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Keywords: Navier-Stokes equations; resolvent; free surface; solution formula; Lp estimates.GraphBy Yongting Huang and Tao LuoReported by Author; Author [Extracted from the article]

ObjectiveThis study investigates the evolution of the interaction between an underwater explosion bubble and the free liquid surface in terms of compressibility and viscous effect. MethodsA numerical model of an underwater explosion bubble coupled with the free liquid surface is developed on the basis of the compressible two-phase flow solver of OpenFOAM and the volume of fluid method (VOF). The validity of the numerical model is then verified by comparison with the experimental results. The effects of different flow field viscosities and distance parameters on the bubble pulsation process and free-surface spike motion are also investigated. ResultsThe flow field viscosity effect has an important influence on the surface spike height, bubble pulsation period and bubble pulsation, especially the bubble morphology in the rebound phase. Ring bubble morphology is not easy to maintain in low viscosity fluid, so the tearing phenomenon of the bubble can easily occur. As the distance parameter increases, the coupling effect between the free surface and the bubble gradually decreases, the bubble pulsation period increases, the heights of the primary and secondary surface spikes decrease, and the widths of the primary spike and liquid jet gradually increase.ConclusionThe results of this study can provide useful references for determining the evolution mechanism of bubbles under different flow field viscosities.

AbstractThe primary objective of the current work is to establish the impacts of planar boundary and non-planar boundary on the displacement components (DCs) of Rayleigh-type wave propagation in an elastic structure. The elastic structure, precisely, incorporates a pre-stressed nearly incompressible elastic material in the half-space along with the non-planar boundary at the free surface. The methodology applied features variable separable technique and Taylor’s series expansion along with substitution method to establish the expressions for DCs and frequency relation. The frequency relation of Rayleigh-type wave is obtained for the situation considering planar free surface, which is further reduced as a special case of the study and validated with the classical result present in the literature. The DCs of Rayleigh-type wave have been numerically computed, and their reliance on wave number have been exhibited graphically. In addition to this, the influences of affecting parameters viz., hydrostatic stress, principal Cauchy stress and curvature parameter on DCs have been traced out. The computational result also manifests the domain of existence of Rayleigh-type wave propagating in the considered model in the presence of planar free surface. [ABSTRACT FROM AUTHOR]

The present study aims to solve analytically a free surface flow above a trapezoidal obstacle with angle β = π 3 β = π 3 . The flow which forms different angles β with the horizontal plane, is assumed to be steady, irrotational and potential. The fluid is considered as inviscid and incompressible. In addition, the gravity and surface tension effects are not taken into consideration. An approximate analytical solution of the free surface shape problem was successfully determined using the Shwartz-Christoffel conformal mapping transformation technique and the free streamline theory which was introduced by Kirchhoff. The main results were obtained for different values of the inclination angle β between the trapezoidal obstacle and the axis of the struts. [ABSTRACT FROM AUTHOR]

In this paper, we present a numerical study of a two-layer fluid flowing around a vertical hollow cylindrical structure. We analyze the effect of two-layer fluid in the presence of hollow cylindrical structure in the surface and internal wave modes. We consider a hollow cylinder within a two-layer fluid wherein the upper fluid is bounded by a free surface above and the lower fluid is bounded by an impermeable solid below. A matched eigenfunction expansion and separation of variables method are used to obtain the diffracted velocity potentials in the identified domains. The obtained diffracted velocity potential gives us the wave elevation at the surface and the internal wave modes. We present the wave elevations with different parameters of the device in various wave modes of motion, including surface waves and internal waves. It is observed that in the surface mode, the free surface elevation is higher than the interface elevation and the free surface and the interface elevations are in same phase whereas in the internal wave mode, the elevation at the interface is greater than that at the free surface. [ABSTRACT FROM AUTHOR]

Most space shuttle fuel tanks use a center column to hold the Propellant Management Device (PMD). This paper analyzes the gas–liquid interface state in the tanks with a central column during microgravity experiments conducted in the Chinese Space Station. It launches an extended study to investigate the gas–liquid interface state under different gravity conditions. Using the perturbation method and boundary layer theory, we numerically calculated the morphology of the gas–liquid interface under varying gravity conditions based on the Young–Laplace equation. The results were then compared to those obtained from existing commercial software and were found to be consistent. Based on this, the study develops two types of calculation procedures. The first procedure generates the corresponding shape of the liquid surface by inputting the height of the liquid surface endpoints and the gravity level. The second procedure is based on the targeting method and generates the corresponding liquid surface by inputting the volume of the liquid in the storage tank and the gravity level. The procedures were used to analyze the variation of gas–liquid interface properties under different gravity conditions. This study offers theoretical support for liquid management in aerospace engineering fuel tanks. [ABSTRACT FROM AUTHOR]

A numerical simulation based on the CFD method is used to study the interaction between a horizontal cylinder and wave flow. Firstly, a two-dimensional numerical calculation model of both a fixed and a rigid moving cylinder, with a free surface under varying wave flow conditions, is created. In the established model, the loads on the horizontal cylinder under different submergence depths, flow velocities, cylinder sizes, wave periods, and k values (spring stiffness) are analyzed and calculated. The results show that, when the cylinder is close to the free surface, its hydrodynamic load under wave flow conditions is more sensitive to changes in submergence depth, which essentially affects wave reflection and blockage. At different flow velocities, k values, cylinder radii, and arm lengths, the main frequency of the Fourier transform of the cylinder motion curve remains unchanged; however, the main frequency does change with the wave period and submergence depth. The efficiency of rotary cylindrical energy harvesting is influenced by various factors, among which an initial increase and then decrease are observed with a gradually increasing k value, arm length, period, and radius, in addition to an observed decrease with increasing flow velocity. [ABSTRACT FROM AUTHOR]

Three-dimensional (3-D) wing moving steadily over free water surface with the effects of finite depth has been investigated numerically using an iterative boundary element method (IBEM), which was developed for cavitating 3-D hydrofoils advancing under a free surface. The IBEM has been modified and extended for this purpose. The water is incompressible, inviscid and the flow is irrotational. All variables and equations are made dimensionless. In this way the convergence of the numerical scheme is achieved very quickly and consistently. The IBEM is based on Green's theorem. The wing part of problem (including its wake), the free surface problem and the bottom surface problem are solved separately with the effects on each other. The 3-D wing surface, the bottom surface and free surface are modeled with constant strength source and doublet panels. The kinematic boundary condition is applied both on the wing surface and on the bottom surface. On the other hand, the linearized kinematic and dynamic combined condition is applied on the free water surface. The method is first applied to a rectangular wing with a high aspect ratio to compare the pressure distribution on mid-section strip with that of two-dimensional method. Later, the IBEM is applied to a tapered swept-back wing and the effects of finite depth on wing performance have been examined. It is noted that the reduced water depth causes an increase in Kelvin wedge angle, wave height and wave length compared to the infinite depth case. It is also found that a decrease in the depth of bottom surface causes an increase in the loading on the wing. [ABSTRACT FROM AUTHOR]

In this study, a boundary element method (BEM) is applied to investigate acoustic radiation from a sphere vibrating in pulsating mode on the free surface of finite or infinite depth water. Effect of the free surface is introduced by employing a half-space Green's function. A modified version of the Helmholtz integral equation (HIE) is used to calculate acoustic radiation from the sphere vibrating in pulsating mode on the free surface. Free-terms of the HIE are calculated using two different forms of integrals and "dummy" boundary elements. Moreover, to simulate finite depth fluid medium, a chain image-source method is used to derive a waveguide Green's function. To demonstrate applicability of the method presented, calculated acoustic pressures are compared with those by finite element method (FEM) and analytical calculations. Additionally, the effects of submergence depth and vibration frequency on acoustic radiation are investigated for infinitely deep water together with those of water depth and field point distance on acoustic radiation for finite water depth medium. The calculations show that there is a good agreement between BEM, FEM and analytical solutions. Also, it is observed that field point distance significantly affects the convergence behavior of waveguide Green's function. Furthermore, it is noted that submergence depth, domain depth and vibration frequency have pronounce influence on radiated pressure amplitude and pressure field pattern. [ABSTRACT FROM AUTHOR]

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An exact three-dimensional hydrodynamic analysis based on the linear potential theory is presented to study the transient liquid sloshing in a prolate spheroidal container which is filled to an arbitrary depth with an inviscid incompressible fluid. Based on this, using the potential fluid theory in the elliptical coordinate system and applying appropriate boundary conditions on the free surface and tank walls, the governing differential equations of the problem were derived. Then, with the proper expansion of orthogonal functions in spheroidal coordinates, the governing partial equations were transformed into a system of ordinary time differential equations. These equations were solved using the Laplace transform and Durbin's numerical inversion under different external excitations. the natural frequencies and the physical parameters such as the height of the free surface, pressure, force, and overturning moment in the spheroidal containers under external excitation were evaluated and compared with cylindrical and spherical tanks of the same volume. The results of the study show that by increasing the semi-axis ratio in prolate spheroidal and cylindrical tanks, due to the increase in the free surface of the fluid, the natural frequencies decrease in all modes, while in the spherical tank, it increases homogeneously and therefore the natural frequencies remain constant. In addition, the transient pressure, force, and overturning moment response of the prolate spheroidal containers are lower than the cylindrical and spherical tanks with same volume. Consequently, a prolate spheroidal tank, in addition to having a more suitable placement space in the body of the space launcher than the spherical tank, conducts lower destructive sloshing effects compared to both cylindrical and spherical tanks. To validate the results, limiting cases are considered and the validity of results is established in comparison with the data in the existing literature and finite element results using commercial software. [ABSTRACT FROM AUTHOR]

Understanding the Hydrogen embrittlement (HE) mechanism on the miscroscopic level has been a long-standing challenge. In this work, a systematic computational work based on the first-principles simulations and Ref as well as the ab initio molecular dynamics unveiled the effects of 19 metallic solutes on the HE of AlMgZnCu alloys with Σ3(111), Σ5(210), Σ5(310), Σ7(123), and Σ9(221) grain boundaries (GBs). The effects of the atomic size of these solutes on the complex segregation energy (SE) and GB energy were investigated, and the effect of temperature on the H concentration of the AlMgZnCu alloys was analyzed using a Gaussian distribution of complex SE. It is determined that the HE process involves the following sequence of phenomena: fracture surface formation → crack propagation → GB fracturing. The key findings of this work are summarized as follows: (i) the SE and GB/free surface energy depends linearly on the atomic sizes of the alloy; (ii) the crack could be healed at a critical temperature of 673 K; (iii) A gene diagram has been developed to show the temperature dependence of the segregation and cohesion of H concentration. [Display omitted] • The crack could be cured at a critical temperature of 673 K. • A gene diagram has been developed to show the temperature dependence of the segregation and cohesion of H. • The SE and GB/free surface energy depends linearly on the atomic sizes of the alloy. [ABSTRACT FROM AUTHOR]

Open-channel flows over a drop structure with a trench, often seen in urban rivers, may cause an oscillating phenomenon of hydraulic jumps depending on the trench geometry and hydraulic conditions. The oscillating hydraulic jumps are accompanied by large-scale water-surface variations with wave breaking, and numerical predictions of such flows are challenging in hydraulics. Using unsteady Reynolds-averaged Navier-Stokes simulations of air-water two-phase flows, we attempted to predict an oscillating hydraulic jump at a drop structure with a trench observed in our laboratory experiment. Several high-Reynolds-number turbulence models were applied, and the effects of turbulence models and grid resolutions on predicting the oscillating hydraulic jump were investigated. Turbulence models other than the k–ω SST model resulted in a steady-state flow with no oscillations regardless of the grid resolution. The k–ω SST model succeeded in predicting the oscillating hydraulic jump using a fine grid while the flow became a quasi-steady state using a coarse grid. Moreover, the period of the oscillation and the flow fields are in good agreement with the experimental results. The k–ω SST model has the ability to predict oscillating hydraulic jumps, including wave breaking, because this model accurately simulates flows with separations or stagnations under adverse pressure gradients. [ABSTRACT FROM AUTHOR]

Cavitation bubbles commonly exist in shipbuilding engineering, ocean engineering, mechanical engineering, chemical industry, and aerospace. Asymmetric deformation of the bubble occurs near the boundary and then has strong destructiveness, such as high amplitude loading. Therefore, the research on non-spherical deformation is of great significance, and the objective of this paper is to investigate the non-spherical collapse dynamics of laser-induced cavitation bubbles when near different boundaries. In this study, experimental data, such as the bubble pulsation process and bubble surface velocity distribution, were obtained by high-speed camera techniques and full-field velocity calculations. Near the different boundaries, the results show that the bubbles appeared to have different collapse shapes, such as near-hemispherical, near-ellipsoidal, near-cone, and near-pea shapes, and the surface velocity distribution is extremely non-uniform. When the bubble near the free surface or rigid boundary collapses, the smaller the stand-off r is, the more obvious the repulsive effect of the free surface or the attractive effect of the rigid boundary is. As the stand-off r decreases, the larger the Bjerknes force and the bubble surface velocity difference and the more pronounced the non-spherical shape becomes. [ABSTRACT FROM AUTHOR]

When an explosive column initiates, it will radiate P‐SV waves. The propagation of P‐SV waves, which carry the majority of the explosion energy, is extremely complex in jointed rock masses. Therefore, studying the propagation of blasting stress waves in jointed rock masses is of great significance for optimizing the parameters of the blastholes and improving the economy and safety of geotechnical engineering construction. In this study, an analytical model of the propagation of P‐SV waves radiated by explosive columns in jointed rock masses is derived. Using this analytical model, the maximum displacement distribution in jointed rock masses with the free surface is analyzed, and the results show: (1) when the stress waves propagate to the free surface, the reflected waves will be generated, which will produce the remarkable superposition effect with the direct waves, while the superposition effect will affect the maximum displacements at the measuring points significantly; (2) the amplitude of transmitted waves generated from the stress waves that propagate through the rock joints is smaller than that of direct waves, thus the maximum displacements at the measuring points are affected by the rock joints within a certain range; (3) the velocity of detonation (VOD) and the length of the explosive column can affect the superposition effect of stress waves, ultimately impacting the maximum displacement distribution in jointed rock masses. Therefore, optimizing the parameters of the blastholes reasonably to achieve the optimal superposition of stress waves is of great significance for improving the construction efficiency of geotechnical engineering. [ABSTRACT FROM AUTHOR]

Nowadays a propellant residual gauging method based on the thermal response of the tanks’ wall is developed. And the liquid distribution and meniscus height have great effects on the thermal response. Profiles of liquid free surfaces in revolved containers under microgravity are studied through theoretical analysis and numerical simulation in this paper. The analytical formula for the static profile of the liquid surface in the spherical tank is established. It shows that the profile is a section of a circle cut off by the tank wall. For given the geometry of the tank, liquid volume and contact angle, the profile of the free surfaces under microgravity can be obtained by using the Shooting method based on the theoretical model. Numerical simulation is carried out with the Volume of Fluid method, and it is verified that the static profiles at different contact angles and liquid filling rates fit the theoretical descriptions. It is concluded that the meniscus height increases slowly as the filling rate increases, and the smaller the contact angle, the more obvious this trend. Then the theory is extended to the tanks of arbitrary shapes, and the critical position of the profile is derived. Below the critical position the propellant may accumulate in some corners or pits, which makes it unable to be fully utilized. The critical position is related to the shape of the tank and the contact angle. This research is of great value for the prediction of the static profiles of liquid surfaces in tanks and the propellant residual gauging. [ABSTRACT FROM AUTHOR]

Simulation of filtration flows under the Zhukovskii sheet pile through a soil mass underlain by an impermeable base or by a highly permeable pressure aquifer was carried out using two schemes within the framework of the theory of flat steady-state filtration of an incompressible fluid according to Darcy's law. The influence of evaporation or infiltration on the free surface of ground water was studied based on solving mixed boundary-value problems of the theory of analytical functions using the Polubarinova-Kochina method. Algorithms have been developed for calculating the saturated zone of soil in the case of water moving in it is determined by the backing of the soil from its impermeable base or the underlying well-permeable aquifer, evaporation or infiltration on the free surface of ground water and by soil capillarity. [ABSTRACT FROM AUTHOR]

This paper is motivated by the study of Lyapunov functionals for the Hele-Shaw and Mullins-Sekerka equations describing free surface flows in fluid dynamics. We prove that the L²- norm of the free surface elevation and the area of the free surface are Lyapunov functionals. The proofs combine exact identities for the dissipation rates with functional inequalities. We introduce a functional which controls the L²-norm of three-half spatial derivative. Under a mild smallness assumption on the initial data, we show that the latter quantity is also a Lyapunov functional for the Hele-Shaw equation, implying that the area functional is a strong Lyapunov functional. Precise lower bounds for the dissipation rates are established, showing that these Lyapunov functionals are in fact entropies. [ABSTRACT FROM AUTHOR]

We investigate analytically and experimentally the flow rate through a biochip in a circuit involving a peristaltic pump and reservoirs with liquid/air interfaces. Peristaltic pumps are a convenient way to achieve recirculation in microfluidic circuits. We consider different cases: reservoirs in contact with ambient air, tight reservoirs, and imperfect tightness leading to air or liquid leaks. We demonstrate that if changes in hydraulic resistance are slow enough, i.e., if cells do not proliferate too fast, the system may reach an equilibrium, with a difference in liquid height between inlet and outlet reservoir compensating the pressure drop in the biochip. We compute the flow rate through the biochip in the transient regime as well as the characteristic time. We also show that depending on the circuit dimensions, this equilibrium may never be reached. We provide guidelines to design tubings and reservoirs to avoid this situation and ensure a smooth recirculation at a desired flow rate, which is a necessary condition for dynamic cell culture. [ABSTRACT FROM AUTHOR]

This article presents a nonhydrostatic model of the dynamics of a stratified slightly compressible fluid with a free surface. An explicit nonhydrostatic CABARET-NH (CABARET Non-Hydrostatic) scheme for the numerical solution of the constructed system of differential equations in mixed Eulerian–Lagrangian coordinates based on the balance-characteristic scheme of the CAB-ARET class is described. The well-balanced property of the numerical scheme is proved. The results of the calculations of the free-surface oscillation problem are presented. [ABSTRACT FROM AUTHOR]

Liquid sloshing is a common phenomenon in the transporting of liquid tanks. A safe liquid transporting needs to control the entered fluctuating forces to the tank walls, before leading these forces to large forces and momentums. Using predesigned baffles is a simple method for solving this problem. Smoothed Particle Hydrodynamics is a Lagrangian method that has been widely used to model such phenomena. In the present study, a three-dimensional incompressible SPH model has been developed for simulating the liquid sloshing phenomenon. This model has been improved using the kernel gradient correction tensors, particle shifting algorithms, turbulence model, and free surface particle detectors. The results of the three-dimensional numerical model are compared with an experimental model, showing a very good accuracy of the three-dimensional numerical method used. This study aims to investigate vertical baffle effects on the control and damping of liquid sloshing. The results of the present investigation show that in this particular case, by using baffles, it is possible to reduce more than 50% of the maximum value of pressure fluctuations in the slashing phenomenon.

Most space shuttle fuel tanks use a center column to hold the Propellant Management Device (PMD). This paper analyzes the gas–liquid interface state in the tanks with a central column during microgravity experiments conducted in the Chinese Space Station. It launches an extended study to investigate the gas–liquid interface state under different gravity conditions. Using the perturbation method and boundary layer theory, we numerically calculated the morphology of the gas–liquid interface under varying gravity conditions based on the Young–Laplace equation. The results were then compared to those obtained from existing commercial software and were found to be consistent. Based on this, the study develops two types of calculation procedures. The first procedure generates the corresponding shape of the liquid surface by inputting the height of the liquid surface endpoints and the gravity level. The second procedure is based on the targeting method and generates the corresponding liquid surface by inputting the volume of the liquid in the storage tank and the gravity level. The procedures were used to analyze the variation of gas–liquid interface properties under different gravity conditions. This study offers theoretical support for liquid management in aerospace engineering fuel tanks.

An anisotropic foundation pit steady-state seepage field under a suspended waterproof curtain support considering the position of the free surface is studied analytically, and an analytical solution for the free surface position is given. The head distribution in the three zones is expressed as a series solution using the separation of variables method, and the explicit solution for the extent of the seepage field in each zone is obtained by combining the continuity condition between zones and the series orthogonality condition. The free surface position is determined according to the condition that the total head of the free surface is equal to the position head. A comparison of the calculation results of the analytical method and the indoor test and finite element analysis results verifies the correctness of the analytical solution, and the analytical method has more calculation efficiency than the finite element numerical method. Employing the aforementioned methods to analyze the influence parameters of the free surface position, the results show that drawdown increases as the ratio of the vertical permeability coefficient to the horizontal permeability coefficient increases; the greater the ratio of pit width to depth, the more significant the drawdown, but when the ratio continues to exceed 1.5, the drawdown is negligible.

A numerical simulation based on the CFD method is used to study the interaction between a horizontal cylinder and wave flow. Firstly, a two-dimensional numerical calculation model of both a fixed and a rigid moving cylinder, with a free surface under varying wave flow conditions, is created. In the established model, the loads on the horizontal cylinder under different submergence depths, flow velocities, cylinder sizes, wave periods, and k values (spring stiffness) are analyzed and calculated. The results show that, when the cylinder is close to the free surface, its hydrodynamic load under wave flow conditions is more sensitive to changes in submergence depth, which essentially affects wave reflection and blockage. At different flow velocities, k values, cylinder radii, and arm lengths, the main frequency of the Fourier transform of the cylinder motion curve remains unchanged; however, the main frequency does change with the wave period and submergence depth. The efficiency of rotary cylindrical energy harvesting is influenced by various factors, among which an initial increase and then decrease are observed with a gradually increasing k value, arm length, period, and radius, in addition to an observed decrease with increasing flow velocity.

When a transmedia vehicle moves across water and air media, the free surface has a great influence on its airfoil, which brings challenges to the overall design and navigation control. To investigate the hydrodynamic characteristics of an airfoil approaching the free surface from the far field in the air and water, numerical simulation models of this process were established for a NACA0012 based on a volume of fluid multiphase flow model using computational fluid dynamics. The feasibility of the models was verified, and the hydrodynamic characteristics of the airfoil working near the free surface were studied. The results showed that the drag coefficient decreased gradually while the lift coefficient and lift-to-drag ratio increased as the airfoil approached the free surface from the far field in the air at a positive angle of attack. The lift coefficient and lift-to-drag ratio both decreased gradually when the airfoil approached the free surface from the underwater far field. When the distance was more than 10 times chord length, the drag coefficient increased gradually because of wave-induced action, and the drag coefficient decreased rapidly when the distance was less than 10 times chord length. These results can provide reference for the overall design and navigation control of transmedia vehicles.

Analyzing the interactions of free surface waves caused by a submerged-body movement is important as a fundamental study of submerged-body motion. In this study, a two-dimensional mini-towing tank was used to tow an underwater body for analyzing the generation and propagation characteristics of free surface waves. The magnitude of the maximum wave height generated by the underwater body motion increased with the body velocity at shallow submerged depths but did not increase further when the generated wave steepness corresponded to a breaking wave condition. Long-period waves were generated in the forward direction as the body moved initially, and then short-period waves were measured when the body moved at a constant velocity. In numerical simulations based on potential flow, the fluid pressure changes caused by the submerged-body motion were implemented, and the maximum wave height was accurately predicted; however, the complex physical phenomena caused by fluid viscosity and wave breaking in the downstream direction were difficult to implement. This research provides a fundamental understanding of the changes in the free surface caused by a moving underwater body.

This work presents the results of a direct numerical simulation of the nonlinear free surface evolution of a finite-depth fluid with a linear shear flow under the action of horizontal electric fields. The method of time-dependent conformal transformation for the description of the combined effects of the electric fields and constant vorticity is generalized for the first time. The simulation results show that strong shear flow co-directed in the wave propagation direction leads to the formation of large-amplitude surface waves, and, for some limiting vorticity value, a wave breaking process with the formation of an air bubble in the liquid is possible. The oppositely directed shear flow can cause the retrograde motion of a surface wave (wave propagation in the opposite direction to the linear wave speed). The simulations conducted taking into account the electro-hydrodynamic effects demonstrate that a high enough external horizontal electric field suppresses these strongly nonlinear processes, and the surface waves tend to preserve their shape. [ABSTRACT FROM AUTHOR]

The flow around an elongated smooth contour under the free surface of a fluid is considered. The fluid is perfect, incompressible, and heavy. The critical flow branching and flow shedding points are located on the contour. The depth of the contour immersion and its length are given. It is assumed that the velocity magnitude on the free surface is close to its value in the undisturbed flow. A nonlinear approximation of the Bernoulli integral on the free surface associated with logarithm is used. Two auxiliary planes in which the flow domain is a half-plane with an excluded circle and an annular region are used. The complex potential is determined in the first parametric plane using a conformal mapping onto the annular region. A system of equations is derived for finding the defining parameters. This system is solved using the minimization of a functional and an iteration method over two sets of parameters. An algorithm and computer program for solving this system are developed. The hydrodynamic characteristics of a specific hydrofoil are computed. Results for the coefficients of wave drag, lift force, moment, and position of the contour center are analyzed depending on the Froude number and circulation of different signs. Examples of computations of nonlinear waves formed on the free surface at significant Froude numbers are given. [ABSTRACT FROM AUTHOR]

Physics Informed Neural Networks (PINN), a deep learning tool, has recently become an effective method for solving inverse Partial Differential Equations (PDEs) where the boundary/initial conditions are not well defined and only noisy sparse measurements sampled in the domain exist. PINN, and other Neural Networks, tends to converge to the low frequency solution in a field that has multiple frequency scales, this is known as spectral bias. For PINN this happens when solving PDEs that exhibit periodic behavior spatially and temporally with multi frequency scales. Previous studies suggested that Fourier Features-Neural Networks (FF-NN) can be used to overcome the spectral bias problem. They proposed the Multi Scale-Spatio Temporal-Fourier Features-Physics Informed Neural Networks (MS-ST-FF-PINN) to overcome the spectral bias problem in PDEs solved by PINN. This has been evaluated on basic PDEs such as Poisson, wave and Gray-Scott equations. In this paper we take MS-ST-FF-PINN a step further by applying it to the incompressible Navier-Stokes equations. Furthermore, a comparative analysis between the PINN and the MS-ST-FF-PINN architectures solution accuracy, the learnt frequency components and the rate of convergence to the correct solution is included. To show this three test cases are shown (a)-Forward time independent double-lid-driven cavity, (b)-Inverse time independent free surface estimation of Kelvin wave pattern, and (c)-Inverse 2D time-dependent turbulent Von Karman vortex shedding interaction downstream of multiple cylinders. The results show that MS-ST-FF-PINN is better at learning low and high frequency components synchronously at early training iterations compared to the PINN architecture that does not learn the high frequency components even after multiple iteration numbers such as the Kelvin wave pattern and the Karman vortex shedding cases. However, for the third test case, the MS-ST-FF-PINN architecture showed a discontinuity for the temporal prediction of the pressure field due to over-fitting. [ABSTRACT FROM AUTHOR]

Three large-eddy simulations of open channel flow over a backward-facing step are performed to investigate the effect of submergence on the turbulence, hydrodynamics, and water surface deformation downstream of the step. The deformation of the water surface, the extent of the recirculation zone as well as the strength of the shear layer are a function of relative submergence. All flows downstream of the step exhibit elevated levels of turbulent shear stress and contain significant amounts of turbulent kinetic energy. The instantaneous flow features rollers immediately behind the step and horseshoe-shaped vortices shed from the shear layer, the latter being advected towards the water surface where they cause deformations. It is shown that these vortices can originate from any location along the dividing streamline; however, they contain more energy the closer to the mean attachment location they originate. [ABSTRACT FROM AUTHOR]

The influence of liquid viscoelasticity on the interaction between cavitation bubbles and free surfaces is of great practical significance in understanding bubble dynamics in biological systems. A series of millimeter cavitation bubbles were induced by laser near the free surfaces of the water and viscoelastic polyacrylamide (PAM) solutions with different concentrations. The effects of liquid viscoelasticity on the interactions of cavitation bubbles with free surfaces are analyzed from the perspectives of the evolution of free surface and bubble dynamics. The experimental results show that as the dimensionless standoff distance increases, the evolutions of free surface behaviors in all experimental fluids can be divided into six types of water mounds, i.e., breaking wrinkles, spraying water film, crown, swallowed water spike, hillock, and slight bulge. All the critical values of the dimensionless distance dividing different types decrease with increasing concentration. The evolutions of first four types of water mounds in PAM solutions differ from those in the water. Water droplets splashing in different directions are produced around the breaking wrinkles in the water. Meanwhile, the breaking wrinkles in PAM solution move with the "liquid filaments" towards the central axis. The water spike in the pattern of spraying water film in PAM solution is more stable than that in the water. As the solution concentration increases, the water skirt in the pattern of crown contracts earlier and faster, and the rate of increase in the height of the water skirt decreases. For swallowed water spike in PAM solution, the upper part of the newly formed water spike is not significantly thicker than the middle part, and thus the water waist structure does not form. Liquid viscoelasticity inhibits the bubble growth and collapse, and the bubble migration as well, especially in the second period. Shorter and thicker cavities are formed in PAM solutions with higher concentration, while slender and stable cavities formed in the water at the same dimensionless distance. The velocity and displacement of the tip of bullet jet both decrease as the solution concentration increases. [ABSTRACT FROM AUTHOR]

This study aimed to examine the acoustic field radiated by propellers and underwater vehicles. For the verification of sound radiation in underwater vehicles, numerical methods are widely used in addition to experiments and propeller blade frequencies for calculation and validation. Numerical convergence and accuracy are more important for near-field and far-field problems. This paper uses the boundary element method (BEM) to assess the convergence of the finite volume method (FVM). In this study, the FVM, including the Reynolds-averaged Navier–Stokes method and the Ffowcs Williams–Hawkings (FW-H) acoustic model, is used to investigate the influence of various geometric inflows on the hydrodynamic and noise performance of the propeller. Then, the sound radiation of the FVM is compared with the BEM at the far field to determine the number of meshed elements. Furthermore, spectral analysis is being conducted to examine the noise generated by the underwater vehicle and propeller. The objective is to investigate the influence of the free surface on propeller efficiency. After verifying the numerical simulation, the results indicate that a relationship can be established between water pressure and propeller thrust under specific conditions. This relationship can be used to estimate the magnitude of propeller thrust at different water depths. The simulated results of propeller thrust, torque coefficient, propulsion efficiency, and sound radiation in this study are consistent with experimental values. This demonstrates the accuracy and practicality of the findings of numerical procedures in engineering applications. [ABSTRACT FROM AUTHOR]

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K–BKZ–PSM (Kaye–Bernstein, Kearsley, Zapas–Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation and the marker particle method (known as marker-and-cell) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K–BKZ–PSM fluid in a pipe. [ABSTRACT FROM AUTHOR]

The expansion and shock wave coexisting failure theory has been widely recognized. However, it is not clear whether the main cause of rock mass blasting failure is the shock wave or gas pressure. In this paper, the contribution proportions of both loads to rock mass failure were investigated in bench blasting. First, the blasting damage in rock mass was simulated with a fluid-structure interaction (FSI) method. Then, a novel method to quantitatively distinguish between the rock-breaking effects (RBEs) of the shock wave and gas pressure was proposed that was based on the damage results. In addition, under different free surface conditions, the blasting failure volume that was caused by both loads was obtained for three typical rock masses, which included poor, middle, and good rock masses. The results showed that the range of the tensile failure zone by reflected waves was small, and the favorable effects of free surfaces on the failure induced by shock waves were limited. The free surface had a minor beneficial influence on the rock mass failure that was induced by the shock waves. In addition, it had a more favorable influence on the failure that was induced by the gas pressure. Finally, the influence of the free surface and rock mass conditions on the contribution proportions of both loads was discussed. A higher proportion of the RBEs of the shock wave was in the good mass with large wave impedance compared with the poor rock mass with small wave impedance. According to the contribution proportions under different rock masses and free surface conditions, the main cause of rock blasting failure was the gas pressure action, which was verified through the field high-speed photography data. The findings revealed the main cause of rock mass failure in bench blasting and could provide a theoretical basis when seeking effective engineering measures to give full play to the gas pressure action. [ABSTRACT FROM AUTHOR]

Liquid sloshing is a common phenomenon in the transporting of liquid tanks. A safe liquid transporting needs to control the entered fluctuating forces to the tank walls, before leading these forces to large forces and momentums. Using predesigned baffles is a simple method for solving this problem. Smoothed Particle Hydrodynamics is a Lagrangian method that has been widely used to model such phenomena. In the present study, a three-dimensional incompressible SPH model has been developed for simulating the liquid sloshing phenomenon. This model has been improved using the kernel gradient correction tensors, particle shifting algorithms, turbulence model, and free surface particle detectors. The results of the three-dimensional numerical model are compared with an experimental model, showing the very good accuracy of the three-dimensional numerical method used. This study aims to investigate vertical baffle effects on the control and damping of liquid sloshing. The results of the present investigation show that in this particular case, by using baffles, it is possible to reduce more than 50% of the maximum value of pressure fluctuations in the slashing phenomenon. [ABSTRACT FROM AUTHOR]

This paper investigates the hysteresis characteristics of force coefficients of an oscillating hydrofoil in a near-free surface cavitation flow field by utilizing unsteady numerical simulation methods. The study primarily focuses on analyzing the effects of dynamic stall conditions, reduced frequency, cavitation number, immersion depth, and Froude number on the hysteresis curve. By comparing the vortex distribution, volume fraction, velocity streamlines, and fluctuating pressure coefficient in the flow field, the authors also examine the reasons for the differences in the hysteresis curve at the same angle of attack under different conditions. The results suggest that cavitation significantly impacts the fluctuation of the hysteresis curve, mainly due to the shedding and collapse of the cavity on the hydrofoil pressure surface, which results in pressure fluctuations at the trailing edge. This issue can be addressed by reducing the stall angle of attack, Froude number, and increasing the reduced frequency, cavitation number, and immersion depth to slow down cavitation in the flow field, thus reducing the fluctuation of the hysteresis loop. Furthermore, the structure of the cavitation flow field under different conditions is clearly distinguished, and the hysteresis loop experiences obvious fluctuations when there is obvious vortex separation in the flow field and many small cavities remaining above the pressure surface. As the immersion depth decreases and the corresponding Froude number increases, the effect of the free surface becomes stronger, leading to an increase in the free surface wave amplitude. This effect causes the hydrofoil pressure surface to gradually evolve into super-cavitation, and the fluctuation of the hysteresis curve tends to be stable. [ABSTRACT FROM AUTHOR]

Morphology‐adaptive multiphase models are becoming more established for the numerical description of complex gas‐liquid flows adapting dynamically to the local flow morphology. In the present study, two different numerical methods originally designed for distinct flow morphologies are combined, namely the volume‐of‐fluid and the Euler–Euler method. Both edge cases have been proven to be capable of delivering reliable predictions in the respective use cases. The long‐term goal is to improve the prediction of gas‐liquid flows, regardless of the flow regime in a specific application. To capture the system dynamics with a given grid resolution, the flow fields need to be predicted as precise as possible, while the shape of structures such as gas bubbles need to be recovered adequately in topology and shape. The goal is to obtain reliable predictions on intermediate mesh resolutions rather than relying on fine meshes requiring more computational resources. Therefore, a procedure is proposed to locally measure the degree of resolution. With this information, the hydrodynamics in the interface region can be controlled by means of a dedicated interfacial drag formulation in order to improve simulation results across several levels of spatial resolution. A modified formulation of buoyancy is proposed to prevent unphysical oscillations of vertical velocity near a horizontal interface. The functionality is demonstrated in a three‐dimensional case of a gas bubble rising in stagnant liquid and in a co‐current stratified air‐water channel flow in two‐dimensional space. The choice of these different applications demonstrates the general applicability of the proposed model framework. [ABSTRACT FROM AUTHOR]

In this paper, the two-dimensional problem of irrotational flow past a wedge located in the center of the channel is considered. Assuming that the fluid is incompressible and non-viscous, the influence of gravity is ignored but the surface tension is considered. The problem which is characterized by the nonlinear boundary conditions on the free surface of the unknown equation is solved numerically by the series truncation technique. The results show that for all given wedge configurations, there is a critical value for the Weber number, for which there is no solution for every Weber number value smaller than this. In addition, the obtained results extend the work done by Gasmi and Mekias [2].

A hydroelastic problem of free vibrations of a thin plate that horizontally separates ideal in-compressible liquids of different densities in a rigid cylindrical tank with an arbitrary cross-section has been considered in the linear formulation. To solve the corresponding complicated inhomogeneous biharmonic equation, the fundamental system of the solutions of biharmonic equation (FSS) and the eigenmodes of ideal liquid oscillations in a cylindrical cavity were used. The frequency equation was obtained for arbitrary fixation of the plate contour. On the example of a clamped plate, the frequency equation was simplified by decomposing the corresponding homogeneous biharmonic equation into two harmonic equations and using Green's formula for the Laplace operator. It was shown that in this case the frequency equation does not depend on the FSS and becomes greatly simplified because the FSS depends on the unknown frequency. The resulting equation has a single form for the cases of a right circular cylinder and a rectangular channel; in particular cases, it coincides with the previously obtained equations. Research of asymmetric vibration frequencies of a plate and a membrane, as well as axisymmetric vibration frequencies of a membrane in a circular cylinder, has been carried out. An approximation formula for high frequencies and approximate conditions for the stability of the plate and membrane vibrations were obtained. [ABSTRACT FROM AUTHOR]

The traditional deep-water analysis of two-dimensional planing is studied in detail and applied to efficient splash-free and optimal profiles, as well as to flat plates. The methodology is used to analyze both free-to-rise and free-to-rise-plus-trim profiles. In some cases, the predictions exhibit unexpected discontinuous behavior for the lift, wetted length and other results, with respect to the parameters describing the curvature of the planing surface. These discontinuities are due to the nonlinearities inherent in the practical planing problem, as opposed to previous simplified analyses in which the wetted length was specified. [ABSTRACT FROM AUTHOR]