Numerical study on ship-generated unsteady waves based on a Cartesian-grid method
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Numerical study on ship-generated unsteady waves based on a Cartesian-grid method* Kyung-Kyu Yang1, Masashi Kashiwagi2, Yonghwan Kim1 1. Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Korea 2. Department of Naval Architecture and Ocean Engineering, Osaka University, Osaka, Japan (Received August 18, 2018, Revised October 26, 2018, Accepted November 27, 2018, Published online March 16, 2020) ©China Ship Scientific Research Center 2020 Abstract: The added resistance of a ship in waves can be related to ship-generated unsteady waves. In the present study, the unsteady wave-pattern analysis is applied to calculate the added resistance in waves for two modified Wigley models using a Cartesian-grid method. In the present numerical method, a first-order fractional-step method is applied to the velocity-pressure coupling in the fluid domain, and one of volume-of-fluid (VOF) methods is adopted to capture the fluid interface. A ship is embedded in a Cartesian grid, and the volume fraction of the ship inside the grid is calculated by identifying whether each grid is occupied by liquid, gas, and solid body. The sensitivity of the location of measuring position of unsteady waves as well as the number of solution grids is examined. The added resistance computed by direct pressure integration and wave pattern analysis is compared with experimental data. In addition, nonlinear characteristics of the added resistance in waves are investigated with detailed analyses of unsteady flow field and resulting wave pattern. Key words: Unsteady wave pattern, added resistance in waves, Cartesian-grid method, grid convergence index
Introduction When a ship is moving in calm water or incoming waves, ship-generated waves can be observed. They can be decomposed into steady and unsteady waves. The former waves are known as Kelvin waves. There have been many studies of the Kelvin wave by means of theoretical, experimental, and computational methods[1-3] and the Kelvin wave is closely related to the wave making resistance of a ship advancing in calm water. On the other hand, there can be an additional steady wave component due to the mean value of interaction between the Kelvin wave and unsteady wave in the presence of incoming waves. The unsteady waves are mainly composed of the radiation waves induced by ship’s oscillation and the diffraction waves induced by scattering of incident waves due to a fixed body. The unsteady waves appear in the * Biography: Kyung-Kyu Yang (1986-), Male, Ph. D., E-mail: [email protected] Corresponding author: Masashi Kashiwagi, E-mail: [email protected]
presence of incident waves. Thus, the resistance of a ship in waves will increase in general due to ship-generated unsteady waves compared with the calm water resistance. This is a main component of the added resistance of a ship in waves, which is of practical importance for designing the propulsion power of a ship. Furthermore, for reduction of greenhouse gas emission, measuring the energy efficiency levels, su
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