On the dynamics of the separation surface in a two liquid layer system (original) (raw)
Related papers
Experimental and theoretical investigation on the sloshing of a two-liquid system with free surface
Physics of Fluids, 2005
In this paper a theoretical and experimental investigation is performed on the sloshing of a two-liquid system with both separation and free surface. The experimental configuration consists of an oscillating tank filled with two layers of immiscible liquids. The mathematical model is obtained by applying the Lagrangian variational approach to the potential formulation of the fluid motion, and a dynamical system which describes the dynamics of motion is derived. In order to account for the damping of the motion, generalized dissipative forces are considered. For this purpose, the logarithmic decrement coefficients are estimated by means of a wavelet analysis performed on the experimental free oscillations of the fluid system. Numerical integration of the mathematical model gives results which are in a fair agreement with the experimental results.
Simulation of liquid sloshing in 2D containers using the volume of fluid method
In this paper, a two-dimensional numerical model is developed to study liquid sloshing in containers considering liquid free surface deformation, liquid viscosity and surface tension. The model is validated by a comparison between the computational and theoretical/experimental results for various sloshing scenarios with different time-dependent linear/angular accelerations. The governing equations for the 2D incompressible fluid flow are continuity and Navier–Stokes equations along with an equation for the free surface advection. The deformation of the liquid–gas interface is modeled using the volume-of-fluid (VOF) method. The fluid flow equations describing the fluid sloshing in the container and the dynamic equation which describes the movement of the container are solved separately in two coupled programs. In each time step of computations, the outputs of the fluid program (forces and torque) are obtained and used as inputs for the dynamic program. The forces and torque are applied to the body of the container resulting in translational and rotational accelerations which are then used as inputs to the fluid program in the next time step. The model is also used to simulate the movement of a liquid container in a general case where a complete interaction between the liquid and solid body of the container exists and the container has both linear and rotational accelerations.
Two phase analysis of sloshing in a rectangular container with Volume of Fluid (VOF) methods
Ocean Engineering, 2013
Free surface oscillations of a liquid confined in a closed container (sloshing phenomenon) are an important issue when big amounts of liquid are industrially transported. The phenomenon involves two fluids that share a free surface boundary separating them, normally the density of the upper fluid is several orders of magnitude less than the bottom one. Due to this density difference, this phenomena has widely been studied considering only one phase fluid and using different assumptions in the physical fluid modeling. In a recent paper, Ansari et al. simulated the sloshing in containers considering two liquid phases with different densities using a multimodal method. In this work, all the results obtained by Ansari have been tested, using different densities for the phase set at the top. Despite observing a good agreement in the cases where Ansari used a zero density assumption for the higher phase, serious discrepancies in the free-surface amplitudes have been found in those cases where the experiment involves two phase fluids. In order to make sure that the results computed for comparison are correct, three different codes were used as reference: one multimodal single phase code for those cases where the upper fluid was much less dense that the bottom one and two different Navier-Stokes/ VOF codes for all cases. Although these reference codes use different physical and numerical hypotheses, we obtained a remarkable agreement among them. In those cases where a second phase was set at the top of the container, the computed amplitudes were clearly lower compared to the ones obtained by Ansari.
A fully nonlinear model for sloshing in a rotating container
In this paper a theoretical and experimental analysis of sloshing in 2D and 3D free-surface con gurations is performed. In particular, the case of a tank rotating around a horizontal axis has been considered. The uid is assumed to be incompressible and inviscid. A fully nonlinear mathematical model is de ned by applying the variational method to the sloshing. The damping of gravity waves has been accounted by introducing a suitable dissipation function from which generalized dissipative forces are derived. A modal decomposition is then adopted for the unknowns and a dynamical system is derived to describe the evolution of the physical system. An experimental technique has been applied to select the leading modes, whose evolution characterizes the physical process, i.e. captures the most of the kinetic energy of the process. A very good agreement between experimental and numerical results con rms the validity of the methodological approach followed.
Recent advances in liquid sloshing dynamics
A liquid free surface in partially filled containers can experience a wide spectrum of motions such as planar, non-planar, rotational, quasi-periodic, chaotic, and disintegration. Civil engineers and seismologists have been studying liquid sloshing effects on large dams, oil tanks and elevated water towers under ground motion. Since the early 1960's, the problem of liquid sloshing dynamics has been of major concern to aerospace engineers studying the influence of liquid propellant sloshing on the flight performance of jet vehicles. Since then, new areas of research activities have emerged. The modern theory of nonlinear dynamics has indeed promoted further studies and uncovered complex nonlinear phenomena. These include rotary sloshing, Faraday waves, nonlinear liquid sloshing interaction with elastic structures, internal resonance effects, stochastic sloshing dynamics, hydrodynamic sloshing impact dynamics, g-jitter under microgravity field, cross-waves, and spatial resonance. The dynamic stability of liquid gas tankers and ship cargo tankers, and liquid hydrodynamic impact loading are problems of current interest to the designers of such systems. This article will address the means of passive control of liquid sloshing and the use of liquid sloshing forces to control vibratory structures. Other important contributions include the development of digital computer codes to solve complex problems that were difficult to handle in the past. The purpose of this article is to review the research work developed in different applications. It will highlight the major achievements and results reported in the literature. Some early work will be cited very briefly in order to provide an updated bibliography of liquid sloshing dynamics. This review article contains 1,319 references.
Scientific reports, 2024
An equivalent analytical model of sloshing in a two-dimensional (2-D) rigid rectangular container equipped with multiple vertical baffles is presented. Firstly, according to the subdomain partition approach, the total liquid domain is partitioned into subdomains with the pure interface and boundary conditions. The separation of variables is utilized to achieve the velocity potential for subdomains. Then, sloshing characteristics are solved according to continuity and free surface conditions. According to the mode orthogonality of sloshing, the governing motion equation for sloshing under horizontal excitation is given by introducing generalized time coordinates. Besides, by producing the same hydrodynamic shear and overturning moment as those from the original container-liquidbaffle system, a mass-spring analytical model of the continuous liquid sloshing is established. The equivalent masses and corresponding locations are presented in the model. The feasibility of the present approach is verified by conducting comparative investigations. Finally, by utilizing normalized equivalent model parameters, the sloshing behaviors of the baffled container are investigated regarding baffle positions and heights as well as the liquid height, respectively.
A 2D numerical study on suppressing liquid sloshing using a submerged cylinder
Ocean Engineering, 2017
In this paper, a two-dimensional numerical model is proposed to study the effect of a submerged cylinder on suppressing liquid sloshing in a moving container. The continuity and Navier-Stokes equations are solved along with an equation for the free surface advection. The Volume of Fluid (VOF) method is used to simulate the freesurface deformation. The numerical model for liquid sloshing is validated with the available experimental, and numerical results in the literature. The results of simulations are in good agreement with those of the measurements. Two scenarios for the liquid sloshing are studied. In the first case, the liquid container is excited with a Constant Acceleration (CA). For the second case, the container is moved with a Single Oscillatory Excitation (SOE). The suppression rate of total kinetic energy of sloshing with the submerged cylinder for two scenarios are calculated and compared to the cases with free sloshing with no cylinder. For the first and second scenarios, using the submerged cylinder reduced the total kinetic energy of sloshing by 26.58% and 71.6%, respectively. Therefore, the effect of submerged cylinder on suppressing the liquid sloshing is more pronounced in the second scenario where the container is excited with the SOE.
Nonlinear Free-Surface and Viscous-Internal Sloshing
Journal of Offshore Mechanics and Arctic Engineering, 2005
This paper examines free-surface and internal-pycnocline sloshing motions in twodimensional numerical wave tanks subjected to horizontal excitation. In all of the cases studied, the rectangular tank of liquid has a width-to-depth ratio of 2. The first set of results are based on an inviscid, fully nonlinear finite difference free-surface model. The model equations are mapped from the physical domain onto a rectangular domain. Case studies at and off resonance are presented illustrating when linear theory is inadequate. The next set of results are concerned with analyzing internal waves induced by sloshing a density-stratified liquid. Nonlinear, viscous flow equations are solved. Two types of breaking are discussed. One is associated with a shear instability which causes overturning on the lee side of a wave that moves towards the center of the container; this wave is generated as the dominant sloshing mode recedes from the sidewall towards the end of the first sloshing cycle. The other is associated with the growth of a convective instability that initiates the formation of a lip of heavier fluid above lighter fluid behind the crest of the primary wave as it moves up the sidewall. The lip grows into a bore-like structure as it plunges downward. It falls downward behind the primary wave as the primary wave moves up the sidewall and ahead of the primary wave as this wave recedes from the sidewall. This breaking event occurs near the end of the first cycle of sloshing, which is initiated from a state of rest by sinusoidal forcing.
Separation dynamics of immiscible liquids
2020
In this paper, the geometric design of a gravity-based separator is studied with a computational fluid dynamics method. ANSYS Fluent (18.2) is used to model the ratio of horizontal and vertical lengths with three dimensionless groups. A dimensional analysis method is used to develop a new correlation of separator geometric design. Corresponding plots were created and analyzed using nonlinear regression on the x–y Cartesian coordinate system. Also, manual iterations were performed to determine the coefficients in the general correlation relationship. The dimensional analysis results show that the Reynolds and Euler numbers have a direct correlation with separator design, which means increasing the Reynolds and Euler numbers require a separator with a larger length to height ratio to achieve the same separation efficiency. However, the Weber number has an inverse correlation with separator design, which means an increase in the Weber number requires a separator with a smaller length t...