Modelling and Simulation in Engineering

Volume 2017 (2017), Article ID 2197150, 14 pages

https://doi.org/10.1155/2017/2197150

## Numerical Modeling and Simulation of Wave Impact of a Circular Cylinder during the Submergence Process

College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China

Correspondence should be addressed to Xiaozhou Hu

Received 19 April 2017; Revised 12 August 2017; Accepted 2 October 2017; Published 3 December 2017

Academic Editor: Dimitrios E. Manolakos

Copyright © 2017 Xiaozhou Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Wave slamming loads on a circular cylinder during water entry and the subsequence submergence process are predicted based on a numerical wave load model. The wave impact problems are analyzed by solving Reynolds-Averaged Navier-Stokes (RANS) equations and VOF equations. A finite volume approach (FV) is employed to implement the discretization of the RANS equations. A two-dimensional numerical wave tank is established to simulate regular ocean waves. The wave slamming problems are investigated by deploying a circular cylinder into waves with a constant vertical velocity. The present numerical method is validated using other numerical or theoretical results in accordance with varying free surface profiles when a circular cylinder sinks in calm water. A numerical example is given to show the submergence process of the circular cylinder in waves, and both free surface profiles and the pressure distributions on the cylinder of different time instants are obtained. Time histories of hydrodynamic load on the cylinder during the submergence process for different wave impact angles, wave heights, and wave periods are obtained, and results are analyzed in detail.

#### 1. Introduction

Wave impact problem is of great interest in the marine and offshore industries, especially for subsea working systems which are widely used in such applications as marine resource development and utilization, maritime exploration and survey; the important problem which needs to be solved before their proper operations is to accurately study the phenomenon of offshore structures impacting ocean wave and the following submergence process. The process of subsea structures lowering through wave zone accompanies the interaction between the air, wave, and the solid body, which is a complicated fluid-solid problem, involving consideration of time-varying hydrodynamic forces (slamming, drag, inertia, and buoyancy) and time-varying waves. In hostile ocean conditions, these forces can result in significant localized and even catastrophic structural damage on structures ranging from deployed structures to deploying equipment and heave compensator systems and so forth. Therefore, the accurate prediction of wave slamming loads and time histories of hydrodynamic force, as well as the sensitivity of these loads to wave parameters, is of significant importance.

Researches on water entry and wave impact problems were firstly carried out by Karman [1], who studied loads on seaplane floats shaped as wedges during water entry. Wagner developed methods of Karman by taking into account the piled-up water surface along the side of the body [2].

For a rigid cylinder, pioneering studies applied several different methods, including flat plate theories, generalized Wagner theory [3], boundary element method (BEM) [4, 5], and Constrained Interpolation Profile (CIP) method [6, 7]. In recent years, researchers applied other computational fluid dynamics (CFD) methods to this field. For example, Zhang et al. numerically simulated the water entry of a cylinder based on Lattice Boltzmann Method (LBM) [8]. Vandamme et al. simulated water entry and exit of a cylinder with a weakly compressible smoothed particle hydrodynamics (SPH) method [9]. Skillen et al. used SPH method to investigate the motion of a circular cylinder dropping onto initially still water numerically [10]. Gu et al. simulated water impact problem of a semicircular cylinder with the free surface captured using level set method [11]. Nguyen et al. studied water entry of a circular cylinder by integrating a moving Chimera grid method to a preconditioned Navier-Stokes solver [12]. Peng and Wei simulated the water entry of a circular cylinder based on a CIP method with the parallel algorithm [13]. Iranmanesh and Passandideh-Fard numerically investigated water entry of a horizontal circular cylinder for low Froude numbers by the combination of the fast-fictitious-domain method and the volume-of-fluid (VOF) technique [14]. NAIR and TOMAR employed an incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate water entry of 2D circular cylinders [15]. Aristodemo et al. performed numerical study on wave-induced forces of submerged circular cylinders by SPH method [16]. Advances in computer technology and CFD have made it possible to use commercial CFD codes to solve wave impact problem. For example, Mnasri et al. used Fluent code with a moving grid to analyze the free surface evolution induced by one or two moving cylinders [17]. Chen et al. studied water entry of a horizontal cylinder based on VOF method by Fluent [18]. Ghadimi et al. utilized FLOW-3D code to study the water entry of a circular cylinder and conducted a comparison between the linear and nonlinear solutions [19]. Tassin et al. investigated water impact problem of a body with time-varying shape by CFD code OpenFOAM [20]. Larsen used the CFD code STAR-CCM+ to calculate impact loads on circular cylinders during water entry [21].

This work is devoted to investigate the complex interaction between a circular cylinder and waves during the submergence process. Firstly, both governing equations and boundary conditions are outlined; to study the interaction between wave and cylinders, a numerical wave tank is established, and numerical wave generation and absorption method are presented. Secondly, snapshots of the simulation of calm water entry of a circular cylinder are compared with those of experiments by previous researches. Then, numerical simulations of a circular cylinder impact with waves are conducted, and free surface profiles of different time instants of submergence process are shown. Finally, slamming loads on the circular cylinder are computed, and influence of wave parameters is discussed.

#### 2. The Numerical Method

##### 2.1. Governing Equations

In this work, governing equations for the CFD calculations are RANS equations for homogeneous, incompressible fluid flows, and they are written as follows:where , 2 for two-dimensional flows; is the average velocity of th coordinate axis; is the density; is the average pressure; is the dynamic viscous coefficient; is the average body force; is the Reynolds stress.where is the turbulence kinetic energy; is the dissipation rate of turbulence kinetic energy; is the eddy viscosity; is the turbulent energy production.

The empirical coefficients in (2) are given as follows [22]:

The complex free surface is tracked by the VOF method, and to accomplish the capturing of the interface between the air phase and the water phase, a continuity equation for the fraction of volume of water is solved, which has the following form:

The sum of the volume fraction of water and air is given bywhere and are the volume fraction of water and air in each cell, respectively.

##### 2.2. Boundary Conditions

To solve governing equations, it is necessary to specify appropriate boundary conditions at all boundaries of the domain. The boundary conditions which need to be satisfied are as follows: () the kinematic and dynamic free surface conditions at the free surface and () the no-slip boundary condition at the tank bottom and the rigid body and () to investigate the dynamic problem during a circular cylinder lowering through wave zone, a 2D numerical wave tank is utilized. The left wall boundary is a wave-maker, while the right part of the domain is a damping zone, as shown in Figure 1.