High Froude Number Research Articles

Numerical investigation of the interaction between a ventilated supercavity and free surface waves at high Froude numbers

Ventilated supercavitation is a hydrodynamic phenomenon where injected air forms a large bubble around a high-speed submerged body, reducing drag to enhance its movement. The study of cavitating flows is crucial near the free surface due to significant interactions between the supercavity and surface waves. In this study, the behavior of the ventilated supercavity and free surface waves at high Froude numbers and varying submersion depths has been investigated using a numerical simulation approach. The accuracy of the predicted results is verified by comparing them with the available experimental data. The results indicate that the supercavity size is simultaneously affected by submersion depth and Froude number. Additionally, as the Froude number increases, the submersion depth at which the free surface effect on the supercavity shape becomes negligible also increases. Moreover, near the free surface, unlike in fully submerged conditions, the supercavity length increases with depth. The results also show that three types of free surface wave patterns are formed, depending on the intensity of the first and second wave systems.

Numerical study of transition hydraulic jumps in different types of stilling basins using lattice Boltzmann methods

Transition hydraulic jumps, also known as low-Froude number jumps, have been less studied compared to high Froude number jumps, despite their significance in high-discharge and low-head dams. A three-dimensional (3D) Lattice Boltzmann method simulation was conducted to investigate submerged transition hydraulic jumps in both normal and expanded stilling basins, focusing on turbulent flow characteristics such as velocity fields, vorticity features, pressure fluctuations, and coherent structures. In expanded basins, two symmetric separated rollers were observed, with the rollers detaching from the submerged jump as the width of basin increased. The length of submerged roller in normal basins is observed as Lr/Ht = 6.19, while it is decreased to Lr/Ht = 4 in expanded basins because of the occurrence of roller lateral diffusion toward sidewalls. The transition of vortex structures from y- to z-vortical was analyzed, and three-dimensional shear layers are captured using the iso-surface of vorticity magnitude ω = 6.5. To further describe the internal structure of turbulence within the transition hydraulic jump, the coherent flow structures are qualitatively examined using the Ω criterion that is the third generation of vortex identification technique. Pressure fluctuations in low-Froude number stilling basins, described using root mean square (RMS), are first presented. High patches of RMS are found in the flow fields and at the bottom of basins, and it is qualitatively noted that shear effects make great contributions to the pressure fluctuations. Distribution of bottom pressure fluctuation RMS in different types of basin was also analyzed. The peak RMS value occurs at the ogee region of the weir, specifically at x/L = −0.2, and it is mainly affected by the width of expansion. Bottom pressure fluctuation RMS decreases in the following order: Normal, 5 m gradual expansion, 10 m gradual expansion, 5 m sudden expansion, and 10 m sudden expansion, due to the lateral diffusion of rollers toward sidewalls. This research introduces an innovative numerical simulation approach to studying pressure fluctuations, offering valuable insights for hydraulic engineering applications.

The influence of static versus dynamic pressure distribution strategies for modelling nonlinear waves generated by ships

A moving static pressure distribution is commonly used to simulate a travelling ship. However, the ship movement changes the fluid velocity around the hull, inducing pressures on the hull surface that are no longer equal to the static pressure. Therefore, we introduce a dynamic pressure correction strategy, which can accurately simulate the impact of the ship movement on the hull-surface pressure and preserve the desired hull shape under both stationary and transient conditions. The strategy is applied to a high-order spectral model and used to investigate ship-induced waves and wave resistance over a both flat and variable topography. We explore various parameters in our study, including the average water depth to ship draft ratio ( $h_0/d$ ), the channel width to ship width ratio ( $W/B$ ), the Froude number ( $Fr_0=U/\sqrt {gh_0}$ ) and variations in bathymetric slope. Compared with experiments on a flat bottom, the numerical results with dynamic correction show better accuracy in the simulation of ship-induced waves and wave resistance than those obtained using a static pressure distribution. The correlation coefficient for wake waves between the numerical and experimental results is improved by approximately 0.25 with the dynamic correction strategy. The amplitude and wavelength of ship-induced mini-tsunamis over a variable topography are found to be reduced when employing a dynamic correction compared with a static pressure distribution, and this effect becomes more pronounced with higher Froude number. The static pressure approach is shown to allow large deformations of the desired hull shape and changes in ship volume which are responsible for the different wave patterns from the two approaches.

Physical Modeling of Tsunamis Generated by Submarine Volcanic Eruptions

AbstractSubmarine volcanic eruptions can induce major local and regional tsunami hazards through varied source mechanisms. Large‐scale experiments of tsunamis generated by submarine volcanic eruptions are conducted to study the cylindrical wave generation and propagation in a three‐dimensional wave basin. A unique volcanic tsunami generator (VTG) was deployed at the bottom of the wave basin to generate volcanic tsunamis with repeatable and controlled source parameters. The physical modeling is based on the generalized Froude number defined with the VTG velocity and the near source water depth. The pneumatically driven vertical stroke motion generates leading elevation waves in the wave basin. The tsunami waves generated by the VTG are measured with a wave gauge array. The wave maker performance is characterized by the dimensionless leading wave amplitudes and periods. The experimental data show the variations of the leading wave amplitude, period, and celerity along the radial propagation distance. The generated cylindrical waves belong to the weakly nonlinear wave regime in the near field with decaying wave amplitude along radial propagation. The attenuation rate of the leading wave exceeds the range from the linear wave theory in runs with higher Froude numbers. The dimensionless leading wave period increases with the dimensionless propagation distance due to the dispersion relation. Empirical equations for the characteristic wave parameters such as amplitudes and periods are derived. The experimental results contribute to the understanding of volcanic tsunami generation processes and may serve rapid volcanic tsunami hazard assessments as well as the advancement and validation of numerical models.

Experimental investigation on oxygenation efficiency of an effective aeration system for ponds

Dissolved oxygen (DO) concentration in water is one of the most important water quality parameters in rivers, lakes, and reservoirs. The most effective way to increase DO concentration in water is aeration. Conduits with high aeration performance are predicted to significantly increase aeration efficiency. Based on this prediction, the physical parameters affecting the aeration efficiency (E20) of the conduit aeration system were experimentally investigated. The effect of different jet plunge angles, flow rates, hydrostatic levels, Froude numbers, and gate opening rates was investigated to optimize the system for the best ventilation efficiency. As a result, the aeration efficiency (E20) improves with increasing air intake performance at low gate openings, high Froude numbers, and hydrostatic levels. The increase in jet plunge angles and hydrostatic level directly increases the aeration efficiency. The study showed that conduit systems can be an important alternative for pond aeration due to initial investment and operating costs, low energy cost, and high aeration efficiency.

Numerical and Experimental Analysis of Lifting Forces of Fin Stabilizers with Fin–Hull Interaction

A fin stabilizer is one of the most effective and frequently used anti-roll devices for maintaining a ship’s operational safety and passengers’ comfort. However, the discrepancy between theoretical hydrofoil-based predictions and the actual dynamic lift force of fin stabilizers due to fin–hull interactions requires more research attention. This study investigates the effect of fin stabilizers on mitigating roll motion through the performance of extensive computational fluid dynamic (CFD) simulations over a range of fin angles and ship speeds. Model tests were carried out to validate the drag and motion results obtained from numerical analyses. The results show that fin stabilizers significantly reduce the roll motion, with the lift coefficient values influenced by the Reynolds number, leading to differences between the theoretical and Reynolds-averaged Navier–Stokes (RANS) calculations. At a high Froude number (Fr), the actual fin lift is about half of the theoretical value. These findings highlight the requirement of selecting an adequate fin area at the predominant ship speeds and ensuring an effective anti-roll effect with fin–hull interaction. This study provides a significant reference for ship design, as well as stabilization system control and optimization.

Wavy approach for fluid–structure interaction with high Froude number and undamped structure

This paper addresses the fluid–structure interaction problem, with an interest on the interaction of a gravity wave with a flexible floating structure, anchored to a seabed of constant depth. To achieve this goal, we make use of the model equations, namely, the Navier–Stokes equations and the Navier–Lamé equation, as well as the associated the boundary conditions. Applying the multi-scale expansion method, these set of equations are reduced to a pair of nonlinearly coupled complex cubic Ginzburg–Landau equations (CCGLE). By applying the proposed modified expansion method, the group velocity dispersion and second-order dispersion relation are deduced. In the same vein, modulation instability (MI) is investigated as a mechanism of formation of pulse trains in fluid–structure system using a CCGLE. For the analytical analysis, we made use of the inverse scattering method to find analytical solutions to the coupled nonlinear equations. Through that method, the obtained solutions depict rogue-shaped waves. Our results suggest that uncontrolled MI within the interaction between a flexible body and gravity waves in viscous flow may be considered as the principal source of many structural ruptures, which are the first cause of critical damage due to the great energy and unpredictability of rogue waves. The present work aims to provide tools to model a wide range of physical problems regarding the interaction of surface gravity waves and an offshore-anchored structure, and it aims to be essential to our understanding of the nonlinear characteristics of offshore structures in real-sea states.

Static hydroelastic study of composite T-foils with beam and lifting line models

Well-designed hydrofoils improve ship resistance and seakeeping by lifting the hull above the water. With greater speeds come greater loads, and the two-way interaction of structural deflections of lifting surfaces on the hydrodynamics must be considered. Tailored structural anisotropy can improve hydrodynamic and structural efficiency of lifting surfaces compared to rigid counterparts by exploiting the layup of composite materials. Structural efficiency here means reduced risk of structural failure for a given amount of material, and hydrodynamic efficiency means lower drag. A T-foil is a prototypical multi-component appendage, consisting of the foil wing and the strut, which we investigate in this work. We use simple composite beam and lifting line theory to explore the static fluid-structure interaction of a composite T-foil for a variety of fiber angles (θf = 0˝ , ˘15˝ ). We apply a simple approximation on lift coefficient at infinite Froude number (F n) to model the free-surface effects, which is valid at high depth-based Froude numbers (F nh ą10a h/c) when CL is independent of F nh and the inertial effects dominate. Results for the moth rudder T-foil geometry studied here indicate that aligning composite fibers towards the leading edge results in a more hydrostructurally efficient foil and that free-surface effects are minor because of the large submergence for this flow condition.

Planing Hull Hydrodynamic Performance Prediction Using LincoSim Virtual Towing Tank

This work shows the performance of LincoSim, a web-based virtual towing tank enabling automated and standardized calm water computational fluid dynamics (CFD) data sampling, extending previous published applications to the case of a high-speed hull. The calculations are performed for a 1:10 scale model of a 43 ft powerboat hull form in the Froude number range from 0.3 to 2.0. The counterpart physical model is the experimental fluid dynamics (EFD) campaign performed at the University of Naples Federico II, where the resistance, sinkage and trim data have been measured. The EFD/CFD data comparison is performed and shown with a discussion of the spotted differences. The average percentage differences between the EFD and CFD data for the whole speed range are 1.84, 6.87 and 6.94 for the resistance, dynamic trim, and sinkage, respectively. These results confirm the maturity of the standardized and automated CFD modeling for calm water hydrodynamic analysis included in LincoSim, even at very high Froude numbers. The wetted length of the keel and chine and the wetted surface are calculated from numerical data using the advanced post-processing. Finally, as a work in progress, we test a first comparison for the same hull of the EFD and CFD data, considering two seakeeping conditions for head waves at a given wavelength for two velocity conditions. Also, this kind of analysis confirms the tight correlation between the measured and computed outcomes. This synergic interplay of EFD and CFD can link the advantages of both methods to support hull design but also requires experiment planning and final data analysis to obtain physical parameters not easily measurable in laboratory, such as the wetted surface, wetted lengths, proper viscous contribution, and pressure distribution both in calm water and in waves.

Vortex waves in fluid–structure interaction with high Froude number and a damped structure

In this paper, we study the non-linear dynamic response generated as a result of a fluid–structure interaction between a flexible structure and a flowing fluid, when the structure is subjected to non-linear excitations. In first place, the use of semi-discrete approximations allowed us to show that the motion of a flexible structure coupled with a surrounding fluid flowing could be modelled and analysed via a coupled Complex Cubic Ginzburg–Landau equations (CCGLEs). Through the obtained CCGLEs, we were able to show that modulational instability (MI) is the main mechanism responsible for the generation of vortex shedding. Moreover, we showed that the stability of continuous wave depends on the coupling parameters between the fluid and the structure. Secondly, using a mathematical method, namely the G’/G expansion method, we found that vortex wave trains could be generated as cylindrical waves. These results are highly significant from a theoretical point of view and could be a plus to explain the process of generation of Kármán Vortex as a consequence of unstable coupling between two continuous wave in the fluid–structure system. Moreover, considering the industrial interest, such as floating wind turbines, this work aims to provide an additional understanding of the interactions between a flexible body and a surrounding flow.

Modular production of small ship models using 3D printing for model tests

This paper presents a cost-effective approach for the production of small-scale ship models, particularly suitable for model testing of high-speed vessels characterized by a high Froude number. In contrast to traditional approach employed in ship model production, the proposed approach uses 3D printing technology integrated with modularity. This strategy enables the mitigation of expenses associated with procuring 3D printers, facilitates dynamic design changes, and accommodates parallel printing using multiple printers, thereby resulting in a reduction in production time. The manufacturing process involves modularization of the original CAD model, build scheduling, interface design, assembly, fabrication, and painting. A case study is presented, which demonstrates the proposed process in ship model production using 3D printing. The geometric similarity between the built model and the original CAD model was assessed by generating a point cloud using a 3D scanner. To evaluate the resistance performance of the 3D printed ship model, experiment and numerical simulation were conducted. These results indicate a high level of similarity and reliability.

Binocular reconstruction of breaking ship bow waves in circulating water channel

This study conducts an experiment on the bow waves generated by a 1:80 KRISO container ship (KCS) model in a circulating water channel. The Froude numbers (characterized by the length of perpendiculars) reach high conditions of 0.377, 0.424, and 0.471. A binocular imaging system is employed to reconstruct three-dimensional configurations of the bow wave surface. The dynamic characteristics of bow wave fields are investigated by observing the standard deviation and employing the Proper Orthogonal Decomposition (POD) method. The power spectral density function presents a power-law relationship with frequency. A novel technique referred as Stereoscopic Foam Image Velocimetry (SFIV) is developed to extract the instantaneous three-dimensional velocity of the foam in breaking area. The velocity field obtained through SFIV defines the nominal time-averaged velocity and nominal turbulent energy. A correlation mapping from pixel coordinates to world coordinates is established to evaluate the actual physical uncertainty. The results demonstrate the superior spatiotemporal accuracy and resolution of binocular imaging technology in measuring the characteristics of bow waves. This research provides significant experimental data of surface three-dimensional configurations for the bow waves breaking issues at high Froude numbers.

Double sill stilling basin to enhance energy dissipation for a strong hydraulic jump with a high Froude number

Roller Compacted Concrete (RCC) is a new and viable construction material for concrete gravity dams. It is gaining popularity due to its low cost and fast deployment. The design of a stilling basin, part of a dam that controls the hydraulic jump and dissipates energy, is crucial. One of the important considerations is the Froude number at the spillway toe (F1), which determines the type of hydraulic jump that will occur. An energy dissipator is also required to prevent scour caused by the change in flow conditions from supercritical to subcritical. Double sills installed downstream of the steep chute way channel can be used as an energy dissipator. This study uses hydraulic modeling to evaluate the flow energy reduction and subcritical flow conditions in a stilling basin with double sills. The investigation is expected to provide better information on hydraulic jump control.

Numerical study of submerged body tail linearization in a strongly stratified fluid on the characteristics of generated internal waves

Underwater motion generates internal waves in a density-stratified seawater environment. These waves can persist for several days in oceanic regions, making them detectable by synthetic aperture radar (SAR). To clarify the effect of tail linearization on the internal wave characteristics of an object, this paper builds a strongly stratified fluid flume based on the delayed detached eddy model (DDES), through which we numerically simulate the internal waves characteristics of two models, namely, a tail-planar type and a cylindrical rear spherical type. The numerical results show that the turbulent wake of the cylindrical rear spherical type diverges to both sides under the low and high Froude (Fr) number, leading to an increase in the amplitude of the generated volume effect internal wave and wake angle, but the wavelength of the volume effect internal wave is almost the same for both. Notably, at high Fr numbers, the influence of the trailing effect internal wave of the object with a linearized tail is significantly reduced. The tail-planar type of internal waves shows violent fluctuations over long distances and high-intensity violent changes in locally concentrated regions. In contrast, the internal waves of the object with tail linearization show slight fluctuations over long distances.

The resistance of a trans-critically accelerating ship in shallow water

ABSTRACT The acceleration resistance of a vessel advancing in shallow water is investigated. Four acceleration intensities and two water depths are modelled using the CFD and potential flow methods. The results show a pronounced peak in resistance exists near the critical depth Froude number, but its location and magnitude are sensitive to the acceleration intensity and water depth. Excellent agreement between the results obtained from the CFD and potential flow methods is found in the low and high depth Froude number ranges regardless of water depth or acceleration, indicating that linear and unsteady methods can provide robust results at a low cost in those ranges. The magnitude of the resistance peak and its position are sensitive to nonlinear effects, evidenced by slight disagreements between the two adopted methodologies. The variation in the results produced by the two solvers is found to be sensitive to the parameters investigated.

Supercritical Froude Number Flow through Ducts with Statistically Roughened Walls

High-speed fluid flows over roughened surfaces occur in many engineering applications; one important application involves high velocity water flows in pipelines with roughened interior walls where the wall roughness affects head loss estimates necessary for engineering design purposes. The present analysis provides an analytical solution of the fluid physics underlying the induced static pressure profile resulting from high Froude number supercritical velocity through duct with random wall roughness. The analytic solution of the hyperbolic governing small perturbation velocity potential equation subject to high Froude number flows brings forward characteristic wave solutions that determine the static pressure profile in a duct with random height wall roughness. While current engineering practice utilizes semi-empirical engineering equations employing test data to determine the friction factor, velocity and static pressure profiles and head loss for different roughness types in different sized ducts as a function of Reynolds number (as summarized in a later section of the paper), the present analysis provides a new analytical method to determine the fluid physics involved in the static pressure change induced by wall random roughness in ducts subject to high Froude number supercritical flows.

Shallow waters resistance of an accelerating ship

This paper investigates the acceleration resistance of a vessel in shallow waters using potential flow and CFD methods. Results indicated a pronounced resistance peak near the critical depth Froude number. The peak’s location and magnitude were sensitive to acceleration intensity and water depth. Excellent agreement between potential flow and CFD methods was found in low and high depth Froude number ranges, suggesting their effectiveness and cost-efficiency. However, non-linear effects affected the resistance peak’s magnitude and position, leading to slight disagreements between the methods. The solvers’ variation was observed to be sensitive to the investigated parameters.

Optimization of a coupled launching process considering hydrodynamic interaction effects

Crane-assisted launching and recovering of small boats from a large vessel is common in a wide range of operational scenarios and may be required during research missions or in emergency situations for rescue boats. As the mothership moves in natural irregular seas, the resulting accelerations and motions of the small boat can lead to dangerous situations, such as a collision between the mothership and the small boat or a slamming of the small boat onto the free water surface can occur, posing a great danger to the people involved. In the paper, the development of a coupled simulation method for the motions of the mothership and the small boat during the launching in the time-domain is described. The developed simulation method is based on the impulse response function. The implementation of the suspension on a crane is realised by a holonomic constraint and a Lagrange’s equation. The parameter influencing the launching operation include the current sea state, the stationary wave field induced by the motherships forward speed, at which the small boat is launched and the initial position of the small boat relative to the water surface. By varying the above mentioned parameters, the process can be optimised for different sea states in terms of forces and accelerations. In considering the forward speed of the mother boat during the launching process, it can be observed that in many cases the small boat is operated at high Froude numbers of greater than 0.4. This leads to an exceedance of the operational limits of the programmes used in this paper.

Multi-GPU multi-resolution SPH framework towards massive hydrodynamics simulations and its applications in high-speed water entry

We propose a multi-phase, multi-resolution SPH method for fluid/solid interaction with multi-GPU implementation and dynamic load balancing following the movement of the refinement regions. The primary design goal of this framework is to maintain the efficiency of the single-resolution SPH model running on a single GPU. To this end, a multi-background mesh is introduced, and the domain is regarded as a nested multi-domain with different resolutions. Validation using both a δ-SPH and Riemann SPH model is shown, and applications to the simulation of the water entry of a projectile with a high Froude number are considered, with comparisons to experimental data from three challenging test cases, showing the proposed model's ability to correctly reproduce the free surface evolution on water entry, the motion of the projectile, and the formation and evolution of multiple cavities depending on entry angle and velocity. An analysis of the computational performance and resolutions achieved (up to 120 million particles) is also provided across several test cases.

The effect of reservoir geometry on the critical submergence depth in hydroelectric power plants intake

The most important design index of water intakes is critical submergence depth of the intake. The depth at which the air core formed by the vortex is about to enter the intake. The emergence of a vortex and air entry into the intake increase head loss and decrease discharge coefficient. The reservoir geometric asymmetry, presence of unevenness in the bottom of the reservoir and angle of approach flow are among the factors that influence formation of the vortex and critical submergence depth. In this research, a physical model has been used to investigate the effect of reservoir geometry on the critical submergence depth. This model is designed in such a way that it can produce the strongest type of vortices with air core and with different strengths. The results showed that by creating asymmetry in the flow approaching the water intake (with side blockage in upstream), the presence of even 10% side blockage can have a great effect on the formed vortex and increase the critical submergence depth by about two times. To create uneven conditions on the reservoir bottom, blockages were created on the bottom of the reservoir upstream of the intake. The results showed that the blockage up to half of the height below the intake caused an increase of about 10–25% of the critical submergence depth, in low and high Froude numbers, respectively. However, in blockages more than half of the height below the intake, this effect increases about 60% of the critical submergence depth. In addition, the effect of the slope of the intake head wall on the order (type) of the vortex and its stability and instability was studied, and it was found that the order of the vortex decreases with the increase in the slope of the head wall toward the vertical position. Also, by increasing the slope of the head wall, the vortices form in an unstable manner. The vertical head wall can act as an anti-vortex structure and cause a reduction in critical submergence depth.