Numerical study on the dynamic response of a truncated ship-hull structure under asymmetrical slamming

Highlights

• A methodology was preliminarily presented to study the characteristic of dynamic response of bow structure under asymmetric impact.

• Asymmetrical slamming loads were predicted well by combining the seakeeping analysis and CFD method.

• Dynamic characteristic of ship-hull structure under asymmetrical impact was clarified.

• Special attention is concentrated on the prediction of asymmetrical pressure in oblique waves.

Abstract

Dynamic response of ship-hull structure under slamming has tracked widespread attention in the marine structural design. However, our understanding on the dynamic characteristics largely relies on the symmetrical slamming cases. This paper presented a preliminary numerical investigation on the dynamic response of a truncated ship-hull structure under asymmetrical slamming based on the uncoupled CFD-FE method. Asymmetrical slamming loads were predicted through combining the seakeeping analysis and CFD method. In there, three kinds of motions (vertical, horizontal and roll motions) of 2D ship sections were obtained through the seakeeping analysis and then the slamming pressure was predicted through simulating the water entry with various motions based on CFD method. The dynamic response was analyzed through finite element method. Numerical predictions including ship motions, slamming loads and dynamic analysis were validated against published experimental data and numerical calculations. The characteristics of asymmetrical slamming loads were analyzed showing obvious asymmetry in space, and the dynamic characteristic of the ship bow structure was further clarified through discussing the deformation and stress distribution. These results are useful for readers for better understanding the dynamic characteristics of the bow structure under slamming.

Introduction

Slamming of the ship bow is quite common in ongoing ships due to the relative motion of the ship and waves. Although the ship bow is required to strengthen in structural design, there is no a uniform analysis method to determine the structural parameters because the complexity in predicting the slamming loads especially for the asymmetrical slamming in oblique waves (Xie et al. [1]). Therefore, it is necessary to find a reasonable method to evaluate the structural strength subjected to slamming loads.

Analysis of ship strength subjected to slamming loads includes two aspects: prediction of slamming loads and structural response analysis. Some work has been done on the prediction of slamming pressure on the ship moving in waves, where the impact theory must combine the relative motion of the ship and wave. Two main methods including k-factor method and the direct method are widely used. The k-factor method is based on the use of slamming coefficients or so-called k-factors (e.g., Ochi and Motter [2]). The slamming pressure is directly proportional to the square of the impact velocity where the proportionality coefficient is firstly obtained by the numerical or experimental methods, prior to the analysis of ship motion. For example, Kvalsvold et al. [3] used slamming coefficients for wedges and semicircles to calculate the total vertical slamming force on the bow-door of a Ro-Ro vessel. Comparisons with results from model tests showed reasonable agreement. In the direct method, ship motions are calculated first, and then a slamming analysis is performed through simulating the water entry progress in the slamming event. Hermundstad and Moan [4] obtained the relative entry velocity of the hull by using the nonlinear slice theory and then a two-dimensional NBE (Nonlinear Boundary Element) method was applied to predict the slamming pressure. It was extended to the case of irregular waves (Hermundstad and Moan [5]). Veen and Gourlay [6] also used the nonlinear slice theory to predict the motion of the hull, but the slamming load was calculated by SPH algorithm. Similar studies have been conducted in Tuitman et al. [7], Oberhagemann et al. [8], Chen et al. [9], Schellin and Moctar [10] and Xie and Ren [1].The direct methods are presumably more accurate since the entire slamming event is simulated and the proper time-variation of the relative velocity is used instead of a constant value. Pile-up effects can also be properly included, provided that the slamming calculation method is sufficiently refined. For example, Sames et al. [11] compared the results from a k-factor method obtained by a 2D VOF method and a direct method based on the boundary element method with data from model tests. The experimental results were compared with two theoretical predictions, and both methods agreed reasonably well with the experiments for most cases. However, for pressure in the bow flare model, the agreement was not good for k-factor method. The hydroelasticity is also important in the hull slamming. Korobkin et al. [12] put forward a general method for the water entry problem of elastic wedges by combining the FEM and Wagner theory. Luo et al. [13] carried out the experimental study on the water entry problem of the elastic wedge with stiffened panels. Hydroelastic effects were discussed through analyzing the oscillations of measured signals in terms of increasing velocity and decreasing deadrise angle. Hassoon et al. [14] presented a numerical model to simulate the slamming water impact of flexible composite panels using an explicit finite element method. Simulation results have been indicated that the lower stiffness panel had a higher hydroelastic effect and became more important when decreasing of the deadrise angle and increasing the impact velocity. Similar work has been done in the open literature, such as Maki et al. [15], Hassoon et al. [16], Xie et al. [17], Wang and Guedes Soares [18], and Xie et al. [19].

Aiming at the prediction of ship slamming loads in the direct method, water entry above mentioned were symmetrical cases. For the asymmetrical water entry appearing in oblique waves, some work has been done. Judge et al. [20] solved the boundary value problem (BVP) for asymmetrical water entry problem based on the vortex distribution model and the corresponding experimental study was carried out. Experimental findings showed the asymmetrical impact was greatly depended on the ventilation occurrence on the low pressure side. Wang and Guedes Soares [21] numerically investigated the water entry of a bow flare section with heel angle through the explicit finite element method. The secondary impact and air pocket phenomena were observed. The results showed the secondary impact happened at the leeward side of the body for all the cases and it became more apparent for a higher impact velocity. Krastev et al. [22] studied the asymmetrical water entry problems of the wedge by coupling a VOF algorithm and Laplacian mesh-motion solver. The gas-liquid two-phase flow was modeled through the VOF method and the free surface was tracked using CICSAM scheme. For the free surface evolution in numerical simulation, obvious flow separation and air cavity could be seen. Some similar researches can be found in Xu et al. [23], Sun and Faltinsen [24], Qin et al. [25],-Xie et al. [26], Russo et al. [27] and Hu et al. [28].

As for structural dynamic response due to time-dependent loads, the subject is more complex than static analysis where some additional issues are required to be considered such as characteristics of loads, structural inertia effect and dynamic constitutive equation of the material. In order to study the dynamic response mechanism subjected to slamming loads, some simple models like stiffened plates are usually used. Srivastava et al. [29] studied the dynamic response of a panel under asymmetrical sine loads through the finite element method. Paik and Shin [30] studied the dynamic response of stiffened plate in theory. The slamming loads were uniformly distributed on the plate whose sides are fixed. The analytic formula of deformation was obtained and the result agrees well with the experimental results. Ji and Wang [31] discussed the effects of load shape on the dynamic response finding that the results of simple semi-sine and triangular load shape were closed to the actual mechanical behavior. There are some other researches such as plates or stiffened plates under impact loads (Zhang et al. [32], Khedmati and Pedram [33] and Hassoon et al. [34]). Although these researches have improved the knowledge on the structural dynamic behavior under the slamming loads, they may be not fully reflect the dynamic characteristics of the actual ship bow according to the simplified stiffened plates. There are only fewer researchers focusing on the analysis of the actual bow structures. Yang et al. [35] analyzed the structural dynamic strength of the bow structure of a 1700 TEU container vessel subjected to slamming impact force through using finite element method (FEM). The formula of slamming load suggested by Lloyd's Register (LR) was used to assess the reliable value of impact force acting on the bow structure. Yang and Wang [36] discussed the dynamic behaviors of large containership's bow structures subjected to slamming pressure with different influence parameters based on 3D finite element method. Various influential parameters including the amplitude of slamming pressure, impact duration, rise time of slamming pressure, load attenuation coefficient, the position of maximum slamming pressure and traveling speed of the slamming pressure over the side shell of the bow flare were discussed.

Although analysis of ship strength subjected to slamming loads is greatly developed, our understanding on the dynamic characteristics largely relies on the symmetrical slamming cases. Therefore, the purpose of this paper is to provide a preliminary numerical investigation on the dynamic response of a truncated ship-hull structure under asymmetrical slamming based on the uncoupled CFD-FE method. An obvious difference comparing to the previous studies is that the determination of slamming loads includes the asymmetrical slamming effect. The analysis method is a combination of linear motion analysis, 2D-CFD analysis and linear FE stress analysis, all of which are uncoupled to save CPU time. Asymmetrical slamming loads were predicted through combining the seakeeping analysis and CFD method. In there, three kinds of motion (vertical, horizontal and roll motions) of 2D ship sections were obtained through the seakeeping analysis and then the slamming pressure was predicted through simulating the water entry with various motions based on CFD method. The dynamic response of truncated ship-hull structure is solved by the finite element method under asymmetrical slamming loads.

The rest of paper is organized as following. In Section 2, mathematical models and research objective are provided. In Section 3, the details of asymmetrical slamming loads prediction are presented. In Section 4, the basic dynamic results are presented, and the asymmetrical characteristics of deformation and stress are discussed. Section 5 draws some important conclusions and outlines further work.