Heat Sink Equivalent Thermal Test Method and Its Application in Low-Orbit Satellites

Abstract

In order to shorten the length of satellite thermal testing and reduce the cost of satellite development, a new method of satellite thermal testing using a heat sink to simulate space heating flow has been proposed. First, based on the characteristics of low-orbit satellites and the current research of thermal tests, the necessity of studying high-efficiency thermal test methods for satellites is expounded, and the advantages of the heat sink equivalent thermal tests compared to conventional tests are explained. Then, the principle of the heat sink equivalent thermal tests is described, the formula to calculate the heat sink temperature is given, and an error analysis of the formula is conducted. It is found that when the emissivity of the heat sink surface is greater than 0.9 and the ratio of the heat sink’s surface area to the satellite’s is greater than 10, the error of the heat sink equivalent tests should be within 1 °C. Next, the application of the heat sink equivalent thermal test is described using the Jilin−1 GF02F satellite as an example. Finally, the test results and the flight temperature of the GF02F satellite are acquired and analyzed. The results show that the error of the heat sink equivalent thermal test is 0.9 °C, the test time is shortened by one-third compared to traditional thermal tests, and the cost of the thermal test is reduced by more than 70%.

1. Introduction

Commercial satellite constellations not only need to achieve reliability, but also require low-cost and time-saving approaches. Among the costs of traditional satellite development, environmental tests account for about 30% to 40% of the total investment in spacecraft development [1,2]. Satellite thermal testing is the most complicated, costly, and time-consuming project in the spacecraft development process. However, it is an effective and necessary way to improve the reliability of the satellites [3,4]. On the basis of traditional thermal tests, exploring an efficient and reliable thermal test method for commercial satellites is of great significance to achieve low cost and reduce time consumption.

Satellite thermal tests include two parts: a thermal balance test and thermal vacuum cycling. The purpose of the thermal balance test is to verify the thermal design, and thermal vacuum cycling tests the reliability of the satellite.

Test cutting is a good approach to saving costs. In the 1980s, the United States manufactured eight identical FLTSATCOM communication satellites [5]. After summarizing the thermal test data and the on-orbit temperature data of the satellites, it was concluded that the thermal balance test, which is an important part of the thermal test, could be eliminated to meet the purpose of reducing expenses. Subsequent mass-produced satellites, such as SUPERBIRD [6], have not conducted thermal balance tests for flight models. Moreover, some tiny satellites, such as FASTSAT-HSV01, have not undergone initial thermal balance tests [7]; rather, only thermal analysis is performed on the satellite instead of the initial thermal balance test and is then directly launched into orbit. However, test simplification is not a good choice for reliability [8].

The space heating flow is the key simulation element of the thermal test. In low-Earth orbit, space heating flow is composed of solar heating, solar heating reflected by Earth, and IR heating from Earth.

Solar simulators are commonly used to simulate the space heating flow in tests, which are expensive to build and maintain [9]. In recent years, there have also been a number of cases that use infrared waves to simulate space heating flow. For example, the GPM satellite developed by NASA and JAXA uses heating panels to simulate the space heating flow in different regions of the satellite, achieving the purpose of the experiment [10]. In thermal tests, ultra-low temperatures are simulated using a heat sink cooled by liquid nitrogen, while the background of space is simulated using a heat sink with a high-emissivity surface. The temperature of the heat sink with liquid nitrogen refrigeration cannot be adjusted during the test, and can only be fixed below 100 K, making the start (cooling) and end (heating) processes of the tests more time-consuming. In addition, infrared heating cages have poor versatility and only fit one type of satellite. If the shape of the satellite is complicated, the error of the heating cage’s heat flow simulation will be considerably increased, and the design of the heating cage would become complicated, which will reduce the safety of the test [11,12].

Some satellite development groups are inclined to propose new temperature stabilization criteria or apply unstable test methods to shorten the duration of thermal tests [13,14]. The algorithm of the unstable thermal balance test has poor portability and cannot adapt to various types of satellites well. Moreover, the unstable thermal balance test method can only shorten the duration of the thermal balance test and does not reduce the length of thermal vacuum cycling or the time it takes to change the heat sink temperature, so the entire thermal test still long.

With the diversification of satellites, it is no longer feasible to simplify the tests according to different types of satellites [15], and a universal, simplified test method must be proposed. A new method without test cutting called the heat sink equivalent thermal test method, which uses the heat sink of vacuum test equipment to complete the heat flow simulation, achieves the goal of reducing costs and shortening the thermal test duration under the premise of ensuring the reliability of the satellite. Without using a heat flow simulation device, the time and cost of the design and manufacture of the infrared heating cage can be avoided, and the safety of the thermal test is also improved. Nitrogen gas is used to control the temperature of the heat sink, which is energy-saving, environmentally friendly, and economical. And the heat sink temperature can be adjusted quickly.

At present, the test method has been successfully applied to the Jilin−1 GF02F and GF03 series satellites, and the test results are remarkable. The TCS (thermal control system) operates stably after the satellite is in orbit. This article will briefly introduce the theoretical basis of the heat sink equivalent test method and take the GF02F satellite as an example to introduce the application of the method.

2. Principle of the Heat Sink Equivalent Thermal Test Method

The satellite thermal test is an effective means to verify the correctness of thermal design [16,17]. The traditional satellite thermal test uses the high-emissivity heat sink surface of the vacuum container to simulate the “cold and dark” environment in space and uses infrared heating cages or other devices to simulate the space heating flow. In the tests, the heat sink temperature should be below 100 K to ensure test accuracy, which is maintained by liquid nitrogen. In heat sink equivalent tests, the heat sink directly plays the role of simulating space heating flow by being set at a reasonable temperature. The temperature of the heat sink, which is generally above 200 K, is obtained by calculation and can be cooled by gaseous nitrogen.

The accuracy of the simulation of the space heating flow directly affects the results of the test. The heat sink equivalent method is suitable to simulate the space heating flow for situations where the heat flow in each direction of the satellite does not differ greatly. The temperature of the heat sink in the test is obtained by converting the space heating flow in all directions of the satellite, so that the heat exchange capacity of the satellite in the test is basically consistent with that in orbit, so as to achieve the purpose of verifying the TCS by simulating the on-orbit state of the satellite.

Usually, remote sensing satellites run in SSOs (Sun synchronization orbits) with small changes in the β angle. Figure 1 shows the space heating flow of the Jilin−1 GF02F satellite. Except for the surface exposed to the sun, the heat flow on other surfaces is similar. It indicates that satellites running in SSOs are suitable for using the heat sink equivalent method to conduct thermal balance tests.

The process of calculating the heat sink temperature in the thermal test is shown in Figure 2 as follows.

When we decided to conduct the heat sink equivalent thermal test on the satellite, the space heating flow was calculated based on the mission orbit, and how to simulate the heat flow in the test is also determined by the heat flow distribution. The satellite surface is divided into two parts. Extra devices are used to simulate the heat flow in the area where the heat sink equivalent method cannot be applied, and the heat flow in the remaining area is then normalized to obtain the average satellite absorption heat flow. The temperature value at which the heat sink should be set in the test can be calculated by using the absorption heat flow, so as to achieve the purpose of simulating the triple tasks of “cold, black” and heat flow. Finally, a simulation model is developed to predict the satellite test results, which are compared with the satellite in-orbit prediction data. If the error is less than the allowable error ΔT, the heat flow simulation is considered accurate and effective; otherwise, it is necessary to re-divide the area where the heat sink equivalent could simulate the heat flow. The implementation steps are shown in the following figure.

In step S1, the heat flow of satellites in all directions is analyzed, including the solar incident heat flow, the Earth-reflected shortwave radiation heat flow, and the Earth-emitted longwave radiation heat flow. The heat flow analysis is conducted using professional engineering software. The analysis result is used as the input conditions for the next step.

In step S2, the satellite surface is divided into n heat flow simulation areas. When the Ki of area i is less than n, the area is considered suitable for the heat sink to simulate the heat flow; otherwise, the area needs to be equipped with an additional heat flow simulation device. See Formula (1) for the calculation method of Ki.

$$K_i=\frac{A_i{\displaystyle \sum _{j=1,j\ne i}^n}\left|q_i-q_j\right|}{C_i{M}_i\mathsf{\Delta }T}\le n$$

(1)

where q_i and q_j are the heat flux of region i and j, C_i is the equivalent specific heat capacity of the satellite in the region, A_i is the equivalent area of the satellite in the region, M_i is the equivalent mass of the satellite in the region, and ΔT is the allowable error of this test.

After completing the calculation step S2, proceed to the judgment step S3. If the heat flow can be completely simulated with the heat sink, skip directly to step S5 to normalize the heat flow. Otherwise, go to step S4 and calculate the control point temperature of the heat flow simulator.

In step S4, the external heat flow simulation device of the area j uses the radiant plate for temperature control in the thermal test, and the temperature of the control point is calculated by Formula (2).

$$T_j=\sqrt[4]{\frac{{\alpha }_j{q}_{solar-j}+{\alpha }_j{q}_{albedo-j}+{\epsilon }_j{q}_{EarthIR-j}}{{\epsilon }_j\sigma }}$$

(2)

where q_Solar-j is the solar incident heat flux arriving in region j; q_albedo-j is the Earth-reflected shortwave radiation flux arriving in region j, and q_EarthIR-j is the Earth-emitted longwave radiation flux arriving in region j; σ is the Stefan–Boltzmann constant; α_j is the solar absorptivity of the satellite surface in region j; and ε_j is the infrared absorption (emission) rate of the satellite surface in region j.

Step S4 completes the heat flow simulation setup of the simulation device.

After setting the control point temperature of the heat flow simulation device, proceed to step S5. Apply the heat sink to simulate the heat flow in area i, and normalize it with Formula (3).

$$q_{avg}=\sum \frac{A_i\left({\alpha }_i{q}_{solar-i}+{\alpha }_i{q}_{albedo-i}+{\epsilon }_i{q}_{EarthIR-i}\right)}{A_S}$$

(3)

where q_avg is the normalized satellite absorbed heat flux, which is used to calculate the heat sink setting temperature in the thermal test; q_Solar-i is the solar incident heat flux arriving at region i, q_albedo-i is the Earth-reflected shortwave radiation flux arriving at region i, and q_EarthIR-i is the Earth-emitted longwave radiation flux arriving at region j; α_i is the solar absorptivity of the satellite surface in region i; ε_i is the infrared absorption (emission) rate of the satellite surface in region i; and A_S is the superficial area of the satellite.

After the normalization of heat flow is completed, calculate the heat sink setting temperature in the heat sink simulation area according to Formula (4), that is, step S6.

$$T_0=\sqrt[4]{\frac{q_{avg}}{\sigma {\epsilon }_S}}$$

(4)

where T₀ is the heat sink temperature of the vacuum chamber and ε_s is the equivalent emissivity of the satellite surface.

The derivation process of Formula (4) is as follows.

The cosmic background temperature is about 3 K, ignoring the cosmic background radiation, the thermal balance equation of the satellite in orbit is

$$Q_{solar}+Q_{albedo}+Q_{EarthIR}+Q_n=Q_o$$

(5)

where Q_Solar is the solar heat radiation absorbed by the satellite, Q_albedo represents the Earth-reflected shortwave radiation absorbed by the satellite, Q_EarthIR is the Earth-emitted longwave radiation absorbed by the satellite, Q_n is the internal heat source of the satellite, and Q_o is the outward radiant heat of the satellite.

Assuming that the satellite has fully convex surfaces, the average heat flow of each surface in orbit is q_avg. After the satellite reaches thermal equilibrium, the in-orbit equilibrium equation can be expressed as:

$$A_S{\epsilon }_S\sigma T_a^4-A_S{q}_{avg}=Q_n$$

(6)

where T_a is the satellite surface temperature in orbit.

The satellite was placed in a vacuum container for thermal tests, and the test state is shown in Figure 3.

Ignoring the shielding of the heat exchange between the satellite and the heat sink exhibited by the test equipment, the thermal balance equation of the test can be expressed as:

$$\frac{A_S\sigma \left(T_S^4-T_0^4\right)}{\frac{1}{{\epsilon }_S}+\frac{A_S}{A_0}\left(\frac{1}{{\epsilon }_0}-1\right)}=Q_n$$

(7)

where T_S is the surface temperature of the satellite in the test, ε₀ is the surface emissivity of the heat sink, and A₀ is the superficial area of heat sink. According to Formulas (6) and (7), we can deduce Formula (8).

$$\frac{A_S\sigma \left(T_S^4-T_0^4\right)}{\frac{1}{{\epsilon }_S}+\frac{A_S}{A_0}\left(\frac{1}{{\epsilon }_0}-1\right)}=A_S{\epsilon }_S\sigma T_a^4-A_S{q}_{avg}$$

(8)

It is considered that the surface temperature of the satellite in the test and in orbit is the same, $T_a\approx T_S$. When the difference between the surface area of the satellite and that of the heat sink is large enough and the emissivity of the heat sink is high enough, it can be considered that $\frac{A_S}{A_0}\left(\frac{1}{{\epsilon }_0}-1\right)\to 0$. Then, the temperature at which the heat sink should be set in the heat sink equivalent heat balance test method can be obtained from Equation (8).

$$T_0=\sqrt[4]{\frac{q_{avg}}{\sigma {\epsilon }_S}}$$

(9)

The error caused by approximation of $\frac{A_S}{A_0}\left(\frac{1}{{\epsilon }_0}-1\right)\to 0$ can be expressed as:

$$\mathsf{\Delta }{T}_0=T_S-T_a=\frac{q_{avg}{\delta }_1/\sigma }{\left(T_a{\delta }_2+T_S\right)\left(T_a^2{\delta }_2^2+T_S^2\right)}$$

(10)

In the formula, ${\delta }_1=\frac{A_S\left(1-{\epsilon }_0\right)}{A_0{\epsilon }_0}$, ${\delta }_2=\sqrt[4]{1+\frac{A_S{\epsilon }_S\left(1-{\epsilon }_0\right)}{A_0{\epsilon }_0}}$.

According to Formula (9), when $A_S/A_0<0.1$, ${\epsilon }_0>0.9$, the principle error of the heat sink equivalent test method is less than 1 °C.

Finally, the heat flow simulation method and control temperature are simulated and checked. In step S7, after setting the temperature of the heat sink in the test, it is necessary to carry out the simulation verification of the test model and compare the temperature result of the test model with the predicted result in orbit to ensure it meets the allowable error ΔT. Otherwise, the area of the heat sink equivalent method applied needs to be re-divided; that is, step S2 needs to be re-performed.

3. Application of Heat Sink Equivalent Test Method

To address the contradictions between low costs, short testing time, and high reliability in the process of satellite development, Jilin−1 satellite development team proposed the heat sink equivalent test method. According to the analysis in Section 2, the remote sensing optical satellite with the orbit of SSO is suitable for the thermal balance test using the heat sink equivalent method. If the vacuum container is large enough and the surface emissivity of the heat sink is high enough, the test error of the equivalent heat sink method is within the acceptable limits. The orbit of the GF02F optical remote sensing satellite is designed to be a 535 km SSO orbit. The local time of the descending node is 11:00, and the mass of the entire satellite is less than 230 kg. GF02F is equipped with two coaxial cameras with an aperture of Φ430 mm. The resolution is 0.75 m, and the fixed coordinates of the satellite are shown in Figure 4 and described below:

• Coordinate origin O: The center of the plane circle where the satellite docking ring and the rocket adapter are connected;
• OZ: Parallel to the optical axis and points to the optical camera;
• OX: In the satellite docking plane, it is in the same direction as the satellite flight direction;
• OY: Set according to the right-hand rule.

After launching into orbit, the −Z axis of the satellite is oriented to the sun in non-mission mode to ensure that the solar array remains fully charged. During the process of photographing and data transmission, the satellite’s +Z axis is oriented to the ground in three-axis stability.

First, an on-orbit heat flow analysis of the GF02F satellite is performed. According to the satellite’s configuration, size, orbit parameters, flight attitude, etc., the orbital average heat flow (including solar radiation, Earth-reflected shortwave radiation, and Earth-emitted longwave radiation) reaching each surface of the satellite is calculated as shown in

Table 1. The average heat flow reaching the surface of the satellite when oriented to the sun (W/m²).

Direction	Heat Flow (Winter Solstice)				Heat Flow (Summer Solstice)
	Sun-Emitted Radiation	Earth-Reflected Radiation	Earth-Emitted Radiation	Total Radiation	Sun-Emitted Radiation	Earth-Reflected Radiation	Earth-Emitted Radiation	Total Radiation
−Z direction	908.9	65.1	77.8	1051.8	836.0	5.5	75.8	917.3
+Z direction	0	70.5	78.0	148.5	0	76.3	75.7	152.0
+X direction	0	38.3	75.4	113.7	0	38.7	70.0	108.7
−X direction	0	38.6	75.0	113.6	0	38.8	70.1	108.9
+Y direction	0	14.1	67.4	81.5	0	19.6	61.4	81.0
−Y direction	0	52.7	67.7	120.4	0	44.7	61.5	106.2

.

The parameters used in the calculation are listed below.

(a)

Solar constant: S = 1414 W/m² (winter solstice), S = 1322 W/ m² (summer solstice);

(b)

Average Earth-emitted longwave radiation: Ee = 0.25(1 − ρ)S;

(c)

Average Earth-reflected shortwave radiation: Er = ρS;

(d)

Earth radius: 6378.14 km;

(e)

Space temperature: 4 K.

where ρ is the average reflectivity of the Earth to shortwave radiation (ρ = 0.35).

Formula (1) is used to calculate the heat flow analysis of each region. Except for the satellite −Z region, other regions could use the heat sink to simulate the heat flow. The −Z region uses the infrared radiation plate with the heat flux meter to achieve the purpose of simulating the orbit heat flow.

First, Formula (2) is used to calculate the temperature value of the satellite’s −Z heat flux meter. According to the average heat flow of the winter solstice (perihelion) and summer solstice (aphelion) on the −Z region in Table 1, the temperature value of the control point of the test in hot and cold conditions are calculated to be 37.3 °C and −19.6 °C, respectively.

Then, according to the optical properties of the satellite’s surface and Formula (3), the heat flow of other regions of the satellite except the −Z region is normalized. The average heat flux absorbed by the satellite on the winter solstice (perihelion) is q_avg = 84 W/m², and the average heat flux absorbed by the satellite on the summer solstice (apohelion) is q_avg = 58 W/m².

According to Formula (4), it can be calculated that the temperature of the heat sink should be −50 °C in the hot condition of the thermal test. The heat sink shall be set at −70 °C in the cold condition. Compared with the −170 °C heat sink temperature of the traditional heat flow simulation method, the heat sink temperature in this test is relatively high, and nitrogen gas can be used for temperature control, which has the advantages of low energy consumption.

Thus, the GF02F satellite’s −Z region uses infrared radiation plates to simulate the heat flow, and other regions of the satellite use heat sinks to simulate the heat flow. In addition, a test simulation model is established. After the verification, a formal test is performed.

The GF02F is the first satellite to use the heat sink equivalent method to conduct a thermal balance test. At the same time, a traditional thermal balance test using an infrared heating cage to simulate the heat flow was carried out for comparison. The test was carried out in the space environment simulation center of CGST. The test equipment was the KM6000 space environment simulator. Figure 5 shows the status of the satellite in different tests. The heat sink surface emissivity of KM6000 was beyond 0.9, and the ratio of the heat sink’s surface area to the satellite’s surface area was also greater than 10, according to Formula (9) in Section 3. The error of the heat sink equivalent thermal balance test result should be within 1 °C.

The Jilin−1 GF02F satellite was launched into orbit on 27 October 2021. The TCS performed well in orbit. Subsequent development of the GF03 satellites all use the heat sink equivalent test method, which shortens the duration of the satellites’ thermal tests and reduces the costs of operating test equipment.

Table 2. Temperatures of GF02F in thermal test and on orbit (°C).

Serial Number	Unit Name	Traditional Thermal Test		Heat Sink Thermal Test		On-Orbit Temperature
		Cold Conditions	Hot Conditions	Cold Conditions	Hot Conditions
1	Three-axis gyroscope	24.3	26.4	24.4	25.8	25.8
2	X+ star sensor	20.4	21.8	23.5	24.3	24.0
3	X− star sensor	20.8	22.4	23.5	24.2	24.0
4	Nano-star sensor	18.3	19.2	21.7	22.4	21.5
5	Single-axis gyroscope	18.3	20.5	18.5	20.9	19.5
6	Power controller	17.4	30.1	21.4	30.6	25.8
7	X wheel	4.8	18.1	6.8	16.0	11.5
8	Y wheel	5.7	20.4	10.5	20.5	13.5
9	Z wheel	7.6	21.9	10.5	20.5	15.3
10	S wheel	5.1	18.0	8.9	17.8	12.2
11	Data transmission electronics A	8.9	27.7	8.1	24.1	14.0
12	GPS receiver	2.9	19.4	7.6	14.8	11.5
13	X-band transponder	−2.2	19.1	3.9	18.1	11.5
14	Imaging processing unit	−7.4	17.6	3.0	28.0	15.0
15	Central computer	−2.9	15.4	7.1	22.6	17.0
16	Data transmission electronics B	6.1	21.8	9.2	22.8	12.0
17	S-band transponder	10.4	23.5	13.0	22.6	17.5

shows the temperature of key units in testing and in orbit.

In order to compare the temperature of the GF02F in testing and on orbit more clearly, the highest and lowest temperatures of the GF02F satellite in the heat sink equivalent test and the average temperature on orbit are presented separately in Figure 6.

According to the data in Table 2, it can be concluded that the on-orbit temperature of the GF02F satellite is between the high and low temperature results of the thermal balance test, which shows that both the traditional thermal balance test and the heat sink equivalent thermal balance test can be used to verify the correctness of the thermal design and predict the performance of the TCS in orbit. The closer the satellite’s on-orbit temperature is to the average of the test temperature, the more accurate the satellite’s thermal balance test is. We can use ${\delta }_{avg}$ to measure the error of the thermal balance test.

$${\delta }_{avg}=\frac{\sum {\delta }_i}{n}$$

(11)

$${\delta }_i=\sqrt{{\left(T_i^{\prime }-T_i\right)}^2}$$

(12)

where ${\delta }_{avg}$ represents the average error of the thermal balance test, ${\delta }_i$ is the temperature error of each unit, n stands for the number of units, $T_i^{\prime }$ is the average temperature of the i-th unit in the test, and $T_i$ is the average temperature of the i-th unit on orbit.

According to the satellite temperature data obtained from the thermal balance test and on-orbit flight using Formulas (7) and (8), the errors of the traditional thermal balance test and the heat sink equivalent thermal balance test of the GF02F satellite are 2.5 °C and 0.9 °C, respectively. This finding shows that the error of the heat sink equivalent method is consistent with the theoretical expectation and proves that the new thermal test method has good accuracy and can fulfill the purpose of the thermal test.

The new method of simulating heat flow using heat sinks not only ensures the reliability of satellite development, but also significantly reduces the duration of thermal testing and the cost of operating equipment compared to traditional thermal testing. According to the statistics of the thermal test results of the GF02F satellite, the traditional thermal test takes about 300 h and consumes about 0.7 m³ of liquid nitrogen per hour, while the heat sink equivalent thermal test takes about 200 h and consumes about 0.3 m³ of liquid nitrogen per hour. The test’s duration is thus shortened by one-third and the consumption of liquid nitrogen per hour is reduced by half. The specific data from the test are shown in the Figure 7.

4. Conclusions

In this paper, we propose a heat sink equivalent thermal test method suitable for SSO satellites. The test method involves simulating the space heating flow by setting the temperature of the heat sink of the vacuum vessel reasonably. This method can shorten the thermal test cycle by one-third and reduce the cost of operating thermal test equipment by more than 70% without cutting tests. Since the heat flow simulation device is no longer used in the test, the time and cost of the design and manufacture of the infrared heating cage can be reduced, and the safety of the test is improved. The principle of using the heat sink to simulate the heat flow is described, the formula to calculate the heat sink temperature in the test is given, and an error analysis is also carried out. It is shown that when the ratio of the heat sink surface area to the satellite surface area is greater than 10, and the heat sink surface emissivity is higher than 0.9, the error of the heat sink equivalent thermal test should be less than 1 °C. The heat sink equivalent thermal test method has been successfully applied to the Jilin−1 GF02 and GF03 series satellites. The on-orbit temperature data of the GF02F satellite demonstrate that the thermal design is great, the TCS performs well, and the error of the heat sink equivalent thermal test method is 0.9 °C, which is in line with theoretical expectations and meets the requirements of satellite development.