Numerical simulation and experiment of a blade management device in microgravity

Currently, most satellite propulsion systems are mainly chemical propulsion, and liquid propellant is the necessary power fuel for the propulsion system. The working environment of microgravity occurs when the satellite is in orbit. According to the working characteristics of the satellite, a propellant management device of vane type is designed. The PMD is composed of a vertical guide plate and a liquid accumulator, which is applied to the propellant tank to store and manage the propellant. In this paper, the microgravity gas-liquid management and control mechanism of a propellant management device of vane type is studied by numerical simulation and tower drop test. The results of numerical simulation and tower drop test are consistent, which verifies the good fluid management characteristics of this type of propellant management device, and provides references for its engineering application and the design of this type of structure.


Introduction
Currently, most satellite propulsion systems are mainly chemical propulsion, and liquid propellant is the necessary power fuel for the propulsion system [1]- [2].The working environment of microgravity occurs when the satellite is in orbit.In a microgravity environment, the effect of gravity disappears, and secondary forces such as liquid surface tension and cohesion dominate.The fluid behavior in a microgravity environment significantly differs from the ground's.The propellant and gas inside the satellite tank are mixed.Therefore, it is necessary to set up a propellant management device in the tank to manage the propellant in microgravity.Most of the tank in the satellite is the surface tension tank [3][4][5].Surface tension tanks are divided into mesh type and vane type, which use surface tension to separate the gas and liquid.At present, the research on liquid behavior in the tank is often carried out using numerical simulation or falling tower test [6]- [7].In this paper, a propellant management device of vane type is designed.The PMD is composed of a vertical guide plate and a liquid accumulator, which is applied to the propellant tank to store and manage the propellant.In order to study the fluid management behavior in a microgravity environment, two flow models of VOF is used to numerically simulate the liquid behavior of the tank in the different microgravity environment.Tower drop tests were carried out.The combination of numerical simulation and tower drop tests verified the good fluid management characteristics [8]- [10].The reference is provided for its engineering application and the design of this kind of structure.

Mechanism of surface tension
Solids, liquids, and gases produce capillarity on their contact surfaces.Due to the interaction between the various molecules in the contact phase, a resultant force at the interface between the liquid and the gas points to the inside of the liquid, which is the surface tension.The balance between the pressure and the surface tension of the fluid determines the surface configuration of the liquid, and the liquid surface shows a tendency to shrink the surface area.In microgravity, the free liquid surface will appear and maintain a large area of curved equilibrium interface.The influencing factors between gravity and surface tension can be measured by the static Bond number, which is defined as follows: Δρ is the density difference between gas and liquid, L is the characteristic scale, and σ is the surface tension.Bo is the ratio of hydrostatic pressure to capillary pressure.When Bo≪1, it indicates that surface tension dominates and gravity is negligible.The principle of capillary flow driving in the vane type tank in microgravity is shown in figure 1. Due to the effect of surface tension, a liquid zone with curvature will be formed at the intersection of the blade and the wall of the tank.The Laplace's formula is: R1 and R2 are the radii of curvature of the liquid zone.For a cross-section, it can be considered a cylinder, i.e.R2=∞.The pressure gradient generated by the different curvature radius of the liquid zone.The calculation formula of capillary driving force is: The capillary drive force and static pressure balance in the ground gravity environment.When gravity disappears, the pressure gradient drives the fluid up the inside Angle or gap between the blade and the tank wall.

The model of the tank
In this paper, the tank's volume is 884L, with an internal diameter of 1126mm as the research object.
The model of the tank is shown in Figure 2. The PMD is composed of four vertical deflectors and a closed accumulator.

Calculation model
In ICEM, a hexahedral structured grid calculates the tank's domain discretely.For the area of the tank and deflector, there are four plates, and the grid is divided by 1/4 periodic basins.For the accumulator area, there are 24 small blades, and a 1/24 periodic basin is used for grid division.The global model of the periodic basin is an array, and the number of grids in the calculation model of the whole tank was 6 million, as shown in Figure 3.In numerical calculations, the liquid is set to NTO, with a density of 1444 kg/m 3 (20°C) and a viscosity coefficient of 4.2×10 -4 Pa.S.The gas is set to helium, with a density of 0.1625 kg/m 3 (20°C) and a viscosity coefficient of 1.99×10 -5 Pa.S.The coefficient of surface tension is 26 dyn/cm.In this paper, the process of liquid relocation in the tank is numerically simulated under the filling ratio of 5%, 25%, 45%, and 60%.The acceleration environment is 1x 10 -5 g(-Y).

Result of the simulation
The initial interface of gas-liquid with different filling ratios is shown in Figure 4, where the gas is blue, and the liquid is red.

5% 25%
45% 60% The relocation interface of gas-liquid with different filling ratios is shown in Figure 5.
5% 25% 45% 60% Figure 5.The relocation interface of gas-liquid.The cloud image of gas-liquid shows no mixing between gas and liquid in the repositioning process.When the gas-liquid interface is stable, the liquid is stored around the accumulator and the blade.The air is in the middle of the tank.These indicate that the plate management structure can effectively manage and transport propellants in microgravity.

The model of the test
In the experiment, the scale model of the tank, whose volume is 884L, is used.The scaling ratio was 1:10, which could ensure that the repositioning time of the scale model is not greater than the microgravity time provided by the falling tower.The microgravity time provided by the falling tower is 3.5s.The inner diameter of the scale model is 112.6mm, and the inner volume is 880mL.The model is made of PMMA, which is a transparent material.The scale model is shown in Figure 6.

Result of the test
The initial and relocation interface of gas-liquid in the tower drop test are shown in Figure 7 when the filling ratio is 5%.Seeing from these figures, the liquid quickly rises along the blade in the microgravity environment.When the liquid passes the top of the blade, the liquid forms a stable liquid surface configuration, and the relocation is completed.Gas and liquid are not mixed, and the liquid is stored around the accumulator and the blade.When the filling rate is 60%, the liquid cannot pass the top of the blade, and the liquid rises a short distance along the inner wall of the tank.

Conclusion
In this paper, the VOF two-phase flow model is used to simulate the fluid behavior in the tank under a microgravity environment and the flow characteristics of the propellant during the filling process.The distribution law of the fluid is obtained.A test system of scale model is built to test the fluid behavior of the vane-type tank in the microgravity environment.The flow characteristics of the tank in a microgravity environment are obtained.The numerical simulation and tower drop test results are in good agreement, indicating that the plate structure device has good fluid management performance in the microgravity environment, and the gas-liquid interface separation in the tank is stable and precise.The results can provide references for its engineering application and the design of this type of structure.

Figure 1 .
Figure 1.The liquid climbs along the blade in microgravity.The principle of capillary flow driving in the vane type tank in microgravity is shown in figure1.Due to the effect of surface tension, a liquid zone with curvature will be formed at the intersection of the blade and the wall of the tank.The Laplace's formula is:

Figure 2 .
Figure 2. The model of the tank.

Figure 3 .
Figure 3.The mesh of the tank.In numerical calculations, the liquid is set to NTO, with a density of 1444 kg/m 3 (20°C) and a viscosity coefficient of 4.2×10 -4 Pa.S.The gas is set to helium, with a density of 0.1625 kg/m 3 (20°C) and a viscosity coefficient of 1.99×10 -5 Pa.S.The coefficient of surface tension is 26 dyn/cm.In this paper, the process of liquid relocation in the tank is numerically simulated under the filling ratio of 5%, 25%, 45%, and 60%.The acceleration environment is 1x 10 -5 g(-Y).

Figure 4 .
Figure 4.The initial interface of gas-liquid.

Figure 7 .
Figure 7.The initial and relocation interface when the filling ratio is 5%.The initial and relocation interface are shown in Figure 8 when the filling ratio is 25%.

Figure 8 .
Figure8.The initial and relocation interface when the filling ratio is 25%.The initial and relocation interface are shown in Figure9when the filling ratio is 45%.

Figure 9 .
Figure9.The initial and relocation interface when the filling ratio is 45%.The initial and relocation interface are shown in Figure10when the filling ratio is 60%.

Figure 10 .
Figure10.The initial and relocation interface when the filling ratio is 45%.Seeing from these figures, the liquid quickly rises along the blade in the microgravity environment.When the liquid passes the top of the blade, the liquid forms a stable liquid surface configuration, and the relocation is completed.Gas and liquid are not mixed, and the liquid is stored around the accumulator and the blade.When the filling rate is 60%, the liquid cannot pass the top of the blade, and the liquid rises a short distance along the inner wall of the tank.