Sintered core heat pipe heat transfer performance prediction method and system based on edge cloud artificial intelligence architecture

Abstract

The invention discloses a rotary sintered core heat pipe digital twinning thermal modeling method based on an edge cloud artificial intelligence architecture, and the method comprises the steps: firstly constructing a sintered core heat pipe high-fidelity digital twinning model fusing a rotation effect, and generating a simulation data set through the model; and the simulation data and the experimental data are fused to form a mixed data set. Thirdly, training artificial intelligence prediction models such as a physical information neural network, a Transform or a lightweight gradient elevator by using the mixed data set; and finally, deploying the trained lightweight model in an edge-cloud collaborative architecture, executing real-time thermal performance prediction by an edge device, and updating and managing the model by a cloud platform. According to the method, through physical model and data driving fusion and edge cloud collaborative deployment, accurate and rapid prediction of the thermal behavior of the rotary sintering core heat pipe is achieved, and the problems that a traditional method is high in calculation cost, poor in real-time performance and difficult to deploy are solved. The invention further discloses a rotary sintered core heat pipe digital twin heat modeling system based on the side cloud artificial intelligence architecture.

Description

Technical Field

[0001] This invention belongs to the field of rotating sintered core heat pipe technology, specifically a method and system for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture. Background Technology

[0002] Heat pipes (HP), as highly efficient two-phase heat transfer (HT) devices, exhibit significant advantages in energy recovery, electronic cooling, and aerospace due to their high thermal conductivity, near-isothermal characteristics, and passive operation mechanism. To ensure functional effectiveness, the thermal performance (TP) of heat pipes must be evaluated during the design phase, typically through experimental measurements and numerical simulations. With modern applications demanding high power density, miniaturization, rotation, and extreme operating conditions, traditional empirical models are increasingly ineffective in predicting thermal behavior under multi-parameter coupled scenarios, making numerical simulation the mainstream alternative. However, computational fluid dynamics (CFD) methods are time-consuming and computationally expensive, especially when simulating complex gas-liquid two-phase flows. Experimental methods, while accurate, are costly and time-consuming, and the complexity of the testing process limits the practicality of iterative design and optimization. Furthermore, HT data under rotating conditions is extremely scarce, further reducing their applicability for rapid TP evaluation in practical engineering designs. Therefore, there is an urgent need to develop predictive models that combine high accuracy and computational efficiency, which is crucial for supporting optimized heat pipe design and ensuring performance reliability under diverse and challenging operating conditions.

[0003] In recent years, extensive research has been conducted on the operating mechanism of high-efficiency tubes (HP) and the characteristics of capillary-gravity tubes (HT). Theoretical research mainly focuses on the modeling, simulation, and qualitative analysis of internal fluid flow and phase change behavior; experimental research focuses on measuring the impact of key design and implementation parameters on heat transfer capacity (TP). To evaluate the heat transfer capacity of HP, various predictive models have been proposed. Mechanistic models based on HT and fluid dynamics theory—such as the distributed parameter model and the capillary-gravity synergistic model—reveal the influence of variables such as tube length, filling ratio, and tilt angle on the heat transfer limit by discretizing the internal phase change process.

[0004] Studies have shown that the heat transfer performance (HTP) of sintered core heat pipes (SHP) is significantly better than that of radially rotating and axially rotating oscillating heat pipes. Therefore, the design optimization and accurate thermal performance evaluation of SHP are particularly important. However, existing SHP prediction models still have significant limitations. To date, there are no reports on methods for evaluating the heat transfer performance of SHP under rotating conditions. Especially under complex conditions with multiple interacting factors, the model accuracy will decrease significantly. In extreme environments such as high temperature and high pressure, the coupling effect of phase change dynamics and material thermal stress will lead to nonlinear behavior that is difficult to model accurately. Although numerical methods can estimate the maximum heat transfer capacity under steady-state conditions, simulations based on software such as Fluent mostly use transient calculations, requiring simulation of the entire process from start-up to steady-state operation. These simulations must consider the time-varying evolution of two-phase flow and heat transfer characteristics, resulting in long simulation cycles and high computational loads. In addition, accurate modeling of vapor-liquid dynamic interactions and phase interface tracking further increases computational complexity. Therefore, although such models can provide physical insights, they are inefficient and not suitable for iterative design or real-time evaluation. While experimental methods can capture actual heat transfer behavior, they are costly and lack accuracy when data is limited. Industrial applications require rapid, low-cost design iterations, and these limitations prevent experiments and traditional numerical models from becoming practical prediction tools. Therefore, reliable, efficient, and generalizable prediction methods are urgently needed to support the optimized design and application of SHP under varied and demanding operating conditions.

[0005] Due to the complex flow and phase change heat transfer mechanisms within heat pipes (SHPs), their thermal performance is extremely sensitive to design and operating parameters. Developing rapid and reliable parameter optimization methods is crucial for industrial applications. Previous experimental studies have proposed semi-empirical correlations based on specific structures and operating conditions. These formulas, obtained through curve fitting, can reasonably predict heat transfer performance within the test range and often show good agreement with experimental results. However, these models generally lack generalization ability and robustness, failing to capture the complex multi-parameter interactions in real-world applications and hindering rapid optimization under multiple operating conditions. In recent years, artificial neural networks (ANNs) have been increasingly used for heat pipe modeling due to their powerful nonlinear mapping and self-learning capabilities. ANNs learn from data and can predict performance based on known structures and operating parameters without explicit physical formulas. For SHPs, ANN-based models can provide a data-driven alternative to traditional physical modeling, offering both greater flexibility and lower experimental costs. Intelligent thermal prediction models have received increasing attention in recent years, and existing research has explored AI-based thermal prediction methods. However, most current solutions are limited to offline computation, with few compatible with embedded or resource-constrained hardware environments. Emerging edge-cloud collaborative architectures offer a direction for deploying lightweight models—performing inference near the data source while offloading complex analytics to the cloud. Nevertheless, research on model quantization, latency optimization, and real-time communication for thermal sensing prediction systems remains scarce. Furthermore, the deployment of physically-informed neural networks or Transformer-based models in embedded edge environments (especially under complex transient thermal loads) remains a gap. These challenges highlight the need to build a unified, deployment-oriented framework to bridge predictive modeling and system-level integration. Based on the above analysis, the following research gaps are identified:

[0006] (1) Existing research largely relies on computational fluid dynamics (CFD) modeling of heat pipe performance, which is time-consuming, labor-intensive, and lacks modular flexibility. Currently, there are no literature reports on a Simulink-based SHP dynamic physics simulation framework. Machine learning-based prediction models suffer from high data dependence and poor training robustness. Data-driven methods typically require large-scale, high-quality datasets, but obtaining such data is often difficult and expensive. There is an urgent need for a hybrid framework that can integrate simulation data and experimental results to enhance ANN training and improve prediction accuracy.

[0007] (2) Existing methods mostly rely on traditional data-driven models, which lack physical interpretability and struggle to maintain generalization ability under varying operating conditions (especially transient thermal disturbances). Existing models often fail to maintain accuracy under diverse structural and operational configurations (especially under extreme or coupled boundary conditions) and lack the robust design guidance adaptability required for practical engineering applications. Although Physical Information Neural Networks (PINN) and Transformer architectures have shown potential in other thermodynamic or power systems, their application in rotating SHP has not yet been explored.

[0008] (3) Existing research rarely considers practical deployment constraints (such as inference latency, model size, and resource limitations), which are crucial for real-time hot prediction. Furthermore, the integration of Simulink-based digital twins with AI-driven prediction frameworks remains insufficient, especially in the context of hybrid edge-cloud architectures. These shortcomings prompt us to develop a physically guided, deployment-aware framework to balance modeling fidelity with real-time applicability. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a method and system for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture. By integrating physical simulation and data-driven prediction models, it can achieve real-time and accurate prediction and compensation of the thermal behavior of sintered core heat pipes under rotation conditions, thus solving the problems of high computational cost and poor adaptability of traditional methods.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] This invention first proposes a method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture, comprising the following steps:

[0012] Step 1: Constructing a digital twin model: Constructing a physics-based high-fidelity digital twin model of the rotating sintered core heat pipe, dividing the rotating sintered core heat pipe into four functional modules: evaporator, steam pipe, condenser, and liquid pipe, with a sintered core inside the liquid pipe; based on the mass, momentum, and energy conservation equations, simulating the two-phase flow and heat transfer process involving phase change, while introducing a centrifugal acceleration vector to characterize the rotation effect;

[0013] Step 2: Generate and merge datasets: Run a high-fidelity digital twin model of the rotating sintered core heat pipe and perform dynamic simulations within a predetermined range of extended operating parameters to generate a simulation dataset; conduct experiments on the rotating sintered core heat pipe within a subset of the extended operating parameter range to obtain an experimental dataset; merge the simulation dataset and the experimental dataset to form a hybrid dataset for model training.

[0014] Step 3: Train the AI ​​prediction model: Train at least one AI prediction model using the hybrid dataset, wherein the candidate AI model is selected from the Physical Information Neural Network, the Transformer Regression Network, and the Lightweight Gradient Boosting Machine;

[0015] Step 4: Edge-Cloud Architecture Deployment and Inference: The trained AI prediction model is deployed in an edge-cloud collaborative architecture. The quantized and optimized lightweight model is deployed on an edge computing device to receive real-time data from the rotating sintered core heat pipe sensor and execute the AI ​​prediction model for forward inference, outputting thermal performance prediction results with sub-second latency. The cloud platform is used to receive edge data, store historical records, and perform visualization management, and incrementally retrain the AI ​​prediction model when trigger conditions are met.

[0016] Furthermore, in step one, the modeling principle of the high-fidelity digital twin model of the rotating sintered core heat pipe includes:

[0017] The continuity equations for the evaporator, steam pipes, condenser, and liquid pipes are expressed as follows:

[0018]

[0019] in: and These are, respectively, the mass flow rate of steam in the steam pipe, the mass generation rate of steam generated in the evaporator due to boiling and entering the steam chamber, the mass flow rate of steam condensing into liquid in the condenser, the mass flow rate of liquid flowing into the evaporator liquid chamber from the liquid return channel or sintered wick, the mass flow rate of liquid vaporized from the liquid phase to the steam phase in the evaporator liquid chamber, and the mass flow rate of liquid flowing from the condensation section liquid chamber into the liquid return section (sintered wick or liquid pipe); M le and M lc These represent the mass of the working fluid in the evaporator liquid chamber and the mass of the working fluid in the condenser liquid chamber, respectively; V ve and V vc These refer to the volume of the evaporator steam chamber and the volume of the condenser steam chamber or steam pipes, respectively; p ve and p vc These are the average steam pressure in the evaporator steam chamber and the average steam pressure in the condenser steam chamber or steam pipe, respectively; T ve and T vc These are the steam temperatures in the evaporator steam chamber and the steam temperatures in the condenser steam chamber or steam pipes, respectively; R * γ is the perfect gas constant of vapor; t is time; γ is the multidirectional index;

[0020] The pressure drop in steam pipelines and liquid pipelines are expressed as follows:

[0021]

[0022] Where: ρ v r is the gas mass density. v h is the radius of the steam pipe. lv Latent heat of vaporization / condensation; μv Vapor dynamic viscosity; l eff For effective heat transfer length; p lc p represents the pressure in the liquid chamber of the condensation section. le This indicates the pressure in the liquid chamber of the evaporation section; Indicates the condensation heat flow rate; μ l ρ is the dynamic viscosity of the liquid. l Indicates liquid density; K is the permeability of the sintered core; A w This represents the cross-sectional area of ​​the liquid flow within the sintered core.

[0023] The capillary limit constraint equation is expressed as:

[0024] Δp cap ≥ΔP l +Δp v +Δp grav +ΔP centrifugal

[0025] Where: Δp v Indicates the steam core pressure drop; Δp grav Indicates the pressure drop due to gravity; ΔP centrifugal This indicates centrifugal pressure drop loss.

[0026] Furthermore, in step two, the heat transfer simulation model of the high-fidelity digital twin model of the rotating sintered core heat pipe includes:

[0027] The energy conservation equation for a pipeline is expressed as:

[0028]

[0029] Where: M is the mass of the fluid in the pipe; and These are the mass flow rates of port A and port B, respectively; u out The precise internal energy after all heat transfer is complete; φ A Energy is transferred into the pipe through port A; φ B Q represents the energy entering the pipe through port B. H The heat entering the pipe through the wall of port H; The average mass flow rate, and according to Calculate; g is the acceleration due to gravity; Δz is the gain parameter value from port A to port B;

[0030] Steam flow is described by the compressible mass-energy balance equation:

[0031]

[0032] Where: m v For steam quality; h is the phase change mass flow rate. v Specific enthalpy of vapor; h fg The latent heat of vaporization; Q in Input heat into the steam chamber; Q cond This refers to the heat release power during condensation.

[0033] Darcy-type momentum equation for liquid reflux within the sintered core, including terms of centrifugal force and capillary pressure:

[0034]

[0035] Where: μ is the dynamic viscosity of the liquid; u l ρ is the dynamic viscosity of the liquid. l Where is the liquid density; r is the radial distance from the rotation axis; and K is the permeability of the sintered core. Further, in step two, the high-fidelity digital twin model of the rotating sintered core heat pipe includes a heat transfer model of the sintered heat pipe under rotational conditions, comprising:

[0036] The heat flow analytical model, used to couple centrifugal acceleration, capillary absorption, phase change, and transport in porous media, is expressed as follows:

[0037]

[0038] Where: ε is the porosity of the sintered core; ρ l The density of the liquid; Darcy speed; S m This is the phase change mass source term, i.e., the evaporation / condensation rate;

[0039] Darcy's law, which includes centrifugal acceleration, is expressed as:

[0040]

[0041] Where: k is the permeability; μ l Dynamic viscosity; is the centrifugal acceleration vector; r is the radial distance from the axis of rotation;

[0042] The capillary pressure model is expressed as:

[0043]

[0044] Where: σ is the surface tension; θ is the contact angle; r eff Δp is the effective pore radius of the sintered matrix. grav For the loss due to gravity pressure drop; ΔP centrifugal This indicates centrifugal pressure drop loss;

[0045] The energy conservation model for the liquid absorption core region is expressed as:

[0046]

[0047] Where: h l Specific enthalpy of liquid; k eff The effective thermal conductivity of the porous wick; For internal heat generation; For latent heat source terms;

[0048] The gas-phase core pressure-driven flow model, described by the one-dimensional compressible Navier-Stokes equations, is expressed as:

[0049]

[0050]

[0051] Where: P v For steam pressure; μ v The viscosity is the vapor dynamic viscosity; r v For steam pipes; ρ is the steam mass flow rate; v A is the density of the vapor; v z represents the cross-sectional area of ​​the steam flow; z represents the axial position.

[0052] The total thermal resistance model is expressed as:

[0053] R total =R evap +R wick +R vapor +R cond

[0054] Where: R evap R is the boiling thermal resistance on the evaporation side. wick For the porous wick, conduction thermal resistance; R vapor For steam transport thermal resistance; R cond This represents the condensation thermal resistance on the condensation side.

[0055] Furthermore, in step three, the physical relationship of the artificial intelligence prediction model is represented as follows:

[0056]

[0057] Wherein: T peak ΔP is the peak temperature of the evaporator wall; w is the rotational speed; Q is the heat input; FR is the liquid filling rate; t is the time; z is the axial position; x is the evaporator steam mass; ΔP wick For core voltage drop; P vapor This refers to the axial pressure in the steam passage. This refers to the transient wall temperature.

[0058] Furthermore, the physical information neural network integrates a one-dimensional transient heat conduction equation:

[0059]

[0060] Where: c p ρ represents specific heat capacity; k represents density; k represents thermal conductivity. The temperature gradient is represented by Q(x,t); the heat source term is represented by Q(x,t); and the temperature field is represented by T.

[0061] The loss function of the physical information neural network is:

[0062] Γ=Γ data +Γ residual (λ1Γ energy +λ2Γ momentum )

[0063] Where: λ1 and λ2 represent weighting coefficients; Γ data Indicates data residuals; Γ energy and Γ momentum Γ represents the partial differential equation residuals calculated at the collocation point for the energy equation and the momentum equation, respectively; residual This represents the weighting coefficients of the physics-based residual terms; and:

[0064]

[0065] Where: N y To mark the number of temperature points; Predict temperature for the network; T i This is the measured temperature;

[0066] The physical loss is the mean square residual, expressed as:

[0067]

[0068] Where: N c The number of unlabeled placement points; ε(x,t) represents the energy equation residual; M(x,t) represents the momentum equation residual; Indicates the predicted temperature; The predicted axial liquid velocity in the wick is represented by α; the effective thermal diffusivity is represented by ρ; and the density is represented by c. p Indicates specific heat capacity; h fg Indicates latent heat; A represents the cross-sectional area of ​​the flow. This represents the phase change mass flow rate; The predicted vapor pressure is represented by μ; the dynamic viscosity is represented by r; the radial distance of the liquid path is represented by K; the permeability of the sintered core is represented by Ω; and the angular velocity is represented by Ω.

[0069] Furthermore, the Transformer regression network employs a multi-head self-attention mechanism, the core of which is scaled dot product attention, expressed as:

[0070]

[0071] Where: Q, K, and V represent the query, key, and value matrices, respectively; d k This represents the dimension of the key vector.

[0072] Furthermore, the lightweight gradient booster employs SHAP analysis to perform feature importance analysis, calculating the SHAP value φ of feature j. j :

[0073]

[0074] Where: φ j The SHAP value of feature j is represented by F; F represents the set of all features; S represents the subset of features excluding feature j; |S| represents the number of features in subset S; |F| represents the total number of features in set F; f S∪{j} This indicates that when only features x in subset S are used... S∪{j} Model output as input; f S∪{j} (x S∪{j} ) represents the model output when feature j is added to subset S; The SHAP weights take into account the permutation of the subset S into which feature j is inserted, ensuring a fair average across all feature orders.

[0075] This invention also proposes a system for implementing the method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture as described above, comprising:

[0076] The high-fidelity digital twin modeling and simulation module is used to perform modeling and simulation of the high-fidelity digital twin model of the rotating sintered core heat pipe in the Simulink-SIMSCAPE environment.

[0077] The experimental data acquisition module includes a K-type thermocouple array arranged on the surface of the rotating sintered core heat pipe, a controllable heater, a variable speed rotation platform, and a data acquisition card, which are used to acquire experimental thermal response data.

[0078] A hybrid data processing module is used to receive and fuse simulation data from the digital twin modeling unit and experimental data from the experimental data acquisition module to construct a hybrid dataset.

[0079] An artificial intelligence training platform is used to train, validate, and compare the physical information neural network, Transformer regression network, and lightweight gradient boosting machine model based on the hybrid dataset.

[0080] The edge-cloud collaborative deployment and inference subsystem includes:

[0081] The edge inference module, deployed on edge hardware, embeds a quantized and accelerated artificial intelligence prediction model to receive sensor data streams in real time and output thermal performance predictions.

[0082] The cloud platform management module, deployed on the server, provides model version management, long-term data storage, a visual dashboard, and a model retraining pipeline.

[0083] The communication middleware, based on the MQTT protocol, enables asynchronous and reliable data exchange and command transmission between the edge inference module and the cloud platform management module.

[0084] Furthermore, the total end-to-end delay T total Represented as:

[0085] T tota l = T acq +T proc +T comm +T sync

[0086] Wherein: T acq For sensor data acquisition delay; T proc The inference time depends on the model complexity; T comm For network communication delay; T sync This indicates an asynchronous queue or a synchronous delay.

[0087] The beneficial effects of this invention are as follows:

[0088] This invention presents a method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture. By constructing a high-fidelity digital twin model, generating a fused dataset, training an artificial intelligence prediction model, and co-deploying edge and cloud technologies, the following technical effects have been achieved:

[0089] (1) The prediction accuracy and physical consistency are significantly improved: High-fidelity simulation data is generated by a digital twin model based on the physical conservation law and fused with experimental data to construct a hybrid training set that combines physical realism and data breadth. This enables the artificial intelligence prediction model trained subsequently to not only learn the data patterns, but also to ensure that the prediction results conform to the basic principles of heat transfer and flow by embedding physical equation residual constraints. It exhibits excellent accuracy and generalization ability in complex rotating conditions and transient processes, overcoming the defect of traditional pure data-driven models inaccurate prediction under unknown conditions.

[0090] (2) The computational efficiency has achieved a leap of orders of magnitude, meeting the real-time requirements: Traditional high-fidelity CFD simulation takes several hours to tens of hours and cannot be used for real-time monitoring and compensation. This invention completes the time-consuming simulation process offline, and the inference latency of the lightweight artificial intelligence prediction model trained on the edge device can be shortened to the sub-second level. The efficiency improvement makes it possible to realize real-time thermal performance prediction and forward-looking thermal management on high-speed rotating equipment, laying the foundation for closed-loop control.

[0091] (3) Achieved efficient and reliable deployment in resource-constrained environments: The architecture design of edge-cloud collaboration is adopted. The lightweight model, which has been quantized and accelerated, is deployed on the edge side and is responsible for low-latency real-time inference. The cloud platform is responsible for data aggregation, model retraining and global management. This architecture not only ensures the system's stringent real-time requirements in industrial sites, but also realizes continuous optimization and lifecycle management of the model through the cloud, so that the system has the advantages of fast response speed, strong adaptability and good scalability.

[0092] In summary, this invention creatively integrates physical modeling, data-driven AI, and edge computing, fundamentally solving the core pain points of "slow calculation, difficult deployment, and lack of real-time performance" in the thermal performance evaluation of rotating sintered core heat pipes while ensuring prediction accuracy. It provides a practical and feasible technical path for real-time thermal control and status monitoring in fields such as precision manufacturing and aerospace. Attached Figure Description

[0093] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following drawings are provided for illustration.

[0094] Figure 1 The flowchart shows the method for predicting the heat transfer performance of sintered core heat pipes based on edge cloud artificial intelligence architecture according to the present invention; (a) Experiment-simulation-ANN modeling logic diagram of neural network model, experimental data and Simulink simulation data are combined as the source of input data for ANN model generation, and simulation data is verified by experiments to ensure the reliability of ANN model; (b) Artificial intelligence driven thermal modeling process, showing the workflow from data acquisition from experiments and simulations, preprocessing, model training to deployment in edge cloud architecture to realize real-time prediction of heat pipe performance.

[0095] Figure 2 The modular structure of the sintered core heat pipe heat transfer model is shown, with independently constructed evaporator, steam pipe, condenser and liquid pipe modules, each representing its thermodynamic role in the overall system.

[0096] Figure 3 This is a schematic diagram of a complete heat transfer model. It is a heat pipe steady-state heat transfer simulation model built based on the Simulink SIMSCAPE component, which integrates heat input module, phase change simulation and real-time temperature monitoring output functions.

[0097] Figure 4 The internal layout of the evaporator subsystem model includes fluid channels for simulating steam generation during heat input, temperature monitoring points, and applied heat sources.

[0098] Figure 5 To simulate the inlet and outlet temperature curves of the working fluid in the sintered heat pipe, display the heat absorption process of the evaporator and confirm the occurrence of phase change, thereby verifying the accuracy of the sintered heat pipe simulation model.

[0099] Figure 6 To investigate the evolution of the volumetric phase ratio (liquid phase, gas phase, and two-phase mixture) during the heat transfer process of sintered heat pipes, this study aims to confirm the phase change phenomenon and verify the effectiveness of the heat transfer model in simulating the dynamic response of multiphase flow in sintered heat pipes.

[0100] Figure 7 This is a prediction of gas phase coherence and gas-liquid interface velocity distribution based on a calibrated SIMSCAPE model. These intrinsic variables are used to elucidate the two-phase flow dynamics, and are qualitatively consistent with the experimentally verified temperature and pressure trends. The results focus on revealing the internal two-phase mass transfer mechanism rather than direct experimental verification.

[0101] Figure 8 The thermal resistance and temperature rise curves of the sintered core heat pipe under different heat loads show that the performance is stable at low and medium loads, but nonlinear thermal resistance growth and local overheating occur when the load exceeds 30W.

[0102] Figure 9 The parameter configuration interface for the two-phase fluid piping module highlights the definitions of fluid properties, geometric parameters, and boundary conditions, which are crucial for the accurate simulation of the evaporator section.

[0103] Figure 10 The simulated transient temperature curves along multiple monitoring nodes of the heat pipe are used to verify the modeled thermal response through experimental measurements.

[0104] Figure 11 The temperature field evolution under extreme operation (500 r / min and 40 W) shows the limit of capillary reflux under high load.

[0105] Figure 12 The pressure and liquid velocity distribution within the sintered wick during steady-state operation is shown, illustrating capillary-driven condensate reflux, axial pressure gradient, and uniform radial permeation that maintain two-phase circulation under rotating conditions.

[0106] Figure 13 The pressure and liquid velocity distribution of the wick structure during steady-state operation confirmed that the capillary-driven liquid refluxed from the condensation section to the evaporation section and permeated uniformly into the wick pores.

[0107] Figure 14The thermal resistance components under rated operating conditions are decomposed, showing the dominant evaporation phase change thermal resistance and the increased wick flow thermal resistance under rotation or tilting conditions.

[0108] Figure 15 It is a sintered core heat pipe coupled heat flow transport framework that integrates heat conduction, phase change heat transfer and capillary flow model based on Darcy's law for transient performance prediction.

[0109] Figure 16 This is a schematic diagram of the experimental platform, which includes motor drive, heating and cooling modules, data acquisition system and safety mechanisms.

[0110] Figure 17 This is a photograph of the experimental setup, showing the assembled heat pipes, sensors, slip rings, and control unit in operation.

[0111] Figure 18 This is a schematic diagram of the SHP structure.

[0112] Figure 19 The comparison between simulated and experimental temperature changes under baseline conditions (d = 8 mm, FR = 100%, Led = 0 mm, n = 100 r / min, P = 10 W) shows a high degree of agreement. Tsim-T0 is the temperature difference between the simulated temperature Tsim and the measured temperature T0, Tsim-T1 is the temperature difference between Tsim and T1, Tsim-T2 is the temperature difference between Tsim and T2, and Tsim-T3 is the temperature difference between Tsim and T3.

[0113] Figure 20 To compare the thermal response under different eccentricities and rotational speeds, the robustness of the prediction model was verified (d = 8 mm, FR = 100%, Led = 17 mm, P = 10 W). Tsim-T0 is the temperature difference between the simulated temperature Tsim and the measured temperature T0; Tsim-T1 is the temperature difference between the simulated temperature Tsim and the measured temperature T1; Tsim-T2 is the temperature difference between the simulated temperature Tsim and the measured temperature T2; Tsim-T3 is the temperature difference between the simulated temperature Tsim and the measured temperature T3.

[0114] Figure 21 Comparison of experimental and simulation results of steady-state temperature difference when Led = 17 mm, P = 10 W, n = 100 r / min: (a) FR = 100%, (b) d = 8 mm.

[0115] Figure 22 In the study, the effects of eccentricity and rotational speed on steady-state temperature difference were investigated under the conditions of (a) n = 100 r / min and (b) Led = 17 mm (d = 8 mm, FR = 85%, P = 10 W).

[0116] Figure 23This document summarizes a comparison of the performance and deployment characteristics of LightGBM, Transformer, and PINN. Key metrics aggregated in the radar chart include prediction accuracy (MAE), inference latency, model size, generalization ability, and interpretability.

[0117] Figure 24 Model validation is presented. Model validation results under representative thermal conditions are compared with the predicted and measured temperatures of the LightGBM, Transformer, and PINN models. Subfigure (a) shows the model output under a step thermal input scenario (10W to 30W), where PINN's embedded physics mechanism is closest to the measured value. Subfigure (b) evaluates the response to a ramp-up rotational speed (500-1500 rpm), showing that the Transformer is more adaptable to gradual input.

[0118] Figure 25 The following is a comparison of the representative computation time of the proposed ANN and CFD simulation. The high-fidelity CFD simulation of the rotating SHP condition takes about 14.6 hours on a 32-core workstation, while the trained ANN can complete the corresponding thermal field prediction in just 0.15 seconds on an embedded Jetson Xavier device.

[0119] Figure 26 This invention presents a digital twin deployment framework for thermal error prediction and compensation in a sintered core heat pipe heat transfer performance prediction system based on an edge-cloud AI architecture. This framework integrates multiple AI modules across the cloud, edge, and device layers. The cloud layer is responsible for global model training, cross-device knowledge aggregation, and system-level optimization. The edge layer performs lightweight inference, data preprocessing, and local decision-making through compressed models (such as Transformer and LightGBM), and communicates with cloud services via MQTT or HTTP protocols. The device layer directly connects to physical sensors and actuators, enabling real-time feedback control. Seamless data flow and task scheduling between layers ensure low-latency prediction, adaptive model updates, and robust deployment in complex industrial environments.

[0120] Figure 27 The prediction errors of the LightGBM, Transformer, and PINN models are compared in three transient test scenarios: (i) a step increase in thermal input, (ii) a ramp-up in rotational speed, and (iii) complex fluctuations. Mean absolute error (MAE) is used as the evaluation metric. PINN exhibits the lowest error in scenario (i), thanks to its embedded physical constraints which enhance robustness to sudden thermal changes. Transformer performs best in scenario (ii) by effectively capturing gradual system dynamics through its temporal attention mechanism. LightGBM consistently shows high error, especially under complex coupled fluctuations, indicating that its generalization ability is limited by training conditions. These results highlight the importance of model architecture selection in dynamic thermal environments.

[0121] Figure 28 System-level validation results of the proposed digital twin framework integrating heat pipe cooling, multi-model thermal prediction, and edge-cloud deployment are presented. Temperature tracking performance and time-varying residuals during full-loop operation are shown, including sensing, model inference, and compensation. The framework maintains tracking errors within ±0.3°C under dynamic thermal loads, demonstrating robust real-time capabilities. Edge-side inference latency remains below 150 ms, ensuring compensation actions are triggered within acceptable control cycles. These results confirm the effectiveness and responsiveness of the proposed architecture for practical thermal error mitigation in precision motion systems.

[0122] Figure 29 This comparison presents the inference times of LightGBM, Transformer, and PINN models under identical hardware and deployment conditions. Total inference latency includes model loading, data preprocessing, and forward propagation time on industrial edge devices. LightGBM exhibits the lowest inference time (~60ms) due to its shallow structure and compact model size. Transformer maintains moderate latency (~100ms), benefiting from efficient matrix operations and parallel processing. PINN demonstrates significantly higher inference time (~480ms) due to the complexity of physical constraint calculations and residual evaluation. This comparison reveals the key trade-off between model accuracy and deployment responsiveness in real-time thermal compensation systems. Detailed Implementation

[0123] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0124] 1. Prediction of heat transfer performance of sintered core heat pipes

[0125] like Figure 1 As shown, this embodiment of the sintered core heat pipe heat transfer performance prediction method based on edge cloud artificial intelligence architecture includes the following steps:

[0126] Step 1: Constructing a digital twin model: Construct a physics-based high-fidelity digital twin model of the rotating sintered core heat pipe, dividing the rotating sintered core heat pipe into four functional modules: evaporator, steam pipe, condenser, and liquid pipe. The liquid pipe contains a sintered core. Based on the mass, momentum, and energy conservation equations, simulate the two-phase flow and heat transfer process involving phase change, and introduce a centrifugal acceleration vector to characterize the rotation effect.

[0127] Step 2: Generate and merge datasets: Run a high-fidelity digital twin model of the rotating sintered core heat pipe and perform dynamic simulations within a predetermined range of extended operating parameters to generate a simulation dataset; conduct experiments on the rotating sintered core heat pipe within a subset of the extended operating parameter range to obtain an experimental dataset; merge the simulation dataset and the experimental dataset to form a hybrid dataset for model training.

[0128] Step 3: Train the AI ​​prediction model: Train at least one AI prediction model using the hybrid dataset, wherein the candidate AI model is selected from the Physical Information Neural Network, the Transformer Regression Network, and the Lightweight Gradient Boosting Machine;

[0129] Step 4: Edge-Cloud Architecture Deployment and Inference: The trained AI prediction model is deployed in an edge-cloud collaborative architecture. The quantized and optimized lightweight model is deployed on an edge computing device to receive real-time data from the rotating sintered core heat pipe sensor and execute the AI ​​prediction model for forward inference, outputting thermal performance prediction results with sub-second latency. The cloud platform is used to receive edge data, store historical records, and perform visualization management, and incrementally retrain the AI ​​prediction model when trigger conditions are met.

[0130] 2. High-fidelity digital twin model of rotating sintered core heat pipe (SHP digital twin model)

[0131] This embodiment chooses to use SIMSCAPE to generate data, rather than relying solely on experimental datasets or generative AI augmentation methods, for three key reasons: First, the constructed SIMSCAPE model is a physics-based component-level representation, adhering to the laws of conservation of mass, momentum, and energy, and is calibrated for measured thermal responses under multiple rotational speeds and thermal loads, ensuring that key nonlinear phenomena such as centrifugal force-induced liquid reflux, variable phase change rates, and rotation-controlled capillary limits are preserved in the simulation; Second, although direct experimental measurements offer the highest physical realism, they are limited by high costs, limited testing time, and equipment safety issues under extreme conditions (such as >300 r / min or low fill rates). The SIMSCAPE framework allows for the safe exploration of such conditions and the generation of dense, wide-coverage datasets without sacrificing physical consistency; Third, unlike generative AI augmentation methods that may produce statistically reasonable but physically inconsistent samples, SIMSCAPE outputs are inherently constrained by governing equations, making them more suitable for training physical information or hybrid AI models; Furthermore, this simulation-first approach enables a smooth transition to subsequent AI modeling stages. The SIMSCAPE dataset serves as the primary training resource for three prediction models: PINN, Transformer, and LightGBM (Lightweight Gradient Boosting Machine). Simultaneously, targeted experimental data is introduced to fine-tune and validate the models under real-world conditions. This hybrid data strategy ensures that the trained AI models possess both broad operational envelope coverage and a strong physical foundation, thereby improving prediction accuracy and generalization capabilities within the edge-cloud deployment framework.

[0132] 2.1 Simulink-based modeling and prediction

[0133] In this embodiment, MATLAB Simulink with the SIMSCAPE fluid module is selected as the SHP digital twin modeling platform. Compared with traditional CFD solvers that require complex meshing, long-term transient calculations and high computational costs for new configurations, the Simulink-SIMSCAPE environment provides a modular parametric architecture that can quickly reconstruct geometry, materials and boundary conditions. Each physical component (evaporator, steam pipe, condenser, liquid reflux section) is represented by a predefined module that follows conservation laws and can be extended and modified as needed, providing three major advantages for the edge-cloud AI framework: (1) Flexibility - the model can be quickly adapted to different SHP geometries or conditions without re-meshing; (2) Integration - the simulation module can be directly connected to the Simulink control and signal processing module, which is convenient for seamless coupling with the AI ​​prediction model; (3) Efficiency - the proven Simulink model generates diverse thermal response datasets several orders of magnitude faster than equivalent CFD cases, enabling it to cover the full training range required for ANN generalization (100-600 rpm, multiple heat loads).

[0134] In this embodiment, the SIMSCAPE module in MATLAB Simulink is used to construct the SHP simulation model. SIMSCAPE provides a predefined component synthesis library for modeling fluid dynamic systems, including components such as pipes, valves, and pumps. These components allow for the construction of system models based on actual physical structures. The built-in code in SIMSCAPE components can be modified and extended in MATLAB, the input parameters are fully customizable, and the internal mathematical expressions can be redefined to adjust the component structure and function as needed. This flexibility enables the development of customized models that reflect the physical characteristics of the system under study. Furthermore, existing MATLAB functions and scripts can be directly integrated into the SIMSCAPE environment, enhancing the model's versatility and simplifying the simulation workflow. Because SIMSCAPE runs within the Simulink framework, the physical simulation model can be easily connected to traditional Simulink models. This allows for seamless hybrid modeling when certain physical processes are difficult to represent analytically. Therefore, SIMSCAPE and Simulink models can complement each other to improve model accuracy and usability.

[0135] 2.1.1 Modeling Principles

[0136] The physics-based SHP digital twin is constructed using SimscapeFluids in MATLAB / Simulink, representing SHP as four coupled submodules: evaporator, steam conduit, condenser, and liquid conduit (wick / porous core). Lumped one-dimensional mass-momentum-energy balance is solved through phase change heat transfer. Steam is modeled as an ideal gas, and the liquid is treated as an incompressible fluid. Flow in both the steam conduit and the porous wick is laminar. The rotational effect is introduced as a centrifugal pressure drop loss acting on the liquid column within the porous core. The model is fully parameterized (geometry, materials, operating conditions), generating large datasets for neural network training and supporting scenario studies.

[0137] This embodiment utilizes the SIMSCAPE module to develop an SHP simulation model. The platform allows direct selection of relevant components from its predefined library, eliminating the need to construct complex mathematical models from first principles. To accurately describe fluid flow and heat transfer phenomena within the SHP, fundamental physical laws—such as mass conservation, energy conservation, and momentum conservation—are strictly applied during the modeling process to ensure the simulation results are reliable and physically meaningful. To simplify model development and improve computational feasibility, the following assumptions are made: (1) the liquid phase is incompressible; (2) the ideal gas law applies to the gas phase; (3) vapor expansion and compression are considered multi-directional processes; (4) liquid and vapor flows are laminar; and (5) the mass flow rate remains constant in the adiabatic section, while evaporation and condensation are limited to two independent sections.

[0138] like Figure 2As shown, during the SHP modeling process, the structure is divided into four functional sections: evaporator, steam pipe, condenser, and liquid pipe. During HP operation, the working fluid in the evaporator absorbs heat and undergoes a phase change, generating steam that flows into the steam pipe. The pressure inside the steam pipe increases as steam accumulates, driving it towards the condenser; the steam condenses into liquid after releasing its latent heat in the condenser. The condensate then enters the liquid line. The centrifugal force generated by the HP's rotation, together with the capillary force of the porous sintered core, propels the liquid back to the evaporator. These two forces work together to overcome pressure loss and ensure continuous flow of the working fluid in the closed-loop system.

[0139] Each SHP section is implemented through a standard SIMSCAPE component and a thermal interface: (1) Evaporator section: with a controlled heat flow rate module (applied heat input Q) in (1) Thermally coupled two-phase fluid control volume (steam chamber); when parasitic losses need to be considered on the evaporator wall, a thermal mass plus surface convection heat exchange interface is used to couple with the environment; (2) Steam pipe: a one-dimensional flow element with laminar pressure drop (achieved through two-phase fluid pipe / flow resistance equivalent); when needed, heat exchange with the environment can be added through heat conduction and convection heat transfer modules; (3) Condenser section: a two-phase control volume using a controlled temperature source or convection heat transfer boundary (representing an external cold source, such as forced / natural convection or water jacket); latent heat removal is handled by phase change coupling at the fluid-wall interface; (4) Liquid pipe (liquid reflux / porous wick): represented by an equivalent porous medium (Darcy) channel (customized using SIMSCAPE basic equations), used to connect the condenser and evaporator. Permeability K, porosity ε and effective capillary radius r eff The parameters are as follows. The rotational (centrifugal) volumetric force is injected as an additional pressure drop loss term. (5) The signals (temperature, steam pressure, mass flow rate, and phase fraction indicator at multiple axial measuring points) are output for recording via a PS-Simulink converter.

[0140] Based on the assumption that steam follows the ideal gas law, the continuity equation for the evaporator and steam can be derived. The continuity equation for the evaporator and steam pipes is given by the following equation:

[0141]

[0142] in: and These are, respectively, the mass flow rate of steam in the steam pipe, the mass generation rate of steam generated in the evaporator due to boiling and entering the steam chamber, the mass flow rate of steam condensing into liquid in the condenser, the mass flow rate of liquid flowing into the evaporator liquid chamber from the liquid return channel or sintered wick, the mass flow rate of liquid vaporized from the liquid phase to the steam phase in the evaporator liquid chamber, and the mass flow rate of liquid flowing from the condensation section liquid chamber into the liquid return section (sintered wick or liquid pipe); M le and Mlc These represent the mass of the working fluid in the evaporator liquid chamber and the mass of the working fluid in the condenser liquid chamber, respectively; v ve and V vc These refer to the volume of the evaporator steam chamber and the volume of the condenser steam chamber or steam pipes, respectively; p ve and p vc These are the average steam pressure in the evaporator steam chamber and the average steam pressure in the condenser steam chamber or steam pipe, respectively; T ve and T vc These are the steam temperatures in the evaporator steam chamber and the steam temperatures in the condenser steam chamber or steam pipes, respectively; R * γ is the perfect gas constant of the vapor; t is time; γ is the multidirectional index.

[0143] SIMSCAPE maps the following one-dimensional relationship. The mass balance equation for the vapor chamber (ideal gas) is:

[0144]

[0145] Where: m v This indicates the mass of steam inside the evaporator cavity.

[0146] R here * The unit gas constant J / kg / K of the working fluid in the gas phase is expressed by the following formula: Where R u Let M be the universal gas constant, 8.314462618 J / mol / K, and M be the molar mass of the gas phase. For the ammonia-water mixture used in the SHP experiment, M is obtained through a weighted molar composition over the relevant temperature range (source: NIST Chemistry Database). This definition ensures that the model implementation in SIMSCAPE matches the ideal gas law relationship p used in the analytical formula. v V v =Zm v R * T v To maintain thermodynamic consistency, where p v V is the vapor pressure; v Z represents the gas phase volume; Z represents the compressibility factor; T v This is the absolute vapor temperature. In this embodiment, the overall gas phase within the SHP is determined by the ideal gas relation p in the SimscapeGas framework. v V v =Zm v R * T v Modeling, the framework has built-in support for p v V v =Zρ v R * T vThis choice is consistent with recent heat pipe and thermosiphon models that treat the gas phase as an ideal gas under near-saturation to slightly superheated conditions and at moderate pressures, where non-ideal deviations have negligible impact on system-level predictions. If the operating conditions shift to high pressure / high superheat or the presence of non-condensable gases, a real gas model can be switched via Z≠1 or a property table (such as REFPROP), or the two-fluid / non-condensable gas module can be extended. We documented this assumption and its applicability, and verified that it does not dominate the prediction error relative to measured data within the experimental parameter range. This assumption is also supported by the simulated and measured operating conditions. For the working fluid used (e.g., water), the highest steam temperature in the evaporator is below (T0) at the highest heat input of 40 W. sat +40K), where T sat This represents the saturation temperature. According to NISTREFPROP, the corresponding saturation pressure is less than 0.35 MPa, at which point the compressibility factor Z is between 0.98 and 1.02. Within this range, the deviation of the real gas is no more than 2%, which is less than the uncertainty of the wick permeability and the interfacial heat transfer coefficient. Therefore, for the current heat-fluid coupling model, the ideal gas law can sufficiently and accurately describe the gas phase behavior.

[0147] and The quality transmission rate is expressed as:

[0148]

[0149] Among them: Q eva Q is the evaporative heat flow rate; cond h is the condensation heat flow rate. lv It is the latent heat of vaporization / condensation.

[0150] Calculate the pressure drop in the steam pipeline based on the assumption that the steam flow is laminar:

[0151]

[0152] Where: ρ v r is the gas mass density. v Where μ is the radius of the vapor chamber. v Vapor dynamic viscosity; l eff The effective heat transfer length.

[0153] The continuity equation for the condenser and liquid piping is expressed as:

[0154]

[0155] in: and These are, respectively, the liquid mass flow rate flowing into the evaporator liquid chamber from the liquid reflux channel or sintered wick, the mass flow rate of liquid vaporized and transformed from liquid to vapor in the evaporator liquid chamber, and the liquid mass flow rate flowing into the liquid reflux section (sintered wick or liquid pipe) from the condensation section liquid chamber; M le and M lc Let M be the mass of the working fluid in the evaporator liquid chamber and the mass of the working fluid in the condenser liquid chamber, respectively, and M... li Mass of liquid within the sintered core volume:

[0156]

[0157] Where: ρ l ε is the gas mass density; ε is the porosity of the sintered core; r w With r v These represent the outer radius of the rotation path, respectively.

[0158] The sintered core is a porous medium, and the internal liquid flow is modeled using Darcy's equation. It is given by the following formula:

[0159]

[0160] Where: v is the flow velocity.

[0161] Pressure drop in a liquid pipeline is expressed as:

[0162]

[0163] Where: p lc p represents the pressure in the liquid chamber of the condensation section. le This indicates the pressure in the liquid chamber of the evaporation section; Indicates the condensation heat flow rate; μ l K is the dynamic viscosity of the liquid; K is the permeability of the sintered core; A w This represents the cross-sectional area of ​​the liquid flow within the sintered core.

[0164] The capillary limit check formula is:

[0165] Δp cap ≥ΔP l +Δp v +Δp grav +ΔP centrifugal

[0166] Where: Δp v Indicates the steam core pressure drop; Δp grav Indicates the pressure drop due to gravity; ΔP centrifugal This indicates centrifugal pressure drop loss; Where σ is the surface tension of the liquid, θ is the contact angle, and r eff The effective capillary radius of the liquid suction core pores.

[0167] 2.1.2 Heat Transfer Simulation Model

[0168] A steady-state heat transfer simulation model for SHP was established using the SIMSCAPE module of the MATLAB / Simulink platform, such as... Figure 3 As shown, a heat pipe consists of four functional parts: an evaporation section, a steam pipe, a condensation section, and a liquid pipe.

[0169] Table 1 details the configuration of the SIMSCAPE model, listing the functions of each module, key parameters, and their sources. The model adopts a modular construction approach, combining physical transparency with ease of experimental data calibration. It also retains key aspects of nonlinear effects that are often oversimplified in traditional lumped parameter models, such as centrifugal force-driven liquid reflux, phase change kinetics, and thermal-fluid coupling.

[0170] Table 1 details the SIMSCAPE modeling process, providing a concise record of the specific parameters used in SIMSCAPE modeling.

[0171]

[0172] The liquid working in the evaporator collects heat and undergoes a phase change during SHP operation, generating steam that enters the steam pipe. The steam is pushed into the condenser by the pressure difference in the steam pipe, where it condenses into liquid and releases latent heat. The condensate is then transported to the liquid pipe. The circulation loop is completed when the liquid returns to the evaporator end under the combined action of capillary force generated by the sintered core and centrifugal force from the rotating pipe. Since the evaporator and condenser operate based on phase change, the condensation process is the reverse of evaporation; therefore, the evaporator is modeled as the core functional module in SHP. To improve simulation accuracy, the evaporator is subdivided into multiple independent modeling segments connected in series, and the simulation results are corrected using a piecewise averaging method. The evaporator structure is as follows: Figure 4 As shown, the system includes components such as a solver block, a two-phase flow boundary condition module, a two-phase fluid pipe, a controlled temperature source, a signal input block, a thermodynamic property sensor, a PS-Simulink converter, and an oscilloscope. The pipe module simulates the two-phase motion of fluid dynamics within a rigid pipe, with port H representing the pipe wall as the location of heat exchange with the surrounding environment. By setting boundary conditions and basic parameters, the working fluid enters the two-phase fluid pipe, absorbs heat and undergoes a phase change during flow, completing the evaporation process.

[0173] When establishing the theoretical model of the evaporator, the following assumptions are used to simplify the calculation: (1) the fluid flow inside the copper tube is considered to be one-dimensional along the axial direction; (2) the airflow outside the copper tube is also assumed to be one-dimensional; (3) the radial temperature of the tube wall is assumed to be constant and the wall thermal resistance is ignored; (4) the gas and liquid phases in the two-phase region are in thermal equilibrium and are uniformly mixed. Based on these assumptions, the energy conservation equation of the pipeline is expressed as:

[0174]

[0175] Where: M is the mass of the fluid in the pipe; and These are the mass flow rates of port A and port B, respectively; u out The precise internal energy after all heat transfer is complete; φ A Energy is transferred into the pipe through port A; φ B Q represents the energy entering the pipe through port B. H The heat entering the pipe through the wall of port H; The average mass flow rate, and according to Calculate; g is the acceleration due to gravity; Δz is the gain parameter value from port A to port B;

[0176] By modeling the heat transfer between the pipe wall and the internal fluid volume as a convection process, the heat transfer rate can be calculated:

[0177] Q H =h coeff S surf (T h -T I )

[0178] Where: h coeff S is the average convective heat transfer coefficient of the pipe; surf T represents the surface area of ​​the pipe. H T represents the pipe wall temperature. I This refers to the temperature of the fluid inside the pipe.

[0179] In this embodiment, the digital twin based on SIMSCAPE is not a nonlinear lumped model, but a component-level dynamic system that forcibly maintains the conservation of mass, momentum, and energy in each subdomain of the rotating sintered core heat pipe. The steam flow is described by a compressible mass-energy balance equation:

[0180]

[0181] Where: m v For steam quality; h is the phase change mass flow rate. v Specific enthalpy of vapor; h fg The latent heat of vaporization; Q in Input heat into the steam chamber; Q cond This represents the heat release power during condensation.

[0182] Darcy's momentum equation for fluid reflux within the core, including terms of centrifugal force and capillary pressure:

[0183]

[0184] Where: μ is the dynamic viscosity of the liquid; u l ρ is the dynamic viscosity of the liquid.l ρ is the liquid density; r is the radial distance from the rotation axis; K is the permeability of the sintered core.

[0185] These equations incorporate nonlinear effects such as vapor compressibility, phase change enthalpy, and rotation-driven liquid reflux, ensuring that the simulation data captures the essential two-phase dynamics. The model's predicted temperature and pressure dynamic responses are consistent with the experimentally observed nonlinear trends, verifying its physical fidelity. SIMSCAPE ensures the conservation of mass, energy, and momentum, accurately reproducing the two-phase flow and heat transfer phenomena inside the SHP.

[0186] To verify the accuracy of the evaporator model, simulation parameters were adjusted to match the actual operating conditions of the sintered heat pipe. An oscilloscope module in Simulink was used to monitor the temperature evolution and phase ratio of the working fluid. The phase ratio plot shows the phase transition process of the working fluid inside the pipe, while the temperature curves present the changes in inlet and outlet temperatures over time during the simulation. These output graphs are key evidence for evaluating the effectiveness and reliability of the model.

[0187] like Figure 5 and Figure 6 As shown, under heat load, the outlet temperature of the pipe gradually increases over time. When t = 220 seconds, the outlet temperature reaches the phase change threshold and evaporation begins. As the liquid phase ratio decreases and the gas-liquid two-phase ratio increases, the working fluid inside the pipe transforms from a liquid to a gaseous state. By t = 300 seconds, continuous vaporization reduces the proportion of liquid and mixed phases, while the gas phase ratio steadily increases. This dynamic behavior is consistent with the actual operation of a heat pipe evaporator, verifying the physical accuracy of the simulation. The model is constructed using an open-loop structure, with the evaporator inlet parameters as initial state variables. The theoretical model is coupled with system components such as the evaporator module through mass, energy, and pressure balance equations. Specifically, the mass conservation equation determines the working fluid flow rate, the energy equation controls the temperature change during heat transfer, and the pressure balance equation describes the pressure distribution and phase change dynamics. By parameterizing the evaporator and its interaction with surrounding modules, a complete closed-loop simulation system is established. This system not only captures the internal thermodynamic processes of the evaporator and condenser but also reflects their coupling relationship with other components, achieving accurate full-system simulation of two-phase flow in a sintered heat pipe.

[0188] Figure 6 Some parameters (such as gas phase mass and interfacial velocity) cannot be directly measured under sintered heat pipe sealing conditions. This embodiment obtains these parameters from the calibrated model by matching the SIMSCAPE model with measurable parameters (including temperature distribution along the heat pipe, total thermal resistance, and pressure drop). Model calibration is based on steady-state and transient measurement data, with errors at all calibration points within ±5%. The predicted gas phase mass is calculated analytically using energy balance. Cross-validation was performed, using measured heat input Q and model-derived gas phase mass flow rate. The interface velocity was verified under comparable operating conditions by high-speed imaging of the flowing tracer in the transparent test section. The deviation between the model prediction and the independent estimate was within 7%, which is within the uncertainty range of the experimental setup.

[0189] To further characterize the dynamic thermofluid behavior inside the sintered heat pipe, a one-dimensional phase fraction evolution model was integrated into the Simulink framework. Figure 7 This demonstrates the transient development of the liquid, gas, and two-phase regions within the evaporator during startup at 100 r / min. Initially, the evaporator is completely filled with liquid (blue curve). As the wall heat flux increases, the proportion of the gas phase steadily rises, and the two-phase region dominates the transition process. The two-phase region exhibits a bell-shaped response, indicating that the boiling front initially expands and then contracts. This behavior is consistent with... Figure 6 The observed wall temperature inflection points are highly consistent. The interaction between centrifugal acceleration and capillary-driven liquid reflux also affects the two-phase region. At steady state (after 300 seconds), the system stabilizes at a state where the gas phase occupies approximately 30% of the evaporator volume, verifying the self-sustaining heat mass transfer mechanism. This model provides a physical basis for interpreting the thermal response curve and lays the foundation for feature selection in AI-driven predictive modeling.

[0190] To further investigate the effect of centrifugal acceleration on the heat transfer performance of sintered core heat pipes, parametric analysis was conducted under a constant heat load of 20W by adjusting the rotation speed from 100 r / min to 600 r / min. The total thermal resistance and corresponding wall temperature rise results are as follows: Figure 8 As shown, the thermal resistance initially decreases with increasing rotational speed, reaching a minimum of 0.30 °C / W at approximately 500 r / min. This trend is attributed to the enhanced liquid reflux driven by centrifugal force, which improves evaporator wetting conditions and suppresses localized drying. However, the thermal resistance increases slightly beyond 500 r / min, possibly due to weakened capillary-assisted redistribution caused by excessive radial separation between the liquid film and the wick structure. The temperature rise ΔT (calculated as ΔT = R × Q) exhibits a similar nonlinear response, decreasing from 8.6 °C at 100 r / min to a minimum of 6.0 °C at 500 r / min. These results confirm the crucial role of rotational effects in optimizing the thermal behavior of sintered core heat pipes under dynamic conditions.

[0191] 2.1.3 Simulation Steps and Results

[0192] The sintered core heat pipe thermofluid model based on SIMSCAPE was solved using a variable step size ode15s (rigid / NDF) solver, with a relative tolerance set to 1×10. -5The maximum step size was 0.1 s. The simulation time was set to 600 s to capture the complete transient response from startup to steady state. All simulations were performed at an initial ambient temperature of 25 °C and a pressure of 1 atm. The rotational speed increased from 100 r / min to 600 r / min in 50 r / min increments, and the heat load was adjusted between 10 W and 40 W. The working fluid filling rate was set to 100% as a baseline condition and reduced to 60% during sensitivity testing. The model's geometry and material parameters were matched to the experimental prototype, including the copper tube wall thickness (1.5 mm), the porosity of the sintered wick (0.62), and the permeability (1.5 × 10⁻⁶). -12 m 2 ).

[0193] The system simulation decomposes the overall operation of the sintered core heat pipe into three consecutive stages: startup, steady-state operation, and shutdown. To ensure the accuracy and consistency of the simulation results, each stage is sequentially connected. The simulation method has been fully described. Before starting the simulation, the constructed heat transfer model needs to be fully initialized, including setting external boundary conditions (such as heat load and ambient temperature) and assigning physical property parameters to each module. For example, the geometry and material properties of the two-phase fluid within the evaporator module are configured according to the actual design specifications. Figure 9 (As shown). These parameter settings ensure that the simulation model accurately reflects the physical behavior of the actual system and provides suitable initial conditions for subsequent stages. The working fluid's thermal properties are defined using the built-in fluid property library of the SIMSCAPE platform, among which density, viscosity, specific heat capacity, and thermal conductivity are key variables. These parameters have a decisive influence on fluid dynamics and heat transfer behavior and need to be accurately assigned to ensure the authenticity and reliability of the simulation results.

[0194] To achieve more flexible control over the simulation process, several variables and parameters in the model are customized and defined using MATLAB scripts. This coding method supports parameterization of modules in a unified manner, facilitating rapid adjustment and efficient execution of simulation tasks. Specifically, MATLAB code is used to define variable names and assign values, adjust module parameters according to specific simulation requirements, and set key physical quantities such as heat load and temperature. The code is not only responsible for initializing and allocating simulation parameters but also for calculating the real-time dynamic states of system components during the simulation. For example, to capture the coupled behavior of fluid flow and heat transfer, the pressure difference between the steam pipe and the condenser is calculated using fluid dynamics equations in the MATLAB environment, and these real-time measurements are input into the simulation model. To improve simulation accuracy and shorten simulation time, a variable step size solver is selected. The calculation accuracy is set to 5 × 10⁻⁶. -5The latency memory budget was set to 1024KB. A variable step size solver was selected, and the memory budget was adjusted to maximize simulation efficiency while maintaining accuracy. This solver dynamically adjusts the step size based on the error in each calculation step, effectively reducing the computational load while maintaining accuracy. For SHP simulations, this type of solver can adapt to temperature fluctuations during startup and steady-state phases, accurately capturing key points in the phase transition process. At the start of the simulation, the code runs synchronously with the calculation, applying a Q-factor to the evaporator. H No steam is generated in the evaporator during this stage. As time progresses, the evaporator outlet temperature gradually increases. When the evaporator phase change node meets the evaporation conditions, steam is generated and rapidly flows into the steam pipe. The code calculates the steam pipe pressure difference and feeds it back to the simulation system. As the simulation continues, the system gradually approaches steady state, obtaining the steady-state temperature difference between the SHP evaporation and condensation sections. The simulation automatically stops when the preset termination time is reached, outputting the temperature curves of each node for subsequent data analysis and processing. All simulation data are saved for later calculations and result verification. The physical properties of the working fluid (ammonia-water mixture) at 25℃ and 1 atmosphere are listed in Table 2. Note: The physical property values ​​are averages within the experimental operating temperature range of 20-35℃.

[0195] Table 2 Physical properties of the working fluid (ammonia-water mixture) at 25°C and 1 atmosphere.

[0196]

[0197] Boundary conditions and inputs are as follows: Hot input Q in 10-40W (programmed step / ramp). Speed: 100-600 r / min. Ambient temperature: 25℃. External h can be selected for parasitic convection. Condenser manifold setting: h. c and T c (Or fixed wall temperature), matched with the test bench. The fill rate benchmark is 100% (pore volume), and 60% and 85-115% are used when sensitivity analysis is required. The total length is 340mm, with the evaporation section, adiabatic section, and condensation section lengths of 120mm, 100mm, and 120mm, respectively. The diameter is 5-8mm. The wall thickness is 0.5mm. The wick thickness is 0.6mm. At the start of the simulation, the MATLAB code and solver execute synchronously, applying a thermal load to the heated wall of the evaporator. Initially, no steam is generated, and the evaporator outlet temperature gradually increases. After reaching the phase change threshold, evaporation starts, and steam rapidly flows into the steam pipe. At this time, the steam zone pressure difference is calculated and updated in real time through the MATLAB code to maintain feedback to the simulation system. As the simulation progresses, the system gradually approaches steady state, and the steady-state temperature difference between the condensation section and the evaporation section is obtained. The simulation ends after the preset termination time is reached, generating the temperature evolution curves of each measurement node as shown below. Figure 10 As shown in the diagram. These outputs provide the foundation for subsequent data analysis and model validation. All simulation results are saved for further processing and validation.

[0198] To evaluate the robustness and thermal reliability of SHP under boundary conditions, a series of numerical simulations were performed under extreme liquid fill rates and rotational speeds. Figure 11 The temperature evolution curves for four scenarios within a 600s range are shown: (1) normal operating condition (100 rpm, 100% fill rate), (2) low fill rate (100 rpm, 60% fill rate), (3) high speed (500 rpm, 100% fill rate) and (4) extreme combined operating condition (500 rpm, 600% fill rate).

[0199] As shown in the figure, the reference case exhibits typical start-up characteristics: a smooth plateau region appears after 200 seconds, indicating stable phase change heat transfer. However, oscillating behavior and delayed stabilization are observed under both low fill rate and high-speed conditions, suggesting unstable fluid reflux and phase distribution. Most notably, under extreme conditions, the evaporator temperature continues to rise without reaching saturation, indicating that insufficient capillary reflux due to excessive centrifugal force prevents the maintenance of two-phase circulation. These results reveal the operating boundary of the SHP under coupled high speed and low fill rate conditions, providing predictive early warning for thermal runaway in practical applications. These simulations enhance the practicality of the proposed Simulink model in design margin assessment and failure risk prediction.

[0200] In SHP (Self-Heating Hydrator), liquid reflux is driven by capillary pressure generated by the porous wick structure. This pressure must overcome the frictional resistance and centrifugal pressure gradient under rotational conditions. To clarify the feasibility and limitations of this reflux mechanism, a simplified one-dimensional model is constructed using Darcy's law and radial centrifugal acceleration:

[0201]

[0202] like Figure 12 As shown, the net driving pressure versus liquid flow rate curves along the wick radius were plotted for two typical rotational speeds (100 r / min and 500 r / min). At 100 r / min, capillary pressure dominates the radial gradient, generating a stable liquid flow back to the evaporator. However, at 500 r / min, the centrifugal pressure increases sharply with the radius, significantly reducing the net pressure. Near the outer edge of the wick, the net pressure approaches zero, and the backflow velocity drops to near stagnation.

[0203] These findings confirm that at excessively high rotational speeds, capillary forces become insufficient to overcome the centrifugal barrier, leading to a decline in heat transfer performance due to evaporator drying out. This analysis provides a quantitative explanation for the subsequently observed failure behavior and reinforces the importance of maintaining a balance between geometric capillary design and rotational operating parameters.

[0204] The axial pressure drop within the vapor chamber of a heat pipe plays a crucial role in determining the vapor flow rate and convective heat transfer capacity. To verify the accuracy of the vapor-side simulation, Poiseuille's equations for compressible laminar circular pipe flow were used to calculate the axial pressure distribution:

[0205]

[0206] Where: μ v Q is the vapor dynamic viscosity. v For volumetric flow rate, r v Let be the radius of the vapor chamber. Under the same boundary conditions, the analytical pressure distribution is compared with the simulated values ​​extracted from the Simulink model.

[0207] like Figure 13 As shown, both curves exhibit a monotonically decreasing pressure trend from the condensation section to the evaporation section, and this relationship is highly consistent throughout the entire steam channel. The simulation shows a slight deviation at the inlet due to inlet effects and nonlinear flow interactions (an effect not covered by the analytical model), but the maximum pressure difference remains within 1.5%, confirming the accuracy of the simulation in capturing the physics of the steam-side flow. This comparative analysis reinforces the physical rationality of the Simulink module and further validates its applicability to quantitative steam flow analysis and design optimization.

[0208] To clarify the main limiting factors in the overall heat transfer process, a thermal resistance decomposition analysis was performed based on theoretical modeling and simulation parameters. The total thermal resistance of the sintered heat pipe was decomposed into four components: the boiling thermal resistance R on the evaporation side. evap The porous wick has a thermal resistance R that conducts. wick Steam transport thermal resistance R vapor and condensation thermal resistance R on the condensation side cond , represented as:

[0209] R total =R evap +R wick +R vapor +R cond

[0210] Figure 14 The data shows that evaporator boiling thermal resistance accounts for the largest proportion of total thermal resistance (37.5%), followed by condenser condensation (30.0%), wick conduction (25.0%), and vapor transport (20.0%). This distribution indicates that the phase change process remains the main bottleneck for improving the performance of sintered heat pipes. In contrast, the vapor chamber contributes less to the total thermal resistance due to its low viscosity and large effective area. This analysis provides important guidance for future design optimization, suggesting that improving the wick structure, surface wettability, or evaporator-enhanced boiling technology can significantly improve overall thermal performance.

[0211] 2.2 Theoretical Modeling of Heat Flux Transfer in Sintered Heat Pipes under Rotation Conditions

[0212] To enhance the physical interpretation of the heat transfer behavior of sintered heat pipes under rotating conditions, this section establishes a heat flux analytical model that couples centrifugal acceleration, capillary absorption, phase change, and porous media transport. The coupled heat flux transport framework of the sintered heat pipe is as follows: Figure 15 As shown.

[0213] The model aims to quantitatively describe the fundamental heat and mass transfer mechanisms, guiding parameter optimization in engineering applications. The basic assumptions are as follows: the working fluid liquid phase is incompressible, and the gas phase is an ideal gas; the porous wick is isotropic and homogeneous, following Darcy's law; liquid-gas equilibrium is assumed at the phase interface; axial heat conduction and radial heat leakage are neglected. The heat transfer model for sintered heat pipes under rotating conditions includes the following contents.

[0214] The heat flow analytical model, used to couple centrifugal acceleration, capillary absorption, phase change, and transport in porous media, is expressed as follows:

[0215]

[0216] Where: ε is the porosity of the sintered core; ρ l The density of the liquid; Darcy speed; S m This is the phase change mass source term, i.e., the evaporation / condensation rate.

[0217] Darcy's law, which includes centrifugal acceleration, is expressed as:

[0218]

[0219] Where: k is the permeability; μ l Dynamic viscosity; is the centrifugal acceleration vector; r is the radial distance from the axis of rotation.

[0220] The capillary pressure model is expressed as:

[0221]

[0222] Where: σ is the surface tension; θ is the contact angle; r eff Δp is the effective pore radius of the sintered matrix. grav For the loss due to gravity pressure drop; ΔP centrifugal This indicates centrifugal pressure drop loss;

[0223] The energy conservation model for the liquid absorption core region is expressed as:

[0224]

[0225] Where: h l Specific enthalpy of liquid; k eff The effective thermal conductivity of the porous wick; For internal heat generation; This is a latent heat source term.

[0226] The gas-phase core pressure-driven flow model, described by the one-dimensional compressible Navier-Stokes equations, is expressed as:

[0227]

[0228]

[0229] Where: P v For steam pressure; μ v The viscosity is the vapor dynamic viscosity; r v For steam pipes; m v ρ is the steam mass flow rate; v A is the density of the vapor; v z represents the cross-sectional area of ​​the steam flow; z represents the axial position.

[0230] The total thermal resistance model is expressed as:

[0231] R total =R evap +R wick +R vapor +R cond

[0232] Where: R evap R is the boiling thermal resistance on the evaporation side. wick For the porous wick, conduction thermal resistance; R vapor For steam transport thermal resistance; R cond The condensation thermal resistance on the condensation side is:

[0233]

[0234] Where: h evap h wick and h cond These are the heat transfer coefficients of the evaporation section, the wick, and the condensation section, respectively; A evap A wick and A cond These are the heat transfer areas of the evaporation section, the wick, and the condensation section, respectively; L v k v and A v These are the steam passage length, steam thermal conductivity, and steam flow cross-sectional area, respectively.

[0235] This analytical framework captures the core coupled physical mechanisms of SHP thermal performance under rotating conditions, including capillary recirculation under centrifugal resistance, porous flow resistance, and gas phase pressure loss. These equations support parameter sensitivity analysis and optimization of geometry and operating conditions, and can serve as a theoretical basis for calibration and constraints of simulation parameters in Simulink-based or data-driven models.

[0236] Figure 7The gas phase coherence and gas-liquid interface velocity shown are internal state variables calculated directly from the mass and energy conservation equations in the SIMSCAPE model, rather than experimental measurements. Specifically:

[0237]

[0238] in: For phase transition mass rate, A i The interfacial area is denoted by . Both are output values ​​from the evaporator and condenser assembly model, governed by the same conservation equations described above, and are not empirical post-processing results. These parameters can physically and consistently describe the internal two-phase evolution process and are used to qualitatively explain the heat transfer mechanism. Experimentally validated observations include wall temperature, pressure drop, and total thermal resistance, with deviations controlled within ±5%. Therefore, internal variables are not presented as independent validation quantities but as calibration model predictions consistent with the validated external response. Although these internal variables cannot be directly measured, their predicted changes are consistent with the observed temperature gradient and exhibit condensation / evaporation asymmetry, supporting their physical plausibility.

[0239] 2.3 Validation of the heat transfer model

[0240] Simulation models are essentially simplified approximations of the key characteristics and behaviors of real systems. During model development, theoretical assumptions, simplifications, and algorithm selection are typically required to reduce computational complexity and improve simulation efficiency. However, these simplifications can also introduce biases and affect the model's predictive accuracy. Experimental validation is crucial to ensuring the effectiveness and reliability of simulation models. By comparing simulation results with experimental data collected from real mechanical systems, experimental validation aims to quantitatively assess the model's predictive accuracy and applicability. This comparison can evaluate the model's performance under different operating conditions. Model validation usually involves a direct comparison of simulation results and experimental data to determine the degree of agreement. If significant differences exist, it indicates that the model's assumptions, parameters, or structural formulas need to be revised. Therefore, iterative validation and adjustment are essential for improving model fidelity and ensuring that it accurately reflects the behavior of real systems.

[0241] In this embodiment, a SHP with the same geometric dimensions as the experiment was prepared to ensure model-experiment consistency. The total length was 340 mm. The evaporation section was 120 mm long, the adiabatic section was 100 mm long, and the condensation section was 120 mm long. The outer diameter was d ∈ {5, 6, 8} mm, and the wall thickness was 0.5 mm. The wick thickness was 0.6 mm (sintered copper). Distilled water was used as the working fluid. First, the porosity of the wick was estimated by mass-volume measurement, and then three liquid filling rates relative to the wick pore volume were set: FR ∈ {85%, 100%, 115%}. The operating variables covered the rotational speed range [100, 300] and the heater input Q ∈ [10, 40] W. When studying eccentric rotation, the eccentricity Led was adjusted.

[0242] To improve reproducibility and clarity, the experimental setup and operating conditions are summarized in Table 3. This table integrates key parameters, including test bench configuration, working fluid specifications, environmental control, measuring equipment, operating range, and uncertainty assessment. The heat load, rotational speed, and fill rate ranges are specifically listed to ensure a clear definition of the model's applicability boundaries.

[0243] Table 3 summarizes the experimental setup and parameters for reproducibility testing. This table lists the key specifications of the sintered core heat pipe, including geometry, material properties, working fluid characteristics, and operating conditions applied during testing. Instrument details, measurement ranges, and data acquisition settings are also provided to ensure accurate experimental reproduction in future studies.

[0244] Table 3 Experimental setup and parameters

[0245]

[0246] 2.3.1 Heat transfer performance experiment

[0247] The rotary drive system used in the experiment consists of three parts: a DC power supply, a servo motor, and a servo driver. The experimental configuration is as follows: Figure 16 As shown. The servo driver receives power from a DC power supply to control the servo motor responsible for driving the rotating platform. The platform speed is adjusted by dedicated control software connected to the control terminal computer. The heating system uses a DC regulated power supply to power the spiral heater, heating the evaporation section of the rotating SHP. Cooling is achieved using an air-cooling system; the condensation section of the SHP is cooled by forced convection cooling with an electric fan to dissipate heat and maintain thermal balance. The data acquisition system consists of K-type thermocouples and a multi-channel data acquisition card, with eight temperature measurement points distributed along the surface of the rotating SHP for real-time thermal monitoring. All data is acquired and recorded using dedicated software. The mechanical structure of the rotating platform includes a coupling, two slip rings, a protective cover, and supporting components. The servo motor is securely fixed to the platform to prevent rotational vibration, and the protective cover ensures that components do not splash out in the event of structural collapse during rotation. The two slip rings are used to route the power and signal lines of the heater and K-type thermocouples, ensuring electrical connection during continuous rotation.

[0248] The experimental procedure is summarized as follows: to implement each test point (d, FR, w, Q, Led).

[0249] (1) Install the SHP inside the protective cover and fix it with a custom-made V-block. Attach K-type thermocouples at designated measurement points on the pipe wall, and arrange spiral heaters around the evaporation section. To reduce heat loss and experimental errors, wrap the evaporation section with insulation material. Set eight temperature measurement points: three points in the condensation section (T0, T1, T2), two points in the isothermal section (T3, T4), and three points in the evaporation section (T5, T6, T7).

[0250] (2) Start the electric fan to provide stable air cooling for the condenser section and start the data acquisition program. To avoid electrical noise interference during motor startup, temporarily close the software after verifying that the K-type thermocouple is working properly. Connect the three-phase power supply to the servo motor and set the target speed through the motor control software. Then restart the data acquisition software to record temperature readings. Turn on the DC regulated power supply to heat the evaporation section and control the heat flux density by adjusting the power. Apply the heater power Q in a step manner and continuously record all channel data until a steady state is reached (judgment criteria are below). Each experiment is repeated three times to calculate the uncertainty.

[0251] (3) The steady-state criterion is that the fluctuation within |dT / dt| < 0.02 K / min at all monitoring points does not exceed 10 min. When the temperature readings of all eight channels stabilize within the specified fluctuation range during data acquisition, the system is considered to have reached thermal equilibrium. This experiment typically requires approximately 600 sampling points to achieve stability, at which point valid data is recorded. To verify dynamic characteristics, a step / ramp sequence is applied to Q, and the rotational speed data corresponding to ≥ 600 s are recorded. Simultaneously, ambient temperature and cabin wind speed are monitored, and a shielding cover is installed on the experimental platform to reduce drift and airflow disturbance. Each test...

[0252] After completion, turn off the DC power supply and allow the system to cool down before proceeding with subsequent experiments. Repeat this procedure as needed to complete the entire experimental series. See the actual experimental setup for details. Figure 17 .

[0253] The influence of key factors on the heat transfer performance of SHP was studied through a series of experiments under different operating conditions. Based on the experimental conditions listed in Table 4, data were collected for various configurations with different pipe diameters, filling ratios, rotational speeds, and heat flux densities.

[0254] Table 4. Experimental Operating Condition Variable Settings. The parameter combinations used in the simulation and physical experiments are detailed, including pipe diameter, working fluid filling rate, eccentricity between the rotation axis and the heat pipe centerline, rotational speed, and applied heating power. These variables were systematically designed to study their individual and combined effects on the heat transfer performance, phase change kinetics, and thermal stability of the sintered core heat pipe under rotating conditions.

[0255] Table 4 Experimental Operating Condition Variable Settings

[0256]

[0257] 2.3.2 Data Processing

[0258] This embodiment carefully considered potential sources of error and measurement uncertainty during the experiment. Experimental errors can stem from various factors, including human error, instrument accuracy, and environmental influences. To minimize their impact, a series of preventative measures were implemented during the experimental preparation and data acquisition phases. For example, to ensure the accuracy of wall temperature measurements, thermocouple contacts were insulated to avoid interference from ambient temperature fluctuations. The impact of calibration uncertainty was considered throughout the data analysis process, and all thermocouples were pre-calibrated and correctly connected to the data acquisition system. Measurement uncertainties in the experiment were categorized into two types: the first type includes uncertainties arising from instrument calibration, manufacturer-provided technical parameters, and tolerances specified in calibration certificates and reference manuals; the second type involves errors introduced by external environmental conditions (such as ambient temperature fluctuations) and manual sensor installation or positioning. By controlling these factors and implementing corresponding measures, the reliability and accuracy of the experimental data were significantly improved. The main sources of uncertainty were identified as Type I uncertainties related to the instrument. Based on the technical data of the measuring equipment used, the corresponding error ranges are summarized in Table 5.

[0259] Table 5. Sources of Instrument Error and Uncertainty. This table lists the measurement accuracy specifications of various sensors in the experimental setup (including thermocouples, pressure sensors, flow meters, and speed sensors). Potential sources of uncertainty (such as sensor calibration tolerances, data acquisition resolution, ambient temperature fluctuations, and signal noise) are identified and quantified as appropriate. These details provide a basis for evaluating the reliability and reproducibility of experimental results, as well as estimating the total uncertainty of derived thermal performance indicators.

[0260] Table 5 Sources of Instrument Error and Uncertainty

[0261]

[0262] This integration provides a formula for the overall error of temperature measurement, taking into account the uncertainties of each component:

[0263]

[0264] Wherein: T ave λ is the time-averaged temperature at each temperature measurement point; ac A ac With ΔH ac These represent the insulation thickness, the area covered, and the thermal conductivity, respectively; T k Temperature measurement error caused by the temperature measurement system; T date Temperature fluctuation error caused by the data acquisition process; W power Q is the input heating power; Q is the nominal heat transferred by the heat pipe; Q ac Δτ is the heat loss of the insulation layer; ΔT is the time step; i This refers to the temperature difference between the two sides of the insulation layer.

[0265] During data acquisition, the temperature signal may fluctuate due to various external interference factors when transmitted through the slip ring. To reduce experimental error and improve data reliability, a sampling strategy of recording one data point every two seconds is adopted. The raw data undergoes subsequent preprocessing to eliminate random errors and ensure measurement accuracy. Specifically, after the SHP wall temperature stabilizes, 300 temperature data points are collected within a predetermined time period for each experimental run, and their arithmetic mean is calculated. The final representative temperature under this operating condition is used to obtain the heat flux density q and convective heat transfer coefficient h of the evaporation section, which are expressed as:

[0266]

[0267] Wherein: T t d represents the temperature being collected; W represents the heating power; d and l represent the heating power. h These are the evaporation section length and the outer diameter of the SHP, respectively; T h The temperature is the average value from T0 to T2, i.e. T c The temperature is the average value from T5 to T7, i.e.

[0268] Eight temperature measurement points were arranged in the condensation section, adiabatic section, and evaporation section of the SHP, such as... Figure 18 As shown. Specifically, three thermocouples (T0, T1, T2) are arranged on the outer surface of the condensation section, two in the insulation section (T3, T4), and three in the evaporation section (T5, T6, T7). High-temperature resistant tape is used for bonding the thermocouples to fix them in place and to reduce the impact on the surface properties of the heat pipe.

[0269] 2.3.3 Results Analysis

[0270] The accuracy of the SHP simulation model needs to be verified by comparing simulation results with experimental data. Key performance indicators such as startup characteristics, steady-state temperature difference, and single-factor variation trends are analyzed in detail. This verification process confirms the prediction accuracy and physical fidelity of the simulation model, and also assesses the reliability of the training data used by the ANN. The consistency between simulation and experimental results provides crucial support for the credibility of the hybrid simulation-prediction framework.

[0271] To validate the established model, 18 experimental conditions were conducted under controlled laboratory conditions. Heating powers of 20, 30, 40, 50, 60, 70, 80, 90, and 100 W were applied, with each condition repeated twice to ensure reproducibility. The ambient temperature was maintained at 25±1℃, and the relative humidity at 45-50%. The system was stabilized for 30 minutes under a given heat load before each test. Surface temperatures at multiple axial positions were recorded during the experiment, with a sampling interval of 1 Hz and a duration of 1800 s. Steady-state data were the average of the last 300 seconds of each run. These conditions cover both partial and fully developed evaporation states, providing comprehensive data support for model validation.

[0272] (1) Steady-state results analysis

[0273] In SHP performance analysis, studying the independent effects of various influencing factors is crucial for understanding its underlying mechanisms and guiding HP design optimization. This study investigated the effects of pipe diameter, filling ratio, eccentricity, and rotational speed on HTP. By changing these parameters to observe changes in its thermal behavior, the accuracy and reliability of the proposed simulation model were verified. Figure 19 The simulated and experimental temperatures of the SHP (Self-Heating and Heating) system were compared. Since the evaporation section initially bears the heat load, its temperature rise is the fastest and reaches the highest temperature among all sections. The temperature in the condensation section also gradually increases over time. At t = 4.4 minutes, the simulation results show that the rate of temperature rise slows down, and the system approaches thermal equilibrium. At t = 4.8 minutes, the experimental data also show that the temperature at the measuring point tends to stabilize, indicating that HP has started. The initial experimental temperature rise is slightly slower than the simulation, and the start-up time is longer, mainly due to the thermal contact resistance of the thermocouples and signal delay during the measurement process. Nevertheless, the simulation and experimental results show a consistent trend throughout the heating process. When the system reaches steady state, the simulated temperature of the evaporation section is 33.56℃, while the average experimental temperature at the same location is 33.78℃. The temperature difference between the simulated and experimental results for both the evaporation and condensation sections remains within ±5%, which is acceptable for thermal simulation of complex two-phase systems. The results indicate that the simulation model has strong predictive ability in capturing the heat transfer dynamics and start-up behavior of SHP.

[0274] Figure 19 and Figure 20 (a) The experimental and simulated temperatures of SHP under different eccentricities were compared. Figure 20(a) and (b) compare the temperatures at different rotational speeds. The simulation results and experimental data show a consistent trend under all operating conditions. The simulated steady-state temperature of the evaporation section is 27.72℃, while the experimental value is 27.87℃. When the rotational speed increases to 200 r / min at the same eccentricity, the simulated temperature of the evaporation section rises to 29.40℃, while the experimental average reaches 29.43℃. Under different combinations of eccentricity and rotational speed, the simulated and experimental temperature curves are in high agreement, with temperature differences in the evaporation section of 0.15℃ and 0.03℃, respectively, corresponding to relative errors of 0.5% and 0.1%. These deviations are within the acceptable range of the two-phase model, verifying the accuracy of HTM. The strong consistency between experimental and simulation data further demonstrates the durability and accuracy of the proposed HTM technology, indicating that this heat transfer simulation model can accurately predict the steady-state two-phase behavior of HP under different operating conditions.

[0275] (2) Single-factor influence trend analysis

[0276] The results of SHP experiments with different diameters show that the diameter significantly affects its performance. Experiments revealed that the steady-state temperature difference of the heat pipe decreases with increasing diameter. This phenomenon indicates that as the diameter increases, the cross-sectional area of ​​the heat pipe increases, allowing heat to be conducted over a larger surface area. The larger cross-sectional area helps improve heat transfer efficiency by reducing the thermal resistance during the SHP heat transfer process. When the SHP diameter increases, the fluid distribution in the phase change zone becomes more uniform, and evaporation and condensation processes can occur over a wider area, effectively reducing local overheating or undercooling, and thus lowering the steady-state temperature difference. The simulation results and experimental data show consistent trends. Figure 21 (a)) and the simulated steady-state temperature difference deviates little from the experimental results. Therefore, this simulation model can accurately predict the effect of diameter on heat transfer performance. Experimental results show that increasing the liquid filling ratio helps to reduce the steady-state temperature difference, and the two have a non-linear relationship ( Figure 21 (b) When the liquid fill ratio is low, the steady-state temperature difference is large and the heat transfer capacity of the SHP is insufficient; a high fill ratio reduces the steady-state temperature difference by injecting more liquid mass and improving the heat exchange efficiency of the evaporation / condensation section. The simulation model can accurately simulate this trend with the error controlled within a reasonable range.

[0277] Eccentricity refers to the offset between the central axis of the SHP and the center of the liquid distribution within the cross-section. This parameter significantly affects the internal flow characteristics and heat transfer performance. Both experimental and simulation results show that increasing the eccentricity exacerbates the internal flow inhomogeneity of the SHP. This inhomogeneity increases the thermal resistance of the evaporation and condensation sections, thereby increasing the steady-state temperature difference. Furthermore, a larger eccentricity causes uneven distribution of internal heat flux and hinders liquid phase recirculation, further increasing the temperature difference of the SHP. Figure 22(a) The experimental and simulated data show a consistent trend in the influence of eccentricity, with the deviation between the two sets of data remaining within ±3%, confirming that the simulation model can accurately capture the influence of eccentricity on SHP performance. Rotational speed is also crucial to the thermal behavior of SHP, especially under high-speed conditions. Experiments show that the steady-state temperature difference increases with increasing rotational speed because the increased centrifugal force hinders liquid reflux and reduces the overall heat transfer capacity of the system. Figure 22 (b) The simulation results show a high degree of agreement with experimental observations, revealing the deteriorating effect of increased rotational speed on heat transfer performance. The prediction error remains within ±5%, further verifying the model's ability to capture the influence of rotational speed.

[0278] 3. Heat transfer performance prediction model

[0279] The choice of an architecture based on artificial neural networks, rather than relying solely on computational fluid dynamics or empirical correlations, is based on three main factors: (1) Inference speed – the trained model predicts up to 10 times faster than high-fidelity computational fluid dynamics simulations. 4 (2) Adaptability – The model can be incrementally retrained in the cloud based on new running data without having to rerun expensive simulations; (3) Generalization capability – The hybrid training set covers a wide range of operating conditions and can make accurate predictions for unseen conditions (including high-speed operating conditions where experimental data is scarce). These characteristics meet the core requirements of the proposed edge cloud deployment for low latency and broad applicability.

[0280] To ensure the robustness and generalization ability of the artificial neural network model, the experimental and simulation data should cover as many operating conditions as possible. To improve the generalization ability of the proposed neural network-based rotating heat pipe performance prediction model, a hybrid approach was adopted to construct the training dataset: First, a fully parameterized SIMSCAPE model validated by multiple sets of experimental data was used to systematically generate synthetic thermal response data over a wide operating range. This allows for the generation of thermal response data within an extended operating envelope, including rotational speeds of 100-600 r / min, eccentricity of 0-29 mm, diameter of 1-20 mm, filling rate of 60-115%, and heat load of 10 W-50 W (see Table 6). Simulation data was introduced at key boundary conditions (such as high rotational speeds >300 r / min and low filling rates) to ensure that the model remains based on the true physical response even at points of high simulation uncertainty. The experimental data covered rotational speeds of 100-300 r / min, eccentricity of 0-45 mm, diameter of 5-8 mm, heat load of 10-30 W, and filling rate of 85-115%.

[0281] To construct the artificial neural network model, the training dataset contained 1250 samples (including 300 sets of experimental data and 950 sets of SIMSCAPE simulation data). A random function was used to select 750 samples as the training set to train the neural network, and the remaining 500 samples were used as the test and validation dataset to evaluate the network's applicability. The network input parameters included measured rotational speed w, heating power Q, liquid filling rate FR, evaporator steam mass x, time t, axial position z, and core pressure drop ΔP. wick axial pressure P in the steam passage vapor and transient wall temperature at the selected sensor location The output parameter is the peak temperature of the evaporator wall.

[0282] Table 6. Construction of Training Dataset

[0283]

[0284] The established PINN, Transformer, and LightGBM models possess self-learning and adaptive capabilities. Once deployed, the edge cloud framework can utilize newly acquired operational data (including rotational speed w, heat input Q, fill rate FR, SHP diameter d, evaporator dryness x, time t, axial position z, and core pressure drop ΔP). wick axial pressure P in the steam passage vapor and transient wall temperature at the selected sensor location This enables incremental retraining of the model, thereby improving its ability to extrapolate to unseen operating conditions. This further mitigates accuracy degradation caused by time or changes in operating conditions. The deployment framework triggers incremental training when the error drift is >15%: edge devices cache running data (>50 samples), and the cloud initiates PINN fine-tuning via Docker push (<5 minutes of updates).

[0285] By integrating physically validated synthetic datasets with targeted experiments, embedding physical constraints into the learning process, and validating under unseen high-speed conditions, our proposed method effectively addresses the inherent generalization challenge of neural network modeling of heat transfer performance in rotating steam turbines (SHPs). These strategies collectively ensure strong generalization capabilities, especially under high-speed conditions with traditional correlated failures. PINN's physical constraints reduce error propagation by 32% in the extrapolation region compared to purely data-driven methods.

[0286] 3.1 Model Structure and Input Features

[0287] To complement the aforementioned dynamic simulation framework, this embodiment develops a physical information data-enhanced AI modeling suite for predicting the thermal behavior of SHP under varying rotational speeds and thermal loads. For comprehensive comparison, three representative methods are deployed: LightGBM, a Transformer-based time regression network, and PINN. To enhance physical interpretability and predictive stability, input features are carefully selected based on thermofluid mechanisms. Key features include rotational speed w, heat input Q, fill rate FR, time t, axial position z, evaporator vapor mass x, and core pressure drop ΔP. wick axial pressure P in the steam passage vapor and transient wall temperature

[0288] These features map to the output variable—the peak temperature of the evaporator wall. The physical relationship of the artificial intelligence prediction model is expressed as:

[0289]

[0290] (1) LightGBM baseline: fast and interpretable, using tree ensemble and SHAP-based eigenvalue decomposition.

[0291] (2) Transformer Regression Model: Based on a temporal attention architecture, this model models the spatiotemporal evolution of wall temperature. It captures the interaction between temperature sequences and operational features through multi-head attention and maintains temporal relationships through positional encoding. The input features of Transformer and LightGBM are not purely empirical parameters, but include rotational speed w, heat input Q, fill rate FR, SHP diameter d, evaporator dryness x, time t, axial position z, and core pressure drop ΔP. wick axial pressure P in the steam passage vapor and transient wall temperature at selected sensor location Parameters with clear physical meaning are used to improve extrapolation capabilities.

[0292] (3) PINN: During the development of the PINN framework, the applicability of the energy balance equation and the capillary pressure drop equation as physical constraints was evaluated. The energy balance equation is correlated with the measured heat input Q and the steam mass flow rate. With latent heat h / g This provides a global consistency check. However, when the loss function is directly embedded, the equation becomes numerically rigid due to its magnitude being much larger than the data fitting loss, resulting in slow and unstable convergence. Therefore, it is used as a data pre-filtering step to verify parameter consistency and remove outliers before training.

[0293] Unlike purely physics-based modeling, artificial neural networks further learn cross-coupled nonlinearities and hidden dependencies (such as the relationship between rotational acceleration and capillary supply), which are not explicitly expressed in the analytical structure of the SIMSCAPE solver. In contrast, the capillary pressure drop equation... As a residual term, it is explicitly embedded in the PINN loss function because it directly enhances the momentum balance at the gas-liquid interface and is on a similar numerical order of magnitude to other loss components. This selective embedding strategy balances model stability and physical fidelity.

[0294] In this embodiment, PINN (Physical Information Neural Network) integrates a one-dimensional transient heat conduction equation:

[0295]

[0296] Where: c p ρ represents specific heat capacity; k represents density; k represents thermal conductivity. is the temperature gradient; Q(x,t) is the heat source term; T is the temperature field.

[0297] PINN employs a composite loss function for training. Although the above equation represents a one-dimensional transient heat conduction (energy balance) equation, it was initially considered for inclusion in the PINN loss function, but was ultimately used for data consistency checks during the preprocessing stage rather than directly as a loss term. We learn a parameterized surrogate model for a rotating SHP, with inputs including axial position, time, and operating parameters s = [Q, w, FR, d] (heat load Q in W, rotational speed w in r / rpm, filling rate FR in %, and diameter d in mm). The network outputs three fields: temperature... Axial liquid velocity inside the suction core and steam pressure

[0298] (1) Physical Information Neural Network

[0299] The loss function of the physical information neural network is:

[0300] Γ=Γ data +Γ residual (λ1Γ energy +λ2Γ momentum )

[0301] Where: λ1 and λ2 represent weighting coefficients; Γ data Indicates data residuals; Γ energy and Γ momentum Γ represents the partial differential equation residuals calculated at the collocation point for the energy equation and the momentum equation, respectively; residual This represents the weighting coefficient of the physical residual term.

[0302] Γ dataForced consistency with measurement / simulation data, Γ energy Penalize violations of the one-dimensional energy balance equations used (including transient convection-diffusion equations with latent heat sources), Γ momentum Penalize behaviors that violate the laminar flow / Darcy momentum balance of the wick under rotating conditions.

[0303] In this statement, the total loss Γ includes the data fidelity item Γ. data and physical residual term Γ residual The values ​​are normalized using their respective standard deviations to ensure numerical comparability. The normalized coefficient Γ... residual Setting it to 1.0 ensures that both contribute equally to the optimization. This explicit approach follows standard practices based on PINN modeling, clarifying the balance between data-driven fitting and physical constraint regularization.

[0304] The capillary pressure drop equation is enforced as a hard constraint through a special output layer design. The complete transient energy balance is excluded due to training instability caused by the conduction-convection-phase transition coupling effect, and physical consistency is maintained through a dataset validated by SIMSCAPE.

[0305]

[0306] Where: N y The number of marked temperature points collected at thermocouple / virtual probe locations from experimental and validation SIMSCAPE runs; Predict temperature for the network; T i This is the measured temperature;

[0307] The physical loss is the mean square residual, expressed as:

[0308]

[0309] Where: N c For unlabeled placement points (z) selected by Latin hypercube sampling within the range z∈[0,L],t∈[0,600]s,d∈[1,20]mm,Q∈[10,50]W,w∈[100,600]r / min},FR∈[30,115]%,... j ,t j ,s j The quantity of ); ε(x,t) represents the residual of the energy equation; M(x,t) represents the residual of the momentum equation; Indicates the predicted temperature; The predicted axial liquid velocity in the wick is represented by α; the effective thermal diffusivity is represented by ρ; and the density is represented by c. p Indicates specific heat capacity; h fg Indicates latent heat; A represents the cross-sectional area of ​​the flow. This represents the phase change mass flow rate; The predicted vapor pressure is represented by μ; the dynamic viscosity is represented by r; the radial distance of the liquid path is represented by K; the permeability of the sintered core is represented by Ω; and the angular velocity is represented by Ω.

[0310] All inputs and outputs are used before training. and and and as well as Dimensionless transformation is performed, where Δp is the estimated capillary limit. α, ρ, c p , K, μ, h fg A and r use the same values / tables as in the SIMSCAPE model and experiments.

[0311] During training, violations of physics-based residual terms (such as energy and momentum balance) are penalized and evaluated at placement points in the spatiotemporal domain. The residual loss is normalized by its batch standard deviation to ensure its scale is comparable to the data fitting loss. The parameter Γ in Equation (39) residual The scalar weights control the relative influence of this residual term. In all experiments, Γ residual The value is fixed at 1 to maintain equal emphasis on meeting physical constraints and fitting the observed data. To avoid manually adjusting λ1 and λ2, each residual is expressed through its running standard deviation σ. energy and σ momentum We perform batch normalization: We minimize the residuals:

[0312]

[0313] where λ1=1.0, λ2=1.0 and κ=1×10 -8 κ is a stabilization constant. This makes the loss weight dimensionless and stable under different operating conditions.

[0314] Employing a fully connected multilayer perceptron with 6 hidden layers (64 neurons per layer), sigmoid linear unit activation function, Glorot uniform initialization, and two linear heads: one for... Another joint head is used for In this embodiment, the symbol x represents the gas phase mass calculated according to the SIMSCAPE model, defined as the gas phase mass fraction in the working fluid (x = 0 for saturated liquid, x = 1 for saturated vapor). All variables are normalized to zero mean and unit variance before training and used as inputs to PINN. The input vector is [x * ,z * ,t * Q * ,w * ,FR * ,Led * (All standardized to zero mean / unit variance). Normalized variable x* This refers to the standardized form (zero mean, unit variance) of the gas phase mass x in SIMSCAPE modeling. * The normalized variable refers to the axial position zt * The standardized form of Q is normalized time. * This is the normalized heat input. * For normalized rotational speed. FR * Normalized fill rate. Led * To normalize LED. (Using Γ) data Injection Boundary / Initial Conditions (using the synthetic label from Section 2): Robin-type evaporator / condenser conditions using measured Q and coolant inlet. The initial temperature for all z is T(z,0) = T0. The no-slip condition for the liquid velocity at the wick at the solid boundary is... Where L is the total length of the SHP. Each training round contains N. y =8,192 temperature tags (mixed experimental and verification simulations) and N c = 16,384 placement points. Using the Adam optimizer (β1 = 0.9, β2 = 0.999), learning rate 1 × 10⁻⁶. -3 After 150 rounds of cosine annealing to 1×10 -5 Mini-batch size 1024 (half-labeled data, half-placement points). Gradient pruning threshold 1.0, early stopping patience value 2 epochs (based on validation Γ). Mixed precision training enabled. Final checkpoint selected is the model with the lowest validation Γ.

[0315] The training dataset consists of two complementary parts: (1) physically consistent data generated based on the SIMSCAPE model under different heat loads, rotational speeds, and charge rates; and (2) experimental measurement data used to calibrate model parameters and correct boundary conditions. The SIMSCAPE model can safely explore extreme or transient conditions that are difficult to reproduce experimentally, while the experimental data is used to correct system biases. Therefore, the ANN learns both the nonlinear mappings in the physical model and captures the residual differences between simulation and experiment. This hybrid training strategy ensures that the network can capture coupled nonlinear relationships and maintain generalization ability beyond the explicitly simulated conditions. Furthermore, the trained model can serve as a real-time digital twin agent, providing accurate predictions with sub-second latency for edge deployments—something that the full SIMSCAPE solver cannot achieve.

[0316] 3.2 Data Augmentation and Training Strategies

[0317] Each model was trained under 750 simulated operating conditions (heat load 10-50W, speed 100-600 rpm, filling rate 60-115%). Gaussian noise was added to simulate sensor uncertainty. The training set, validation set, and test set were divided into 750 / 250 / 250 sets. The optimization strategies are as follows: (1) LightGBM uses early stopping and the mean absolute error objective function; (2) For Transformer, the adaptive moment estimation (Adam) optimizer and learning rate scheduler are used, and the mean absolute error (MAE) is used as the objective function; (3) For Physical Information Neural Network (PINN), a composite loss function (data loss + partial differential equation residual) is used, and the model is trained by gradient descent.

[0318] Using mean absolute error (MAE) and R-squared (R 2 The value is used as a performance metric. The training objective is to minimize:

[0319]

[0320] in: Indicates the measured temperature; This represents the simulation results.

[0321] Model quality is evaluated using the following metrics:

[0322]

[0323] in: This represents the average value of the simulation results.

[0324] The trained LightGBM model achieved an MAE of 0.82℃ and an R-value of 0.974 on the test set. 2 The Transformer model achieved a MAE of 0.76℃ and an R-value of 0.98. 2 The PINN model yielded a MAE of 0.95 °C and an R-value of 0.96. 2 Values. All models achieve robust predictions. Transformer excels at capturing complex nonlinear relationships. PINN maintains a physical consistency trend and performs exceptionally well in generalization scenarios with limited data. Generalization tests on unseen operating conditions (higher speeds, novel thermal loads) demonstrate that Transformer is the most stable. SHAP analysis (LightGBM) and gradient attribution (Transformer) are employed to enhance interpretability.

[0325] 3.3 Physical Interpretability

[0326] (1) Lightweight gradient lift machine

[0327] To improve interpretability, SHAP analysis was performed on LightGBM. SHAP decomposes the model predictions into additive contributions from each feature, expressed as:

[0328]

[0329] Where: φ j The SHAP value of feature j is represented by |S|; F represents the set of all features; s represents the subset of features excluding feature j; |S| represents the number of features in subset S; |F| represents the total number of features in set F; f S∪{j} This indicates that when only features x in subset S are used... S∪{j} Model output as input; f S∪{j} (x S∪{j} ) represents the model output when feature j is added to subset S; The SHAP weights take into account the permutation of the subset S into which feature j is inserted, ensuring a fair average across all feature orders.

[0330] φ here j The contribution of features is represented, revealing their impact on prediction. Analysis shows that steam quality and charge rate are dominant features, consistent with thermophysical understanding. Gradient-based significance (Transformer) exhibits attention peaks in regions of thermal abrupt change, especially in rapid heating events. For PINN, visualization of the partial differential equation residuals validates that the model follows physical laws even in unmeasured regions. This modeling framework provides a data-driven and physics-guided temperature prediction toolkit for SHP systems. Transformer models demonstrate high-accuracy prediction potential, while PINN ensures strong physical consistency, making it particularly suitable for scenarios with high generalization requirements. The learning objective is to learn through data... Approximation function f:X→T peak , where X i The input vector is denoted as . To capture nonlinear relationships and improve accuracy, benchmark tests are performed on the three models.

[0331] LightGBM is a gradient boosting decision tree ensemble model optimized for small to medium-sized structured data. This decision tree-based ensemble model employs a histogram learning strategy and leaf growth, making it particularly adept at handling tabular data. It supports feature importance ranking by SHAP values ​​and offers high interpretability. Its decision function is defined as:

[0332]

[0333] Wherein: T k For k th Regression tree.

[0334] (2) Transformer Regression Network

[0335] The Transformer regression network is a sequence-based model that employs a multi-head attention mechanism to extract interactions between hot features. This model uses positional encoding and multi-head self-attention to model dependencies between different feature modalities; its core mechanism is scaled dot-product attention.

[0336]

[0337] Where: Q, K, and V represent the query, key, and value matrices, respectively; d k This represents the dimension of the key vector.

[0338] (3) Physical Information Neural Network (PINN)

[0339] PINN directly embeds the governing equations (such as energy balance and capillary pressure drop) into the loss function:

[0340]

[0341] The second and third terms correspond to the thermal conduction and mass conservation residuals, respectively. This method is used to enhance physical consistency, especially under unseen or extrapolated conditions.

[0342] The regressive Transformer maps each scalar input feature to a 32-dimensional embedding vector and uses sinusoidal positional encoding to preserve feature order. The encoder consists of three layers, each with four multi-head attention mechanisms, a hidden dimension of 128, a feedforward network dimension of 256, and a ReLU activation function. Both the attention and feedforward sub-layers use a dropout rate of 0.1. The output head is mapped to two linearly activated outputs after global average pooling followed by a fully connected layer. The model uses the Adam optimizer (η = 5 × 10⁻⁶). -4 The training mode features weight decay, a batch size of 64, a maximum of 500 epochs, and early stopping at 30 epochs. It is implemented using PyTorch 2.0.1 and HuggingFaceTransformers 4.31.0.

[0343] LightGBM serves as a lightweight, non-deep learning baseline for edge deployment, with the regression objective optimized using the L2 loss function. The model is configured with 31 leaf nodes, no maximum depth limit, a learning rate of 0.05, and a maximum of 500 iterations (stopping early if no improvement is seen after 50 iterations). The feature sampling rate and data sampling rate are set to 0.8, with sampling performed every 5 iterations. The LightGBM regressor is configured for R... eff ΔT training was used to reduce output coupling bias. Training was performed on the CPU using LightGBM 3.3.5, utilizing all available cores in parallel.

[0344] Each model was divided into training, validation, and test sets with values ​​of 750 / 250 / 250, and optimized using Adam (neural network) and LightGBM (decision tree boosting) respectively. Figure 23 (a) Showing a comparison between the predicted and simulated values ​​of each model, with the Transformer model achieving the best R-value. 2 The score was 0.982, followed by LightGBM (0.974) and PINN (0.965). Figure 23 (b) shows the histogram of absolute prediction errors. All models exhibit low error concentration, with the Transformer network showing the narrowest distribution. To test generalization ability, extrapolated datasets (such as high-speed or thermal load datasets) were evaluated; the results are shown below. Figure 23 (c) Compared to Simulink output, the AI ​​model achieves accurate real-time predictions and reduces computation time by more than 90%. Figure 23 (d) Demonstrating a comparison between AI and physics-based prediction under typical operating conditions: While PINN has the advantage of physics-prior encoding, its modeling is complex; Transformer strikes a balance between accuracy and flexibility; and LightGBM maintains lightweight computation. This framework provides a data-driven and physics-guided temperature prediction toolkit for SHP systems. Transformer has the potential for high-fidelity prediction, and PINN ensures strong physical consistency in generalized key scenarios. LightGBM exhibits the best real-time performance with low latency and small model size, making it suitable for edge deployment, but its adaptability to complex transient conditions is limited; Transformer strikes a balance between speed and accuracy, performs excellently in steady-state scenarios, and has scalable inference; PINN has the highest accuracy under strong thermal inertia conditions, but has the highest computational cost and deployment latency. These trade-offs provide important guidance for model selection under different application constraints.

[0345] A summary comparison of the three AI models is shown in Table 7. LightGBM offers high interpretability and low computational cost, making it suitable for deployment in real-time systems. Transformer networks provide the best accuracy and generalization performance, especially under complex feature interactions, but require more training resources. PINN, while having lower accuracy, naturally satisfies physical constraints and is favored when following control equations. In summary, the AI-based regression framework provides a high-fidelity, low-latency complement to detailed simulations, supporting system optimization and control deployment.

[0346] The developed AI model achieved prediction accuracy exceeding experimental measurement uncertainty (temperature ±0.2℃, power ±2%). This indicates that the model not only reproduced the measurement response but also filtered out sensor noise and effectively reconstructed the underlying system state. This capability is crucial for applications requiring sub-measurement level accuracy (such as thermal error compensation for high-precision machine tools). To eliminate high-precision false positives caused by overfitting, multiple strategies were adopted: (1) hierarchical cross-validation across operating conditions; (2) early stopping when there is no validation set improvement for 100 consecutive rounds; (3) L2 regularization of all model parameters; the dropout rate of ANN and Transformer layers ranged from 0.1 to 0.2; and the physical information loss term was constrained to the physical reasonable solution. These measures ensured that the model maintained physically consistent predictions while having robust generalization ability for unseen operating conditions.

[0347] Table 7 provides a quantitative comparison of the LightGBM, Transformer, and PINN models based on key performance and deployment metrics. These metrics include mean absolute error (MAE), inference latency, model size, generalization ability, and feasibility for deployment on edge devices. LightGBM exhibits extremely low latency and a compact structure, making it suitable for real-time edge scenarios with moderate accuracy requirements. Transformer balances accuracy and speed. PINN offers superior physical consistency and performance under transient conditions, but at a higher computational cost. These results can guide model selection in thermal error prediction systems based on specific application constraints.

[0348] Table 7. Quantitative Comparison of Key Performance and Deployment Metrics of LightGBM, Transformer, and PINN Models

[0349]

[0350] 3.4 Model Validation

[0351] To further confirm the practical applicability of the AI ​​model, experimental data from a rotating SHP prototype device were used for comparative verification. Direct measurement of vapor dryness and interfacial velocity in a rotating SHP is not feasible due to optical access limitations and potential measurement interference. Instead, these parameters were estimated using the coupled mass-energy balance in the SIMSCAPE model and benchmarked against empirical correlations for similar heat pipe systems—observed deviations were within ±7%

[41] . Furthermore, consistent estimates were obtained from back-calculation of experimental wall temperature distribution, total heat transfer, and condensation rate, all falling within the combined uncertainty range of modeling and experiment. All sensing devices were pre-calibrated and propagation error analysis was performed to provide uncertainty bands for inferring vapor dryness and interfacial velocity, enhancing the credibility of the reported results. The test bench included a controllable heating section, a variable-speed rotating platform, and a multi-point thermocouple array. Key parameters such as evaporator temperature, wall heat flux, and internal vapor pressure were recorded. The prototype heat pipe had an outer diameter of 12 mm, with evaporation and condensation section lengths of 80 mm and 60 mm, respectively, and was filled with deionized water at a filling rate of 0.65. The rotational speed changes from 0 to 1500 r / min, and the input power changes from 10 W to 40 W. Figure 24 (a) shows a comparison of the prediction accuracy of the Transformer and PINN models with the measured evaporator temperature. Both models effectively track thermal trends, with PINN showing a better fit during the transient rise phase due to its physics-based constraints. Figure 24 (b) Present the MAE and RMSE values ​​of each model based on the experimental validation dataset.

[0352] The transient prediction differences among the three AI models (PINN, Transformer, and LightGBM) are negligible. Figure 24 This is primarily because the system's thermal response is dominated by a single, slow mode with a time constant of hundreds of seconds, corresponding to the large heat capacity of the heat pipe components. All models successfully captured this first-order behavior after learning on a training dataset covering all operating conditions. Furthermore, the transient temperature data has a high signal-to-noise ratio, and the smooth evolution of the thermal field reduces the chance of model-specific differences becoming apparent. Therefore, the model prediction discrepancies remain small in this scenario. In more complex scenarios involving rapid transients, nonlinear coupling, or multi-timescale interactions, model dependency differences are expected to be more pronounced.

[0353] The generalization performance of three prediction models (PINN, Transformer, and LightGBM) was evaluated using cross-condition test cases not included in the training set. Specifically, robustness outside the baseline range was assessed using unseen high-speed scenarios at 350, 450, and 500 rpm. Results show that all models maintained a root mean square error below 1.2°C in these cases, with PINN achieving the best stability by embedding physical constraints. These findings demonstrate that hybrid dataset design, physically guided feature selection, and targeted experimental calibration can accurately extrapolate to conditions not covered by the training data, addressing common limitations of purely data-driven models.

[0354] In addition to qualitative analysis, this paper also quantitatively compares the computational efficiency of the proposed artificial neural network method with that of conventional CFD simulation. Taking a typical operating condition of a rotating SHP with a rotation speed of 300 r / min and a heating power of 100 W as an example, a single high-fidelity CFD simulation on a 32-core workstation takes approximately 14.6 hours to resolve the multiphase flow and heat transfer field. Figure 25 In contrast, a trained ANN can predict the corresponding temperature field in just 0.15 seconds on an embedded Jetson Xavier device. Even considering that a one-time ANN training using a hybrid simulation-experiment dataset would take approximately 5.2 hours, the cost amortized to each prediction is negligible in repetitive prediction scenarios. This computational advantage is crucial for real-time edge-cloud deployments, where predictions must be generated within 100-200 milliseconds to support active thermal control.

[0355] 4. Digital Twin System

[0356] This embodiment is used to implement the system for predicting the heat transfer performance of sintered core heat pipe based on the edge cloud artificial intelligence architecture as described above, including: (1) a high-fidelity digital twin modeling and simulation module, used to perform modeling and simulation of the high-fidelity digital twin model of the rotating sintered core heat pipe in the Simulink-SIMSCAPE environment; (2) an experimental data acquisition module, including a K-type thermocouple array, a controllable heater, a variable speed rotation platform and a data acquisition card arranged on the surface of the rotating sintered core heat pipe, used to acquire experimental thermal response data; (3) a hybrid data processing module, used to receive and fuse simulation data from the digital twin modeling unit and experimental data from the experimental data acquisition module to construct a hybrid dataset; (4) (5) An artificial intelligence training platform, used to train, verify and compare the physical information neural network, Transformer regression network and lightweight gradient booster model based on the hybrid dataset; (6) An edge-cloud collaborative deployment and inference subsystem, including: an edge inference module, deployed on edge hardware, with an embedded quantized accelerated artificial intelligence prediction model, used to receive sensor data streams in real time and output thermal performance predictions; a cloud platform management module, deployed on a server, providing model version management, long-term data storage, visualization dashboard and model retraining pipeline; and a communication middleware, based on the MQTT protocol to realize asynchronous and reliable data exchange and command transmission between the edge inference module and the cloud platform management module.

[0357] 4.1 Application Deployment Architecture

[0358] Although this embodiment focuses on SHP thermal prediction rather than control, actual SHP devices need to operate under dynamic long-term conditions. The combination of digital twins and cloud-edge deployment provides a flexible and scalable framework for continuous evaluation and analysis of heat transfer performance under field conditions. The proposed system adopts a three-layer architecture, including data acquisition (sensor / device layer), edge inference, and cloud management. Thermal and motion data are acquired in real time through the NicDAQ module and transmitted to the edge device (NVIDIA Jetson Xavier NX) via the MQTT protocol to run the compressed prediction model. The cloud layer deployed on the local server is responsible for visualization, logging, and remote model updates.

[0359] Figure 26This paper demonstrates the application of an edge-cloud deployment framework integrating AI prediction models in a digital twin-based SHP thermal management system. Embedded hardware sensor data streams are transmitted to edge nodes (such as industrial gateways) for real-time inference using compressed models (LightGBM, Transformer, or PINN). Long-term optimization, anomaly detection, and retraining pipelines are deployed on cloud servers. The core modules include: (1) a sensor layer responsible for collecting wall temperature, heat input, pressure, and rotational speed data; (2) an edge device layer embedding a lightweight runtime engine, equipped with quantized versions of LightGBM, Transformer, or PINN models; and (3) a cloud layer containing digital twin replicas, offline retraining pipelines, data archiving, and control optimization logic. The user interface is a web-based dashboard that displays comparisons between predicted and actual data, health diagnoses, and fault warnings. In this architecture, the digital twin acts as a synchronous proxy model, driven by simulation dynamics (based on Simulink) and AI-enhanced prediction. Edge devices run lightweight prediction models (such as LightGBM or TransformerLite) to support real-time thermal monitoring, while the cloud server manages historical data analysis, periodic retraining, and model optimization. Unlike control-oriented digital twin frameworks, this system focuses on performance characterization and degradation tracking, ensuring reliable thermal modeling in long-term deployments, especially suitable for industrial scenarios where high-precision thermal components such as SHPs are subjected to time-varying workloads. The deployment architecture design guarantees real-time response (latency <200ms) and reduces cloud communication frequency. On-device LightGBM inference supports anomaly pre-screening, and the cloud server performs weekly retraining based on cumulative thermal drift. In a real-world example of a spindle motor cooling system, TransformerLite is deployed on an NVIDIA Jetson NX edge device, achieving a measured latency of less than 150ms at a 20Hz sampling rate. All edge components communicate with the cloud via a publish-subscribe MQTT protocol, coordinated by a central agent on the cloud server. Latency measurements cover end-to-end inference time from sensor data acquisition and model processing to execution signal generation. These deployment and runtime configurations are crucial for interpreting the inference latency, model size, and energy efficiency metrics reported in Section 4.2.

[0360] 4.2 System Verification

[0361] The edge-deployed ANN surrogate model reproduced the nonlinear transient behavior of two-phase flow with a computation time two orders of magnitude shorter than the full SIMSCAPE solver, validating its advantages in real-time digital twin applications. The combination of physics-based digital twins and data-driven intelligence enables physically interpretable real-time modeling, bridging the gap between detailed thermofluid simulation and edge control applications. To evaluate the model's performance under transient conditions, three test scenarios were designed: (1) a step increase in heat input (10W to 30W), (2) a ramp-up in rotational speed (500-1500 r / min), and (3) a combined fluctuation of both. Figure 27 As shown in the horizontal comparison, PINN maintains the lowest prediction error (0.85℃, 0.90℃, and 0.88℃) across all scenarios, indicating its superior robustness in capturing physically driven thermal responses. Transformer follows closely, especially in steady-state or mildly dynamic conditions, with errors ranging from 0.89℃ to 0.95℃. LightGBM, however, has the highest error (1.20-1.35℃), reflecting its insufficient generalization of time-related features due to a lack of temporal modeling capabilities. Vertical analysis shows that PINN is most effective at handling high thermal inertia (step input), while Transformer performs better in smooth transient processes (speed ramps and complex fluctuations). These results highlight PINN's advantages in strongly physically coupled scenarios and Transformer's stable accuracy under moderate dynamic conditions. LightGBM's bias mainly stems from its weaker generalization ability to temporal correlations.

[0362] Figure 27 A comparison of prediction errors for LightGBM, Transformer, and PINN models in three transient test scenarios: (i) a step increase in thermal input, (ii) a ramp-up in rotational speed, and (iii) complex fluctuations. Mean absolute error (MAE) was used as the evaluation metric. PINN showed the lowest error in scenario (i), thanks to its embedded physical constraints which enhanced its robustness to sudden thermal changes. Transformer performed best in scenario (ii) by effectively capturing gradual system dynamics through its temporal attention mechanism. LightGBM consistently showed high errors, especially under complex coupled fluctuations, indicating that its generalization ability is limited by training conditions. These results highlight the importance of model architecture selection in dynamic thermal environments.

[0363] To comprehensively evaluate the performance and real-time capabilities of the proposed prediction framework, all models were deployed and benchmarked in a hybrid cloud-edge environment simulating typical industrial settings. Edge deployment was carried out on an NVIDIA Jetson Xavier NX platform, equipped with a 6-core ARM Cortex-A57 CPU, a 384-core Volta GPU (including 48 Tensor Cores), and 8GB of LPDDR4x memory to simulate resource-constrained real-time edge inference scenarios. Cloud computing was performed by a high-performance server configured with an Intel Xeon Silver 4314 CPU, 128GB of memory, and an NVIDIA RTX 3080 GPU (10GB GDDR6X VRAM), supporting model training, long-term storage, and digital twin synchronization.

[0364] Sensor data acquisition is achieved through the NICDAQ-9178 data acquisition hardware interface with LabVIEW 2021, supporting multi-channel analog inputs (such as thermocouples, thermal flux sensors, and encoder signals) with a maximum sampling rate of 10kHz. The system uses Python 3.10 in conjunction with PyTorch 2.0 and LightGBM 3.3.5 to execute the model. To optimize deployment, the Transformer model is converted to the Open Neural Network Exchange (ONNX) format and quantized using TensorRT 8.5 for edge-side inference, significantly reducing latency. LightGBM is deployed as a serialized binary model and called via the liblightgbm C++ API, while PINN is containerized using Docker and executed through a PyTorch runtime that supports graphics processing units (GPUs).

[0365] The total system latency is:

[0366] T total =T acq +T proc +T comm +T sync

[0367] Wherein: T acq For sensor data acquisition delay; T proc The inference time depends on the model complexity; T comm For network communication delay; T sync This represents an asynchronous queue or synchronous delay (such as an MQTT buffer). This equation forms the basis for comparing system architectures under different hardware and communication constraints.

[0368] To correlate the model structure and inference efficiency, the processing time can be approximated as:

[0369] T proc ∝v·FLOPs+λ

[0370] Where: FLOPs is the number of floating-point operations required for the model; v is the hardware-related scaling factor; λ represents the fixed initialization or loading overhead.

[0371] For example, the Transformer model has a self-attention layer that varies with O(N). 2 Scaling is required, and PINN often involves iterative numerical solvers with embedded differential operators, leading to higher computational costs. To quantify model efficiency under resource constraints, a real-time inference exponent is introduced:

[0372]

[0373] Where M m This refers to the model's memory size (in MB). Higher R... s The value indicates better real-time response capability per unit of resources.

[0374] System stability under sudden inputs or high sampling frequencies can be characterized by processing margin.

[0375] ΔT system =T cycle -T total

[0376] Wherein: T cycle To control the loop sampling period, the system must maintain a real-time response and meet the following requirements:

[0377] ΔT system ≥δ

[0378] Where: δ is the minimum margin required for safety feedback control (e.g., 50ms). If ΔT system A value less than 0 may indicate accumulated delays or prediction backlogs, leading to a decrease in control performance.

[0379] The real-time response factor is:

[0380] The throughput under burst input is:

[0381] In addition to prediction accuracy, this embodiment also evaluated deployment-related metrics, including inference latency, model size, and steady-state mean absolute error (MSE). Figure 28LightGBM achieves the lowest inference latency (80ms) and the smallest model footprint (9MB), making it suitable for resource-constrained environments. However, this comes at the cost of accuracy. PINN, while the most accurate, exhibits the highest computational overhead. Transformer offers a balanced trade-off, with moderate latency (150ms), a compact model size (36MB), and acceptable accuracy, making it the most efficient candidate for deployment in edge-cloud architectures. In addition to average prediction accuracy, the temporal stability of each model under acyclic hot loads was analyzed. PINN exhibits minimal oscillations and excellent convergence behavior, reflected in its smooth loss reduction and bounded physical residuals, while Transformer occasionally shows convergence fluctuations under irregular inputs. Deployment efficiency was further evaluated by measuring end-to-end response latency across different architectures. The LightGBM model deployed at the edge demonstrates the lowest memory footprint (below 10MB) and inference latency below 100ms, but with a compromise in accuracy. In contrast, the distilled TransformerLite model effectively balances accuracy and latency, making it suitable for real-time control integration. To further analyze the computational requirements of each model, the number of floating-point operations (FLOPs) was estimated as a surrogate indicator of model complexity. For example... Figure 28 As shown, PINN has the highest computational burden due to its embedded differential solver and multi-pass residual evaluation, requiring 2.2 billion FLOPs per inference estimation. In contrast, while the Transformer model is more complex than traditional machine learning methods, it requires only 750 million FLOPs due to its efficient attention mechanism and parallelizable matrix operations. LightGBM exhibits the lowest complexity, requiring only 180 million FLOPs because it relies on structured decision trees without deep networks. This comparison illustrates that PINN's superior accuracy comes at the cost of significantly higher inference latency, while the Transformer offers a balanced trade-off between complexity and speed. LightGBM remains the most computationally efficient, making it a suitable candidate for real-time edge deployment scenarios with limited hardware resources.

[0382] The relationship between model complexity and inference time is as follows: Figure 29 As shown, the relationship between inference latency and estimated FLOPs for the three models is plotted. A linear fit of the form y = 0.06795x + 81.99 was obtained, indicating that inference time increases proportionally with computational complexity. Among the evaluated models: LightGBM has approximately 1.8 × 10⁻⁶ FLOPs. 8 This achieves a minimum inference latency of approximately 94 milliseconds, with FLOPs per second. The Transformer has approximately 7.5 × 10⁻⁶ FLOPs. 8It exhibits a moderate latency of approximately 130 milliseconds, achieving 2.2 × 10⁻⁶ FLOPs. PINN, as the most complex model, has a latency of 2.2 × 10⁻⁶ FLOPs. 9 These FLOPs resulted in a peak latency exceeding 500 milliseconds. This linear trend validates the rationale for using FLOPs as a metric for real-time feasibility prediction. It also highlights the trade-off between model expressiveness and deployment latency, where PINN sacrifices accuracy for speed, while LightGBM prioritizes responsiveness to reduce complexity. The Transformer offers a compromise, achieving reasonable latency within edge device constraints.

[0383] This framework supports active control of sintered heat pipe devices under complex thermal loads and is suitable for fault-tolerant operation in industrial or aerospace applications. In summary, the AI-based regression framework provides a high-fidelity, low-latency complement to detailed simulations, supporting system optimization and control deployment. Experimental results and a practical deployment framework further validate the feasibility and innovation of the proposed method in real-world thermal system applications. This hybrid modeling method combines physically constrained SIMSCAPE simulation with data-driven learning, bridging the gap between high-fidelity modeling and real-time applicability. Experimental verification confirms external accuracy, while the model-inferred internal variables provide insights into the nonlinear heat transfer behavior inside rotating heat pipes.

[0384] V. Conclusion

[0385] First, a high-fidelity digital twin model was built in Simulink to simulate heat transfer in a sintered core heat pipe, integrating real rotating thermal loads and contact conduction effects to provide a foundation for reliable data generation and verification under steady-state and transient conditions. Second, three prediction models—Physical Information Neural Network (PINN), Transformer, and Lightweight Gradient Booster—were trained and evaluated. The PINN demonstrated the highest accuracy in strong thermal inertia scenarios (mean absolute error = 0.85℃), while the Transformer achieved the best balance between accuracy and efficiency under steady-state conditions (root mean square error = 0.58℃). Finally, the proposed edge-cloud AI framework was deployed for real-time thermal modeling. Accelerated by the Turing Tensor R engine, it achieved a 150ms response latency and a compact 36MB model size, demonstrating its feasibility for embedded applications in intelligent precision motion systems.

[0386] Beyond its contribution to thermal prediction methods, the proposed edge-cloud AI framework for sintered heat pipes embodies a scalable energy-aware paradigm aligned with industrial-grade energy optimization goals. Continuous real-time thermal prediction can significantly reduce parasitic energy consumption in high-density electronic and aerospace systems. By directly integrating AI into the thermal control loop, this research supports a broader vision for energy-aware thermal system design. The framework demonstrates direct application potential in precision manufacturing systems requiring real-time thermal error awareness. Multi-condition experimental validation shows that the modeling accuracy is sufficient for integration into the feedback control loop, enabling active thermal compensation without additional sensors.

[0387] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture, characterized in that: Includes the following steps: Step 1: Constructing a digital twin model: Constructing a physics-based high-fidelity digital twin model of the rotating sintered core heat pipe, dividing the rotating sintered core heat pipe into four functional modules: evaporator, steam pipe, condenser, and liquid pipe, with a sintered core inside the liquid pipe; based on the mass, momentum, and energy conservation equations, simulating the two-phase flow and heat transfer process involving phase change, while introducing a centrifugal acceleration vector to characterize the rotation effect; Step 2: Generate and merge datasets: Run the high-fidelity digital twin model of the rotating sintered core heat pipe, perform dynamic simulation within the predetermined extended operating condition parameter range, and generate a simulation dataset; Experiments were conducted on rotating sintered core heat pipes within a subset of the extended operating condition parameter range to obtain an experimental dataset; the simulation dataset and the experimental dataset were then merged to form a hybrid dataset for model training. Step 3: Train the AI ​​prediction model: Train at least one AI prediction model using the hybrid dataset, wherein the candidate AI model is selected from the Physical Information Neural Network, the Transformer Regression Network, and the Lightweight Gradient Boosting Machine; Step 4: Edge-Cloud Architecture Deployment and Inference: The trained AI prediction model is deployed in an edge-cloud collaborative architecture. The quantized and optimized lightweight model is deployed on an edge computing device to receive real-time data from the rotating sintered core heat pipe sensor and execute the AI ​​prediction model for forward inference, outputting thermal performance prediction results with sub-second latency. The cloud platform is used to receive edge data, store historical records, and perform visualization management, and incrementally retrain the AI ​​prediction model when trigger conditions are met.

2. The method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture according to claim 1, characterized in that: In step one, the modeling principle of the high-fidelity digital twin model of the rotating sintered core heat pipe includes: The continuity equations for the evaporator, steam pipes, condenser, and liquid pipes are expressed as follows: in: and These are, respectively, the mass flow rate of steam in the steam pipe, the mass generation rate of steam generated in the evaporator due to boiling and entering the steam chamber, the mass flow rate of steam condensing into liquid in the condenser, the mass flow rate of liquid flowing into the evaporator liquid chamber from the liquid return channel or sintered wick, the mass flow rate of liquid vaporized from the liquid phase to the vapor phase in the evaporator liquid chamber, and the mass flow rate of liquid flowing from the condenser liquid chamber into the liquid return section; M le and M lc These represent the mass of the working fluid in the evaporator liquid chamber and the mass of the working fluid in the condenser liquid chamber, respectively; V ve and V vc These refer to the volume of the evaporator steam chamber and the volume of the condenser steam chamber or steam pipes, respectively; p ve and p vc These are the average steam pressure in the evaporator steam chamber and the average steam pressure in the condenser steam chamber or steam pipe, respectively; T ve and T vc These represent the steam temperature in the evaporator steam chamber and the steam temperature in the condenser steam chamber or steam pipe, respectively; R is the complete gas constant of the steam; t is time; γ is the multidirectional index. The pressure drop in steam pipelines and liquid pipelines are expressed as follows: Where: ρ v r is the gas mass density. v h is the radius of the steam pipe. lv Latent heat of vaporization / condensation; μ v Vapor dynamic viscosity; l eff For effective heat transfer length; p lc p represents the pressure in the liquid chamber of the condensation section. le This indicates the pressure in the liquid chamber of the evaporation section; Indicates the condensation heat flow rate; μ l ρ is the dynamic viscosity of the liquid. l Indicates liquid density; K is the permeability of the sintered core; A w This refers to the cross-sectional area of ​​the liquid flow within the sintered core. The capillary limit constraint equation is expressed as: Δp cap ≥ΔP l +Δp v +Δp grav +ΔP centrifugal Where: Δp v Indicates the steam core pressure drop loss; Δp grav Indicates the pressure drop due to gravity; ΔP centrifugal This indicates centrifugal pressure drop loss.

3. The method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture according to claim 1, characterized in that: In step two, the heat transfer simulation model of the high-fidelity digital twin model of the rotating sintered core heat pipe includes: The energy conservation equation for a pipeline is expressed as: Where: M is the mass of the fluid in the pipe; and These are the mass flow rates of port A and port B, respectively; u out The precise internal energy after all heat transfer is complete; φ A Energy is transferred into the pipe through port A; φ B Q represents the energy entering the pipe through port B. H The heat entering the pipe through the wall of port H; The average mass flow rate, and according to Calculate; g is the acceleration due to gravity; Δz is the gain parameter value from port A to port B; Steam flow is described by the compressible mass-energy balance equation: Where: m v For steam quality; h is the phase change mass flow rate. v Specific enthalpy of vapor; h fg The latent heat of vaporization; Q in Input heat into the steam chamber; Q cond This refers to the heat release power during condensation. Darcy-type momentum equation for liquid reflux within the sintered core, including terms of centrifugal force and capillary pressure: Where: μ is the dynamic viscosity of the liquid; u l ρ is the dynamic viscosity of the liquid. l ρ is the liquid density; r is the radial distance from the rotation axis; K is the permeability of the sintered core.

4. The method for predicting the heat transfer performance of sintered core heat pipes based on edge cloud artificial intelligence architecture according to claim 1, characterized in that: In step two, the high-fidelity digital twin model of the rotating sintered core heat pipe includes the heat flow transport model of the sintered heat pipe under rotational conditions: The heat flow analytical model, used to couple centrifugal acceleration, capillary absorption, phase change, and transport in porous media, is expressed as follows: Where: ε is the porosity of the sintered core; ρ l The density of the liquid; Darcy speed; S m This is the phase change mass source term, i.e., the evaporation / condensation rate; Darcy's law, which includes centrifugal acceleration, is expressed as: Where: k is the permeability; μ l Dynamic viscosity; is the centrifugal acceleration vector; r is the radial distance from the axis of rotation; The capillary pressure model is expressed as: Where: σ is the surface tension; θ is the contact angle; r eff Δp is the effective pore radius of the sintered matrix. grav For the loss due to gravity pressure drop; ΔP centrifugal This indicates centrifugal pressure drop loss; The energy conservation model for the liquid absorption core region is expressed as: Where: h l Specific enthalpy of liquid; k eff The effective thermal conductivity of the porous wick; For internal heat generation; For latent heat source terms; The gas-phase core pressure-driven flow model, described by the one-dimensional compressible Navier-Stokes equations, is expressed as: Where: P v For steam pressure; μ v The viscosity is the vapor dynamic viscosity; r v For steam pipes; ρ is the steam mass flow rate; v A is the density of the vapor; v z represents the cross-sectional area of ​​the steam flow; z represents the axial position. The total thermal resistance model is expressed as: R total =R evap +R wick +R vapor +R cond Where: R evap R is the boiling thermal resistance on the evaporation side. wick For the porous wick, conduction thermal resistance; R vapor For steam transport thermal resistance; R cond This represents the condensation thermal resistance on the condensation side.

5. The method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture according to claim 1, characterized in that: In step three, the physical relationship of the artificial intelligence prediction model is represented as follows: Wherein: T peak ΔP is the peak temperature of the evaporator wall; w is the rotational speed; Q is the heat input; FR is the liquid filling rate; t is the time; z is the axial position; x is the evaporator steam mass; ΔP wick For core voltage drop; P vapor This refers to the axial pressure in the steam passage. This refers to the transient wall temperature.

6. The method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture according to claim 1, characterized in that: The physical information neural network integrates a one-dimensional transient heat conduction equation: Where: c p ρ represents specific heat capacity; k represents density; k represents thermal conductivity. The temperature gradient is represented by Q(x,t); the heat source term is represented by Q(x,t); and the temperature field is represented by T. The loss function of the physical information neural network is: C=C data +C residual (λ1Γ energy +λ2Γ momentum ) Where: λ1 and λ2 represent weighting coefficients; Γ data Indicates data residuals; Γ energy and Γ momentum Γ represents the partial differential equation residuals calculated at the collocation point for the energy equation and the momentum equation, respectively; residual This represents the weighting coefficients of the physics-based residual terms; and: Where: N y To mark the number of temperature points; Predict temperature for the network; T i This is the measured temperature; The physical loss is the mean square residual, expressed as: Where: N c The number of unlabeled placement points; ε(x,t) represents the energy equation residual; M(x,t) represents the momentum equation residual; Indicates the predicted temperature; The predicted axial liquid velocity in the wick is represented by α; the effective thermal diffusivity is represented by ρ; and the density is represented by c. p Indicates specific heat capacity; h fg Indicates latent heat; A represents the cross-sectional area of ​​the flow. This represents the phase change mass flow rate; The predicted vapor pressure is represented by μ; the dynamic viscosity is represented by r; the radial distance of the liquid path is represented by K; the permeability of the sintered core is represented by Ω; and the angular velocity is represented by Ω.

7. The method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture according to claim 1, characterized in that: The Transformer regression network employs a multi-head self-attention mechanism, the core of which is scaled dot product attention, expressed as: Where: Q, K, and V represent the query, key, and value matrices, respectively; d k This represents the dimension of the key vector.

8. The method for predicting the heat transfer performance of sintered core heat pipes based on edge cloud artificial intelligence architecture according to claim 1, characterized in that: The lightweight gradient booster uses SHAP analysis to perform feature importance analysis and calculates the SHAP value φ of feature j. j : Where: φ j The SHAP value of feature j is represented by F; F represents the set of all features; S represents the subset of features excluding feature j; |S| represents the number of features in subset S; |F| represents the total number of features in set F; f S∪{j} This indicates that when only features x in subset S are used... S∪{j} Model output as input; f S∪{j} (x S∪{j} ) represents the model output when feature j is added to subset S; The SHAP weights take into account the permutation of the subset S into which feature j is inserted, ensuring a fair average across all feature orders.

9. A system for implementing the method for predicting the heat transfer performance of sintered core heat pipes based on an edge cloud artificial intelligence architecture as described in any one of claims 1-8, characterized in that: include: The high-fidelity digital twin modeling and simulation module is used to perform modeling and simulation of the high-fidelity digital twin model of the rotating sintered core heat pipe in the Simulink-SIMSCAPE environment. The experimental data acquisition module includes a K-type thermocouple array arranged on the surface of the rotating sintered core heat pipe, a controllable heater, a variable speed rotation platform, and a data acquisition card, which are used to acquire experimental thermal response data. A hybrid data processing module is used to receive and fuse simulation data from the digital twin modeling unit and experimental data from the experimental data acquisition module to construct a hybrid dataset. An artificial intelligence training platform is used to train, validate, and compare the physical information neural network, Transformer regression network, and lightweight gradient boosting machine model based on the hybrid dataset. The edge-cloud collaborative deployment and inference subsystem includes: The edge inference module, deployed on edge hardware, embeds a quantized and accelerated artificial intelligence prediction model to receive sensor data streams in real time and output thermal performance predictions. The cloud platform management module, deployed on the server, provides model version management, long-term data storage, a visual dashboard, and a model retraining pipeline. The communication middleware, based on the MQTT protocol, enables asynchronous and reliable data exchange and command transmission between the edge inference module and the cloud platform management module.

10. The sintered core heat pipe heat transfer performance prediction system based on edge cloud artificial intelligence architecture according to claim 9, characterized in that: End-to-end total delay T total Represented as: T total =T acq +T proc +T comm +T sync Wherein: T acq For sensor data acquisition delay; T proc The inference time depends on the model complexity; T comm For network communication delay; T sync This indicates an asynchronous queue or a synchronous delay.

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