Physics of Fluids

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Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.
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An interface-compressed diffuse interface method and its application for multiphase flows

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
In this paper, an interface-compressed diffuse interface method is proposed for simulating multiphase flow with a large density ratio. In this method, an interface-compression term is introduced into the Cahn-Hilliard equation to suppress the interface dispersion caused by the numerical and modeling diffusion. The additional term only takes effect in the region of phase interface and works normal to the interface. The compression rate can be adjusted synchronously according to the local gradient of normal velocity at the interface. Numerical validations of the proposed method are implemented by simulating Rayleigh-Taylor instability, bubble deformation in shear flow, bubble merging, and bubble rising with a density ratio of 1000 and a viscosity ratio of 100. Good agreement of interface shapes and flow properties has been achieved as compared with both analytical solutions and published data in the literature. The obtained results also show that the present method makes great improvement of interface sharpness and avoids the occurrence of unphysical phenomenon. Meanwhile, the tiny interfacial structures can be captured effectively.

A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. These phenomena are commonly described by the two-layer shallow-water equations (SWE). When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer SWE. It has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions to correct the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly capture the behavior of shocks and contact discontinuities without additional closure relations. The result shows that simplification to an effective one-layer model is justified mathematically and can be made without additional knowledge of the shock behavior. The shock speed in the proposed model is consistent with empirical models and identical to front conditions that have been found theoretically by von Kármán and Benjamin. This suggests that the breakdown of the SWE in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the SW framework to shocks by studying one-dimensional lock-exchange/-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. The equations are solved numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer SWE. We also compare numerical results from the model with results from experiments and find good agreement.

Oscillatory flow of Maxwell fluid in a tube of isosceles right triangular cross section

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
In the present study, the oscillatory flow of a Maxwell fluid in a long tube of isosceles right triangular cross section is considered. The analytical expressions for the velocity and phase difference for the flow driven by the periodic pressure gradient are obtained explicitly. The numerical solutions are calculated by using a high-order compact finite difference method. The effects of relaxation time and the Deborah number on the velocity and phase difference are discussed numerically and graphically.

Instabilities of particle-laden layers in the stably stratified environment

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
The stability of the interface formed by fine suspended particles is studied through linear stability analysis. Our derivation using the regular perturbation expansion with respect to the particle’s settling velocity shows that the unstable modes are independent of the gravitational settling of individual particles. These modes can be obtained from the six-order ordinary differential equation obtained from the analysis of zero-order quantities. In addition to the four boundary conditions applied at the interface in the traditional Rayleigh-Taylor problem in the semi-infinite domain, two conditions based on the continuity of the concentration of the background stratification agent and its gradient are introduced. Our stability results show transition of modes from a small value in a regime of Rayleigh-Taylor instability to the large values of double-diffusive convection when the background density stratification becomes increasingly significant. In the latter case, our analysis shows growth of small perturbations with dominant wavelengths scaled by the double-diffusion length scale. The transition of unstable modes depends on the density ratio, the Prandtl number of the stratification agent, and the viscosity ratio between the two fluid layers. The analysis is further confirmed by the results from the direct numerical simulation.

Boundary layer transition over a foil using direct numerical simulation and large eddy simulation

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
Transitional boundary layers over lifting bodies represent an important class of flows in many industrial applications, and accurately capturing the transition is crucial for the prediction of important phenomena such as lift, drag, and trailing-edge noise. In this study, we consider how large eddy simulations (LESs) can be used to capture the natural boundary layer transition and compare the results to fully resolved direct numerical simulations that provide a detailed picture of the transition and trailing edge flow. The ability of LES to capture the transition is considered by looking at different elements of the subfilter scale modeling and discretization. The behavior of the subfilter scale model is shown to be critical, and it must remain inactive during the early stages of transition to avoid erroneous predictions due to excessive dissipation. Dispersion errors, when present, can cause the natural transition mechanism to be bypassed at an earlier stage, which leads to higher levels of turbulent kinetic energy at the trailing edge.

Large scale instabilities in coaxial air-water jets with annular air swirl

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
The aim of this paper is to characterize large-scale instabilities during the primary breakup process in liquid centered coaxial air-water jets. The interest here is to investigate the role of annular air swirl on such instabilities. A coaxial airblast atomizer that incorporates an axial swirler is considered for this purpose. The atomizer was operated in a wide range of the Weber number, Weg(80–958), momentum flux ratio, M(1–26), and air swirl strength, S(0–1.6). High-speed shadowgraphic images of the primary jet breakup process were recorded. Proper orthogonal decomposition (POD) analysis of the time-resolved images was performed for each operating condition. The 2nd and 3rd POD modes depicted some universal spatial features which refer to large scale instabilities. Three different dominant large scale instabilities were identified, viz., jet flapping, wavy breakup, and explosive breakup, for the entire range of the injector operating condition either in the presence or absence of air swirl. It was found that jet flapping (referred to as the lateral oscillation of the tail end of the jet) is the dominant mode of jet instability for a lower range of M, while explosive jet breakup (referred to as the radial expansion of the jet) governs jet breakup unsteadiness for a higher range of M. The wavy or sinuous mode of breakup is a secondary mechanism relevant under low M conditions. The mechanisms of large scale instabilities and the role of air swirl in that context are explained based on the Fourier analysis of the temporal coefficients of the corresponding POD modes.

Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 106 ≤ Ra ≤ 107 and the Prandtl number (Pr) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number (Nu) and Reynolds number (Re) are Nu = 0.21Ra0.25 and Re = 6.11Ra0.50, respectively, indicating that scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relatively lower Ra, while they approach the Gaussian profile at relatively higher Ra. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of Ra and Re.

Parameter extension simulation of turbulent flows

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
The use of parameter extension simulation (PES) as a mathematical method for simulating turbulent flows is proposed in this study. It is defined as the calculation of a turbulent flow with the help of a reference solution. A typical PES calculation includes three steps, as follows: setting up an asymptotic relationship between the exact solution of the Navier–Stokes equations and the reference solution for the initial parameter values, calculating the reference solution and the necessary asymptotic coefficients, and extending the reference solution to the parameter values to produce the exact solution. The method of controlled eddy simulation (CES) has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special case of large eddy simulation (LES), in which a weighting coefficient and an artificial force distribution are used to damp part of the turbulent motions. The distribution of artificial force is modeled with the help of eddy viscosity. The reference-weighting coefficient can be determined empirically or in a convergence study. To demonstrate potential uses, the proposed PES method is used to simulate four types of turbulent flows. The flows are decaying homogeneous and isotropic turbulence, smooth-wall channel flows, rough-wall channel flows, and compressor-blade cascade flows. The numerical results show that the PES solution is more accurate than a Reynolds-average Navier–Stokes simulation solution. Unlike a traditional LES method, which uses the Smagorinsky, k-equation-transport, or WALE subgrid model, the PES requires a lower mesh resolution. These characteristics make it a potential method for simulating the engineering of turbulent flows with complex geometry and a high Reynolds number.

Effects of upstream perturbations on the solution of the laminar and fully turbulent boundary layer equations with pressure gradients

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
The aim of this work is to contribute to the understanding of sensitivity of boundary layers to the upstream boundary condition and history effects for both laminar and fully turbulent states in equilibrium conditions as well as some nonequilibrium turbulent boundary layers. Solutions of the two-dimensional boundary layer equations are obtained numerically for this study together with the Reynolds-averaged Navier-Stokes approach for turbulence modeling. The external pressure gradient is imposed through an evolution of the external velocity of the form [math], and boundary layers are initialized from a profile giving a perturbed shape factor. It is found that laminar boundary layers require very long distances for convergence toward the nondisturbed profiles in terms of the initial boundary layer thickness (∼104δin) and that this distance is dependent on m. In turbulent boundary layers, much shorter distances, although still large (∼102δin), are observed and they are also dependent on m. The maximum adverse pressure gradient for which convergence to a reference solution is possible is also studied finding that there is no limit for attached laminar boundary layers, whereas turbulent boundary layers do not converge once they are out of equilibrium. The convergence distances in turbulent boundary layers are also studied in terms of the turnover length ([math]) because it has been shown to be more appropriate to refer the convergence distance to this length rather than the boundary layer thickness. The values for convergence using this criterion are extended to pressure gradient boundary layers. Moreover, an equivalent criterion is proposed and studied for laminar boundary layers based on the viscous characteristic time.

Direct numerical simulation of effects of a micro-ramp on a hypersonic shock wave/boundary layer interaction

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
A direct numerical simulation study is performed on the hypersonic shock wave/boundary layer interaction controlled by using a microramp vortex generator (MVG). The mean structures around the microramp generator are obtained and the comparison on the shock structures and surface flow patterns is made between cases with and without the MVG. The evolution of the vortical structures in the wake of the MVG is described and the evolution process is found to be similar to that in a supersonic flow. The detailed three-dimensional voritcal structures are presented. Furthermore, the effects of the MVG on the shock wave/boundary layer interaction are investigated. The results show that the heat flux and friction after the interaction have been reduced apparently by the MVG. Such reduction is mainly caused by the flow pattern near the reattachment and the alteration of the vortical structures after the interaction.

A novel spatial-temporal prediction method for unsteady wake flows based on hybrid deep neural network

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
A fast and accurate prediction method of unsteady flow is a challenge in fluid dynamics due to the high-dimensional and nonlinear dynamic behavior. A novel hybrid deep neural network (DNN) architecture was designed to capture the spatial-temporal features of unsteady flows directly from high-dimensional numerical unsteady flow field data. The hybrid DNN is constituted by the convolutional neural network, convolutional long short term memory neural network, and deconvolutional neural network. The unsteady wake flow around a cylinder at various Reynolds numbers and an airfoil at a higher Reynolds number are calculated to establish the datasets as training samples of the hybrid DNN. The trained hybrid DNNs were then tested by predicting the unsteady flow fields in future time steps. The predicted flow fields using the trained hybrid DNN are in good agreement with those calculated directly by a computational fluid dynamic solver.

New method for dynamic mode decomposition of flows over moving structures based on machine learning (hybrid dynamic mode decomposition)

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume 31, Issue 12, December 2019.
Dynamic Mode Decomposition (DMD) is a data-driven reduced order method, which is known for its power to capture the basic features of dynamical systems. In fluid dynamics, modal analysis of unsteady fluid flows over moving structures is significant in terms of state estimation and control. However, the underlying algorithm of the DMD requires a fixed spatial domain, which is an obstacle for applying the DMD on the numerically investigated problems using dynamic meshes. In this study, a hybrid method called Hybrid Dynamic Mode Decomposition (HDMD) is presented for analysis of unsteady fluid flows over moving structures based on the DMD and machine learning. According to the assessment of several data interpolation methods, the K-nearest neighbor algorithm is employed for the interpolation of the numerical data from dynamic meshes at each time step to a single stationary grid. Three different case studies (rotating cylinder, oscillating airfoil, and Savonius wind turbine) are assessed to ensure the validity of the proposed method. Minimum mean R2 equal to 0.92 has been obtained for all of the mentioned cases, indicating the robustness of the HDMD algorithm for a variety of fluid flow simulations.

Drag reduction in turbulent flow along a cylinder by circumferential oscillating Lorentz force

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume PACT2019, Issue 1, December 2019.
Direct numerical simulations are performed to study the drag reduction effect in turbulent flow along a cylinder by the circumferential oscillating Lorentz force at the Reynolds number Reτ = 272 based on the reference friction velocity and the thickness of the boundary layer. The maximum drag reduction rate obtained in the present work is 42.6%. The intensity, penetration thickness, distribution (idealized or realistic), and oscillation period of the Lorentz force are all crucial in determining the drag reduction rate. As the Lorentz force is intensified or its penetration thickness and oscillation period increase, the wall friction drag will prominently decrease as long as the circumferential flow is stable. The Stokes layer, introduced by the circumferential oscillating Lorentz force, effectively manipulated the near-wall coherent structures, leading to the decrease of the wall friction drag. However, the occurrence of the force-induced vortices in the near-wall region can also lead to significant drag increase by enhancing the radial momentum transportation due to centrifugal instability. By estimating the energy consumption rate, it is clear that the extra power to implement the Lorentz force is far more than the power saved due to drag reduction, which is the result of the low conductivity of the fluid media. Taking the coupling between the electromagnetic field and the flow field into consideration, the wall friction drag is nearly zero and the turbulence intensity in the near-wall region is very low when the induced Lorentz force is high. But the induced Lorentz drag is greatly increased and the turbulence fluctuations are enhanced in the outer region.

Bi-global stability analysis in curvilinear coordinates

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume PACT2019, Issue 1, December 2019.
A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability.

Mechanisms of broadband noise generation on metal foam edges

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume PACT2019, Issue 1, December 2019.
The turbulent flow over a porous trailing edge of a NACA 0018 airfoil is experimentally investigated to study the link between the hydrodynamic flow field and the acoustic scattering. Four porous trailing edges, obtained from open-cell metal foams, are tested to analyze the effects on far-field noise of the permeability of the material and of the hydrodynamic communication between the two sides of the airfoil. The latter is assessed by filling the symmetry plane of two of the porous trailing edges with a thin layer of adhesive that acts as a solid membrane. Experiments are performed at a zero degree angle of attack. Far-field noise measurements show that the most permeable metal foam reduces noise (up to 10 dB) with respect to the solid trailing edge for Strouhal numbers based on the chord below 16. At higher nondimensional frequencies, a noise increase is measured. The porous inserts with an adhesive layer show no noise abatement in the low frequency range, but only a noise increase at higher frequency. The latter is, therefore, attributed to surface-roughness noise. Flow field measurements, carried out with time-resolved planar particle image velocimetry, reveal correlation of near-wall velocity fluctuations between the two sides of the permeable trailing edges only within the frequency range where noise abatement is reported. This flow communication suggests that permeable treatments abate noise by distributing the impedance jump across the foam in the streamwise direction, promoting noise scattering from different chordwise locations along the inserts. This is further confirmed by noise source maps obtained from acoustic beamforming. For the frequency range where noise reduction is measured, the streamwise position of the main noise emission depends on the permeability of the insert. At higher frequencies, noise is scattered from upstream the trailing edge independently of the test case, in agreement with the roughness-generated noise assumption.

Transition of flow field of acoustically levitated droplets with evaporation

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume DFAL2019, Issue 1, December 2019.
We investigated the multidimensional velocity field of acoustically levitated droplets using stereoscopic particle image velocimetry. To clarify the correlation between evaporation behavior and internal and external flows, binary droplets of ethanol and water were used as test fluids. Immediately following droplet levitation, toroidal vortices were generated in the droplet; however, the internal flow transitioned to uniaxial rotational flow as the ethanol component evaporated. In the external flow field, initially, the flow direction was distant from the top and bottom of the droplet with circulating vortices near the droplet surface. As evaporation progressed, the external flow direction transitioned to the opposite direction as the circulation vortices expanded. To investigate the driving force of the uniaxial rotation of the levitated droplet, we simulated the internal flow of the rotating droplet. The simulation and experimental results were in good agreement relative to the order and distribution profile of the flow velocity. Based on these results, we consider the transition mechanism of internal and external flow structures of acoustically levitated droplets with evaporation. Our experimental and simulation results provide deeper physical insights into noncontact fluid manipulation and indicate potential future applications.

Internal flow during mixing induced in acoustically levitated droplets by mode oscillations

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume DFAL2019, Issue 1, December 2019.
In this paper, we describe a mixing method with mode oscillation on the internal flow field of a levitated droplet. The effect of internal flow on the mixing performance of droplets acoustically levitated via ultrasonic phased arrays remains unclear. To better understand the mixing mechanism of a levitated droplet, clarifying the effect of the internal flow field on droplet mixing from mode oscillation during acoustic levitation is necessary. We used a 50 wt. % glycerol aqueous solution with 6th mode oscillation. We applied particle image velocimetry (PIV) to study the internal flow fields under interfacial oscillation. The PIV results indicated that the visualized flow field enhanced mixing performance with increasing Reynolds number. We demonstrated the nonlinear characteristics of droplet mixing compared to potential flow. The nonlinearity of the droplet oscillation was driven by the nonlinear acoustic field exerted on the levitated droplet. Mode oscillation on the droplet surface induced a pressure gradient and caused internal flow in the droplet. The pressure gradient in the droplet from the interfacial oscillation was quantitatively analyzed. Pressure induced by the interfacial oscillation, which can be roughly ten times larger than the hydrostatic pressure in the droplet, drastically enhanced the mixing performance in the droplet. Our experimental findings provide deeper physical insights into noncontact fluid manipulation for potential lab-in-a-drop applications.

Review of transport processes and particle self-assembly in acoustically levitated nanofluid droplets

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume DFAL2019, Issue 1, December 2019.
Acoustic levitation has been the cornerstone of many interesting studies across multiple application domains ranging from biomedical engineering to spray drying. In the sphere of colloidal or nanofluid droplets, acoustic levitation allows researchers to probe deep into the physical mechanisms concerning stability, heat and mass transfer processes, and subsequent particle self-assembly. It also offers a plethora of opportunities to custom engineer the transport mechanisms, thereby enabling unique morphological features of the dried precipitate. The high degree of spatial control in a levitator and ease of experimental diagnostics ensure one to study any such transport process in great detail. In this review, we have systematically elucidated three important paradigms in acoustic levitation of nanofluid droplets. First, we have provided a detailed understanding of the fluid mechanics of the process by delving into the pressure and velocity fields the droplet encounters. We have provided descriptions about the key nondimensional number responsible for successful levitation of the droplet. Second, we have studied the transport processes in nanofluid droplets and investigated the important transport mechanisms that are affected by flow and the acoustic field of the levitator. In particular, we look into the heat and mass transfer limitation for particle laden droplets. Third, we have analyzed the particle self-assembly and formation of nanoporous viscoelastic shell. Subsequently, we provided detailed insights into the morphological transitions of the shell through buckling and cavity ingression. We also showcase how the morphology of the shell can be controlled using differential heating and doping. Finally, we conclude by showcasing some unique application context-like photonic crystal behavior that can emerge from unique particle assembly in acoustic levitation.

Numerical and experimental investigation of the stability of a drop in a single-axis acoustic levitator

Sun, 12/01/2019 - 08:00
Physics of Fluids, Volume DFAL2019, Issue 1, December 2019.
Acoustic levitation can be employed to hold liquid drops in midair, enabling novel applications in X-ray scattering of proteins, amorphous crystallization of solutions, or contactless mixing. Multiple studies have characterized the physical behavior of a levitated drop inside an acoustic field. Here, we present a numerical and experimental study on the acoustic levitation of water drops in a single-axis acoustic levitator consisting of an ultrasonic transducer and an opposing reflector. Instead of modeling an abstract incident acoustic field, our model considers the shape of the drop as well as the real geometry of the levitator. We also use a high-speed camera to observe the disintegration and the undesired oscillations of the drops. Our results show that the insertion of a drop in the levitator provokes a shift in its resonant frequency that depends on the shape of the drop. Second, the levitation behavior depends on whether the levitator operates slightly below or above the resonance. Third, if the levitator is driven above the resonant frequency, it is possible to levitate with more strength and avoid disintegration of the drop. This research provides an insight on how to achieve more stable experiments that avoid the bursting and undesired oscillations of the levitated sample. We hope that it will facilitate numerous experiments involving acoustically levitated liquid drops.

The suction effect during freak wave slamming on a fixed platform deck: Smoothed particle hydrodynamics simulation and experimental study

Thu, 11/21/2019 - 02:58
Physics of Fluids, Volume 31, Issue 11, November 2019.
During the process of wave slamming on a structure with sharp corners, the wave receding after wave impingement can induce strong negative pressure (relative to the atmospheric pressure) at the bottom of the structure, which is called the suction effect. From the practical point of view, the suction force induced by the negative pressure, coinciding with the gravity force, pulls the structure down and hence increases the risk of structural damage. In this work, the smoothed particle hydrodynamics (SPH) method, more specifically the δ+SPH model, is adopted to simulate the freak wave slamming on a fixed platform with the consideration of the suction effect, i.e., negative pressure, which is a challenging issue because it can cause the so-called tensile instability in SPH simulations. The key to overcome the numerical issue is to use a numerical technique named tensile instability control (TIC). Comparative studies using SPH models with and without TIC will show the importance of this technique in capturing the negative pressure. It is also found that using a two-phase simulation that takes the air phase into account is essential for an SPH model to accurately predict the impact pressure during the initial slamming stage. The freak wave impacts with different water depths are studied. All the multiphase SPH results are validated by our experimental data. The wave kinematics/dynamics and wave impact features in the wave-structure interacting process are discussed, and the mechanism of the suction effect characterized by the negative pressure is carefully analyzed.

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