Free Surface Effects Research Articles

Generation of internal waves in a two-layered stratified system with a free surface by coupled mass sources

The generation of internal waves (IWs) is of fundamental concern in numerical studies on the IWs and particularly their interaction with the currents and structure topography. In this study, a coupled mass sources (CMS) approach is proposed to generate IWs in a two-layer stratified system considering the free-surface effect. The numerical verifications are performed in the NEWTANK model solving full Navier-Stokes equations. The multi-layered VOF (ML-VOF) method is employed to track the movement of the interface and free surface simultaneously. The verifications indicate that the CMS method is capable of generating internal solitary waves (ISWs) with weak and strong nonlinearity under the free surface. The prescribed ISW can be generated at the very beginning with no obvious trailing waves compared with the commonly used gravity-collapse method. Furthermore, the free-surface soliton aroused at the top of ISW is consistent with the theoretical solution. The verifications also demonstrate that the CMS method is competent to generate ideal internal periodic waves (IPWs) in both Boussinesq and non-Boussinesq conditions considering the free-surface effect. Finally, the internal wave interaction with the currents simulated by the CMS method is discussed to demonstrate the advantages of this approach.

Analysis of Attack Angle Effect on Flow Characteristics Around Torpedo-Like Geometry Placed Near the Free-Surface via CFD

In this study, the flow characteristics of torpedo-like geometry placed near the free-surface at various angles of attack were investigated numerically. The study was carried out at the Reynolds number of Re=4x104 between immersion ratios of 0.75≤h/D≤3.5 and angles of attack α=0°,4°, 8°, and 12°. Large Eddy Simulation (LES) turbulence model was used along with the Volume of Fluid (VOF) multiphase model to investigate the effects of free-surface. Wake region had an asymmetrical structure near the free-surface as a result of the interaction. A jet-like flow region was observed between the geometry and the free-surface at lower immersion ratios due to the restriction of the flow area. This flow region had a downward movement towards the lower pressure wake region. The drag coefficient, CD, values were increased with the decrease of immersion ratio. At angles of attack α=8° and 12°, the flow separation occurring near the nose caused an additional restriction in the flow area and directed the jet-like flow toward free-surface. Variation of Froude numbers (Fr) depending on the immersion ratio is examined, and it is found that Fr number and corresponding drag coefficient have higher values for the lower immersion ratio. The free-surface effect was found negligible at h/D≥2.5 for all cases.

Free Alternate Bars in Rivers: Key Physical Mechanisms and Simple Formation Criterion

AbstractFree alternate bars are large‐scale, downstream‐migrating bedforms characterized by an alternating sequence of three‐dimensional depositional fronts and scour holes that frequently develop in rivers as the result of an intrinsic instability of the erodible bed. Theoretical models based on two‐dimensional shallow water and Exner equations have been successfully employed to capture the bar instability phenomenon, and to estimate bar properties such as height, wavelength and migration rate. However, the mathematical complexity of the problem hampered the understanding of the key physical mechanisms that sustain bar formation. To fill this gap, we considered a simplified version of the equations, based on neglecting the deformation of the free surface, which allows us to: (a) provide the first complete explanation of the bar formation mechanism as the result of a simple bond between variations of the water weight and flow acceleration; (b) derive a simplified, physically based formula for predicting bar formation in a river reach, depending on channel width‐to‐depth ratio, Shields number and relative submergence. Comparison with an unprecedented large set of laboratory experiments reveals that our simplified formula appropriately predicts alternate bar formation in a wide range of conditions. Noteworthy, the hypothesis of negligible free surface effect also implies that bar formation is fully independent of the Froude number. We show that this intriguing property is intimately related to the three‐dimensional nature of river bars, which allows for a gentle lateral deviation of the flow without significant deformation of the water surface.

BENCHMARK TESTS OF FINETM/MARINE CFD CODE FOR THE CALCULATION OF SHIP RESISTANCE AT HIGH FROUDE NUMBERS

Benchmark tests of FINETM/ Marine CFD code were performed to verify the ship-resistance calculation results at high Froude numbers. The CFD code solves the Reynolds-averaged Navier-Stokes (RANS) equations with modelling of the free surface effects, that is, the generation of waves due to the ship movement on the water surface. A high-speed OSV boat was considered at three speeds (17, 20 and 26 knots), which correspond to the Froude numbers based on the volume of displacement FrV = 1.29, 1.52, and 1.98.The CFD results show a good agreement with the results of Savitsky’s formula and the numerical results obtained from Maxsurf Modeller. Further, a reasonable agreement was found between the CFD results and available experimental data. Flow visualisations show that the wave pattern behind the boat consists of transverse and divergent waves. As the boat’s speed increases, the wave height increases, and the wave pattern becomes more dominated by the divergent waves. These observations are consistent with the classical analytical predictions.

Depth-dependent free surface effect to predict ground motion at depth for the design of underground structures

Depth-dependent free surface effect to predict ground motion at depth for the design of underground structures

Numerical study of the effect of tip-speed ratio on hydrokinetic turbine wake recovery

The predictive capabilities of blade-resolved unsteady Reynolds averaged Navier-Stokes (URANS) and detached eddy simulation (DES), the most commonly used hybrid RANS/large eddy simulation (LES) model, are assessed for hydrokinetic turbine performance and mean and turbulent flows in the intermediate-wake region, and results for a range of tip-speed ratio encompassing design and off-design conditions are analyzed to understand the wake recovery mechanism. The performance predictions compared within 5% of the experimental data. Both URANS and DES models performed reasonably well for the near wake predictions, where the errors were <15%. DES outperformed URANS for both mean wake deficit and turbulence predictions in the intermediate-wake region and both quantities compared within 10% of the experiments. The improved prediction by DES is because of its ability to predict the tip vortex breakdown, which plays a critical role in the wake recovery, especially for higher tip speed ratios (λ). However, DES significantly underpredicted the turbulence predictions in the near-wake region, which could be partly due to the negligence of free-surface effects and partly due to modeling issues, namely modeled stress depletion. The study reveals that the tip vortex breakdown mechanism depends on λ. For lower values of λ, instabilities generated in the root vortex core are identified to be the cause of breakdown. For higher values, the breakdown occurred because of the instabilities generated during the vortex filament entanglement. Future work should focus on investigation of other hybrid RANS/LES models to address the limitations of the DES models, and extension of the study to include free-surface effects.

A numerical analysis to determine wake recovery distance for the longitudinal arrangement of hydrokinetic turbine in the channel system

ABSTRACT Hydrokinetic technology is developing rapidly from model to prototype testing. The principle of hydrokinetic technology involves the passage of flow through the hydrokinetic turbine, which reduces the velocity downstream of turbine due to the energy extraction and obstruction created by turbine operation. This reduced velocity regains its initial velocity after certain distance known as wake recovery distance due to mixing regime and available discharge. This study aims to analyze the wake recovery distance under different flow velocities considering various dimensions of turbine. In order to study the impact of turbine operation on the flow condition, a 3D unsteady and rotational numerical analysis has been carried out by incorporating free surface effect. It is a first prototype based study and the analysis has been carried out on actual dimensions of the turbine taking 0.5, 1.0, 1.5, and 2.0 m dia. operating at varying water depth (2, 3, 4, 5, 6, and 7 m). Impact of velocity, turbine diameter and water depth on wake recovery distance is analyzed in the study to define the distance between two units along the channel length under different operating conditions. The distance between two units should be the summation of upstream (back water effect) and downstream (wake recovery distance) disturbance created by the turbine operation. It is observed that more than 90% of initial flow velocity gets recovered at ‘25D’ downstream of rotor.

Effects of free surface on a flapping-foil based ocean current energy extractor

We study numerically the effects of free surface on a flapping-foil based ocean current energy extractor. A two-dimensional NACA0015 foil, subjected to a coupled pitching and heaving motions, at a fixed Reynolds number of 900, and varied Froude numbers between 0 and 2, is considered. We fix the non-dimensional frequency at f∗ = 0.16 and pitching amplitude at θ0 = 75°. The previous studies suggested that an energy extracting efficiency up to 0.30 could be achieved in a single-phase fluid flow at these specific parameters. In the current study, as the free surface is considered, we report that both the submergence depth and Froude number affect the energy extracting efficiency. As the submergence depth increases from H = 1 to H = 20, for all the Froude numbers considered, the efficiency converges eventually to 33.7%, though slightly higher efficiencies can be observed when both the depth and Froude number are small. At a fixed submergence depth, the efficiency decreases monotonically with the increasing Froude number, which trend is more pronounced when the depth is small, i.e., the foil is very close to the free surface. It is apparently suggested that the free surface plays an unfavorable role in the energy harvesting efficiency, therefore the foil should be deployed with a sufficiently large distance from the free surface, particularly when it operates at high Froude numbers.

An Analytical Solution for the Vibration and Far-Field Sound Radiation Analysis of Finite, Semisubmerged Cylindrical Shells

The vibration response and far-field sound radiation of a semisubmerged, finite cylindrical shell with low-frequency excitation are studied. The solution to this problem can be divided into two steps. The first step is to apply the wave propagation approach to determine the vibration response of the cylindrical shell. In the cylindrical coordinate system, the Flügge shell equations and Laplace equation are used to describe the cylindrical shell and surrounding fluid so that the vibration responses of the shell can be addressed analytically. The fluid free surface effect is taken into account by applying the sine series to force the velocity potential on the free surface to be zero. Furthermore, compared with the FEM (the finite element method), the present method is not only reliable but also effective. In the second step, the far-field sound radiation is solved by the Fourier transform technique and the stationary phase method in accordance with the vibration responses of the shell from the previous step. The boundary element method is applied to validate the reliability of the acoustical radiation calculation. The circumferential directivity of far-field sound pressure is discussed, and it is found that the maximum value of the sound pressure always appears directly under the structure when the driving frequencies are relatively low. Besides, in consideration of simplicity and less computation effort, the present method can be used for the rapid prediction of the vibration and far-field sound pressure of a semisubmerged cylindrical shell with low-frequency excitation.

Determination method of tunnel blasting parameters using electronic detonator under changing condition of free surface

The technical potential of electronic detonator has not yet been fully utilized in tunnel engineering. An important reason is that there is no calculation method of blasting parameters supported by rigorous theory. The pivotal blasting parameters such as charge and delay time, etc. are mostly designed following ordinary mining method. And it can not solve the problem of calculation accuracy of blasting parameters after the formation of the second free surface. Taking Guanyinqiao Tunnel in Chongqing as the research background, based on the Anderson principle and the delay characteristics of the electronic detonator, a new method for designing the blasting parameters of electronic detonator is proposed under the different free surface conditions changing in the process of tunnel blasting, from single free surface to dual free surface. Firstly, based on the single-hole and single free surface blasting vibration curves of different charges acquired on site, the superimposed vibration of multiple blast-holes under each delay time was calculated one by one. After comparing the superimposed vibration curves of different charges and delays, it was determined the blasting parameters of single free surface, including the maximum single-hole charge and the optimal inter-hole delay. Secondly, according to the characteristics of the electronic detonator, the short-delay cut blasting field test was designed. By comparing the calculated waveform without considering the influence of the second free surface with the measured waveform affected by the vibration reduction effect of the second free surface, it was found that the second free surface had formed at 48 ms after initiation. Based on this, a single-hole blasting test was designed after the formation of the second free surface. By calculating the superimposed vibration velocity based on the single-hole waveforms before and after the formation of the second free surface, it was determined the blasting parameters under the dual free surfaces condition, including single-hole charge, inter-hole delay time, and delay between different types of holes. Finally, the calculation method of blasting parameters in the whole blasting process was formed. After the comprehensive analysis of the calculated results, the single-hole charge of the main cutting holes is 1.2 kg, and it is 1.4 kg of the auxiliary cutting holes, then the delay time between holes is 5 ms on site; the minimum delay time between the main cut holes and the auxiliary cut holes is 35 ms. The field test was carried out with the optimized parameters mentioned above, and it got high-efficiency footage as well as a low vibration velocity.

Three-Bladed Horizontal Axis Water Turbine Simulations with Free Surface Effects

The water level above a hydrokinetic turbine is likely to vary throughout the season and even along the day. In this work, the influence of the free surface on the performance of a three bladed horizontal-axis turbine is explored by means of a three-dimensional, transient, two-phase flow computational model implemented in the commercial CFD software ANSYS Fluent 19.0. The &lt;i&gt;k –&lt;/i&gt; ω SST Transition turbulence model coupled with the Volume of Fluid (VOF) method is used to track the air-water interface. The rotor diameter is &lt;i&gt;D&lt;/i&gt; = &lt;i&gt;0 8m&lt;/i&gt;. Two operating conditions are analyzed: deep tip immersion (&lt;i&gt;0.55D&lt;/i&gt;) and shallow tip immersion (&lt;i&gt;0.19D&lt;/i&gt;). Three tip speed ratios are evaluated for each immersion. Simulation results show a good agreement with experimental data reported in the literature, although the computed torque and thrust coefficients are slightly underestimated. Details of the free surface dynamics, the flow past the turbine and the wake near the rotor are also discussed.

Free surface and near-wall effects on the cloud cavitating flow over an axisymmetric projectile

For high-speed underwater vehicles, cavitation can be one of the most important speed barriers. The cavitating flow can be even complex when an underwater vehicle is sailing close to the free surface/wall. In this study, the mutual effects of the free surface and near-wall on the cloud cavitating flow that surrounds an axisymmetric projectile are investigated by water tank experiment and the computational fluids dynamics (CFD). The Split-Hopkinson pressure bar (SHPB) technology is applied in the experiment to accelerate the projectile in a short time. In our numerical approach, the volume of fluid (VOF) method, the large eddy simulation (LES) turbulence model, and the Zwart-Gerber-Belamri (ZGB) cavitation model are used. The cloud cavitating flow under the free surface/wall effect is investigated by changing the distance between the projectile and free surface (df) or wall (dw). Both the experiment and the simulation show that the unstable cavity evolution includes four stages induced by the re-entrant jet: cavity growth, re-entrant jet, cavity shedding and collapsing. The results further show that as df decreases, the cavity length is shorter and the cavity becomes more stable; as dw decreases, the cavity length is longer and the cavity becomes less stable. By understanding the free surface/wall effect on the stability of the cloud cavitating flow, the parameters space spanned by df and dw can be divided into several distinct flow regimes, in which the entire shedding cavity (symmetry/asymmetry), steady and non-shedding cavity, partial cavity shedding, and ventilated cavity are identified.

Molecular dynamics simulation and theoretical modeling of free surface effect on nanocrack initiation induced by grain boundary sliding in nanocrystalline materials

Free surfaces have significant effects on plastic deformation and fracture of nanocrystalline materials (NMs), especially for nano- or micro- scale specimens. To reveal the influence mechanism of free surfaces on crack initiation and growth, molecular dynamics (MD) simulations are carried out. The results show nanocrack initiation at triple junctions near free surfaces and the intergranular fracture due to nanocrack growth and coalescence. Based on the mechanism captured by MD, a theoretical model is established to describe the process of grain boundary (GB) dislocation evolution and nanocrack initiation. The critical stress for nanocrack initiation and the critical magnitude of GB sliding step are obtained for nanocrystalline nickel, aluminum and copper. Based on the proposed theoretical model, the fracture behaviors are discussed for the three nanomaterials.

Nonlinear vertical accelerations and mooring loads of a semi-submersible offshore fish farm under extreme conditions

Semi-submersible offshore fish farm has been considered a step forward to the new aquaculture era. To make it more durable to the excitations caused by waves and current, this paper examines the nonlinear vertical accelerations and mooring loads of a semi-submersible offshore fish farm model under extreme conditions. The steady-state non-dimensional first- and second-order harmonic accelerations at five different positions along the frame and the mooring tensions are obtained via experimental measurements and numerical simulations. The results show that both the first- and second-order harmonic accelerations are independent of the positions on the model but dependent on the wave period. Under wave-only conditions, when H≤0.15m, there is little difference between the experimental measurements and the numerical predictions on the accelerations. When H≥0.20m, the increasement of acceleration amplitude is 0.5 %–4.1 % for experiment, while the value is 3.3 %–19.0 % for numerical simulation. Under combined waves and current conditions, compared with H≤0.15m, the second-order harmonic acceleration increases exponentially under larger wave height, and most of the experimental results are larger than the numerical predictions when the current velocity V2=0.2m/s. The damping from the net enhances the nonlinearity of the second-order acceleration but it has little effect on the first-order. The current has a pronounced effect on the mooring tensions. When T=1.39s, the mean values of front mooring load at V2=0.2m/s are 6.4 times of that at V1=0.1m/s in maximum, but when the wave height reaches H=0.25m, the increase rate of mooring force gradually decreases. The free surface effect is also assessed in this paper.

Dynamic Modeling of Spent Fuel Rack Pool Subjected to Seismic Excitation Considering Fluid–Structure Interaction

Abstract The spent fuel of a nuclear power plant is generally stored in a wet storage pool. In case of a seismic event, one has to ensure the integrity of the spent fuel and structures holding them called spent fuel racks. In this study, a simple model accounting for 12 racks is proposed and compared with experimental results involving reduced scale racks. Fluid–structure interactions are modeled in terms of added coupling mass and damping, and free surface effects are accounted for. Comparison between simulations and experimental results showed good agreement. In spite of the simplicity of the model, simulations succeed to give a reasonable estimation of racks accelerations and were able to reproduce the effect of excitation amplitude and water level.

Influence of mixed free-surface and pressurized flow on transients process in a tailrace tunnel of a tailrace surge chamber

In the calculation of hydraulic transients in a hydropower station, the hydraulic problems caused by free-surface and pressurized flow are relatively complex. In consideration of this phenomenon, numerical simulation is used in this paper to study the effect of the transient free-surface, pressurized flow in a tailrace tunnel on the minimum pressure at inlet of the draft tube and the lining segment of the tailrace tunnel and the effect on the primary frequency regulation of the unit. The results show that the existence of tailrace surge tank can reduce the disturbance of the mixture flow on the units. Meanwhile, free-surface and pressurized flow can speed up the attenuation of the surge in the surge tank. Reasonable arrangement can mitigate transients in the tailrace system, which may provide a reference for similar projects.

Free-surface effects induced by internal solitons forced by shearing currents

Free-surface effects induced by internal solitary waves (ISWs) propagating through a background shear current are theoretically investigated in a shallow water framework. Following the Hamiltonian approach, we implement a mathematical formulation valid for a free surface, two-layer stratified system in the presence of mobile layers. Associated to the undisturbed condition characterized by the background fluid at rest, solitons with both positive and negative polarities are considered. To reproduce the typical oceanic conditions, we focus on theoretical predictions for a density ratio set to 0.99. Although under Boussinesq conditions a rigid-lid at the top of the theoretical domain is considered a good approximation, our analysis shows that main ISWs features may change when the fluid system, forced by shear currents, is modeled with a free surface. Signs assumed by three dimensionless quantities, i.e., the deformation parameter, the background velocity, and the undisturbed amplitude, allowed us to uniquely predict how the undisturbed solitons modify their interfacial profiles and change their celerity, in response to the background forcing. Our results show that waves celerity predicted by the rigid-lid model can be lower than the one resulting from the Hamiltonian formulation, although this never occurs in the absence of mobile layers. Theoretical predictions reveal that shearing current can induce deviations from the standard ISWs free-surface profile. We discuss the role of nonhydrostatic pressures in inducing free-surface short disturbances, in the form of undulated or multihumped profiles. The typical phase-opposition between interfacial and surface displacements can be lost as the free-surface displacements assume multihumped configurations.

RANS simulation of open propeller dynamic loads in regular head waves considering coupled oblique-flow and free-surface effect

To offer references for ventilation and load fluctuation of propeller in actual seaway, this paper presents a RANS (Reynolds-Averaged Navier-Stokes equations) investigation on open propeller dynamic loads in regular head waves at variant submergence depths, from the perspective of the coupled oblique-flow and free-surface effect. Discussions are made concerning the dynamic integral loads and single-blade loads (both axial and in-plane), and instantaneous single-blade loads at different azimuthal positions. CFD (Computational Fluid Dynamics) verification and validation are conducted based on an experiment in calm water and regular head waves conducted in a circulating water channel. As conclusions, under fully-submerged condition, single-blade load variations are related solely to the unsteady oblique-flow environment, with shifts of azimuthal positions corresponding to the maximum and minimum thrust and torque due to inflow non-uniformity. Under periodical-emerging condition, high-frequency integral-load fluctuations are identified by both simulation and experiment, resulting from the enhanced propeller-surface interactions due to upward wake inclination; this enhanced propeller-surface interaction also causes serious ventilation, abrupt rises or drops of axial single-blade loads, and destruction and dissipation of propeller vortex system. Furthermore, the self-induction effect on the load distribution non-uniformity is found to be unobvious in regular waves due to the unsteady and non-uniform inflow environment.

An iterative time-marching scheme for the investigation of hydrodynamic interaction between multi-ships during overtaking

An iterative time-marching scheme is developed to investigate the hydrodynamic interactions between multiple ships. Such an unsteady interactive effect could be magnified in restricted waterways, e.g., a channel or harbor area. To the author’s knowledge, nearly all the research on the ship-to-ship interaction neglecting the free surface effects. The free surface is usually treated as a rigid wall. This assumption is only reasonable when the speed of the ships is very low in deep water condition, due to the hydrodynamic interaction between the ships is mainly induced by near-field disturbances. However, when the moving speeds are moderately higher, especially with a small lateral separation between ships, the far-field effects arising from the ship waves become important. The main objective of the present paper is to develop an iterative time-matching algorithm to solve the hydrodynamic interaction between high-speed ships taking into account the nonlinear free surface boundary condition in time domain.

Contributions of different scales of turbulent motions to the mean wall-shear stress in open channel flows at low-to-moderate Reynolds numbers

Abstract