【正文】 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。VV!TC17i254。rV!V!222。 1.A single momentum equation is solved throughout the domain,and the resulting velocity field is shared among the phases. Themomentum equation, shown below, is dependent on the volumefractions of all phases through the properties r and m.vvt240。240。1C0a2222。 3222。 j。 Iii188。z0(6)where the angle s 188。0)andweobtaintheequationthatrepresentstheformM. Toumi et al. / European Journal ofof the free surface:mass centrecoordinatesforthe tank withcircularorellipticsectioninthelateral(oyz)turningmanoeuvresimposesequalandoppositeaccelerationontheliquid load, resulting in motion of the liquid in the lateral plane.Assuming negligible longitudinal acceleration and negligiblecontribution due to slosh frequency and knowing that the totalderivative of the pressure is null on the free surface, the gradient ofthe fluid bulk subject to a deceleration can be calculated from Eq.(5) by integration as:z 188。V$V222。0), therefore the Navier–Stokes equations will bee the Euler equations.V$V 188。 P is thepressure。254。l254。V$V222。rV222。C18vPvyC19dy 254。 y。C01rvPvxi254。 lateral and longitudinal load shift during typical highway manoeuvres such asImpact of liquid sloshing on the behaviourM. Toumia, M. Bouazaraa,*, . RichardbaDepartment of Applied Sciences, University of Quebec at Chicoutimi, Quebec, CanadabDepartment of Mechanical Engineering, Laval University, Quebec, Canadaarticle infoArticle history:Received 25 September 2020Accepted 25 April 2020Available online 5 May 2020Keywords:Tank vehiclesNavier–Stokes equationsVolume of fluid technique and impact ofliquid sloshingabstractThe purpose of this papercarrying liquid fuel cargo.problems strongly related toliquid sloshing is developedplex Navier–Stokes eqsimplified analytical modelmodel. The results show aIn the second part for thissimulation result is paCrownjournal homepage: 09 Published by Elsevier Massonof vehicles carrying liquid cargostudy the stability and the behaviour of the dynamics of tank vehiclesforces and moments due to liquid sloshing is one of the most seriousinstability of tank vehicles. In this paper, a simplified analytical model ofing the Navier–Stokes equations. Simulation results obtained using the fullons modulated with numerical mercial software are pared to theparison highlights the validity assumptions used on the analyticalcorrelation under single or double lane change and turning manoeuvres., a full dynamic vehicle is coupled with the analytical liquid model. Thisto a rigid vehicle cargo.Copyright C211 2020 Published by Elsevier Masson SAS. All rights reserved.at ScienceDirectMechanics A/SolidsSAS. All rights reserved.0 188。 wwatersloshinginnuclearfuelstorageproblem is plex and strongly nonlinear09977538/$ – see front matter Crown Copyright C211 20doi:in liquid storagehas been theIt has frequentsloshing in vehiclessuspensionbridges。 and liquidstructure dynamicinteractions. Various accident analysis studies have reported thattank vehicles are more frequently involved in single vehiclehighway accidents than rigid cargo vehicles. It has been reportedthat 40% of road accidents involving tank trucks were single vehicleaccidents (Matteson et al., 2020). Nearly 50% of the single vehicleaccidents and almost 80% of multiple vehicle accidents involved atleast one fatality. The majority of single vehicle accidents occurredduring cornering, 52% of which resulted in a rollover.1. IntroductionSloshing is a potential source ofcontainers. The motion of liquids insubject of many studies in the pastapplication in several engineering disciplines:carryingliquidfuelcargo,inaircraftsoscillation in large storage tanks。 fill level。 0 188。x。C18vPvxC19dx 254。V$240。240。240。V$V222。 V represents the velocity。0) and not viscous (m188。240。Fr(3)If the liquid free surface moves with low speed, then it is in equilibrium(V188。y 254。RRRVxidVV。 i。 2。240。 a2m2254。1aq188。V$240。VhmC16VV!254。 Van Der Vegt and Van Der Ven, 2020。 Iii188。Fpxi188。 j。 3222。 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。966 kg/m3,n188。 muaus254。 y。1Mi188。 ih240。 jh240。vV254。 jh240。 0。vfvt。240。T。ys。 r is mass centre vectorposition。f222。i(13)DFzr188。254。 Fzf254。 FzfC0DFzfFzLr188。FzRC0 FzLFzR254。1.For straight driving on a horizontal road with a symmetric load theLTR equals zero because FzR188。 and c2188。wuC2 ruijC1x!254。 rear222。 (18)where V is the mass centre velocity。 Kiei25