Factors Affecting the Slamming Pressure Peak Value of Trimaran Cross Structure

CAO Zheng-lin,WU Wei-guo

(1 School of Transportation,Wuhan University of Technology,Wuhan 430063,China;2 Key Laboratory of High-speed Ship,Ministry of Education,Wuhan 430063,China)

1 Introduction

When trimaran sails in rough sea,the slamming of bottom and cross structure caused by wave occurs.And the serious wave slamming can lead to damage of hull structure.Calculating the value of slamming pressure has been concerned.

The trimaran slamming is the nonlinear issue that includes structure-air-water coupling.The early research of water entry analyzed and calculated the velocity potential of fluid field,then,the slamming pressure acting on the object was obtained.In the deduction,some hypothesizes on fluid field and ignoring the air effect led to great error.Because of the complexity,many scientists studied the slamming problem with the help of experiments and improved the theories.The tests(Chuang,1966[1])indicated that the slamming pressure of flat-bottom structure was far less than theoretical value.The main reason was too many simplifications and ignoring of comparatively important factors in theoretical analysis.

The trimaran is composed of a main hull and two side hulls,and the structure character makes its slamming problem complicated(Fig.1).Because the slamming of main hull is affected by side hull and cross structure,it can not be treated like slamming of the wedge structure；Because the slamming of cross structure is affected by deadrise degree of main hull,width of cross structure of trimaran,structure mass and air cushion between the main hull and the side hull,it can not be treated like slamming of the plate.

By using simulation software LSDYNA,a 2-D finite element model was built up and the slamming of trimaran cross structure was studied.In the study manyfactorsaffectingtheslamming pressure peak value of trimaran cross structure were considered.These factors are air cushion,structure mass,width of cross structure and degree of main hull deadrise.From analyses,the rules that these factors affect slamming pressure peak value are established.

2 Simulation model

The slamming of trimaran is a typical fluid-structure coupling problem.In the analysis,the flat-bottom structure is simulated by Lagrange element,the water and air are simulated by Euler element,and the interface between is defined as the fluid-structure coupling surface.In the process,the pressure caused by Euler material flowing automatically acts on the structure’s finite element mesh by coupling.Because of the pressure,the structure’s finite element mesh will have some deformation,the deformation has effect on the Euler material flowing and the pressure in reverse.With the interaction between the deformation and the pressure,the fluid-structure response of fully coupling can be obtained(Chen zheng,2006[2]).

The simulation model of trimaran is shown in Fig.2,in this paper,the trimaran impacts on the surface of water at the velocity V.Owing to the symmetry of structure,the calculation only uses half of the model,and constraint is put on the symmetrical face.Taking the 2-D characteristics into consideration,the model in the normal direction only uses unit length and 2-D fluid boundary condition is put on the model,in this way,not only the rationality of model is guaranteed but the task of calculation can be reduced greatly.

In Fig.2,the below part is water medium that is not viscous and compressible linear fluid.The pressure inside the water fluid field can be expressed by polynomial state equation(Bereznitski,2001[3];Li,2002[4]):

where p is pressure;μ=ρw/ρ0-1,ρwis the density of water,ρ0is referenced density,e is per mass internal energy.If the state equation only uses linear item,the state equation can be:

where a1is volume elastic modulus,a1=2.25GPa.

The above part is air medium that is compressible ideal air.The pressure inside the water fluid field can be expressed by Gamma state equation:

where γ=1.401 is specific heat of air;ρais density of air;eais air internal energy.Under the standard atmospheric pressure 101.3kPa and normal temperature,ρa=1.2kg/m3,ea=211.041J/g.

The material of the trimaran structure is steel whose elastic modulus and Poisson’s ratios are 206GPa and 0.3 respectively.

The exterior surface of the trimaran structure is defined as fluid-solid coupling surface.The Lagrange and Euler coupling arithmetic are adopted,and the nods of meshes of Lagrange and Euler coupling arithmetic must coincide with each other in the interface.When the Lagrange element deforms,the coupling surface will slide,then the Euler meshes will slide,too.In the course of calculation,the coupling surface is regarded as fluid boundary of Euler material,meanwhile the pressure on the fluid boundary caused by Euler material makes the Lagrange element of the model under the fluid loads.

Because of the symmetry of model,the Euler elements on both sides of the normal direction and at the symmetric face adopt rigid wall boundary condition,while the upside of air element adopts free boundary condition.

3 Effect of various factors on slamming peak value of cross structure of trimaran

When the object enters the water,its velocity decreases because of slamming,and the decrease degree is relative to its mass.The velocity decrease has a great effect on the slamming pressure peak value,so the mass must be considered when the slamming pressure is studied.However,because of the great mass of trimaran,the slamming pressure persists for very little time(usually less than 0.01 second),which makes little contribution to changing the velocity.Therefore,the water entry of trimaran can be regarded as constant velocity.

3.1 Effect of air cushion

The simulation indicates that the air cushion still exist between the hulls and the water surface even when the slamming pressure peak value occurs.And this phenomenon was also shot by high-frequency underwater camera in Chuang’s test(Fig.3)(Chuang,1966).The air cushion acts as a buffer cushion between the structure and the water surface and reduces the slamming pressure greatly,so it must be considered.It’s the air cushion that makes it difficult to build up a full mathematical model including structure,air and fluid.At present,the recursive formula on the basis of tests is employed to calculate the slamming pressure.

In the paper,the model is simulated slamming at the velocity of 5m/s to 50m/s.The results of included air cushion are shown in Tab.1

The water surface change is shown in Fig.4 when trimaran slams at the velocity of 5m/s.

Fig.5 shows the pressure peak values(the air cushion included and excluded),from which it can be seen that the former is less than the later at every velocity.So the air cushion plays the role of lessening pressure peak value in the slamming.

Fig.6 shows the difference in percentum between two conditions,from which it can be seen that the more slaming velocity,the less difference in percentum.So the effect of air cushion on the pressure peak value decreases with the slamming velocity increasing.

Tab.1 The water-entry velocity and the slamming pressure peak value

3.2 Effect of structure mass

The structure mass has remarkable effect on pressure peak value in the slamming.

In this paper,the initial mass of model is assumed as m.In the condition of keeping other parameters constant,the mass is assumed as 2m,3m and 4m,and the simulation has been done.The result is shown in Fig.7.In Fig.7 it can be seen that the pressure peak value increases with the structure mass increasing;and it keeps constant when the mass reaches to some critical value.The phenomenon can be explained as follows:the trimaran decelerates as a result of the slamming pressure while it slams;the deceleration effect becomes more obvious with the less structure mass.

3.3 Effect of width of cross structure

The width b of cross structure also has remarkable effect on pressure peak value in the slamming.In this paper the width of main hull is assumed as B.In the condition of keeping other parameters constant,the width of cross structure is assumed as 1/3B,2/3B,3/3B and 4/3B,and the simulation has been done.The result is shown in Fig.8.In Fig.8 it can be seen that the pressure peak value increases linearly with the width of cross structure increasing.

3.4 Effect of deadrise degree of main hull

Although the cross structure is similar to a plate,it can not be treated like slamming of the plate.This can be explained as follows:when the trimaran slams,the main hull slams firstly,then the cross structure slams by the wave resulting from the main hull slamming(This can be seen in Fig.4).So the deadrise degree β of main hull greatly affects the pressure peak value of cross structure.In the condition of keeping other parameters constant,the deadrise degree β of main hull is assumed as 15°,25°,35°,45°and 55°,and the simulation has been done.The result is shown in Fig.9.When the β is lesser,the wave resulting from the main hull slamming can not directly reach the cross structure,so β weakly affects the slamming pressure peak value;when the β exceeds some critical value,the wave can directly reach the cross structure,so β obviously affects the slamming pressure peak value.

4 Conclusions

In this paper by using simulation software LS-DYNA,the slamming of trimaran cross structure was studied,and some conclusions were obtained:

(1)The air cushion plays the role of lessening pressure peak value in the slamming,and its effect decreases with the slamming velocity increasing.

(2)The pressure peak value increases with the structure mass increasing;and it keeps constant when the mass reaches to some critical value.

(3)The pressure peak value increases linearly with the width of cross structure increasing;

(4)When the deadrise angle β is lesser,it weakly affects the slamming pressure peak value;when the β exceeds some critical value,it obviously affects the slamming pressure peak value.

[1]Chuang S L.Experiments on flat-bottom slamming[J].Journal of Ship Research,1966,10(1):10-27.

[2]Chen Zhen,Xiao Xi.Analysis about slamming pressure peak value on a flat-bottom structure[J].Journal of Shanghai Jiaotong University,2006,40(5):983-987.

[3]Bereznitski A.Slamming:The role of hydroelasticity[J].Int.Ship build Progr,2001,48(4):333-351.

[4]Li W P,Liu G R,Chan E S.Elasticity effects on the water impact of an elastic flat-bottom box[J].Journal of Hydrodynamics,Ser.B,2002(2):64-70.