On the behavior of nonlinear hydrodynamic coefficients of a submerged cylinder beneath the water surface

This study aims at numerically exploring the behavior of flow fields and nonlinear hydrodynamic coefficients of a horizontal cylinder beneath the free surface flow considering the effects of nonlinear surface waves and various cylinder shapes. The computational model is based on two-dimensional incompressible Navier-Stokes solvers along with the treatment of the free surface flow using the volume of fluid method. The effect of the turbulent flow is also considered by using the shear stress transport turbulence model. The simulation result of a benchmark case study of the submerged cylinder is first validated with available experiment data, where a mesh convergence analysis is also performed. Afterward, the flow fields and hydrodynamic force coefficients around the cylinder surface are analyzed, and the influences of various cylinder shapes and Reynolds numbers on the hydrodynamic coefficients are investigated. A state diagram representing the hydrodynamic behavior including stable and unstable stages is finally proposed; this is an important criterion for the practice design of submerged civil structures under the free surface flow.

Hydrodynamic Forces of a Semi-Submerged Cylinder in an Oscillatory Flow

This work experimentally investigated the performance of hydrodynamic forces on a semi-submerged cylinder under an oscillatory flow. To generate the equivalent oscillatory flow, the semi-submerged cylinder is forced to oscillate in several combinations of different periods and amplitudes. The mean downward lift force was observed to be significant and the fluctuating lift forces show dominant frequency is twice that of oscillatory flow and amplitude that is the same as the mean lift force. Based on this main hydrodynamic feature, a novel empirical prediction formula for the lift forces on semi-submerged cylinder under oscillatory flow is proposed where the lift forces expression is proportional to the square of oscillatory flow velocity. This novel empirical formula directly assigns the fluctuating lift force with frequency twice of oscillatory flow and the amplitude that is the same as the mean lift force. This assignment of empirical lift force formula reduces parameters required to determine a dynamic lift force but is demonstrated to well predict the fluctuating lift force. The lift coefficient can reach 1.5, which is larger than the typical value 1.2 of the drag coefficient for a fully submerged cylinder with infinite depth. Moreover, relationships among hydrodynamic coefficients, Keulegan-Carpenter (KC) number, Stokes number and Froude number are studied. With the increase of KC number, the Froude number has a more significant influence on the distribution of hydrodynamic coefficients. As Froude number is increasing, the drag coefficient shows a nonlinear decay (KC < 20) but a linear increase (KC > 20), while the added mass coefficients show a nonlinear (KC < 20) and a linear (KC > 20) increase trend. The present work can provide useful references for design of the relevant marine structures and serve as the useful guideline for future research.

Hydrodynamic Forces on a Submerged Horizontal Circular Cylinder in Uniform Finite Depth Ice Covered Water

Hydrodynamic forces on a submerged cylinder in uniform finite depth ice-covered water is formulated by using the method of multipoles, the ice-cover being modelled as an elastic plate of very small thickness. The forces (vertical and horizontal) are obtained analytically as well as numerically and depicted graphically for various values of flexural rigidity of the ice-cover to show the effect of its presence. When the flexural rigidity and surface density of the ice-cover are taken to be zero, then the curves for the forces almost coincide with the curves for the case of uniform finite depth water with free surface.

Three Dimensional Radiated Water Wave with a Submerged Cylinder in Presence of Circular Plate

This work deals with the problem of radiated by wave interaction with a couple of submerged cylinders in water which can be considered as a wave energy device and the problem arising from the rotational motion of submerged upper cylinder which one contains in the device. In this work, we approach theoretically to solve the problem based on the method of separation of variables and we derive the radiated velocity potentials numerically based on linear wave theory and eigenfunctions are introduced for each region by using free surface condition. Then we calculate the hydrodynamic coefficients due to rotational of the upper cylinder by using Bernoulli’s equation of pressure by neglecting the atmospheric pressure and unknown constants are calculate by using matched conditions between the regions Finally, we present all numerical results graphically for different radii of the cylinders

Radiated Force due to Surge Motion by a Pair of Submerged Cylinder in Water

Evaluation of hydrodynamic coefficients due to surge of submerged structure is great significant to designing a device which can be consider as a device of wave energy. In the present work, a theoretical approach is developed to describe radiation of water wave by fully submerged cylinder placed above a submerged circular plate in water of finite depth which is based on linear water wave theory The radiation problem due to surge motion by this pair of cylinders have investigated with the suspicion of linear water wave theory. To determine the radiated potentials in every area, we utilize the eigenfunction expansion method and variables separation method. Finally, we derived the analytical expressions of Hydrodynamic coefficients i. e. added mass and damping coefficient due to surge and associated unknown coefficients are calculated by utilizing the matching conditions between the physical and virtual boundaries. A set of added mass and damping coefficient have presented graphically for various radius of the submerge cylinder.