Free Surface
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2022 ◽  
Vol 27 (1) ◽  
pp. 19-37
Author(s):  
Ning Duan ◽  
Xiaopeng Zhao

This paper is concerned with a sixth-order diffusion equation, which describes continuum evolution of film-free surface. By using the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors we verified the existence of global attractor for this surface diffusion equation in the spaces H3(Ω) and fractional-order spaces Hk(Ω), where 0 ≤ k < ∞.


Processes ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 69
Author(s):  
Aldo Benavides-Morán ◽  
Luis Rodríguez-Jaime ◽  
Santiago Laín

This paper presents computational fluid dynamics (CFD) simulations of the flow around a horizontal axis hydrokinetic turbine (HAHT) found in the literature. The volume of fluid (VOF) model implemented in a commercial CFD package (ANSYS-Fluent) is used to track the air-water interface. The URANS SST k-ω and the four-equation Transition SST turbulence models are employed to compute the unsteady three-dimensional flow field. The sliding mesh technique is used to rotate the subdomain that includes the turbine rotor. The effect of grid resolution, time-step size, and turbulence model on the computed performance coefficients is analyzed in detail, and the results are compared against experimental data at various tip speed ratios (TSRs). Simulation results at the analyzed rotor immersions confirm that the power and thrust coefficients decrease when the rotor is closer to the free surface. The combined effect of rotor and support structure on the free surface evolution and downstream velocities is also studied. The results show that a maximum velocity deficit is found in the near wake region above the rotor centerline. A slow wake recovery is also observed at the shallow rotor immersion due to the free-surface proximity, which in turn reduces the power extraction.


2021 ◽  
Vol 3 (2) ◽  
pp. 75-87
Author(s):  
О. Lymar ◽  

The frequency spectrum of plane vibrations of an elastic plate separating a two-layer ideal fluid with a free surface in a rectangular channel is investigated analytically and numerically. For an arbitrary fixing of the contours of a rectangular plate, it is shown that the frequency spectrum of the problem under consideration consists of two sets of frequencies describing the vibrations of the free surface of the liquid and the elastic plate. The equations of coupled vibrations of the plate and the fluid are presented using a system of integro-differential equations with the boundary conditions for fixing the contours of the plate and the condition for the conservation of the volume of the fluid. When solving a boundary value problem for eigenvalues, the shape of the plate deflection is represented by the sum of the fundamental solutions of a homogeneous equation for a loose plate and a partial solution of an inhomogeneous equation by expanding in terms of eigenfunctions of oscillations of an ideal fluid in a rectangular channel. The frequency equation of free compatible vibrations of a plate and a liquid is obtained in the form of a fourth-order determinant. In the case of a clamped plate, its simplification is made and detailed numerical studies of the first and second sets of frequencies from the main mechanical parameters of the system are carried out. A weak interaction of plate vibrations on vibrations of the free surface and vice versa is noted. It is shown that with a decrease in the mass of the plate, the frequencies of the second set increase and take the greatest value for inertialess plates or membranes. A decrease in the frequencies of the second set occurs with an increase in the filling depth of the upper liquid or a decrease in the filling depth of the lower liquid. Taking into account two terms of the series in the frequency equation, approximate formulas for the second set of frequencies are obtained and their efficiency is shown. With an increase in the number of terms in the series of the frequency equation, the previous roots of the first and second sets are refined and new ones appear.


2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jianxin Yu ◽  
Zhibin Zhou ◽  
Xin Zhang ◽  
Xiaolin Yang ◽  
Jinxing Wang ◽  
...  

The vibration caused by the tunnel blasting and excavation will harm the surrounding rock and lining structure of the adjacent existing tunnels. This paper takes a two-lane large-span highway tunnel as the research object, conducts on-site monitoring tests on the impact of vibration caused by the blasting and excavation of new tunnels on the existing tunnels under different blasting schemes, and analyses in detail the three-dimension vibration velocity by different excavation footages. From the vibration speed, it is concluded that the influence of the existing tunnel of the newly built tunnel blasting team is affected by various factors, such as distance, free surface, charge, and blasthole distribution. With different blasting schemes, the greater the amount of charge, the greater the vibration caused by blasting. Existing tunnels correspond to the front of the tunnel, and the axial and radial vibration peaks are greater than the vertical. Although the cut segment uses a less amount of explosive and has a less blasthole layout, there is only one free surface. Because of the clamping of the rock, it is compared with the other two segments. The vibration caused is the largest. Although the peripheral holes are filled with a large amount of explosive, the arrangement of the blast holes is relatively scattered and there are many free surfaces. Hence, the vibration caused is the smallest. Corresponding to the back of the tunnel face, since there is no rock clamp, the vibration caused by the cut segment is the smallest, and the vibration caused by the peripheral segment and the floor segment is relatively large. The vibration caused by the front explosion side is significantly greater than the vibration caused by the back explosion side. The vibration velocity caused by the unit charge of 1.5 m footage is greater than that of the 3.0 m footage. The vibration velocity caused by the unit charge of the cut segment is the largest, and the vibration velocity caused by the peripheral segment and the floor segment is smaller. The research results provide a reference for the blasting control of similar engineering construction.


Author(s):  
Fabian Thiery ◽  
Fabian Fritz ◽  
Nikolaus A. Adams ◽  
Stefan Adami

AbstractWe comment on a recent article [Comput. Mech. 2020, 65, 487–502] about surface-tension modeling for free-surface flows with Smoothed Particle Hydrodynamics. The authors motivate part of their work related to a novel principal curvature approximation by the wrong claim that the classical curvature formulation in SPH overestimates the curvature in 3D by a factor of 2. In this note we confirm the correctness of the classical formulation and point out the misconception of the commented article.


2022 ◽  
Vol 244 ◽  
pp. 110447
Author(s):  
Jing-Ping Wu ◽  
Tian-Long Mei ◽  
Zao-Jian Zou

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