Study of the effect of baffles on longitudinal stability of partly filled fuel tanker semi-trailer using CFD

Use your smartphone to scan this QR code and download this article ABSTRACT Sloshing of liquid in partially filled fuel tanker vehicles has a strong effect on the directional stability and safety performance. Under the maneuver of the vehicle, such as steering, braking, or accelerating, the liquid fuel in the tanker tends to oscillate. As a result, hydrodynamic forces andmoments raise. It leads to reduce the stability limit and the controllability of the vehicle. To minimize the effect of sloshing, the baffles are usually added to the tanker. This paper presents the study of the effect of baffles on the longitudinal stability of the fuel tanker semi-trailer using the computational fluid dynamics (CFD) approach. A three-dimensional fluid dynamic model of a typical tanker with different baffle configurations is developed. The User Defined Function (UDF) is used to control the acceleration of the tanker according to the simulation scheme. Transient simulations are performed for the cases of constant acceleration longitudinal maneuvers with different levels of fuel in the tanker. The volume of fluid (VOF) and air obtained from the simulation is used to indirectly calculate the center of gravity of the tanker. The post-processing results show that the baffles could provide resistance to the fluid sloshing, resulting in an improvement of the longitudinal stability of the tanker semi-trailer. The results also prove that the benefit of the baffle to the fuel tanker vehicle's stability depends on the size of the baffle, as well as the number of baffles. The 40% height three bafflesmodel is the proper bafflemodel to resist the longitudinal sloshing in the partially filled tanker of the studied trailer. By adding baffles, shifting of load on the kingpin and the rear axis are less than 5% and 2% as the tanker is filled with 50% and 70% fluid level respectively.


INTRODUCTION
As a tanker semi-trailer with a partially filled liquid tanker is in acceleration or deceleration, the carrying fluid tends to oscillate. This phenomenon is preferred as sloshing, a form of fluid-structure interaction. One of the major effects of sloshing is to cause the change of the center of gravity of the fluid when the tanker semi-trailer doing the braking or turning maneuver. As a result, the dynamic load shift in the roll and pitch planes could affect the roll and pitch moments, and the mass moments of inertia of the fluid cargo and may lead to a reduction in the directional stability limits and the controllability of the vehicle. To prevent large scale sloshing, baffles are usually added to the tanker structure. Studies on the effect of baffle configuration on sloshing phenomenon using both theoretical and experimental approach have been carried out for the past several decades. However, only a few theoretical studies deal with the complicated case of sloshing such as tanker semi-trailer in braking or turning maneuver. The experimental approach could give a visual view of sloshing. But, it requires well preparation of equipment such as excitation system, acceleration acquisition system and wave-height measurement system 1 . In addition, it is difficult to carry out the experiment on large testing objects 2 . In recent years, the numerical approach using Computational Fluid Dynamics (CFD) analysis plays an important role in predicting the behavior of fluidstructure interaction in the sloshing. Time and costsaving can be achieved by using the CFD as a tool to find out the proper model in a group of potential models. Besides that, CFD can deal with the flow limitation and the complicated boundary condition. Several techniques have been used to numerical simulate of liquid sloshing, consisting of boundary element integral methods, finite element methods for potential flow, finite difference/volume methods solving the Navier-Stokes equations, and the smoothed particle hydrodynamics method 2 . Among these numerical approaches, the method based on Navier -Stokes solver coupled with the Volume-of-Fluid (VOF) technique is proper to simulate large-amplitude fluid slosh under time-varying excitation acceleration, as well as to track the liquid free surface 3 . In this paper, the study of the effect of baffles configuration on the longitudinal stability of an ellipse cross- section tanker semi-trailer is discussed. The Ansys Fluent software is used to solve the Navier -Stoke equation. The Volume of Fluid model is chosen to formulate the interaction of multiphase of fluid in the tanker 4 . The User-Defined-Function (UDF) is used to vary the acceleration of the tanker according to the simulation scheme.

METHODOLOGY Physical Model and Static Stability Analysis
The study is carried out on the tanker semi trailer's model of KCT G43-BX40-02 made by Tan Thanh Trading Mechanic Corp, Viet Nam 5 . The main components of the trailer are shown in Figure 1. Detail of load distribution on the kingpin and the rear axles is illustrated in Table 1.

Numerical Model
The numerical simulation is done on the fuel tanker semi-trailer G43-BX40-02. To simplify, the tanker is considered to have ellipse cross-section with the dimension of 2.5 m in height 1.96 m in wide. The total length of the tanker is 10.5 m. The fore and aft bulkheads of the tanker are assumed to be flat, and the baffles are also flat. The origin of the coordinate system used is located at the geometric center of the tanker, the x-axis is along the longitudinal axis of the tanker, the z-axis is in the vertical direction. The baffles are installed in the lateral plane with equal distance along the x-axis, and symmetry about the OXY plane axis is in the vertical direction. Figure 2 depicts the overall dimension of the tanker. There baffle configurations that have quantity of baffle of 3, 4, and 5 are considered. On each configuration, the baffles' height is set to 30%, 40%, and 50% of the tanker's height. In general, baffles are flat, the overall shape of baffle is similar to the tanker cross-section. The baffle is symmetric about the longitudinal and lateral axles. The baffles that have a height of 40% and 50% of the tanker's height are shown in Figure 3. The simulations were performed under time-varying acceleration along the longitudinal axis as showed in Figure 4. In the first 0.1 seconds of the simulation, the acceleration is set to zero. The fuel tanker vehicle is then accelerated at a constant acceleration of 0.7m/s 2 in 7.9 seconds. As the vehicle reaches the velocity of 20 km/h, its acceleration is then set to 0 and remain at that value for the rest of simulation. For all of the simulation, the translation acceleration is set to 9.81 m/s 2 in the direction of -Z-axis 6 .

Simulation method
The simulation of sloshing of fluid in the fuel tanker under the time-varying acceleration excitation is done using the commercial Computation Fluid Dynamics software, namely Ansys Fluent version 18.2. The process of simulation and post-processing of the results is illustrated in the flowchart in Figure 5. The Fluid Flow (Fluent) module of Ansys Workbench is used to create the geometry of the tanker and baffles. The unstructured mesh is used to smooth the transition at the tanker wall and the baffles. The mesh quality is controlled to be fined during the automatic mesh generation. The wireframe view of the mesh is shown in Figure 6, while the detail of the mesh is listed in Table 2. In order to track the center of gravity of the fluid sloshing, the Volume of Fluid (VOF) multiphase model is activated in the solving model of Ansys Fluent. Two phases of air and gasoline are used to represent the gasoline and air in the partially filled tanker. The VOF model was designed to capture the position of the interface between two immiscible fluids. The volume fraction of each phase in every cell is tracked throughout the domain by a set of momentum equation between phases. The VOF model relies on the hypothesis that the fluids are not interpenetrating. In each computational cell, the total volume fraction of all phases equal to 1 4 . The detail of the solver and the fluid properties are illustrated in Table 3. In order to model the time-varying acceleration motion of the tanker, the User-Defined-Function (UDF file) is used. This file describes the motion of the tankers' geometry according to the model of the tanker's acceleration. By running the Ansys Fluent on the Visual Studio Developer Command Prompt, the UDF file can be built, loaded into a library in Fluent. The functions defined by the UDF file will control the motion of the mesh via the setting in the dynamic mesh task page of Fluent 7 .

Post processing of simulation results
The exported data is set to contain the information of the volume of each computational cell of the mesh V c , and the volume fraction of liquid in each cell, vof(c) gas . As a result, the mass of liquid in each cell can be calculated by the formula: In which, x c , y c , z c are the coordinate of the centroid of the cell c respect to the original coordinate of the tanker.

RESULTS AND DISCUSSIONS Static Stability
The static stability of the trailer can be obtained by taking into account the load of gasoline to the change of the static center of gravity. As changing the liquid level, the load of fluid will be changed, while the weight of other components is remaining. Resulting SI17 Figure 6: The wireframe mesh of tanker with 3 baffles, baffle height = 50%

Dynamic Stability
The dynamic stability of the trailer is evaluated by calculating the shifting of load due to the sloshing of fluid under a time-varying acceleration excitation. At a certain level of fluid in the tanker, the free surface of the liquid will be changed as the sloshing is occurred. As a result, the location of the center of gravity of fluid is varied, leading to a redistribution of load on the kingpin and the rear axles. The calculation of load on the kingpin during sloshing is done by: ( L 1 + △x cg_ tan ker ) /L 0 . In which, △x cg_ tan ker is the shifting of the center of gravity of the liquid fluid obtained from the post processing of simulation results. Therefore, the shifting of load on the kingpin due to sloshing can be obtained by: load shi f ting on the kingpin = G ′ 1t − G 1t . Similarly, the load and the shifting of load on the rear axles can be obtained by applied the following formulates:

Effect of the Number of the Baffle on the Load Distribution
To study the effect of the quantity of baffle to the dynamic stability of the semi-trailer, the lateral baffles are inserted to the tanker. The baffle's height equals 40% the height of the tanker, while the baffle quantity is set to be three, four, or five baffles. In these simulation cases, the gasoline is set up at 70% of the tanker volume. The simulation result in term of volume fraction of gasoline is depicted in Figure 7.

SI18
As seen in Figure 7a, b, c, the liquid fluid is moving toward the rear of the tanker at the time of observation. Therefore, it can be predicted that dynamic load will increase in the rear of the tanker, and decrease in the front of the tanker. Detail of the redistribution of load on the kingpin and the rear axles is shown in Table 5, the static gross weight of the trailer is 20720 kg.    However, as evaluating the term of cost and simplicity, the three baffles model has more advantages than the five baffles model. Therefore, the tanker with three lateral baffles will be used for further study on the effect of baffle height on the longitudinal stability of the trailer. Three baffle height of 30%, 40%, and 50% are used to find out which model will give better results in reducing of shifting of the center of gravity of the trailer as under sloshing. The simulation results in terms of volume fraction of fluid for the liquid level of 50% are depicted in Figure 10a, b, c. Detail of load distribution on the kingpin and the rear axles at the static condition and sloshing is shown in Table 6. At the liquid fluid level of 50%, the baffle model of 30% baffle height has less effect on reducing the movement of the fluid. As shown in Figure 10a, the fluid tends to move toward the right end of the tanker at the time of observation. Therefore, the dynamic load significantly increases on the rear axles of the tanker (24.99%), and highly reduce on the kingpin (32.61%).
In the models that have a baffle height of 40% and 50%, the baffles effectively limit the oscillation of fluid. As a result, the shifting of the center of gravity of the fluid is rather small as compared with the 30% baffle height model. Among the three models of baffle height, the model of 40% baffle height gives the smallest movement of the center of gravity of the trailer, resulting in the smallest shifting of load on the kingpin and the rear axles (-3.33% and 2.55%). This dominance of the 40% baffle height model will be validated on other liquid fluid levels of 70% and 90%. The simulation result of these cases is detailed in Table 7 and Table 8. The simulation result of the 70% liquid level is similar to the case of the fluid level of 50%. The 40% baffles' height model gives the best result in preventing the load shifting, while the largest load shifting occurs in the 30% baffles' height model. The volume fraction of gasoline for three models of baffle height is illustrated in Figure 11. The result of load shifting for the case of 90% liquid level is shown in Table 8. The volume of fluid on the computational domain is depicted in Figure 12. It can be seen that the fluid does not have much space for sloshing. With the baffle height of 30% and 40% the baffles nearly submerse in the liquid fluid and have less effect in reducing the fluid oscillation. Baffle height of 50% provides a better reduction of slosh-SI20

CONCLUSIONS
The study of the effect of adding lateral baffles on the longitudinal stability of a tanker semi-trailer has been conducted by using a computational fluid dynamics approach. Lateral baffles characteristic in terms of a number of the baffle, and height of baffle have been examined to find out the appropriate baffle configuration.
It could be concluded that the simulation approach using multiphase Volume of Fluid Model in Ansys Fluent can be used to capture the air-liquid fluid interface. Analyses of the simulation results show that lateral baffles could be damping the oscillation of fluid under sloshing. The 40% height three baffles model is the proper tanker model to resist the longitudinal sloshing in the partially filled tanker of the studied trailer.
Validation on different liquids levels shows that the effectiveness of the baffle against the sloshing is high at a low liquid level. This effect reduces as the tanker is full or nearly full of liquid.

CONFLICTS OF INTEREST
The authors declare that they have no conflicts of interest.