Dynamic response of a wedge through asymmetric free fall in 2 degrees of freedom

Abstract

In this article, a mathematical model is presented for simulation of the coupled roll and heave motions of the asymmetric impact of a two-dimensional wedge body. This model is developed based on the added mass theory and momentum variation. To this end, new formulations are introduced which are related to the added mass caused by heave and roll motions of the wedge. These relations are developed by including the asymmetrical effects and roll speed. In addition, by considering the roll speed, a particular method is presented for the time derivative of half-wetted beam of an asymmetric wedge. Furthermore, two equations are derived for the roll and heave motions in which damping terms appear. Validity of the proposed method is verified by comparing the predicted results against available experimental data in two conditions of roll motion and no roll motion. Favorable agreement is observed between the predicted results and experimental data. The pressure and hydrodynamic load are computed, and the differences between the results associated with the considered conditions are explored. Subsequently, the effects of different physical parameters including deadrise angle, initial roll angle, and initial velocity on the dynamic response of a two-dimensional wedge section are investigated. Ultimately, time histories of hydrodynamic coefficients are determined in order to provide a better understanding of the derived equations.

Effects of step configuration on hydrodynamic performance of one- and doubled-stepped planing flat plates: A numerical simulation

“…In addition, it is clear that, position of peak pressure in aft-body moves backward as step moves toward the transom, which is accompanied with increase in cavity length. Therefore, total wetted length and wetted length of the rear body are decreased as it can be seen in Figures 5(d) and 16. Figure 16 also demonstrates that predicted wetted surface of current numerical simulation agrees with the results of Garland and Maki.…”

“…Systematic experimental studies of the stepped planing hull series have been conducted by Morabito et al, 3 Lee et al, 4 Ma et al 11 and Taunton et al 12 Besides the mentioned experimental studies, mathematical models have also been used to model nonstepped/stepped planing hulls. 13,14 Some of these mathematical methods have been established by using the 2D + T method, where the results of water entry of a wedge [15][16][17] are used to simulate motion of planing hulls in both calm water and waves (see, for example, Tavakoli et al, 14 Tavakoli and Dashtimanesh 15 and Ghadimi and colleagues [18][19][20][21] ). The 2D + T method has even shown the ability to model yawed planing motion 15,22,23 and has been recently used to model stepped boats by Niazmand Bilandi et al 24 In addition to this model, the theoretical simulations of Matveev 25 have been used for modeling of the flow around stepped planing ships.…”

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

“…This phase refers to condition at which wedge is symmetric and water has not reached any of chines. 20 Therefore, half wetted beam of a section and its time derivative has been computed using…”

Statistical Analysis of Wedge Effect on the Seakeeping of a Planing Hull in Irregular Waves at the Onset of the Planing Region

“…From 1990 until now, the study of water entry of various sections, especially wedge sections, in terms of pressure distribution and induced motion analysis have been widely followed via numerical modeling (Arai et al (1995), Yang and Qiu (2012), Farsi and Ghadimi (2014a, Feizi et al (2016), Ghadimi et al (2012Ghadimi et al ( , 2013cGhadimi et al ( , 2014a, Shademani and Ghadimi (2017a, 2017c, 2017d), analytical (Mei et al (1999), Yettou et al (2007), Ghadimi et al (2013dGhadimi et al ( , 2017b) and experimental analysis (Judge et al (2004), Yettou et al (2006), Nikfarjam et al (2014)). The main aim of these studies have been the utilization of the results of these studies in motion prediction of planning hulls.…”