order MW capacity. The strategy is first described with technical requirements. Wave basin testing was undertaken to demonstrate the system and validate linear diffraction-radiation modelling, used for initial assessment and to generalise the configurations. Froude-scale modelling including power takeoff has been demonstrated for the first, possibly only, time. Further wave basin testing was undertaken to validate a multi-float generalisation. Moorings are a critical component with the elasticity of (synthetic) cables reducing snap loads markedly but with complex dynamics requiring wave basin testing and further model development. Preliminary results are presented. Limitations of wave basins with regard to the control of wave (and current) conditions and associated measurement are discussed along with suggested improvements. Computational modelling ranges from efficient linear diffraction-radiation modelling to massively resource-intensive computational fluid dynamics (CFD). The former extended to second order is of main practical importance and is well suited to generalise WEC configurations and model complexity, such as nonlinear power takeoff control and moorings, but are limited in accurately representing physics such wave nonlinearity, slamming and viscous effects. However, CFD has yet to become a practical tool for realistic irregular wave conditions. Wave basin modelling based on Froude scaling is of vital importance for both concept exploration and model validation.

Performance-scaled rotor design method for model testing of floating vertical axis wind turbines in wave basins

The wave basin model tests of floating wind turbines typically follow the Froude scaling law, where a geometric-scaled rotor cannot achieve the target thrust due to the Reynolds-number scaling effect. To tackle this issue, a performance-scaled rotor (PSR) has been successfully used in the wave basin model testing of floating horizontal axis wind turbines (HAWTs). Unlike HAWT, the thrust and side forces of a vertical axis wind turbine (VAWT) present periodic and large amplitude variations with the azimuth angle. In this study, a novel PSR design method is proposed for the model testing of floating VAWTs. An alternative airfoil with good aerodynamic performances at low-Reynolds-number is selected to replace the original one. The relationship between the thrust coefficient and the chord length is derived analytically, with accuracy-enhancing corrections. The chord length of the PSR is then determined. The method and procedure are demonstrated by designing and testing a PSR of a 5 MW floating VAWT with three straight blades and a scale ratio of 1:50. Thrust and lateral forces of the floating VAWT are compared and analyzed. Results indicate that the designed PSR can reproduce the thrust and side forces and is applicable for model testing of floating VAWTs.

Variability of Kinetic Response Estimates of Froude Scaled DeepCwind Semisubmersible Platforms Subjected to Wave Loading

Abstract Froude scaling for Floating Offshore Wind Turbine (FOWT) platforms is typical for understanding and interpreting their behavior and subsequent designs for testing in wave basins. Despite its popularity, the variability and uncertainty of the kinetic responses of such floating structures as a function of scaling require more attention. This work addresses the question of consistency of Froude scaling by comparing the hydrodynamic responses of a range of DeepCwind semisubmersible FOWT scaled models (full model, 1/2, 1/4, 1/9, 1/16, 1/25, 1/36, 1/49, and 1/50). The comparison was made both in the mooring-line tension and bending moment of structural members, which are directly related to their safety limit states. Hydrodynamic forces due to diffraction, radiation, and viscosity along with hydrostatic forces and mooring boundaries are modeled by ansys-Aqwa, which were subsequently converted to bending moment estimates. The variability of kinetic responses like mooring-line tensions and bending moment estimates was investigated for each scaled model, along with the identification of regions of inconsistencies. In the context of offshore renewable energy development through technological readiness levels, the study is especially pertinent for understanding how force variabilities and uncertainties are related to these kinetic responses of semisubmersible platforms.

Numerical verification of the dynamic aerodynamic similarity criterion for wind tunnel experiments of floating offshore wind turbines

Model tests and real-time hybrid simulation tests of floating offshore wind turbines have recently been extensively conducted to explore the aero-hydro-servo-elastic coupling mechanism. The traditional thrust similarity criterion under the Froude scale cannot satisfy the dynamic aerodynamic similarity in the wave basin experiments. Meanwhile, the traditional model wind turbine in model tests shows huge differences in Reynolds number and significant deviations in the optimal tip speed ratio, and the dynamic performance is different from that of the prototype wind turbine. Therefore, a new criterion based on the mapping of the optimal tip speed ratio is proposed, and a new model wind turbine is designed to physically reproduce the dynamic aerodynamics of the prototype wind turbine accurately in wind tunnel experiments. Then the dynamic aerodynamic similarity in this criterion is numerically verified and compared with that in the traditional criterion. The simulation is performed in steady and unsteady inflows by the open-source OpenFAST. The platform motions of the prototype and model wind turbine are inflow-motivated and program-forced, respectively. The calculation results show that the dynamic thrust, power and their coefficients in the new criterion all maintain better similarity compared to those in the traditional criterion. This study is important for wind tunnel model tests and RTHS tests to accurately obtain unsteady aerodynamics, and it can guide the aero-hydro-structure load evaluations and turbine-floater-mooring integrated designs for large-scale floating offshore wind turbines.

Experimental Study for Wave Energy Converter of Wavestar Type using Real-Time Hybrid Model Testing Technique

An experimental investigation of the performance of a wave energy converter of wavestar type was conducted. A PTO system of downscale is difficult to directly apply in the model test because the experiment in the wave basin is based on Froude scaling. In case of the hydraulic PTO system, modelling of oil pressure and accumulator is more difficult in the wave basin test. To overcome the limitation of modelling of hydraulic PTO system, new model test technique was applied in this study. The model tests were performed in regular and white noise waves, and existed model test technique and new model test technique were compared in each other. From the results, characteristics of new model test technique were introduced.

Hydrodynamic Response of Mocean Wave Energy Converter in Extreme Waves

The design of moored floating wave energy converters (WECs) must take into account extreme responses and mooring line loads in order to ensure their survival and continued wave power generation in the ocean environment. This study focuses on Mocean Energy's hinged raft WEC and aims to provide a comprehensive understanding of its hydrodynamic characteristics in survival wave conditions. To achieve this, a physical model study was conducted on a Froude scale of 1 in 50 at the FloWave Ocean Energy Research Facility, University of Edinburgh.
 The experiments involved the use of NewWaves focusing of crest and trough at the model hinge location, as well as long irregular waves. Motion responses of the fore and aft bodies of the WEC were measured using a Qualisys camera, and single component load cells were used to measure the forces in the 3-point catenary mooring line. The hydrodynamic characteristics of the WEC were evaluated in terms of response amplitude operators and non-dimensional mooring line loads.
 Results indicate that the fore and aft bodies of the WEC exhibit similar motion responses, except for the pitch motion. The aft body has a pitch response 2 to 3 times higher than the fore body. Concerning the moorings, the wave load on the mooring line in line with the wave direction was found to be higher than the other two mooring lines which were arranged at an angle to the wave direction.
 In this paper, a brief discussion of the model set-up, parameters, test procedure, analysis of results, and discussion will be reported. The results will provide insight into the behaviour of the Mocean device in survival wave conditions and will aid with the determination of appropriate design parameters for optimal performance and survival in the ocean environment.

Numerical validation of novel scaling laws for air–water flows including compressibility and heat transfer

Air–water flows are among the most important flow types in hydraulic engineering. Their experimental modelling at reduced size using Froude scaling laws introduces scale effects. This study introduces novel scaling laws for compressible air–water flows in which the air is considered compressible. This is achieved by applying the one-parameter Lie group of point-scaling transformations to the governing equations of these flows. The scaling relationships between variables are derived for the fluid properties and the flow variables including temperature. The novel scaling laws are validated by computational fluid dynamics modelling of a Taylor bubble at different scales. The resulting velocity, density, temperature, pressure and volume of the bubble are shown to be self-similar at different scales, i.e. all these variables behave the same in dimensionless form. This study shows that the self-similar conditions of the derived novel scaling laws for compressible air–water flows have the potential to improve laboratory modelling.

Experimental investigation of a reverse osmosis desalination system directly powered by wave energy

Powering desalination processes with renewable energy is a promising solution to address the global issue of water shortage with minimum carbon footprint and environmental impact. We experimentally investigate a sustainable reverse osmosis (RO) desalination system directly powered by wave energy. In this system, seawater is pressurized and pumped to a RO desalination module via a piston pump directly driven by an oscillating surge wave energy converter (OSWEC). An accumulator is adopted on the feed inlet to mitigate the pressure fluctuations under time-varying ocean conditions. Meanwhile, a needle valve on the brine outlet is used to adjust the system pressure and water recovery. A 1:10 scaled model was designed, fabricated, and tested in a wave tank based on the Froude scaling law. The optimal specific water productivity (SWP) obtained in the tank tests with 3.5 g/L feed salinity was 2.23 m3/kWh, indicating a full-scale specific water productivity of 0.22 m3/kWh for 35 g/L seawater salinity. The influence of needle valve tuning on the specific water productivity was experimentally investigated and analyzed. Under a specific operational condition, tuning this valve improved specific water productivity by about 17 % and reduced the system pressure by 24 %, thereby avoiding extreme pressure and improving the system’s capability. This pilot study demonstrates that ocean wave energy is a promising source to sustainably power reverse osmosis desalination and provide freshwater water for coastal regions.

Wind turbine model-test method for achieving similarity of both model- and full-scale thrusts and torques

For model tests of a floating offshore wind turbine (FOWT) system, a great challenge is how to model the interaction between the wind turbine and floating platform with correctly-scaled aerodynamic and hydrodynamic loads because of a well-known contradiction between Reynolds and Froude scaling. Several approaches have been proposed in the literature to tackle the challenge but none of them can correctly and simultaneously model the scaled thrust and torque, and so the interaction between turbine and platform. This paper will present a new model-test method for achieving similarity of both thrust and torque. This is achieved by redesigning the model blades with keeping the blade twist angle same as that of the full-scale turbine and by adjusting the pitch angle of blades and rotational speed of wind turbine in model tests. Numerical simulations and wind tunnel model tests are carried out to validate the present method. Both numerical results and experimental data show that the present method can realize the similarity of thrust and torque simultaneously, and thus, making it possible to study full interaction between turbine and floating platform by physical testing in wind-wave basins.

A study of scale effects in experiments of monopile scour protection stability

Small scale hydraulic experiments are widely used to model the stability of a scour protection around an offshore monopile foundation. Knowing the associated scale effects is important for evaluating the validity of the obtained experimental and design results. This paper provides a quantification analysis of scale effects that exist in monopile scour protection experiments, with a focus on the shear damage of a dynamically stable scour protection. Large scale models (scale ratio 1:8.33 and 1:16.67) and similar small scale models (scale ratio 1:50) have been adopted in the experiments with waves against current hydrodynamic conditions applied. For the waves and current conditions, the Froude scaling rule is used; for the armour stones, the so-called Best Model scaling rule suggested by Hughes (1993) is used. The scaling scheme achieves similarities between large and small scale models with regard to Shields number, relative density, geometry and settling velocity of particle. The scour protection damage patterns are measured and the three dimensional damage numbers are analysed. For better comparing the small and large scale test results, the small scale tests are performed repeatedly to obtain reliable damage results with associated range of deviation. Visual assessment of the damage patterns shows some agreements between small and large scale tests with regard to the damage and accretion locations. However, detailed analysis shows that the small scale tests introduce higher global and subarea damage numbers compared to large scale tests. The damage areas in small scale tests are larger than that in large scale tests. Significant lee-side damage due to the presence of lee-wake vortices is found in small scale tests. The dissimilarities of pile Reynolds number ( R e , D P ), ratio between Shields numbers ( θ m a x / θ c r ) and vortex shedding frequency in the different scaled models are believed to be the primary reasons of obtained scale effects. • Scale effects in monopile scour protection experiments are investigated quantitatively. • Large scale (1:8.33 and 1:16.67) and small scale (1:50) experiments are performed under wave opposing current conditions. • Repeated small scale experiments are carried out to obtain reliable mean damage numbers and 95% confidence intervals. • Scour protection damages are analyzed and compared between small and large scale experiments. • Time scale of scour protection progressive damage development is investigated. • Different Reynolds numbers ( R e , D P ) and ratios between Shields numbers ( θ m a x / θ c r ) are the main reasons for the scale effects.

Dynamic responses of a novel floating tapered trash blocking net system due to wave-current combination

To ensure the safe operation of coastal power plants in nearshore regions, an innovative tapered net system has been widely applied to block the floating bio-fouling and debris. Exposed to the combination of coastal waves and currents, these flexible nets are prone to significant deformation and excessive drawing force, which arises high risk of the system failure. To explore the hydrodynamic performance of the tapered fouling interception system, large-scale model tests have been conducted in wave-current flume under various pure current and wave-current combined conditions. Specifically, a dual-scale similarity is applied in the tapered net model to overcome the dilemma of Reynolds Similarity in Froude scaling tests. The results show that the existence of wave action leads to significant dynamic loading on the connector between the supporting frame and tapered nets, subsequently provoking frequent slack-taut on the connector. This nonlinear characteristics of the drawing force is easier to be triggered by the increased wave height and the enlarged current velocity. Whereas for the effect of wave period, the changing law deviates from the previous studies for a net panel, which demonstrates the importance of the overall shape consideration in the hydrodynamic study of the novel tapered trash blocking system.