Radiator with high-flow and low-flow zones and control system therefor

Abstract

A multi-zone radiator comprising a first zone and a second zone. The first zone includes a first plurality of fluid conduits thermally coupled to a first surface, and is configured to allow flow of a coolant fluid through the first plurality of fluid conduits at up to a first maximum flow rate. The second zone includes a second plurality of fluid conduits thermally coupled to a second surface, and is configured to allow flow of a coolant fluid through the second plurality of fluid conduits at up to a second maximum flow rate lower than the first maximum flow rate.

Description

RADIATOR WITH HIGH-FLOW AND LOW-FLOW ZONES AN D CONTROL SYSTEM THEREFOR

[0001] This application claims the benefit of U. S. provisional patent application no.63 / 714,301, filed on October 31, 2024, which is incorporated by reference herein in its entirety.BACKGROUND

[0002] Freezable radiators represent a significant innovation in spacecraft thermal control systems. These radiators are designed to efficiently manage temperature fluctuations encountered during space missions. During colder mission phases, such as extended periods in Earth’s shadow, the radiator tubes are engineered to withstand fluid freezing. When exposed to heightened external heat fluxes, such as prolonged solar exposure, the radiator actively thaws these frozen tubes. This dynamic functionality ensures effective heat rejection while utilizing human-friendly fluids, all without compromising safety or introducing unnecessary complexity.

[0003] One notable implementation of freezable radiators was proposed by Broeren and Duschatko in 1995 for the International Space Station (ISS) for ammonia, which is a toxic, low viscosity liquid. See Broeren, R. and Duschatko, R., “International Space Station Alpha Design-To-Freeze Radiators,” SAE Technical Paper 951652, 1995, https: / / doi.org / 10.4271 / 951652.) However, that technology presents certain drawbacks when using a working fluid having high viscosity at low temperatures (e.g., a mixture of water and propylene glycol). Those drawbacks include challenges related to flow assurance, partial recovery, radiator control, extended thawing time, and control of heat transfer surface area. Flow Assurance Challenges

[0004] When working fluid freezes within the radiator, particles of the frozen material can inadvertently enter the fluid loop. This poses a risk of pipe blockages or damage to critical components such as pumps. Ensuring a reliable flow path without clogs or obstructions becomes crucial for maintaining system performance.Partial Recovery

[0005] Achieving full recovery' of the radiating surfaces after thawing can be challenging. The highly viscous flow in parallel-cooling channels often leads to the phenomenon of static instability during the recovery process, a condition in which a flow channel may exhibit multiple steady states under identical boundary conditions (see WuChangchun et al., “Some Interesting Flow Characteristics of A Heavy Crude Pipeline,” Proceedings of 1PC 2006 6th International Pipeline Conference September 25 - 29, 2006, Calgary, Alberta, Canada IPC2006-10352. Static instability in a radiator with highly viscous working fluid can hinder the thawing process in its larger sections. Hence, a portion of the radiator may remain frozen, potentially reducing the overall effectiveness of the radiator.Challenges in Radiator Control

[0006] Managing the radiating area of the unfrozen part of the radiator also presents challenges. In regions where the viscosity of the working fluid exceeds a certain threshold, static flow instability occurs in parallel pipes (flow tubes) of the radiator. Controlling the transition between frozen and thawed sections requires precise management to optimize heat rejection.Extended Thawing Time

[0007] Thawing the frozen working fluid can be time-consuming. During this process, the radiator may not respond promptly to fluctuating thermal conditions. The delay in thawing could impact the spacecraft’s overall thermal performance.Control of Heat Transfer Surface Area

[0008] Achieving a required area of the unfrozen portion of the radiator remains a challenge. Broeren and Duschatko’s approach involves using thermal insulators (multi-layer insulation blankets) and structural support with thermal insulators to prevent working fluid from freezing in manifolds. However, that method may not consistently provide the required temperature for highly viscous working fluids.BRIEF DESCRIPTION OF DRAWINGS

[0009] FIG. 1 illustrates a schematic diagram of a cooling system including a dual-zone radiator including a high-flow zone and a low-flow zone.

[0010] FIG. 2 illustrates a side view of a cooling pipe of the low-flow zone with a heat absorbing surface to heat up the working fluid (coolant fluid) inside the cooling pipe.

[0011] FIG. 3 illustrates a schematic diagram of an apparatus for dual-radiator including a cooling pipe adapted for preventing the working fluid from freezing within a cooling pipe of the low-flow zone.

[0012] FIG. 4 illustrates a schematic diagram of an apparatus for dual-zone radiator including an inlet pipe and an outlet pipe of the low-flow zone disposed within the inlet pipe and outlet pipe of the high-flow zone, respectively.

[0013] FIG. 5 A shows a cross-section of a fluid conduit of a radiator, including an internal pipe enclosed within a casing, where the working fluid is in a liquid state.

[0014] FIG. 5B shows a cross-section of a fluid conduit of a radiator, including an internal pipe enclosed within a casing, where the working fluid is at least partially in a frozen (solid) state.

[0015] FIG. 6 is a schematic representation of the dual-panel radiator showing panels exposed to distinct thermal environments, fluid-carrying tubes, and an eclipse valve for setting flow configuration.

[0016] FIG. 7 is a block diagram of a cooling system with a control system that includes a flow controller, a digital twin, and a combinatorial evaluator.

[0017] FIG. 8 shows an example of a digital twin-generated temperature distribution map of a radiator panel, used to assess internal gradients and thermal management needs.

[0018] FIG. 9 illustrates a two-fluid modeling approach, showing a cold liquid film or solidified layer and a warm liquid core within the radiator tube.

[0019] FIG. 10 is a thermal network schematic diagram showing the heat transfer path from warm liquid core to a heat sink representing the external thermal environment of a radiator panel.

[0020] FIG. 11 illustrates cooling pipes attached to a combined radiating surface that serves both high-flow and low-flow zones, providing thermal support for flow re-establishment and system redundancy in case of damage or leakage.

[0021] FIG. 12 shows an embodiment of a cooling system that includes a one-way valve with an integrated position sensor disposed between the outlet of the radiator tube and the eclipse valve.

[0022] FIG. 13 shows a flowchart of an example process for operating a cooling system including a multi-zone radiator.

[0023] FIG. 14 shows an example of a process for controlling a cooling system that includes a multi -zone radiator.DETAILED DESCRIPTION

[0024] The techniques introduced here include a multi-zone radiator and a control system for the same, as will now be described in detail.I. Multi -Zone Radiator

[0025] Referring to FIG. 1, a cooling system 1 is shown, which includes a dual-zone (two-zone) radiator 4, a radiator inlet 51 in fluid communication with the dual -zone radiator 4, and a radiator outlet 53 in fluid communication with the dual-zone radiator 4, Dual-zone radiator 4 includes a high-flow zone 6 and a low-flow zone 8. High-flow zone 6 includes a first inlet pipe 10 (e.g., an inlet manifold), a first outlet pipe 12 (e.g., an outlet manifold), a first cooling pipe 14 attached to a first heat radiating surface 15 having a first predetermined absorptivity to emissivity ratio (e.g., a radiator panel surface coated with a high-emissivity white paint). First inlet pipe 10 is connected to a radiator inlet 51. First cooling pipe 14 is connected to first inlet pipe 10 and first outlet pipe 12. First outlet pipe 12 is connected to a radiator outlet 53. High-flow zone 6 may include a plurality of cooling pipes 14.

[0026] Low-flow zone 8 includes a second inlet pipe 18 (e.g., a second inlet manifold) in fluid communication with first inlet pipe 10, a second outlet pipe 20 (e.g., a second outlet manifold), a second cooling pipe 22 attached to a first heat absorbing surface 24 having a second predetermined absorptivity to emissivity ratio (e.g., a red-painted surface having an absorptivity ranging from about 0.57 to about 0.9), a third cooling pipe 25 attached to a second heat radiating surface 17 having the first predetermined absorptivity to emissivity ratio (e.g., a second radiator panel surface coated with the high-emissivity white paint). Second inlet pipe 18 is connected to radiator inlet 51. Second outlet pipe 20 is connected to radiator outlet 53. High-flow zone 6 and low-flow zone 8 include a working fluid (e.g., a coolant liquid such as water or a mixture of water and propylene glycol). First heat absorbing surface 24 is adapted to transfer heat from second cooling pipe 22 to third cooling pipe 25 through second heat radiating surface 17. The second predetermined absorptivity to emissivity ratio is greater than the first predeterminedabsorptivity to emissivity ratio. Both second cooling pipe 22 and third cooling pipe 25 connect the second inlet pipe 18 to the second outlet pipe 20. Low-flow zone 8 may include multiple second cooling pipes 22 and third cooling pipes 25.

[0027] Note that a two-zone (dual-zone) radiator is described here for the sake of simplicity. However, the approach introduced here also can be applied to design and operate a radiator that has more than two flow-rate zones. For example, a radiator designed in accordance with the present disclosure may include multiple zones for each of two flow rates (e.g., high and low, as above), or it may include one or more zones for each of three or more different flows rates.

[0028] In some embodiments, as shown, low-flow zone 8 further includes an eclipse valve 26 in fluid connection downstream from second outlet pipe 20. Eclipse valve 26 (e.g., an on / off ball valve or a needle-valve) provides a predetermined flow rate of the working fluid through low-flow zone 8, which can be adjusted down to zero. Eclipse valve 26 is operated in synchronization with the spacecraft’s exposure to solar flux. Specifically, it is closed when the external solar flux to dual-zone radiator 4 is reduced, such as when the spacecraft is entering Earth’s shadow. This closure reduces the heat transfer area of the dual -zone radiator 4 that is thermally coupled to the working fluid to a predetermined value. Additionally, it creates low-flow or stagnant conditions inside second cooling pipe 22 and third cooling pipe 25, effectively reducing the rate of heat transfer from the working fluid within these pipes to second heat radiating surface 17. This action eliminates the risk of the working fluid freezing or reduces the amount of frozen working fluid in low-flow zone 8. When the external solar flux is reestablished — when the spacecraft exits Earth’s shadow and is again illuminated by the sun — eclipse valve 26 is opened to resume flow in low-flow zone 8. This action re-establishes the heat transfer area of the dual-zone radiator 4 that is thermally coupled to the working fluid. First heat absorbing surface 24 accelerates this process by reducing the viscosity of the working fluid and / or by melting any frozen working fluid more quickly within the second cooling pipe 22.

[0029] Also, placing eclipse valve 26 downstream of the second outlet pipe 20 ensures that the unfrozen portions of second cooling pipe and third cooling pipe 25 remain substantially connected with the radiator inlet 51. This approach can prevent pressure build-up in case the working fluid in these pipes freezes.

[0030] A heater 32 may be used for heating the working fluid entering second cooling pipe 22. Additionally or alternatively, a one-way valve 30 may be included to prevent the working fluid from entering second outlet pipe 20 from first outlet pipe 12. A filter 28 in fluidcommunication with second outlet pipe 20 may also be included, downstream from second outlet pipe 20. The function of filter 28 includes preventing the particles of frozen working fluid from flowing out from low-flow zone 8. Dual-zone radiator 4 may also include a regulating valve 36 (e.g., a needle valve), as shown, adapted to increase the flow rate though cooling pipe 22 to a predetermined value.

[0031] Note that in any of the embodiments disclosed herein, instead of having multiple pipes that traverse the low-flow zone as shown in FIG. 1, a single, longer pipe may be routed in a serpentine path through the low-flow-zone.

[0032] Referring to FIG. 2, second cooling pipe 22 may also include a second heat absorbing surface 34. Second heat absorbing surface 34 has a predetermined area, a predetermined orientation with respect to sun, and / or a third predetermined absorptivity to emissivity ratio to heat up the working fluid inside second cooling pipe 22.

[0033] In another embodiment, shown in FIG. 3, low-flow zone 8 includes a fourth cooling pipe 40 in fluid communication with first inlet pipe 10 and first outlet pipe 12. Its function includes substantially preventing the working fluid from freezing in third cooling pipe 25.

[0034] In yet another embodiment, shown in FIG.4, first inlet pipe 10 having an interior 42 is adapted to transfer heat from interior 42 to an interior 44 of second inlet pipe 18. For example, pipe 10 can be disposed within interior 44. Second outlet pipe 12 having an interior 46 is adapted to transfer heat from interior 46 to an interior 48 of second outlet pipe 20. For example, second outlet pipe 12 can be disposed within interior 48. The direction of the flow is indicated by the arrows.

[0035] In at least one embodiment, a method of operation of a cooling system including the radiator 4 includes the following steps:1. Circulating the working fluid through high-flow zone 6 following the direction indicated by the arrow labeled as 16 in FIG.l.2. Opening eclipse valve 26 to allow the working fluid to flow through second cooling pipe 22.3. Closing eclipse valve 26 to reduce the flow' rate of the working fluid in third cooling pipe 25 to a predetermined value (e.g., to keep the working fluid substantially stagnant insidecooling pipe 25), when the external solar flux to the dual-zone radiator 4 is reduced (e.g., when the spacecraft is entering Earth’s shadow).

[0036] Opening eclipse valve 26 to increase the flow rate of the working fluid in third cooling pipe 25 to re-establish normal flow conditions, when the external solar flux is reestablished (e.g., when the spacecraft exits Earth’s shadow and is again illuminated by the sun).

[0037] Additionally, the method may include absorbing heat (e.g., absorbing solar radiation when facing sun) by heat absorbing surface 24 to heat up the working fluid in cooling pipe 22; heating second cooling pipe 25 by heat transferred from second cooling pipe 22; and melting the frozen working fluid in third cooling pipe 25.

[0038] In a further embodiment, operation of the cooling system may include heating the working fluid entering second cooling pipe 22 using heater 32. In yet another embodiment, the method includes preventing the working fluid from entering second outlet pipe 20 from first outlet pipe 12. In yet another embodiment, the method includes preventing an amount of frozen working fluid from flowing out of low-flow zone 8. Moreover, the method may include increasing the flow rate through cooling pipe 22 or cooling pipe 25 using regulating valve 36 to a predetermined value throughout a predetermined time interval (e.g., to displace a volume of substantially stagnant or highly viscous working fluid from cooling pipe 22).

[0039] In some embodiments (see, e.g., FIG. 3), Step 4 above alternatively includes heating third cooling pipe 25 by circulating fluid through fourth cooling pipe 40.

[0040] In some embodiments, (see, e.g., FIG. 4), Step 2 includes transferring heat from interior 42 to interior 44 and from interior 46 to interior 48. This is to prevent excessive cooling or freezing of the working fluid in second inlet pipe 18 and second outlet pipe 20.

[0041] In some embodiments (see, e.g., FIGs. 5A and 5B), the radiator includes a casing pipe 50 that connects a radiator inlet 51 to a radiator outlet 53, with an internal pipe 52 disposed within casing pipe 50. Casing pipe 50 is attached to a surface 57 (e.g., a radiator panel) that radiates heat to the surroundings (e.g., space). Internal pipe 52 is designed to create an annular space, generally designated by numeral 55, inside casing pipe 50. One or more openings 56 may be present in internal pipe 52 to hydraulically connect annular space 55 with the interior of internal pipe 52.

[0042] When the radiator is exposed to a warm external thermal environment (e.g,, during a period of exposure to the sun), a working fluid flows through both annular space 55 (indicatedas flow 58) and internal pipe 52 (indicated as flow 60) as shown in FIG. 5 A. Internal pipe 52 transfers heat from flow 60 to flow 58. Conversely, when the radiator is exposed to a cold external thermal environment (e.g., during an eclipse period or when it is in the Earth’s shadow), the working fluid in annular space 55 freezes, forming a solid 54 (e.g., ice) within annular space 55 as shown in FIG. 5B. This results in a reduction or cessation of working fluid flow 58 of the working fluid. Solid 54 in annular space 55 functions as an insulating layer preventing working fluid 60 flowing through internal pipe 52 from freezing. Upon reentry into a warm external environment, solid 54 melts, reestablishing working fluid flow 58 as shown in FIG. 5A.

[0043] FIG. 13 shows a flowchart of an example process 1300 for operating a cooling system including a multi-zone radiator, such as described above. The process 1300 may be performed, or caused to be performed, by a control system such as that described below. As shown, the process 1300 includes circulating a coolant fluid through a first zone of the multi-zone radiator (step 1302). The process 1300 further includes causing the cooling system to enter a first configuration to allow the coolant fluid to flow through a first cooling conduit disposed in a second zone of the multi-zone radiator when an external thermal flux to the multi-zone radiator is at a first level (step 1304). The process 1300 further includes causing the cooling system to enter a second configuration to reduce a flow rate of the coolant fluid flowing through a second cooling conduit disposed in the second zone of the multi-zone radiator when the external thermal flux to the multi-zone radiator is reduced to a second level lower than the first level (step 1306). The process 1300 further includes causing the cooling system to return to the first configuration to increase the flow rate of the coolant fluid in the second cooling conduit when the external thermal flux to the multi-zone radiator increases to a third level higher than the second level (step 1308). Although FIG. 13 shows example steps of process 1300, in some implementations, process 1300 may include additional steps, fewer steps, different steps, or differently arranged steps than those depicted in FIG. 13.II. Control System

[0044] The above description can be summarized, in at least one aspect, as disclosing a multizone (e.g., dual-zone) radiator incorporating both freezing and non-freezing zones, and an eclipse valve designed to prevent frozen working fluid particles from exiting the radiator. In such a system, radiator panels may be exposed to significantly different thermal environments--- such as warm, solar-facing zones and cold, eclipse-shadowed zones -posingchallenges in determining which panels should serve as freezing zones and which should remain thermally active, at any given point in time.

[0045] Thermal control in Low Earth Orbit (LEO) is particularly difficult due to drastic variations in external heat fluxes throughout each orbital cycle. These fluctuations result in substantial temperature swings within radiator panels, especially in freezing zones. In conventional systems operating at a nominal, constant flow rate designed for the maximum thermal load, even minor internal heat dissipation may trigger the controller to open the radiator line. This introduces a cold slug of coolant — sometimes as low as -80°C — which rapidly reaches a temperature-sensitive element. When this temperature drops below the lower limit of a setpoint range tn ± ΔTn, the controller closes the valve. Continued heat dissipation raises the temperature again to tn + ATn (typically between +12°C and +20°C), triggering the controller to reopen; and so forth.

[0046] This oscillatory behavior imposes high-amplitude, alternating thermal stresses on the radiator structure and internal tubing. Over time, such cycles lead to fatigue cracking, as observed in legacy systems such as the Mir orbital station’s thermal control loops. One possible approach to temperature regulation is to use fixed setpoints, but this is insufficient for managing the dynamic flow assurance requirements of modern, dual-zone radiator systems. The above description of a multi-zone radiator partially addressed this by using a low-flow zone to limit heat rejection and mitigate large temperature gradients in freezing zones, especially when freezing occurs within the tubes. However, a more robust, predictive, and adaptive solution is desirable to reduce temperature amplitude caused by external heat flux variability.

[0047] Modern radiator architectures complicate flow management further due to the inclusion of multiple panels, each exposed to different thermal conditions depending on orbital position and spacecraft orientation. A single panel may alternate between cold and warm exposure within a single orbit. This makes manual operation of the eclipse valve impractical. Moreover, traditional one-dimensional thermal models fail to capture the large temperature gradients across radiator tube cross-sections, resulting in inaccurate predictions of freezing onset — a key risk in flow assurance and thermal control. While high-fidelity CFD simulations could offer more accuracy, they are computationally intensive and unsuitable for real-time control applications.

[0048] An additional layer of complexity stems from the number of valid operational configurations. For a four-panel radiator (Panels A, B, C, and D), each panel can be either activeor disconnected. Valid configurations allow exactly one, two, or three panels to be off, producing: four combinations when one panel is off, six combinations when two panels are off, and four combinations when three panels are off, yielding a total of 14 valid activation configurations. Each of these panel configurations can occupy eight distinct spatial orientations (x, y and z axes), leading to 112 total configurations. When evaluated under both minimum and maximum internal heat load conditions — relevant within each orbital cycle — the total number of cases reaches at least 224. Manual decision-making across such a large solution space is infeasible.

[0049] The approach introduced here solves these challenges by introducing a model-based control system for thermal control systems that use viscous working fluids, particularly for spacecraft (though not exclusively so). The control system integrates real-time telemetry, a digital twin simulation engine with learning capabilities, and an artificial intelligence (Al) powered combinatorial evaluator.

[0050] The digital twin includes a time-dependent thermal-hydraulic model of the radiator that simulates the real-time thermal state of the spacecraft system. It predicts temperature distribution, freezing onset, and the displacement of frozen fluid during eclipse valve actuation. The model continuously refines itself through telemetry data and machine learning, compensating for material degradation, shifting coolant properties, and unforeseen flow behavior,

[0051] The Al-powered combinatorial evaluator explores hundreds of panel -valve configurations per orbit, by using a set of heuristics that are adaptive based on changing outputs from the digital twin over time. It identifies configurations where freezing does not occur, minimizes internal temperature variations, and selects the optimal eclipse valve position to ensure that temporal variation in wall temperature across panels is reduced. This intelligent automation supports adaptive, flow-assured thermal control, minimizes energy consumption, and prevents fatigue-induced failure modes over extended missions.

[0052] For decades, radiator systems — both in the U. S. and Russian segments of the International Space Station (ISS) -have relied exclusively on coolants with very low freezing points to avoid freezing altogether. The entire design philosophy of prior systems has been to prevent freezing by coolant selection, not by engineering flow control.

[0053] In contrast, introduced here is a technique (method and apparatus) that intentionally allows freezing of the working fluid in radiator sections, but under controlled and recoverable conditions. This is achieved, at least in part, through the integration of the eclipse valve 26, which enables directed flow redistribution during cold phases and promotes reactivation of frozen pipes during warm orbital conditions. Unlike prior systems — such as the Russian ISS radiators, which rely on low-freezing-point working fluids, or the US radiators, which utilize small-diameter tubes with predetermined spacing — this approach provides hardware / software-based control over freezing and thawing. Low-freezing-point working fluids cannot be used within crewed modules due to safety and compatibility constraints, and radiators employing small-diameter tubes with predetermined spacing are not suitable for working fluids that exhibit high viscosity at low temperatures. In contrast, the system introduced here operates effectively with non-hazardous working fluids compatible with crewed environments, ensuring thermal resilience and operability under such conditions.

[0054] FIG. 6 illustrates another example of a radiator 110, such as may be used on a spacecraft. The radiator 110 includes two panels, 112 and 114, each subjected to distinct thermal environments. A heat flow 115 represents heat rejection from panel 112 to space 113, while a heat flow 117 represents heat rej ection from panel 114 to space 113. A plurality of pipes 118 are embedded within the radiator panels, positioned between the inlet pipe 119 and the outlet pipe 120. Since the pipes are structurally and functionally identical, they are collectively labeled 118. Flow through the pipes in each panel is controlled by the eclipse valve 26, and the flow direction is indicated by arrow 16. The magnitude of heat flows 115 and 117 depends on the temperature of panels 112 and 114, as well as external heat fluxes (including solar radiation, albedo, and Earth infrared radiation). These fluxes vary with the spacecraft’s orientation relative to the sun and the Earth, which in turn depends on orbital altitude and attitude.

[0055] FIG. 7 is a block diagram of a cooling system 150 with a control system 138 in accordance with the technique introduced here. The cooling system 150 may include a multizone radiator 110 and associated peripheral components (e.g., inlets, valves, etc.) such as described above. As illustrated, the control system 138 includes a flow controller 124, a digital twin 126, and a combinatorial evaluator (or simply “evaluator”) 128. Together, these components form an integrated predictive control system that continuously adapts radiator operation to dynamic orbital conditions. Each of these three components may be implemented in software, special-purpose hardwired circuitry (hardware), or a combination of software and special-purpose hardwired circuitry. If and to the software is used to implement any of thesecomponents, such software may be stored in one or more machine-readable storage media, such as one or more read-only memory (ROM), random access memory (RAM), magnetic disk, optical disk or other optical storage medium; flash memory, etc., or a combination thereof. The term “software” as used herein is intended to encompass firmware. If and to the extent hardwired circuitry is used to implement any of these components, such circuitry may include, for example, one or more application-specific integrated circuits (ASICs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), systems-on-a-chip (SOCs), etc., or a combination of such components

[0056] The flow controller 124 implements a flow configuration selected by the evaluator 128 at any given time, to maintain thermal balance within the system. It also manages telemetry data from the radiator 110 and other components of the cooling system, including transferring the telemetry data to the digital twin 126 for use in predictive modeling and thermal state estimation. The flow controller 124 is configured to modulate the flow of a viscous working fluid (coolant) across radiator panels 112 and 114 by actuating the eclipse valve 26 to selectively enable or disable flow, either completely or partially, through each panel. The flow controller 124 adjusts the flow distribution based on signals from the evaluator 128 corresponding to the instantaneous thermal state of the radiator panels — namely, their temperature distribution — and on predicted heat loads and heat flows 115, 117 over a future time interval, such as during the next orbital cycle. These predictions are generated and evaluated by the evaluator module 128 based on outputs from the digital twin 126.

[0057] As noted above, the flow controller 124 receives telemetry data from the cooling system and provides the telemetry data as inputs to the digital twin 126. The telemetry may include, for example, measurements from a pressure differential sensor 132, a flow meter 133, a temperature sensor 134 located in inlet pipe 119, a temperature sensor 136 located in outlet pipe 120, and an infrared (IR) camera or sensor 129 configured and mounted to monitor radiator panel surface temperatures. These telemetry inputs enable the digital twin 126 to replicate the real-time thermal and hydraulic behavior of the system for predictive analysis and control optimization

[0058] The digital twin 126 is or includes a time-dependent thermal-hydraulic model that replicates the real-time behavior of the cooling system. It simulates heat transfer from internal sources to space through panels 112 and 114, predicts the onset of fluid freezing in pipes 118, and models displacement of cold or frozen fluid upon opening eclipse valve 26. Digital twin126 also receives spacecraft orientation and orbital data from guidance and navigation system (GNC) 130 to forecast future thermal environments and flow conditions. The digital twin 126 includes a predictive computational model that simulates the future thermal behavior of the radiator system under varying heat loads and environmental conditions. The evaluator 128 analyzes these predictions and determines the optimal control actions required to achieve minimum temperature variations across the radiator panels during the next orbital cycle and serves as the primary decision-making unit that governs fluid flow to maintain thermal balance within the system.

[0059] The evaluator 128 analyzes these predictions from the digital twin 126 and determines the optimal control actions (flow configuration) required to achieve minimum temperature variations across the radiator panels during the next orbital cycle. It serves as the primary decision-making unit that governs fluid flow in the system to maintain thermal balance within the system. The evaluator 128 — which may be implemented in software, hardwired circuitry (hardware), or a combination thereof- -evaluates candidate flow configurations using adaptive heuristic and algorithmic logic, to determine the optimal flow configuration for the cooling system during each time increment of the system (e.g., once per orbital cycle in the case of a spacecraft cooling system).

[0060] In some embodiments, both the evaluator 128 and the digital twin 126 incorporate di stinct Al features addressing different functions. For example, the evaluator 128 may employ adaptive heuristic search to efficiently explore and filter candidate flow configurations, reducing the computational burden of exhaustive evaluation. The digital twin 126 may include a machine-learning (ML) module / algorithm that processes discrepancy (error) signals and contextual telemetry data to improve model-prediction accuracy and identify potential sources of deviation (e.g., pipe resistance drift, coating degradation, or sensor faults). These two Al functions operate independently but complement one another — one optimizing configuration selection (in the evaluator 128), the other (in the digital twin 126) maintaining long-term predictive fidelity of the system model.

[0061] In some embodiments, the evaluator 128 performs the following three high-level steps:1. Configuration Filtering: Identifies flow configurations for which the digital twin 126 predicts that no freezing will occur in at least one pipe of at least one radiator panel during the next orbital cycle. The flow configurations can be identified by applying heuristic search criteriaderived from outputs of the digital-twin 126. In certain embodiments, this prediction is performed by executing iterative simulation calls to the digital twin 126, each corresponding to a different candidate configuration within the set C, and evaluating thermal states over the duration of the upcoming orbital period.2. Thermal Evaluation: For each candidate configuration identified in Step 1, the evaluator 128 evaluates the temporal variation in wall temperatures across panels during the next orbital cycle.3. Optimization and Selection: The evaluator 128 selects the configuration corresponding to the eclipse valve 26 positions that yield the minimum temporal temperature variation evaluated in Step 2. The evaluator 128 then provides the selected optimal configuration to the flow controller 124, which implements the configuration by actuating the eclipse valve 26 to achieve the desired flow distribution and minimize temperature variations across the radiator panels during the next orbital cycle.

[0062] An example implementation of this three-step process employs brute-force optimization with the objective of minimizing thermal oscillations. The optimization can be expressed mathematically as follows:where:T j Wall temperature of pipe i at time step j under configuration cC: set of candidate flow configurations, simulated by digital twin 126c*: Optimal flow configuration selected by the algorithm

[0063] Each configuration cGC, which is a member of the set of candidate flow configurations C simulated by the digital twin 126, may specify one or more of:Eclipse valve 26 position (partially open, fully open, or closed);Radiator inlet temperature (e g., at sensor 134);Total flow rate (e.g., at flow meter 133);Heat flows (115, 117).

[0064] This formulation enables selection of a flow strategy that minimizes the greatest temperature oscillation experienced by any pipe, thus reducing the potential for fatigue due to thermal cycling.

[0065] In certain embodiments, the digital twin 126 incorporates a machine-learning model / algorithm configured to enhance model fidelity through continuous learning (note that in this description, the terms “machine-learning model” and “machine-learning algorithm” are used interchangeably). To accomplish this, the machine-learning model may receive a discrepancy (error) signal representing the difference between the predicted temperature distribution generated by the digital twin 126 and the telemetry data it receives from the flowcontroller 124. This discrepancy quantifies deviations between simulated and observed thermal behavior, enabling adaptive model correction.

[0066] The machine-learning algorithm can process this discrepancy signal along with contextual operating data from the controller 124 to classify the most probable cause of the deviation. Examples of candidate causes include:(i) drift in hydraulic resistance values of one or more pipes 118;(ii) degradation of surface coating 134 on radiating panels 112 or 114, altering emissivity or absorptivity;(iii) bias or malfunction of one or more temperature sensors 129; and(iv) malfunction or degradation of one or more GNC sensors 130 used to determine spacecraft attitude and corresponding view factors for predicting heat flows 115 and 117.

[0067] The digital twin 126 may output to the evaluator 128 both a classification label identifying the likely cause of the discrepancy and an associated confidence score quantifying the certainty of that classification. The evaluator 128 may then apply an adaptation strategy to its included heuristic(s) based on the identified cause, with the degree of adaptation weighted by the confidence score.

[0068] Pipe parameter drift: If drift in hydraulic resi stance values i s indicated, the digital twin 126 updates the corresponding resistance coefficients of pipes 118 in its internal hydraulic model. The adjustment may be performed incrementally according to the direction and magnitude of the discrepancy signal, using a recursive update rule such as Ri,new= Ri,oid(l+a A(APi) / APi,pred), where a is a tuning coefficient and where A(APi) = APi,meas - APi.pred is thedifference between the pressure drop AP / .meas measured by the pressure differential sensor 132 and the predicted pressure drop APi,pred across pipe i as predicted by the digital twin 126. This correction refines predicted flow rates and pressure drops in the digital twin 126.

[0069] Coating degradation: If degradation of surface coating 134 is indicated, the controller 124 modifies the radiative property database within the digital twin 126 by adjusting the emissivity or absorptivity coefficients of affected panels 112, 114. The update may introduce a time-dependent degradation factor 5(t), representing gradual surface aging, which scales radiative flux computations in subsequent simulations.

[0070] Temperature sensor fault: If a bias or fault in one or more temperature sensors 129 is detected, the evaluator 128 reduces the sensor’s influence in both real-time estimation and predictive simulation by applying data de-weighting or exclusion filters. This may involve assigning a lower weighting factor in the data fusion process or substituting estimated values from adjacent nodes or redundant sensors.

[0071] GNC sensor fault: If a malfunction in one or more GNC sensors 130 is detected, the evaluator 128 recalibrates the digital twin’s boundary conditions to preserve model fidelity. This includes updating the spacecraft attitude parameters and corresponding radiative view factors that define external heat flow inputs 115, 117. The correction may rely on backup attitude data from secondary GNC systems or predicted orientation from orbital propagation algorithms.

[0072] All adaptations are constrained within physically valid operating limits to ensure system stability and safety. Resistance values remain within certified tolerance ranges; emissivity and absorptivity are bounded between 0 and 1; and substituted telemetry data are flagged for subsequent validation.

[0073] As noted above, the digital twin 126 may incorporate a machine-learning model configured to determine the most probable cause of the discrepancy between predicted panel temperatures generated by the digital twin 126 and the measured telemetry data, including infrared imagery and onboard temperature sensor readings. The machine-learning model can employ, for example, a supervised classification algorithm, such as a feedforward neural network, a support vector machine (SVM), or a Bayesian inference model, trained on historical correlations between discrepancy patterns (i.e., differences between predicted and measured temperatures) and known fault conditions. By processing the current discrepancy signal together with contextual operating data from the model -based flow controller 124, the modeloutputs a classification label identifying the likely cause of the discrepancy and an associated confidence score. The evaluator 128 then applies an appropriate constrained adaptation strategy.

[0074] The adaptation is performed subject to physical constraints. Resistances of pipes 118 remain positive and within operational ranges, while emissivity of surface 134 remains bounded between zero and one. In some embodiments, the update is carried out using a gradient-based learning rale, such as:where represents a discrepancy metric between measured and predicted temperatures. In other embodiments, the controller 124 employs alternative optimization techniques, including finite-difference perturbation, simultaneous perturbation stochastic approximation (SPSA), Kalman filtering, Gauss-Newton estimation, or Bayesian inference.

[0075] This configuration — including a digital twin 126 with an integrated machine-learning cause-classification algorithm for physically constrained parameter updates — enables the cooling system 150 to dynamically adapt to pipe-parameter drift, coating degradation, temperature sensor bias, and GNC sensor errors. As a result, the digital twin 126 maintains long-term predictive accuracy, ensuring reliable thermal management of radiator panels 112 and 114 in space environments.

[0076] Digital twin 126 generates high-resolution thermal maps of the radiator panel, which are validated using thermographic data from the IR camera or sensor 129. FIG. 8 shows an example of a temperature distribution map of a radiator panel, which may be generated by the digital twin 126 and used to assess internal gradients and thermal management needs. A simulation such as this can be compared with thermographic data collected by the IR camera or sensor 129, enabling model validation without requiring intrusive temperature measurements within tubes 118. Based on a thermal image such as this, the distribution of flow rates in tubes 118 can also be determined, allowing the controller to infer and adjust flow behavior non-invasively. These thermal maps support non-invasive estimation of flow rate distribution within pipes 118, enabling intelligent controller decisions without embedded sensors. The radiator panel shown in FIG. 7 includes eight pipes 118, and the IR camera or sensor 129, which monitors temperatures at one or more locations 148 across the panel surface. These data can be used to validate and refine the thermal-hydraulic model in the digital twin 126 by using machine-learning techniques.

[0077] FIG. 9 shows an example of the two-fluid modeling approach that can be used in the digital twin 126, which separately calculates the temperatures of cold liquid film or solidified layer 140 and warm liquid core 142. The model also estimates the mass and distribution of each field (fluid region) over time, improving both thermal prediction and hydrodynamic flow analysis within pipes 118.

[0078] FIG. 10 shows a thermal network representation that models heat transfer from warm liquid core 142 to the space environment. This modeling framework is central to the disclosed method of coupling thermal and hydraulic models without iterative computation, enabling accurate, efficient simulation that supports real-time control. Subscript k refers to a panel node k adjacent to a pipe 118 segment i. The surrounding temperature in space is represented by a heat sink temperature Ts.k. TF, I is the temperature of the cold film or solidified layer 140, Tc,i is the temperature of warm liquid core 142, Tpj is the temperature of a panel node j adjacent to panel node k. Thermal conductance values — Gconvi, Gconv2, Gcondt, Gcond2, and Grad — are defined as the rate of heat transfer between system elements per unit temperature difference.

[0079] The thermal and hydrodynamic models are fully coupled in the digital twin 126 by using a time-dependent formulation of the heat flux continuity equation at the fluid-solid interface, avoiding iterative calculations and ensuring energy conservation during time integration. This coupled approach enables faster-than-real-time simulation and a predictive control framework, allowing the controller to anticipate environmental changes and proactively select optimal flow configurations (where “optimal” is determined in terms of which valves are open and which valves are closed, and the degree of openness for valves that are open, so as to minimize temperature variations over time over all points in the radiator).

[0080] FIG. 11 illustrates yet another embodiment, in which cooling pipes 14 and 25 are thermally coupled to a combined radiating surface 100, which may include an aluminum or aluminum-alloy panel engineered to simultaneously serve as a high-flow zone 6 and a low-flow zone 8. Radiating surface 100 is thermally and structurally configured to maintain a predetermined minimum temperature in cooling pipe 25. This thermal conditioning enables the re-establishment of flow in the low-flow zone 8 following the opening of the eclipse valve 26, as previously descri bed with respect to FIG. 1. In particular, panel 100 provides passive thermal buffering and pre-warming of the stagnant working fluid, thereby reducing the likelihood of blockages caused by viscous or frozen fluid during eclipse recovery.

[0081] Additionally, this embodiment introduces functional redundancy to the thermal transport system, enhancing operational reliability in scenarios involving micrometeoroid or orbital debris (MMOD) damage or localized fluid leakage. Either of the two parallel flow subsystems may be independently utilized to transfer heat to the radiating surface 100, i.e., the first subsystem, comprising inlet pipe 10, cooling pipe 14, and outlet pipe 12, or the second subsystem, comprising inlet pipe 18, cooling pipe 25, and outlet pipe 20. This redundancy ensures continued radiator function even in the event of partial system failure, and allows for autonomous or command-driven selection of flow paths based on system diagnostics, thermal load distribution, or mission phase requirements.

[0082] In yet another embodiment, shown in FIG. 12, the system includes a one-way valve 60 with an integrated position sensor disposed between the outlet of the radiator tube (e.g., pipe 118) and the eclipse valve 26. A powered valve 64 is positioned at the inlet of pipe 18 and is controlled by a controller 62, which receives position information from the one-way valve 60.

[0083] If an opening 66 occurs in pipe 18 (for example, a rupture caused by micrometeoroid or orbital debris impact), working fluid flows in direction 16 toward the opening 66. Under this condition, the eclipse valve 26 is configured to produce a predetermined flow rate of working fluid in direction 68 sufficient to close the one-way valve 60. When closure of the one-way valve 60 is detected, the controller 62 actuates the powered valve 64 to close, thereby isolating the damaged pipe section.

[0084] An advantage of this embodiment is that it provides automatic detection and isolation of a ruptured pipe without reliance on complex leak detection systems. This approach enhances system reliability, reduces hardware and control complexity, and minimizes the risk of working fluid loss, thereby improving overall safety and efficiency of the radiator system.Equations

[0085] The following additional equations can form a basis of the design of the system, according to at least one embodiment disclosed herein:Conservation of cold liquid film mass in a segment i of pipe 118:wherePf'. density of the working fluidVf. Volume of the segment of a fluid-carrying pipe 118HF-. Holdup (local volumetric fraction) of cold liquid film 140mp^p. mass flow rate of cold liquid film 140 flowing into the segment of a fluidcarrying pipe 118mF i- mass flow rate of cold liquid film 140 flowing out of the segment of a fluidcarrying pipe 118This equation represents the continuity of mass in the cold liquid film along the radiator pipe.

[0086] Momentum conservation applied separately to cold liquid film or solidified layer 140 and warm liquid core 142 in zero gravity conditions in segment i, respectively:whereAFarea occupied by cold liquid film 140pressure gradientTjj Shear stress at the cold liquid film 140-warm liquid core 142 interfaceSf Interface perimeterArea occupied by warm liquid core 142TF-. Shear stress in cold liquid film 140SFPerimeter wetted by cold liquid film 140

[0087] The shear stress in cold liquid film 140 is given bywhereVF: Velocity of cold liquid film 140fF- Friction factor obtained using a Moody diagram for a Reynolds number defined bywhere5: Dimensionless film thicknessWorking fluid viscosity at the temperature of cold liquid film 140D: Pipe internal diameter

[0088] The shear stress at the cold liquid film 140-warm liquid core 142 interface is given bywheref - Interfacial friction factor defined byfl = fsc<^ + 24«) Eq (9)whereVelocity of warm liquid core 142ft. Friction factor obtained using a Moody diagram for a Reynolds number defined bywhereWorking fluid viscosity at the temperature of warm liquid core 142Jc: Superficial velocity of warm liquidwhereA- Cross-sectional area of the pipemc-. Mass flow rate of warm liquidConservation of cold liquid film massmc,t +mF.i —mEq. (12)

[0091] Energy conservation in cold liquid film 140 in segment i of pipe 118whereTFp Temperature of cold liquid film 140Tcp Temperature of warm liquid core 142cF iFluid specific heat at TF ihconvl iConvective heat transfer from warm liquid core 142 to cold liquid film 140 Aconv1,iArea of heat transfer from warm liquid core 142 to cold liquid film 140 Qftubei- ^eattransfer rate from cold liquid film 140 to pipe 118

[0092] Energy conservation in warm liquid core 142whereccp Fluid specific heat at temperature Tc i

[0093] Energy conservation in a radiator panel for panel node i, which is not adjacent to a pipe segmentwhereTp i-. Temperature of panel node ipp. Density of panel materialVp, Volume of panel node ic: Specific heat capacity of panel materialGi j-. thermal conductance between nodes i and jArad i- Radiation area of node ie: emissivityTs i: sink temperature of panel node i

[0094] Heat Flux Continuity Equation at the internal surface of pipe 118k: Subscript referring to panel node k adjacent to pipe segment i

[0095] Convective heat transfer coefficient hconv2,t is calculated using Seider-Tate for annular flow:NuD= 1.24 Eq. (18)Dhhydraulic diameter for cold liquid film (40) Dh= D — 2δLiquid viscosity at Tp i.PikLiquid viscosity at Tp kXj -. Distance between the inlet of pipe 118 and pipe segment iEqs. (3), (13), (14) and (16) are a set of N coupled first-order differential equations having the general formwhereN: sum of total number of nodes of panels and total number of pipe segments multiplied by threef '. the functions on the right-hand side of Eq. (19).

[0097] The system of equations in Eq. (19) can be solved (by the digital twin 126) using a numerical method (e.g., the Runge-Kutta method), where the function evaluations at each time step are parallelized to take advantage of multi-core architectures and reduce computational time. The time-dependent formulation of the Heat Flux Continuity Equation, Eq, (16), at the fluid-solid interface is employed, eliminating the need for iterative coupling between the thermal and hydrodynamic models. This approach ensures an accurate solution, as the thermal balance across the interface is inherently maintained during time integration.Machine-Learning Parameter Update Rule for Model Adaptation

[0098] As noted, the digital twin 126 may implement a machine-learning model to model the thermal-hydraulic state of the radiator. The following describes an example of a parameter update rule that may be implemented for the purpose of model adaptation of the machinelearning model in the digital twin 126.

[0099] Let 0k represent the model parameter (e.g., the hydraulic resi stance of pipe 118 at time step k, and <b be the objective function measuring the error between temperatures predicted by digital twin 126 and measured temperatures. The update equation is given byWhere:rj is the learning rateVed» is the gradient of the error with respect to the model parameter 0O is: O S |T_predicted - Tjmeasured|2

[0100] This rule allows the digital twin model to self-adjust key thermal-hydraulic parameters using telemetry inputs such as IR camera data and onboard sensors, improving predictive accuracy over time.Derivation of Local Nusselt Number from Mean Correlation

[0101] In some embodiments, the local convective heat transfer coefficient is determined by the digital twin 126 using a closed-form approximation derived from the Sieder-Tate correlation for the mean Nusselt number applicable to laminar internal flow under constant wall temperature. The mean Nusselt number from the inlet to axial location x is given by:where:Re is the Reynolds number,Pr is the Prandtl number,D is the hydraulic diameter of cooling pipe 25, FIG.lx is position (distance) relative to pipe inletfib and pware the dynamic viscosities at the bulk and wall temperatures, respectively. The local Nusselt number Nuxis derived by differentiating the product x ■ Nu(x), which represents the cumulative heat transfer up to position x, as follows:Thus:Substituting the full expression:0.14Eq. (24)

[0102] This provides a practical estimate of the local convective heat transfer coefficient hxwhere k is the thermal conductivity of the working fluid. This formulation ensures that the local Nusselt number at a given location x=L is less than the mean Nusselt number over that same length:

[0103] This inequality reflects the decay of the local heat transfer rate along the thermal entrance region and is consistent with classical solutions for laminar flow in circular tubes. Advantages

[0104] Embodiments of the techniques introduced each here provide one or more of the following advantages:

[0105] 1. Enhanced Flow Assurance: The system and method effectively prevent particles of frozen working fluid from flowing out of the radiator. Even if the filter downstream of the low-flow zone is temporarily blocked, the working fluid can still circulate through the high-flow zone. This ensures uninterrupted fluid flow, minimizing the occurrence of pipe blockages and safeguarding essential components such as pumps from damage. As a result, the thermal control system maintains optimal operational efficiency and reliability even in challenging environmental conditions.

[0106] 2. Pressure Management and System Integrity: The eclipse valve offers significant benefits in maintaining system integrity and performance. By reducing flow through the low-flow zone to a predetermined value, while maintaining the cooling pipes connected to the inlet pipe, the valve prevents pressure buildup during freezing. This feature contributes to the system's longevity and safe operation, particularly in environments with frequent temperature fluctuations.

[0107] 3. Precise Radiator Control: The system offers unparalleled control over the radiating area of the radiator, addressing an inherent challenge in radiator control. Providing a predetermined ratio between the area of the heat radiating surface of the high-flow zone to the area of the second heat radiating surface of the low-flow zone, the system optimizes the distribution of heat dissipation across the radiator surface within a wide range of internal heat loads and external heat fluxes. This precise control capability enhances the system's efficiency and performance, ensuring effective heat rejection without compromising on thermal management requirements. Additionally, the system’s flexibility allows for dynamic adjustments in response to varying thermal conditions, further optimizing radiator performance under diverse operational scenarios.

[0108] 4. Reduced Thawing Time: By employing innovative thawing mechanisms, the improved system significantly reduces the time required to melt frozen working fluid. Thermal management techniques including a combination of selective heat-absorbing surfaces and cabinheaters expedite the thawing process while maintaining system integrity and reliability. Pipein-pipe design of manifolds and a selected cooling pipe within the low-flow zone with a high flow rate prevent working fluid from freezing in the interior of these elements. All these features reduce the need for lowering the heat load associated with prolonged thawing periods, ensuring prompt responsiveness to fluctuating thermal conditions. As a result, the system enhances overall operational efficiency, minimizes energy consumption, and improves responsiveness to dynamic thermal environments, thereby optimizing mission performance and longevity.

[0109] 5. Increased Radiator Efficiency: By displacing a volume of substantially stagnant or highly viscous working fluid from the cooling pipes within the low-flow zones, full recovery of the radiating surfaces can be achieved by ensuring stable flow conditions in these pipes.

[0110] 6. The embodiment with annular space and internal pipe design offers several benefits, particularly in regulating heat transfer during varying thermal conditions. During eclipse periods, ice formation in the annular space significantly reduces the heat transfer rate to the radiator panel, thus conserving thermal energy while the working fluid in the internal pipe remains unfrozen and capable of flow. The strategic placement of openings in the internal pipe prevents pressure buildup in the annular space, ensuring structural integrity. Furthermore, these openings contain ice particles within the annular space, preventing them from exiting the radiator and thereby avoiding potential plugging in the fluid loop where the radiator is installed.

[0111] 7. Improved Flow Recovery: By maintaining a minimum temperature in the low-flow zone, the combined radiating surface facilitates the re-establishment of working fluid flow after eclipse periods.

[0112] 8. Redundancy for Fault Tolerance: By enabling either flow path to operate independently, the system maintains functionality in the event of leakage or MMOD-related damage.

[0113] 9. Real-time adaptation to environmental and operational variations using a continuously updated digital twin.

[0114] 10. Reduced thermal fatigue and crack formation due to minimized temperature oscillations in tubing.

[0115] 11. Scalable architecture applicable to various spacecraft designs.

[0116] 12. AI-enhanced decision-making that outperforms manual control in evaluating configuration options.

[0117] 13. Machine learning-based self-correction using telemetry to improve long-term model accuracy.

[0118] 14. Non-invasive monitoring of flow distribution via infrared imaging.

[0119] 15. Faster-than-real-time simulation for predictive valve actuation.

[0120] 16. High fidelity without the computational overhead of full CFD.

[0121] 17. Analytical Local Heat Transfer Control: By deriving the local Nusselt number from the mean Sieder-Tate correlation, the system enables precise spatial resolution of convective heat transfer, supporting both design optimization and real-time thermal control.

[0122] FIG, 14 shows an example of a process 1400 for controlling a cooling system that includes a multi-zone radiator, such as that illustrated in FIG. 7. The process 1400 may be performed by the flow controller 124, the digital twin 126 and the evaluator 128, collectively. As shown, the process 1400 includes generating, during operation of the cooling system, a plurality of predicted thermal states of the cooling system by simulating the cooling system under a plurality of different sets of conditions (step 1402). The process 1400 further includes identifying a desired flow configuration of the cooling system, based on the plurality of predicted thermal states (step 1404). The process 1400 further includes setting a flow configuration of the radiator, based on the desired flow configuration, by controlling at least one valve of the cooling system (step 1406). Although FIG. 14 shows example steps of process 1400, in some implementations, process 1400 may include additional steps, fewer steps, different steps, or differently arranged steps than those depicted in FIG. 14.

Claims

CLAIMS:What is claimed is:

1. A multi-zone radiator comprising:a first zone including a first plurality of fluid conduits thermally coupled to a first surface, the first zone being configured to allow flow of a coolant fluid through the first plurality of fluid conduits at up to a first maximum flow rate; anda second zone including a second plurality of fluid conduits thermally coupled to a second surface, the second zone being configured to allow flow of a coolant fluid through the second plurality of fluid conduits at up to a second maximum flow rate lower than the first maximum flow rate.

2. The multi-zone radiator of claim 1, further comprising a valve to selectively allow or prevent flow of the coolant fluid through the second zone in response to a selection signal.

3. The multi-zone radiator of claim 2, wherein the valve is an eclipse valve.

4. The multi-zone radiator of claim 1, wherein:a first fluid conduit of the first plurality of fluid conduits is attached to the first surface, the first surface having a first absorptivity to emissivity ratio;a second fluid conduit of the second plurality of fluid conduits is attached to the second surface, the second surface having a second absorptivity to emissivity ratio different from the first absorptivity to emissivity ratio; andthe second surface is attached to a third surface, the third surface having the first absorptivity to emissivity ratio.

5. The multi-zone radiator of claim 4, the second zone further comprising a third fluid conduit attached to the third surface.

6. The multi-zone radiator of claim 5, the second zone further comprising a fourth fluid conduit in fluid communication with the first plurality of fluid conduits, the fourth fluid conduit being disposed adjacent to at least one fluid conduit of the second plurality of fluid conduits.

7. The multi -zone radiator of claim 1, further comprising:a radiator inlet;a radiator outlet;a first inlet conduit in fluid communication with a radiator inlet and the first plurality of fluid conduits;a second inlet pipe in fluid communication with the radiator inlet and the second plurality of fluid conduits;a first outlet conduit in fluid communication with a radiator outlet and the first plurality of fluid conduits; anda second outlet conduit in fluid communication with the radiator outlet and the second plurality of fluid conduits.

8. The multi-zone radiator of claim 7, further comprising a valve in fluid communication with the second outlet conduit and the radiator outlet, the valve being configured to allow or prevent flow of the fluid through the second zone selectively in response to a selection signal.

9. A multi-zone radiator comprising:a first zone includinga first plurality of fluid conduits thermally coupled to a first surface, the first zone being configured to allow flow of a coolant fluid through the first plurality of fluid conduits at up to a first maximum flow rate, wherein a first fluid conduit of the first plurality of fluid conduits is attached to the first surface, the first surface having a first absorptivity to emissivity ratio;a first inlet conduit in fluid communication with a radiator inlet and the first plurality of fluid conduits;a first outlet conduit in fluid communication with a radiator outlet and the first plurality of fluid conduits;a second zone includinga second plurality of fluid conduits thermally coupled to a second surface, the second zone being configured to allow flow of a coolant fluid through the second plurality of fluid conduits at up to a second maximum flow rate lower than the first maximum flow rate, wherein a second fluid conduit of the second plurality of fluid conduits is attached to the second surface, the second surface having a second absorptivity to emissivity ratio different from the first absorptivity to emissivity ratio;a second inlet conduit in fluid communication with the radiator inlet and the second plurality of fluid conduits; anda second outlet conduit in fluid communication with the radiator outlet and the second plurality of fluid conduits;anda first eclipse valve to selectively allow or prevent flow of the coolant fluid through the second zone in response to a selection signal.

10. The multi-zone radiator of claim 9, wherein the second surface is attached to a third surface, the third surface having the first absorptivity to emissivity ratio.

11. The multi -zone radiator of claim 10, the second zone further comprising a third fluid conduit attached to the third surface.

12. The multi-zone radiator of claim 11, the second zone further comprising a fourth fluid conduit in fluid communication with the first plurality of fluid conduits, the fourth fluid conduit being disposed adjacent to at least one fluid conduit of the second plurality of fluid conduits.

13. The multi-zone radiator of claim 9, further comprising a filter in fluid communication with the second outlet conduit and the first eclipse valve.

14. The multi-zone radiator of claim 9, further comprising a second eclipse valve in fluid communication with the radiator inlet and the first inlet conduit.

15. The multi-zone radiator of claim 14, further comprising a third valve in fluid communication with the first eclipse valve and the radiator outlet.

16. The multi-zone radiator of claim 9, further comprising a heater in fluid communication with the radiator inlet and the second inlet conduit.

17. A method of operating a cooling system including a multi-zone radiator, the method comprising:circulating a coolant fluid through a first zone of the multi-zone radiator;causing the cooling system to enter a first configuration to allow the coolant fluid to flow through a cooling conduit disposed in a second zone of the multi-zone radiator when an external thermal flux to the multi-zone radiator is at a first level;causing the cooling system to enter a second configuration to reduce a flow rate of the coolant fluid flowing through the cooling conduit disposed in the second zone of the multi-zone radiator when the external thermal flux to the multi-zone radiator is reduced to a second level lower than the first level; andcausing the cooling system to return to the first configuration to increase the flow rate of the coolant fluid in the cooling conduit when the external thermal flux to the multi-zone radiator increases to a third level higher than the second level.

18. The method of claim 17, wherein the third level is equal to the first level.

19. The method of claim 17, wherein causing the cooling system to enter the first configuration comprises causing a valve to enter a first state, and wherein causing the cooling system to enter the second configuration comprises causing the valve to enter a second state.

20. The method of claim 19, wherein the valve is an eclipse valve.

21. The method of claim 17, wherein the external thermal flux comprises a solar flux.

22. A radiator with annular freeze protection, comprising:a first fluid conduit coupled between a radiator inlet to a radiator outlet, the first fluid conduit configured to be attached to a heat-radiating surface; anda second fluid conduit disposed within the first fluid conduit so as to form an annular space between the first fluid conduit and the second fluid conduit, such thatwhen the first fluid conduit and the second fluid conduit are in a first external thermal environment, a coolant fluid flows through both the annular space and an interior of the second fluid conduit, allowing heat transfer from coolant fluid in the second fluid conduit to coolant fluid in the annular space;when the first fluid conduit and the second fluid conduit are in a second external thermal environment that is colder than the first external thermal environment, the coolant fluid in the annular space freezes to form a solid insulatinglayer that reduces or stops a flow of the coolant fluid in the annular space and prevents the coolant fluid in the second fluid conduit from freezing; andwhen the first fluid conduit and the second fluid conduit re-enter the first external thermal environment, the solid insulating layer melts so as to reestablish the flow of the coolant fluid through the annular space.

23. A method of controlling a cooling system that includes a radiator, the method comprising:generating, during operation of the cooling system, a plurality of predicted thermal states of the cooling system by simulating the cooling system under a plurality of different sets of conditions;identifying a desired flow configuration of the cooling system, based on the plurality of predicted thermal states; andsetting a flow configuration of the radiator, based on the desired flow configuration, by controlling at least one valve of the cooling system.

24. The method of claim 23, wherein the valve is an eclipse valve.

25. The method of claim 23, wherein the identifying the desired flow configuration comprises identifying a candidate configuration, from among a plurality of candidate configurations of the cooling system, that satisfies a specified criterion for minimal temperature variation within a plurality of zones of the cooling system.

26. The method of claim 23, wherein the identifying the desired flow configuration comprises:evaluating each of the plurality of predicted thermal states;identifying, based on the evaluating, a predicted thermal state, of the plurality of predicted thermal states, that meets a specified criterion for minimal temperature variation within a plurality of zones of the cooling system; andidentifying a flow configuration of the cooling system that corresponds to the identified predicted thermal state.

27. The method of claim 23, wherein the simulating is based on real-time telemetry data from a plurality of physical components of the cooling system.

28. The method of claim 23, wherein the generating the plurality of predicted thermal states of the cooling system comprises using a time-dependent thermal-hydraulic model of the radiator, during operation of the cooling system.

29. The method of claim 23, wherein the generating the plurality of predicted thermal states of the cooling system comprises using a digital twin of the radiator to simulate the cooling system under a plurality of different sets of conditions, during operation of the cooling system.

30. The method of claim 29, wherein using the digital twin comprises executing and continuously training a machine-learning model configured to output a most probable cause of a discrepancy between a desired thermal profile of the radiator and an actual thermal profile of the radiator as indicated by real-time sensor data.

31. The method of claim 30, wherein the machine-learning model comprises a supervised classification algorithm for determining the most probable cause.

32. The method of claim 30, wherein the generating the plurality of predicted thermal states of the cooling system comprises:executing iterative simulation calls to the digital twin of the radiator during operation of the cooling system, each simulation call corresponding to a different candidate configuration of a plurality of candidate configurations of the cooling system; andevaluating thermal states of the radiator over a duration of a future time interval, based on a corresponding response to the simulation call from the digital twin of the radiator for each of the plurality of candidate configurations.

33. The method of claim 32, wherein the identifying the desired flow configuration comprises identifying a candidate configuration, from among a plurality of candidate configurations of the cooling system, that satisfies a specified criterion for minimal temperature variation within a plurality of zones of the cooling system.

34. The method of claim 33, wherein each of the candidate configurations comprises:a configuration of the valve;a temperature of a radiator inlet of the cooling system;a total flow rate of the cooling system; anda heat flow of the cooling system.

35. The method of claim 23, wherein the identifying the desired flow configuration comprises applying heuristic search criteria to evaluate and filter candidate flow configurations;the method further comprising adapting the heuristic search criteria based on real-time telemetry data associated with the radiator.

36. The method of claim 35, wherein the adapting the heuristic search criteria comprises adapting the heuristic search criteria based on an identified cause of a discrepancy between a predicted temperature distribution associated with a selected flow configuration and an actual temperature distribution of the selected flow configuration as determined from the real-time telemetry data.

37. A control system to control a cooling system that includes a radiator, the control system comprising:a digital twin of the radiator, including a time-dependent thermal-hydraulic model of the radiator, configured to generate a plurality of predicted thermal states of the radiator by simulating the radiator under a plurality of different sets of conditions;an evaluator configured to use outputs of the digital twin to identify a desired flow configuration of the cooling system for a future time interval; anda controller configured to receive an indication of the desired flow configuration from the evaluator and to set a flow configuration of the cooling system, based on the indication of the desired flow configuration, by controlling at least one valve of the cooling system.

38. The control system of claim 37, wherein the valve is an eclipse valve.

39. The control system of claim 37, wherein the evaluator is configured to identify a candidate configuration, from among a plurality of candidate configurations of the cooling system, that satisfies a specified criterion for minimal temperature variation within a plurality of zones of the cooling system.

40. The control system of claim 39, wherein the evaluator is configured to identify the candidate configuration by:evaluating each of the plurality of predicted thermal states;identifying, based on the evaluating, a predicted thermal state, of the plurality of predicted thermal states, that meets a specified criterion for minimal temperature variation within a plurality of zones of the cooling system; andidentifying a flow configuration of the cooling system that corresponds to the identified predicted thermal state.

41. The control system of claim 37, wherein the evaluator is configured to:execute iterative simulation calls to the digital twin, each simulation call corresponding to a different candidate configuration of a plurality of candidate configurations; and evaluate thermal states of the radiator over a duration of a future time interval, based on a corresponding response to the simulation call from the digital twin for each of the plurality of candidate configurations.

42. The control system of claim 41, wherein each of the candidate configurations comprises:a configuration of the valve;a temperature of a radiator inlet of the cooling system;a total flow rate of the cooling system; anda heat flow of the cooling system.

43. The control system of claim 37, wherein the controller is configured to acquire real-time telemetry data from a plurality of physical components of the cooling system and to provide the real-time telemetry data to the digital twin, and wherein the digital twin is further configured to use the real-time telemetry data to simulate the radiator.

44. The control system of claim 37, wherein the digital twin comprises a machine-learning model configured to output a most probable cause of a discrepancy between a desired thermal profile of the radiator and an actual thermal profile of the radiator as indicated by real-time sensor data.

45. The control system of claim 37, the radiator being a multi-zone radiator including a plurality of zones, wherein the plurality of zones are configured or configurable by actuation of the valve to convey a coolant fluid at different flow rates from each other.

46. The control system of claim 37, wherein the evaluator is configured to:identify the desired flow configuration by applying heuristic search criteria to evaluate and filter candidate flow configurations; andadapt the heuristic search criteria based on real-time telemetry data associated with the radiator.

47. The control system of claim 46, wherein the evaluator is configured to adapt the heuristic search criteria based on an identified cause of a discrepancy between a) a predicted temperature distribution from the digital twin, associated with a selected flow configuration, and b) an actual temperature distribution of the selected flow configuration as determined from the real-time telemetry data.

48. A control system to control a cooling system, the control system comprising:at least one processor; andat least one memory coupled to the at least one processor and storing instructions, execution of which by the at least one processor causes performance of a thermal management process including:generating, during operation of the cooling system, a plurality of predicted thermal states of the cooling system by simulating the cooling system under a plurality of different sets of conditions;identifying a desired flow configuration of the cooling system, based on the plurality of predicted thermal states; andsetting a flow configuration of a radiator in the cooling system, based on the desired flow configuration, by controlling at least one valve of the cooling system.

49. The control system of claim 48, wherein the identifying the desired flow configuration comprises identifying a candidate configuration, from among a plurality of candidate configurations of the cooling system, that satisfies a specified criterion for minimal temperature variation within a plurality of zones of the cooling system.

50. The control system of claim 48, wherein the identifying the desired flow configuration comprises:evaluating each of the plurality of predicted thermal states;identifying, based on the evaluating, a predicted thermal state, of the plurality of predicted thermal states, that meets a specified criterion for minimal temperature variation within a plurality of zones of the cooling system; andidentifying a flow configuration of the cooling system that corresponds to the identified predicted thermal state.

51. The control system of claim 48, wherein the simulating is based on real-time telemetry data from a plurality of physical components of the cooling system.

52. The control system of claim 48, wherein the generating the plurality of predicted thermal states of the cooling system comprises using a time-dependent thermal-hydraulic model of the radiator, during operation of the cooling system.

53. The control system of claim 48, wherein the generating the plurality of predicted thermal states of the cooling system comprises using a digital twin of the radiator to simulate the cooling system under a plurality of different sets of conditions, during operation of the cooling system.

54. The control system of claim 53, wherein using the digital twin comprises executing and continuously training a machine-learning model configured to output a most probable cause of a discrepancy between a desired thermal profile of the radiator and an actual thermal profile of the radiator as indicated by real-time sensor data.

55. The control system of claim 54, wherein the machine-learning model comprises a supervised classification algorithm for determining the most probable cause.

56. The control system of claim 53, wherein the generating the plurality of predicted thermal states of the cooling system comprises:executing iterative simulation calls to the digital twin of the radiator during operation of the cooling system, each simulation call corresponding to a different candidate configuration of a plurality of candidate configurations of the cooling system; andevaluating thermal states of the radiator over a duration of a future time interval, based on a corresponding response to the simulation call from the digital twin of the radiator for each of the plurality of candidate configurati ons.

57. The control system of claim 56, wherein the identifying the desired flow configuration comprises identifying a candidate configuration, from among a plurality of candidate configurations of the cooling system, that satisfies a specified criterion for minimal temperature variation within a plurality of zones of the cooling system.

58. The control system of claim 56, wherein each of the candidate configurations comprises:a configuration of the valve;a temperature of a radiator inlet of the cooling system;a total flow rate of the cooling system; anda heat flow of the cooling system.

59. The control system of claim 48, wherein the identifying the desired flow configuration comprises applying heuristic search criteria to evaluate and filter candidate flow configurations;the thermal management process further comprising adapting the heuristic search criteria based on real-time telemetry data associated with the radiator.

60. The control system of claim 59, wherein the adapting the heuristic search criteria comprises adapting the heuristic search criteria based on an identified cause of a discrepancy between a predicted temperature distribution associated with a selected flow configuration and an actual temperature distribution of the selected flow configuration as determined from the real-time telemetry data.

61. A cooling system comprising:a radiator inlet through which to receive a coolant fluid;a radiator outlet through which to output the coolant fluid;a multi-zone radiator in fluid communication with the radiator inlet and the radiator outlet, the multi-zone radiator including a plurality of zones, each zone of the plurality of zones including one or more fluid conduits for conveying the coolant fluid, wherein the plurality of zones are configured or configurable to convey the coolant fluid at different flow rates from each other;a valve in fluid communication with the multi -zone radiator such that actuation of the valve alters a flow rate through a first zone of the plurality of zones relative to a flow rate of a second zone of the plurality of zones; anda control system to control flow of the coolant fluid by controlling the valve, the control system includinga digital twin of the radiator, including a time-dependent thermal-hydraulic model of the radiator, configured to generate a plurality of predicted thermal states of the radiator by simulating the radiator under a plurality of different sets of conditions, an evaluator configured to use outputs of the digital twin to identify a desired flow configuration of the cooling system for a future time interval, anda controller configured to receive an indication of the desired flow configuration from the evaluator and to set a flow configuration of the cooling system, based on the indication of the desired flow configuration, by controlling at least one valve of the cooling system.

62. The control system of claim 61, the valve being an eclipse valve,63. The control system of claim 46, wherein the evaluator is configured to identify a candidate configuration, from among a plurality of candidate configurations of the cooling system, that satisfies a specified criterion for minimal temperature variation within a plurality of zones of the cooling system.

64. The control system of claim 63, wherein the evaluator is configured to identify the candidate configuration by:evaluating each of the plurality of predicted thermal states;identifying, based on the evaluating, a predicted thermal state, of the plurality of predicted thermal states, that meets a specified criterion for minimal temperature variation within a plurality of zones of the cooling system; andidentifying a flow configuration of the cooling system that corresponds to the identified predicted thermal state.

65. The control system of claim 61, wherein the evaluator is configured to:execute iterative simulation calls to the digital twin, each simulation call corresponding to a different candidate configuration of a plurality of candidate configurations; and evaluate thermal states of the radiator over a duration of a future time interval, based on a corresponding response to the simulation call from the digital twin for each of the plurality of candidate configurations.

66. The control system of claim 65, wherein each of the candidate configurations comprises: a configuration of the valve;a temperature of a radiator inlet of the cooling system;a total flow rate of the cooling system; anda heat flow of the cooling system.

67. The control system of claim 61, wherein the controller is configured to acquire real-time telemetry data from a plurality of physical components of the cooling system and to provide the real-time telemetry data to the digital twin, and wherein the digital twin is further configured to use the real-time telemetry data to simulate the radiator.

68. The control system of claim 61, wherein the digital twin comprises a machine-learning model configured to output a most probable cause of a discrepancy between a desired thermal profile of the radiator and an actual thermal profile of the radiator as indicated by real-time sensor data.

69. The control system of claim 68, wherein the machine-learning model comprises a supervised classification algorithm for determining the most probable cause.

70. The control system of claim 61, the radiator being a multi-zone radiator including a plurality of zones, wherein the plurality of zones are configured or configurable by actuation of the valve to convey the coolant fluid at different flow rates from each other.

71. A computer-implemented method for determining local convective heat transfer characteristics of a fluid flowing through a conduit of a cooling system, the method comprising:receiving, by a controller, telemetry data from one or more sensors indicative of flow rate, fluid properties, and wall temperature along the conduit;computing, by a digital twin, a Reynolds number Re and a Prandtl number Pr for the fluid;determining, by the digital twin, a local Nusselt number Nuxat an axial position x using an adaptive empirical correlation of the formwhere D is a diameter of the conduit, nhand μware bulk and wall viscosities of the fluid, and where C, m, and n are constants tuned by the digital twin based on measured data to account for flow regime, temperature, and viscosity variation; andcalculating, by the digital twin, a local convective heat transfer coefficient / ixaccording to the equation,where k is a thermal conductivity of the fluid,wherein the digital twin updates a thermal model of the cooling system to refine predicted wall temperature and heat transfer distribution along the conduit.

72. The method of claim 71, wherein an initial value of C is set to approximately 1.24 for laminar flow under constant wall temperature conditions and is subsequently adjusted by the digital twin to match measured data.

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