SIMULATION OF DYNAMIC BEHAVIOR OF HOVERCRAFT HULL STRUCTURAL SUBJECTED TO UNDERWATER EXPLOSION SHOCKWAVE mô PHỎNG TÍNH TOÁN THUỘC TÍNH ĐỘNG lực học của mô HÌNH tàu đệm KHÍ dưới tác ĐỘNG SÓNG sốc gây RA bởi vụ nổ dưới nước

SIMULATION OF DYNAMIC BEHAVIOR OF HOVERCRAFT HULL STRUCTURAL SUBJECTED TO UNDERWATER EXPLOSION SHOCKWAVE MÔ PH ỎNG TÍNH TOÁN THUỘC TÍNH ĐỘNG LỰC HỌC CỦA MÔ HÌNH TÀU ĐỆM KHÍ DƯỚI TÁC ĐỘ

SIMULATION OF DYNAMIC BEHAVIOR OF HOVERCRAFT HULL STRUCTURAL SUBJECTED TO UNDERWATER EXPLOSION

SHOCKWAVE

MÔ PH ỎNG TÍNH TOÁN THUỘC TÍNH ĐỘNG LỰC HỌC CỦA MÔ HÌNH TÀU ĐỆM KHÍ DƯỚI TÁC ĐỘNG SÓNG SỐC GÂY RA BỞI VỤ NỔ DƯỚI NƯỚC

Nguyen Ngoc Kien1a, Hai-Anh Nguyen2b

1Hanoi University of Science and Technology, Hanoi, Vietnam

2National Chiao Tung University, Hsinchu, Taiwan

a kien.nguyenngoc@hust.edu.vn; b haianh.me04g@nctu.edu.tw

ABSTRACT

A hovercraft, also known as an air-cushion vehicle or ACV, is a craft capable of traveling overland, water, mud or ice and other surfaces Hovercraft must be designed to survive in the extreme loading conditions, such as an underwater explosion (UNDEX) However, for the previous study, the UNDEX response was primarily studied focus on ships, submarines and the other submerged structures For this reason, this study selected a finite element model based Zubr-class like LCAC (Air-cushioned landing craft) subjected to UNDEX, dynamic responses of structure analysis were conducted This study develops a procedure which links together the finite element method (FEM) and Acoustic-Structure Coupling (ASC) method to simulate an UNDEX by using ABAQUS software and investigated the survival capability of a damaged craft The explosive charge of TNT (9 kg) were located 10 m on the normal line passing through the center of hovercraft model The characteristic of body structure and skirt response of the hovercraft model are discussed The numerical results show that the structure of hovercraft sustains severe local response especially is the main deck and skirt The analytical results offer a valuable reference to the research of underwater explosion

Keywords: Underwater Explosion, Hovercraft, Modeling and Simulation, Shockwave

TÓM T ẮT

Tàu đệm khí được biết đến như một phương tiện di chuyển nhờ lớp đệm không khí (air-cushion vehicle - ACV) Nó có khả năng di chuyển trên bộ, mặt nước, đầm lầy, băng đá và

một số bề mặt phức tạp khác mà tàu thường khó có thể di chuyển được Nhìn chung, tàu đệm khí phải được thiết kế để tồn tại được trước những tác động nguy hiểm bên ngoài, như các tác động gây ra bởi một vụ nổ dưới nước Trong những nghiên cứu trước, nghiên cứu về nổ dưới nước chủ yếu tập trung cho tàu thuyền, tàu ngầm và các cấu trúc ngập nước khác Vì vậy trong nghiên cứu này, một mô hình phần tử hữu hạn dựa trên nguyên mẫu tàu đệm khí Zubr dưới tác động của vụ nổ dưới nước, các phản ứng động lực học về cấu trúc của tàu được phân tích Nghiên cứu này được phát triển từ phương pháp phần tử hữu hạn (FEM) và phương pháp Acoustic-Structure Coupling (ASC) nhằm mô phỏng một vụ nổ dưới nước bằng phần mềm ABAQUS nhằm đánh giá khả năng hư hại của thân tàu Với 9 kg chất nổ TNT được đặt ở dưới nước cách đáy tàu 10 m và thuộc đường thẳng đứng đi qua điểm chính giữa của tàu Tác động gây ra bởi sóng sốc lên phần thân tàu và phần váy của tàu được trình bày và đánh giá

Kết quả mô phỏng cho thấy cấu trúc của tàu trải qua các tác động hư hại mang tính cục bộ, đặc biệt là tại vị trí sàn tàu và phần váy đệm khí Các kết quả của phân tích này cung cấp một tài liệu tham khảo hữu ích cho nghiên cứu về nổ dưới nước

Từ khóa: nổ dưới nước, tàu đệm khí, mô hình hóa và mô phỏng, tải trọng sốc

1 INTRODUCTION

In this research, a full-scale hovercraft subjected to underwater explosion simulation is presented Shock analyzes were conducted using a finite element based coupled Zubr-class like LCAC with a fluid model and an underwater explosion simulation that detonates 9 kg of TNT Zubr-class hovercraft shock modeling and simulation has been performed The investigation is accomplished via the validation of the Acoustic-Structure Coupling (ASC) method in an underwater explosion During underwater explosion (UNDEX), the sudden release of energy from a conventional high-explosive or nuclear weapon generates a shockwave and forms a superheated, highly compressed gas bubble in the surrounding water For example, approximately 53% of the total energy released from a 1500 lb (680.39 kg) Trinitrotoluene (TNT) UNDEX is applied to the shockwave and 47% is applied to bubble pulsation [1] The primary concern in naval engineering and offshore structure research is predicting how submerged structures are damaged by UNDEX Numerical methods for analyzing submerged structures exposed to UNDEX shock loadings have been successfully implemented For example, Shin [2] presented ship shock modeling and simulation for far-field underwater explosion by applying the LS-DYNA code coupled with USA code (2004) Liang and Tai [3] presented a preliminary study of the transient responses of a 2000-ton patrol boat with shock loading using the finite element method (FEM) coupled with the second Doubly Asymptotic Approximation (DAA2) (2006) Jin and Ding [4] presented numerical simulations of a ship section dynamically responding to a non-contact UNDEX by using ABAQUS (2011) Zong, Zhao and Li [5] conducted a numerical study of whole ship structural damage caused by close-in UNDEX shock (2013) Wang, Zhu, Cheng and Lin [6] examined the dynamic response of ship structures with the combined effect of shock wave load and bubble pulsation subjected to close-in non-contact UNDEX (2014) Gong and Khoo [7] presented a stiffened composite submersible hull subjected to underwater explosion bubble, the coupled BEM-FEM is used to handle the interaction of the composite structures and the underwater explosion bubble, mutual effects of relative location between the bubble and the composite submersible hull are investigated However, all of the aforementioned literature the UNDEX response was primarily studied for ships and submerged structures; no studies exist on dynamic responses of an air cushion vehicle (ACV) For that reason, applying

an UNDEX situation to ACV is the main issue of this research The response of a hovercraft Russian Zubr-Class model 1232-2 (Fig.1) is the main concern within, including such aspects

as dynamic behavior and structure response This study developed procedures to study investigated the dynamic response of 3D hovercraft model exposed to UNDEX, including shock wave damage as applied Acoustic-Structure Coupling (ASC) method by using ABAQUS software version 6.11-1

Figure 1 The Russian Zubr-Class amphibious hovercraft

2 THE SPECIAL FEATURE OF ZUBR-CLASS

The Zubr-class (Project 1232.2 class, NATO reporting name Pomornik [8]) is class of

air-cushioned landing craft of Soviet design This class is the world’s largest hovercraft and built by Almaz Shipbuilding in St Petersburg High strength and buoyancy of the craft are provided by a rectangular pontoon, the main load-carrying part of the ship's hull The superstructure built on the pontoon is divided into 3 compartments with two longitudinal bulkheads: combat material compartment in the midsection fitted with tank ramps, and outboard sections housing main and auxiliary propulsion units, troop compartments, living quarters, and protection systems The Zubr hovercraft has a range of 480 kilometers at 100km/h and is capable of carrying 136 tons, including up to three medium tanks or 500 marines Its top speed is more than 60 knots (110 km/h) on land, water and ice, and it is capable of clearing obstacles 1.5 meters high [9] The general characteristics of Zubr-class LCAC are list in Table 1

Table 1 General characteristics of Zubr class LCAC [8]

General characteristics

3 NUMERICAL METHOD

3.1 Empirical Formulation for Shockwave

An explosion is a chemical reaction that converts the initial material into a gas at an extremely high temperature and pressure; the process occurs with extreme rapidity and emits

a substantial amount of heat The temperature in the product gases is approximately 3000oC and the pressure is 50,000 atm Empirical equations were determined to define the profile of the shock wave and can be expressed as follows [1]:

1

1 3

max 1

R

2

1 3

1 3 2

W W

A

K

R

t max

P t =P e− λ (3) K1, A1, K2 and A2 are constants depending on various explosive charge types (Table 2) Other variables in the equations are:

W: the weight of the explosive charge (Kg)

R: the distance between explosive charge and target (m)

P(t): the pressure profile of the shock wave (MPa)

Pmax: the peak of the pressure of the wave (MPa)

λ:the shock wave decay constant (millisecond, ms)

Table 2 Shock wave constants [3]

HBX-1 TNT PETN Nuclear

K1 53.44 52.2 53.59 1.07×104

A1 1.144 1.18 1.194 1.13

K2 0.092 0.0894 0.086 3.627

A2 -0.247 -0.185 -0.257 -0.22

3.2 Acoustic-Structure Coupling Method

In the numerical simulation of interaction between shock wave and structure, the acoustic structural coupling method used in ABAQUS software is applied [10] Acoustic element is introduced into the flow field, and its size is selected according to literature [10], as the model shown in Fig.2 The main principle and theoretical formula of acoustic-structural coupling method can refer to the theory of ABAQUS software manual [10] Acoustic fields are strongly dependent on the conditions at the boundary of the acoustic medium The boundary of a region

of acoustic medium can be divided into sub regions S Consider a surface cylinder floating on the free surface, as shown in Fig.2 The boundaries of this model are: Sfp where the value of the acoustic pressure p is prescribed; Sft where we prescribe the normal derivative of the acoustic medium; Sfr the “reactive” acoustic boundary, where there is a prescribed linear relationship between the fluid acoustic pressure and its normal derivative; Sfi the “radiating” acoustic boundary; Sfs,where the motion of an acoustic medium is directly coupled to the motion of a solid; Sfrs,an acoustic-structural boundary, where the displacements are linearly coupled but not necessarily identically equal due to the presence of a compliant or reactive intervening layer; Sft,

a boundary between acoustic fluids of possibly differing material properties [10]

Sfr

Sfi

Sfs

Sfp

Figure 2 Fluid domain and boundaries

4 MODELING AND SIMULATION

The overall length of the hovercraft is 57 m The beam of the hovercraft are 25.6m The whole finite element model is shown in Fig.3 The numerical model includes 10 stiffeners (springs) and a keel arranging as illustrated in Fig.4 The stiffener, the keel are all box steel with the cross section and the specifications are lists in Table 3 The body structure was constructed by aluminum (7075 Alloy), modeled using the average thickness technique of the hovercraft was 20 mm, meanwhile the thickness of skirt part is 2.5mm and made by coated fabric [11] The mechanical properties of the hovercraft material are shown in Table 4 There are 30,393 elements in this model, including 28,884 linear quadrilateral elements of type S4R shell elements, 688 B31 linear beam line elements and 821 linear triangular of type S3 elements with the element size is 0.5 m For simplicity, the light footprint pressure 3,000 Pa is adopted to describe the cushion pressure when the fan speed is increasing further (Fig.5), pressure remains almost constant [11]

Shell element model Side view Front view Top view

Figure 3 FE model of Zubr-class like LCAC

Figure 4 Beam locations and beam cross section

Figure 5 Footprint pressure for ACV [11] Figure 6 Incident pressure wave transient

(shock pulse) Table 3 Beam dimensions (a,b,t reference in Fig.4)

Width Height Thickness

Stiffener beam 0.15m 0.1m 0.014m Keel beam 0.2m 0.12m 0.02m This study adopts the Keel Shock Factor (KSF) to describe the shock severity The work assumes the KSF value is 0.3, and the charge is positioned directly underneath the bottom of hovercraft A spherical charge of 9kg TNT was centered at the bottom of the cylinder and located 10m from the hovercraft surface Fig.6 shows a time history curve of the incident pressure wave calculated by Eq.(1), (2) and (3) As shown in the graphs, from 0 s to 0.006 s, the pressure according to Cole’s formula was generated by a charge of 7.8 MPa This simulation is made by ABAQUS version 6.11-1 using ASC method Fig.7 depicts the external fluid (for shockwave numerical) was meshed with linear tetrahedral elements of type AC3D4 that consisted of 1,552,759 elements The outer boundary of the external fluid was represented by a cylindrical surface with spherical ends The characteristic radius of the outer boundary was 78.3m The mechanical properties of body structure, skirt and beam are shown

in Table 4 The zero-pressure boundary condition is applied on the free surface of the flow field, and non-reflecting boundary condition is set on the other surfaces of the fluid model Table 5 shown properties of the fluid (water and air domain)

Y

EXPLOSION CHARGE

AIR DOMAIN

WATER DOMAIN

10 m

Table 4 Material properties Parameters Body

structure

Skirt Beam

Density (kg/m3)

2780 2700 7800

Young’s modulus (GPa)

75.6 70 213 Poisson’s ratio 0.33 0.3 0.3 Yielding stress

(MPa)

Figure 7 Profile of external fluid models

Table 5 Properties of fluid

Water Air

Density (kg/m3) 1000 1 Bulk modulus (Mpa) 2140.4 0.101 Fig.8 show a sequence of the response of a hovercraft subjected to an underwater explosion shock wave at typical times The filled contours figures illustrate the von Mises stress

of the whole hovercraft model It can be clearly observed that the yielding of materials under shock loading condition of the hovercraft model is mainly the local response The shock load is transmitted through the fluid and reaches the skirt and main deck of hovercraft At the time t=0

ms, the shock loading with high pressure and has no influence on the hovercraft, so there is no response From t=0.1ms to 1.8ms, an obvious impact of shock wave onto the whole surface of the skirt; at t= 2.4ms, damaged location is visible at the front of the skirt At t=4.8ms, the main deck begins deformed under the influence of the load (pressure) and the middle part of the skirt that is located closest to the explosion being affected by explosions At t= 6.0ms, the vertical displacement of the whole structure reaches the maximum value, the main deck moves upwards with the underwater explosion loads Fig.8 show that some locations of the underside of the skirt and the middle of the main deck also exhibit local response

Time Whole ACV View Cut (A-A) Time Whole ACV View Cut (A-A)

1.8ms

6.0ms

Figure 8 The dynamic response of hovercraft model

Fig.9 has shown that obvious local von Mises stress occur at the middle of skirt part and mid of main deck near close to the location of explosive charge Fig.10 indicates two types of value for von-Mises stress of hovercraft model at different locations from 0 to 0.006 second Choose test points A1 (at the skirt) and A2 (at the main deck) have a significant local response of the peak von Mises stress (Fig.9) In general, most von Mises stress showed an increase with the locations in the underside of the skirt (A1) adjacent to the water sustain the biggest von Mises stress 4.3×108 Pa, nearly 4.21 times of the von-Mises of A2 is 1.02×108 Pa For example, after a rise slowly from 0s to 0.004s, the von Mises stress at A1 reached a peak

in 0.006 seconds of 4.34.3×108 Pa Similarly, von Mises stress at A2 experienced the same trend from the lowest point to a peak of nearly 1.02×108 Pa That is because the skirt was damaged are more significantly compared with the main hull of the hovercraft

Figure 9 Von Mises stress of hovercraft

model

Figure 10 Time histories of von-Mises

stress of A1,A2 CONCLUSION

The purpose of this study is to investigate a procedure to analyze the dynamic structural response of a hovercraft This is the first time to simulate the dynamic response of the structure of air cushion vehicle with the underwater explosion (UNDEX) It shows the possibility of using Acoustic-Structure Coupling (ASC) method in ABAQUS Through case studies, it is found that the high precision of the evaluation method As a result, it can be applied to checking hovercraft’s overall capacity against underwater explosion ultimate damage The analytical results were offering a reference for evaluating the damage of hovercraft structure under the underwater explosion

ACKNOWLEDGEMENT

The authors would like to acknowledge the Ministry of Science and Technology of R.O.C for financially supporting this work under contract MOST 103-2221-E-212-018-MY3

REFERENCES

[1] Cole,R.H., Underwater Explosion Princeton University Press, New York, 1948

[2] Shin YS Ship shock modeling and simulation for far-field underwater explosion Computers & Structures, 2004, Vol 82, p.2211-2219

[3] Liang CC, Tai YS Shock response of a surface ship subjected to noncontact underwater explosions Ocean Engineering, 2006, Vol 33, p.748-772

[4] Jin Q, Ding G A finite element analysis of ship sections subjected to underwater explosion Impact Engineering, 2011, Vol 38, p.558-566

[5] Zong Z, Zhao Y, Li H A numerical study of whole ship structural damage resulting from close-in underwater explosion shock Marine Structures, 2013, Vol 31, p.24-43

[6] Wang H, Zhu X, Cheng YS, Lin J Experimental and numerical investigation of ship structure subjected to close-in underwater shock wave and following gas bubble pulse Marine Structures, 2014, Vol 39, p.90–117

[7] Gong SW, Khoo BC Transient response of stiffened composite submersible hull to underwater explosion bubble Composite Structures, 2015, Vol 122, p.229-238

[8] Zubr Class (Pomornik), Russia http://www.naval-technology.com/projects/zubr/

[9] Zubr LCAC, http://www.globalsecurity.org/military/world/china/zubr.htm

[10] ABAQUS user's and theory manuals, version 6.11.1 Dassault Systèmes, RI, USA, 2011 [11] Liang Yun., A.Bliault Theory and Design of Air Cushion Craft First published in Great Britain in 2000

AUTHOR’S INFORMATION

1 Nguyen Ngoc Kien Department of Mechanical Engineering - Hanoi University of Science

and Technology Email: kien.nguyenngoc@hust.edu.vn Phone: +84-966-992-255

2 Nguyen Hai Anh Department of Mechanical Engineering - National Chiao Tung

University Email: haianh.me04g@nctu.edu.tw Phone: +886-978-921-842