Cooling Management Method and System for High-Temperature Superconducting Cables Based on Heat Transfer Mechanism Model

Abstract

This invention discloses a cooling management method and system for high-temperature superconducting cables based on a heat transfer mechanism model, relating to the field of cooling management technology. The method includes the following steps: dividing the high-temperature superconducting cable pipeline into spatial structures and constructing a first structural feature set based on the division results; converting the first structural feature set into a first time series according to the liquid nitrogen flow direction, and aligning the first time series with a preset benchmark sequence using the DTW algorithm; extracting the centrifugal force offset change gradient of liquid nitrogen after passing through several pipe bends based on the alignment results, and constructing a centrifugal force offset gradient curve; extracting features from the centrifugal force offset gradient curve, and dynamically adjusting the heat transfer parameters in the preset heat transfer mechanism model based on the feature extraction results to obtain a corrected heat transfer mechanism model; predicting the cable temperature based on the corrected heat transfer mechanism model, and performing cooling management based on the prediction results, thus solving the problem of uneven local heat load caused by flow offset in bends.

Description

Technical Field

[0001] This invention relates to the field of refrigeration management technology, and more specifically, to a method and system for refrigeration management of high-temperature superconducting cables that incorporates a heat transfer mechanism model. Background Technology

[0002] High-temperature superconducting cables generate heat when transmitting large currents. If this heat cannot be dissipated effectively and promptly, the temperature of the superconducting material will rise, affecting its critical current and stability, and even causing quench failure. To ensure the long-term safe and stable operation of the cable, scientific cooling management is necessary. By combining heat transfer mechanism models and establishing mathematical models of heat transfer processes such as conduction, convection, and thermal radiation within the cable and its surrounding environment, the temperature distribution and heat flow characteristics of the cable under different operating conditions can be accurately described. This provides a theoretical basis and decision support for the design, optimization, and operation strategies of the cooling system.

[0003] However, during the cooling process of high-temperature superconducting cables, liquid nitrogen usually flows uniformly in laminar or turbulent flow in straight pipe sections. But when liquid nitrogen flows through curved pipe sections, the centrifugal force generated by the bend causes the liquid nitrogen to shift outwards, thus forming a low-speed or even almost static fluid zone inside the pipe. This local stagnant zone leads to insufficient contact between liquid nitrogen and the cable conductor, resulting in reduced local heat exchange efficiency, increased temperature, and increased prediction errors of conventional heat transfer models, while also increasing the difficulty of cooling management.

[0004] To address the above problems, this invention proposes a solution. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a high-temperature superconducting cable cooling management method and system that incorporates a heat transfer mechanism model. By studying the changes in liquid nitrogen flow and the centrifugal force shift when passing through a curved pipe section, flow anomalies are identified and the heat transfer model is dynamically corrected to solve the problem of uneven local heat load caused by flow shift in the curved section.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A cooling management method for high-temperature superconducting cables based on a heat transfer mechanism model includes the following steps: The high-temperature superconducting cable duct is spatially divided, and a first structural feature set is constructed based on the division results; the first structural feature set is converted into a first time series according to the liquid nitrogen flow direction, and the DTW algorithm is used to align the first time series with a preset reference series; based on the alignment results, the centrifugal force offset change gradient of liquid nitrogen after passing through several pipe bends is extracted, and a centrifugal force offset gradient curve is constructed; features are extracted from the centrifugal force offset gradient curve, and the heat transfer parameters in the preset heat transfer mechanism model are dynamically adjusted based on the feature extraction results to obtain a modified heat transfer mechanism model; the cable temperature is predicted based on the modified heat transfer mechanism model, and cooling management is performed based on the prediction results.

[0008] In a preferred embodiment, the step of spatially dividing the high-temperature superconducting cable pipeline and constructing a first structural feature set based on the division results specifically involves: dividing the high-temperature superconducting cable pipeline into several pipeline segments, including curved pipeline segments and straight pipeline segments; extracting the spatial coordinate sequence of each pipeline segment and calculating the rate of curvature change and directional angle offset of each pipeline segment to obtain a spatial feature set for each pipeline; encoding the flow direction of several pipeline segments according to the liquid nitrogen flow direction to obtain a flow feature set for each pipeline; and fusing the spatial feature set and flow feature set of each pipeline to obtain the first structural feature set.

[0009] In a preferred embodiment, the step of converting the first structural feature set into a first time series according to the liquid nitrogen flow direction, and aligning the first time series with a preset reference sequence using the DTW algorithm, specifically involves: obtaining the actual pipeline layout and performing topological sorting of the first structural feature set according to the actual pipeline layout to obtain a first structural feature map; arranging the feature points in the structural feature map according to a preset time order based on the liquid nitrogen flow direction to obtain a first time series; calculating the minimum path distance between the first time series and the preset reference sequence using the DTW algorithm; performing nonlinear alignment between the first time series and the preset reference sequence based on the minimum path distance to obtain an aligned sequence; and constructing a liquid nitrogen flow feature change trajectory based on the aligned sequence.

[0010] In a preferred embodiment, the step of constructing the liquid nitrogen flow characteristic change trajectory based on the aligned sequence specifically involves: extracting the timestamp sequence and structural feature data of liquid nitrogen flowing through each pipe segment based on the aligned sequence; mapping the structural feature data to the spatial coordinates of the pipe segment based on the timestamp sequence to obtain the first liquid nitrogen flow spatial trajectory; and optimizing and correcting the first liquid nitrogen flow spatial trajectory based on preset flow continuity constraints and fluid dynamics smoothness conditions to obtain the liquid nitrogen flow characteristic change trajectory.

[0011] In a preferred embodiment, the step of extracting the centrifugal force offset change gradient of liquid nitrogen after passing through several pipe bends based on the alignment results and constructing a centrifugal force offset gradient curve specifically involves: identifying the flow velocity and pressure changes of liquid nitrogen as it flows through each pipe bend based on the flow velocity and pressure change values; calculating the centrifugal force on liquid nitrogen at each bend based on the flow velocity and pressure changes, and calculating the centrifugal force offset of liquid nitrogen at each bend relative to the pipe centerline; accumulating the centrifugal force offset according to the flow sequence, and calculating the centrifugal force offset gradient at preset different flow times; and constructing a centrifugal force offset gradient curve with flow time as the horizontal axis and centrifugal force offset gradient as the vertical axis.

[0012] In a preferred embodiment, the step of extracting features from the centrifugal force offset gradient curve and dynamically adjusting the heat transfer parameters in the preset heat transfer mechanism model based on the feature extraction results to obtain the corrected heat transfer mechanism model specifically involves: extracting the curve change trend features from the centrifugal force offset gradient curve and identifying flow anomalies in the liquid nitrogen flow based on the curve change trend features; dynamically adjusting the convective heat transfer coefficient and heat conduction parameters of the corresponding segments in the heat transfer model based on the flow anomaly results; verifying the model based on historical data; iteratively optimizing until the prediction error converges to obtain the corrected heat transfer mechanism model.

[0013] In a preferred embodiment, the step of identifying flow anomalies in liquid nitrogen flow based on curve trend characteristics specifically involves: constructing a graph model with each curved pipe segment as a node, the connection relationship of the curved pipe segments as edges, and the integral mean of the centrifugal force offset gradient curve as the edge weight; traversing the graph model using a shortest path algorithm to obtain a first flow path; comparing the first flow path with a preset sequence of actual liquid nitrogen flow pipe segments, and identifying flow anomalies based on the comparison results.

[0014] In a preferred embodiment, the step of dynamically adjusting the convective heat transfer coefficient and heat conduction parameters of the corresponding segment in the heat transfer model based on the flow anomaly results specifically involves: locating the abnormal pipe segment based on the flow anomaly results and extracting the first gradient sequence of the abnormal pipe segment; using an adaptive threshold segmentation algorithm to divide the first gradient sequence into multiple levels to obtain several gradient change intervals; evaluating the gradient changes of the several gradient change intervals and generating parameter adjustment amounts based on the evaluation results; and dynamically adjusting the convective heat transfer coefficient and heat conduction parameters of the corresponding segment in the heat transfer model based on the parameter adjustment amounts.

[0015] In a preferred embodiment, the process of predicting cable temperature based on the modified heat transfer mechanism model and managing refrigeration based on the prediction results specifically involves: inputting real-time collected data on liquid nitrogen flow rate, temperature, and pressure within the pipe into the modified heat transfer mechanism model; calculating the temperature distribution of each pipe segment of the cable using the modified heat transfer mechanism model; and generating refrigeration adjustment commands based on the temperature distribution to dynamically adjust the liquid nitrogen flow rate and cooling power.

[0016] The technical effects and advantages of the high-temperature superconducting cable cooling management method and system based on the heat transfer mechanism model of this invention are as follows:

[0017] This invention divides the high-temperature superconducting cable duct into spatial structures, extracts the three-dimensional spatial features and liquid nitrogen flow characteristics of each duct segment, and generates a time sequence of these features according to the liquid nitrogen flow direction. This sequence is then aligned with a preset benchmark sequence using the DTW algorithm to construct the liquid nitrogen flow characteristic change trajectory and centrifugal force offset gradient curve. The changing trends are extracted from the curves to identify flow anomalies, and the heat transfer parameters of the heat transfer mechanism model are dynamically corrected based on the identification results, achieving accurate temperature prediction for each cable segment. Finally, the system generates cooling adjustment commands based on the predicted temperature, dynamically optimizing the liquid nitrogen flow rate and cooling power to ensure uniform and stable cable temperature, significantly improving cooling efficiency and heat transfer control accuracy. Simultaneously, it can promptly address local flow offset or stagnation problems caused by duct bends, solving the problem of inaccurate temperature prediction and cooling optimization using traditional methods, thereby achieving safe, reliable, and efficient operation of the high-temperature superconducting cable. Attached Figure Description

[0018] Figure 1 This is a schematic flowchart of the high-temperature superconducting cable cooling management method based on the heat transfer mechanism model of the present invention.

[0019] Figure 2 This is a schematic diagram of the high-temperature superconducting cable refrigeration management system based on the heat transfer mechanism model of this invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0021] Example 1, Figure 1 This invention presents a high-temperature superconducting cable cooling management method based on a heat transfer mechanism model, comprising the following steps:

[0022] S1, divide the high-temperature superconducting cable duct into spatial structures, and construct the first structural feature set based on the division results;

[0023] In this example, the high-temperature superconducting cable duct is spatially divided, and a first structural feature set is constructed based on the division results, specifically:

[0024] The high-temperature superconducting cable pipeline is divided into several pipeline sections, which include pipeline bend sections and pipeline straight sections;

[0025] Extract the spatial coordinate sequence of each pipe segment, and calculate the rate of curvature change and orientation angle offset of each pipe segment to obtain the spatial feature set of each pipe.

[0026] Based on the direction of liquid nitrogen flow, the flow direction of several pipe sections is encoded to obtain the flow feature set of each pipe;

[0027] The spatial feature set and flow feature set of each pipe are fused to obtain the first structural feature set.

[0028] It should be noted that in the design or actual layout of high-temperature superconducting cables, the entire pipeline is first continuously segmented according to its geometry. Curved sections are identified as curved segments, while straight sections with negligible curvature are classified as straight segments. This segmentation can be based on a bending radius threshold or the rate of change of angle. When the curvature exceeds a set threshold or the directional angle changes significantly, the segment is considered a curved segment; otherwise, it is classified as a straight segment. Through this segmentation method, the entire cable pipeline can be precisely decomposed into a series of segments with clearly defined geometric characteristics.

[0029] Furthermore, within each divided pipe segment, a series of continuous spatial coordinate points are generated using the three-dimensional coordinate data of the pipe centerline (e.g., obtained from the design model or sensor data), forming a spatial coordinate sequence for that pipe segment. Then, the local tangent direction change is calculated using adjacent coordinate points, and the rate of curvature change—the rate of increase or decrease of curvature per unit length—is further determined to describe the severity of pipe bending. Simultaneously, the directional angle offset is calculated based on the tangent direction change; this is the angular change of the pipe segment from its initial direction in three-dimensional space. Combining the rate of curvature change, directional angle offset, and corresponding spatial coordinate sequence for each pipe segment forms a complete spatial feature set for that segment, providing the necessary geometric information for liquid nitrogen flow trajectory analysis and thermodynamic modeling.

[0030] Furthermore, based on the actual flow direction of liquid nitrogen in the high-temperature superconducting cable, a unique flow direction code is assigned to each pipe segment along the flow path, starting from the liquid nitrogen inlet. The code can be sequentially numbered or vectorized, clearly defining the flow sequence of liquid nitrogen in each pipe segment. For complex pipe networks, the flow path can be mapped onto the pipe segment topology to ensure that the code for each pipe segment accurately reflects the actual flow direction of the liquid nitrogen. Through this flow direction coding, each pipe segment not only possesses geometric spatial information but also includes the sequence and directional characteristics of the liquid nitrogen flow, thus obtaining a flow feature set for each pipe, providing flow dynamics information for subsequent sequence alignment and heat transfer analysis.

[0031] Finally, the fusion process integrates the geometric spatial information (rate of curvature change, azimuth offset, and coordinate sequence) of each pipe segment with the corresponding flow characteristic information (flow direction encoding, flow sequence, etc.) in a one-to-one correspondence. Specifically, flow characteristics are attached as additional attributes to each point or pipe segment in the spatial feature sequence, forming a joint feature vector. In this way, each pipe segment not only describes its own spatial morphology but also contains information about the liquid nitrogen flow state, forming a complete structural and flow fusion feature set, i.e., the first structural feature set. This fused feature set can be directly used to construct time series, perform DTW alignment, and for subsequent liquid nitrogen flow and heat conduction modeling and analysis.

[0032] S2, the first structural feature set is converted into a first time series sequence according to the liquid nitrogen flow direction, and the DTW algorithm is used to align the first time series sequence with the preset reference sequence;

[0033] In this example, the first structural feature set is converted into a first time series according to the liquid nitrogen flow direction, and the DTW algorithm is used to align the first time series with a preset reference sequence, specifically:

[0034] Obtain the actual layout of the pipeline and sort the first structural feature set according to the actual layout of the pipeline to obtain the first structural feature map;

[0035] Based on the direction of liquid nitrogen flow, the feature points in the structural feature map are arranged in a preset time sequence to obtain the first time sequence;

[0036] The minimum path distance between the first time series sequence and the preset reference sequence is calculated using the DTW algorithm.

[0037] The first time series sequence is nonlinearly aligned with a preset reference sequence based on the minimum path distance to obtain the aligned sequence.

[0038] Construct the characteristic change trajectory of liquid nitrogen flow based on the aligned sequence.

[0039] It should be noted that the actual pipeline layout refers to the real spatial arrangement of the high-temperature superconducting cable in the field installation or design model, including the three-dimensional position, curvature, interconnection, and inlet / outlet locations of each pipeline segment. Topologically sorting the first structural feature set according to the actual pipeline layout means arranging the spatial features of each pipeline segment according to its connection relationship within the pipeline network to form a structured topological map. Specifically, based on the connection sequence of the pipeline segments, starting from the liquid nitrogen inlet, tracing each pipeline segment along the pipeline network, and sequentially arranging the feature points of adjacent segments, while retaining the spatial feature information of curved and straight segments, ultimately forming a first structural feature map that reflects the actual connection relationships and spatial distribution of the pipeline.

[0040] Furthermore, based on the liquid nitrogen flow direction, each feature point in the first structural feature map is mapped to the actual flow path of the liquid nitrogen, and the feature points are arranged according to the flow sequence of the liquid nitrogen from the inlet to the outlet. To form a time series, a preset timestamp needs to be assigned to each feature point. This timestamp can be calculated based on the liquid nitrogen flow rate or the pipe section length, thus transforming the spatial feature points into time series points. In this way, the spatial information in the structural feature map is transformed into a time series according to the liquid nitrogen flow sequence, forming the first time series.

[0041] Furthermore, the preset baseline sequence is a reference time series generated by the pipeline design model under ideal or standard liquid nitrogen flow conditions. It typically contains spatial characteristic changes, flow direction, and time series information of each section of the pipeline as liquid nitrogen flows along the pipeline, representing the expected liquid nitrogen flow state and heat transfer conditions. The baseline sequence serves as a reference for comparison and alignment with the first time series actually measured, in order to identify possible anomalies or deviations in the liquid nitrogen flow, thereby guiding the dynamic adjustment of the heat transfer model and refrigeration management.

[0042] Finally, the nonlinear alignment, based on the DTW (Dynamic Time Warping) algorithm, flexibly matches the first time series with the reference series in the time dimension, allowing local time scaling within the series to find the optimal correspondence between them. First, the distance matrix between each feature point in the series is calculated, and the path with the minimum total cumulative distance, i.e., the minimum path distance, is found. Then, along this path, each feature point in the first time series is mapped to its corresponding feature point in the reference series, achieving nonlinear alignment. The resulting aligned sequence retains the actual measurement information of the first time series while also corresponding to the time reference of the ideal reference series, thus providing a precise temporal basis for the analysis of liquid nitrogen flow characteristic trajectories and centrifugal force.

[0043] In this example, the characteristic change trajectory of liquid nitrogen flow is constructed based on the aligned sequence, specifically as follows:

[0044] Based on the aligned sequence, the timestamp sequence and structural feature data of liquid nitrogen flowing through each pipe segment are extracted;

[0045] The structural feature data is mapped to the spatial coordinates of the pipeline segment based on the timestamp sequence to obtain the spatial trajectory of the first liquid nitrogen flow.

[0046] Based on the preset flow continuity constraints and fluid dynamics smoothness conditions, the spatial trajectory of the first liquid nitrogen flow is optimized and corrected to obtain the characteristic change trajectory of liquid nitrogen flow.

[0047] It should be noted that the timestamp sequence refers to the time information of liquid nitrogen flowing through each feature point or pipe segment in the pipeline. It is typically calculated based on the liquid nitrogen flow rate and the pipe segment length, representing the arrival time or residence time of liquid nitrogen in each pipe segment. Structural feature data includes the spatial features of each pipe segment, such as three-dimensional coordinates, rate of curvature change, directional angle offset, and flow direction encoding. Based on the aligned sequence, the timestamps and structural feature data corresponding to each pipe segment can be extracted segment by segment according to the liquid nitrogen flow order. Each feature point in the aligned sequence is mapped to the actual pipe segment and its measurement time, thus forming a dataset corresponding to the time and spatial features of liquid nitrogen flowing through the pipeline.

[0048] Furthermore, using a timestamp sequence as a time reference for the movement of liquid nitrogen within the pipe, each structural feature data point is mapped to its actual coordinate position in three-dimensional space. Specifically, the spatial coordinates of each pipe segment are arranged sequentially according to the flow order of the liquid nitrogen, forming a continuous trajectory curve. For each timestamp, the precise position of the liquid nitrogen within the pipe can be calculated linearly or through interpolation, making the spatial trajectory of the liquid nitrogen continuously visualized in the three-dimensional pipe model. Through this mapping, the first liquid nitrogen flow spatial trajectory fully describes the movement path of the liquid nitrogen along the pipe over time, providing a spatial basis for subsequent centrifugal force and heat transfer analysis.

[0049] Furthermore, the flow continuity constraint means that the flow of liquid nitrogen in the pipeline must satisfy the principle of mass conservation, that is, in a leak-free pipeline, the flow rate of liquid nitrogen at any cross-section is continuous and without abrupt changes. The fluid dynamics smoothness condition means that the velocity and direction changes of liquid nitrogen in the pipeline should be smooth and continuous, without drastic jumps or oscillations, which is consistent with the viscous and inertial characteristics of actual liquid nitrogen flow. Both constraints jointly constrain the rationality of the liquid nitrogen flow trajectory, ensuring that the constructed spatial trajectory conforms to real fluid dynamics behavior and avoiding discontinuities or abnormal fluctuations caused by measurement errors or discrete sequences.

[0050] Finally, optimization and correction are performed by adjusting the coordinates of various points in the first liquid nitrogen flow trajectory to ensure that the trajectory closely approximates the measured data while satisfying the constraints of flow continuity and hydrodynamic smoothness. Specific methods include interpolation, curve fitting, or smoothing filtering techniques to continuously process the velocity and direction changes in the trajectory, while correcting local anomalies, resulting in a continuous and smooth three-dimensional curve of liquid nitrogen flow along the pipe. After optimization and correction, the obtained liquid nitrogen flow characteristic change trajectory accurately reflects the actual movement of liquid nitrogen and conforms to the physical laws of flow, providing reliable input data for subsequent centrifugal force offset calculations and heat transfer model corrections.

[0051] S3. Based on the alignment results, extract the gradient of centrifugal force offset change of liquid nitrogen after passing through several pipe bends, and construct the centrifugal force offset gradient curve.

[0052] In this example, based on the alignment results, the gradient of centrifugal force offset change of liquid nitrogen after passing through several pipe bends is extracted, and a centrifugal force offset gradient curve is constructed, as follows:

[0053] Identify the changes in velocity and pressure of liquid nitrogen as it flows through each bend in the pipe based on the trajectory of liquid nitrogen flow characteristics.

[0054] Calculate the centrifugal force on liquid nitrogen at each bend based on the changes in flow rate and pressure, and calculate the centrifugal force offset of liquid nitrogen at each bend relative to the centerline of the pipeline.

[0055] Accumulate the centrifugal force offset according to the flow sequence, and calculate the centrifugal force offset gradient at different preset flow times;

[0056] A centrifugal force offset gradient curve is constructed with flow time as the horizontal axis and centrifugal force offset gradient as the vertical axis.

[0057] In this example, the formula for calculating the flow velocity of liquid nitrogen as it flows through each bend in the pipe is as follows:

[0058]

[0059] in, Let be the liquid nitrogen flow velocity in the i-th pipe bend. Let be the inlet pressure value of the i-th pipe bend. Let be the outlet pressure value of the i-th pipe bend. The density is that of liquid nitrogen. Let be the friction coefficient of the i-th pipe bend. Let u be the length of the i-th pipe bend. This refers to the pipe diameter.

[0060] In this example, the formula for calculating the pressure change of liquid nitrogen as it flows through each bend in the pipe is as follows:

[0061]

[0062] in, Let be the pressure change value at the i-th bend in the pipe. Let be the liquid nitrogen flow rate at the (i+1)th bend in the pipe. It is the acceleration due to gravity. For the height difference of the pipe section, Let be the bending radius of the i-th pipe bend.

[0063] It should be noted that, based on the optimized liquid nitrogen flow characteristic trajectory, the position, time, and spatial coordinates of each feature point in the pipeline are matched with the geometric information of the corresponding pipeline segment to identify each bend in the pipeline through which the liquid nitrogen passes. Then, combining the length, curvature, and bending angle of the pipeline segment, as well as the inlet velocity and pressure data of the liquid nitrogen, the local velocity and pressure changes of the liquid nitrogen in the bend are calculated using a fluid dynamics model.

[0064] Furthermore, in each bend of the pipeline, the centrifugal force acting on the liquid nitrogen is calculated based on the changes in liquid nitrogen flow rate and pressure, and the centrifugal force offset relative to the pipeline centerline is further determined. Along the liquid nitrogen flow direction, the centrifugal force offsets of each pipeline segment are accumulated sequentially to form a cumulative offset curve. Then, the cumulative centrifugal force offset is correlated with the corresponding flow time, and the offset gradient at different time points is calculated according to preset time intervals or time points; that is, the rate of change of centrifugal force offset per unit time. This yields the gradient of centrifugal force change with time throughout the entire pipeline flow process.

[0065] Finally, the centrifugal force offset gradient data calculated in the previous step at different time points are plotted with the liquid nitrogen flow time as the x-axis and the centrifugal force offset gradient as the y-axis, sequentially generating gradient values ​​for each time point. By connecting these points, a continuous centrifugal force offset gradient curve is generated. This curve visually reflects the changing trend of the influence of centrifugal force on the liquid nitrogen flow during the bend in the pipe. The shape and variation characteristics of the curve can be used to analyze anomalies in the liquid nitrogen flow state and assess heat transfer uniformity.

[0066] S4. Extract features from the centrifugal force offset gradient curve and dynamically adjust the heat transfer parameters in the preset heat transfer mechanism model based on the feature extraction results to obtain the corrected heat transfer mechanism model.

[0067] In this example, features are extracted from the centrifugal force offset gradient curve, and the heat transfer parameters in the preset heat transfer mechanism model are dynamically adjusted based on the feature extraction results to obtain the corrected heat transfer mechanism model, specifically:

[0068] Extract the curve change trend characteristics from the centrifugal force offset gradient curve, and identify flow anomalies in the liquid nitrogen flow based on the curve change trend characteristics.

[0069] Based on the flow anomaly results, the convective heat transfer coefficient and heat conduction parameters of the corresponding segments in the heat transfer model are dynamically adjusted, and the model is verified based on historical data. The model is iteratively optimized until the prediction error converges, and the corrected heat transfer mechanism model is obtained.

[0070] It should be noted that after obtaining the centrifugal force offset gradient curve, the overall trend of the curve is first extracted using time-series analysis methods. This includes calculating indicators such as the slope change, the distribution of local extreme points, and the frequency and amplitude of fluctuations, to determine whether the liquid nitrogen flow maintains a stable trend. If the curve shows a gentle change, it indicates that the liquid nitrogen flow is normal; if the curve exhibits significant steep rises, falls, or large periodic fluctuations, it suggests abnormal flow conditions in certain curved pipe sections. The extracted trend features are not only used to determine whether flow anomalies have occurred but also provide a preliminary basis for the first gradient sequence of subsequent abnormal pipe sections.

[0071] Furthermore, after extracting the trend characteristics of the curve changes and initially identifying anomalies, the corrected heat transfer mechanism model is compared and verified with historical monitoring data. Specifically, historical liquid nitrogen flow rate, pressure, and temperature data are input into the corrected model, and the calculated temperature prediction value is compared with the actual historical measurement value. If the error is still large, the local convective heat transfer coefficient and heat conduction parameters are further corrected by combining the gradient change characteristics of the abnormal pipe section, and prediction and comparison are performed again. Through this iterative process, the deviation between the predicted and measured values ​​is continuously reduced until the error converges to a preset threshold range, at which point the final corrected heat transfer mechanism model is confirmed. This not only ensures the model's adaptability under abnormal conditions but also provides reliable temperature prediction support for subsequent refrigeration management.

[0072] In this example, flow anomalies are identified based on the characteristics of the curve's changing trend. Specifically:

[0073] A graph model is constructed by taking each curved pipe segment as a node, the connection relationship between the curved pipe segments as edges, and the integral mean of the centrifugal force offset gradient curve as the weight of the edges.

[0074] The shortest path algorithm is used to traverse the graph model to obtain the first flow path;

[0075] The first flow path is compared with the preset sequence of actual liquid nitrogen flow pipe segments, and flow anomalies are identified based on the comparison results.

[0076] It should be noted that in the modeling process using curved pipe segments as nodes, all curved pipe segments in the cable are first treated as independent graph nodes, each representing a local geometry through which liquid nitrogen flows. Since there is a clear upstream and downstream flow relationship between different curved pipe segments, directed edges between nodes are established based on the physical connections of the pipes, ensuring that the graph structure accurately reflects the flow path of the liquid nitrogen. Simultaneously, for each edge, the integral mean of the gradient curve generated by the centrifugal force during the connection process is calculated on the corresponding curved segment, and this value is used as the edge weight. In this way, the weight not only reflects the flow resistance and instability encountered by the liquid nitrogen when flowing through that segment, but also quantifies the flow cost of liquid nitrogen in different curved segments, thus constructing a complete weighted graph model.

[0077] Furthermore, after obtaining the weighted graph model, a shortest path algorithm (such as Dijkstra's or Floyd's algorithm) is used to traverse the entire graph starting from the liquid nitrogen inlet node, calculating the path with the minimum cost to the liquid nitrogen outlet node. The minimum cost refers to the path with the smallest total cost under the weighted average of the accumulated centrifugal force offset gradient integrals, i.e., the theoretically most likely stable flow path chosen by liquid nitrogen. This path obtained by the shortest path algorithm is the first flow path. The first flow path represents a possible optimal flow trajectory of liquid nitrogen in a real curved pipe network, inferred from liquid nitrogen flow characteristic data. It is a data-driven predicted path, not a pre-defined ideal path.

[0078] Finally, the preset sequence of actual liquid nitrogen flow pipe segments refers to the true flow sequence obtained during the cable design or experimental verification phase, based on the actual pipe layout and liquid nitrogen flow direction records. It reflects the set and connection order of the curved pipe segments that liquid nitrogen should ideally pass through. During comparison, the first flow path generated by the shortest path algorithm is compared segment by segment with this preset sequence: if the first flow path is highly consistent with the preset actual sequence, it indicates that the liquid nitrogen flow process is normal; if deviations occur (such as path detours, skipping certain curved sections, or passing through undesigned sections), it indicates the presence of flow anomalies. These anomalies are usually caused by physical phenomena such as uneven local velocity distribution, sudden pressure changes, or excessive centrifugal force shift, thus enabling accurate identification of flow anomalies through comparison results.

[0079] In this example, based on the flow anomaly results, the convective heat transfer coefficient and heat conduction parameters of the corresponding segments in the heat transfer model are dynamically adjusted, specifically as follows:

[0080] Based on the flow anomaly results, the abnormal pipe segment is located, and the first gradient sequence of the abnormal pipe segment is extracted.

[0081] An adaptive threshold segmentation algorithm is used to divide the first gradient sequence into multiple levels, resulting in several gradient change intervals;

[0082] Gradient change is evaluated for several gradient change intervals, and parameter adjustment is generated based on the evaluation results;

[0083] The convective heat transfer coefficient and heat conduction parameters of the corresponding segments in the heat transfer model are dynamically adjusted based on the parameter adjustment amount.

[0084] It should be noted that after the flow anomaly identification is completed in the previous stage, the flow trajectories of which curved pipe segments are inconsistent with the preset sequence will be identified, and these pipe segments will be marked as abnormal pipe segments. The localization process is mainly based on the path deviation in the graphical model: once it is found that the first flow path jumps or detours from the preset path at certain nodes, the corresponding node pipe segment can be identified as an abnormal segment. Subsequently, in order to further quantify the flow characteristics of the abnormal segment, the sequence of centrifugal force offset change gradient over time or flow distance of the abnormal pipe segment will be extracted from the liquid nitrogen flow characteristic change trajectory, i.e., the first gradient sequence.

[0085] Furthermore, after obtaining the first gradient sequence of the abnormal pipeline segment, an adaptive threshold segmentation algorithm is used for multi-level partitioning to identify the gradient change characteristics at different stages. Specifically, the algorithm first calculates statistical indicators such as the mean and standard deviation based on the global distribution characteristics of the first gradient sequence; then, it dynamically sets multiple thresholds, which are automatically adjusted according to local fluctuations in the gradient sequence rather than remaining fixed. The algorithm sequentially scans the sequence data, and when a gradient value crosses a certain threshold, it automatically treats that interval as a new segment, thus dividing the entire gradient sequence into multiple gradient change intervals. This adaptive approach effectively distinguishes stable sections from drastically changing sections under different flow conditions, avoiding the rigidity of manually set thresholds.

[0086] Furthermore, after obtaining several gradient variation intervals, each interval needs to be evaluated to determine the intensity of the anomaly and its impact on heat transfer performance. Evaluation methods typically include calculating the average gradient value, maximum gradient abrupt change amplitude, and gradient fluctuation frequency within the interval, and comparing these values ​​with the baseline characteristics of historical normal intervals. If the variation level of a certain gradient interval is significantly higher than the normal baseline, it indicates severe flow disturbance in that interval. Based on the evaluation results, the degree of disturbance is quantified into parameter adjustment amounts, namely, correction values ​​for the convective heat transfer coefficient and heat conduction parameters. The magnitude of the adjustment amount is proportional to the degree of anomaly in the interval; intervals with severe fluctuations will receive larger adjustment amounts, while relatively stable intervals will only require minor corrections.

[0087] Finally, after generating the parameter adjustments, these adjustments are applied to the corresponding segments of the heat transfer mechanism model. Specifically, the process involves: first, identifying the heat transfer sub-model corresponding to the abnormal pipe segment, and using the convective heat transfer coefficient and heat conduction parameters in this sub-model as parameters to be corrected; then, dynamically updating the model based on the generated adjustments, for example, reducing the convective heat transfer coefficient to simulate turbulence and enhance heat transfer resistance, or increasing the heat conduction parameters to reflect the shift in the local heat conduction path; after correction, the model recalculates the cable temperature distribution. To ensure stability, this dynamic adjustment process often employs an iterative optimization approach, continuously inputting real-time monitoring data to compare model predictions and errors, gradually converging to an accurate and reliable corrected model.

[0088] S5 predicts cable temperature based on the modified heat transfer mechanism model and performs cooling management based on the prediction results.

[0089] In this example, cable temperature is predicted based on the modified heat transfer mechanism model, and cooling management is implemented based on the prediction results, specifically:

[0090] The real-time collected data on liquid nitrogen flow rate, temperature, and pressure inside the pipeline are input into the corrected heat transfer mechanism model.

[0091] The temperature distribution of each cable pipe segment was calculated using the modified heat transfer mechanism model.

[0092] Cooling control commands are generated based on temperature distribution to dynamically adjust liquid nitrogen flow rate and cooling power.

[0093] It should be noted that the liquid nitrogen flow rate, temperature, and pressure data within the pipeline refer to key flow parameters of liquid nitrogen monitored in real time within each section of the high-temperature superconducting cable. Specifically, this includes the instantaneous flow rate of liquid nitrogen in each pipeline section, representing the speed at which the liquid nitrogen moves along the pipeline; the liquid nitrogen temperature, representing the actual temperature distribution of the liquid nitrogen within the pipeline; and the liquid nitrogen pressure, representing the static pressure exerted on the liquid nitrogen within the pipeline. These data are typically collected in real time by sensors installed within the pipeline, providing input to a modified heat transfer mechanism model to accurately calculate the cable temperature and cooling requirements.

[0094] Furthermore, the real-time collected flow rate, temperature, and pressure data are input into the corrected heat transfer mechanism model. The model utilizes the flow state, heat capacity, thermal conductivity of liquid nitrogen, and the geometric characteristics of each pipe segment to calculate the temperature distribution of each cable segment according to the convective heat transfer and heat conduction equations for each pipe segment. The calculation process includes convective heat transfer of liquid nitrogen to the inner surface of the pipe, heat conduction between the pipe wall and the cable conductor, and corrections for possible local temperature rises or flow anomalies. Finally, a temperature profile curve along the pipe is obtained, reflecting the temperature distribution of the cable at different locations, providing accurate data for refrigeration management.

[0095] Finally, based on the calculated cable temperature distribution, it is first determined which pipe sections have temperatures exceeding the set safety threshold or areas with excessive heat load, and then a cooling regulation strategy is generated. The strategy includes adjusting the liquid nitrogen flow rate: increasing the flow rate to accelerate heat removal, or decreasing the flow rate to avoid overcooling; and adjusting the cooling power: increasing the output power of the refrigeration unit to improve cooling efficiency, or decreasing the power to save energy. The regulation commands are sent to the liquid nitrogen pump and refrigeration system in the form of real-time control signals to achieve dynamic optimization of liquid nitrogen flow rate and cooling power, maintaining the cable temperature within a safe and stable operating range while improving energy efficiency.

[0096] Example 2, Figure 2 This invention presents a high-temperature superconducting cable refrigeration management system based on a heat transfer mechanism model, comprising a structure partitioning module, a sequence alignment module, a gradient extraction module, a model correction module, and a refrigeration management module.

[0097] The structure partitioning module is used to partition the high-temperature superconducting cable duct into spatial structures and construct the first structural feature set based on the partitioning results.

[0098] The sequence alignment module is used to convert the first structural feature set into a first time sequence according to the liquid nitrogen flow direction, and to align the first time sequence with a preset reference sequence using the DTW algorithm.

[0099] The gradient extraction module is used to extract the gradient of centrifugal force offset change of liquid nitrogen after passing through several pipe bends based on the alignment results, and to construct the centrifugal force offset gradient curve.

[0100] The model correction module is used to extract features from the centrifugal force offset gradient curve and dynamically adjust the heat transfer parameters in the preset heat transfer mechanism model based on the feature extraction results to obtain the corrected heat transfer mechanism model.

[0101] The cooling management module is used to predict cable temperature based on the modified heat transfer mechanism model and to manage cooling based on the prediction results.

[0102] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0103] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0104] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0105] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0106] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0107] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for refrigeration management of a high temperature superconducting cable incorporating a heat transfer mechanism model, characterized by, The method comprises the following steps: The high-temperature superconducting cable pipeline is divided into a spatial structure, and a first structure feature set is constructed according to the division result, specifically: The high-temperature superconducting cable pipeline is divided into a plurality of pipeline segments, the pipeline segments include pipeline curved segments and pipeline straight segments; the spatial coordinate sequence of each pipeline segment is extracted, and the curvature change rate and the direction angle offset of each pipeline segment are calculated to obtain the spatial feature set of each pipeline; the flow direction coding is performed on the plurality of pipeline segments according to the liquid nitrogen flow direction to obtain the flow feature set of each pipeline; the spatial feature set and the flow feature set of each pipeline are fused to obtain the first structure feature set; The first structure feature set is converted into a first time sequence according to the liquid nitrogen flow direction, and the first time sequence is aligned with a preset reference sequence by using a DTW algorithm; Based on the alignment result, the centrifugal force offset change gradient of the liquid nitrogen after passing through the plurality of pipeline curved segments is extracted to construct a centrifugal force offset gradient curve; The centrifugal force offset gradient curve is feature-extracted, and the heat transfer parameters in the preset heat transfer mechanism model are dynamically adjusted according to the feature extraction result to obtain a corrected heat transfer mechanism model, specifically: The curve trend feature in the centrifugal force offset gradient curve is extracted, and the flow state of the liquid nitrogen flow is flow anomaly-recognized according to the curve trend feature; based on the flow anomaly result, the convective heat transfer coefficient and the heat conduction parameter of the corresponding segment in the heat transfer model are dynamically adjusted, and the model is verified based on historical data, and iteratively optimized until the prediction error converges to obtain the corrected heat transfer mechanism model; The cable temperature is predicted based on the corrected heat transfer mechanism model, and refrigeration management is performed according to the prediction result.

2. The high temperature superconducting cable refrigeration management method incorporating heat transfer mechanism models of claim 1, wherein, The first structure feature set is converted into a first time sequence according to the liquid nitrogen flow direction, and the first time sequence is aligned with a preset reference sequence by using a DTW algorithm, specifically: The actual layout of the pipeline is obtained, and the first structure feature set is topologically sorted according to the actual layout of the pipeline to obtain a first structure feature map; According to the liquid nitrogen flow direction, the feature points in the structure feature map are arranged in a preset time sequence to obtain a first time sequence; The minimum path distance between the first time sequence and the preset reference sequence is calculated by using a DTW algorithm; The first time sequence and the preset reference sequence are nonlinearly aligned according to the minimum path distance to obtain an aligned sequence; A liquid nitrogen flow feature change trajectory is constructed according to the aligned sequence.

3. The high temperature superconducting cable refrigeration management method incorporating heat transfer mechanism models of claim 2, wherein, The first structure feature set is converted into a first time sequence according to the liquid nitrogen flow direction, and the first time sequence is aligned with a preset reference sequence by using a DTW algorithm, specifically: Based on the aligned sequence, the timestamp sequence and the structure feature data of the liquid nitrogen flowing through each pipeline segment are extracted; The structure feature data is mapped to the pipeline segment spatial coordinates according to the timestamp sequence to obtain a first liquid nitrogen flow space trajectory; Based on the preset flow continuity constraint and the fluid dynamics smoothness condition, the first liquid nitrogen flow space trajectory is optimized and corrected to obtain a liquid nitrogen flow feature change trajectory.

4. The high temperature superconducting cable refrigeration management method incorporating heat transfer mechanism models of claim 3, wherein, The first structure feature set is converted into a first time sequence according to the liquid nitrogen flow direction, and the first time sequence is aligned with a preset reference sequence by using a DTW algorithm, specifically: According to the liquid nitrogen flow feature change trajectory, the flow velocity and the pressure change value of the liquid nitrogen flowing through each pipeline curved segment are identified; The centrifugal force of the liquid nitrogen at each bending section is calculated based on the flow rate and the pressure change value, and a centrifugal force offset of the liquid nitrogen at each bending section relative to the center line of the pipeline is calculated; The centrifugal force offsets are accumulated in the order of flow, and a centrifugal force offset gradient at different preset flow times is calculated; A centrifugal force offset gradient curve is constructed with the flow time as the horizontal axis and the centrifugal force offset gradient as the vertical axis.

5. The high temperature superconducting cable refrigeration management method incorporating heat transfer mechanism models of claim 4, wherein, The flow state of the liquid nitrogen flow is identified according to the curve variation trend characteristics, specifically: A graph model is constructed with each bending pipeline section as a node, the connection relationship of the bending pipeline sections as edges, and the integral mean of the centrifugal force offset gradient curve as the weight of the edges; The graph model is traversed using a shortest path algorithm to obtain a first flow path; The first flow path is compared with a preset sequence of actual liquid nitrogen flow pipeline sections, and flow anomalies are identified according to the comparison result.

6. The high temperature superconducting cable refrigeration management method incorporating heat transfer mechanism models of claim 5, wherein, Based on the flow anomaly result, the convective heat transfer coefficient and the thermal conductivity parameter of the corresponding section in the heat transfer model are dynamically adjusted, specifically: Based on the flow anomaly result, the abnormal pipeline section is located, and a first gradient sequence of the abnormal pipeline section is extracted; The first gradient sequence is divided into several gradient change intervals using an adaptive threshold segmentation algorithm; The gradient change intervals are evaluated, and a parameter adjustment amount is generated according to the evaluation result; The convective heat transfer coefficient and the thermal conductivity parameter of the corresponding section in the heat transfer model are dynamically adjusted based on the parameter adjustment amount.

7. The high temperature superconducting cable refrigeration management method incorporating heat transfer mechanism models of claim 6, wherein, The cable temperature is predicted based on the corrected heat transfer mechanism model, and refrigeration management is performed according to the prediction result, specifically: The real-time collected liquid nitrogen flow rate, temperature and pressure data in the pipeline are input into the corrected heat transfer mechanism model; The temperature distribution of each pipeline section of the cable is calculated through the corrected heat transfer mechanism model; Based on the temperature distribution, a refrigeration adjustment instruction is generated to dynamically adjust the liquid nitrogen flow and the cooling power.

8. The cryogenic management system for high temperature superconducting cable incorporating heat transfer mechanism model according to any one of claims 1 to 7, characterized in that, It includes a structure division module, a sequence alignment module, a gradient extraction module, a model correction module, and a refrigeration management module: The structure division module is used to divide the high-temperature superconducting cable pipeline in space, and to construct a first structure feature set according to the division result; The sequence alignment module is used to convert the first structure feature set into a first time sequence according to the flow direction of the liquid nitrogen, and to align the first time sequence with a preset reference sequence using the DTW algorithm; The gradient extraction module is used to extract the centrifugal force offset change gradient of the liquid nitrogen after passing through several pipeline bending sections based on the alignment result, and to construct a centrifugal force offset gradient curve; The model correction module is used to extract features from the centrifugal force offset gradient curve, and to dynamically adjust the heat transfer parameters in the preset heat transfer mechanism model according to the feature extraction result, to obtain a corrected heat transfer mechanism model; The refrigeration management module is used to predict the cable temperature based on the corrected heat transfer mechanism model, and to perform refrigeration management according to the prediction result.

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