Sharif Digital Repository

This paper presents a matrix form model for determination of sloshing frequencies and modes in 3D liquid tanks. The governing equations of the incompressible inviscid potential flow are used to derive the governing boundary integral equation and then the boundary element method along with the collocation method is applied to obtain a matrix form standard eigenvalue problem. The sloshing mass and stiffness matrices are computed using analytical formulas which are given for quadratic boundary elements. Two typical examples are used to validate the introduced model and very good results are achieved in comparison with the exact results in the literature  

This study presents a method to determine an equivalent mechanical model (EMM) for multi-baffled containers with arbitrary geometries. The method is implemented for 2D and axisymmetric containers. The Laplace equation and Green's theorem are used to develop the fluid model and the boundary element method (BEM) is used to solve the fluid field governing equation. Moreover, a zoning method is utilized to model arbitrary arrangements of baffles in multi-baffled containers and a reduced order model is developed to model the free-surface sloshing. The exerted hydrodynamic pressure distribution, forces and moments on the walls of the container are determined based on the Bernoulli equation and a... 

A numerical model based on the boundary element method is proposed for the sloshing of a flowing liquid in a three-dimensional tank. Assuming a mean flow in the tank in addition to a perturbation flow, the nonlinear boundary conditions of the liquid free-surface are linearized. Using the boundary element method along with the modal analysis technique a reduced order model is obtained which is used to calculate the fundamental sloshing frequencies and modes in the tank with an inlet and outlet. The obtained results for a test case are compared with the literature data to validate the proposed model. The results are in a very good agreement with analytical results and show an acceptable... 

The free vibrations analysis of liquid sloshing is carried out for arbitrary axisymmetric containers under low-gravity condition using boundary element method. A potential flow theory is used to model the flow field and the free-surface Laplace-Young equation is used to model the surface tension effect. The obtained governing equations are solved using eigenanalysis techniques to determine the natural frequencies and mode shapes of the sloshing liquid. The results for a circular cylindrical container are compared to the analytical values and very good agreement is achieved for the slipping and anchored contact line assumptions. Furthermore, some baffled containers are also analysed and the... 

In this paper, dynamic modeling and control problem for transfer of a sloshing liquid container suspended through rigid massless links from a team of quadrotors are investigated. By the proposed solution, pose of the slung container and fluid sloshing modes are stabilized appropriately. Dynamics of the container-liquid-quadrotors system is modeled by Euler-Lagrange method. Fluid slosh dynamics is included using multi-mass-spring model. According to derived model, a proper control law is designed for a system with three or more quadrotors. Implementing the proposed control law, quadrotors can control pose of the container, directions of the links and liquid sloshing modes simultaneously.... 

Numerical simulation of floating or submerged body motions is presented based on a Volume of Fluid (VoF)-fractional step coupling. Solving a scalar transport equation for volume fraction of two phases results in a single continuum with a fluid property jump at the interface. In addition, velocity and pressure fields are coupled using the fractional step method. Based on integration of stresses over a body, acting forces and moments are calculated. Using the strategy of non-orthogonal body-attached mesh and calculation of motions in each time step result in time history of hydrodynamic motions. To verify the accuracy of the numerical procedure in simulation of two-phase flow, sloshing and dam... 

In order to study the interaction of sloshing and structural vibrations of baffled tanks, a reduced order model based on modal analysis of structure model and boundary element method for fluids motion is developed. For this purpose, the governing equations of elastic structure and incompressible flow are used to derive simple models to simulate both fields. Using the modal analysis technique, the structural motions are applied to the fluid model and on the other hand by using boundary element method, the fluid loads are applied to the structural model. Based on this formulation, a code is developed which is applicable to an arbitrary elastic tank with arbitrary arrangement of baffles. The... 

This paper aims at developing a modal approach for the non-linear analysis of sloshing in an arbitrary-shape tank under both horizontal and vertical excitations. For this purpose, the perturbation technique is employed and the potential flow is adopted as the liquid sloshing model. The first- and second-order kinematic and dynamic boundary conditions of the liquid-free surface are used along with a boundary element model which is formulated in terms of the velocity potential of the liquid-free surface. The boundary element model is used to determine the natural mode shapes of sloshing and their corresponding frequencies. Using the modal analysis technique, a non-linear model is presented for... 

A numerical model is developed for investigation of coupled dynamics of fuel contained elastic launch vehicles in planar atmospheric flight. Finite element method along with the linear quasi-steady piston aerodynamic theory is used for developing an aeroelastic model. A reduced order boundary element model is used for modeling the liquid sloshing in tanks. The interaction of sloshing and aeroelasticity is studied using stability analysis of the coupled system. Results show that the slosh-aeroelastic coupling in an elastic launch vehicle occurs for low tank filling ratios and may lead to decreasing the system damping. Due to more interactions between the slosh and rigid body modes, larger... 

This paper presents a dynamic analytical model for tank train vibrations. The train is considered as a system of 27 degrees of freedom consisting of lateral, roll, yaw, vertical, and pitch motions for the vehicle body and its two bogies and lateral, roll and vertical motions for the four wheel-sets. Liquid sloshing in the tank is modeled using an equivalent mechanical mass-spring model. Coupling between the vehicle system and the railway track is realized through the interaction forces between the train and the rail, where the vertical and lateral irregularity profiles of the track are regarded as stationary ergodic Gaussian random processes and simulated by polynomial functions. Random... 

This paper aims to revisit the effect of sloshing on the flutter characteristics of a partially liquid-filled cylinder. A computational fluid-structure interaction model within the framework of the finite element method is developed to capture fluid-structure interactions arising from the sloshing of the internal fluid and the flexibility of its containing structure exposed to an external supersonic airflow. The internal liquid sloshing is represented by a more sophisticated model, referred to as the liquid sloshing model, and the shell structure is modeled by Sanders' shell theory. The aerodynamic pressure loading is approximated by the first-order piston theory. The initial geometric... 

This paper presents the application of reduced order modeling technique for investigation of liquid sloshing in three-dimensional tanks. The governing equations of sloshing are written using a boundary element formulation for incompressible potential flow. Then, the governing equations are reduced to a more efficient form that is represented only in terms of the velocity potential on the liquid free surface. This particular form is employed for eigen-analysis of fluid motion and the sloshing frequencies and mode shapes are determined. Then, the sloshing frequencies and the corresponding right- and left-eigenvectors are used along the modal analysis technique to find a reduced order model... 

The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode... 

This paper aims to revisit the effect of sloshing on the flutter characteristics of a partially liquid-filled cylinder. A computational fluid-structure interaction model within the framework of the finite element method is developed to capture fluid-structure interactions arising from the sloshing of the internal fluid and the flexibility of its containing structure exposed to an external supersonic airflow. The internal liquid sloshing is represented by a more sophisticated model, referred to as the liquid sloshing model, and the shell structure is modeled by Sanders' shell theory. The aerodynamic pressure loading is approximated by the first-order piston theory. The initial geometric... 

The lateral response of a single degree of freedom (SDOF) structural system containing a rigid circular cylindrical liquid tank, under harmonic and earthquake excitations is considered. The governing differential equations of motion for the combined system is derived considering the first 3 liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The system is considered nonlinear due to the convective term of liquid acceleration and the nonlinear surface boundary conditions, both caused by the inertial nonlinearity. The harmonic and seismic response of the system is investigated in the neighborhood of 1:1 and 1:2 internal resonances between the SDOF system and the first... 

Seismic response of a Single Degree of Freedom (SDOF) system containing a rigid circular cylindrical liquid tank under the earthquake excitations is considered in the presence of fluid/structure interaction. The governing differential equations of the system is derived considering the first three liquid sloshing modes (1, 1), (0, 1) and (2, 1) under different strong ground motions. The dynamic response of the system is investigated in the neighborhood of 1:1 and 1:2 internal resonances between the SDOF system and the liquid sloshing modes. These internal resonances take place by tuning the frequency of the first asymmetric sloshing mode of the liquid to the fundamental frequency of the SDOF... 

The present work aims at developing a boundary element method to determine the natural frequencies and mode shapes of liquid sloshing in 3D baffled tanks with arbitrary geometries. Green's theorem is used with the governing equation of potential flow and the walls and free surface boundary conditions are applied. A zoning method is introduced to model arbitrary arrangements of baffles. By discretizing the flow boundaries to quadrilateral elements, the boundary integral equation is formulated into a general matrix eigenvalue problem. The governing equations are then reduced to a more efficient form that is merely represented in terms of the potential values of the free surface nodes, which...