Abstract
This paper presents a smoothed particle hydrodynamics (SPH) modeling technique based on the cylindrical coordinates for axisymmetrical hydrodynamic applications, thus to avoid a full three-dimensional (3D) numerical scheme as required in the Cartesian coordinates. In this model, the governing equations are solved in an axisymmetric form and the SPH approximations are modified into a two-dimensional cylindrical space. The proposed SPH model is first validated by a dam-break flow induced by the collapse of a cylindrical column of water with different water height to semi-base ratios. Then, the model is used to two benchmark water entry problems, i.e., cylindrical disk and circular sphere entry. In both cases, the model results are favorably compared with the experimental data. The convergence of model is demonstrated by comparing with the different particle resolutions. Besides, the accuracy and efficiency of the present cylindrical SPH are also compared with a fully 3D SPH computation. Extensive discussions are made on the water surface, velocity, and pressure fields to demonstrate the robust modeling results of the cylindrical SPH.
Highlights
The Smoothed Particle Hydrodynamics (SPH) method is a robust numerical modeling technique without the use of fixed mesh grids. It originated from the 3D astrophysical applications [1] and its 2D form in a Cartesian coordinate has been widely used in the hydrodynamic calculations [2], as well as a variety of industry fluid flows [3,4,5,6]
Quite a few interesting hydrodynamic problems involve the axisymmetric features, such as those happening during the water entry of a cylindrical plate and a circular sphere, or the collapse of an axisymmetric column of water and granular materials
We aim to develop a simple and effective cylindrical SPH method for axisymmetric hydrodynamic applications
Summary
The Smoothed Particle Hydrodynamics (SPH) method is a robust numerical modeling technique without the use of fixed mesh grids. To further demonstrate the spatial and temporal dam-break flow features computed by the 2D cylindrical SPH model, Figures 3 shows the particle snapshots with pressure contour at several time instants. Since Fr number represents the counterbalance between gravitational and inertia forces, it should generate different effects on the fluid particle motion For a more quantitative validation of the numerical model, the time histories of the sphere entry depth are shown, for the four different sphere densities This clearly demonstrates the accuracy of the present 2D cylindrical SPH computations for all the test conditions. There is a satisfactory agreement among three sets of the data across all the sphere densities, but in some cases it can be observed that the SPH results seem to be closer to the theoretical values
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