Numerical Simulation of the Water Entry of a Structure in Free Fall Motion

J. Marine Sci. Appl. (2014) 13: 173-177DOI: 10.007511804-014-1242-1Numerical Simulation of the Water Entry of aStructure in Free Fall MotionQingtong Chen'，Baoyu Ni*", Shuping Chen' and Jiangguang Tang'1. China Helicopter Research and Development Isiue, Jingdezhen 33001, China2. Cllege of Sipbulding Engieering, Harbin Enineerng Universin: Harbin 1000 ChinaAbstract: To solve the problems concerning water entry of aof a two-dimensional (2D) elastic wedge. Based on thestructure, the RANS equations and volume of fluid (VOF) methodhydroelasticity theory, Chen et al. (2012) used a numericalnericalare used. Combining the user-defined function (UDF) proceduresimulation and model test to investigate the water impact on a .with dynamie grids, the water impact on a structure in free fall issimulated, and the velocity, displacement and the pressureship's cabin in waves. With the aspect of theoreticaldistribution on the structure are investigated. The results of thecalculation, the water entry problem of the 2D cross planesnumerical simulation were compared with the experimental data,was solved by using a boundary element method developedand solidly consistent results have been achieved, which validatesby Sun (2010).Zhang et al. (2010) utilized the softwarethe numeical model. Teefore, this mehod ecan be use wo stuesthe wtrimpactproblensofastucturemethod can be used to study FLUENT to simulate numerically the water entry of theKeywords: structure; free fall motion; water impact; RANSwedge-shaped sections with dfferent deadrise angles at aequations; VOF; water entryconstant velocity. Zhang (2003) calculated and analyzed theinitial flow of the wedge entering into water using the VOFArticle ID: 1671-9433(2014)02-0173-05methodnumerically,d thenumerical simulation wacompared with the PIV experiments and high-speedphotographic visualization. Based on the potential flow theory,Ni (2012) researched the additive mass variation of a misile1 Introductionduring its entry into water by using the semi-analytic andThe phenomenon of water entry of a wedge in free fllingsemi-numerical methods. Duan and Wu (2011, 2012) have .widely exists in acrospace, underwater weapons, the shippingalso done some theoretical research on the water entry of thefield, etc. Well known examples include the landing on waterstructures in recent years.with air planes, helicopters, spaceships in the aerospace field,In this paper, the water entry of helicopters is taken as thevater entry of arial torpedos in the weapons field, the research background and fundamental prediction method forsailing of planing boats at high speeds in the shipping field,water impact of a simple structure entering into water. For theetc. In the process of a structure entering into water, the waterproblem of water entry of a structure, a large number ofslams the structure. Not only does the fluid have a greatdomestic researches regards flling velocity as constant,slamming force on the structure, but it also significantlywhich does not reflect truly the water entry state of a structure.impacts the flow field. The water surface produces seriousSo, to simulate the true state of a structure enering into water,fluid splashing, which is prone to damage the structures.the water entry)f a 2D wedge in freefall motion is simulatedTo attempt to solve the problems of a structure entering intonumerically based on the software FLUENT with UDF bywater, scholars have done extensive research, both withusing VOF to capture the free water surface. The calculationexperimental studies and theoretical calculations. With theresults are consistent with the experimental results withexperimental aspect, El-Mahdi et al. (2006) had anEl-Mahdi et al. (2006), which validates this numericalexperimental study done on the water impact on;procedure presented. The motion state and surface pressuresymmetrical wedge. Sun et al. (2003) had experimentaldistribution of the wedge are obtained.research done on the fluid-structure interaction in water entry2 Numerical calculation methodReceived date: 2013-09-14.Accepted date: 2013- 10-23.2.1 Governing equationof China (11302056)， China Postdotorl Science FoundationBasic governing equations inelude continuity, momentum(2013M540272)，Heilongjiang Postdoctoral Fund (LBH-Z13051)。 theconservation (Nav中国煤化工:onservationFundamental Research Funds for the Central Universities (HEUCF140116)equations. Energyand Rescarch Fund of State Key Laboratory of Ocean Engineering, Shanghaiconversion of ene:fYHCNMHGd because. uations are*Corresponding author Email: nibaoyu@hrbeu.cdu.cnexpressed as follows (2004):◎Harbin Enincering University and Springer- Verlag Bertin Heidelberg 2014Continuity equation:17Chen Qingtong, et al. Numerical Simulation of the Water Entry of a Structure in Free Fall Motionaρ、0(pu) 8(pv). 8(pw)(1)B=-v5)Constant viscous Navier-Stokes equations:The mass of a body is always a constant, so dm isexpressed as follows:dm= d(pV)= Vdp+ pdV =06)|0tCxdyowhere ρ can be calculated by combining Eqs. (5) and (6).1 Cp .. (o2u Bu, B2u2x22y2+P=1-dP/B7). t+“ax+vov+"2=where B is the bulk modulus, V is volume, P is pressure, ρ(2)is the changed density of the liquid, and Po is the initialJρ8y°2xt0yzdensity.2.4 The numerical simulation process|aDx 0The real-time motion state1 cp+u(numerically with UDF. Motion in y direction is justρaz(ax2° ay2 0z2considered. The forces and moments of the wedge at thiswhere u, v, w are the components of the fluid veocity in the moment can be obtained by solving the RANSE equation,x，y, z directions respectively; fx, fj， f: are the unitand the forces and moments are then put into thcomponents of the volume force in the x, y, z directionsix-degrees- of- freedom equation of motion. By solving theespectively; p is the fluid pressure force;p is the fluid accelerations of the motion, velocities and displacementsdensity; u is the fluid motion viscosity.(translations and rotations) are obtained by integrating intime. The new position of the wedge is updated and the fluid2.2 VoF methodflow is computed again for the new position. By iteratingIn computational fluid dynamics, the volume of the fluid this procedure over the time, the wedge trajectory ismethod is a numerical technique used for tracking andobtained. The flow chart is shown in Fig.1.locating the free surface (or fluid-fluid interface). Themethod is based on the idea ofso-called fractionStartfunction F. It is defined as the integral of the fluid'scharacteristic function in the control volume (namely thevolume of a computational grid cell). Basically, when theInitialization-planingcell is empty (there is no traced fluid inside), the value of Fwedge position etc.is zero; if the cell is full, then F = 1. And if the interphasalinterface cuts the cell, then 0