Design and simulation of anti-sloshing baffles applied to detumbling payload propellant tanks

The method to suppress the liquid sloshing in the tank applied to the jet detumbling payload is investigated in this study. Among all kinds of anti-sloshing structures, the symmetrical annular baffle was chosen due to the features of impact on the payload’s tank. The damped mass-spring liquid sloshing model established is used to compare the damping ratio of the baffle with different baffle layers and different baffle heights. Using FLUENT software, based on VOF (volume of fluid) numerical simulation technology, the damping effect of baffles with different layers and heights is simulated. The results show that 3-layer 15mm or 4-layer 10mm baffles can effectively reduce the influence of liquid sloshing. The damping ratio of the storage tank with a 3-layer 15mm anti-sloshing baffle is at least 18.3 times that of a smooth tank, and the damping ratio of the tank with a 4-layer 10mm anti-sloshing baffle is at least 18.7 times that of a smooth tank.


Introduction
As the pace of human exploration of the universe gradually accelerates, space debris becomes a problem that cannot be ignored [1].Based on ESA models, the true number of debris larger than 1 cm in size is likely over one million [2].Most of them are tumbling due to their residual angular momentum [3].As a result, detumbling process is required before using capture mechanisms like robotic arms and tentacles to capture space debris [4].A variety of methods have been proposed to eliminate rotation, such as deceleration brush detumbling [5], mechanical pulse detumbling [6], tethered space robot detumbling [7], electrostatic detumbling [8], electromagnetic detumbling [9], gas shock detumbling [10], ion beam detumbling [11], etc.However, during the detumbling process, the free floating of the target makes it necessary for the service satellite to constantly adjust its attitude to carry on the detumbling operation.To solve this problem, jet detumbling payload is proposed.The detumbling payload is designed based on the principle of jet detumbling, launched from the service satellite, formed a rigid connection with the target through the attachment mechanism, and generated detumbling torque through the jet.Considering the volume limitation of the service satellite, the jet propulsion system uses liquefied gas as the propellant.The actual storage state of the propellant is gas-liquid coexistence.The cold-gas propulsion system has been widely used in the orbital maneuvering task of micro-nano aircrafts.But due to the acceleration generated by the thruster is relatively small, the liquid sloshing in the propellant tank is rarely researched.The accelerations caused by the impact of the detumbling payload when launched from the service satellite and attached to the target surface are much bigger than the acceleration generated by the jet.The problem of propellant sloshing caused by external impact will directly affect the launch accuracy and attitude stability.Therefore, it is necessary to study the suppression of liquid sloshing in jet detumbling payload tanks.The commonly used anti-sloshing structures mainly include anti-sloshing baffle, flexible diaphragm and floater, among which the antisloshing baffle is more common.Maleki et al. developed an estimation of hydrodynamic damping ratio of liquid sloshing in baffled tanks undergoing horizontal excitation using Laplace's differential equation solution.The results implied that the ring baffles are more effective in reducing the sloshing oscillations [12].Hasheminejad et al. studied the effects of liquid filling level, baffle arrangement, and length on liquid sloshing in horizontally placed cylindrical tanks [13], and the effect of baffles in the semi-filled tank under transverse excitation on liquid sloshing [14].Cho et al. designed a bottom-hinged, toptensioned porous membrane baffle for rolling rectangular storage tanks and studied their performance as anti-sloshing devices [15].Arun et al. studied the anti-sloshing effect of horizontal porous baffles in rectangular storage tanks [16].Sobia et al. studied the use of slat screens to damp fluid sloshing during the refuel process of the tank under microgravity conditions.The images captured by the high-speed camera showed that the slat screen could effectively increase the sloshing damping [17].Reza et al. compared the damping effect of the fixed baffle and the spring-connected movable baffle, and found that the double spring movable baffle can reduce the sloshing force on the sidewall by 30%~35% [18].Both the floater method and the flexible diaphragm method aim to destroy the original free liquid surface to increase the energy dissipation.Bauer et al. proposed that if the free liquid surface of a viscous liquid is completely covered by an elastic structure, the damped natural frequencies will be larger than those obtained with a free liquid surface [19].The coupled frequencies will increase with increasing liquid fill ratio and quickly reach a value that is close to constant [20].Dillon et al. proposed a coupled fluidstructure CFD model to capture the damping effects of a flexible diaphragm on the propellant [21].Koh et al. designed a constrained floating plate device [22].It was demonstrated through numerical simulation and experiments that the floating plate can reduce the sloshing pressure of liquid on the tank.From 2010 to 2013, Anai Kim et al. designed a floating pad for large LNG storage tanks [23], which is made of melamine foam wrapped in marble, the quality can be determined by the size of the marble, and the flexural stiffness is controlled by the connection between the foams.Chongwei Zhang et al. studied the effect of the number of floating layers on liquid sloshing in storage tanks, and showed that as the number of layers increases, the amplitude of liquid level sloshing also decreases [24].However, the formal anti-sloshing designs were aimed at large storage tanks, and set large external impacts and large shaking amplitudes.The structures designed were complex and difficult to process.As a result, they are not suitable for the detumbling payload proposed in this paper.The detumbling payload is a 10kg class micro-nano vehicle.In this paper, impact conditions during the detumbling payload task are analyzed, and the damped massspring system model is used to simplify the linear simplification of liquid sloshing.Different forms of anti-sloshing method are compared, and a multi-layer symmetrical annular anti-sloshing baffle is designed.Taking the sloshing characteristic parameters in account, the VOF-based numerical simulation technology of Fluent software is used to describe the sloshing effect.Through simulation, the sloshing situation, sloshing damping and sloshing force of the propellant in different baffle designs are obtained, and the anti-sloshing baffle design suitable for jet detumbling payload is proposed by comparing various schemes.

Task background
The detumbling payload is carried on the service satellite, which is moored at a certain distance to the unstable target.After completing the observation of the target and stabilizing the attitude, the solid launch motor of the detumbling payload is ignited.Once hitting the target, the detumbling payload is fixed on it through the attachment mechanism, as shown in figure 1.Then, through the sensitive device carried by the detumbling payload, the angular rotational velocity of the unstable target is sensed.The propulsion system is controlled to reverse jet based on the designed detumbling control law to provide the torque to achieve rapid detumbling of the unstable target.The detumbling payload is mainly composed of an attachment mechanism, a control module, Reaction Control System (RCS) thrusters, a launch motor, etc.The structure is shown in figure 2. As the core component of the detumbling payload, the cold-gas propulsion system provides a certain range of thrust and sufficient total impulse.The payload is launched from a certain distance from the target, which means the pointing accuracy required is especially high.In the process of the payload approaching the unstable target the propellant will be impacted twice, as shown in figure 3. The first impact which directly acts on the storage tank is caused by the ignition of the launch motor.The second impact is caused by the attachment mechanism penetrating the unstable target, which causes the speed of the payload drops to zero instantaneously.

Design of anti-sloshing method
2.2.1 Principle of anti-sloshing.Methods to describe liquid sloshing mainly include analytical theoretical method, numerical simulation calculation and experimental method.This paper will combine theory and simulation, start from the sloshing characteristic parameters, and use VOF-based numerical simulation technology to describe the sloshing effect.The volume of fluid (VOF) method is widely used in the application field of liquid sloshing and free liquid flow.The VOF model is based on the N-S equation to represent the interface state between the two phases of surface, and the flow field is divided by the volume fraction   of the  phase.The volume fraction of a single unit is calculated as follows: In this design, there are only two phases, and under the premise of limited tank volume, the VOF model is used to calculate parameters such as sloshing damping.
Based on the theoretical analysis of the equivalent dynamic model, the analytical theory uses the damped mass-spring system or the equivalent pendulum model to study the dynamic effect of liquid sloshing, and makes a linear simplification [25].The sloshing mode is described in equation ( 2): Where   represents the displacement relative to the axis,  represents the sloshing mode of the first order,   corresponds to the sloshing mass,   is the equivalent stiffness of the  t h order,   is the damping coefficient of the th order.Based on the above formula, the calculation formula of the sloshing frequency   , the sloshing damping ratio   , the shaking force   and the torque   can be further obtained: where ℎ  is the height in the established tank coordinate system.It can be seen from experiments that the result project obtained after linear simplification is still available.Therefore, the anti-sloshing design will start from the four sloshing characteristic parameters   ,   ,   and ℎ  .The realization of the anti-sloshing function mainly depends on changing the free boundary conditions of the sloshing fluid surface or increasing the sloshing damping.
Changing the free fluid level boundary condition is to reduce the impact of sloshing by reducing the area of the fluid surface, changing the kinetic boundary condition, and absorbing the sloshing energy, as is shown in figure 4.However, this method will greatly reduce the amount of propellant.The commonly used diaphragm and float methods may be force-coupled with the storage tank, which greatly increases the local stress at the connection and causes problems such as ring deformation.

Figure 4.
Anti-sloshing methods based on changing the boundary condition.The main form of increasing sloshing damping is adding anti-sloshing baffles.Anti-sloshing baffles can also be processed with the tank by additive manufacturing, which is very suitable for the situation where the shape and size of the tank are difficult to adjust.For the detumbling payload, an anti-sloshing baffle will be set inside the tank to reduce the effect of liquid propellant sloshing.For smooth storage tanks without anti-sloshing baffles, part of the damping comes from the viscosity of the liquid itself, and the viscosity of the liquid when sloshing produces a large energy dissipation in a thin layer of the inner wall of the tank, which is called the Stokes boundary layer.The other part comes from the energy dissipation caused by the viscosity of the remaining fluid.After adding anti-sloshing baffles, the boundary of the fluid is changed, which aggravates the energy dissipation of the above two types and produces winding damping.Because the relative speed of the storage tank and the liquid exists at the moment of sloshing, the baffle will hinder the flow of the liquid, resulting in different pressures on different sides of the baffle, and eventually creating passing flow resistance to reduce the sloshing of the liquid.The dynamic viscosity coefficient of the propellant selected for this design is 3.0439×10 -4 Pa ⋅ s (R236fa at 20℃).The dissipation of the Stokes boundary layer and the internal dissipation due to viscous flow are much smaller than the dissipation generated by passing flow resistance, so the passing flow damping is the only form of damping to be considered in the calculation.The essence of the passing flow resistance is the pressure difference resistance.The pressure difference resistance hinders the liquid when sloshing and causes energy dissipation, which is given by: where  ⃗⃗ is the unit normal vector of the designed anti-sloshing baffle,   is the maximum amplitude of shaking. is related to the curvature of the baffle.For the plate, the value of  is 8.5.The Reynolds number will limit the value range of   .The total mechanical energy of liquid sloshing in a cycle is: The damping ratio of this section can be calculated as:  0.5 (7) In the formula,  and  are both coefficients, the values are 2.83~3 and 1.5~1.8.The value of  depends on the specific design, which represents the ratio of the sum of the area of all semi-circular baffles to the cross-sectional area of the tank. (  , ) is generally obtained by fitting all the data.There is no fixed analytical expression.Radial baffles, also known as vertical strip baffles, are evenly arranged along the circumference of the cross-sectional circumference of the tank, as shown in figure 6.The damping of this type can remain unchanged when the liquid level position changes, but will be affected by the change of sloshing direction.The design parameters of this type of baffle mainly include the width of the baffle , the height of the baffle ℎ, and the number of baffles  (the angle between adjacent baffles).For radial baffles, the height of the baffle represents the range it functions.With the number of baffles increases, the anti-sloshing effect will also increase.Meanwhile the mass will increase and the directionality of damping will be effected.In the case of normal filling ratio, the influence of damping caused by different shapes of the tank bottom is usually ignored.The damping ratio of this type of baffle can be calculated with the following empirical formula: where  is the shaking width of the storage tank.  is the angle between the first radial baffle and the direction of liquid sloshing, which is affected by the number of baffles.The symmetrical annular baffle is generally a circular ring parallel to the liquid surface, as shown in 0. This type of baffle has the same damping in different directions.The thickness of the baffle is designed to be sufficient to consider the baffle as rigid baffle, the specific calculation formula is as follows: where  is the flexibility parameter,  is the liquid density,  is the radius of the tank,  is the Poisson's ratio of the baffle processing material, corresponds to the modulus of elasticity . is the width of the baffle, and  is the thickness of the baffle. (   ) describes the effect of boundary conditions on the baffle.When the flexibility parameter is zero, the baffle is considered as rigid.The thickness of the baffle is designed according to the strength conditions, which can effectively improve the damping and antishake efficiency.Considering the size of the tank, the anti-sloshing effect of the single-layer baffle is not ideal, so it is necessary to install a multi-layer baffle.The main design parameters are the width of the baffle  and the layer spacing  as shown in figure 7. The distance between the annular baffle and the liquid level is .When  is negative, the baffle exceeds the liquid level.The range of d which makes the baffle effective is −0.1 ≤  ≤ 0.45.Unless there is very little liquid in the storage tank, the anti-sloshing effect of the bottom baffle is not obvious.The distance between the baffles is designed as 0.2 ≤  ≤ 0.4 to make the overall damping of the storage tank relatively uniform.In the primary stage of design, the damping of multi-layer baffles can be approximated as the linear superposition of anti-sloshing damping of multiple single-layer baffles.For the calculation of the damping ratio of symmetrical annular baffles, there is the following empirical formula: (10) where  is the coefficient, the value is 2.83~3. is the width of the storage tank.There are different calculation expressions of  (   ) when the ratio of baffle width to the radius of the storage tank is different, as follows: Since the impact conditions designed in this paper are all radial loads, the anti-sloshing effect of the radial baffle is not obvious, so the radial baffle is not selected.The propellant has complex sloshing behavior in the space environment without gravity, which requires the design of the baffle should be able to withstand large stress.Considering the processing method of additive manufacturing, the semicircular baffle is difficult to process and prone to stress concentration.So the semicircular baffle is not selected.Finally, a symmetrical ring baffle was chosen to suppress propellant sloshing in the tank.Damping ratio is an important parameter to evaluate the anti-sloshing effect of the baffle.For the attenuation vibration system with anti-sloshing damping, the common vibration attenuation curve is shown in figure 8 below: The damping ratio obtained indicates the structural damping of the corresponding baffle.For structures with strict weight requirements, the ratio of damping value to baffle area can be further obtained, that is, the average damping ratio, which is used as a technical index to optimize the design.

Simulation model
In this paper, the algorithm SIMPLEC is selected for the sloshing characteristics of the impacted liquid, and the mesh motion conditions are added using UDF.The selected propellant R236fa has a density of 1377.5168kg/m 3 , a dynamic viscosity coefficient of 3.0439×10 -4 Pa ⋅ s, a surface tension coefficient of 0.0102N/m at 20°C and an internal pressure of 0.4MPa.The cylindrical tank used in simulation is shown in figure 9, with a size of Ф150mm×200mm and a wall thickness of 3mm.The coordinate origin is centered on the base, and the Z axis coincides with the cylindrical axis.9), the thickness is calculated to be 5mm.the layer spacing  characterizes the range of action of the singlelayer baffle.The range of action given by the empirical formula is 0.25 ≤  ≤ 0.55, that is, between 18.75mm ~ 41.25mm.The sloshing generated by the propellant at the bottom of the tank has little effect on the entire load.In order to achieve the optimal layer spacing, set the width of the baffle to 10mm unchanged, respectively draw the 3-layer baffle the 4-layer baffle and 5-layer baffle.Models are shown in the figures below after importing Fluent: The tank and the liquid propellant can be considered as a mechanical system with a free liquid level.During the mission, the launch impact produces a strong nonlinear effect.Although the sloshing time is

Numerical simulation analysis
Taking the impact condition of the launch as the initial condition, the tank with three different numbers of layers were simulated and analyzed.The liquid-filling ratio of 50% was set.The first contact with the top after the impact was used as a control and the following results were obtained by simulation:  It can be seen that the topping time of tanks with no baffle, 3-layer baffle, 4-layer baffle, and 5-layer baffle increases sequentially, indicating that the baffle has an anti-sloshing effect.The topping time extension of the 5-layer tank is relatively small compared to the 4-layer tank, indicating that the increase of anti-sloshing effect is not obvious.Taking the 4-layer baffle with a 50% filling ratio as an example, the sloshing force on tank's inner wall was analyzed, as shown in figures below: Compared with the smooth tank under the same circumstances, it can be seen that the overall sloshing time becomes shorter, the sloshing force decreases.The damping of tank can be obtained under numerical simulation using equation (12).Meanwhile the damping calculation expression of the ring baffle is given in equation (10), and the damping ratio of different baffles in attachment impact condition can be obtained, and the specific result comparison is as follows: It can be seen from the simulation results that the damping ratio under different filling ratios will change.
The analytical solution of the damping ratio of the tank without baffles is close to the simulated value, which proves that the simulation is credible.Compared with smooth tank, 3-layer baffle can improve the damping ratio by about 4.65 times.The damping ratio in launch condition is relatively larger than that in attachment condition.The dot line diagrams are shown below: The damping ratio of the baffle should theoretically be linearly superimposed with the increase of the number of layers.It can be seen from the simulation results that the damping ratio of the three and four layers is almost three and four times that of the single layer, but the 5-layer baffle does not increase the damping ratio according to this law.The increase of the baffle will increase the mass of the overall structure, so the priority is given to the design of the baffle for 3-layers (layer spacing 40mm) or 4-layers (layer spacing 30mm).Literature [26] concludes that the anti-sloshing effect increases with the increase of the width of the baffle, and gives the following experience formula: and   are the area of the baffle and the area of the free liquid level.The radius of the chamber of the storage tank is known as  = 75mm, so it can be solved that  ≤ 20.39mm.Taking 50% filling ratio as an example, tests were performed to obtain the optimal baffle width.20 Now taking the attachment condition as the initial condition, in which the 3-layer 10mm baffle and 4layer 10mm baffle scheme have been analyzed in the above baffle layer spacing design process and obtained the damping ratio.The remaining four schemes are analyzed now, and the sloshing situation at the same moment is shown in figures below: From the sloshing situation simulation, it can be seen that the anti-sloshing effect of the 3-layer and 4layer baffles increases with the increasing width of the baffle.But the effect increase is not as large as the width increase.Taking the force on the side wall of the tank with 3-layer 15mm baffle as an example, the simulation curve is shown in the figure below:  It can be seen from the comparison that the increase in the number of baffle layers is more suitable for the impact of the launch condition, while the increase of the width of the baffle is more suitable for the attachment condition.Although the mass of the 3-layer 10mm baffle is relatively small, the damping ratio is small as well.The 20mm width scheme has the highest damping ratio, while the mass is correspondingly larger.With the huge increase in baffle width, the 4-layer 15mm baffle is not greatly improved in damping ratio.In summary, the 3-layer 15mm and 4-layer 10mm schemes are more suitable for this design, of which the 3-layer 15mm is more suitable for the impact of the attachment condition, and the 4-layer 10mm is more suitable for the impact of the launch condition.Finally, it is known that 75% filling ratio is in line with the filling situation in the actual project.In order to further verify the effectiveness of the symmetrical ring baffles, in the case of a filling ratio of 75%, the sloshing of the tank without a baffle (left) and the sloshing of the 4-layer 10mm baffle (right) are compared, as shown in figures below: Sloshing conditions with a filling ratio of 75%.It can be seen from the simulation that the sloshing of the tank with the baffle at each moment is significantly weaker than that of the tank without the baffle, which confirms that the symmetrical annular baffle can effectively prevent sloshing, and quickly and effectively suppress the sloshing after the two impacts, ensuring the pointing accuracy of the detumbling payload and the stability of attitude control.

Conclusion
In this paper, the jet detumbling payload propellant tank is taken as the research object.The two impacts when launching and hitting the unstable target are selected as the research conditions.The liquid sloshing characteristic parameters are analyzed by the equivalent kinetic model.The anti-sloshing design is proposed by increasing the sloshing damping.Comparing different anti-sloshing baffle forms, considering the limitations of processing technology and actual working conditions, the symmetrical annular baffle was finally selected as the anti-sloshing baffle form.The parameter design of the baffle is carried out, the control variables of the width and number of layers of the baffle are numerically simulated, and the Fluent simulation conditions are set based on the liquid sloshing mechanism.Finally two baffle design schemes are selected, namely the 3-layer (layer spacing 40mm) 15mm baffle and the 4-layer (layer spacing 30mm) 10mm baffle.The damping ratio of the storage tank with a 3-layer 15mm anti-sloshing baffle is at least 18.3 times that of a smooth tank, and the damping ratio of a storage box with a 4-layer 10mm anti-sloshing baffle is at least 18.7 times that of a smooth tank.The simulation results show that the overall sloshing time of the propellant becomes shorter and the sloshing force decreases after adding the anti-sloshing baffle, which verifies the effectiveness of anti-sloshing baffle.

Figure 1 .
Figure 1.Detumbling payload mission process.The detumbling payload is mainly composed of an attachment mechanism, a control module, Reaction Control System (RCS) thrusters, a launch motor, etc.The structure is shown in figure2.As the core component of the detumbling payload, the cold-gas propulsion system provides a certain range of thrust and sufficient total impulse.

Figure 2 .
Figure 2. Structure of detumbling payload.The payload is launched from a certain distance from the target, which means the pointing accuracy required is especially high.In the process of the payload approaching the unstable target the propellant will be impacted twice, as shown in figure3.The first impact which directly acts on the storage tank is caused by the ignition of the launch motor.The second impact is caused by the attachment mechanism penetrating the unstable target, which causes the speed of the payload drops to zero instantaneously.
6)2.2.2 Design of anti-sloshing baffle.Commonly used anti-sloshing baffles are generally divided into three types: semicircular baffles, radial baffles and symmetrical ring baffles.Semicircular baffle is typically a kind of asymmetric baffle, as shown in figure5.Single-layer or multilayer baffles are set in the tank There exists an angle between the central axis and the liquid sloshing direction.When the angle is bigger than 60°, the baffle doesn't work efficiently.

Figure 5 .
Figure 5. Schematic diagram of a semicircular baffle.The higher damping efficiency of the semicircular baffle requires a larger radius , and the efficiency is not completely positively correlated with the radius.Meanwhile the bearing capacity of the larger semicircular baffle is poor, and the stiffness is much weaker than that of the annular baffle.Usually the empirical value range of radius is 0.2~0.3.The damping ratio of this type of baffle can be calculated with the following empirical formula:

Figure 6 .
Figure 6.Schematic of the radial baffle.For radial baffles, the height of the baffle represents the range it functions.With the number of baffles increases, the anti-sloshing effect will also increase.Meanwhile the mass will increase and the directionality of damping will be effected.In the case of normal filling ratio, the influence of damping caused by different shapes of the tank bottom is usually ignored.The damping ratio of this type of baffle can be calculated with the following empirical formula:

Figure 7 .
Figure 7. Schematic of the symmetrical annular baffles.The distance between the annular baffle and the liquid level is .When  is negative, the baffle exceeds the liquid level.The range of d which makes the baffle effective is −0.1 ≤  ≤ 0.45.Unless there is very little liquid in the storage tank, the anti-sloshing effect of the bottom baffle is not obvious.The distance between the baffles is designed as 0.2 ≤  ≤ 0.4 to make the overall damping of the storage tank relatively uniform.In the primary stage of design, the damping of multi-layer baffles can be approximated as the linear superposition of anti-sloshing damping of multiple single-layer baffles.For the calculation of the damping ratio of symmetrical annular baffles, there is the following empirical formula:

Figure 8 .
Figure 8. Attenuation vibration graph.  and  +1 in the figure are two adjacent vibration amplitudes, and the natural logarithm of the ratio of the two is called the logarithmic attenuation rate.The damping ratio is further solved by the following formula:

Figure 9 .
Figure 9. Storage tank model and meshing.Different filling ratios are set with the internal pressure unchanged.The filling ratio is set to 50%, 75% and 90% to describe the sloshing situation under the two working conditions.

Figure 10 .
(a)Filling ratio 50% (b) Filling ratio 75% (c) Filling ratio 90% Simulation models with different filling ratios.The main design parameters of the ring baffle are the width of the baffle  and the layer spacing .The thickness of the baffle only needs to consider the stress situation inside the tank.Using equation ( (a)3-layer (b)4-layer (c)5-layer Figure 11.The different number of layers baffle in FLUENT.

Figure 12 .
Figure 12.Sloshing conditions first time over the top.As shown in figure12, tank with a 3-layer baffle has an obvious damping effect compared to the smooth tank.The damping effect of the 4-layer baffle is significantly improved compared to the 3-layer baffle.Compared with the 4-layer baffle, the 5-layer baffle does not improve the anti-sloshing effect obviously.The first topping time of the three types of tanks with baffles and tanks without baffles is compared, the specific time is shown in the following table: Table2.First Topping time of tanks with different baffles

Figure 13 .
Figure 13.Sloshing force of tank with 4-layer baffle and no baffle under a filling ratio of 50%.Compared with the smooth tank under the same circumstances, it can be seen that the overall sloshing time becomes shorter, the sloshing force decreases.The damping of tank can be obtained under numerical simulation using equation(12).Meanwhile the damping calculation expression of the ring baffle is given in equation(10), and the damping ratio of different baffles in attachment impact condition can be obtained, and the specific result comparison is as follows:Table3.Damping ratios for different number of layers.

Figure 14 .
Figure 14.Damping ratio of baffles in launch condition and attachment condition.The damping ratio of the baffle should theoretically be linearly superimposed with the increase of the number of layers.It can be seen from the simulation results that the damping ratio of the three and four layers is almost three and four times that of the single layer, but the 5-layer baffle does not increase the damping ratio according to this law.The increase of the baffle will increase the mass of the overall structure, so the priority is given to the design of the baffle for 3-layers (layer spacing 40mm) or 4-layers (layer spacing 30mm).Literature[26] concludes that the anti-sloshing effect increases with the increase of the width of the baffle, and gives the following experience formula:

Figure 16 .
Figure 16.Sidewall shaking power of a 3-layer 15mm baffle storage tank.From this curve, the damping ratio can be calculated.Similarly, the damping ratios of the other schemes in 0can be calculated.Because the density is certain, the volume of the baffle can reflect the weight.The results of each scheme are shown in the following table:

Figure 17 .
Figure 17.Sloshing conditions with a filling ratio of 75%.It can be seen from the simulation that the sloshing of the tank with the baffle at each moment is significantly weaker than that of the tank without the baffle, which confirms that the symmetrical annular baffle can effectively prevent sloshing, and quickly and effectively suppress the sloshing after the two impacts, ensuring the pointing accuracy of the detumbling payload and the stability of attitude control.

Table 1 .
short, it has a huge influence on accuracy.The sloshing of the propellant caused by the attachment impact may cause lateral vibration of the payload, resulting in unstable attitude control.The specific impact values set are shown in the following table: Specific impact condition 9

Table 2 .
First Topping time of tanks with different baffles

Table 3 .
Damping ratios for different number of layers.

Table 5 .
Damping ratio and volume of each scheme.