Liquid Sloshing in a Cylindrical Tank with Multiple Baffles Under Horizontal and Pitching Motions

2020 ◽  
Vol 12 (07) ◽  
pp. 2050080
Author(s):  
Ying Sun ◽  
Ding Zhou ◽  
Jiadong Wang ◽  
Huixuan Han
Keyword(s):  
Velocity Potential ◽  
Low Frequency ◽  
Lateral Force ◽  
Liquid Structure ◽  
Liquid Sloshing ◽  
Influence Coefficient ◽  
Cylindrical Tank ◽  
Pitching Motion ◽  
Fluid Sloshing ◽  
Mass Spring

The sloshing response of fluid in a rigid circular cylindrical tank with multiple rigid annular baffles and subjected to horizontal and pitching excitations is investigated. The subdomain method for fluid sloshing is utilized to obtain exact solutions to the convective velocity potential of liquid. By substituting the velocity potential of liquid into free surface sloshing equation, the response equation under the horizontal excitation is constructed. According to producing the similar lateral force and moment as analytical solutions undergoing horizontal motion, an equivalent mass-spring model is developed to replace continuous liquid. Based on the model, dynamic response of liquid sloshing in the tank under the horizontal and pitching excitations is obtained. Compared with the reported results, the lateral force is in excellent agreement with literature solutions and the overturning moment shows good agreement with available solutions under the excitation with low frequency. The proposed model can be employed to simplify dynamics of complicated liquid-structure systems undergoing pitching motion without tedious derivation and great amount of calculation. The effects of the liquid height, the positions and sizes of the baffles on the influence coefficient factor of pitching motion and the steady-state response are revealed in detail.

Fluid Pressures on Unanchored Rigid Flat-Bottom Cylindrical Tanks Under Action of Uplifting Acceleration

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Yoshinori Ando
Keyword(s):  
Velocity Potential ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Angular Acceleration ◽  
Bottom Plate ◽  
Center Line ◽  
Cylindrical Tank ◽  
Cylindrical Coordinates ◽  
Flat Bottom ◽  
Cylindrical Tanks

To protect flat-bottom cylindrical tanks against severe damage from uplift motion, accurate evaluation of accompanying fluid pressures is indispensable. This paper presents a mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank in the same manner as the procedure outlined and discussed previously by the authors (Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011801). With perfect fluid and velocity potential assumed, the Laplace equation in cylindrical coordinates gives a continuity equation, while fluid velocity imparted by the displacement (and its time derivatives) of the shell and bottom plate of the tank defines boundary conditions. The velocity potential is solved with the Fourier–Bessel expansion, and its derivative, with respect to time, gives the fluid pressure at an arbitrary point inside the tank. In practice, designers have to calculate the fluid pressure on the tank whose perimeter of the bottom plate lifts off the ground like a crescent in plan view. However, the asymmetric boundary condition given by the fluid velocity imparted by the deformation of the crescent-like uplift region at the bottom cannot be expressed properly in cylindrical coordinates. This paper examines applicability of a slice model, which is a rigid rectangular tank with a unit depth vertically sliced out of a rigid flat-bottom cylindrical tank with a certain deviation from (in parallel to) the center line of the tank. A mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with Fourier series. It well converges with a few first terms of the Fourier series and accurately calculates the values of the fluid pressure on the tank. In addition, the slice model approximates well the values of the fluid pressure on the shell of a rigid flat-bottom cylindrical tank for any points deviated from the center line. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. The proposed mathematical and graphical methods are cost effective and aid in the design of the flat-bottom cylindrical tanks that allow the uplifting of the bottom plate.

scholarly journals Study on liquid sloshing characteristics of a swaying rectangular tank with a rolling baffle

2019 ◽  
Vol 119 (1) ◽  
pp. 23-41 ◽  
Author(s):  
Jing-Han Wang ◽  
Shi-Li Sun
Keyword(s):  
Free Surface ◽  
Present Method ◽  
Velocity Potential ◽  
Solution Procedure ◽  
Liquid Sloshing ◽  
Published Data ◽  
Free Surface Elevation ◽  
Separate Variable ◽  
Rectangular Tank ◽  
Vertical Baffle

Abstract This study addresses the sloshing characteristics of a liquid contained in a tank with a vertical baffle mounted at the bottom of the tank. Liquid sloshing characteristics are studied through an analytical solution procedure based on the linear velocity potential theory. The tank is forced to sway horizontally and periodically, while the baffle is fixed to the tank or rolling around a hinged point. The rectangular tank flow field is divided into a few sub-domains. The potentials are solved by a separate variable method, and the boundary conditions and matching requirements between adjacent sub-domains are used to determine the sole solution. The free surface elevations with no baffle or a low fixed baffle are compared with those in published data, and the correctness and reliability of the present method are verified. Then the baffle is forced to rotate around the bottom-mounted point. It is found that the baffle’s motion, including the magnitude and the phase together, can be adjusted to suppress the free surface elevation, and even the sloshing wave can be almost eliminated.

On Investigation of Liquid Sloshing in Cylindrical Tanks With Single and Multiply Connected Domains Using Isogeometric Boundary Element Method

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Quansheng Zang ◽  
Jun Liu ◽  
Yang Zhou ◽  
Gao Lin
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Basis Functions ◽  
Liquid Sloshing ◽  
Multiply Connected Domains ◽  
Cylindrical Tank ◽  
Multiply Connected ◽  
Computer Aided ◽  
Cylindrical Tanks ◽  
Lagrange Basis

Abstract This paper explores an isogeometric boundary element method (IGA-BEM) for sloshing problems in cylindrical tanks with single and multiply connected domains. Instead of the Lagrange basis functions used in the standard BEM, the nonuniform rational B-splines (NURBS) basis functions are introduced to approximate the geometries of the problem boundaries and the unknown variables. Compared with the Lagrange basis functions, NURBS basis functions can accurately reconstruct the geometric boundary of analysis domain with almost no error, and all the data information for NURBS basis functions can be directly obtained from the computer-aided design (cad) or computer-aided engineering (cae) commercial software, which implies the modeling process of IGA-BEM is more simple than that of the standard BEM. NURBS makes it possible for the IGA-BEM to realize the seamless connection between cad and cae software with relative higher calculation accuracy than the standard BEM. Based on the weighted residual method as well as the divergence theorem, the IGA-BEM is developed for the single and multiply connected domains, whose boundaries are separately defined in the parameter space by different knot vectors. The natural sloshing frequencies of the liquid sloshing in a circular cylindrical tank with a coaxial or an off-center circular pipe, an elliptical cylindrical tank with an elliptical pipe, a circular cylindrical tank with multiple pipes are estimated with the introduced method by assuming an ideal (inviscid and incompressible) liquid, irrotational small-amplitude sloshing, and the linear free-surface condition. The comparison between the results obtained by the proposed method and those in the existing literatures shows very good agreements, which verifies the proposed model well. Meanwhile, the effects of radius ratio, liquid depth, number, and location of internal pipe (pipes) on the natural sloshing frequency and sloshing mode are analyzed carefully, and some conclusions are outlined finally.

INVESTIGATING THE EFFECT OF SLOSHING ON THE ENERGY ABSORPTION OF TANK WAGONS CRASH

2015 ◽  
Vol 39 (2) ◽  
pp. 187-200 ◽  
Author(s):  
Reza Razaghi ◽  
Majid Sharavi ◽  
Mohammad Mahdi Feizi
Keyword(s):  
Energy Absorption ◽  
Solution Method ◽  
Crash Test ◽  
Test Results ◽  
Software Simulation ◽  
Fluid Sloshing ◽  
Mass Spring Model ◽  
Solution Methods ◽  
Height Increase ◽  
Mass Spring

One of the main fluid mechanics phenomena is fluid sloshing which is originated from the free surface of fluid and should be taken into account in design of fluid structures such as fuel tank wagons, ships and so on. The aim of this paper is to investigate the effect of tank fluid sloshing on energy absorption and reducing tank acceleration during the tank wagon impact. For this purpose, methods of software simulation and dynamics solution methods are accomplished. The assumed wagon includes a tank with the approximate volume of 95 m3 and capacity of 65 tons of fluid. Using finite element method, the tank impact is simulated based on the corresponding standards for different heights of fluid in the tank. Obtained results show fluid height increase has an inappropriate effect on energy absorption among impact however the more fluid in tank, the more time would be consumed for energy absorption in general. At the end, by using crash test results for a tank with aforementioned scale, validity of impact software simulation and dynamic solution method considering the tank fluid as mass-spring model are checked.

Bandgap Properties of Two-Layered Locally Resonant Phononic Crystals

2020 ◽  
Vol 12 (07) ◽  
pp. 2050075
Author(s):  
Hongyun Wang ◽  
Heow Pueh Lee ◽  
Wei Xu
Keyword(s):  
Coating Thickness ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Formation Mechanisms ◽  
Frequency Range ◽  
The Third ◽  
Resonance Frequencies ◽  
Rubber Coating ◽  
Lower Frequency Range ◽  
Mass Spring

Multi-layered locally resonant phononic crystals (LRPCs) with wider and multiple bandgaps (BGs) in low frequency range and small size of the unit cell have promising applications in noise and vibration controls. In this paper, a 2D two-layered ternary LRPC consisting of a periodical array of cylindrical inclusions embedded in an epoxy matrix is investigated by the finite element method (FEM), where the inclusion is comprised of two coaxial cylindrical steel cores with rubber coating. It is found that the size of the inclusion of the 2D two-layered ternary LRPC has significant effects on the BG properties. With the increase of the core radius and coating thickness, the first BG would shift to lower frequency range with its width decreasing, and the second BG width would become wider until the third BG appears. Especially, with the increase of the coating thickness, more bands and BGs would appear in the lower frequency range. Based on the formation mechanisms of the BGs, several mass-spring models to predict the frequencies of the first two BG edges are developed. The results calculated by these mass-spring models are in good agreement with those by the FEM except for the upper edge frequency of the second BG when the rubber coating thickness exceeds a certain value and the third BG is opened up. These proposed mass-spring models would allow for quick pre-estimation of the resonance frequencies, and facilitate the selection of possible parameters for the wider and lower frequency BGs to obtain the desired attenuation bands. The studies would also benefit the design of multiple BGs for some device applications.

scholarly journals Two-dimensional resonators with small openings

1982 ◽  
Vol 24 (1) ◽  
pp. 2-27 ◽  
Author(s):  
G. R. Bigg ◽  
E. O. Tuck
Keyword(s):  
Natural Frequency ◽  
Asymptotic Expansions ◽  
Velocity Potential ◽  
Low Frequency ◽  
Matched Asymptotic Expansions ◽  
Two Dimensional ◽  
Acoustic Response ◽  
Closed Cavity ◽  
Small Opening

AbstractThe acoustic response of a two-dimensional nearly-closed cavity to an excitation through a small opening is examined, using the method of matched asymptotic expansions. The Helmholtz mode of vibration is discussed using a low-frequency expansion of the velocity potential in the cavity interior. The variation in frequency and magnitude of the resonator response is explored, both for the Helmholtz and the natural-frequency modes.

scholarly journals Numerical study of the liquid sloshing in the cylindrical tank with baffles

2021 ◽  
Vol 1985 (1) ◽  
pp. 012050
Author(s):  
Linlin Duan ◽  
Cenfan Liu ◽  
Fang Ji ◽  
Zhirong Yang ◽  
Chongchong Zhang
Keyword(s):  
Numerical Study ◽  
Liquid Sloshing ◽  
Cylindrical Tank
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