Analytical Solution of Wedge Water Entry by Using Schwartz–christoffel Conformal Mapping

Abstract

Water impact is one of the most critical phenomena from the viewpoint of the structural design of ships and offshore structures. The impact force can impose a large load with high local pressure on the body surface. On the other hand, determination of the maximum impact force during impact and acting point itself is very important in the design of floats. In this paper, the water entry of a two-dimensional wedge section is considered. This study is carried out in the framework of a potential-flow assumption. In particular, water impact on a dropping wedge with a constant velocity is pursued analytically by using the Schwartz–Christoffel conformal mapping. In order to determine a position of the wedge where the instantaneous effective force is largest during the impact, a particular equation is introduced here for the first time. The pressure distribution and maximum impact force are also calculated. The obtained results are compared against other numerical and experimental works and favorable agreement is displayed.

Numerical Assessment of turbulence effect on Forces, Spray parameters, and secondary impact in wedge water entry problem using k-ε method

“…Moreover, Wang and Wei [7], Yin and Qian [8], and Sun et al [9] used Boundary Element method to solve the water entry problem by using potential theory, which basically neglects the viscosity e ects and hence the turbulence e ects. On the other hand, analytical method has been used by Ghadimi et al [10] by applying the Schwartz-Christo el conformal mapping, a solution which neglects viscosity e ects. The works by Gao et al [11] and Wu et al [12] are other studies, which have used potential theory to solve the wedge water entry problem.…”

Experimental Study of the Wedge Effects on the Performance of a Hard-chine Planing Craft in Calm Water

“…It is considered that the model passes through a transverse plane and the three dimensional problem can be reduced to a water entry of a solid body with wedge section, as shown in Figure 19. Dynamic pressure distribution over the wall of the wedge can be computed using analytical scheme, numerical methods [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67] or experimental measurements [68][69][70][71][72][73][74]. Here, the Wagner solution [75] is used as in when the water has not drenched the chine.…”

Asymmetric Water Entry of Twin Wedges with Different Deadrises, Heel Angles, and Wedge Separations using Finite Element Based Finite Volume Method and VOF

“…Boundary element method was also used by Zhao and faltinsen (1993), Battistin and Iafrati (2004), Sun et al (2011), Wang and Wei (2012), Yousefnezhad and Zeraatgar (2014) and Gao et al (2011). In a different approach, the Shwartz-Christoffel conformal mapping was used by Ghadimi et al (2011) as an analytical solution to the problem. Moreover, Shah et al (2015) analyzed the impact of rigid wedges on water in 2D fluid flow through experimental and SPH methods.…”