impactofliquidsloshingonthebehaviourofvehiclescarryingliquidcargo-外文文献(编辑修改稿)

impactofliquidsloshingonthebehaviourofvehiclescarryingliquidcargo-外文文献(编辑修改稿)内容摘要：

The most popular are:C15 Combined Lagrangian Eulerian (ALE): In this formulation themesh partly moves and bees deformed because it followsthe material (Lagrangian formulation). At the same time thematerial can also cross the mesh (Eulerien formulation) (Geuzaine et al., 2020。 Van Der Vegt and Van Der Ven, 2020。 VanLoon et al., 2020).C15 Averypopularmethodforadvectinganinterfaceisthevolumeoffluid method (VOF) originally developed by Hirt and Nichols(1981). This method makes use of a fluid volume fraction aq,with values between zero and one, indicating the fraction offunction F is then advected according to the local flow velocity.Ineachcontrolvolume,thevolumefractionsofallphasessumtophases and represent volumeaveraged values, as long as thevolume fraction of each phase is known at each location.VOF is probably the most successful technique because of itssimplicity and its robustness. In this study we use the Fluent software v which uses this technique. The properties appearing inthe transport equations are determined by the presence of theponent phases in each control volume. There is a twophasesystem. The phases are represented by the subscripts 1 for the gasand 2 for the liquid. If the volume fraction of the liquid is beingtracked, the density in each cell is given by:0 20 40 60 80 100 120 140 160020406080100Y (m)X (m)Fig. 3. Step steer4. Liquid simulation parisonIn order to pare the numerical model to the analyticalmodel, we use the results obtained from the Fluent software interms of the instantaneous coordinates of the centre of the mass,pressure forces and inertia moments. These results are analyzed todetermine the dynamic liquid load shift. These results are calculated using the volume integral over the wetted area of the tankwall, such that:xi188。 Pliquidc188。 1xiVcVliquid。 Iii188。 Xliquidc188。 1C16x2j254。 x2kC17Vc。 Fpxi188。 Xliquidc188。 1PcAxi。 i。 j。 kh240。 1。 2。 3222。 240。 10222。 where xCand ycare the coordinates of the centroid of a cell ‘c’ thetank wall。 and Fpxiare the ponents of the forces acting on thecentroid of the face of cell ‘c’ as shown by Fig. 2.In this approach the transitory response of the nonlinear liquidsloshing is evaluated by the instantaneous displacement of themass centre coordinates, the inertia moments and the equivalentforce exerted by the liquid on the tank. These quantities arecalculated by using the numerical integration which covers theliquid domain. These results are pared with results fromthe analytical model calculated by analytical integration. Theparisons are evaluated for steady and transient manoeuvres,including step steer inputs and single lane change manoeuvres(Figs. 3 and 4) to study the steadystate and transient directionalperformance.In this study the elliptic tank model (a188。 m, b188。 1 m andL188。 m) is partially filled (50%) with domestic oil (r188。 966 kg/m3,n188。 kg/ms). The shift of the liquid load is evaluated accordingδ (deg)06100,00,51,01,52,0Time (s)24 8input.totheinstantaneousdisplacement mass centre coordinatesandtheequivalent force exerted by the liquid on the tank. These quantitiesare calculated by using the numerical integration which covers thefield of the liquid.For a steadystate turning as shown in Fig. 5, we obtain a goodcorrelation between the two models. In the early stages, there isa small difference due to free surface oscillation, which is neglectedin the analytic model. Once liquid oscillation starts, the value isstabilized and the mean value approaches the analytical model.The correlation is also good between the twomodels fora singlemanoeuvre illustrated by Fig. 6. However, the amplitude is largerfor the numerical model pared to the analytical model. A small5. Nonlinear vehicle modelSeveral methods can be exploited to develop a vehicle model,such as Virtual Work, Lagrange and Newton. Alternativeapproaches to dynamic vehicle models use simple models witha reasonable puting time. Our model is developed using theNewton method, based on the conservation of the linear andangular momentum of a solid body.The dynamic equations of motion are derived for a unit vehiclethat possesses both front and rear steering capabilities as well asadapted to simpler vehicles, such as vehicles with only front wheel0 20 40 60 80 100 120 140 160 180 200012345678910Y (m)X (m)0481021012δ (deg)Time (s)62Fig. 4. Single lane change manoeuvre.M. Toumi et al. / European Journal of Mechanics A/Solids 28 (2020) 1026–1034 1029delay was also noted in the response of the numerical modelpared to the analytical model. The small difference betweenthe two models is probably due to the assumption of linearity andthe iterative calculation of the free surface for the analytical modelpared to the numerical model.0,10,00,10,20,30,40,5NumericAnalyticYL (m)0100,2Time (s)10,010,511,011,512,012,5NumericAnalyticIxx (kg m2)103246801Time (s)2468Fig. 5. Response to constant radiussteering, by the assignment of a constant control input of zero tothe appropriate (unavailable) control effectors. The free bodydiagram (FBD) for the vehicle under consideration is shown inFig. 7. The body fixed reference frame is labelled on the FBD with itsorigin atthe vehicle’s centre of gravity. The z axis is pointing up, the0,540,570,600,630,660,69 NumericAnalyticZL (m)048100,51Time (s)01530456075NumericAnalyticLateral pressure force (KN)2604810Time (s)26cornering manoeuvre.0 100,40,30,20,10,00,10,20,30,40,5NumericAnalyticTime (s)YL (m)ZL (m)0,510,540,570,600,630,660,69 NumericAnalytic14Numeric1032 468 010Time (s)2468lan。