An Analysis of Baffles Designs for Limiting Fluid Slosh in Partly Filled Tank Trucks

Transcription

1 The Open Transportation Journal, 21, 4, Open Aess An Analysis of Baffles Designs for Limiting Fluid Slosh in Partly Filled Tank Truks T. Kandasamy, S. Rakheja * and A.K.W. Ahmed CONCAVE Researh Centre, Conordia University, 1455 de Maiosnneuve West, Montréal, QC, H3G 1M8, Canada Abstrat: This study presents an analysis of effetiveness of different designs of baffles, inluding the onventional, partial and oblique, in limiting the manoeuvre-indued transient as well as steady-state fluid slosh fores and moments in a partly-filled tank truk. The effet of an alternating arrangement of partial baffles is also explored. A three-dimensional omputational fluid dynamis model of a partly-filled tank is developed to study the relative anti-slosh properties of different baffles designs and layouts under ombined idealized longitudinal and lateral aeleration fields and different argo loads. The analyses are also performed for a leanbore tank, whih is validated using the widely-used quasi-stati slosh model. The results suggest that the onventional transverse baffles offer important resistane to fluid slosh under braking manoeuvres, while the obliquely plaed baffles ould help limit the longitudinal as well as lateral fluid slosh under ombined lateral and longitudinal aeleration exitations. Keywords: Tank truks, lateral and longitudinal dynami fluid slosh, antislosh, baffles, oblique baffles. 1. INTRODUCTION In road tankers, the free surfae of argo may experiene large exursions for even very small motions of the ontainer. The resulting dynami load shifts in the roll and pith planes ould influene the roll and pith moments, and mass moments of inertia of the fluid argo, and may ontribute to degradation of the handling and diretional stability limits. This problem is ommon in fuel tanks of automobiles, airrafts and large ships and tankers. Reported studies on dynamis of partly filled tank vehile ombinations have invariably shown that the roll dynamis and braking properties of suh vehiles are strongly influened by fluid slosh in an adverse manner [e.g., 1-3]. It has been shown that the free surfae osillations of low visosity fluids in partly-filled tank truks persist over long durations, and an lead to signifiantly lower roll stability limits and braking performane [4-6]. The magnitudes of dynami load shift, slosh fores and moments are strongly dependent upon the fill volume and the tank geometry. Baffles are ommonly used as effetive means of suppressing the magnitudes of fluid slosh, apart from enhaning the integrity of the tank struture, although only a few studies have assessed roles of baffles design fators in view of the braking and roll dynamis performane. The slosh motion of the free surfae has been extensively studied sine early 196 s using various approahes. The quasi-stati hydrodynami modeling is a simple and onvenient method for deriving the steady-state surfae position, whih has been mostly used for the diretional stability analysis of tank truks. The steady-state roll stability limits of various tank truk ombinations have *Address orrespondene to this author at the CONCAVE Researh Centre, Conordia University, 1455 de Maiosnneuve West, Montréal, QC, H3G 1M8, Canada; Tel: (514) , Ext. 3162; Fax: (514) ; Rakheja@alor.onordia.a been investigated using the quasi-stati load shift in the roll plane [3,7]. Wang et al. [1] used the quasi-stati approah to analyze the influene of number and size of ompartments on the longitudinal load transfer and straightline braking performane of a partially filled tank truk, and onluded that equally spaed ompartments yield minimum longitudinal load shift under straight-line braking manoeuvres, irrespetive of the fill level. A quasi-stati slosh model, however, is limited to fluid slosh in the steady state, and annot be applied to study effets of baffles, partiularly the fores and moments arising from the transient slosh. Moreover, the fundamental slosh frequenies in a full size leanbore tank our in the Hz range in the longitudinal mode, and in Hz in the lateral mode, depending upon the fill volume and tank size [6,8-1]. These frequenies may lie in the viinity of the steering frequeny and the rotational modes of the sprung mass, and ould lead to resonant osillations. It has been further shown that the magnitudes of destabilizing fores and moments during the transient slosh are signifiantly higher than those attributed to steady-state or quasi-stati slosh [4,6,11]. Alternatively, mehanial analogous of fluid slosh and analytial methods have been employed to analyze the transient as well as steady-state dynami fluid slosh responses [5,12-15]. The mehanial-equivalent models, however, may pose onsiderable hallenges in parameter identifiation and are generally limited to low amplitude slosh. Furthermore, suh models have been limited to leanbore tanks only. The transient fluid slosh analyses have been inreasingly onduted using the omputational fluid dynamis (CFD) methods based on the Navier-Stokes solvers oupled with the Volume-of-Fluid (VOF) tehnique. These numerial approahes are known to be effetive for simulating large-amplitude fluid slosh, under time-varying manoeuvre-indued aelerations [5,11,16,17]. Only limited appliations of the CFD methods, however, ould be found for three-dimensional slosh analyses of baffled highway /1 21 Bentham Open

2 24 The Open Transportation Journal, 21, Volume 4 Kandasamy et al. tanks. Modaressi-Tehrani et al. [6] and Yan et al. [4] studied the fores due to transient 3-D fluid slosh in a full size ylindrial and an optimal baffled tank, proposed in [3], using the CFD methods, and showed that the peak longitudinal slosh fore is strongly dependent upon the baffle design. The longitudinal and lateral load transfer aused by fluid slosh in a partly-filled tank an be substantially limited by anti-slosh or slosh damping devies. The tank truks generally employ transverse baffles with a large entral orifie and a nearly semi-irular equalizer opening at the bottom. The effets of suh baffles on the longitudinal and lateral fluid slosh have been investigated in only a few experimental and analytial studies [4,6,18-21]. These have shown that presene of transverse baffles ould limit slosh only in the longitudinal diretion. The longitudinal baffles, on the other hand, ould substantially limit the lateral load transfer, but are onsidered impratial due to additional exessive weight and interfere with the leaning tasks. The effet of size and loation of baffle orifie on the slosh has been reported in only two studies involving retangular [11] and a generi [4] ross-setion tank. Popov et al. [11] studied the effet of size and loation of the orifie of a transverse baffle using a 2-dimensional saled retangular tank model, and onluded that an orifie opening equal to 5% of the baffle area would yield a 29% inrease in the peak overturning moment for a fill depth ratio of 7%, when ompared to that aused by tank with a separating wall. Comparable magnitudes of slosh fores and moments, however, have been reported for orifie opening ranging from 8 to 2% of the ross-setion area [4]. The study also investigated the effets of an equalizer and alternate baffle designs on the magnitude of transient slosh fore and moments, and onluded that an equalizer has negligible effet on slosh, while a multi orifie baffle behaves similar to a onventional single orifie baffle. Alternatively, anti-slosh properties of baffles designs have been investigated through laboratory experiments employing small size tanks of different geometry [18,2-22]. These have generally studied damping properties from free osillations or slosh under harmoni or single-yle sinusoidal inputs. Suh exitations do not provide suffiient data relevant to the effetiveness of baffles under a braking input. In a reent study, Yan et al. [2] onduted experiments using saled baffled and unbaffled tanks of ross-setion, similar to the optimal tank geometry proposed in [3] to identify slosh frequenies, and resultant fores and moments. The experimental results showed that addition of transverse baffles aused a signifiant inrease in longitudinal mode natural frequeny, while the lateral mode frequeny was not affeted. The peak magnitudes of longitudinal slosh fore and pith moment also dereased signifiantly in the presene of transverse baffles. Lloyd et al. [18] experimentally investigated various baffles, inluding solid dished, oblique, spiral, round, and perforated designs, and onluded that the lightweight perforated baffle ould serve as the best anti slosh devie. The effetiveness of baffles in suppressing fluid slosh, however, is dependent upon its geometry and layout. Furthermore, the slosh ontrol analyses of baffles designs neessitate onsiderations of the transient fluid slosh behaviour. In the present paper, onepts in different designs of lateral baffles are proposed and a dynami CFD slosh model of a irular ross-setion tank with different baffle designs is formulated. The model validity is evaluated using the results attained from a quasi-stati model. The relative antislosh effetiveness of the baffles is evaluated in terms of transient slosh fores and moments, and fundamental slosh frequenies for different argo loads under manoeuvreindued lateral and longitudinal aeleration fields. 2. FLUID SLOSH MODELING The fluid flow within a partly-filled tank subjet to lateral and/or longitudinal aeleration field an be onsidered as a two-phase flow omprising the gas and phases. The motion of the inompressible an be represented by the momentum and mass onservation equations. Assuming that the fluid slosh under typial diretional manoeuvres ours at relatively low veloities, the three-dimensional flow is onsidered to be laminar [23]. For the onstant visosity flow, the governing equations of fluid flow with respet to an inertial Cartesian oordinate system an be expressed as [4]: u t + u u x + v u y + w u z = g 1 P x x + u (2 x + 2 u 2 y + 2 u 2 z ) 2 v t + u v x + v v y + w v z = g 1 P y y + ( 2 v x + 2 v 2 y + 2 v 2 z ) 2 w t + u w x + v w y + w w z = g 1 P z z + w (2 x 2 and + 2 w y + 2 w 2 z ) (1) 2 u x + v y + w z = (2) where u, v and w are the veloity omponents along x, y and z diretions, respetively, P is fluid pressure, is the kinemati visosity of the fluid, and g x, g y and g z are the unit body fores ating along the x, y and z diretions, respetively, representing longitudinal and lateral aeleration exitations, and the fluid mass. A homogeneous field of body fore has been assumed in the formulations of momentum and mass onservation equations, whih are solved in onjuntion with appropriate boundary onditions to ompute the veloity omponents and pressure distribution in the flow domain as a funtion of time and spae. It would be reasonable to assume that the tank is bounded by a rigid wall, whih yields that the veloity omponent normal to the wall is zero at the boundary, implying no-slip boundary ondition. The deformation of the free surfae at eah instant of time ould be derived assuming irrotational flow with no horizontal displaement of partiles at the free surfae, whih leads to a kinemati restrition in the following form: v = t + u x ; (3) where is the displaement of the free surfae from its mean position.

3 An Analysis of Baffles Designs for Limiting Fluid Slosh The Open Transportation Journal, 21, Volume 4 25 The above equation exhibits limitations in analyses, when a folded free surfae ours. The onept of traking the volume of instead of free surfae has thus been widely used. The methodology known as VOF (Volume of Fluid) permits the analysis of deformation of free surfae flow through numerial solution tehniques [16, 24]. The VOF model is a surfae-traking tehnique applied to a fixed mesh. It is designed for two or more immisible fluids where position of the interfae between the fluids suh as the gas and, in the ase of a partly filled tank, is of interest. In the VOF model, a single set of momentum equations is shared by the fluids, and the volume fration of eah of the fluids in eah omputational ell is traked throughout the domain Method of Solution The equations of three dimensional fluid flows, satisfying the boundary onditions are solved using the FLUENT software [25]. The VOF method, available within the FLUENT environment, is applied to solve for transient flows involving free surfae separation and air within the non filled ross setion of the tank. The momentum and mass onservation equations are disretized using finite volume tehnique onsidering eah ell as a ontrol volume. For the transient analyses, the governing equations must be disretized in both spae and time. The spatial disretization for the time dependent equations is idential to the steady state ase, while the temporal disretizations involve integration over a time step. The FLUENT software applies segregated solver to obtain sequential solutions of the governing equations using the PISO (Pressure-Impliit with Splitting of Operators) pressure orretion and pressureveloity oupling tehnique [26]. The traking of volume of fluid (VOF) method is used to loate the interfae between the two fluid phases: and air. The dynami load shift due to sloshing argo is generally expressed by variations in the instantaneous g oordinates with respet to the stati g oordinates. The instantaneous oordinates of enter of gravity of the (g) an be obtained from the volume integrals over the phase of the domain. Alternatively, for the disrete mesh, the oordinates are evaluated from: Y g = y A ; Z g = A z A A and X g = x A A where x, y and z are instantaneous oordinates of a ell with respet to mid-point of the tank, M, as shown in Fig. (1). In the above equations, the limit defines the domain of integration, and A is the ell area in the onerned plane. The resultant fores ating on the ontainer struture are omputed from the distributed pressure ating on the wall. The integration over the wetted area of the wall ells yields: F x = (4) wetted area wetted area ( P Ax ); F y = P Ay and F z = ( P Az ) (5) wetted area ( ) where F x, F y and F z are the resultant fores ating on the tank wall, P is fluid pressure at the entroid of the ell in the wall zone, wetted area defines the wetted area of the wall, and A x, A y and A z are the effetive areas of the boundary ell along x, y and z diretions, respetively. The pith, roll and yaw moments due to slosh are omputed about the tank base O from the distributed pressure or fore ating on the wetted struture boundary and position vetor of the individual ells, as shown in the roll plane in Fig. (2), suh that: A w M = r ( P A ) (6) Fig. (1). Steady-state free surfae of in a partly-filled lean bore tank subjet to longitudinal and lateral aeleration.

4 26 The Open Transportation Journal, 21, Volume 4 Kandasamy et al. where M is moment vetor and r is position vetor of ell with respet to the tank base O. Fig. (2). Computation of moments due to transient slosh fores from the distributed pressure on the wetted boundary Analysis of Baffle Designs A 7.55 m long irular ross-setion tank of 1.15m radius and m 3 volume is onsidered for the analyses of fluid slosh and baffles designs. The full load apaity of the tank is approximately 22, kg, assuming a full load of gasoline ( = 85kg / m 3, =.687kg / ms ). The geometry is onsidered adequate for a three or four-axle straight tank in aordane with the urrent weights and dimensional regulations. The origin of the oordinate system used is loated at the geometri entre of the tank. The moments due to fluid slosh, however, are alulated with respet to projetion of the geometri entre at the bottom of the tank, point O, as shown in Fig. (3). The geometry of the baffles bulkheads is hosen in aordane with DOT CFR ode [27] and ASME boiler and pressure vessel ode [28]. Three nearly equally-spaed baffles are onsidered, and eah baffle is provided with an equalizer at the bottom with total opening area being 1% of the tank ross setion area, as shown in Fig. (3). The tank models were developed using four different baffles designs and layouts, as shown in Fig. (4). These inluded the tank models employing: 1. onventional baffles with a large entral orifie of opening area of 12% of the total tank ross-setion area, denoted as onfiguration B1 and shown in Fig. (4b); 2. obliquely plaed onventional baffles, shown in Fig. (4) and denoted as B2 ; 3. partial baffles arranged in an alternating pattern without an equalizer, as shown in Fig. (4d), denoted as B3 ; and 4. semi-irular orifie baffles of idential opening area, as shown in Fig. (4e), denoted as onfiguration B4. The analyses are also performed for a lean-bore tank, whih is denoted as onfiguration B and shown in Fig. (4a). The baffles employed in onfiguration B3 would help redue the tank weight, while those in B2 would yield larger tank weight. The urvature of baffles used in onfigurations B3 and B4 is idential to that of the onventional baffles for tank onfiguration B1 and the tank heads. The longitudinal spaing between the baffles is in the order of 1.72 m, whih is less than the maximum baffle spaing speified in the CFR ode [27]. The simulations were performed to investigate the effet of different baffle onfigurations, fill volume, and magnitude and diretion of aeleration exitations on the magnitudes of slosh fores and moments. The dynami fluid slosh analyses were performed for three different fill levels to explore the effetiveness of baffles. These inluded the low (4%), intermediate (6%) and high (8%) fill levels, where the perent fill level is defined as the ratio of fill height from the bottom of the tank to the tank diameter. The three fill levels orrespond to fluid volumes of 1.21, and 2.42 m 3, respetively, and argo loads of , and kg ( = 85kg / m 3, =.687kg / ms ). Fig. (3). The geometry of the tank equipped with three onventional lateral baffles.

5 An Analysis of Baffles Designs for Limiting Fluid Slosh The Open Transportation Journal, 21, Volume 4 27 Fig. (4). Shematis of the tank and baffle onfigurations onsidered for the analyses. The simulations were performed under simultaneous lateral and longitudinal aeleration idealizing a braking-ina-turn maneuver. Rounded ramp-step variations in aeleration exitations were onsidered along the longitudinal and lateral axes. The exitation was synthesized to realize linearly varying aeleration for t<.5 s and a onstant magnitude at t.5 s, as shown in Fig. (5). The disontinuity assoiated with the ramp-step funtion was eliminated by introduing an ar funtion around t=.5 s, tangent to both the linear and onstant aeleration segments. The onstant G in Fig. (5) refers to the onstant aeleration magnitude, and T a denotes the upper limit of linearly inreasing segment with slope a. 3. RESULTS AND DISCUSSIONS 3.1. Model Validation The dynami fluid slosh model for eah tank onfiguration was analyzed using the seleted mesh size and

6 28 The Open Transportation Journal, 21, Volume 4 Kandasamy et al. step size, and the steady-state slosh fore and moment responses were omputed from the pressure distributions using Eqs. (6) and (7). The responses were evaluated under rounded ramp-step aeleration exitations applied along the longitudinal ( g x =.3g ) and lateral ( g y =.25g ) axis. The model validity was examined by omparing the slosh fores and moments responses with those derived from the quasistati formulations [3]. Sine the quasi-stati formulations are valid only for lean-bore tanks, the three-dimensional quasi-stati and dynami slosh models of the partly-filled lean-bore tank (onfiguration B) were initially solved under ramp-step longitudinal ( g x =.3) and lateral ( g y =.25) aeleration exitations for three fill onditions (4, 6 and 8%). The simulations were performed over an extended period of 2 s so as to ahieve steady-state values, whih were found to be idential to those derived from the quasistati (QS) model, reported in [3]. The steady-state values were also idential to the mean values of the transient responses. Fig. (5). Rounded ramp-step aeleration exitation. Fig. (6) illustrates omparisons of the steady-state longitudinal ( F x ) and lateral ( F y ) slosh fore responses under seleted manoeuvres with those derived from the QS analysis, while the orresponding roll and pith moment responses are ompared in Fig. (7) for the three fill volumes onsidered. The omparisons suggest reasonably good agreements between the steady-state or mean dynami and the quasi-stati responses for all the fill levels onsidered. Some deviations between the two, however, are also observed, partiularly, under intermediate and higher fill levels. The steady-state responses tend to be slightly higher than the orresponding QS responses, while the peak differene was found to be below 4%. This deviation is attributed to slightly different fluid volume and fluid mass estimated from the mesh defined in the Fluent software. The results suggest that a higher fill volume yields higher steadystate and QS fores due to higher inertia. The model validity was also examined by omparing the fundamental slosh frequenies of the lean-bore tank with those reported in the published studies. For this purpose, the transient lateral and longitudinal fore responses of the partly-filled tanks obtained over the 2 s period were resampled at a rate of 4 Hz. The dominant frequenies of slosh fores were subsequently identified through Fast Fourier Transform (FFT) of the time-histories of the fore responses with frequeny resolution of.5 Hz. The analyses revealed fundamental slosh frequenies in the pith plane of.15,.2 and.26 Hz under fill onditions of 4, 6 and 8%, respetively. These frequenies ompare very well with those reported by Abramson [8] for a ylindrial tank with flat end aps (.16,.21 and.26 Hz). The fundamental slosh frequenies in the roll plane were obtained as.56,.61 and.74 Hz for the 4, 6 and 8% fill levels, respetively, whih were also quite omparable with those reported in [8,1] Influenes of Baffles Design and Layout The transient fluid slosh responses of the seleted baffles onfigurations (B1, B2, B3 and B4) were evaluated under Fig. (6). Comparisons of steady-state lateral and longitudinal fore responses of the dynami fluid slosh and quasi-stati (QS) models of the partly-filled lean-bore tank under g x =.3g and g y =.25g: (a) lateral fore ( F y ); and (b) longitudinal Fore ( F x ).

7 An Analysis of Baffles Designs for Limiting Fluid Slosh The Open Transportation Journal, 21, Volume 4 29 Fig. (7). Comparisons of steady-state roll and pith moment responses of the dynami fluid slosh and quasi-stati (QS) models of the partlyfilled lean-bore tank under g x =.3g and g y =.25g: (a) roll moment ( M x ); and (b) pith moment ( M y ). rounded ramp-step aeleration exitations applied along the longitudinal ( g x =.3g ) and lateral ( g y =.25g ) axis to study the effets of baffles. Figs. (8, 9) illustrate the time histories of longitudinal and lateral slosh fore responses, respetively, attained for the 4 and 6% filled tanks. The figures also show the responses of the lean-bore tank for both fill levels. The results learly show the signifiant benefits of transverse baffles in limiting the fluid slosh in the longitudinal diretion. For the lower fill, the peak lateral and longitudinal fore responses of a partly-filled tank with onventional baffles (B1) are only slightly higher than those of an oblique or partial baffle tanks (B2 and B3). The osillations in the lateral fore response of the oblique baffled tank (B2) tend to diminish rapidly ompared to those of the other baffled tank onfigurations with lower fill. The lateral fore responses of B1, B3 and B4 onfigurations exhibit ontinued osillations of onsiderable magnitudes. It has been generally suggested that transverse baffles do not offer resistane to fluid slosh in the roll plane [6, 21]. The results in Fig. (9) suggest that presene of baffles ould help redue the peak magnitude of lateral slosh fore developed under appliations of simultaneous lateral and longitudinal aeleration exitations, and that an oblique plaement of transverse baffles would yield greater redution in the peak lateral fore. This is attributed to the oblique baffles providing onsiderable resistane to slosh in both roll and pith planes. The flow visualization further illustrated delayed aumulation of at the front end of the oblique baffled tank, whih aused the osillations in longitudinal fore to diminish that are observed for the lateral baffled tanks. The lateral fore aused by slosh in the leanbore tank under lower fill tends to diminish rapidly, whih is attributable to flow separation. The results also show that the fluid motion in the B4 tank yields lower magnitudes of steady-state lateral and longitudinal slosh fores, partiularly under the higher fill level. This suggests ineffetiveness of the transverse baffles in suppressing the lateral fore, whih is attributed to the dominant load shift ourring in the roll plane, where transverse baffles provide negligible resistane, while oblique baffles provide relatively greater resistane. Figs. (1, 11) illustrate the time histories of roll and pith moment responses, respetively, attained for the 4% and 6% filled seleted tank onfiguration subjet to g x =.3g and g y =.25g. The results suggest that the roll moment osillations for the lean-bore tank (B) and oblique baffled tank(b2) tend to diminish rapidly, while the transverse baffled tanks (B1, B3 and B4) responses exhibit ontinued osillations of onsiderable magnitudes, as observed for the lateral slosh fore in Fig. (9). While the peak roll moment response of the oblique baffled tank is only slightly higher than that of other baffled tank. Continuous osillations are mostly attributed to the onstraints imposed by the transverse baffle walls on the fluid motion. The absene of this onstraint, as in the ase of the lean-bore tank tends to suppress osillations in the slosh moment. The lower magnitudes of osillations of the roll moment due to oblique baffles is also attributable to relatively lower degree of onstraint aused by these baffles. The semi-irular orifie and onventional baffles yield omparable magnitudes of roll and pith moment for the low fill level (4%). The semiirular orifie baffle (B4), however, yields lower magnitudes of roll moment ompared to the onventional B1 baffles under the intermediate (6%) fill level, as observed for the lateral fore response in Fig. (9). This is attributed to relatively lower load shift in the longitudinal diretion through the semi-irular orifie baffles. The lower roll moment response would help ahieve enhaned roll stability of a partially-filled tank truk. The peak roll moment response of the alternating arrangement of partial baffles (B3) is omparable to that of the onventional baffles under lower fill but higher under the higher fill volume. The pith moment aused by fluid slosh is most signifiantly influened by the baffles design, as seen in Fig. (11). Considering that the dynami load transfer and thus the braking performane of a vehile is diretly influened by

8 3 The Open Transportation Journal, 21, Volume 4 Kandasamy et al. Fx (kn) higher fill level. The steady-state pith moment response of onfiguration B4 is nearly 4% of the orresponding magnitude of the onventional baffled B1 tank under the 6% fill level B B1 B2 B3 B4 5 1 t (s) 15 2 Fy (kn) 2 1 B B1 B2 B3 B t (s) Fx (kn) B B1 B2 B3 B4 5 1 t (s) 15 2 Fy (kn) 3 2 Fig. (8). Time-histories of longitudinal slosh fore responses of seleted baffled tanks subjet to g y =.25g and g x =.3g : (a) 4% fill level; and (b) 6% fill level the pith moment aused by the sprung mass, the pith moment response of the partly-filled tank truk ould be diretly related to its braking performane [1,3]. The results show most signifiant variations in the magnitude of the pith moment response of the lean-bore tank (B), irrespetive of the fill level onsidered. The presene of baffles not only diminishes the peak pith moment but also yields lower steady values due to portions of fluid being trapped in lower setion of the tank between two onseutive baffles or between the baffle and the end ap. The onventional baffle tank exhibits this behaviour under lower fill level, while the steady-state moment magnitude is larger under the intermediate fill ompared to the other baffles, as seen in Fig. (11b). The steady state pith moment response of the oblique baffled onfiguration (B2) is omparable to that of the B1 onfiguration under lower fill but signifiantly lower under the 6% fill level. This may be attributed to relatively greater amount of fluid trapped between the oblique baffles under a higher fill level. The alternating arrangement of partial baffles also yields lower steady-state pith moment under the higher fill ompared to the onventional baffles. This suggests that partial baffles ould provide slosh ontrol omparable to the onventional baffles, while the struture weight ould be redued. The semi-irular orifie baffles ( B4 ) attain signifiantly lower peak as well as steady-state pith moment ompared to all other onfigurations for the 6% fill level, while the responses are either omparable or lower under the lower fill level. This is attributed to relatively lower load shift in the longitudinal diretion through the semi-irular orifies, partiularly under the 1 B B1 B2 B3 B4 2 4 t (s) Fig. (9). Time-histories of lateral slosh fore responses of seleted baffled tanks subjet to g y =.25g and g x =.3g : (a) 4% fill level; and (b) 6% fill level. The load transfer in the longitudinal plane of different partly-filled tank onfigurations were also examined through flow visualization. As an example, Fig. (12) ompares the nearly steady-state (t = 2 s) load transfers and the fluid free surfae in the onfigurations with onventional (B1) and semi-irular orifie (B4) baffles with 6% fill level. It an be seen that the tends to aumulate towards the front end of the tank while the aumulation is signifiantly more in B2 tank than B4, while the free surfae gradient is uniform in all the baffled segments. The flow pattern in B4 tank shows more uniform load distribution ompared to the B2 tank, partiularly in the three leading segments, whih ontributes to lower pith as well as roll moment in the steady-state, as seen in Figs. (1, 11), respetively. The results suggest that proposed semiirular orifie baffles provide better slosh ontrol in the longitudinal plane, whih is attributable to the geometry whih serves as a solid ompartment for the fluid within in the upper-half of the tank. Considering that the tanks would generally transport loads with fill greater than 5%, the baffles with semi-irular orifie in the lower-half setion ould provide more effetive ontrol of load shift and thus improved braking performane. 4. CONCLUSIONS The effetiveness of different baffles designs in ontrolling the magnitudes of fluid slosh and thus load

9 An Analysis of Baffles Designs for Limiting Fluid Slosh The Open Transportation Journal, 21, Volume 4 31 Mx (knm) Mx (knm) B B1 B2 B3 B4 2 4 t (s) transfers in the roll as well as pith planes of a partly-filled irular ross-setion tank is investigated. The transient as well steady-state fores and moments aused by fluid slosh under simultaneously applied longitudinal and lateral aelerations were evaluated through development and solutions of a CFD model of the partly-filled tank. The steady-state magnitudes of fores and moment responses of the leanbore tank agreed very well with those evaluated from the widely used quasi-stati fluid slosh model. The validity of the model is further demonstrated through good agreements of the fundamental slosh frequenies with those reported in a few published studies. The slosh fores and moments responses of the partly-filled tank learly show most signifiant effets of baffles on the longitudinal load transfers, while the effets on the lateral load transfer is very small. The pith plane load transfer, however, is strongly dependent on the baffle design. The onventional baffles provide effetive ontrol of fluid slosh in the longitudinal diretion but offer negligible resistane in the roll plane. An oblique arrangement of baffles offers onsiderable resistane to lateral fluid slosh in the roll plane as well as longitudinal fluid slosh in the pith plane. The partial baffles are generally ineffetive in the roll plane but anti-slosh performane in the longitudinal diretion is omparable to the onventional baffle. Considering that the partial baffles yield lower struture weight and thus the ost, these may be onsidered meritorious over the onventional baffles. The semi-irular orifie baffles offer most signifiant redutions in the longitudinal load transfer, and the peak and steadystate magnitudes of the pith moment, partiularly when the stati free surfae ours above the baffles opening. Suh baffles ould thus yield improved braking performane and yaw stability limits of partly-filled tank truks. The semiirular orifie baffles also yield lower magnitude of steadystate roll moment under the intermediate fill level onsidered in this study, whih is attributable to greater ontainment of fluid between the suessive baffle or between the baffles and tank heads. My (knm) B B1 B2 B3 B t (s) 1 B B1 B2 B3 B4 2 4 t (s) Fig. (1). Time-histories of roll moment responses of seleted baffled tanks subjet to g y =.25g and g x =.3g : (a) 4% fill level; and (b) 6% fill level. My (knm) B B1 B2 B3 B t (s) Fig. (11). Time-histories of pith moment responses of seleted baffled tanks subjet to g y =.25g and g x =.3g : (a) 4% fill level; and (b) 6% fill level (a) (b) Fig. (12). Comparison of free surfae position of argo in tanks with.25 g and.3g exitation at 2 se: (a) 6% fill level for B1 ; (b) 6% fill level for B4

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