Numerical analysis of two and three dimensional buoyancy driven water-exit of a circular cylinder

International Journal of Naval Architecture and Ocean Engineering.
2014.
Jun,
6(2):
219-235

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Published : June 30, 2014

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INTRODUCTION

Among the different types of transient phase problems, the water-exit phenomenon is one of the less studied and known cases. Prediction of hydrodynamic loads during water-exit of a body is of a great significance in the structural design of marine vehicles. There is no available theoretical tool to completely handle this complicated phenomenon. The water-exit of an initially fully immersed circular cylinder with a constant velocity was first studied by
Greenhow and Lin (1983)
, who have done experimentally and theoretically fundamental studies of non-linear free surface effects. Their physical investigation was based on video recording of the tests. Because of the time-consuming and expensive procedures of the experimental methods in the laboratory, nowadays, Computational Fluid Dynamics (CFD) methods are used widely for handling complicated phenomena and their accuracy in different applications is documented.
Colicchio et al. (2009)
made some experimental and numerical analysis on a circular cylinder either freely falling on or exiting the water. They used a Navier-stokes solver based on an approximated projection method and Cartesian grid with a level set function scheme for the air-water interface interaction with the solid body. In their experimental work, a detailed measurement of velocity field and the local loads around the cylinder is obtained. In another work, the nonlinear problem of a circular cylinder rising vertically to an interface between liquid media was studied by
Gorlov (2000)
. He considered the nonlinear initial-boundary-value problem in a contour approaching of an interface between two liquid media.
Gorlov (2000)
presented the perturbations which are generated by a circular cylinder approaching the free surface.
Kleefsman et al. (2004)
improved VOF method for displacement of free surface. They solved the standard dam breaking problem and also they simulated the drop test of a circular cylinder and a wedge. They presented several snapshots of simulations of a circular cylinder exiting the water and compared it with photographs of experiments. Their visual comparison between simulation and experiment was showed a good agreement.
Qian et al. (2005)
used a free-surface capturing method to simulate two fluid flows with moving bodies. They simulated a two-dimensional body emerging from beneath the water surface. They proposed a new scheme in which the normal pressure gradient term splits into hydrostatic and kinematic terms, therefore the gravity source term is exactly balanced by the normal hydrostatic pressure gradient term and no errors will be introduced at the interface with this method of calculating the pressure gradient term.
Zhu et al. (2005)
made a study on a circular cylinder and free surface interaction using finite difference method on a non-uniform, staggered Cartesian grid. They used a new numerical method called Constrained Interpolation Profile (CIP) by which no sharp interface between air and water is obtained i.e., density changes continuously between the values of air and water densities at the free surface.
Lin and Xu (2006)
used a computer model for simulation of general turbulent free surface flows. They solved the Reynolds-averaged Navier-Stokes equations and employed the VOF method to track the free surface. They simulated water-exit of a horizontal cylinder in Froude number equal to 0.39 and compared their results with Greenhow results.
Lin (2007)
used a fixed-grid model for simulation of a moving body in free surface flow. In his model, a body is approximated by Partial Cell Treatment (PCT) and the body motion is tracked by Lagrangian method whereas the fluid motion around the body is solved by Eulerian method.
Yang and Stern (2007)
studied on a combined-boundary/ghost-fluid sharp interface method for the simulations of 3D two phase flows interacting with moving bodies on fixed Cartesian grids. In the water-exit case, they compared their results with boundary element simulation of
Greenhow and Moyo (1997)
. Another problem is prediction of hydrodynamic slamming loads during water-entry of a body. The slamming force on the step of a flying boat in landing, or the slamming force on the bow of ships is very large and has a great significance. The hydrodynamic force of impact problem (slamming) on seaplanes can damage the structure or lead to hull vibration and cause ship speed reduction.
The water impact problem was first simulated by
Von Karman (1929)
, using the momentum and the water-added mass theory to predict the impact force during the seaplanes landing without the effect of water pile-up during impact. Von Karman made an important assumption that during the initial stages of the impact, the momentum of the water/body system is conserved. Von Karman analysis was refined by
Wagner (1931)
, who had predicted the impact force on the seaplane. Further improvements of this work were proposed by
Fabula (1957)
. Most previous studies on the water impact problem are based on the potential flow assumption. During the past decade some numerical studies were carried out to improve results and overcome the limitations of the traditional analytical approach. Numerical analyses with free surface model by VOF method have been recently conducted by
Arai et al. (1994)
.
Nikseresht et al. (2004)
have solved the impact problem of a circular cylinder based on viscous incompressible flow. They showed that in the impact problem with the viscous effect the numerical results show better agreement with the experimental data especially in water entry time intervals. Rastegari and
Nikseresht (2007)
solved the classical problem of water impact of a wedge using finite volume discretization and the VOF scheme for two phase flow. Also they studied the effect of concave and convex curvatures of the wedge on the pressure distribution and the slamming force.
Greco et al. (2009)
developed an iterative Domain-Decomposition strategy to examine the coupling between the global motions of a Very Large Floating Structure (VLFS) and bottom-slamming events.
In the present paper, numerical simulation of the two and three dimensional buoyancy driven water-exit of a circular cylinder in two-phase flow is made with coupling the rigid body dynamic equations of motion. The two-phase flow is solved based on the finite volume method and the interface is tracked with the VOF scheme. Dynamic equations and a dynamic mesh are used to obtain the real velocity distribution during the water-exit and entry of circular cylinder. Moreover, the oblique exit and entry of a circular cylinder with two exit angles are simulated.
GOVERNING EQUATIONS

- Fluid motion & free surface equation

The equations represent a mathematical model for describing viscous flows in the form of Eq. (1) reported by Versteeg and
Malalasekera (1995)
. They are usually called Navier-Stokes equations in honor of two men, the Frenchman M. Navier and the Englishman Stockes, who independently obtained the equations in the first half of the nineteenth century (see
Sheikhalishahi et al. (2009)
):
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- • Interface tracking methods
- - Height Function
- - Line Segment
- - Arbitrary Lagrangian - Eulerian
- • Volume tracking methods
- - Marker And Cell (MAC)
- - Volume Of Fluid (VOF)
- - Level Set (LS)

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- A typical VOF algorithm generally consists of two parts (seeRansau (2002)):
- - A device to track the volume and locate the free surface. This device must be able to keep the interface as sharp as possible.
- - A way to impose boundary conditions at the surface.

- Dynamic mesh theory

The dynamic mesh model can be used to model flows where the shape of the domain is changing with time due to the motion on the domain boundaries. The motion can be a prescribed motion, or an un-prescribed motion where the subsequent motion is determined based on the solution at the current time. Three groups of mesh motion methods are available to update the volume mesh in the deforming regions subject to the motion defined at the boundaries:
- • Smoothing Methods
- - Spring-Based Smoothing Methods (SBSM)
- - Laplacian Smoothing Methods (LSM)
- - Boundary Layer Smoothing Methods (BLSM)
- • Dynamic Layering Methods (DLM)
- • Local Re-meshing Methods (LRM)

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- Solid-body kinematics

Dynamic equations of solid body motion in the inertial coordinate system are as follows:
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Input data for motion description.

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- Problem domain and boundary condition

A cylinder with weight equal to 0.62 times the weight of the water and diameter of 30
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- Parallel processing for 3D simulation

In parallel processing, according to the number of the processors that are used in the calculation, the domain has been decomposed to several sub-domains. In order to obtain a good load balance, each sub-domain must contain the suitable number of cells (see
Sheikhalishahi et al. (2009)
). Speedup of calculations by increasing the number of processors is an important problem in parallel processing. More details about parallel processing and partitioning in different kinds of mesh domains can be found in
Schiffermuller et al. (1998)
. Specifications of Hybrid Cluster which is used in 3D simulation are listed in
Table 2.
Specification of hybrid cluster.

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RESULTS AND DISCUSSION

Water exit results of a circular cylinder are presented in four parts. At first, a cylinder rising only due to its buoyancy is simulated and the results are compared with other numerical and experimental data available in the literature in order to validate the numerical method used in this research. The conditions of this simulation are noted as Test No. 1 in
Table 3
. In this case no thrust is exerted to the cylinder.
In the second part, the effect of cylinder mass is investigated for the Test cases 2 to 5 described in
Table 3
. In these cases an external vertical force is added such that the net vertical (body and external) force remains unchanged. The third part of the results shows the applicability of the present numerical method in modeling other complicated phenomena. In this part, waterexit of a circular cylinder with the path angle of 30° and 45° is simulated. For this purpose an external horizontal force is added to the Test case No. 4 such that the net resulting force vector makes an angle of 30° or 45° with the vertical direction. More details are shown in
Table 4
.
Parameters of the water-exit simulations.

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Parameters of the oblique water-exit simulations.

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VALIDATION

In the first simulation (Test No. 1), buoyancy force causes the upward motion of the circular cylinder. The free surface will deform continuously till the cylinder exits completely. During the exit of the cylinder, a thin water layer around the cylinder is lifted. By further raising the cylinder up, the water layers in the circumference of the cylinder are drawn down to the water surface and cause the breaking of the free surface. This phenomenon takes near 1.0
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Maximum velocity and height during the water-exit.

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- Cylinder mass effect

In Test No. 2 as it is shown in Table 3, the forces that act on the cylinder are thrust plus buoyancy force. Also the mass changes so that the total force remains constant like Test No. 1. Therefore in Eq. (7) the total force F remains constant and the mass is increased and so the acceleration is decreased. It causes the velocity and position of the cylinder to change. It can be repeated with various masses in test cases 3, 4, and 5.
Fig. 10
shows the time variation of the velocity for different masses. As it shows, increasing the mass reduces the pick value of velocity because of greater inertia.
The effect of different masses on the position of the center of the cylinder is plotted in
Fig. 11
. It is apparent that increasing the mass delays the exit time of the cylinder from the water surface, but the cylinder goes more up in the air.
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- Oblique water-exit

In order to show the applicability of the present method for modeling other complicated phenomena, water-exit of a circular cylinder with the path angle of 30° and 45° is carried out. More details are shown in
Table 4
. After releasing the cylinder, with an acting vertical force equal to 980.6N and an acting horizontal force equal to 151.77
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- 3D simulation of water-exit

A cylinder with weight equal to 0.62 times the weight of the water and diameter of 30
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Maximum velocity and height during the water-exit in 2D and 3D simulations.

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CONCLUSIONS

This paper presents a numerical simulation of water-exit of a circular cylinder using the equation of solid body motion. The finite volume method is used to solve the Navier-Stokes equations. Volume tracking method VOF is used for simulation of free surface deformation during the water-exit of the circular cylinder. For calculating the effect of the velocity change, dynamic mesh method is used. The present simulation shows an excellent agreement with experimental data in water-exit phase and also in its motion outside water before impacting the free surface. This numerical method, based on VOF model is more accurate than level set model used in another numerical simulation.
The velocity and motion of the cylinder in water-exit simulation agrees well with the numerical results of
Colicchio et al. (2009)
. The complicated free surface deformation is simulated having a good agreement with the experimental results of
Kleefsman et al. (2004)
. Furthermore, the effects of changing mass and thrust with superposition of the buoyancy force with the limitation of having a constant total force is simulated. The numerical results show the applicability of the present method for modeling complicated phenomena. After investigation of mass effects, oblique exit of a circular cylinder for two exit angles is simulated. Then using parallel processing, water-exit of the circular cylinder in 3D is simulated and compared with 2D simulation. The results of 2D and 3D simulatons showed a good agreement. The strongly non-linear free surface deformation in waterexit of a circular cylinder is simulated successfully with an excellent agreement with the experiments.
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Citing 'Numerical analysis of two and three dimensional buoyancy driven water-exit of a circular cylinder
'

@article{ E1JSE6_2014_v6n2_219}
,title={Numerical analysis of two and three dimensional buoyancy driven water-exit of a circular cylinder}
,volume={2}
, url={http://dx.doi.org/10.2478/IJNAOE-2013-0174}, DOI={10.2478/IJNAOE-2013-0174}
, number= {2}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Moshari, Shahab
and
Nikseresht, Amir Hossein
and
Mehryar, Reza}
, year={2014}
, month={Jun}