Abstract
In order to numerically investigate the free surface flow evolution in a cylindrical tank, a regular structured grid system in the cylindrical coordinates is usually applied to solve control equations based on the incompressible two-phase flow model. Since the grid spacing in the azimuthal direction is proportionate to the radial distance in a regular structured grid system, very small grid spacing would be obtained in the azimuthal direction and it would require a very small computational time step to satisfy the stability restriction. Moreover, serious mass disequilibrium problems may happen through the convection of the free surface with the Volume of Fluid (VOF) method. Therefore in the present paper, the zonal embedded grid technique was implemented to overcome those problems by gradually adjusting the mesh resolution in different grid blocks. Over the embedded grid system, a finite volume algorithm was developed to solve the Navier–Stokes equations in the three-dimensional cylindrical coordinates. A high-resolution scheme was applied to resolve the free surface between the air and water phases based on the VOF method. Computation of liquid convection under a given velocity field shows that the VOF method implemented with a zonal embedded grid is more advanced in keeping mass continuity than that with regular structured grid system. Furthermore, the proposed model was also applied to simulate the sharp transient evolution of circular dam breaking flow. The simulation results were validated against the commercial software Fluent, which shows a good agreement, and the proposed model does not yield any free surface oscillation.
Highlights
The phenomenon of interfacial fluid motions in a cylindrical enclosure, driven by density difference and/or external force, often occurs in technical applications and industrial processes, which will cause a great impact on the working characteristic of the device
In order to demonstrate the advantage of the embedded grid technique in the cylindrical coordinates, movements of a volume of fluid were simulated under a given velocity, and comparison of the volume loss with that using the regular grids was presented
The present two-phase flow model was applied to compute sharp transient evolution of the circular dam break flow, which was validated against the simulation results predicted by Fluent
Summary
The phenomenon of interfacial fluid motions in a cylindrical enclosure, driven by density difference and/or external force, often occurs in technical applications and industrial processes, which will cause a great impact on the working characteristic of the device. That problem arises in applications like liquid sloshing caused by the motion of the cylindrical container. The sloshing behavior in the cylindrical liquid tank has been numerically studied by Hernández-Barrios et al in [1] and based on the potential theory. In order to simulate the fully nonlinear free surface motions accurately, some recent examples of the computational fluid dynamics (CFD) sloshing simulations have been carried out based on the incompressible two-phase flow model by solving the Navier–Stokes equations and applying appropriate free surface tracking methods, including the studies in [2,3,4,5]. The resolution of the Navier–Stokes equations in cylindrical coordinates involves some specific difficulties, especially when the computational domain contains the axis r = 0. When the cylindrical center is within the computational domain, terms like 1/r or ∂φ/∂r become undefined, which causes a singularity at Algorithms
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