Method for analyzing mass center offset of high-orbit satellite gas cylinder under action of external heat flow

Abstract

The invention belongs to the technical field of satellite structure thermal control, and particularly discloses a high-orbit satellite gas cylinder mass center offset analysis method under the action of external heat flux, which comprises the following steps: S1, based on known satellite orbit parameters, calculating a satellite solar incident angle, a rotation angle of a satellite relative to an initial point in an orbit and a deviation angle of a meeting day point; s2, based on the heat radiation and heat conduction theory, calculating the external heat flow and the temperature change condition of each surface of the hexahedral square satellite; and S3, based on the Van der Waals gas theory, analyzing the temperature and gas pressure in the gas cylinder and the change condition of the mass center position between the gas cylinders at each moment. The method has the beneficial effects that the change condition of the mass center between the gas cylinders in the satellite can be obtained in advance through computer simulation, so that whether the change affects the high-precision requirement during the working period of the satellite or not is analyzed, and the cost of an actual satellite experiment is greatly saved.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite structure thermal control, and in particular relates to a method for analyzing the center of mass deviation of a high-orbit satellite gas cylinder under the action of an external heat flow. Background Art

[0002] With the development of micro-electromechanical (MEMS) technology, microsatellites are gaining increasing attention. In the communications sector, low-orbit internet constellation projects like Starlink and OneWeb are booming, providing high-speed internet services to users around the world. In remote sensing, microsatellites can carry optical and radar remote sensing equipment for Earth resource exploration, environmental monitoring, and disaster warning. In scientific exploration, microsatellites can detect space environmental parameters such as radiation, magnetic fields, and plasma, providing data support for space science research.

[0003] Due to the short orbital period of low-orbit satellites, the corresponding space thermal environment research has been simplified accordingly. However, for high-orbit scientific satellites using cold gas micropropulsion systems, it is necessary to consider the changes in the center of mass position of the satellite's internal gas cylinder caused by temperature differences. Existing methods have the following problems: 1. Due to the long orbital period of high-orbit deep-space exploration satellites, existing methods ignore the deviation angle of the heliocentric point, resulting in large errors in the calculation of external heat flux; 2. Existing methods calculate external heat flux by treating the satellite's outer shell as a whole, ignoring the heat exchange caused by actual temperature differences between the satellite's various surfaces, making it impossible to accurately calculate the changes in the center of mass position of the internal gas cylinder.

[0004] Therefore, there is an urgent need for an efficient and high-precision analysis method for the changes in the center of mass position of symmetrically placed gas cylinders on high-orbit satellites. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention proposes a method for analyzing the center of mass offset of high-orbit satellite gas cylinders under the action of external heat flux. The change of the solar point angle is introduced into the calculation of the external heat flux on the satellite surface, and the heat conduction and heat radiation between different surfaces and between the surface and the internal gas cylinders are taken into account, and the changes in the center of mass position of symmetrically placed gas cylinders are accurately calculated.

[0006] The method for analyzing the center of mass deviation of a high-orbit satellite gas cylinder under the action of an external heat flow of the present invention comprises the following steps:

[0007] S1. Based on the known satellite orbit parameters, calculate the satellite solar incidence angle, the satellite's rotation angle relative to the initial point in orbit, and the deviation angle of the heliocentric point. Using the cosine formula of spherical trigonometry in the geocentric equatorial coordinate system, the expression for the satellite solar incidence angle β is:

[0008] sinβ=cosisinδ s +sinicosδ s sinΔα

[0009] Where i represents the orbital inclination, δ s is the solar declination, Δα is the difference between the orbital plane and the solar right ascension;

[0010] The expression of the satellite's rotation angle γ relative to the initial point in orbit is:

[0011]

[0012] Among them, t represents the moment of the satellite’s current orbital position, t start is the time of the satellite's initial position, τ orbit is the satellite orbit period, and “\” is the remainder symbol;

[0013] The expression of the deviation angle θ of the conjunction point is:

[0014]

[0015] Among them, τ earth is the Earth's revolution period, which is 365 days;

[0016] S2. Based on the theory of thermal radiation and heat conduction, the external heat flux and temperature change of each surface of the hexahedral square satellite are calculated. The surface is defined by the satellite coordinate system as +X, -X, +Y, -Y, +Z, -Z, where the +Z axis points to the center of the earth and the -X axis points to the direction of movement. The solar radiation q1 received by each surface is

[0017]

[0018] Where S is the solar constant, which is 1367W / m 2 , is the angle between the normal of each surface and the sunlight, and the As follows: +X surface is -sin(γ+θ)cosβ; -X surface is sin(γ+θ)cosβ; +Y surface is -sinβ; -Y surface is sinβ; +Z surface is -cos(γ-θ)cosβ; -Z surface is cos(γ-θ)cosβ;

[0019] The Earth's reflected radiation q2 received by each surface is

[0020] q2=XSρcosω

[0021] Where X is the radiation angle coefficient of the surface to the earth, ρ is the earth's albedo, which is taken as 0.3, and ω is the angle between the satellite's center and the sun's rays;

[0022] The X size of each surface of the satellite is different. For the +Z surface, the angular coefficient is

[0023]

[0024] Among them, R E is the radius of the Earth, which is 6378.14 km, and a is the semi-major axis of the orbit. For the -Z plane, since it faces away from the Earth, the angular coefficient is 0. For other surfaces, which are perpendicular to the Earth's surface, the angular coefficients are

[0025]

[0026] in,

[0027] The earth's thermal radiation q3 received by each surface is

[0028] q3=XE i0

[0029] Among them, E i0 is the average infrared radiation heat flux density of the earth, which is taken as 239.2W / m 2 ;

[0030] Based on this, the magnitude of the external heat flux absorbed by a certain surface of the satellite is:

[0031] q=α s (q1+q2)+εq3

[0032] Among them, α s is the surface absorptivity of solar radiation, and ε is the surface emissivity;

[0033] S3. Based on the van der Waals gas theory, analyze the changes in the temperature, pressure, and center of mass position of the gas cylinders at each moment. The van der Waals gas theory is expressed as:

[0034]

[0035] Where T, p, and V represent the temperature, pressure, and volume of the actual gas, respectively. g is the gas constant, R g =8.314 J / (mol·K), n is the amount of gas substance, a and b are the Van der Waals corrections introduced to take into account the gravitational force between Van der Waals gas molecules and the definite volume occupied by molecules. Taking nitrogen as an example, α = 0.137 J·m 3 / mol 2 , b=3.86×10 -5 m 3 / mol;

[0036] The volume flow rate between the two cylinders is:

[0037]

[0038] Where γ is the gas specific heat ratio, nitrogen is a diatomic molecule, and γ = 1.4, C d is the flow coefficient, take C d =0.5, A is the outlet cross-sectional area, subscripts us and ds represent upstream and downstream respectively;

[0039] Use the center of mass formula to calculate the change in center of mass position between cylinder 1 and cylinder 2:

[0040]

[0041] Where n0 is the sum of the amounts of gas in the two symmetrical gas cylinders, and n1 and n2 are the amounts of gas in gas cylinder 1 and gas cylinder 2 at different times.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The offset analysis method of the present invention effectively solves the problem of external heat flux calculation errors caused by the long period of high-orbit satellites. By considering heat conduction and heat radiation between different surfaces and between the surface and the internal gas cylinder, transient analysis of the temperature and pressure inside the gas cylinder at different times is performed, and the changes in the center of mass position between symmetrical gas cylinders are calculated. This significantly improves the accuracy of the analysis results and provides an intuitive reference basis for the improvement of satellite thermal control structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments.

[0045] Figure 1 Schematic diagram of the overall steps of the analysis method in the embodiment.

[0046] Figure 2 Graph showing the change of the solar incident angle β during operation in the embodiment.

[0047] Figure 3 Graph showing changes in solar radiation heat flux q1 on each surface in the embodiment.

[0048] Figure 4 Graph showing changes in the Earth's reflected heat flux q2 at various surfaces in the embodiment.

[0049] Figure 5 Graph showing changes in the Earth's reflected heat flux q3 at various surfaces in the embodiment.

[0050] Figure 6 Schematic diagram of the layout of high-pressure gas cylinders on the satellite in the embodiment.

[0051] Figure 7 This is a three-dimensional modeling diagram of the satellite structure in the embodiment.

[0052] Figure 8Graph showing the temperature changes of various surfaces in the examples.

[0053] Figure 9 Graph showing temperature changes of two gas cylinders in the embodiment.

[0054] Figure 10 Graph showing the changes in gas pressure in the two gas cylinders in the embodiment.

[0055] Figure 11 Graph showing the amount of material in the two gas cylinders in the embodiment.

[0056] Figure 12 Graph showing the change in gas volume flow between the two gas cylinders in the embodiment.

[0057] Figure 13 Graph showing the change in center of mass position between the two gas cylinders in the embodiment. DETAILED DESCRIPTION

[0058] The following is a further description of the specific embodiments of the present invention. It should be noted that the description of these embodiments is used to help understand the present invention, but does not constitute a limitation of the present invention.

[0059] Example 1

[0060] See Figure 1 The method for analyzing the center of mass deviation of a high-orbit satellite gas cylinder under the action of an external heat flow comprises the following steps:

[0061] S1. Based on the known satellite orbit parameters, calculate the satellite's solar incidence angle, the satellite's rotation angle relative to the initial point in orbit, and the deviation angle of the heliocentric point. Using the cosine formula of spherical trigonometry in the geocentric equatorial coordinate system, the expression for the satellite's solar incidence angle β can be obtained as:

[0062] sinβ=cosisinδ s +sinicosδ s sinΔα

[0063] Where i represents the orbital inclination, δ s is the solar declination, and Δα is the difference between the orbital plane and the solar right ascension.

[0064] The expression of the satellite's rotation angle γ relative to the initial point in orbit is:

[0065]

[0066] Among them, t represents the moment of the satellite’s current orbital position, t start is the time of the satellite's initial position, τ orbit is the satellite orbit period, and “\” is the remainder symbol.

[0067] The expression of the deviation angle θ of the conjunction point is:

[0068]

[0069] Among them, τ earth is the Earth's revolution period, which is 365 days.

[0070] S2. Based on the theory of thermal radiation and heat conduction, calculate the external heat flux and temperature changes on each surface of the hexahedral square satellite. The surfaces are defined in the satellite coordinate system as +X, -X, +Y, -Y, +Z, and -Z, where the +Z axis points to the center of the earth and the -X axis points to the direction of motion. The solar radiation q1 received by each surface is

[0071]

[0072] Where S is the solar constant, which is 1367W / m 2 , is the angle between the normal of each surface and the sunlight. As follows: +X surface is -sin(γ+θ)cosβ; -X surface is sin(γ+θ)cosβ; +Y surface is -sinβ; -Y surface is sinβ; +Z surface is -cos(γ-θ)cosβ; -Z surface is cos(γ-θ)cosβ;

[0073] The Earth's reflected radiation q2 received by each surface is

[0074] q2=XSρcosω

[0075] Among them, X is the radiation angle coefficient of the surface to the earth, ρ is the earth's albedo, which is taken as 0.3, and ω is the angle between the satellite's center and the sun's rays.

[0076] The X size of each surface of the satellite is different. For the +Z surface, the angular coefficient is

[0077]

[0078] Among them, R E is the radius of the Earth, which is 6378.14 km, and a is the semi-major axis of the orbit. For the -Z plane, since it faces away from the Earth, the angular coefficient is 0. The other surfaces are perpendicular to the Earth's surface, and the angular coefficients are

[0079]

[0080] in,

[0081] The earth's thermal radiation q3 received by each surface is

[0082] q3=XE i0

[0083] Among them, E i0 is the average infrared radiation heat flux density of the earth, which is taken as 239.2W / m 2 .

[0084] Based on this, the magnitude of the external heat flux absorbed by a certain surface of the satellite is:

[0085] q=α s (q1+q2)+εq3

[0086] Among them, α s is the surface absorptivity of solar radiation, and ε is the surface emissivity.

[0087] On this basis, the external heat flux of each surface is calculated, and the heat conduction and thermal radiation of each surface are simulated using finite element software to calculate the temperature of the satellite surface at each moment.

[0088] S3. Based on the van der Waals gas theory, analyze the changes in the temperature, pressure, and center of mass position of the gas cylinders at each moment. Considering the high pressure in the gas cylinders, if the ideal gas is used to describe the pressure change process in two connected gas cylinders, completely ignoring the interaction between gas molecules, the error will be large. The van der Waals gas theory can be expressed as

[0089]

[0090] Where T, p, and V represent the temperature, pressure, and volume of the actual gas, respectively. g is the gas constant, R g =8.314 J / (mol·K), n is the amount of gas substance, a and b are the Van der Waals corrections introduced to take into account the gravitational force between Van der Waals gas molecules and the definite volume occupied by molecules. Taking nitrogen as an example, a=0.137 J·m 3 / mol 2 , b=3.86×10 -5 m 3 / mol.

[0091] The volume flow rate between the two cylinders is

[0092]

[0093] Where γ is the gas specific heat ratio, nitrogen is a diatomic molecule, and γ = 1.4, C d is the flow coefficient, take C d =0.5, A is the outlet cross-sectional area, and the subscripts us and ds represent upstream and downstream, respectively.

[0094] Since the gas released by the two cylinders during operation is not considered, the total amount of material in the cylinders remains unchanged, and the residual gas inside the pipeline is ignored. The total length of the pipeline is 1m. Assume that the coordinate of the center between the cylinders is 0, the coordinate of cylinder 1 is -0.5m, and the coordinate of cylinder 2 is 0.5m. Use the center of mass formula to calculate the change in the center of mass position between cylinders 1 and 2.

[0095]

[0096] Where n0 is the sum of the amounts of gas in the two symmetrical gas cylinders, and n1 and n2 are the amounts of gas in gas cylinders 1 and 2 at different times.

[0097] Simulation experiment 1:

[0098] Taking the gravitational wave detection satellite in the Tianqin project as an example, its parameters are shown in Table 1 below.

[0099] Table 1 Satellite orbit parameters

[0100]

[0101] The satellite's operating cycle is 90 days, so this period is the research object. After calculation, the changes in the solar incidence angle β during the operating period are as follows Figure 2 As shown in the figure, β shows a trend of first increasing and then decreasing as the number of days increases during the 90-day working period.

[0102] The changes in external heat flux on each surface of the satellite are as follows: Figure 3 、 4 , as shown in 5. Figure 3 The changes in the solar radiation heat flux q1 on each surface are shown. Except for the -Y and +Y surfaces pointing to the normal direction of the solar orbital plane, the solar radiation heat flux on other surfaces shows oscillation, while the solar radiation on the +Y surface during this working window is zero. Figure 4 and Figure 5 From the above, we can see that the Earth's reflected heat flux q2 and the Earth's infrared radiation heat flux q3 received by each surface are much weaker than q1. Except for the -Z surface facing away from the Earth, the values ​​of q2 and q3 are both zero. The Earth's reflected heat flux q2 received by each surface shows oscillation, while the Earth's infrared radiation heat flux q3 received by each surface is constant within the working window period.

[0103] Two nitrogen cylinders are placed symmetrically inside the satellite. The layout is as follows: Figure 6 The material parameters of the satellite panel and the gas cylinder are shown in Table 2 below.

[0104] Table 2 Satellite panel and gas cylinder material parameters

[0105]

[0106] The gas cylinders are spherical with an inner diameter of 470 mm. The two gas cylinders are connected by a 1000 mm long pipe. The initial nitrogen pressure is 30 MPa and the initial temperature is 293.15 K. Finite element software is used to simulate the satellite. Considering the complexity of the actual structure, the calculation amount of heat transfer simulation for complete modeling is extremely large. Therefore, only the necessary main structure and internal gas cylinders are retained for the satellite structure, and simplified and modeled. Figure 7 As shown. The satellite panel is a laminate of carbon fiber and aluminum honeycomb sandwich, and the gas cylinder is made of TC4 material. Due to the temperature of each surface of the satellite and the infrared absorption rate of the surface α s It has a great relationship with the surface emissivity ε. Taking an appropriate value can ensure that the satellite fluctuates within a smaller temperature range. The temperature of the satellite and the cylinder surface at each moment is the average of the surface temperature. The temperature changes of each structural surface and the cylinder inside the satellite are shown in Figure 8 and Figure 9 .

[0107] Consider two nitrogen cylinders placed symmetrically inside the satellite. When the isolation valve is closed, the gases in the two cylinders are not connected, so the temperature change does not change the position of the center of mass between the cylinders. When the isolation valve is opened, the gas between the cylinders will flow due to the different temperatures of the two cylinders, resulting in a change in the amount of gas inside the two cylinders. Figure 10 It reflects the changes in the internal pressure of the two gas cylinders. Figure 11 It reflects the change in the amount of gas in the two cylinders. Figure 12 It reflects the change of gas volume flow between the two cylinders. Due to the difference in the amount of gas substance in the two cylinders, the position of the center of mass between the cylinders changes. Figure 13 It reflects the change of the center of mass position between the gas cylinders. The change of the center of mass position of the gas cylinders at different times is fluctuating, which shows that the present invention can intuitively describe the close relationship between the change of the center of mass position between the gas cylinders and the temperature difference of the satellite surface.

[0108] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. The preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification.

Claims

1. A method for analyzing the center of mass deviation of a high-orbit satellite gas cylinder under the action of external heat flux, characterized in that: The following steps are involved: S1. Based on the known satellite orbit parameters, calculate the satellite solar incidence angle, the satellite's rotation angle relative to the initial point in orbit, and the deviation angle of the heliocentric point. Using the cosine formula of spherical trigonometry in the geocentric equatorial coordinate system, the expression for the satellite solar incidence angle β is: sinβ=cosisinδ s +sinicosδ s sinΔα Where i represents the orbital inclination, δ s is the solar declination, Δα is the difference between the orbital plane and the solar right ascension; The expression of the satellite's rotation angle γ relative to the initial point in orbit is: Among them, t represents the moment of the satellite’s current orbital position, t start is the time of the satellite's initial position, τ orbit is the satellite orbit period, "\" is the remainder symbol; The expression of the deviation angle θ of the conjunction point is: Among them, τ earth is the Earth's revolution period, which is 365 days; S2. Based on the theory of thermal radiation and heat conduction, the external heat flux and temperature change of each surface of the hexahedral square satellite are calculated. The surface is defined by the satellite coordinate system as +X, -X, +Y, -Y, +Z, -Z, where the +Z axis points to the center of the earth and the -X axis points to the direction of movement. The solar radiation q1 received by each surface is Where S is the solar constant, which is 1367W / m 2 , is the angle between the normal of each surface and the sunlight, and the As follows: +X surface is -sin(γ+θ)cosβ; -X surface is sin(γ+θ)cosβ; +Y surface is -sinβ; -Y surface is sinβ; +Z surface is -cos(γ-θ)cosβ; -Z surface is cos(γ-θ)cosβ; The Earth's reflected radiation q2 received by each surface is q2 = XSρcosω Where X is the radiation angle coefficient of the surface to the earth, ρ is the earth's albedo, which is taken as 0.3, and ω is the angle between the satellite's center and the sun's rays; The X size of each surface of the satellite is different. For the +Z surface, the angular coefficient is Among them, R E is the radius of the Earth, which is 6378.14 km, and a is the semi-major axis of the orbit. For the -Z plane, since it faces away from the Earth, the angular coefficient is 0. For other surfaces, which are perpendicular to the Earth's surface, the angular coefficients are in, The earth's thermal radiation q3 received by each surface is q3=XE i0 Among them, E i0 is the average infrared radiation heat flux density of the earth, which is taken as 239.2W / m 2 ; Based on this, the magnitude of the external heat flux absorbed by a certain surface of the satellite is: q=a s (q1+q2)+εq3 Among them, α s is the surface absorptivity of solar radiation, and ε is the surface emissivity; S3. Based on the van der Waals gas theory, analyze the changes in the temperature, pressure, and center of mass position of the gas cylinders at each moment. The van der Waals gas theory is expressed as: Where T, p, and V represent the temperature, pressure, and volume of the actual gas, respectively. g is the gas constant, R g =8.314 J / (mol·K), n is the amount of gas substance, a and b are the Van der Waals corrections introduced to take into account the gravitational force between Van der Waals gas molecules and the definite volume occupied by molecules. Taking nitrogen as an example, a=0.137 J·m 3 / mol 2 , b=3.86×10 -5 m 3 / mol; The volume flow rate between the two cylinders is: Where γ is the gas specific heat ratio, nitrogen is a diatomic molecule, and γ = 1.4, C d is the flow coefficient, take C d =0.5, A is the outlet cross-sectional area, subscripts us and ds represent upstream and downstream respectively; Use the center of mass formula to calculate the change in center of mass position between cylinder 1 and cylinder 2: Where n0 is the sum of the amounts of gas in the two symmetrical gas cylinders, and n1 and n2 are the amounts of gas in gas cylinder 1 and gas cylinder 2 at different times.

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