CN113665853A - Vacuum thermal test method of satellite system - Google Patents

Vacuum thermal test method of satellite system Download PDF

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CN113665853A
CN113665853A CN202111054563.5A CN202111054563A CN113665853A CN 113665853 A CN113665853 A CN 113665853A CN 202111054563 A CN202111054563 A CN 202111054563A CN 113665853 A CN113665853 A CN 113665853A
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CN113665853B (en
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张晓峰
刘红
程睿
梁旭文
吴立
冯建朝
高扬
诸成
刘会杰
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Shanghai Engineering Center for Microsatellites
Innovation Academy for Microsatellites of CAS
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Innovation Academy for Microsatellites of CAS
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Abstract

The invention provides a vacuum thermal test method of a satellite system, which comprises the following steps: carrying out theoretical analysis on feasibility of a multi-satellite test to explore influence factors of the temperature of the satellite in the vacuum tank and carrying out theoretical analysis; the theoretical basis of the thermal test is a radiation heat transfer system with a closed cavity formed by two diffuse grey surfaces, wherein the closed cavity with a fully convex surface is similar to a spacecraft in a vacuum tank, and the closed cavity on the outer side is similar to the vacuum tank; carrying out a multi-star simultaneous test and a single-star single test; when a multi-satellite simultaneous test and a single-satellite single test are carried out, the external heat flow conditions are similar to each other as much as possible or the temperatures of the satellites are not different as much as possible, the similarity between the multi-satellite simultaneous test and the single-satellite single test is improved, and the thermal balance test of a single satellite is improved; and determining the reliability of the temperature maintaining range of the thermal vacuum test of the satellite system according to the thermal balance test result.

Description

Vacuum thermal test method of satellite system
Technical Field
The invention relates to the technical field of aerospace, in particular to a vacuum thermal test method for a satellite system.
Background
At present, the satellite industry is developing towards miniaturization and mass production, and the efficient vacuum thermal test is an effective mode which is suitable for the rapid and flexible production development requirements of mass satellites, reduces the development period and improves the cost-effectiveness ratio.
The task of the spacecraft thermal control system is to ensure that all instruments and equipment on the satellite meet the temperature index requirements under the conditions of a set orbit, attitude and working mode. In order to verify the overall function of the spacecraft in a space environment and ensure the on-orbit reliable operation of the spacecraft, all the spacecrafts are required to be examined in a vacuum thermal test in a ground development stage, wherein the most important and complex test with the longest period is the whole-satellite vacuum thermal test in space environment simulation equipment. The spacecraft ground vacuum thermal test is divided into a thermal balance test and a thermal vacuum test, wherein the thermal balance test and the thermal vacuum test are mainly used for verifying the correctness of thermal control design, the capability of a thermal control system for maintaining each instrument and equipment on a satellite in a specified working temperature range is mainly examined, the working performance of a satellite-mounted thermal control product and the effectiveness of various thermal control measures are examined, a thermal analysis physical model is perfected, and a high-low temperature holding range of the thermal vacuum test is predicted; the later tests mainly examine the capability of each instrument on the satellite to resist high temperature, low temperature and temperature alternation under the vacuum condition, expose single machines, raw materials, components and process defects on the satellite in advance, and obtain test data under different temperature environment conditions.
In the existing multi-satellite parallel vacuum thermal test method, a thermal balance test is usually performed only on a single satellite, the temperature holding range of the thermal vacuum test of the satellite system is determined according to the thermal balance test result, and the thermal vacuum test of the satellite system is performed according to the temperature holding range. The method needs to carry out test design by the experience of designers, has low reliability and credibility, and is easy to cause unnecessary economic loss due to large difference between the test result and the data in actual use.
Disclosure of Invention
The invention aims to provide a vacuum thermal test method of a satellite system, which aims to solve the problem of low credibility of the existing multi-satellite parallel vacuum thermal test method.
In order to solve the technical problem, the invention provides a multi-satellite vacuum thermal test method, which comprises the following steps:
carrying out theoretical analysis on feasibility of a multi-satellite test to explore influence factors of the temperature of the satellite in the vacuum tank and carrying out theoretical analysis;
the theoretical basis of the thermal test is a radiation heat transfer system with a closed cavity formed by two diffuse grey surfaces, wherein the closed cavity with a fully convex surface is similar to a spacecraft in a vacuum tank, and the closed cavity on the outer side is similar to the vacuum tank;
carrying out a multi-star simultaneous test and a single-star single test;
when a multi-satellite simultaneous test and a single-satellite single test are carried out, the external heat flow conditions are similar to each other as much as possible or the temperatures of the satellites are not different as much as possible, the similarity between the multi-satellite simultaneous test and the single-satellite single test is improved, and the thermal balance test of a single satellite is improved;
and determining the reliability of the temperature maintaining range of the thermal vacuum test of the satellite system according to the thermal balance test result.
Optionally, in the vacuum thermal test method for a satellite system, the thermal equilibrium condition between the satellite and the inner surface of the space environment simulation device is as follows: the satellite is a fully convex surface, the space environment simulation equipment is a vacuum closed chamber, and the inner surfaces of the satellite and the space environment simulation equipment are both ash-diffusing surfaces; heat transfer amount between the satellite and the space environment simulation apparatus
Figure BDA0003254138680000021
Comprises the following steps:
Figure BDA0003254138680000022
wherein: a. theAIs the surface area of the satellite; ebAAnd EbBBlack body radiation intensities of the inner surfaces of the satellite and the space environment simulation equipment respectively; epsilonAAnd εBThe emissivity of the inner surface of the satellite and the emissivity of the inner surface of the space environment simulation equipment are respectively; xA,BThe radiation angle coefficient of the surface satellite to the inner surface of the space environment simulation equipment is obtained; satellite surface temperature TA=f(TB,AA,AB,εA,εB,XA,B)。
Optionally, in the vacuum thermal test method for a satellite system, the multi-satellite vacuum thermal test method includes:
simultaneously carrying out vacuum thermal tests on a plurality of satellites, and respectively evaluating the thermal balance condition of each satellite and the inner surface of the space environment simulation equipment to form a plurality of first heat transfer amounts;
when a plurality of satellites are subjected to vacuum thermal test at the same time, the number of the satellites is 3, and the satellites are symmetrically distributed by taking 1 satellite 2 as a center; each satellite is a regular hexahedron with the side length of 1 meter, the distance between the satellite 2 positioned at the center and other satellites 1 and 3 is 0.7 meter, and the space environment simulation equipment is a lying cylinder with the diameter of 3.5 meters and the height of 5.5 meters; the heat sources in the satellites are arranged to be the same, the infrared heating cages with uniform surface temperature simulate to form external heat flow, and the heat exchange among the satellites is 0.
Optionally, in the vacuum thermal test method for the satellite system, the heat transfer amount between the central satellite 2 and the inner surface of the space environment simulation apparatus is as follows:
Figure BDA0003254138680000031
the heat transfer amount between other satellites and the inner surface of the space environment simulation equipment is as follows:
Figure BDA0003254138680000032
wherein A is1And A2Surface areas of the central satellite and the other satellites, AKMSurface area of the interior surfaces of the apparatus for the simulation of the spatial environment, Eb1、Eb2And EbKMBlack body radiation intensity, epsilon, of the central satellite, other satellites and the inner surface of the space environment simulation equipment respectively1、ε2And εKMSurface emissivity, X, of the inner surfaces of the central satellite, the other satellites and the space environment simulation equipment, respectively1,KMRadial angle coefficient, X, of the outer surface of the central satellite to the inner surface of the space environment simulation device2,KMAnd simulating the radiation angle coefficient of the inner surface of the equipment for the outer surface of other satellites to the space environment.
Optionally, in the vacuum thermal test method for a satellite system, the method further includes:
in the multi-satellite vacuum thermal test method, the radiation angle coefficient of the outer surface of the satellite to the inner surface of the space environment simulation equipment is as follows:
Figure BDA0003254138680000033
wherein: wiIs the length of the outer surface of the satellite, WjL is the shortest distance between the two surfaces, which is the length of the inner surface of the space environment simulation device. In the multi-satellite vacuum thermal test method, calculating the thermal equilibrium condition of a single satellite and the inner surface of the space environment simulation equipment comprises the following steps: setting the radiation angle coefficient X of the outer surface of a single satellite to the inner surface of the space environment simulation equipments,KMIs 1, the heat transfer amount between the single satellite and the inner surface of the space environment simulation apparatus is:
Figure BDA0003254138680000041
wherein A issSurface area of a single satellite; ebsBlackbody radiation intensity for a single satellite; epsilonsThe surface emissivity of a single satellite.
Optionally, in the vacuum thermal test method for the satellite system, a vacuum thermal test is performed on a single satellite, and a thermal balance condition between the single satellite and an inner surface of the space environment simulation device is calculated to form a second heat transfer amount;
comparing each first heat transfer quantity with each second heat transfer quantity to form each external heat flow ratio; and
according to the respective external heat flow ratio values when the same balance temperature is reached and/or the temperature difference of each satellite when the same external heat flow is reached in a heat balance state when a plurality of satellites are tested simultaneously and a single satellite is tested, evaluating the influence of each parameter on the external heat flow ratio values, and adjusting each parameter to enable the respective external heat flow ratio value to be equal to 1 and/or enable the temperature difference of each satellite to be equal to 0;
defining respective external heat flow ratio values when the same balance temperature is reached in a multi-star simultaneous test and a single-star test
Figure BDA0003254138680000042
Wherein, C1sAnd C2sThe values of (a) are respectively reflected by phi1,KMPhi and phis,KMAnd phi2,KMPhi and phis,KMThe difference size of (a); phi is a1,KMIs the heat transfer amount, phi, of the central satellite and the inner surface of the space environment simulation equipment2,KMFor the heat transfer between other satellites and the inner surface of the space environment simulation apparatus, phis,KMHeat transfer amounts for a single satellite and an inner surface of the space environment simulation apparatus;
setting A1=A2=As,ε1=ε2=εs=εhComparison when the satellite reaches the same equilibrium temperature (i.e., T)1=Ts、T2=Ts) The difference of external heat flow of time, then
Figure BDA0003254138680000051
Figure BDA0003254138680000052
Wherein A is1And A2Surface areas of the central satellite and the other satellites, AKMSurface area of the interior surfaces of the apparatus for the simulation of the spatial environment, Eb1、Eb2And EbKMBlack body radiation intensity, epsilon, of the central satellite, other satellites and the inner surface of the space environment simulation equipment respectively1、ε2And εKMSurface emissivity, X, of the inner surfaces of the central satellite, the other satellites and the space environment simulation equipment, respectively1,KMRadial angle coefficient, X, of the outer surface of the central satellite to the inner surface of the space environment simulation device2,KMSimulating the radiation angle coefficient of the inner surface of the equipment for the space environment for the outer surface of other satellites; a. thesSurface area of a single satellite; ebsBlackbody radiation intensity for a single satellite; epsilonsSurface emissivity of a single satellite;
when X is present1,KMAnd X2,KMWhen equal to 1, As/AKMSmaller, epsilonhThe smaller, the1sAnd C2sThe larger and closer to 1 the value of (A), the adjustment of X1,KM、X2,KM、As/AKMAnd/or epsilonhThe value of (c).
Optionally, in the vacuum thermal test method for a satellite system, estimating an influence of each parameter on the temperature difference according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single satellite test reach a thermal equilibrium state and have the same external heat flux, and adjusting each parameter so that the temperature difference of each satellite is equal to 0 includes: setting phi1,KM=φs,KM,φ2,KM=φs,KMAnd then:
Figure BDA0003254138680000053
Figure BDA0003254138680000054
setting A1=A2=As,ε1=ε2=εs=εhAnd then:
Figure BDA0003254138680000061
Figure BDA0003254138680000062
when C is present1sAnd C2sThe closer to 1 the value of (d), the closer to 0 the temperature difference of each star; increase the angular coefficient between the satellite and the heat sink, and reduce the ratio A of the satellite surface area to the heat sink internal surface areas/AKMOr reducing the surface emissivity epsilon of the satelliteh
Optionally, in the vacuum thermal test method for a satellite system, the method further includes:
according to the geometric dimension of the existing satellite, selecting space environment simulation equipment with proper specification and the number of satellites to be tested simultaneously, so that the ratio of the surface area of the satellites to the inner surface area of the space environment simulation equipment is equal to 0, the layout distances among the satellites are far as possible, the satellites can be staggered with each other, the shielding effect is reduced, and the angular coefficient of the satellites to a heat sink is increased; during testing, according to the technical state of the satellites, the opposite surfaces among the satellites are coated with the multi-layer heat insulation assemblies, and the main heat dissipation surfaces of the satellites face the inner surface of the space environment simulation equipment, so that the temperature difference among the satellites during simultaneous testing and the temperature difference between each satellite and a single satellite during testing are reduced.
Optionally, in the vacuum thermal test method for a satellite system, the method further includes:
analysis of satellite surface emissivity epsilonhInfluence of (A) X1,KM=0.913,X2,KM=0.826,As/AKM≈0.075,εKMSubstituting 0.9 into the expression and taking several typical satellite surface emissivities, we find the variation with epsilonhDecrease of (C)1sAnd C2sThe more close to 1, the smaller the difference in heat flow between each satellite in the multi-satellite test and its individual test; because two sides of the satellite 2 are shielded, the difference of the heat flow of the satellite 2 and that of a single satellite is larger compared with that of the satellite 1;
the values of C2s/C1s characterize the heat flow differences between satellites in a multi-satellite simultaneous test, again with εhThe closer the value of C2s/C1s is to 1, the smaller the heat flow difference between stars is;
based on the above results, the difference in temperature between stars as ε was obtainedhAssuming the heat sink temperature TKMTaking T as 100Ks=305K、TsThe temperature difference of each star at the high and low temperature ends was analyzed 265K.
Optionally, in the vacuum thermal test method for the satellite system, under the same external heat flow condition, the equilibrium temperatures of the satellite 1 and the satellite 2 are both higher than that of a single satellite, and the temperature difference is reduced with the reduction of the surface emissivity of the satellite; when the surface of the satellite is fully coated with a plurality of layers of heat insulation assemblies, the temperature difference at the high and low temperature ends is less than 0.5 ℃; the temperature difference between the satellite 2 and the single satellite is approximately twice of the temperature difference between the satellite 1 and the single satellite; the balance temperature is increased, and the temperature difference between the multi-star test and the single-star test is slightly increased; therefore, the multi-layer heat insulation assembly is coated as completely as possible according to the technical state of the satellite during the test, so that heat leakage is reduced, and the temperature difference between the satellites during the simultaneous test and the temperature difference between the satellites during the single satellite test are reduced.
According to the vacuum thermal test method of the satellite system, the influence of each parameter on the external heat flow ratio is evaluated according to the respective external heat flow ratio when the multi-satellite simultaneous test and the single satellite test reach the same balance temperature, and each parameter is adjusted so that the respective external heat flow ratio is equal to 1; and/or evaluating the influence of each parameter on the temperature difference according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single-satellite test reach the thermal balance state and have the same external heat flux, adjusting each parameter to enable the temperature difference of each satellite to be equal to 0, realizing that the external heat flux conditions are similar to each other or the temperature of each satellite is not different as much as possible when the multi-satellite simultaneous test and the single-satellite single test are carried out, improving the similarity of the multi-satellite simultaneous test and the single-satellite single test, improving the thermal balance test of the single satellite, and determining the reliability of the temperature holding range of the thermal vacuum test of the satellite system according to the thermal balance test result.
Drawings
FIG. 1 is a schematic view of a radiant heat transfer system comprised of two bodies according to one embodiment of the present invention;
FIG. 2 is a schematic layout of three satellites within a vacuum tank according to one embodiment of the invention;
FIG. 3 is a schematic diagram of an angle coefficient calculation equation according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of the arrangement of three satellites in a vacuum tank in an actual test according to an embodiment of the present invention;
fig. 5 is a thermal vacuum test temperature cycle curve for a battery pack according to an embodiment of the present invention.
Detailed Description
The method for vacuum thermal testing of a satellite system according to the present invention is further described in detail with reference to the accompanying drawings and specific examples. Advantages and features of the present invention will become apparent from the following description and from the claims. It is to be noted that the drawings are in a very simplified form and are not to precise scale, which is merely for the purpose of facilitating and distinctly claiming the embodiments of the present invention.
The core idea of the invention is to provide a vacuum thermal test method of a satellite system to solve the problem of low credibility of the existing multi-satellite parallel vacuum thermal test method.
In order to realize the idea, the invention provides a vacuum thermal test method of a satellite system, wherein the multi-satellite vacuum thermal test system comprises a multi-satellite test module, a single-satellite test module, a first evaluation module and a second evaluation module, wherein: the multi-satellite test module is configured to simultaneously perform vacuum thermal tests on a plurality of satellites, and respectively evaluate the thermal balance condition of each satellite and the inner surface of the space environment simulation equipment to form a plurality of first heat transfer amounts; the single-satellite test module is configured to perform vacuum thermal test on a single satellite, calculate the thermal balance condition of the single satellite and the inner surface of the space environment simulation equipment and form a second heat transfer quantity; the first evaluation module is configured to compare each first heat transfer quantity with the second heat transfer quantity respectively to form each external heat flow ratio; and the first evaluation module is configured to evaluate the influence of each parameter on the external heat flow ratio according to the respective external heat flow ratio when the multi-satellite simultaneous test and the single-satellite test reach the same equilibrium temperature, and adjust each parameter so that the respective external heat flow ratio is equal to 1; and/or the second evaluation module is configured to evaluate the influence of various parameters on the temperature difference according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single-satellite test reach the thermal equilibrium state and the same external heat flow, and the various parameters are adjusted to enable the temperature difference of each satellite to be equal to 0.
< example one >
The embodiment provides a multi-satellite vacuum thermal test method, which comprises the following steps: simultaneously carrying out vacuum thermal tests on a plurality of satellites, and respectively evaluating the thermal balance condition of each satellite and the inner surface of the space environment simulation equipment to form a plurality of first heat transfer amounts; carrying out vacuum thermal test on a single satellite, and calculating the thermal balance condition of the single satellite and the inner surface of the space environment simulation equipment to form a second heat transfer quantity; comparing each first heat transfer quantity with each second heat transfer quantity to form each external heat flow ratio; evaluating the influence of each parameter on the external heat flow ratio according to the respective external heat flow ratios when the multi-satellite simultaneous test and the single-satellite test reach the same balance temperature, and adjusting each parameter to enable the respective external heat flow ratio to be equal to 1; and/or evaluating the influence of each parameter on the temperature difference according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single satellite test reach the thermal equilibrium state and have the same external heat flux, and adjusting each parameter to enable the temperature difference of each satellite to be equal to 0.
As shown in fig. 1, in the multi-satellite vacuum thermal test method, the thermal equilibrium between the satellite and the inner surface of the space environment simulation device is as follows: the satellite is a fully convex surface, the space environment simulation equipment is a vacuum closed chamber, and the inner surfaces of the satellite and the space environment simulation equipment are both ash-diffusing surfaces; heat transfer amount between the satellite and the space environment simulation apparatus
Figure BDA0003254138680000091
Comprises the following steps:
Figure BDA0003254138680000092
wherein: a. theAIs the surface area of the satellite; ebAAnd EbBBlack body radiation intensities of the inner surfaces of the satellite and the space environment simulation equipment respectively; epsilonAAnd εBThe emissivity of the inner surface of the satellite and the emissivity of the inner surface of the space environment simulation equipment are respectively; xA,BThe radiation angle coefficient of the surface satellite to the inner surface of the space environment simulation equipment is obtained; satellite surface temperature TA=f(TB,AA,AB,εA,εB,XA,B)。
Further, in the multi-satellite vacuum thermal test method, as shown in fig. 2, when vacuum thermal tests are simultaneously performed on a plurality of satellites, the number of the satellites is 3, and the satellites are symmetrically distributed around 1 satellite 2; each satellite is a regular hexahedron with the side length of 1 meter, the distance between the satellite 2 positioned at the center and other satellites 1 and 3 is 0.7 meter, and the space environment simulation equipment (vacuum tank) is a lying cylinder with the diameter of 3.5 meters and the height of 5.5 meters; the heat sources in the satellites are arranged to be the same, the infrared heating cages with uniform surface temperature simulate to form external heat flow, and the heat exchange among the satellites is 0. In the multi-satellite vacuum thermal test method, the heat transfer amount between the central satellite 2 and the inner surface of the space environment simulation device is as follows:
Figure BDA0003254138680000093
the heat transfer amount between other satellites and the inner surface of the space environment simulation equipment is as follows:
Figure BDA0003254138680000094
wherein A is1And A2Surface areas of the central satellite and the other satellites, AKMSurface area of the interior surfaces of the apparatus for the simulation of the spatial environment, Eb1、Eb2And EbKMBlack body radiation intensity, epsilon, of the central satellite, other satellites and the inner surface of the space environment simulation equipment respectively1、ε2And εKMSurface emissivity, X, of the inner surfaces of the central satellite, the other satellites and the space environment simulation equipment, respectively1,KMRadial angle coefficient, X, of the outer surface of the central satellite to the inner surface of the space environment simulation device2,KMAnd simulating the radiation angle coefficient of the inner surface of the equipment for the outer surface of other satellites to the space environment. As shown in fig. 3, in the multi-satellite vacuum thermal test method, the radiation angle coefficient of the outer surface of the satellite to the inner surface of the space environment simulation equipment is as follows:
Figure BDA0003254138680000101
wherein: wiIs the length of the outer surface of the satellite, WjL is the shortest distance between the two surfaces, which is the length of the inner surface of the space environment simulation device. In the multi-satellite vacuum thermal test method, calculating the thermal equilibrium condition of a single satellite and the inner surface of the space environment simulation equipment comprises the following steps: setting the radiation angle coefficient X of the outer surface of a single satellite to the inner surface of the space environment simulation equipments,KMIs 1, the heat transfer amount between the single satellite and the inner surface of the space environment simulation apparatus is:
Figure BDA0003254138680000102
wherein A issSurface area of a single satellite; ebsBlackbody radiation intensity for a single satellite; epsilonsThe surface emissivity of a single satellite. In the multi-satellite vacuum thermal test method, according to respective external heat flow ratios when a multi-satellite simultaneous test and a single satellite test reach the same equilibrium temperature, evaluating the influence of each parameter on the external heat flow ratios, and adjusting each parameter so that each external heat flow ratio is equal to 1 comprises: defining respective external heat flow ratio values when the same balance temperature is reached in a multi-star simultaneous test and a single-star test
Figure BDA0003254138680000103
Wherein, C1sAnd C2sThe values of (a) are respectively reflected by phi1,KMPhi and phis,KMAnd phi2,KMPhi and phis,KMThe difference size of (a); setting A1=A2=As,ε1=ε2=εs=εhComparison when the satellite reaches the same equilibrium temperature (i.e., T)1=Ts、T2=Ts) The difference of external heat flow of time, then
Figure BDA0003254138680000104
Figure BDA0003254138680000105
When X is present1,KMAnd X2,KMWhen equal to 1, As/AKMSmaller, epsilonhThe smaller, the1sAnd C2sThe larger and closer to 1 the value of (A), the adjustment of X1,KM、X2,KM、As/AKMAnd/or epsilonhThe value of (c).
Specifically, in the multi-satellite vacuum thermal test method, according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single satellite test reach the thermal equilibrium state and have the same external heat flux, evaluating the influence of each parameter on the temperature difference, and adjusting each parameter so that the temperature difference of each satellite is equal to 0 includes: setting phi1,KM=φs,KM,φ2,KM=φs,KMAnd then:
Figure BDA0003254138680000111
Figure BDA0003254138680000112
setting A1=A2=As,ε1=ε2=εs=εhAnd then:
Figure BDA0003254138680000113
Figure BDA0003254138680000114
when C is present1sAnd C2sThe more value ofWhen the temperature is close to 1, the temperature difference of each star is closer to 0; increase the angular coefficient between the satellite and the heat sink, and reduce the ratio A of the satellite surface area to the heat sink internal surface areas/AKMOr reducing the surface emissivity epsilon of the satelliteh
As shown in fig. 4, in the multi-satellite vacuum thermal test method, the multi-satellite vacuum thermal test method further includes: selecting space environment simulation equipment with proper specification and the number of satellites to be tested simultaneously according to the geometric dimension of the satellites, so that the ratio of the surface area of the satellites to the inner surface area of the space environment simulation equipment is equal to 0, and the layout distance between the satellites is as far as possible; during testing, according to the technical state of the satellites, the opposite surfaces among the satellites are coated with the multi-layer heat insulation assemblies, and the main heat dissipation surfaces of the satellites face the inner surface of the space environment simulation equipment, so that the temperature difference among the satellites during simultaneous testing and the temperature difference between each satellite and a single satellite during testing are reduced.
In summary, the above embodiments have described the different configurations of the vacuum thermal test method of the satellite system in detail, and it is understood that the present invention includes, but is not limited to, the configurations listed in the above embodiments, and any modifications based on the configurations provided by the above embodiments are within the scope of the present invention. One skilled in the art can take the contents of the above embodiments to take a counter-measure.
< example two >
The embodiment provides a multi-satellite vacuum thermal test system, which comprises a multi-satellite test module, a single-satellite test module, a first evaluation module and a second evaluation module, wherein: the multi-satellite test module is configured to simultaneously perform vacuum thermal tests on a plurality of satellites, and respectively evaluate the thermal balance condition of each satellite and the inner surface of the space environment simulation equipment to form a plurality of first heat transfer amounts; the single-satellite test module is configured to perform vacuum thermal test on a single satellite, calculate the thermal balance condition of the single satellite and the inner surface of the space environment simulation equipment and form a second heat transfer quantity; the first evaluation module is configured to compare each first heat transfer quantity with the second heat transfer quantity respectively to form each external heat flow ratio; the first evaluation module is configured to evaluate the influence of each parameter on the external heat flow ratio according to the respective external heat flow ratio when the multi-satellite simultaneous test and the single-satellite test reach the same balance temperature, and adjust each parameter so that the respective external heat flow ratio is equal to 1; and/or the second evaluation module is configured to evaluate the influence of various parameters on the temperature difference according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single-satellite test reach the thermal equilibrium state and the same external heat flow, and the various parameters are adjusted to enable the temperature difference of each satellite to be equal to 0.
According to the vacuum thermal test method of the satellite system, the influence of each parameter on the external heat flow ratio is evaluated according to the respective external heat flow ratio when the multi-satellite simultaneous test and the single satellite test reach the same balance temperature, and each parameter is adjusted so that the respective external heat flow ratio is equal to 1; and/or evaluating the influence of each parameter on the temperature difference according to the temperature difference of each satellite when the multi-satellite simultaneous test and the single-satellite test reach the thermal balance state and have the same external heat flux, adjusting each parameter to enable the temperature difference of each satellite to be equal to 0, realizing that the external heat flux conditions are similar to each other or the temperature of each satellite is not different as much as possible when the multi-satellite simultaneous test and the single-satellite single test are carried out, improving the similarity of the multi-satellite simultaneous test and the single-satellite single test, improving the thermal balance test of the single satellite, and determining the reliability of the temperature holding range of the thermal vacuum test of the satellite system according to the thermal balance test result.
In one embodiment of the invention, a theoretical analysis of feasibility of a multi-satellite test is firstly carried out, and the theoretical analysis is carried out for researching the influence factors of the temperature of the satellite in the vacuum tank. The theoretical basis of the thermal test is a closed-cavity radiant heat transfer system consisting of two diffuse grey surfaces as shown in fig. 1, wherein a is a fully convex surface similar to a spacecraft inside a vacuum tank and B is a closed cavity similar to a vacuum tank.
A. Heat transfer amount between B
Figure BDA0003254138680000131
Can be written as:
Figure BDA0003254138680000132
in the formula: a. theAA surface area of A; ebAAnd EbBA black body radiation intensity of A, B, respectively; epsilonAAnd εBA, B surface emissivity respectively; xA,BIs the radiance factor of surface a versus B. Surface temperature T of visible satelliteA=f(TB,AA,AB,εA,εB,XA,B)。
As shown in fig. 2, three satellites are taken as an example, and physical modeling and calculation of a three-satellite simultaneous experiment are performed. The positions of three stars in the tank are shown in fig. 2, wherein 1, 2 and 3 are the satellite numbers, the satellite is a 1m regular hexahedron, the distance between the satellites is 0.7m, the diameter of the vacuum tank is 3.5m, the depth of the vacuum tank is 5.5m, and the following simplification and assumption are made: the internal heat sources of the satellite are the same, and the external heat flow is simulated by an infrared heating cage and is an isothermal body with uniform surface temperature; not considering all forms of heat exchange between satellites, only considering shielding of heat sinks among each other, namely, assuming that three satellites are not large in temperature difference in advance, the heat exchange among the satellites is negligible relative to the heat exchange with the heat sinks. Due to symmetry, only the differences between satellite 1 and satellite 2 are analyzed.
With reference to the radiant heat transfer system of the closed chamber formed by the two diffuse grey surfaces, the following thermal balances can be written for satellite 1 and the vacuum tank (indicated by the subscript KM) and satellite 2 and the vacuum tank, respectively:
Figure BDA0003254138680000133
Figure BDA0003254138680000134
the engineering calculation of the angular coefficients for the two parallel surfaces shown in fig. 3 is as follows:
Figure BDA0003254138680000135
the heat exchange in the single star test regime is calculated simultaneously for comparison, the subscripts being denoted by s (meaning single) and being in accordance with X s,KM1 is equal to
Figure BDA0003254138680000141
Defining the ratio of the respective external heat flows when the same balance temperature is reached in the multi-star simultaneous test and the single-star test
Figure BDA0003254138680000142
C1sAnd C2sThe values of (a) are respectively reflected by phi1,KMPhi and phis,KMAnd phi2,KMPhi and phis,KMThe size of the difference in (c). In model A1=A2=As,ε1=ε2=εs=εhComparison when the satellite reaches the same equilibrium temperature (i.e., T)1=Ts、T2=Ts) The difference of external heat flow of time is
Figure BDA0003254138680000143
Figure BDA0003254138680000144
If the same external heat flow is considered, the temperature difference of each satellite in the heat balance state can be calculated, and phi is respectively controlled1,KM=φs,KM,φ2,KM=φs,KMIs obtained by
Figure BDA0003254138680000145
The surface temperature and the surface emissivity of the heat sink of the vacuum tank are generally constant values, and the analysis can be carried outKnown as X1,KMAnd X2,KMThe larger, As/AKMSmaller, epsilonhThe smaller, the1sAnd C2sThe larger the value of (A) is and the closer to 1 is, therefore, in the test, in order to reduce the temperature difference between the simultaneous test and the single-satellite test, the angle coefficient between the satellite and the heat sink should be increased, and the ratio A of the surface area of the satellite to the internal surface area of the heat sink should be reduceds/AKMOr reducing the surface emissivity epsilon of the satelliteh
Therefore, in an actual test, according to the geometric dimension of the existing satellite, the vacuum tanks with proper specifications and the number of satellites to be tested at the same time need to be selected, so that the ratio of the surface area of the satellites to the internal surface area of the heat sink is smaller, and meanwhile, the satellites are far away from each other in layout as much as possible and can be staggered with each other, the shielding effect is reduced, and the angular coefficient of the satellites to the heat sink is increased. Surface emissivity epsilon of satellitehThe influence of (a) was analyzed as follows.
Specifically, mixing X1,KM=0.913,X2,KM=0.826,As/AKM≈0.075,εKMThe expressions are substituted for 0.9, and several typical satellite surface emissivity values of 0.9 (black paint), 0.85 (white paint), 0.6 (polyimide film), 0.03 (multilayer assembly equivalent emissivity) are taken, and the results are shown in table 1.
TABLE 1 εhVariation of (A) and (C)1sAnd C2sIn relation to (2)
Figure BDA0003254138680000151
As can be seen from the data in the table, with εhDecrease of (C)1sAnd C2sThe value of (a) increases significantly and closer to 1, i.e. the smaller the difference in heat flow for each satellite in the multi-satellite trial compared to its respective individual trial. The satellite 2 has a larger heat flow difference than the satellite 1 under the condition that the satellite 2 is single due to the fact that two sides of the satellite are shielded.
The value of C2s/C1s characterizes the heat flow difference between satellites in a multi-satellite simultaneous test, again with εhThe more C2s/C1s are reducedClose to 1, i.e. the smaller the heat flow difference between stars.
Based on the results in Table 1, it can be further found that the difference between the temperatures of the stars depends on εhAssuming the heat sink temperature TKMTaking T as 100Ks=305K、TsThe temperature difference between the high and low temperature ends was analyzed at 265K, and the calculation results are shown in tables 2 and 3.
TABLE 2 εhIs related to (T)s305K) (temperature unit: K)
Figure BDA0003254138680000152
TABLE 3 εhChange and relationship (T)s265K) (temperature unit: K)
Figure BDA0003254138680000153
Figure BDA0003254138680000161
the data in the table show that under the same external heat flow condition, the equilibrium temperature of the satellite 1 and the satellite 2 is higher than that of a single satellite, and the temperature difference is reduced along with the reduction of the surface emissivity of the satellite. When the satellite surface is fully coated with the multi-layer heat insulation assembly, the temperature difference at the high and low temperature ends is less than 0.5 ℃. The temperature difference between satellite 2 and the single satellite test is approximately twice the temperature difference between satellite 1 and the single satellite test. Comparing tables 2 and 3, it is understood that the equilibrium temperature is increased and the temperature difference between the multi-star test and the single-star test is slightly increased. Therefore, the multi-layer heat insulation assembly is coated as completely as possible according to the technical state of the satellite during the test, so that heat leakage is reduced, and the temperature difference between satellites during the simultaneous test and the temperature difference between satellites during the single-satellite test can be reduced.
Based on the analysis and the actual conditions of the projects, a scheme that three stars enter a KM3 vacuum tank at the same time to perform a hot vacuum test is adopted. The arrangement of the satellite in the tank is shown in fig. 4, the + -Y surface of the satellite is a main heat dissipation surface, the + -X surface mainly covers the multi-layer heat insulation assembly, the-Y surface faces to a heat sink when the satellite is installed, and the + -X surfaces are opposite to each other, so that the thermal interference between the satellites is reduced.
Secondly, based on the test and flight verification of a certain project, a three-star simultaneous test is taken as a background and a scheme, and according to the development requirement of a certain model, all the work from the scheme to the launching test of a low-cost constellation consisting of 15 satellites is completed in 3 years. In order to reduce development cost and development period, a scheme of simultaneously carrying out thermal tests by three stars is adopted. The test was conducted in a KM3 space environment simulator with the satellite arrangement inside the tank as shown in fig. 4. The participating satellites are the positive sample launching satellites and are pushed into the storage tank without simulation liquid; the solar sailboard did not participate in the test; the external heat flow is simulated by an infrared heating cage. In the test, an infrared heating cage is adopted to simulate external heat flow, combined temperature control is carried out by combining with an on-satellite active heater, four high-low temperature cycles are completed, and the test of a high-low temperature maintaining stage is carried out after the temperature is increased to the expected temperature every time.
The test result comprises the control condition of the thermal vacuum temperature field, the test temperature control judgment of the general thermal vacuum test is based on the temperature index of a typical single machine or an important single machine of the satellite, and the single machine of the thermal vacuum test control point of the project is a storage battery. The temperature rise and fall curve of a certain group of satellite storage battery packs is shown in fig. 5. As can be seen from the figure, each thermal test is subjected to four high-low temperature cycles, in the test of the same group of satellites, the contact ratio of the temperature curves of three satellites is good, the temperature rising and falling rates of the three satellites are basically consistent, the high-low temperature keeping temperatures are basically consistent, the temperature control of the three satellites in the simultaneous test meets the requirements of the test outline, and the scheme passes test verification.
The test result comprises the statistics of the test time of each group of satellites and the efficient and feasible conclusion: the five groups of satellite thermal vacuum tests respectively spend 7 days, 8 days and 8 days, the total time is 38 days, if each satellite independently performs single 6-day tests, 90 days is needed, and it can be seen that the mode of simultaneously testing three satellites is adopted, the test time can be saved by 57.8%, the test frequency is reduced from 15 times to 5 times, the test cost is greatly reduced, the test time and the labor cost are reduced, and the cost effectiveness of the tests is greatly improved.
On-orbit flight verification surface, all the current on-orbit satellites work normally, all the performances meet the index requirements, the first 12 satellites sequentially reach the design life, and the satellites work normally in the out-of-service stage. The in-orbit flight shows that the working performance of the satellite in a vacuum thermal environment can be fully checked by the method for simultaneously carrying out thermal tests on three satellites.
At present, the satellite industry is developing towards miniaturization and mass production, and the efficient vacuum thermal test is an effective mode which is suitable for the rapid and flexible production development requirements of mass satellites, reduces the development period and improves the cost-effectiveness ratio.
The multi-satellite vacuum thermal test method provided by the invention provides that when a multi-satellite simultaneous thermal test is carried out, the larger the angular coefficient of a satellite to a heat sink is, the smaller the ratio of the surface area of the satellite to the surface area of the heat sink is, the lower the emissivity of the surface of the satellite is, the smaller the temperature difference between the satellites under the same heat flow condition is, the smaller the difference with a single-satellite test is, or the smaller the external heat flow difference when the heat balance temperature is reached during the simultaneous test is.
According to the multi-satellite vacuum thermal test method, under the existing satellite surface characteristic condition, when the test is carried out simultaneously, the difference between the satellites can be effectively reduced by reasonably organizing the layout and the orientation of the satellites, so that the temperature field consistency of the thermal balance test is improved, and the temperature control difficulty in the thermal vacuum test is reduced.
The three-satellite simultaneous test scheme of a certain project can save test time by 57.8%, test cost and labor cost are greatly reduced, the cost effectiveness ratio of the test is greatly improved, and the on-orbit running condition of the project shows that the multi-satellite simultaneous thermal test is real and effective and the examination is sufficient.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The above description is only for the purpose of describing the preferred embodiments of the present invention, and is not intended to limit the scope of the present invention, and any variations and modifications made by those skilled in the art based on the above disclosure are within the scope of the appended claims.

Claims (10)

1. A vacuum thermal test method of a satellite system is characterized by comprising the following steps:
carrying out theoretical analysis on feasibility of a multi-satellite test to explore influence factors of the temperature of the satellite in the vacuum tank and carrying out theoretical analysis;
the theoretical basis of the thermal test is a radiation heat transfer system with a closed cavity formed by two diffuse grey surfaces, wherein the closed cavity with a fully convex surface is similar to a spacecraft in a vacuum tank, and the closed cavity on the outer side is similar to the vacuum tank;
carrying out a multi-star simultaneous test and a single-star single test;
when a multi-satellite simultaneous test and a single-satellite single test are carried out, the external heat flow conditions are similar to each other as much as possible or the temperatures of the satellites are not different as much as possible, the similarity between the multi-satellite simultaneous test and the single-satellite single test is improved, and the thermal balance test of a single satellite is improved;
and determining the reliability of the temperature maintaining range of the thermal vacuum test of the satellite system according to the thermal balance test result.
2. The vacuum thermal test method of the satellite system according to claim 1, wherein the thermal equilibrium condition of the satellite and the inner surface of the space environment simulation device is: the satellite is a fully convex surface, the space environment simulation equipment is a vacuum closed chamber, and the inner surfaces of the satellite and the space environment simulation equipment are both ash-diffusing surfaces; heat transfer amount between the satellite and the space environment simulation apparatus
Figure FDA0003254138670000011
Comprises the following steps:
Figure FDA0003254138670000012
wherein: a. theAIs the surface area of the satellite; ebAAnd EbBBlack body radiation intensities of the inner surfaces of the satellite and the space environment simulation equipment respectively; epsilonAAnd εBThe emissivity of the inner surface of the satellite and the emissivity of the inner surface of the space environment simulation equipment are respectively; xA,BThe radiation angle coefficient of the surface satellite to the inner surface of the space environment simulation equipment is obtained; satellite surface temperature TA=f(TB,AA,ABAB,XA,B)。
3. The method for vacuum thermal testing of a satellite system of claim 2, wherein the multi-satellite vacuum thermal testing method comprises:
simultaneously carrying out vacuum thermal tests on a plurality of satellites, and respectively evaluating the thermal balance condition of each satellite and the inner surface of the space environment simulation equipment to form a plurality of first heat transfer amounts;
when a plurality of satellites are subjected to vacuum thermal test at the same time, the number of the satellites is 3, and the satellites are symmetrically distributed by taking 1 satellite 2 as a center; each satellite is a regular hexahedron with the side length of 1 meter, the distance between the satellite 2 positioned at the center and other satellites 1 and 3 is 0.7 meter, and the space environment simulation equipment is a lying cylinder with the diameter of 3.5 meters and the height of 5.5 meters; the heat sources in the satellites are arranged to be the same, the infrared heating cages with uniform surface temperature simulate to form external heat flow, and the heat exchange among the satellites is 0.
4. The vacuum thermal test method of a satellite system according to claim 3, wherein the heat transfer amount between the central satellite 2 and the inner surface of the space environment simulation apparatus is:
Figure FDA0003254138670000021
the heat transfer amount between other satellites and the inner surface of the space environment simulation equipment is as follows:
Figure FDA0003254138670000022
wherein A is1And A2Surface areas of the central satellite and the other satellites, AKMSurface area of the interior surfaces of the apparatus for the simulation of the spatial environment, Eb1、Eb2And EbKMBlack body radiation intensity, epsilon, of the central satellite, other satellites and the inner surface of the space environment simulation equipment respectively1、ε2And εKMSurface emissivity, X, of the inner surfaces of the central satellite, the other satellites and the space environment simulation equipment, respectively1,KMRadial angle coefficient, X, of the outer surface of the central satellite to the inner surface of the space environment simulation device2,KMAnd simulating the radiation angle coefficient of the inner surface of the equipment for the outer surface of other satellites to the space environment.
5. The method for vacuum thermal testing of a satellite system of claim 3, further comprising:
in the multi-satellite vacuum thermal test method, the radiation angle coefficient of the outer surface of the satellite to the inner surface of the space environment simulation equipment is as follows:
Figure FDA0003254138670000023
wherein: wiIs the length of the outer surface of the satellite, WjL is the shortest distance between the two surfaces, which is the length of the inner surface of the space environment simulation device. In the multi-satellite vacuum thermal test method, calculating the thermal equilibrium condition of a single satellite and the inner surface of the space environment simulation equipment comprises the following steps: setting the radiation angle coefficient X of the outer surface of a single satellite to the inner surface of the space environment simulation equipments,KMIs 1, the heat transfer amount between the single satellite and the inner surface of the space environment simulation apparatus is:
Figure FDA0003254138670000031
wherein A issSurface area of a single satellite; ebsBlackbody radiation intensity for a single satellite; epsilonsThe surface emissivity of a single satellite.
6. The method for vacuum thermal testing of a satellite system according to claim 5,
carrying out vacuum thermal test on a single satellite, and calculating the thermal balance condition of the single satellite and the inner surface of the space environment simulation equipment to form a second heat transfer quantity;
comparing each first heat transfer quantity with each second heat transfer quantity to form each external heat flow ratio; and
according to the respective external heat flow ratio values when the same balance temperature is reached and/or the temperature difference of each satellite when the same external heat flow is reached in a heat balance state when a plurality of satellites are tested simultaneously and a single satellite is tested, evaluating the influence of each parameter on the external heat flow ratio values, and adjusting each parameter to enable the respective external heat flow ratio value to be equal to 1 and/or enable the temperature difference of each satellite to be equal to 0;
defining respective external heat flow ratio values when the same balance temperature is reached in a multi-star simultaneous test and a single-star test
Figure FDA0003254138670000032
Wherein, C1sAnd C2sThe values of (a) are respectively reflected by phi1,KMPhi and phis,KMAnd phi2,KMPhi and phis,KMThe difference size of (a); phi is a1,KMIs the heat transfer amount, phi, of the central satellite and the inner surface of the space environment simulation equipment2,KMFor the heat transfer between other satellites and the inner surface of the space environment simulation apparatus, phis,KMHeat transfer amounts for a single satellite and an inner surface of the space environment simulation apparatus;
setting A1=A2=As,ε1=ε2=εs=εhComparison when the satellite reaches the same equilibrium temperature (i.e., T)1=Ts、T2=Ts) The difference of external heat flow of time, then
Figure FDA0003254138670000041
Figure FDA0003254138670000042
Wherein A is1And A2Surface areas of the central satellite and the other satellites, AKMSurface area of the interior surfaces of the apparatus for the simulation of the spatial environment, Eb1、Eb2And EbKMBlack body radiation intensity, epsilon, of the central satellite, other satellites and the inner surface of the space environment simulation equipment respectively1、ε2And εKMSurface emissivity, X, of the inner surfaces of the central satellite, the other satellites and the space environment simulation equipment, respectively1,KMRadial angle coefficient, X, of the outer surface of the central satellite to the inner surface of the space environment simulation device2,KMSimulating the radiation angle coefficient of the inner surface of the equipment for the space environment for the outer surface of other satellites; a. thesSurface area of a single satellite; ebsBlackbody radiation intensity for a single satellite; epsilonsSurface emissivity of a single satellite;
when X is present1,KMAnd X2,KMWhen equal to 1, As/AKMSmaller, epsilonhThe smaller, the1sAnd C2sThe larger and closer to 1 the value of (A), the adjustment of X1,KM、X2,KM、As/AKMAnd/or epsilonhThe value of (c).
7. The vacuum thermal test method of a satellite system according to claim 6, wherein each satellite is evaluated based on the temperature difference of each satellite when the multi-satellite simultaneous test and the single satellite test reach the thermal equilibrium state and the same external heat fluxAn effect of a parameter on the temperature difference, the adjusting the respective parameters such that the temperature difference of the respective stars is equal to 0 comprising: setting phi1,KM=φs,KM,φ2,KM=φs,KMAnd then:
Figure FDA0003254138670000043
Figure FDA0003254138670000044
setting A1=A2=As,ε1=ε2=εs=εhAnd then:
Figure FDA0003254138670000051
Figure FDA0003254138670000052
when C is present1sAnd C2sThe closer to 1 the value of (d), the closer to 0 the temperature difference of each star; increase the angular coefficient between the satellite and the heat sink, and reduce the ratio A of the satellite surface area to the heat sink internal surface areas/AKMOr reducing the surface emissivity epsilon of the satelliteh
8. The method for vacuum thermal testing of a satellite system of claim 3, further comprising:
according to the geometric dimension of the existing satellite, selecting space environment simulation equipment with proper specification and the number of satellites to be tested simultaneously, so that the ratio of the surface area of the satellites to the inner surface area of the space environment simulation equipment is equal to 0, the layout distances among the satellites are far as possible, the satellites can be staggered with each other, the shielding effect is reduced, and the angular coefficient of the satellites to a heat sink is increased; during testing, according to the technical state of the satellites, the opposite surfaces among the satellites are coated with the multi-layer heat insulation assemblies, and the main heat dissipation surfaces of the satellites face the inner surface of the space environment simulation equipment, so that the temperature difference among the satellites during simultaneous testing and the temperature difference between each satellite and a single satellite during testing are reduced.
9. The method for vacuum thermal testing of a satellite system of claim 8, further comprising:
analysis of satellite surface emissivity epsilonhInfluence of (A) X1,KM=0.913,X2,KM=0.826,As/AKM≈0.075,εKMSubstituting 0.9 into the expression and taking several typical satellite surface emissivities, we find the variation with epsilonhDecrease of (C)1sAnd C2sThe more close to 1, the smaller the difference in heat flow between each satellite in the multi-satellite test and its individual test; because two sides of the satellite 2 are shielded, the difference of the heat flow of the satellite 2 and that of a single satellite is larger compared with that of the satellite 1;
the values of C2s/C1s characterize the heat flow differences between satellites in a multi-satellite simultaneous test, again with εhThe closer the value of C2s/C1s is to 1, the smaller the heat flow difference between stars is;
based on the above results, the difference in temperature between stars as ε was obtainedhAssuming the heat sink temperature TKMTaking T as 100Ks=305K、TsThe temperature difference of each star at the high and low temperature ends was analyzed 265K.
10. The vacuum thermal test method of the satellite system according to claim 9, wherein under the same external heat flow condition, the equilibrium temperature of the satellite 1 and the satellite 2 is higher than that of a single satellite, and the temperature difference is reduced as the emissivity of the satellite surface is reduced; when the surface of the satellite is fully coated with a plurality of layers of heat insulation assemblies, the temperature difference at the high and low temperature ends is less than 0.5 ℃; the temperature difference between the satellite 2 and the single satellite is approximately twice of the temperature difference between the satellite 1 and the single satellite; the balance temperature is increased, and the temperature difference between the multi-star test and the single-star test is slightly increased; therefore, the multi-layer heat insulation assembly is coated as completely as possible according to the technical state of the satellite during the test, so that heat leakage is reduced, and the temperature difference between the satellites during the simultaneous test and the temperature difference between the satellites during the single satellite test are reduced.
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