Experimental study on liquid sloshing of a vane type surface tension tank for satellite

doi:10.21203/rs.3.rs-1727036/v1

Experiment research on liquid sloshing performance of a vane type tank used in high orbit satellite is carried out. The liquid sloshing tests of the tank without propellant management device (PMD) are developed under different liquid filling ratios. Experimental test results are in good agreement with theoretical results, which shows the reliability of test system. Liquid sloshing tests of the tank with PMD are performed with different directions and liquid filling ratios. There has a linear relationship between sloshing frequency and liquid filling ratio of vertical installation test when the liquid-gas interface is in the hemisphere. When the gas-liquid interface is in the cylindrical section, the sloshing frequency of vertical installation test remains basically unchanged. The inverted conical accumulator structure of PMD can increases the damping in the tank of vertical installation. The sloshing mass for vertical direction is less than the result of horizontal direction. Liquid sloshing results of the vane type propellant tank will provide a guidance for the design of spacecraft structure and control system.

Vane type tank

liquid sloshing

sloshing performance

propellant management device

experimental test.

Propellant tank is one of the most important components of spacecraft. It is used to store and manage propellant and provide non air entrained propellant for engine or thruster under the specified flow and acceleration conditions. With the continuous development of aerospace technology, the proportion of liquid fuel mass to the total mass of spacecraft is increasing. At the same time, the requirements for the orbit control and attitude control accuracy of launch vehicle and spacecraft are becoming higher and higher[1]. Therefore, the performance of tank liquid sloshing must be considered in the design of spacecraft structure and control system[2]. The sloshing effects of liquid moving inside propellant tank can significantly affect the GN&C system performance, due to the coupling between fuel and structure dynamics [3].

Theoretical analysis, numerical calculation and experiment are usually used to analyze and study the liquid sloshing characteristics and related parameters of the tank[4, 5]. The attitude and orbit control system of launch vehicle and satellite can be optimized according to the sloshing result[6]. The interaction between the fluid and the tank walls can lead to instability problems and even to mission failure. The combined liquid–structure dynamic coupling is usually extremely difficult to model for a space system[7].

The characteristic parameters of sloshing can be obtained directly by experimental test[8, 9]. The fluids sloshing behaviour within a spherical tank under microgravity conditions is investigated through FLUIDICS experiment carried out in the ISS [10]. The Control of Fluids in Microgravity with Vibrations experiment was carried out to observe the potentially complex behaviour of vibrated liquids in weightless environments[11]. Hu [12] investigated the liquid sloshing of a net-type surface tension tank by experiment, and made a conclusion that the middle partition of tank could reduce liquid sloshing. Lapilli[13] designed of a liquid sloshing experiment to operate in the International Space Station.

Li[14] investigated the dynamic sloshing behavior in a model tank using volume of fluid method. It is concluded that the sloshing behavior could be captured well using the selected dynamic contact angle model. Chiba[15] analyzed the influence of liquid sloshing on the pitching dynamics of flexible space structure with liquid on-board. Colagrossi [16] developed a vibration suppression attitude control system for spacecrafts, with flexible appendages and internal liquid sloshing, undergoing a generic nonprescribed three-dimensional motion subjected to environmental disturbances. Finite volume method and Lattice Boltzmann method were proposed to perform the quick evaluation of liquid slosh behaviour under different container designs[17]. Veldman [18] described a combined theoretical and experimental approach to study the influence of sloshing liquid on the dynamics of spacecraft. There are few studies on liquid sloshing test of large capacity prototype propellant tank of satellite.

A large capacity propellant tank with vane type propellant management device (PMD) is used for the experiment. The liquid sloshing performance of the tank is studied by resonance free attenuation sloshing test method and forced sloshing test method.

The test tank is composed of shell and vane type propellant management device (PMD). The volume of the tank is 880L. The shell is composed of two hemispheres and a cylindrical section. The structure of the vane type tank is shown in Fig. 1.

The PMD of the tank is mainly composed of one accumulator and four uniformly distributed vanes. The inner diameter of the upper hemisphere is 974mm, and the height of column section is 535mm. The internal storage medium volume is 880L.

The test simulation tank shell and the prototype PMD were used in the liquid sloshing test. The tank tested in the experiment was composed of plexiglass inner shell and aluminum alloy frame, as shown in Fig. 2. The inner diameter of the shell was the same as that of the prototype tank, which can meet the observation and shooting requirements of the test. It had sufficient strength and stiffness to ensure the normal progress of the test. The upper hemisphere, cylindrical section and lower hemisphere of the test tank are welded with the vane type PMD as a whole structure.

The installation diagram of vane type tank on the satellite is shown in Fig. 3. The tank is installed along the z-axis of the satellite, and the z-axis of the satellite in the launch state is consistent with the longitudinal axis of the carrier. According to the installation form of PMD in the tank, the included angle between a pair of vanes and X direction is 56.1 °.

The sloshing test system consists of excitation, support, lifting system, test tank, liquid filling and discharge system, measurement system and other subsystems. The push-pull equipment adopts a mechanical eccentric part with a frequency of 0 ~ 5Hz and a thrust of 10kN. The transmission device connects the test piece with the push-pull equipment, including clutch and braking devices. The supporting device can be used for the installation, lifting, weighing and turnover of the test tank. A small water pump is used to fill and discharge liquid in the tank. The filling liquid capacity for various filling ratio are calibrated by a load cell. Displacement measurement is performed by laser displacement sensor. Π type sensor is used to measurement the sloshing force and moment, as shown in Fig. 4.

The test system is shown in Fig. 5. The test supporting device with a height of 4 meters is set up and hanged with 4 pull rods which connects the load cell in the middle of the pull rod to measure the liquid filling ratio of the tank. The rectangular structure is a supporting beam, which is arranged along the sloshing direction. The spacing for the rectangular structure can be adjusted. Π Type sensors are installed in the middle of the beam and used to fix the test tank. When the test tank is installed vertically, the liquid sloshing direction is horizontal (X direction), as shown in Fig. 5. When the tank is installed horizontally (θ = 0), the horizontal sloshing of the liquid is in the X direction and the longitudinal direction is in the Z direction. The front cross beam of rectangular structure is connected with the driving rod of the push-pull equipment to transmit the horizontal movement, and the clutch braking device is connected in series in the middle of the driving rod. The rear cross beam of the rectangular structure is connected with the laser displacement sensor to measure the horizontal movement of the test tank. Since the tank is an axial symmetrical structure, the sloshing results in X and Y directions are consistent.

The installation and excitation application direction of sloshing test are shown in Fig. 6.

Sloshing tests of the tank were carried out at the condition of constant ground gravity (1g_o). Liquid sloshing parameters of the tank required for the design of attitude and orbit control system during launch, satellite apogee orbit change and position maintenance are obtained, including sloshing frequency, sloshing mass and sloshing damping at various working conditions. The above data are transformed into an equivalent pendulum model and the corresponding parameters are obtained. The sloshing force and sloshing torque can be tested by Π type sensors. The other parameters are fitted by free attenuation test and forced sloshing test. The free attenuation test is to obtain the sloshing frequency, sloshing center of mass height and sloshing damping value. The forced sloshing test can obtain the sloshing mass and the total mass centroid height. The height sloshing center of mass height is the distance from the center of mass to the bottom of the tank.

Experimental information for sloshing test is shown in Table 1.

Table 1

Experimental information
No.	Experimental subject	Installation direction	Excitation direction	Test methods	Number of experiments
1	Tank without PMD	vertical	X	forced sloshing test	24
3	Tank with PMD	horizontal	X	forced sloshing test	104
3		horizontal	X	resonance attenuation sloshing test	78
4		horizontal	Z	forced sloshing test	32
4			Z	resonance attenuation sloshing test	24
5			X	forced sloshing test	32
5			X	resonance attenuation sloshing test	24

During the forced sloshing test, the positioning displacement excitation was adopted. The sloshing equipment was started, and the vibration frequency was adjusted. After the movement was stable, the time history of sloshing displacement, force and torque of the test tank was recorded. More than 50 vibration cycles were recorded for each test. According to the recorded time history data, the amplitude, phase and frequency of displacement, force and torque could be calculated. The value of frequency response function could be estimated. After changing the vibration frequency, the recording process was repeated until tests of all frequencies were completed. The test frequency shall covered 0.5 ~ 2 times the first-order sloshing frequency.

During the resonance attenuation sloshing test, the vibration frequency of the sloshing equipment was set up with the liquid resonance frequency. The rectangular structure was lock after the sloshing amplitude reached a certain range. the time history data of the sloshing force was recorded to calculate the sloshing damping coefficient and sloshing frequency. Each test repeated for 6 ~ 8 times.

The appropriate test medium for liquid sloshing test is selected according to the analysis of similarity criteria and similar conditions. In order to simulate the conditions of launch, satellite apogee ignition and position maintenance, the sloshing tests of the tank in X, Y and Z directions were performed. The acceleration generated by satellite remote ignition was about 0.06 ~ 0.12m/s², and the acceleration under east-west and North-South maintenance conditions was about 0.0045 ~ 0.009m/s².

In order to reduce the measurement error caused by temperature change, it was required to measure the specific gravity of the test medium (ρ) and viscosity coefficient (ν). The Galileo number of the test medium before each test should be calibrated. According to the requirements of similar criteria, the mixture of 60% glycerol and water was used as the test liquid.

Liquid sloshing test was carried out under 14 working conditions of liquid filling ratio. As shown in Table 2, tests with selected working conditions were carried out under the vertical installation state and horizontal installation state of the test tank. Weights of liquid in tank under different liquid filling ratios are shown in Table 2.

Table 2

Weights of liquid in tank under different liquid filling ratios
No.	Filling ratio	Propellant weight of fuel tank (kg)	Propellant weight of oxidant tank (kg)
1.	0.95	731.33	1209.05
2.	0.90	692.84	1145.42
3.	0.85	654.35	1081.78
4.	0.77	592.77	979.97
5.	0.75	577.36	954.51
6.	0.70	538.87	890.88
7.	0.65	500.39	827.24
8.	0.60	461.90	763.61
9.	0.45	346.42	572.71
10.	0.30	230.95	381.80
11.	0.25	192.46	318.17
12.	0.20	153.96	254.54
13.	0.15	115.47	190.90
14.	0.10	76.98	127.27

4.1 Relationship between viscosity and temperature of test medium

Before the sloshing test, the temperature and kinematic viscosity of 60% glycerol and water mixture is measured. According to the measurement results, the relationship between kinematic viscosity and temperature of 60% glycerol and water mixture can be obtained, as shown in Fig. 7. The linear fitting formula is shown as follows,

y=-0.04768x + 21.96

During the test, the coverage range of liquid temperature is 8.9 ℃~29.7 ℃, and the corresponding liquid kinematic viscosity range is 9.09 ~ 18.7 mm²/s. The kinematic viscosity of glycerol solution decreases with the increase of liquid temperature, which conforms to the theoretical law.

4.2 X direction sloshing on vertically installation without PMD

Sloshing tests of tank vertically installation without PMD was carried out to verify the test system. The liquid filling ratios were 0.2, 0.45 and 0.77, respectively. Comparisons between the sloshing frequency of experimental result (F_se) and theoretical value (F_te) are shown in Fig. 8. Results of the fitted total mass(M_f), the weighed total mass(M_w), the sloshing mass of experiential result (M_se) and the sloshing mass of theoretical value(M_st) are shown in Fig. 9.

The test results show that the maximum error of sloshing frequency is 2.58% when the filling ratio is 0.77. The minimum error sloshing frequency is 0.53% when the filling ratio is 0.45. The maximum error of sloshing mass is 6.44% when the filling ratio is 0.77, and the minimum error of sloshing mass is 2.14% when the filling ratio is 0.45. The maximum error between the fitted total mass and the weighed total mass is 5.55% when the filling ratio is 0.2, and the minimum error is 0.99% when the filling ratio is 0.77. The system error meets the test requirements.

4.3 X direction sloshing on vertically installation with PMD

X direction sloshing test of the tank with PMD on vertically installation are carried out. The relationship between sloshing frequency and liquid filling ratio is shown in Fig. 20. The sloshing frequency increases approximately linearly from 0.1 to 0.3. The filling ratio increases slowly from 0.3 to 0.6. From 0.6 to 0.77, the filling ratio is basically unchanged. The filling ratio increases rapidly from 0.77 to 0.95. The liquid-gas interface with filling ratio from 0.1 to 0.3 is in the bottom hemisphere of the tank, so the frequency has a linear relationship with filling ratio. The liquid-gas interface with filling ratio from 0.3 to 0.77 is in the part of the column section, so the frequency increases slowly due to the same liquid level condition. The frequency is basically unchanged when the liquid-gas interface filling ratio from 0.6 to 0.77. The liquid-gas interface with filling ratio from 0.77 to 0.95 is in upper hemisphere, so the frequency increases rapidly. There has a linear relationship between sloshing frequency and liquid filling ratio when the liquid-gas interface is in the hemisphere. When the gas-liquid interface is in the cylindrical section, the sloshing frequency remains basically unchanged.

Curve of damping with liquid filling ratio is shown in Fig. 11. The damping decreases rapidly with liquid filling ratio from 0.1 to 0.3. The main reason is that the inverted conical accumulator structure of PMD increases the damping in the tank. When the liquid filling ratio is from 0.3 to 0.9, the damping is basically stable between 0.36% ~ 0.43%. When the liquid filling ratio is from 0.9 to 0.95, the damping increases slightly. It can be seen that the effect of accumulator on damping is still obvious when the liquid-gas interface is in the bottom hemisphere. At medium and high liquid filling ratio, the influence of four vanes of PMD is not obvious. At the high liquid filling ratio when the liquid-gas interface is in the upper hemisphere, the structure of four vanes increases the resistance slightly, which is due to the four vanes are concave and tending to be more and more horizontal.

Curves of pendulum point height and sloshing center of mass with different filling ratios are shown in Fig. 12. The height of the pendulum point decreases slightly from 0.1 to 0.3, then rises continuously from 0.3 to 0.77, and rises slowly from 0.77 to 0.95. The height of sloshing center of mass increases approximately linearly from 0.1 to 0.95. The difference between the height of the pendulum point and the height of the sloshing center of mass (i.e. the pendulum length) decreases first, then basically remains unchanged, and then decreases rapidly, which can correspond to the change trend of frequency.

Curves of sloshing mass(M_s) and M_w with different liquid filling ratios are shown in Fig. 13. Curves of M_f and the M_w with the liquid filling ratio have good consistency. The relative error of all tested liquid filling ratios is in the range of 1.41% ~ 7.48%. The sloshing mass increases with the increase of liquid filling ratio from 0.1 to 0.3. From 0.3 to 0.85, the sloshing mass is basically unchanged and fluctuates slightly. From 0.85 to 0.95, the sloshing mass decreases significantly. When the liquid filling ratio is 0.75, the sloshing mass is the largest.

Curve of sloshing mass ratio(M_s/M_w) with liquid filling ratio is shown in Fig. 24. In general, the proportion of sloshing mass decreases with the increase of liquid filling ratio. When the liquid filling ratio is 0.15, the proportion of sloshing mass is the largest, which is 70.14%.

4.4 Z direction sloshing on horizontal installation with PMD

The horizontal sloshing of the tank occurs in the process of attitude control, after the satellite enters orbit. The residual fuel in the tank is almost less than 30% of the whole capacity, so filling ratios including 0.1, 0.15, 0,20 and 0.25 are chosen for the horizontal sloshing test.

Z direction sloshing results on horizontal installation with PMD are shown in Fig. 15 and Fig. 16. The sloshing frequency increases approximately linearly with the increase of liquid filling ratio. Sloshing damping decreases with the increase of liquid filling ratio. The height of sloshing center of mass increases with the increase of liquid filling ratio. The M_s has a linearly relationship with the liquid filling ratio. Liquid-gas interfaces of the four filling ratios are in the bottom of the tank, the area of liquid-gas interface is large than the value of vertical installation. M_s and M_s/M_w are both larger than values of vertical installation.

4.5 X direction sloshing on horizontal installation with PMD

The horizontal sloshing of the tank occurs in the process of attitude control, after the satellite enters orbit. The residual fuel in the tank is almost less than 30% of the whole capacity, so filling ratios including 0.1, 0.15, 0,20 and 0.25 are chosen for the horizontal sloshing test.

X direction sloshing results on horizontal installation with PMD are shown in Fig. 17 and Fig. 18. The sloshing frequency has a relationship with the increase of filling ratio. Sloshing damping decreases with the increase of liquid filling ratio. The height of sloshing point changes little with the increase of liquid filling ratio. The height of sloshing center of mass increases slightly with the increase of liquid filling ratio. The sloshing mass increases with the increase of liquid filling ratio. The proportion of sloshing mass decreases with the increase of liquid filling ratio.

The sloshing frequency increases with the increase of liquid filling ratio. Sloshing damping decreases with the increase of liquid filling ratio. The height of pendulum point changes little with the increase of liquid filling ratio. The height of sloshing center of mass increases slightly with the increase of liquid filling ratio.

The sloshing mass increases with the increase of liquid filling ratio. Since the storage tank is placed obliquely in the horizontal direction, when shaking in the X direction, it is asymmetric along the shaking direction, so the error between the fitted total mass and the weighed total mass is relatively large, so the total mass of the shaking mass is calculated according to the weighed total mass. The proportion of sloshing mass decreases with the increase of liquid filling ratio.

Sloshing characteristic of a new vane type propellant tank is experimentally studied. The liquid sloshing performance of the tank is investigated by resonance free attenuation sloshing test method and forced sloshing test method. When there is no PMD in the tank, the maximum error of sloshing frequency is 2.58% compared with the theoretical value. The maximum error of shaking mass is 6.44%. The maximum error between the M_f and the M_w is 5.55%. The test result of the system are in good agreement with theoretical result. There has a linear relationship between sloshing frequency and liquid filling ratio of vertical installation test when the liquid-gas interface is in the hemisphere. When the gas-liquid interface is in the cylindrical section, the sloshing frequency of vertical installation test remains basically unchanged. The inverted conical accumulator structure of PMD can increases the damping in the tank of vertical installation. When the liquid filling ratio is large than 0.3, the sloshing damping of vertical installation test remains basically unchanged. The M_s has a linearly relationship with the liquid filling ratio when the filling ratio is less than 0.3. The proportion of sloshing mass has a linear relationship with filling ratio. The sloshing mass for vertical direction is less than the result of horizontal direction. Liquid sloshing results of the vane type propellant tank will provide a guidance for the design of spacecraft structure and control system.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 52176034).

Availability of data and material

The data of this article can be obtained by contacting the corresponding author .

Authors' contributions

Jintao Liu and Yong Li offered support and guidance. Wen Li, Kun Cai and Lei Chen carried out the experiments. Jintao Liu, Zhen Qu and Nanji Yang wrote the manuscript text.

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Fries, N., Behruzi, P., Arndt, T., Winter, M., Netter, G.: Modelling of fluid motion in spacecraft propellant tanks-sloshing. In: Space Propulsion 2012 Conference Proceedings, Bordeaux, France, May 7–10 (2012)
Chiba, M., & Magata, H.. (2017). Influence of liquid sloshing on dynamics of flexible space structures. Journal of Sound Vibration, 401, 1–22.
de Souza, A.G., de Souza, L.C.G.: Satellite attitude control system design taking into account the fuel slosh and fexible dynamics. Math. Probl. Eng. 2014, 820586 (2014).
Zheng, Jh., Xue, MA., Dou, P. et al. A review on liquid sloshing hydrodynamics. J Hydrodyn 33, 1089–1104 (2021).
Schröck, J., Wenninger, J., Karer, E., Eitzlmayr, A. (2022). Modeling, Simulation, and Experimental Analysis of Liquid Sloshing Dynamics. Springer.
Fries, N., Behruzi, P., Arndt, T., Winter, M., Netter, G.: Modelling of fuid motion in spacecraft propellant tanks—sloshing. In: Space Propulsion 2012 Conference Proceedings, Bordeaux, France, May 7–10 (2012)
Angeletti, F., Stolfi, A. & Gasbarri, P. Learning-based Control of a Spacecraft with Sloshing Propellant. Aerotec. Missili Spaz. 99, 33–42 (2020).
Chintalapati, S., Holicker, C, Schulman, R., Contreras, E., Gutierrez, H, and Kirk, D., “Design of an Experimental Platform for Acquisition of Liquid Slosh Data aboard the International Space Station”, 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA 2012–4297, 30 July – 01 August 2012, Atlanta, GA
Chintalapati, S., Holicker, C, Schulman, Wise, B., Lapilli, G., Gutierrez, H, and Kirk, D. “Update on SPHERES Slosh for Acquisition of Liquid Slosh Data aboard the ISS”, 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA 2013–3903, July 14–17, 2013, San Jose, CA
Dalmon, A., Lepilliez, M., Tanguy, S. et al. Comparison Between the FLUIDICS Experiment and Direct Numerical Simulations of Fluid Sloshing in Spherical Tanks Under Microgravity Conditions. Microgravity Sci. Technol. 31, 123–138 (2019).
Fernandez, J., Sánchez, P.S., Tinao, I. et al. The CFVib Experiment: Control of Fluids in Microgravity with Vibrations. Microgravity Sci. Technol. 29, 351–364 (2017).
Hu. Q., Li. Y., Yao, C., & Liu, J.. (2016). Experiment of liquid sloshing performance in bulky propellant tank. Aerospace Control and Application. 42(3):44–48.
Lapilli, G. Design of a liquid sloshing experiment to operate in the International Space Station. 51st AIAA/SAE/ASEE Joint Propulsion Conference. July 27–29, 2015, Orlando, FL.
Li, JC., Lin, H., Li, K. et al. Dynamic Behavior in a Storage Tank in Reduced Gravity Using Dynamic Contact Angle Method. Microgravity Sci. Technol. 32, 1039–1048 (2020).
Chiba, M., & Magata, H.. (2020). Coupled pitching dynamics of flexible space structures with on-board liquid sloshing. Acta Astronautica. 181, 151–166 (2021).
Colagrossi, A., Lavagna, M. Integrated vibration suppression attitude control for flexible spacecrafts with internal liquid sloshing. Multibody Syst Dyn 51, 123–157 (2021).
Yang C., Niu R., Zhang P. Numerical analyses of liquid slosh by finite volume and lattice boltzmann methods [J]. Aerospace Science and Technology, 2021, 113: 106681.
Veldman, A., Gerrits, J., Luppes, R., Helder, J. A., & Vreeburg, J.. (2007). The numerical simulation of liquid sloshing on board spacecraft. Journal of Computational Physics, 224(1), 82–99.

No competing interests reported.

Experimental study on liquid sloshing of a vane type surface tension tank for satellite

Status:

Version 1

Abstract

Figures

1 Introduction

2 Structure Of Test Tank

3 Test System And Test Method

4 Test Results

4.1 Relationship between viscosity and temperature of test medium

4.2 X direction sloshing on vertically installation without PMD

4.3 X direction sloshing on vertically installation with PMD

4.4 Z direction sloshing on horizontal installation with PMD

4.5 X direction sloshing on horizontal installation with PMD

5 Conclusions

Declarations

Conflicts of Interest

Acknowledgments

Availability of data and material

Authors' contributions

Ethics approval

Consent to participate

Consent for publication

References

Additional Declarations

Status:

Version 1