Fluid-structure interaction dynamic analysis of large civil aircraft tank sloshing

To meet the requirements of passengers, the tank volume of large civil aircraft is gradually increasing, which brings certain risks. Under different 0 pertaining conditions during the flight, the liquid in the tank will cause structural failure and affect the aircraft’s safety. Therefore, based on the assumption of an ideal fluid, the smooth particle method (SPH) combined with the finite element method (FEM) is used to establish the coupling dynamic equation between the tank and the liquid. The effects of sloshing impact on the water tank under different filling rates were studied, and the influences of the water wave shape, the center of gravity shift, stress distribution, and deformation of the tank were obtained. The results show that the mass accumulation of water particles occurs in the acceleration stage, the relative center of gravity changes greatly in less water, and the accumulated liquid greatly influences the tank under the action of inertia. The more liquid in the tank is, the more the impact effect on the tank increases. The analysis results provide some reference for the analysis and design of tank anti-sway plates and flight attitude adjustment.


Introduction
Liquid sloshing is a widespread problem in aerospace, shipbuilding, petrochemical, and other fields.In aviation, fuel sloshing in the fuel tank caused by aerodynamic disturbance, engine thrust imbalance, and aircraft acceleration during takeoff, flight, and landing will cause adverse effects.The fuel tank problem has accumulated rich and perfect research results in various fields.With the expansion of the civil aviation market, the problem of water tank sloshing has gradually become the object of attention and urgent research.In the course of the flight, due to the change of motion attitude, such as climbing and braking, the liquid in the tank is subjected to the action of inertial force, and the fluid-structure coupling effect between the tank and the filling medium appears.Under the action of this fluidstructure coupling effect, the shaking of the medium in the tank will produce an impact force on the tank and even cause damage [1].The change of center of gravity caused by tank shaking may affect the center of gravity location of the whole aircraft and is one of the factors affecting the attitude stability of the aircraft [2,3].
Based on the SPH method, for the first time, Liu et al. [4] conducted a numerical simulation and shaking test on the liquid of a certain type of aircraft subtank.They derived the calculation expression of the liquid center of gravity at any time.Fang et al. [5] and Zhong et al. [6] used the VOF method to analyze the fuel sloshing characteristics when studying the impact effect of fuel tank sloshing under large overload maneuvering.Zhao et al. [7] and Lai et al. [8] used the SPH algorithm to conduct fluidstructure coupling analysis on the research of the wing fuel tank.They concluded that the liquid-filled

Smoothed particle hydrodynamics method
This paper adopts the smooth particle fluid dynamics method, which is a grid-free Lagrange algorithm with the characteristics of adaptive and grid-free particle form and Lagrange element.It avoids the mesh deformation problem in the traditional Lagrange solution and is suitable for dealing with large deformation and impact problems [2].
The Lagrange form of the fluid dynamics N-S equations can be expressed as: where F denotes force per unit mass;  denotes the total stress tensor.It consists of two parts: isotropic pressure and viscous stress.Applying the SPH particle approximation method to transform the momentum equation, the following expression can be obtained: According to the unit gradient SPH kernel particle approximation formula, the momentum equation is transformed and arranged, and the total stress tensor is decomposed into isotropic pressure and viscous stress.Then, the SPH particle approximation method is used to transform and arrange the energy equation, and the final particle approximation formula of the energy Equation (4) can be obtained: SPH method often produces non-physical oscillation when solving the problem of fluid impact.To accurately simulate the fluid dynamics problem and eliminate the huge error of non-physical oscillation in the solution results in the impact domain, it is necessary to specially treat the SPH algorithm and use Monaghane [11] artificial viscosity.x , x x x x where   and   are constants.  is 1 and   is 1 or 2, which can effectively prevent the nonphysical penetration of particles.c denotes the speed of sound; v is the velocity vector of the particle.To prevent numerical divergence when particles are close to each other, a factor =0.1 ij h is introduced into the calculation.When using the SPH method for fluid simulation, the selection of initial smoothing length has an important impact on the calculation results.For the process of large deformation of complex fluid in tank shaking, the change of particle spacing must be considered to recalculate the suitable smooth length.Therefore, correcting the smooth length according to the average density is used.For incompressible flow, the artificial compression rate is treated as compressible flow to meet the requirements of solving the pressure on time derivative [11].

Analysis of sloshing result
Under the experimental verification of many scholars, the SPH method has fully proved the accuracy of swaying calculation and analysis and the authenticity of swaying morphology under liquid particle simulation.Therefore, this paper will not repeat the experimental verification of the SPH method.

System modeling
Based on ensuring the simulation accuracy and reducing unnecessary calculation cost consumption, the water tank system is simplified to a certain extent, ignoring the pipe inlet and outlet pores, clamp structure, and other components.The excitation is directly acting on the tank.A simplified structural plane model is established in CATIA, and the structural model of the tank, water particles, and coordinate system are shown in Figure 1.Taking the water tank on a certain civil aircraft as the research object, the tank body is a cylindrical, spherical horizontal tank set as an elastic body.The axial section radius of the tank is 252.8 mm, the shell thickness of the tank is 1.2 mm, and the furthest distance between the inner walls of the two ends of the tank is 1082 mm.The material of the tank is ordinary hard aluminum alloy, and the fluid medium is water.The specific parameters are shown in Table 1.Shell elements are used for meshing in import LS-Pre Post.Liquid, considering three kinds of water filling, the filling ratio K is 75%, 50%, and 25%.Among them, the number of tank shell units is 13005, and the number of water particles is generated according to the volume filling ratio in the tank, which is 15744, 28970 and 40380, respectively.

Boundary condition
Acceleration movement refers to the process in which the thrust generated by the engine exerts traction on the aircraft during takeoff to help the aircraft quickly obtain the initial speed required for takeoff.According to the dynamic data of a certain type of commercial aircraft in the process of accelerating takeoff, the large aircraft in the process of accelerating taxiing has variable acceleration motion.The motion law is affected by the different thrusts of the engine, which is a very complex process.For simplicity, only the accelerated motion of the aircraft on the horizontal surface is considered, the impact effect of water slosh generated in a short time during the acceleration phase is analyzed, and the velocity excitation formula suitable for the slosh analysis of the water tank is simplified and established, as shown in Equation ( 8).50 0 0.2 0 0.2 1

Analysis of simulation results
To explore the influence law of different filling rates K on the slosh impact effect of water body in accelerated takeoff, this paper analyzed the changes of fluid morphology in the tank, the displacement of the center of gravity, and the interaction force of the tank under load.

3.3.1
The liquid level changes in the tank.The velocity excitation in x direction was applied to the entire tank, and the tank stopped and stood still after 0.2 s.The boundary setting constrained the displacement of the tank along the z-axis, namely the gravity direction.Combined with the maximum pressure time history curve and the fuel sloshing pattern, the water sloshing during the accelerated takeoff can be divided into three stages.The first stage is the accumulation stage, which corresponds to the stage from 0 s to 0.2 s.At this time, the water particle accelerates and accumulates in the opposite direction of the water tank movement due to the traction generated by the acceleration of the water tank in a short time.The second stage is the shock slosh stage, corresponding to 0.2 s to 0.6 s.In this stage, the accumulated liquid accelerates into the front end of the water tank under the action of inertia, causing a violent slosh accompanied by a water particle splash.The third stage is stabilization, which corresponds to the weakening of the liquid from the violent sloshing to the slight sloshing after the acceleration shock effect is reduced.With different K, the simulation software calculates the liquid sloshing shape in the acceleration process, as shown in Figure 2.

Center of Gravity variation at different filling ratios.
In the keyword setting of LSDYNA, the liquid mass parameter can be independent of the water tank so that the change of the center of gravity position of the water body during the slosh can be learned.The resulting barycenter data are negative since the global coordinate system is used.
In the swaying process of the water tank after swaying under the action of excitation, the movement of the particles is quite disordered.The neatly arranged particles are discretized into a series of SPH units with mass, so the position of the center of gravity can be obtained according to the weighted sum of the divided SPH unit groups.
The displacement change curves of the liquid center of gravity in X, Y, and Z directions under different liquid filling ratios K can be seen from Figure 3 to Figure 5. Since the water tank model is symmetric about the XZ plane, the boundary excitation of fluid-structure interaction is also within this plane.Therefore, the change of the center of gravity in the Y-axis direction is not large, and the uncertainty of the shaking of water particles in the tank makes the displacement of the Y-axis weight center slightly offset, and the maximum change is within 12 mm.The particle motion in the X-axis and z-axis mainly manifests the large deviation of the center of gravity.Due to the acceleration of the tank along the X-axis, the center of gravity of the water particles shifted along the tank from 0 to 0.2 s, resulting in a large shift of the weight center of the water along the X-axis, and gradually stabilized at the same value as the displacement of the tank after shaking.The most prominent variation of the center of gravity displacement along the z-axis is K of 25%.The main reason is that the liquid accumulated after the instantaneous excitation fuses along the wall from the bottom to the still wall, shifting the center of gravity to the z-axis.However, water particles with a high liquid filling rate have a higher center of gravity position, and the displacement change is not high after impact shaking.

Analysis of liquid-solid interaction.
Under the three different filling rates of K 25, 50, and 75, the impact force on the tank structure constantly changes during the shaking process.After the water tank stopped accelerating, a large impact effect was produced.The stress distribution cloud diagram of the tank at a certain time in the process of shaking impact is shown in Figure 6.It can be seen that after the acceleration excitation, the water tank is displaced in the positive direction of the X-axis.That is, the front end of the water tank produces a high-stress distribution area.The monitoring unit is selected here, and the change curve of the impact equivalent stress on the front end of the monitored water tank under different filling rates is shown in Figure 7.
It can be seen from the figure that as the filling ratio K increases, the impact caused is stronger.Multiple peak levels appear under the instantaneous acceleration impact caused by the rotation and advancement of part of the high-speed flow body against the inner wall of the tank.It can be seen in the figure that there are multiple zigzag changes in the curve, which are mainly caused by the instability of the fluid.The equivalent stress gradually flattens out after 1 s, and the third phase is consistent, as described in the previous section.

Conclusions
In this paper, based on the slosh analysis of a large civil aircraft water tank, the efficient SPH algorithm is used to apply the FEA software LSDYNA to simulate and analyze the slosh of the water tank filled with liquid.The data research shows that under instantaneous excitation, the liquid splash in the water tank at low filling rate will cause dramatic changes in the center of gravity in a short time, and the impact equivalent stress, which satisfies the strength requirements, is at low level.The center of gravity is relatively stable under high liquid filling rate, the deviation of the center of gravity is small, and the stable liquid can be reached faster.However, the peak load on the wall of the tank is high under excitation, and there is a certain risk.Therefore, the anti-sway mechanism is considered to be added in the future simulation test.The data demonstration in this paper has certain theoretical

Figure 2 .
Figure 2. Fluid morphology distribution under different K.

Figure 3 .Figure 4 .
Figure 3. Displacement of X-axis center of gravity under different K.

Figure 5 .
Figure 5. Displacement of Z-axis center of gravity under different K.

Figure 7 .
Figure 7. Curves of monitor unit stress curves.