SIMULATION OF FLUID-SOLID INTERACTION ON WATER DITCHING OF AN AIRPLANE BY ALE METHOD

637Available online at www.sciencedirect.comScienceDirecttTTDtJoumal of HydrodynamicsEL SEVIER201 1 ,23(5):637-642www.sciencedirect.com/DOt: 10.1016/S1001-6058(10)60159-Xscienceljounal/10016058SIMULATION OF FLUID-SOLID INTERACTION ON WATER DITCHINGOF AN AIRPLANE BY ALE METHODHUA Cheng, FANG ChaoDepartment of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China,E-mai: huacheng@fudan.edu.cnCHENG JinSchool of Mathematical Sciences, Fudan University, Shanghai 200433, China(Received March 21, 2011, Revised May 8, 2011)Abstract: Ditching is considered as one of the important aspects of safety performances of airplanes. It is related primarily with thefluid-solid interaction, whose studies mainly depend on experiments at the present time. Numerical and analytical methods forfluid- solid interaction by using 3-D full scale airplane' s model will reduce the dependence on the expensive model tests. Numericalstudies can be used to estimate the safety of ditching and provide a reference for the crashworthiness design. This article proposes a3-D dynamical structural model aftere real shapnape 'in airplane and an Arbitrary Lagrange-Euler (ALE) fluid-field model, tosimulate the fluid-solid interactions caused by low speed ditching. The simulation is based on interaction computational methods,within LS-DYNA nonlinear finite-element code. The results of pressure distributions and accelerating time histories of the airplane'ssubfloor are discussed in the context of the safety of ditching, and the simulation results and the analytical methods are verified.Key words: dithing, fluid structure interaction, Arbitrary Lagrange Euler (ALE), finite element methodIntroductiontheretically, experimentally or numerically. VonDitching means that a plane has no altermativeKarman (1929) developed the first theory for this pro-but to land on water surface such as sea or lake, inblem. This pioneering work uses the concept of addedview of the safety of crews and passengers. There aremass for investigation of impact loads on a seaplanesome cases of successful ditching, also some cases ofduring ditching. The majority of the subsequent theo-crashes. Airline companies have strict rules for di-retical work in the early period was based on Vontching". According to structural dynamics, an air-Karman's concept. The experimental techriques rela-plane should be in very low speed when ditching, theted with the problem were mainly developed bdeformation of an airplane can be approximately con-NASA since the late 1950s. Boeing airplanes weresidered as elastic-plastic, and it is feasible to simulatetested and the operating specifications of ditchingan airplane's ditching by using numerical analysiswere developed at that time. Recently, the numericalmethods such as finite element analysis.analysis is widely used in this respect.Unlike a ground impact, a large area of the air-Seddon and Moatamedil2l reviewed the studies ofplane's outer skin contacts with water in ditching.water entry and impact between 1929 and 2003, and itThusthe fluid-solid interaction and someis pointed out that the numerical analysis should be .mechanical problems should be primarily addressed.considered as a main choice, and accurate numericalThe problem of water entry and impact can be studiedmodels of fluid-solid jinteraction may replace expen-sive and time-consuming full-scaled tests. Brooks andAnderson'B] first used the finite element software, LS-* Project supported by the Shanghai Key Basic ResearchDYNA, to investigate the water entrv of spacecraft.Program of China (Grant No. 07JC14001).The simulation中国煤化工comparisonBiography: HUA Cheng (1963-), Male, Pb. D, Associatewith the full-HC N M H Gsponse afterProfessor30 ms-40 ms isut vcty atisiavwiy uause the fieldof fluid was calculated as a kind of solids in this soft-638with the development of ArbitraryKaren and Yvonnel3] used this program to analyze theLagrange-Euler (ALE)41 finite element method, Tuttvertical drop of a fuselage section, and the simulationand Taylor59 used an updated software to simulate theresults were compared with experimental tests, with awater landing characteristics of space vehicles, wheregood agreement.the fluid-field was defined by ALE elements. A com-In this article, we use this ALE solver in LS-parison between test data and numerical analysisDYNA for the part of the fluid-field.shows the value of using the finite element methodsIn the ALE description, the material derivativefor simulating the water entry and impact. Further-can be described as'more, numerical analysis of water impact was used foroptimal designs. Li et al.!6l used a cylinder model andaf(X,1)_ af(x,1)af(x,t)a similar method, to simulate the shell structure dro-(1)0tpping into water, and a comparison between simula-tion and experiment was made. Based on a numericalwhere x is the ALE coordinate, X is the Lagra-model, they optimized the material and the structure toenhance the safety of the, structure and to save thengian coordinate, x is the Eulerian coordinate.experiment time. Sun et al!T used a V-shaped plate inThe relative velocity c; =u, -v is introducedthe experiment to simulate a 2-D elastic wedge, theto simplify the equation, where u; is the velocity ofresponse of the structures in the water entry processthe material and v; is the velocity of the referentialwas dynamically measured, and the influences ofsome parameters were analyzed. Gong et al.o studiedcoordinate. Thus when x=X; or x=x, the ALEthe water entry of a wedge by the SPH method, anddescription becomes the Lagrange description or thewith an improved non-reflection boundary treatment.Euler description.Wei et al.9I studied the high-speed water entry impactThe goveming equations are as follows:of an underwater vehicle by the ALE method using(I) The equation for conservation of massMSC Dytran software, where the underwater vehiclewas treated as a rigid body, and different impact con-ap(x,t)__o 24_. apditions were considered.(2)Ditching problems were not well studied byDtx，C1xusing the 3-D full-scaled numerical model up to now.However, it is important to study the airplane's crash-where ρ is the density of fluidworthiness by using actual and accurate models. In(2) The motion equation or the Navier-Stokesthis article, a 3-D numerical model with the shape of aequation in hydrodynamicsreal-scaled airplane is built. Simulations of the dit-ching under related conditions are conducted using thedu;(x,1)_ dσydu,finite element method, including the ALE and intera-(3)ctive computational approaches. The pressure appliedAtdxjdx;to the subfloor, and the acceleration of the passengercabin are obtained in the simulations. Based on thesewhere b; is the unit body force.results, the safety of the low speed ditching is dis-The stress tensor σ; in a Newtonian fluid iscussed, and the validity of this model and the methodsare also verified.related with velocities asJu;、du;1. Computation schemeσgy=-p8q +μ\xx(4)1.1 ALE formulationThe ALE description allows an arbitrary move-ment of the reference domain, as compared with thewhere μ is the coefficient of kinematic viscosity,material description or the spatial description. Thep is the pressure.large deformation can thus easily described, togetherThe equations are to be solved with the followingwith the moving boundary of fluidlo. So ALE des-boundary conditions:cription is widely used for fluid-solid interaction pro-blems. Hughes et al. developed the ALE descri-ption for the finite element method, and later, Souli et0yn=0 on r(5a)al10,12] added an ALE solver for the finite element中国煤化工software, LS-DYNA, with smoothing algorithms andu=u' on.MYHCNMHG(5b)advection processes. They also presented some nume-rical examples to show that the program worked well.639where n; is the outward unit normal vector on theStarttraction free boundary厂, and u? is the velocity onthe constrained boundary F2Generate mesb, setup initial conditionsThe ALE equations are implemented by two pha-ses, using the alternative approach:nitial time step(1) First is a Lagrangian phase, in which themesh moves with the material, to calculate the velo-Trace coupled interface,apply penalty force,city changes due to the intermnal and external forces.setup boundaryThe equilibrium equation isFluid par2u1_ dσyLagrange phase ofALE |+ pb(6)Lagrange solution2t dx;Advection phase(2) Second, the advection phase, to transport the[ Reconstructive the interface of fluia Trace interfacemass and the momentum:(a) to decide which nodes to move,les(b) to move the boundary nodes,Penetration is detected?(C) to move the interior nodes,No|(d) to calculate the transport of the element-cen-Next time steptered variables,(e) to calculate the momentum transport and up-