A spacecraft-oriented radiator design method

Abstract

The application discloses a spacecraft-oriented radiator design method and system, and belongs to the technical field of spacecraft thermal control. In order to solve the problems of non-uniform area and aperture, inaccurate extreme condition identification and lack of cross-validation in the prior art, the method comprises the following steps: obtaining an orbit and a radiator parameter; calculating an orbit position, a solar vector and an eclipse; independently calculating five types of external heat flow sub-items of a solar direct radiation, an earth albedo, an earth infrared, a deep space radiation and an earth radiation on a front surface and a back surface of the radiator, and summing up to obtain a total net heat flow density; according to a solving mode, a first mode of inversely solving a radiator area with a fixed temperature constraint is executed, or a second mode of inversely solving a balance temperature with a fixed area is executed; and finally, energy closure diagnosis and sub-item conservation checking are performed. Through double-sided sub-item modeling, reciprocal solving and three-stage extreme condition searching, the application realizes the improvement of design accuracy, the reduction of calculation cost and the quantitative evaluation of model self-consistency, and is suitable for the thermal control design of various low earth orbit spacecrafts.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft thermal control design technology, specifically relating to a heat sink design method for spacecraft. Background Technology

[0002] During spacecraft operation in orbit, onboard computers, payloads, battery packs, and other internal equipment continuously generate heat, which must be dissipated into deep space through radiators to maintain the cabin temperature within acceptable ranges. In recent years, high-heat-load missions such as space data centers and high-power SAR radars have emerged, making radiator area a key constraint affecting spacecraft mass budgets, configuration layouts, and launch costs.

[0003] Existing spacecraft thermal control design methods have the following shortcomings: (1) Identification of extreme thermal conditions relies on empirical point selection. In engineering, a certain moment of the winter solstice or summer solstice is usually used as the design point. However, in sun-synchronous orbits with different LTAN (local time of ascending node), the occurrence time of extreme thermal conditions varies with the combination of orbital parameters, attitude mode and radiator orientation. A single empirical point may be too conservative or may miss the true envelope condition.

[0004] (2) The area diameter of the two-sided heat sink is inconsistent. Some methods use 2A instead of calculating each side separately (i.e., "area doubling approximation"). When the external heat absorption of the back side is large, this approximation introduces uncontrollable deviations. Existing literature lacks a unified definition of the area diameter for summing after independent modeling of the front and back sides.

[0005] (3) Lack of detailed information on external heat flow output. Heat flow calculations usually only give the total net heat flow value, without providing detailed outputs for direct solar radiation, Earth's albedo, Earth's infrared absorption, and radiation emission towards deep space / Earth, making it difficult to trace the physical causes of changes in heat dissipation capacity.

[0006] (4) Forward and reverse solutions cannot be cross-validated. Existing thermal design tools usually only provide unidirectional solutions (finding area from known temperature, or finding temperature from known area), and do not have the ability to verify the closure of the two solution paths on the same example. Numerical accuracy and physical consistency cannot be quantitatively evaluated.

[0007] (5) It is difficult to balance computational cost and coverage. The computational cost of full-parameter high-density orbital scanning throughout the year is extremely high, while low-density sampling may miss peak values ​​under extreme thermal conditions. There is a lack of multi-level search strategies that balance engineering efficiency and reliable identification.

[0008] The aforementioned problems are all reflected in existing literature. Chapter 6 of Gilmore DG's "Spacecraft Thermal Control Handbook, Volume I: Fundamental Technologies" (2nd ed., The Aerospace Press, 2002) presents the classic heat sink thermal balance equation and area design method, but it only models single-sided heat sinks and does not address the issues of double-sided component calculations and area unification. Bulut M and Sözbir N's ​​"Optimized Analytical Solution of Platform Panel Radiative Area Dimensioning of Geostationary Communications Satellites" (Sakarya University Journal of Science, 2019, 23(5): 986-992, DOI: 10.16984 / saufenbilder.546894) discusses an analytical method for optimizing the heat sink area of ​​GEO communication satellites under extreme cold / hot conditions, but it is limited to geostationary orbit and does not involve multi-mode solutions and cross-validation mechanisms. Hou Zengqi and Hu Jingang's book "Spacecraft Thermal Control Technology - Principles and Applications" (China Science and Technology Press, 2007) systematically introduces the three heat source models of direct solar radiation, Earth albedo, and Earth infrared radiation, as well as the heat balance equations. However, the identification of extreme thermal conditions still relies mainly on empirical point selection and lacks a systematic multi-level search strategy. Summary of the Invention

[0009] To address the aforementioned shortcomings in existing technologies, this invention aims to provide a heat sink design method for spacecraft, thereby solving the problems in existing spacecraft heat sink thermal control design methods, such as inconsistent area and diameter of double-sided heat sinks, reliance on experience for identifying extreme thermal conditions with low efficiency, lack of cross-verification mechanism for forward and reverse solutions, and poor physical traceability of calculation results.

[0010] To address the aforementioned technical problems, this invention provides a heat sink design method for spacecraft, comprising the following steps: Step 1: Obtain the spacecraft's orbital parameters, attitude parameters, radiator pointing parameters, surface thermo-optical parameters, internal thermal load, equivalent thermal resistance, and solution mode parameters; Step 2: Based on the orbital parameters and epoch time, calculate the spacecraft's position vector sequence within the target time range through time system conversion and orbit propagation, and calculate the solar direction vector and eclipse shadow factor; Step 3: For each radiating surface of the radiator, based on the attitude parameters, radiator pointing parameters, and surface thermo-optical parameters, independently calculate the five categories of external heat flux: direct solar heat flux, Earth albedo heat flux, Earth infrared heat flux, heat flux radiated into deep space, and heat flux radiated towards the Earth. Then sum the net heat flux densities of each radiating surface to obtain the total net heat flux density. Step 4: Based on the solution mode parameters, select one of the following two solution modes: When the first solution mode is selected, the radiator design temperature is calculated based on the upper limit of the bus temperature and the equivalent thermal resistance. At this design temperature, the required area at each time is calculated using the total net heat flux density, and the maximum value throughout the year is taken as the design area. When the second solution mode is selected, a nonlinear thermal balance equation is constructed for each time under a given radiator area and the radiator equilibrium temperature is numerically solved. Then the bus temperature is calculated and the extreme bus temperature, radiator temperature and the time of occurrence throughout the year are output. Step 5: Perform energy closure diagnosis and component conservation verification on the output results.

[0011] The spacecraft-oriented radiator design method of this invention first establishes a standardized input parameter system to provide a foundation for subsequent calculations. Then, through precise orbital and geometric calculations, a spatiotemporal reference is provided for external heat flow analysis. Next, by calculating the external heat flow in components, the complex space thermal environment is decomposed into traceable physical components. Finally, through two inverse solution modes and rigorous verification diagnostics, a complete closed loop from input to output, from calculation to verification, is formed. This method decomposes the complex radiator design problem into modular and standardized steps, improving the clarity and operability of the design process. By decoupling the component calculation of external heat flow from the two solution modes, the method can be used for both preliminary area estimation and temperature verification in detailed design, exhibiting high versatility and flexibility. The final energy closure diagnostics ensure the numerical reliability of the calculation results.

[0012] Furthermore, in step three, the radiator has two radiating surfaces, a front and a back. The normal direction of the back is the opposite direction of the normal direction of the front. The five types of external heat flow components are calculated independently for each radiating surface and summed one by one. The radiator area is defined as the geometric area of ​​a single surface. The heat dissipation capacity of both surfaces is reflected by summing the calculations of the front and back components, without using the area doubling approximation.

[0013] The aforementioned technical solution specifies that the radiator has a clearly defined front and back side, with the back side normal being opposite to the front side. During calculation, external heat flux analysis is performed independently on both sides, and then the net heat flux density is summed. Here, "area" specifically refers to the geometric area of ​​a single side; the total heat dissipation capacity of both sides is represented by the sum of the heat fluxes on both sides, rather than simply multiplying the area by 2. This eliminates the significant bias introduced by the traditional "area doubling approximation" method when the back side is subjected to a large external heat flux (such as Earth's infrared radiation or reflected sunlight). This face-by-face modeling method more realistically reflects the physical reality of the radiator, improving the accuracy of area calculation, especially under complex attitudes and orbits, avoiding overestimation or underestimation of heat dissipation capacity.

[0014] Furthermore, in step three, the direct solar heat flux is calculated based on solar absorptivity, solar constant, the cosine of the angle between sunlight and the surface normal, and the eclipse shadow factor; the Earth albedo heat flux is calculated based on solar absorptivity, Earth albedo, solar constant, the apparent factor of the surface relative to the Earth, and the eclipse shadow factor; and the Earth infrared heat flux is calculated based on infrared emissivity, Earth infrared radiation flux, and the apparent factor of the surface relative to the Earth. The above technical solution precisely defines the calculation methods for these three types of absorptive external heat fluxes: direct solar radiation, Earth albedo, and Earth infrared radiation. It links the absorbed external heat fluxes to material properties, environmental flux, geometric relationships, and shading conditions, clarifying the physical sources and calculation basis of each external heat flux, thus giving the calculation results clear physical meaning. Designers can analyze the magnitude of each component to trace whether orbital position, satellite attitude, or material properties dominate the heat flux changes at a particular moment, providing clear physical guidance for optimized design.

[0015] Furthermore, the total net heat flux density The calculation formula is: ; in, The net heat flux density at the front of the radiator. This refers to the net heat flux density at the back of the radiator. The net heat flux density at the front and back of the radiator is calculated using the following formula:

[0016] in, , , and These are, respectively, direct solar heat flow, Earth's albedo heat flow, Earth's infrared heat flow, radiation emission into deep space, and radiation emission towards Earth; direct solar heat flow The calculation formula is: ; in, Solar absorptivity; The solar constant is 1361 W / m². The angle between the sunlight and the surface normal (s-axis). The eclipse shadow factor; Earth's albedo heat flow The calculation formula is: ; in, Solar absorptivity; a The Earth's average albedo is taken as 0.30. Let be the apparent factor of surface s relative to Earth; Earth's infrared heat flow The calculation formula is: ; in, Infrared emissivity; The infrared radiation flux of the Earth; Let be the apparent factor of surface s relative to Earth; Radiating into deep space The calculation formula is: ; in, It is the Stefan-Boltzmann constant; This represents the deep-space apparent factor; the negative sign indicates the direction of heat dissipation. It is the fourth power of the radiator's thermodynamic temperature; Radiating towards Earth The calculation formula is: ; in, It is the Earth's equivalent radiation temperature.

[0017] Furthermore, in step two, the methods for calculating the solar direction vector and the eclipse shadow factor include: Step 2.1, Time System Conversion: Convert the mission epoch from UTC to Julian day and establish the J2000 inertial frame time reference; Step 2.2, Construction of a Sun-Synchronous Orbit: Based on the orbital altitude h Earth's gravitational constant μ J2 calculates the required inclination angle for a sun-synchronous orbit. i The precession rate of the right ascension Ω of the ascending node is equal to 0.9856° / day, and the initial right ascension Ω is determined by the local time of the ascending node. Step 2.3, Orbit Propagation: Using the J2 perturbation analytical formula, calculate the satellite's position and velocity vectors in the inertial frame within the target time range; Step 2.4, Calculation of Solar Direction Vector: Calculate the unit direction vector of the sun in the J2000 system based on the Julian day, with an accuracy that meets the requirements of engineering thermal analysis; Step 2.5, Solar Eclipse Determination: Determine the solar eclipse state at each moment based on the geometric relationship between the Sun, Earth, and satellite, and output the shadow factor shadow_factor(t). [0,1], where 0 represents full sunlight, 1 represents full shadow, and the intermediate value corresponds to penumbra transition.

[0018] Furthermore, in step four, the first solution mode also includes a feasibility criterion step: when the calculated radiator design temperature is lower than a preset physical lower limit, the operating condition is marked as an unreachable thermal conductivity condition; the solution method of the first solution mode includes: Step SA1: Based on the upper limit of bus temperature The equivalent thermal resistance R is used to calculate the heat sink design temperature from the two-node heat chain. : ; in, For internal heat load; Step SA2: At this temperature, calculate for each time t ( t , ); Step SA3: When When <0, instantaneous area demand for: ; Step SA4: Take the maximum value for the whole year. This is the design area; Step SA5: Feasibility criterion, when If the temperature is below the physical lower limit, the condition is marked as "heat conduction is not reachable" to distinguish it from "insufficient radiation area". The solution methods for the second solution mode include: Step ST1: Given the heat sink area A and thermal resistance R, construct the nonlinear thermal balance equation for each time t: ; Step ST2: Iteratively solve the problem within the physical temperature range using the interval bisection method. ; Step ST3: From Calculate the busbar temperature: ; Step ST4: Output the annual extreme bus temperature Radiator temperature It also outputs the front / back / total external heat components at that time, along with the time of occurrence.

[0019] The above technical solutions describe in detail the internal logic of the two solution modes. The first solution mode deduces the required area by reversing the given upper temperature limit and innovatively introduces the "thermal inaccessibility" criterion to distinguish between design infeasibility due to excessive thermal resistance and insufficient area due to insufficient radiation capacity. The second solution mode, given the area, obtains the equilibrium temperature by solving the nonlinear thermal balance equation, ensuring convergence to the correct physical temperature solution under various operating conditions.

[0020] Furthermore, such as Figure 3 As shown, following step four, a three-stage search step for extreme thermal conditions is also included: The first stage involves coarse sampling over the entire year using a first preset step size, recording the peak values ​​within each sampling track. Specifically, the first preset step size for the first stage is 1 to 5 days, and the number of sampling points within each sampling track is 30 to 50.

[0021] The second stage involves sorting the peak values ​​in descending order and selecting the top N candidates; specifically, the value of N in the top N candidates ranges from 3 to 10. The third stage uses high-density sampling to accurately locate the peak moment of extreme thermal conditions within the time window corresponding to each candidate peak; specifically, the number of sampling points for high-density sampling in the third stage is 300 to 400 per track.

[0022] The aforementioned technical solution proposes a funnel-shaped search strategy of "coarse scan → screening → fine search". First, it traverses the entire year with a large step size to capture potential thermal peak regions; then, these candidate peaks are sorted and screened; finally, high-density sampling is performed within hourly windows near the candidate peaks to accurately locate the actual extreme operating conditions and their occurrence times. Compared to the huge computational load of high-density scanning throughout the year, this method can reduce the computational load by about 90%. At the same time, the fine search step ensures the reliability of capturing extreme peaks, making it possible to perform a detailed scan of thermal conditions throughout the year in engineering practice, avoiding omissions or over-design caused by relying on experience-based point selection.

[0023] Furthermore, step five also includes a cross-validation step and a closure error index calculation step; The cross-validation steps include: using the design area output by the first solution mode as the input area of ​​the second solution mode, running the second solution mode to obtain the equilibrium temperature, comparing the equilibrium temperature with the design temperature of the first solution mode, calculating the temperature closure error, and using it as a quantitative indicator of model self-consistency. The formula for calculating the closure error index is: ; ; in, This refers to the radiator temperature closure error. This refers to the busbar temperature closure error. The second solution mode yields the heat sink equilibrium temperature; The busbar temperature is obtained using the second solution mode; The extreme busbar temperature throughout the year is obtained using the second solution mode; The design temperature of the radiator is obtained using the first solution mode; the root mean square error, 95th percentile, and maximum deviation are calculated for all operating conditions; engineering accuracy reference: RMSE < 1K is excellent, 1-3K is good, and > 5K requires investigation; Energy closure diagnosis involves checking the thermal balance residual at each time step. Ideally, the residual should be zero. The maximum absolute value and RMS value of the statistical residuals for the entire year's time series are used as quantitative indicators of numerical accuracy. The component conservation check is performed by examining each time step. Check if the condition is exactly true; if not, indicate a model implementation error.

[0024] The above technical solution establishes a self-checking mechanism for the model. Cross-validation involves using the area calculated by the first model as input for the second model and comparing the equilibrium temperature derived from it with the design temperature of the first model. Energy closure diagnosis checks whether the residuals of the heat balance equation are zero. Partial conservation verification verifies whether each part satisfies the relationship that the sum of the front and back sides equals the total value. Cross-validation provides quantitative indicators (such as temperature closure error) for the model's self-consistency and is a powerful tool for verifying the correctness of the algorithm and its numerical accuracy. Energy closure diagnosis and partial conservation verification ensure the accuracy and traceability of the calculation results from two dimensions: energy conservation and physical decomposition, providing highly reliable data support for engineering design.

[0025] Furthermore, the attitude parameters include a whole-satellite attitude mode and a radiator independent pointing mode. The radiator independent pointing mode includes at least one of the following: fixed to the body installation direction mode, solar edge pointing mode, Earth edge pointing mode, zenith pointing mode, and switching mode between solar edge pointing during illumination and Earth pointing during eclipse.

[0026] Furthermore, the surface thermo-optical parameters also include end-of-life degradation parameters, which are corrected for solar absorptivity and infrared emissivity based on on-orbit ultraviolet irradiation and atomic oxygen exposure doses. During the spacecraft's on-orbit lifespan, the surface material properties gradually degrade, typically manifested as an increase in solar absorptivity. Considering the degradation model, the designed heat sink area can meet the most stringent thermal control requirements at the end of the mission, ensuring the spacecraft's thermal safety throughout its entire lifespan and avoiding the risk of exceeding on-orbit temperature limits due to material aging.

[0027] Compared with existing spacecraft radiator thermal control design methods, the advantages of this invention are as follows: At the modeling level, this invention's radiator design method for spacecraft uses a single-sided geometric area as a uniform caliber to calculate and sum the results for each face of the double-sided radiator, eliminating the systematic bias caused by the area doubling approximation. At the solution level, two inverse modes (fixed temperature to calculate area, fixed area to calculate temperature) share the same heat flux definition, allowing for direct comparison and regression of the output results. In terms of engineering efficiency, the three-stage funnel search reduces the computational load for locating extreme thermal conditions throughout the year to approximately one-tenth of that for full-domain dense sampling, while ensuring envelope safety. Furthermore, the cross-validation mechanism and energy closure diagnostics provide quantitative evidence for model self-consistency, and the independent outputs of the five external heat flux components make the physical origins of the calculation results traceable. Attached Figure Description

[0028] Figure 1 This is a flowchart of a heat sink design method for spacecraft.

[0029] Figure 2 This is a schematic diagram of the heat flow breakdown on the double-sided radiating surface of the radiator.

[0030] Figure 3 This is a schematic diagram of a three-stage search under extreme thermal conditions.

[0031] Figure 4 A scatter plot for cross-validation of radiator temperatures.

[0032] Figure 5 This is a diagram showing the temperature margin analysis of the busbars, where... Figure 5 The upper part shows the annual maximum busbar temperature curves for LTAN=18.0h and LTAN=13.5h under different fixed radiator area conditions, and the lower part shows the temperature difference between the two curves.

[0033] Figure 6 A quantitative comparison chart of radiator area requirements under different local time conditions at different ascending node points is provided. Figure 6 The upper part shows the radiator area demand curves for LTAN=18.0h and LTAN=13.5h under different upper limit constraints of bus temperature, and the lower part shows the area difference and percentage change between the two.

[0034] Figure 7 This is an energy-closed residual analysis plot, where, Figure 7 The left side shows the time series curve (logarithmic scale) of the absolute value of the thermal balance residual under representative operating conditions, while the right side shows the statistical histogram of the residual distribution for all operating conditions. Detailed Implementation

[0035] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0036] This embodiment takes a space data center satellite operating in a 600 km sun-synchronous orbit (SSO) with an internal heat load of 10 kW as the object, combined with... Figures 1 to 7 This invention describes the specific implementation process of the spacecraft radiator design method provided by the present invention.

[0037] Step 1: Obtain input parameters First, construct a standardized set of input parameters, such as Figure 1 As shown, this provides a foundation for subsequent calculations.

[0038] Orbital parameters: The orbital altitude is set at 600 km, and the orbital inclination is calculated to be approximately 97.78° based on sun-synchronous conditions. To study the influence of the ascending node local time LTAN, this embodiment performs a parametric scan of LTAN, taking six values: 6.0h, 8.0h, 10.5h, 12.0h, 13.5h, and 18.0h. The mission epoch is set to January 1, 2026, at 12:00 UTC.

[0039] Attitude and pointing parameters: The overall satellite attitude mode is set to "Anti-Sun Mode" (ANTI_SUN), meaning the radiator mounting surface always faces away from the sun. To compare the impact of different independent radiator pointing modes on heat dissipation capacity, this embodiment sets the radiator pointing modes to "Sun Edge Orientation Mode" (edge_on_sun), "Earth Edge Orientation Mode" (earth_edge_on), and a pointing mode simulating the International Space Station radiator (iss_radiator).

[0040] Surface thermo-optical parameters: To compare material properties, two typical surface coatings were selected: End of OSR lifetime, solar absorptivity , ) and radiation-cooling coating, solar absorptivity , , .

[0041] Heat load and heat conduction path: Internal heat load The equivalent thermal resistance between the busbar (mounting plate) and the heat sink is 10000 W. R The value was scanned as a key design variable, ranging from 0.005 to 0.015 K / W.

[0042] Solution Modes and Constraints: This embodiment will execute two solution modes respectively. In the first solution mode (fixed temperature inverse area calculation), the upper limit of the busbar temperature is... The scan range is from 313.15 to 373.15 K. In the second solution mode (fixed area inverse temperature calculation), a fixed heat sink area A is given for verification calculation.

[0043] Step Two: Track and Geometric Calculations Time system conversion: Convert UTC time to Julian Day (JD) to establish the time reference for the J2000 inertial frame.

[0044] Orbital propagation and solar vector calculation: Using the J2 perturbation analytical formula, the spacecraft's position vector r(t) and velocity vector v(t) are calculated over the entire year of 2026. Simultaneously, a high-precision unit vector s(t) of the solar direction is calculated based on the Julian day.

[0045] Solar eclipse determination: Based on the geometric relationship between the Sun, Earth, and spacecraft, calculate the shadow factor (t) at each moment. [0,1]. This factor is a continuous value, between 0 (full sun) and 1 (full shadow), used to accurately describe the penumbra transition zone and provide accurate shading information for subsequent external heat flow calculations.

[0046] Step 3: Calculation of External Heat Flow This step is the core modeling process. For example... Figure 2 As shown, the front and back radiating surfaces of the radiator are calculated independently. The radiator area is defined as the geometric area of ​​a single surface, and the total heat dissipation capacity of both surfaces is represented by summation, abandoning the traditional approximation of "doubling the area". For each radiating surface, five categories of components are calculated: direct solar heat flux, Earth albedo heat flux, Earth infrared heat flux, heat flux radiated into deep space, and heat flux radiated towards the Earth. The sum of these components constitutes the net heat flux density of that radiating surface.

[0047] For each radiating surface, based on the surface normal determined by the attitude and pointing parameters, the following five types of external heat flux components are calculated: direct solar heat flow The calculation formula is: ; in, Solar absorptivity; The solar constant is 1361 W / m². The angle between the sunlight and the surface normal (s-axis). The eclipse shadow factor; Earth's albedo heat flow The calculation formula is: ; in, Solar absorptivity; a The Earth's average albedo is taken as 0.30. Let be the apparent factor of surface s relative to Earth; Earth's infrared heat flow The calculation formula is: ; in, Infrared emissivity; The infrared radiation flux of the Earth; Let be the apparent factor of surface s relative to Earth; Radiating into deep space The calculation formula is: ; in, It is the Stefan-Boltzmann constant; This represents the deep-space apparent factor; the negative sign indicates the direction of heat dissipation. It is the fourth power of the radiator's thermodynamic temperature; Radiating towards Earth The calculation formula is: ; in, It is the Earth's equivalent radiation temperature.

[0048] The net heat flux density of each radiating surface is the sum of five terms: The total net heat flux density of the radiator is the sum of that on both sides: ; in, The net heat flux density at the front of the radiator. This refers to the net heat flux density at the back of the radiator. With LTAN=10.5h, Taking 313.15 K, R=0.005 K / W, RC coating material, and edge_on_sun pointing mode as an example, the values ​​at various times throughout the year are calculated. (t), (t) and (t). Verify the conservation relationship of the components. The condition holds true precisely for all external heat flow components.

[0049] Step 4: Execution of the two solution modes. Based on the input solution mode parameters, select one of the following two modes to execute.

[0050] Mode 1: First Solution Mode (Size Area). The solution methods for the first solution mode include: Step SA1: Based on the upper limit of bus temperature The equivalent thermal resistance R is used to calculate the heat sink design temperature from the two-node heat chain. : ; in, For internal heat load; Step SA2: At this temperature, calculate for each time t ( t , ); Step SA3: When When <0, instantaneous area demand for: ; Step SA4: Take the maximum value for the whole year. This is the design area; Step SA5: Feasibility criterion, when If the temperature is below the physical lower limit, the condition is marked as "heat conduction inaccessible," distinguishing it from "insufficient radiative area." In the first solution mode, the radiator design temperature... At this temperature, taking the RC coating / edge_on_sun combination as an example, the net cooling density is approximately 233.7 W / m², and the required area is... Taking the OSR_EOL / edge_on_sun combination as an example, the net cooling density is approximately 183.2 W / m², and the required area is... The RC coating reduces the area by approximately 21.6% compared to OSR_EOL.

[0051] Mode 2: Second solution mode (Solve Temperature), Step ST1: Given the heat sink area A and thermal resistance R, construct the nonlinear thermal balance equation for each time t: ; Step ST2: Iteratively solve the problem within the physical temperature range using the interval bisection method. ; Step ST3: From Calculate the busbar temperature: ; Step ST4: Output the annual extreme bus temperature Radiator temperature It also outputs the front / back / total external heat components at that time, along with the time of occurrence.

[0052] Using the RC coating / iss_radiator / LTAN=18.0h combination and a fixed area A=7.0 m² as input, the heat balance equation is solved time-by-time using the interval bisection method. The results show an annual extreme busbar temperature of approximately 450.0 K and a maximum radiator temperature of approximately 354.1 K, with the extreme moment occurring in early May 2026. Feasibility criterion: If during the calculation process, if it is found that… If the temperature is below the preset physical lower limit (e.g., 2.7K), the condition is marked as "heat conduction unreachable," prompting the designer to optimize the heat conduction path (reduce thermal resistance R) rather than simply increasing the heat dissipation area.

[0053] like Figure 3 As shown, to improve the search efficiency for extreme thermal conditions, a three-stage search strategy was adopted during the year-round time scan: Phase 1 (coarse scan): Sample a complete orbital cycle with a step size of 5 days. Take 36 points evenly within each orbit and record the peak temperature or area requirements of each orbit.

[0054] The second stage (screening) involves sorting the peaks obtained from the coarse scan in descending order and selecting the top 5 as candidate peaks.

[0055] The third stage (precise search): Within the time window corresponding to each candidate peak (e.g., ±0.5 orbital periods), high-density sampling of 360 points per orbit is used to accurately locate the global extreme thermal conditions. Compared with global high-density sampling, this method reduces the computational load by approximately 90% while ensuring capture reliability.

[0056] Step 5: Verification and Diagnosis After the calculation is completed, a rigorous verification and diagnostic process is performed.

[0057] Cross-validation: The design area obtained from the first solution mode is cross-validated. Use this as input for the second solution mode, and rerun the second solution mode. Compare the temperature results under the two modes: ; like Figure 4 As shown in the scatter plot, the vast majority of operating conditions in this example... The results are concentrated within ±1.5K, and the root mean square error (RMSE) is less than 1K, demonstrating that the model has excellent self-consistency and numerical accuracy.

[0058] Energy closure diagnosis: Check the thermal balance residuals at each time step in the second solution mode. .like Figure 7 As shown, the absolute value of the residuals at all times throughout the year is ~10. -7 Up to 10 - ¹²W, close to machine zero, proves the accuracy of the numerical solution.

[0059] Partial conservation check: For each type of external heat flux component (e.g., direct sunlight, Earth's albedo, etc.), check if the following conditions are met: In this example, the relationship holds strictly at all times, ensuring the correctness of the physical decomposition.

[0060] Quantitative Impact Analysis of LTAN on Heatsink Area: To further demonstrate the analytical capabilities of this invention, the impact of LTAN parameters was quantified using the aforementioned method. With R = 0.010 K / W, iss_radiator pointing, and RC coating material fixed, the area requirements for LTAN = 18.0h (morning / evening orbit) and LTAN = 13.5h (afternoon orbit) under different busbar temperature constraints were compared. The results show that: Figure 6 As shown, at the low-temperature confinement end ( At 63°C, the area requirement for LTAN=13.5h is approximately 40 m² (about 16%) higher than that for LTAN=18.0h; as temperature constraints are relaxed, this difference gradually decreases to approximately 1.5 m² (about 3%). This quantitative comparison provides a direct basis for selecting LTAN during the overall spacecraft design phase.

[0061] like Figure 5 As shown, under different fixed area conditions, the difference in bus temperature curves between LTAN=18.0h and LTAN=13.5h is on the order of 0.7~1.5 K, further verifying the consistency of the model under different orbital conditions.

[0062] In summary, this embodiment fully demonstrates the implementation process of the method proposed in this invention. Through two-sided component modeling, inverse solving, three-stage search, and rigorous verification and diagnosis, this invention effectively solves the problems mentioned in the background art, such as inconsistent area diameters, inaccurate identification of extreme working conditions, and lack of cross-validation, significantly improving the accuracy and efficiency of spacecraft heat sink design.

Claims

1. A heat sink design method for spacecraft, characterized in that, Includes the following steps: Step 1: Obtain the spacecraft's orbital parameters, attitude parameters, radiator pointing parameters, surface thermo-optical parameters, internal thermal load, equivalent thermal resistance, and solution mode parameters; Step 2: Based on the orbital parameters and epoch time, calculate the spacecraft's position vector sequence within the target time range through time system conversion and orbit propagation, and calculate the solar direction vector and eclipse shadow factor; Step 3: For each radiating surface of the radiator, based on the attitude parameters, radiator pointing parameters, and surface thermo-optical parameters, independently calculate the five categories of external heat flux: direct solar heat flux, Earth albedo heat flux, Earth infrared heat flux, heat flux radiated into deep space, and heat flux radiated towards the Earth. Then sum the net heat flux densities of each radiating surface to obtain the total net heat flux density. Step 4: Based on the solution mode parameters, select one of the following two solution modes: When the first solution mode is selected, the radiator design temperature is calculated based on the upper limit of the bus temperature and the equivalent thermal resistance. At this design temperature, the required area at each time is calculated using the total net heat flux density, and the maximum value throughout the year is taken as the design area. When the second solution mode is selected, a nonlinear thermal balance equation is constructed for each time under a given radiator area and the radiator equilibrium temperature is numerically solved. Then the bus temperature is calculated and the extreme bus temperature, radiator temperature and the time of occurrence throughout the year are output. Step 5: Perform energy closure diagnosis and component conservation verification on the output results.

2. The heat sink design method for spacecraft according to claim 1, characterized in that, In step three, the radiator has two radiating surfaces, a front and a back. The normal direction of the back is the opposite direction of the normal direction of the front. The five types of external heat flow components are calculated independently for each radiating surface and summed one by one. The radiator area is defined as the geometric area of ​​a single surface. The heat dissipation capacity of both surfaces is reflected by summing the front and back component calculations, without using the area doubling approximation.

3. The heat sink design method for spacecraft according to claim 1, characterized in that, In step three, the direct solar heat flux is calculated based on solar absorptivity, solar constant, cosine of the angle between sunlight and the surface normal, and eclipse shadow factor; the Earth albedo heat flux is calculated based on solar absorptivity, Earth albedo, solar constant, apparent surface factor relative to Earth, and eclipse shadow factor; and the Earth infrared heat flux is calculated based on infrared emissivity, Earth infrared radiation flux, and apparent surface factor relative to Earth.

4. The heat sink design method for spacecraft according to claim 3, characterized in that, The total net heat flux density The calculation formula is: ； in, The net heat flux density at the front of the radiator. This refers to the net heat flux density at the back of the radiator. The net heat flux density at the front and back of the radiator is calculated using the following formula: in, , , and These are, respectively, direct solar heat flow, Earth's albedo heat flow, Earth's infrared heat flow, radiation emission into deep space, and radiation emission towards Earth; direct solar heat flow The calculation formula is: ； in, Solar absorptivity; The solar constant is 1361 W / m². The angle between the sunlight and the surface normal (s-axis). The eclipse shadow factor; Earth's albedo heat flow The calculation formula is: ； in, Solar absorptivity; a The Earth's average albedo is taken as 0.

30. Let be the apparent factor of surface s relative to Earth; Earth's infrared heat flow The calculation formula is: ； in, Infrared emissivity; The infrared radiation flux of the Earth; Let be the apparent factor of surface s relative to Earth; Radiating into deep space The calculation formula is: ； in, It is the Stefan-Boltzmann constant; This represents the deep-space apparent factor; the negative sign indicates the direction of heat dissipation. It is the fourth power of the radiator's thermodynamic temperature; Radiating towards Earth The calculation formula is: ； in, It is the Earth's equivalent radiation temperature.

5. The heat sink design method for spacecraft according to claim 1, characterized in that, In step two, the methods for calculating the solar direction vector and the eclipse shadow factor include: Step 2.1, Time System Conversion: Convert the mission epoch from UTC to Julian day and establish the J2000 inertial frame time reference; Step 2.2, Construction of a Sun-Synchronous Orbit: Based on the orbital altitude h Earth's gravitational constant μ J2 calculates the required inclination angle for a sun-synchronous orbit. i The precession rate of the right ascension Ω of the ascending node is equal to 0.9856° / day, and the initial right ascension Ω is determined by the local time of the ascending node. Step 2.3, Orbit Propagation: Using the J2 perturbation analytical formula, calculate the satellite's position and velocity vectors in the inertial frame within the target time range; Step 2.4, Calculation of Solar Direction Vector: Calculate the unit direction vector of the sun in the J2000 system based on the Julian day, with an accuracy that meets the requirements of engineering thermal analysis; Step 2.5, Solar Eclipse Determination: Determine the solar eclipse state at each moment based on the geometric relationship between the Sun, Earth, and satellite, and output the shadow factor shadow_factor(t). [0,1], where 0 represents full sunlight, 1 represents full shadow, and the intermediate value corresponds to penumbra transition.

6. The heat sink design method for spacecraft according to claim 1, characterized in that, In step four, the first solution mode also includes a feasibility criterion step: when the calculated radiator design temperature is lower than the preset physical lower limit, the working condition is marked as an unreachable thermal conductivity working condition. The solution methods for the first solution mode include: Step SA1: Based on the upper limit of bus temperature The equivalent thermal resistance R is used to calculate the heat sink design temperature from the two-node heat chain. : ； in, For internal heat load; Step SA2: At this temperature, calculate for each time t ( t , ); Step SA3: When When < 0, instantaneous area demand for: ； Step SA4: Take the maximum value for the whole year. This is the design area; Step SA5: Feasibility criterion, when If the temperature is below the physical lower limit, the condition is marked as "heat conduction is not possible" to distinguish it from "insufficient radiation area". The solution methods for the second solution mode include: Step ST1: Given the heat sink area A and thermal resistance R, construct the nonlinear thermal balance equation for each time t: ; Step ST2: Iteratively solve the problem within the physical temperature range using the interval bisection method. ; Step ST3: From Calculate the busbar temperature: ; Step ST4: Output the annual extreme bus temperature Radiator temperature It also outputs the front / back / total external heat components at that time, along with the time of occurrence.

7. The heat sink design method for spacecraft according to claim 1, characterized in that, Following step four, a three-stage search step for extreme thermal conditions is also included: The first stage involves coarse sampling over the entire year using a first preset step size, recording the peak values ​​within each sampling track. The second stage involves sorting the peak values ​​in descending order and selecting the top N candidates. The third stage uses high-density sampling to accurately pinpoint the peak moment of extreme thermal conditions within the time window corresponding to each candidate peak.

8. The heat sink design method for spacecraft according to claim 1, characterized in that, Step five also includes a cross-validation step and a closure error index calculation step; The cross-validation steps include: using the design area output by the first solution mode as the input area of ​​the second solution mode, running the second solution mode to obtain the equilibrium temperature, comparing the equilibrium temperature with the design temperature of the first solution mode, calculating the temperature closure error, and using it as a quantitative indicator of model self-consistency. The formula for calculating the closure error index is: ； ； in, This refers to the radiator temperature closure error. This refers to the busbar temperature closure error. The second solution mode yields the heat sink equilibrium temperature; The busbar temperature is obtained using the second solution mode; The extreme busbar temperature throughout the year is obtained using the second solution mode; The first solution mode is used to obtain the radiator design temperature; the root mean square error, 95th percentile, and maximum deviation are calculated for all operating conditions; engineering accuracy reference: RMSE < 1K is excellent, 1-3K is good, and >5K requires investigation; Energy closure diagnosis involves checking the thermal balance residual at each time step. Ideally, the residual should be zero. The maximum absolute value and RMS value of the statistical residuals for the entire year's time series are used as quantitative indicators of numerical accuracy. The component conservation check is performed by examining each time step. Check if the condition is exactly true; if not, indicate a model implementation error.

9. The heat sink design method for spacecraft according to claim 1, characterized in that, The attitude parameters include the overall satellite attitude mode and the independent radiator pointing mode. The independent radiator pointing mode includes at least one of the following: fixed to the body installation direction mode, solar edge pointing mode, Earth edge pointing mode, zenith pointing mode, and switching mode between solar edge pointing during illumination and Earth pointing during eclipse.

10. The heat sink design method for spacecraft according to claim 1, characterized in that, The surface thermo-optical parameters also include lifetime-end degradation parameters, which are corrected for solar absorptivity and infrared emissivity based on on-orbit ultraviolet irradiation and atomic oxygen exposure doses.

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