A digital pump operation method and system

Abstract

The present invention relates to the field of digital pump operation control technology, and in particular to a digital pump operation method and system. The present invention proposes the following scheme: by collecting the winding temperature gradient distribution, axial strain and coolant dielectric property parameters, inputting them into a preset finite element thermal model, and using the adjoint matrix method to correct the boundary conditions, the three-dimensional transient heat flux density field is reconstructed to achieve precise positioning of local overheating areas. Based on sensitivity analysis, the contribution of the heat source term to the temperature field is calculated, and the heat flux density field is optimized in combination with Fourier's law to improve the calculation accuracy. The present invention is suitable for urban water supply, petrochemical industry, aviation fuel pumps and other fields, and can improve the thermal management accuracy of the equipment, extend its service life, and improve its operating efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of digital pump operation control, and in particular to a digital pump operation method and system. Background Art

[0002] In the existing digital pump operation management technology, although the traditional method can obtain the basic operating status of the pump body, such as temperature, pressure, flow and other parameters, through monitoring equipment such as temperature sensors and flow meters, it is difficult for existing technologies to accurately grasp the thermodynamic evolution process inside the pump, especially under complex working conditions (such as high-load operation, hot and cold shock, changes in fluid properties, etc.), the precise positioning of local overheating areas still faces great technical obstacles. The measurement method of traditional temperature sensors is limited by the installation position and spatial resolution, and cannot provide continuous three-dimensional temperature distribution information, making it difficult to capture temperature anomalies in key areas in real time. In addition, existing cooling systems usually rely on fixed parameter settings and cannot be dynamically adjusted according to changes in the real-time heat flux density field, which may lead to insufficient cooling in local areas or low cooling efficiency.

[0003] For example, a Chinese patent with a grant announcement number of CN108386351B discloses a thermal management system including an electric coolant pump, a power supply, and a controller. The pump is in fluid communication with a heat source and a radiator, and has a pump sensor for determining pump voltage, speed, and current. The battery supplies power to the sensor. The controller receives voltage, speed, and current from the sensor, determines the performance of the pump across multiple operating regions, calculates a digital health state (SOH) that quantifies the severity of degradation of each of multiple pump characteristics across regions, and performs a control action when the calculated digital SOH of any region is less than a calibrated SOH threshold. Pump characteristics include pump circuits, leaks / blockages, bearings, and motor states. The vehicle includes an engine or other heat source, a radiator; and a thermal management system. The controller can perform a prediction method on an electric coolant pump in a vehicle.

[0004] The above existing technologies all have the problems raised by this background technology: they cannot be dynamically adjusted according to changes in the real-time heat flux density field, which may lead to insufficient cooling in local areas or too low cooling efficiency. To solve the above problems, this application designs a digital pump operation method and system. Summary of the invention

[0005] The technical problem to be solved by the present invention is to address the deficiencies of the prior art and provide a digital pump operation method and system. By collecting the winding temperature gradient distribution, axial strain and coolant dielectric property parameters, inputting them into a preset finite element thermal model, and using the adjoint matrix method to correct the boundary conditions, the three-dimensional transient heat flux density field is reconstructed to achieve precise positioning of local overheating areas. The contribution of the heat source term to the temperature field is calculated based on sensitivity analysis, and the heat flux density field is optimized in combination with Fourier's law to improve the calculation accuracy. The present invention is applicable to the fields of urban water supply, petrochemical industry, aviation fuel pumps, etc., and can improve the thermal management accuracy of the equipment, extend its service life, and improve its operating efficiency.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A digital pump operation method, the operation method comprising:

[0008] Generate winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters based on the collected digital pump sensor data;

[0009] The winding temperature gradient distribution, axial strain and coolant dielectric property parameters are input into the preset finite element thermal model, the boundary conditions are corrected by the adjoint matrix method, the three-dimensional transient heat flux density field is reconstructed, and the local overheating area is located;

[0010] Select a cooling mode from a library of predefined modes and generate operation control instructions.

[0011] The generating of winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters includes:

[0012] The real-time temperature value of each thermocouple is collected according to the distributed temperature sensor network, and a two-dimensional temperature field is generated through a spatial interpolation algorithm. The temperature changes of adjacent measuring points are calculated to generate the winding temperature gradient distribution.

[0013] Collect axial wavelength data of the rotating shaft and winding parts according to the fiber grating sensor chain, decouple the axial wavelength data according to the photoelastic effect and thermal expansion characteristics, and generate axial strain;

[0014] The dielectric characteristic signal of the coolant is collected according to the interdigital electrode sensor, and the dielectric constant, loss factor and conductivity are calculated.

[0015] The training process of the finite element thermal model includes:

[0016] Refining the geometry of the digital pump into a finite element model with a specific mesh distribution;

[0017] According to the preset heat load operating conditions, the temperature distribution under each operating condition is recorded by inputting different heat powers to generate multiple sets of data sets;

[0018] Initialize heat source terms and boundary conditions of the finite element model according to the plurality of data sets;

[0019] The finite element model is adjusted through iterative optimization until the number of iterations reaches a preset number or the model reaches a convergence condition.

[0020] The step of adjusting the finite element model by iterative optimization includes:

[0021] According to the initialized heat source terms and boundary conditions, the heat conduction equations corresponding to multiple sets of data are calculated by the finite element method;

[0022] Evaluate the energy conservation of the heat conduction equation and calculate the transmission loss value of the heat flux between the grid units of the finite element model;

[0023] Determining whether the number of iterations reaches a preset number or whether the transmission loss value reaches a convergence condition;

[0024] If neither is achieved, the heat flux density change rate is calculated according to the loss distribution of the transfer loss value, the mesh division of the finite element model is adjusted according to the heat flux density change rate, and the evaluation is re-performed.

[0025] The method of locating the local overheating area comprises:

[0026] The boundary conditions are modified according to the axial strain and the dielectric characteristic parameters of the coolant;

[0027] Calculate the three-dimensional transient temperature field based on the corrected boundary conditions and the winding temperature gradient distribution;

[0028] Discretizing the three-dimensional transient temperature field, calculating the sensitivity matrix of the heat source term, reconstructing the sensitivity matrix by Fourier's law, and calculating the three-dimensional transient heat flux density field;

[0029] The local overheating area is located according to the three-dimensional transient heat flux density field.

[0030] The modifying of the boundary conditions according to the axial strain and the dielectric characteristic parameters of the coolant includes:

[0031] Obtain the initial length and initial temperature rise of the shaft of the finite element model, and calculate the thermal expansion of the shaft;

[0032] updating the convection heat transfer coefficient according to the thermal expansion amount;

[0033] Obtain the dielectric constant of the matrix material of the finite element model and calculate the volume fraction of nanoparticles;

[0034] The equivalent thermal conductivity of the coolant is updated according to the volume fraction.

[0035] The method of calculating the three-dimensional transient heat flux density field comprises:

[0036] The three-dimensional transient temperature field is discretized by using a discrete heat conduction control equation, wherein the discretization includes spatial discretization and temporal discretization;

[0037] After the spatial discretization is completed, the heat balance equation is established on each grid unit, and the temperature evolution trend of the temperature field is gradually solved according to the time discretization result. In each time step, the heat balance equation is updated according to the temperature evolution trend of the previous time step;

[0038] A unit change is applied to each heat source term according to the heat balance equation, and the temperature contribution of the heat source term is calculated based on the change result to generate a sensitivity matrix;

[0039] Map the row index and column index of the sensitivity matrix to the three-dimensional coordinates of the grid unit, and convert each element of the matrix into a sensitivity tensor through Fourier's law according to the mapping result;

[0040] The heat flux density of each grid is calculated according to the sensitivity tensor and the temperature gradient corresponding to the grid unit, and all the heat flux densities are aggregated to generate a three-dimensional transient heat flux density field.

[0041] Locating a local overheating area according to the three-dimensional transient heat flux density field includes:

[0042] Analyze the distribution of heat flux density, identify the concentrated areas and abnormal flow areas of heat flow direction, and screen out heat accumulation points;

[0043] According to the heat accumulation point, the difference between the input heat flow and the output heat flow of the area is calculated to determine whether there is heat flow imbalance;

[0044] If there is an imbalance in heat flow, it is marked as a local overheating area.

[0045] A digital pump operation system, the system comprising a data generation module, a model training module, a regional positioning module and a cooling control module;

[0046] The data generation module is used to generate winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters according to the collected digital pump sensor data;

[0047] The model training module is used to train the finite element thermal model. The training includes performing finite element meshing on the geometric structure of the digital pump, constructing initial boundary conditions, and inputting thermal power data under different thermal load conditions to generate a training data set. The model training module is also used to iteratively optimize the finite element thermal model, adjust heat source terms, boundary conditions and meshing until the model meets convergence conditions;

[0048] The regional positioning module is used to input the winding temperature gradient distribution, axial strain and coolant dielectric property parameters into a preset finite element thermal model, correct the boundary conditions through the adjoint matrix method, reconstruct the three-dimensional transient heat flux density field, and locate the local overheating area;

[0049] The cooling control module is used to receive the local overheating area information output by the area positioning module, and select a cooling strategy that adapts to the current operating state from a predefined cooling mode library.

[0050] The regional positioning module includes:

[0051] The temperature field calculation unit is used to calculate the three-dimensional transient temperature field according to the modified boundary conditions and the winding temperature gradient distribution in combination with the finite element thermal model, and iteratively solve the temporal evolution process of the temperature field using the time stepping method;

[0052] The sensitivity analysis unit is used to generate a sensitivity matrix using the heat source term perturbation method after the temperature field calculation is completed, and to evaluate the contribution of the heat source term to the temperature field;

[0053] The heat flux density field calculation unit is used to reconstruct the sensitivity matrix based on Fourier's law, and calculate the heat flux density of each grid in combination with the temperature gradient of the grid unit to generate a three-dimensional transient heat flux density field;

[0054] The overheating area identification unit is used to analyze the time-series changes of the heat flux density field, extract the areas with large heat flux density gradient, and calculate the equilibrium state of the input heat flux and output heat flux of the local grid unit. If the heat flux input of a certain area is much greater than the output, the area is marked as a potential overheating area.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] The present invention collects the winding temperature gradient distribution, axial strain and coolant dielectric property parameters, combines the finite element thermal model and sensitivity analysis, and accurately reconstructs the three-dimensional transient heat flux density field. It can identify the local overheating area inside the digital pump in real time and accurately, avoiding the monitoring blind spots caused by insufficient spatial resolution of traditional temperature sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0058] Figure 1 This is a flow chart of a digital pump operation method according to Embodiment 1 of the present invention;

[0059] Figure 2 This is a schematic diagram of the operation control of a digital pump according to Embodiment 1 of the present invention;

[0060] Figure 3 This is a schematic diagram of the overheating area positioning process of Example 1 of the present invention;

[0061] Figure 4 This is a module diagram of a digital pump operation system according to Example 2 of the present invention. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0063] Example 1

[0064] See also Figure 1 , an embodiment provided by the present invention: a digital pump operation method, the specific steps are as follows:

[0065] S1: Collect digital pump sensor data;

[0066] S2: Generate winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters based on sensor data;

[0067] In this step, the collected raw data is interpolated and normalized using a data processing algorithm to ensure data continuity and computational stability. The winding temperature gradient distribution is calculated using a spatial interpolation algorithm to form an accurate two-dimensional temperature field, and combined with time step analysis to obtain the temperature change trend over time. The axial strain data uses a decoupling algorithm to eliminate the interference caused by mechanical loads so that it only reflects the strain effect caused by thermal expansion, ensuring the accuracy of the strain data. The acquisition of the coolant dielectric property parameters not only takes into account the dielectric constant, loss factor and conductivity, but also corrects the equivalent thermal conductivity of the coolant based on the correlation between dielectric properties and heat exchange capacity to adapt to cooling performance fluctuations under different working conditions.

[0068] S3: training finite element thermal model;

[0069] In this step, the training process of the finite element thermal model is based on the geometric structure and material properties of the digital pump to construct a high-resolution gridded calculation domain. During the training process, by presetting a variety of heat load conditions and inputting different thermal powers, the temperature field evolution trend of each grid unit is calculated, and multiple sets of data sets are recorded. These data are used to initialize the heat source terms and boundary conditions, and the boundary heat flux density is continuously adjusted under the optimization of the existing adjoint matrix method to ensure that the error between the model and the actual measured data is minimized. Through iterative optimization, the model can not only accurately predict the steady-state heat flux distribution, but also respond to the dynamic changes of temperature, strain and coolant performance in real time, providing high-precision thermal field calculation capabilities for accurately locating local overheating areas.

[0070] S4: input the winding temperature gradient distribution, axial strain and coolant dielectric property parameters into the finite element thermal model to locate the local overheating area;

[0071] In this step, the finite element thermal model receives the sensor data as dynamic input to modify the boundary conditions and material parameters of the model. Based on the axial strain data, the convective heat transfer coefficient is adjusted to change dynamically with the axial deformation; based on the dielectric characteristic parameters of the coolant, its equivalent thermal conductivity is calculated and the heat transfer capacity of the fluid-solid heat transfer boundary is updated. Subsequently, the three-dimensional transient temperature field is calculated by the finite element method, and the sensitivity matrix is ​​generated based on the sensitivity analysis method. The sensitivity matrix is ​​reconstructed using Fourier's law, the transient heat flux density field is calculated, and the abnormal heat flux density concentration area is extracted in combination with the time series analysis method. The imbalance between the heat flux input and output is evaluated by energy conservation, and the location and cause of the local overheating area are further determined. Finally, the area where local overheating may occur is accurately identified, providing a decision-making basis for the optimization of subsequent cooling modes.

[0072] S5: Select a cooling mode from a predefined mode library and generate an operation control instruction;

[0073] In this step, the optimal cooling strategy is automatically selected from the predefined pattern library based on the characteristics of the local overheating area located. The cooling pattern library contains a variety of cooling strategies, including increasing the coolant flow rate, optimizing the coolant path, adjusting the coolant type, and adjusting the working status of the heat exchanger in real time. The cooling control module combines the distribution information of the heat flux density field to analyze the characteristics of the overheating area, including the overheating intensity, duration, and possible heat dissipation bottlenecks. Based on this information, the operating parameters of the cooling system are automatically adjusted, such as increasing the coolant flow rate, reallocating the cooling path, or adjusting the heat exchange capacity of the heat exchange interface to maximize the cooling efficiency and reduce the risk of local overheating. Finally, through the closed-loop control method, the temperature field changes are continuously monitored, and the finite element thermal model is updated again after the cooling mode is executed to ensure that the cooling effect meets the set goals and achieve stable and efficient operation of the digital pump.

[0074] Specifically, in the existing digital pump operation management technology, although the traditional method can obtain the basic operating status of the pump body, such as temperature, pressure, flow and other parameters, through monitoring equipment such as temperature sensors and flow meters, it is difficult for the existing technology to accurately grasp the thermodynamic evolution process inside the pump, especially under complex working conditions (such as high-load operation, hot and cold shock, changes in fluid properties, etc.), the precise positioning of local overheating areas still faces great technical obstacles. The measurement method of traditional temperature sensors is limited by the installation position and spatial resolution, and cannot provide continuous three-dimensional temperature distribution information, resulting in temperature anomalies in key parts that are difficult to capture in real time. In addition, the existing cooling system usually relies on fixed parameter settings and cannot be dynamically adjusted according to changes in the real-time heat flux density field, which may lead to insufficient cooling in local areas or too low cooling efficiency. These technical defects make digital pumps prone to local overheating during long-term operation, affecting system stability and even shortening equipment life.

[0075] See also Figure 2 , a schematic diagram of the digital pump operation control of an embodiment of the present invention. In this embodiment, taking the digital pump operation system in the urban water supply network as an example, a digital pump operation method is proposed to achieve accurate positioning of the local overheating area of ​​the digital pump and intelligent cooling strategy adjustment, thereby effectively solving the above-mentioned problems in the prior art.

[0076] For example, in a water supply network, the key power unit of the main pump station runs for a long time, and the temperature distribution of the internal winding is affected by multiple factors such as load changes, water flow rate, ambient temperature and cooling efficiency, resulting in significant differences in heat accumulation in different areas. In traditional technology, maintenance personnel usually make manual adjustments based on the results of regular patrol temperature tests, but this method is not only lagging, but also unable to accurately identify local hot spots. If the cooling strategy is inappropriate, it may cause overheating of the winding, accelerate insulation aging, and ultimately affect the service life of the pump.

[0077] Furthermore, this embodiment constructs a high-precision three-dimensional transient heat flux density field by combining axial strain data, coolant dielectric property parameters and winding temperature gradient distribution, and predicts possible overheating risk areas in real time based on the finite element thermal model. For example, in the main pump station of the water supply network, suppose a digital pump has a non-uniform temperature rise phenomenon in its winding due to long-term high-load operation. Traditional methods may only be able to detect the increase in the overall temperature of the winding during regular inspections, while this embodiment can collect axial strain data through fiber grating sensors, and combine the temperature field calculation results to infer the problem of reduced heat dissipation capacity caused by thermal expansion in this area. Furthermore, through the analysis of the dielectric properties of the coolant, the system can detect the reduction in the heat exchange capacity of the coolant (for example, the reduction in cooling efficiency due to contamination, aging or decreased flow rate), and automatically correct the boundary conditions of the thermal model to reflect the actual cooling state.

[0078] Furthermore, based on the above thermal field information, the cooling strategy can be accurately adjusted to avoid the inefficiency of traditional cooling methods. Assuming that at a certain point in time, it is found that the heat flux density of a certain winding area is significantly higher than that of other areas, and the heat input is much greater than the output, it indicates that there may be a risk of local overheating in this area. Traditional cooling methods may adopt a global cooling method, such as increasing the coolant flow rate of the entire water supply network or lowering the water inlet temperature. This method not only consumes a lot of energy, but may also affect the normal operation of other components. However, this embodiment improves the cooling efficiency only for specific overheated areas by dynamically adjusting the coolant flow path, such as by optimizing the flow channel distribution, locally enhancing the coolant flow rate, etc., to ensure that the overheated area can obtain cooling resources first, rather than indiscriminate cooling. This adaptive cooling optimization strategy can not only effectively reduce the risk of local overheating, but also reduce unnecessary energy consumption and improve the operating efficiency of the overall cooling system.

[0079] Preferably, in this embodiment, the digital pump operation method can also be applied to high-precision manufacturing equipment (such as the spindle cooling system of a CNC machine tool) to monitor the temperature distribution of the spindle in real time and optimize the cooling strategy to improve processing accuracy and extend the service life of the equipment.

[0080] In addition, in the liquid cooling system of the data center, this embodiment can be used to optimize the flow path of the coolant and improve the thermal management efficiency of the server rack. The cooling of the current data center servers mainly relies on the liquid cooling system, and the existing methods are difficult to optimize the cooling flow according to the server load distribution. By establishing a three-dimensional transient heat flux density field in the server rack, the high heat load area can be accurately identified, and the coolant flow direction can be optimized through intelligent cooling strategies to achieve precise heat dissipation, reduce server energy consumption, and improve the heat dissipation efficiency and equipment stability of the data center.

[0081] The specific steps of S2 are as follows:

[0082] S2.1: Collect the real-time temperature value of each thermocouple according to the distributed temperature sensor network, generate a two-dimensional temperature field through the spatial interpolation algorithm, calculate the temperature changes of adjacent measuring points, and generate the winding temperature gradient distribution;

[0083] In this embodiment, the distributed temperature sensing network is composed of a plurality of high-precision thermocouples, which are arranged on the surface of the winding and key internal parts according to a preset distribution method to ensure the coverage and data accuracy of the temperature measurement;

[0084] Furthermore, since the temperature distribution inside the winding is often highly non-uniform, single-point measurement is difficult to accurately describe the overall thermal field changes of the winding. The Kriging interpolation method is used to fit the discrete measurement point data into a continuous two-dimensional temperature field, and combined with time step analysis, dynamic monitoring of temperature change trends can be achieved. The introduction of the spatial interpolation algorithm can not only fill the temperature data gaps between the measurement points, but also effectively suppress measurement errors and improve the continuity and accuracy of the temperature field.

[0085] Furthermore, after obtaining the two-dimensional temperature field, the temperature change rate of adjacent measuring points is calculated, the thermal gradient distribution on the winding surface is analyzed, and the winding temperature gradient field is obtained. The construction of the winding temperature gradient field is the key to the subsequent three-dimensional transient heat flux field calculation, because the change of the winding temperature gradient directly reflects the efficiency of local heat transfer and the potential overheating trend.

[0086] S2.2: collecting axial wavelength data of the rotating shaft and the winding parts according to the fiber grating sensor chain, decoupling the axial wavelength data according to the photoelastic effect and thermal expansion characteristics, and generating axial strain;

[0087] Specifically, because the change of strain directly affects the geometric dimensions of the winding and the shaft, and thus indirectly affects its heat transfer path and thermal conductivity, the accurate measurement of axial strain is crucial for the construction of a high-precision thermal model. Compared with the traditional mechanical strain measurement method, the fiber Bragg grating sensor chain not only has the advantages of high resolution and real-time performance, but also can adapt to high temperature and high pressure environments, ensuring the reliability and long-term stability of the measurement, providing accurate material strain parameters for the finite element thermal model, and improving the accuracy and applicability of the model calculation;

[0088] In this embodiment, the fiber Bragg grating sensor chain is arranged along the key positions of the rotating shaft and the winding to measure the axial wavelength change in real time. Since the winding is affected by temperature changes and mechanical loads during operation, its axial deformation is not only caused by thermal expansion, but also by electromagnetic forces, fluid dynamics effects and other factors. Therefore, when calculating the axial strain, the wavelength data of the fiber Bragg grating needs to be decoupled to distinguish the strain caused by pure thermal expansion from other stress effects;

[0089] Furthermore, the change in the reflected wavelength of the fiber Bragg grating is first used to correct the temperature drift effect through the known temperature sensing data, eliminating the direct influence of temperature on the wavelength change, ensuring the accuracy of the subsequent strain calculation. Then, based on the theory of photoelastic effect, the mapping relationship between thermal expansion and axial strain is constructed, and the strain interference caused by mechanical load is decoupled by numerical analysis method, so as to obtain the axial strain distribution caused only by thermal expansion.

[0090] S2.3: Collect the dielectric characteristic signal of the coolant according to the interdigital electrode sensor, and calculate the dielectric constant, loss factor and conductivity;

[0091] In this embodiment, the interdigital electrode sensor is installed at a key position of the coolant flow channel to monitor the dielectric characteristic parameters of the coolant in real time, including dielectric constant, loss factor and conductivity. These parameters can reflect the physical properties of the coolant and its heat transfer capacity. In particular, when the coolant ages, is contaminated or the flow rate changes, the dielectric properties will change significantly. Therefore, the measurement of these parameters can provide important real-time information for cooling system optimization.

[0092] Furthermore, the interdigital electrode sensor measures the impedance response of the coolant at different frequencies by applying a high-frequency AC electric field, and uses the impedance spectrum analysis method to extract the dielectric constant and loss factor. The change in dielectric constant can reflect the polarization ability of the coolant, thereby indirectly characterizing the molecular structure and thermal conductivity changes of the coolant, while the loss factor characterizes the degree of charge loss in the coolant, which is closely related to the thermal convection heat transfer efficiency. In addition, the measurement of conductivity records the conductivity of the coolant and evaluates its ion concentration level to determine whether the coolant has accumulated conductive impurities due to long-term use, affecting the heat transfer performance.

[0093] The specific steps of S3 are as follows:

[0094] S3.1: Refine the geometry of the digital pump into a finite element model with a specific mesh distribution;

[0095] In this embodiment, the construction of the finite element model needs to take into account both computational accuracy and computational efficiency. Therefore, when dividing the mesh, an adaptive meshing strategy based on local features is adopted, combined with an unstructured mesh refinement method, to ensure the accuracy of key parts while optimizing the overall computational cost.

[0096] Specifically, firstly, based on the CAD three-dimensional model of the digital pump, its key heat transfer structures are extracted, including windings, shafts, cooling chambers, shells and fluid channels. A multi-scale meshing method is adopted, and hexahedral meshes are used for high-density meshing in areas with large thermal gradient changes, such as the inside of the windings, the contact interface between the windings and the shell, and the boundary area between the coolant and the solid, to improve the calculation accuracy. For areas with relatively stable thermal gradients, such as the outer shell or cooling channels far away from the heat source, tetrahedral meshes are used to reduce the number of meshes to reduce the calculation burden. In addition, near the bearing seat and the shaft, due to the strong coupling effect between mechanical stress and thermal field, a local encryption strategy is adopted to associate the mesh size with the distribution of axial strain, ensuring that the calculation accuracy in this area will not lose key information due to mesh coarsening;

[0097] Furthermore, in order to solve the problem of accuracy loss at the heat transfer interface of the traditional meshing method, this embodiment adopts a boundary layer optimization strategy, especially at the interface where the winding contacts the coolant, and introduces a multi-layer boundary layer mesh structure;

[0098] Specifically, 3 to 5 layers of boundary layer grids with gradient thickness are established on the surface of the winding. The thickness of the first layer of grids is calculated according to the thickness of the fluid heat exchange boundary layer, and it is expanded outward in an exponential growth manner to more accurately capture the temperature gradient changes at the heat exchange interface. In addition, inside the coolant flow channel, a turbulent partitioning grid strategy is used to refine the high flow velocity area to accurately simulate the heat exchange capacity of the coolant, while in the low flow velocity area, the grid size is appropriately increased to optimize the calculation efficiency.

[0099] S3.2: According to the preset heat load operating conditions, the temperature distribution under each operating condition is recorded by inputting different heat powers to generate multiple sets of data sets;

[0100] In this embodiment, the preset of the heat load working condition is based on the typical operation scenarios of the digital pump, such as low flow and high load, high flow and low load, continuous operation, start-stop cycle and other different working conditions. Under each working condition, the heat source distribution inside the pump body is significantly different, so it is necessary to input the heat source item for different operating states;

[0101] Specifically, the thermal power in actual operation is simulated by controlling the current input of the motor windings, and the temperature field data is collected at different time steps to obtain the temperature rise law under different working conditions. At the same time, in order to enhance the generalization ability of the data set, this embodiment introduces a perturbation experiment, that is, during the thermal power input process, a small amplitude perturbation is applied to simulate the impact of external environmental changes (such as ambient temperature fluctuations, coolant flow rate changes) on the thermal field distribution of the digital pump, ensuring that the finite element model finally trained can adapt to different operating conditions;

[0102] Furthermore, in order to reduce experimental errors, a multi-point measurement method was used in the data acquisition process, that is, temperature sensors were arranged at different positions of the pump body, and the temperature data of unmeasured points were supplemented in combination with a spatial interpolation algorithm to ensure the integrity and accuracy of the data set.

[0103] S3.3: Initializing heat source terms and boundary conditions of the finite element model according to the multiple sets of data sets;

[0104] In this embodiment, the initialization of the heat source term needs to be calculated in combination with the winding structure, current distribution and material thermal conductivity to ensure that the finite element thermal model can accurately reflect the heat source distribution and heat transfer characteristics of the digital pump under different working conditions;

[0105] Specifically, the initialization of the heat source term first determines the local heating power based on the winding structure and current distribution. The winding is the main heat source of the digital pump, and its temperature rise mainly comes from electromagnetic loss, including copper loss and iron loss. To this end, this embodiment obtains the loss distribution of the winding under different current input conditions based on the finite element electromagnetic field calculation model, and uses it as the initial input parameter of the heat source term. In addition, considering the structural complexity of the winding, there are significant differences in the heat transfer paths of different coil layers. Therefore, this embodiment further introduces a hierarchical modeling method to divide the winding into multiple different heat source areas, and independently calculates the loss distribution for each area, thereby improving the accuracy of the thermal field calculation.

[0106] Furthermore, during the experiment, the steady-state temperature distribution of the winding under different input powers is measured and compared with the finite element calculation results. If there is an error, the error inversion method is used to optimize the input value of the heat source term. The sensitivity of the temperature field to the heat source term is calculated based on the adjoint matrix method, the key heat source distribution areas that affect the temperature error are identified, and the heat source input values ​​in these areas are optimized to make the simulated temperature field gradually approach the experimental data. In addition, in order to avoid local accumulation of errors, the global error minimization method is also used, that is, the global error of the calculated temperature field is optimized through the least squares optimization algorithm, thereby ensuring the rationality of the final heat source term.

[0107] In this embodiment, in terms of initialization of boundary conditions, different boundary heat transfer conditions are set according to the operating characteristics of the cooling system;

[0108] Specifically, at the contact interface between the pump housing and the environment, a convection heat transfer boundary is set, and its heat transfer coefficient is dynamically adjusted according to the coolant flow rate and ambient temperature to ensure that the heat dissipation capacity of the external cooling system can be truly reflected in the finite element calculation. For the inside of the winding, since its direct contact with the coolant is limited, a fixed heat flux boundary is set to simulate the process of heat dissipation from the winding to the outside;

[0109] Specifically, in view of the heat exchange characteristics of the coolant, the heat exchange boundary conditions are dynamically adjusted based on the coolant dielectric characteristic parameters. The heat exchange capacity of the coolant is affected by changes in flow rate, temperature and composition. Therefore, this embodiment measures the dielectric constant, electrical conductivity and loss factor of the coolant to calculate its heat exchange capacity and adjust the heat exchange boundary conditions in the finite element model in real time. For example, when the electrical conductivity of the coolant is measured to be reduced (indicating that the coolant is aged or contaminated), the equivalent thermal conductivity of the coolant will be automatically reduced, thereby truly reflecting the decrease in cooling efficiency and improving the adaptability of the model to the actual operating environment;

[0110] Furthermore, in the process of finite element calculation, the temperature deviation of the finite element model is calculated based on the actual temperature field measured experimentally, and the calculated temperature field is matched with the actual measured data by adjusting the boundary heat flux. This can effectively compensate for the calculation error caused by the uncertainty of material parameters or the complexity of fluid heat exchange in the finite element model and improve the accuracy of the calculation results.

[0111] S3.4: adjusting the finite element model through iterative optimization until the number of iterations reaches a preset number or the model reaches a convergence condition;

[0112] In this embodiment, the model calculation results are compared with the experimental data through the error analysis method. The error analysis mainly includes global error and local error. The global error is used to evaluate the deviation of the overall temperature field, while the local error is used to perform a detailed analysis on the high temperature gradient area. If the error exceeds the preset threshold, the heat source term, material parameters and boundary conditions are adjusted, and the temperature field is recalculated until the error converges to the allowable range;

[0113] Furthermore, in order to improve the convergence speed during the iteration process, this embodiment adopts an adaptive grid optimization method, that is, the grid distribution is refined in the high temperature gradient area to improve the calculation accuracy, and in the area where the temperature change is relatively stable, the number of grids is appropriately reduced to optimize the calculation efficiency.

[0114] The specific steps of S3.4 are as follows:

[0115] S3.4.1: Calculate the heat conduction equations corresponding to multiple sets of data using the finite element method based on the initialized heat source terms and boundary conditions;

[0116] In this embodiment, the calculation of the finite element thermal model is carried out based on the initialized heat source terms and boundary conditions. To ensure the accuracy of the calculation and the physical consistency of the model, a high-precision finite element mesh is first established based on the geometric structure of the digital pump, and the mesh is encrypted in the key heat source area to improve the calculation resolution. The initialized heat source terms are derived from the fitting calculation of the experimental measured values ​​and the operating parameters to ensure that the spatiotemporal distribution of the heat source terms conforms to the actual heating conditions of the digital pump under different loads. The boundary conditions are set based on the data collected by the sensor in real time, including the temperature of the winding surface, the heat transfer coefficient of the coolant, and the influence of the axial strain of the shaft on thermal expansion;

[0117] Specifically, in the solution process, the finite element method is used to solve the transient heat conduction equation, the time dimension is discretized using the time stepping method, and the temperature change of each grid unit is calculated in each time step to simulate the heat transfer path and the dynamic evolution trend of the temperature. In order to ensure the stability and accuracy of the calculation, an adaptive time stepping strategy is adopted, that is, when the temperature changes rapidly, the time step is automatically reduced to improve the accuracy of the numerical calculation; when the temperature change tends to be stable, the time step is appropriately increased to improve the calculation efficiency. In addition, in the process of spatial discretization, the local encrypted grid strategy is used to adaptively refine the grid in areas where the temperature gradient changes drastically (such as the interface between the winding and the coolant) to improve the calculation resolution of the high gradient area and prevent numerical errors caused by too coarse grids;

[0118] Furthermore, nonlinear material property input is used in the solution process, that is, the thermal conductivity, specific heat capacity and density of the material are dynamically adjusted with temperature changes, so that it can truly reflect the heat transfer characteristics of the digital pump under different working conditions, enhance the generalization ability of the model, make it applicable to simulations under different loads and cooling conditions, and improve the accuracy and reliability of the prediction;

[0119] Specifically, in the material property input stage, a temperature dependence model of the material's thermophysical parameters is established so that it can be updated with temperature changes. For metal parts (such as pump bodies and rotating shafts), their thermal conductivity usually shows a nonlinear downward trend with increasing temperature. Therefore, in finite element calculations, the thermal conductivity of metal materials is dynamically adjusted through interpolation or function fitting methods to ensure that the thermal conductivity at different temperatures can be correctly input during the calculation process and improve the calculation accuracy. Similarly, the change in specific heat capacity directly affects the time scale of heat transfer. When the temperature rises, the specific heat capacity usually shows an increasing trend. Therefore, a temperature dependence model of specific heat capacity is established so that it can be dynamically updated during the calculation process to ensure that the storage and transfer of heat conform to the real heat capacity characteristics of the material. In addition, similar methods are also used to dynamically adjust the thermophysical parameters of the coolant, such as density, viscosity and thermal conductivity. In particular, when the dielectric constant changes, the equivalent heat transfer coefficient model is constructed so that the heat transfer capacity of the coolant under different dielectric states can be correctly reflected in the thermal model.

[0120] S3.4.2: Evaluate the energy conservation of the heat conduction equation and calculate the transmission loss of heat flux between the grid elements of the finite element model;

[0121] In this embodiment, in order to ensure the physical accuracy of the finite element calculation, it is necessary to evaluate the energy conservation of the calculated temperature field, that is, to verify whether the heat input, output and storage inside the system satisfy the law of energy conservation within a time step. To this end, the heat flux calculation is performed on each grid unit to analyze the heat transfer between the units;

[0122] Specifically, the input heat flux and output heat flux of each grid unit are calculated, and the deviations from the theoretical predictions are compared. If the deviation exceeds the set threshold, it indicates that the calculation of the area may have error accumulation or unreasonable grid division problems;

[0123] Furthermore, in order to accurately evaluate the transfer loss value, the heat flow balance of each grid unit is calculated, that is, the difference between the heat entering the grid unit and the heat transferred out per unit time, and the entire calculation area is integrated to ensure that the total energy change of the entire system matches the energy input by the heat source term. If there is a large deviation, it may be due to unreasonable boundary condition settings, excessively coarse grids, or numerical errors caused by time stepping.

[0124] S3.4.3: Determine whether the number of iterations reaches a preset number or whether the transmission loss value reaches a convergence condition;

[0125] In this embodiment, in order to ensure the convergence of the finite element calculation results, it is necessary to set a reasonable convergence criterion to determine whether the calculation has reached a stable state. There are two main ways to make the judgment. One is through a fixed number of iterations, that is, when the set maximum number of iterations is reached, even if the calculation has not yet converged, the calculation is forced to terminate to prevent the calculation time from being too long and causing resource waste; the other is through the convergence standard of the heat flux transfer loss value, that is, if the heat flux change rate of two adjacent iterative calculations is less than the set threshold, it is considered that the system has reached a stable state and no subsequent iterations are performed. The combination of these two standards can not only ensure that the calculation is completed within a reasonable time, but also ensure that the heat flux density calculation will not cause error accumulation due to numerical oscillations.

[0126] S3.4.4: If none of the above is achieved, calculate the heat flux density change rate based on the loss distribution of the transfer loss value, adjust the meshing of the finite element model based on the heat flux density change rate, and re-evaluate;

[0127] In this embodiment, in order to improve the calculation accuracy and reduce the accumulation of numerical errors, when it is found that the calculation has not converged, it is necessary to optimize the grid division;

[0128] Specifically, an adaptive meshing method based on the heat flux density change rate is used, that is, in the area where the heat flux density change rate is large, the mesh density is increased to improve the calculation accuracy of the area, and in the area where the heat flux density change is small, the mesh density is appropriately reduced to reduce the calculation amount and improve the calculation efficiency;

[0129] Furthermore, the spatial distribution of the transfer loss value is first analyzed, the areas with large heat transfer losses are identified, and the rate of change of heat flux density in these areas is calculated. If the rate of change exceeds the set threshold, the mesh of the area is encrypted and the time step parameter is adjusted to improve the calculation accuracy. The mesh encryption method adopts local encryption technology, that is, the mesh is refined in the key area, while the original mesh size is maintained in the low gradient area far away from the heat source to balance the calculation accuracy and computing resource consumption. In addition, after re-evaluation, energy conservation analysis needs to be performed again to ensure that the optimized mesh division will not introduce new errors. The mesh density is adjusted in real time according to the calculation results, rather than fixing the mesh division in the initial stage, so as to improve the flexibility of the calculation and reduce unnecessary calculations, so that the finite element thermal model can maintain high accuracy and optimize the calculation efficiency, thereby improving the operational stability of the entire system.

[0130] See also Figure 3 , a schematic diagram of the overheating area positioning process according to an embodiment of the present invention, the specific steps of S4 are as follows:

[0131] S4.1: Modify the boundary conditions according to the axial strain and coolant dielectric property parameters;

[0132] Specifically, since the shaft will produce axial strain due to thermal expansion when running under high load, this strain will cause the stress distribution inside the material to change, thereby affecting the heat transfer capacity of the local area. The axial strain data of the shaft and winding are collected by fiber grating sensors, and the equivalent thermal conductivity of different parts is calculated in combination with the thermal expansion effect, and the heat transfer coefficient in the finite element model is adjusted to correct the change in thermal resistance caused by thermal expansion. In addition, the dielectric properties of the coolant are closely related to its thermal conductivity. The dielectric constant, loss factor and conductivity of the coolant are measured in real time by the interdigital electrode sensor, and based on the experimental calibration data, these parameters are mapped to the key thermophysical parameters such as the equivalent thermal conductivity, viscosity and specific heat capacity of the coolant, so as to achieve real-time correction of the heat exchange capacity of the coolant.

[0133] S4.2: Calculate the three-dimensional transient temperature field according to the corrected boundary conditions and the winding temperature gradient distribution;

[0134] S4.3: discretize the three-dimensional transient temperature field, calculate the sensitivity matrix of the heat source term, reconstruct the sensitivity matrix according to Fourier's law, and calculate the three-dimensional transient heat flux density field;

[0135] In this embodiment, the physical structure of the digital pump is divided into a finite number of grid cells through spatial discretization, each of which represents a small area with uniform material properties and temperature distribution; the continuous time process is divided into a finite number of time steps through temporal discretization, each of which corresponds to a static snapshot of the temperature field in the model, thereby facilitating the numerical solution of the evolution law of the temperature field at different time points;

[0136] In this embodiment, the sensitivity matrix is ​​a two-dimensional matrix that describes the influence of the heat source term on the temperature field of the grid unit, and each element thereof represents the contribution of the heat source term to the temperature of the grid unit:

[0137] Specifically, in order to expand the two-dimensional sensitivity matrix to the three-dimensional transient heat flux density field, the temperature distribution results within each grid cell are first used to calculate the temperature gradient in each direction through the connection relationship between the grid cells. This process involves identifying the temperature difference between the grid cells and decomposing it into each direction in the three-dimensional space. The calculation of the temperature gradient relies on the basic principle of Fourier's law, that is, heat is always transferred in the direction of the temperature gradient. Therefore, the temperature gradient provides a directional basis for the calculation of the three-dimensional transient heat flux density field;

[0138] Furthermore, by combining the sensitivity matrix with the temperature gradient, the local heat flux density distribution is calculated in each grid unit. The weight value in the sensitivity matrix determines the adjustment ratio of the amplitude and direction of the heat flux density, while the temperature gradient provides the specific path information of the heat transfer. This combination method enables the heat flux density to not only reflect the direction of the temperature gradient, but also to combine the influence of the change of the heat source term, showing a dynamically adjusted three-dimensional field distribution;

[0139] Furthermore, after completing the heat flux calculation for each grid unit, it is extended to the three-dimensional structure of the entire finite element model. To achieve this goal, it is necessary to coordinate the heat flux transfer between grid units so that the heat flux field has continuity and physical consistency in three-dimensional space. The spatial distribution of heat flux is further optimized through Fourier's law to ensure that the dynamic changes of the global heat flux field in time and space can accurately reflect the evolution of the temperature field.

[0140] Furthermore, the three-dimensional transient heat flux field is constructed by integrating the results of sensitivity analysis, temperature gradients, and dynamic changes in heat source terms. This field distribution clearly depicts the heat transfer path during the operation of the digital pump, and can effectively locate local areas where heat flux is concentrated, providing an accurate basis for determining potential overheating areas. The entire method uses Fourier's law to convert temperature gradients into heat flux, and at the same time ensures that the influence of heat source terms can be truly presented in space through the three-dimensional expansion of the sensitivity matrix, thereby achieving high-precision reconstruction of the heat flux field.

[0141] S4.4: Locate the local overheating area according to the three-dimensional transient heat flux density field;

[0142] In this embodiment, the local overheating area is located based on the abnormal analysis of the three-dimensional transient heat flux density field. By analyzing the spatial distribution and time variation characteristics of the heat flux density, the area where overheating may occur is determined. First, the average heat flux distribution of the entire heat flux density field is calculated, and the area where the local heat flux density is significantly high is extracted. For the abnormal heat flux density area, the energy balance analysis method is used to calculate the difference between the input heat flux and the output heat flux of the area. If the input heat flux is much greater than the output heat flux, it indicates that there may be heat accumulation in the area.

[0143] Furthermore, combined with time series analysis, it is detected whether the heat flux density in the area has a continuous growth trend. If the heat flux density in the area continues to increase in multiple time steps, it is further confirmed as a possible overheating area. In order to improve the positioning accuracy, while determining the overheating area, the material properties of the finite element thermal model are combined to analyze the thermal diffusion capacity of the area. If the thermal diffusion capacity of the area is low, it means that the heat may be difficult to dissipate, thereby increasing the risk of overheating. Finally, all areas that meet the overheating judgment conditions are marked as local overheating areas.

[0144] The specific steps of S4.1 are as follows:

[0145] S4.1.1: Obtain the initial length of the shaft and the initial temperature rise of the shaft of the finite element model, calculate the thermal expansion of the shaft, and update the convection heat transfer coefficient according to the thermal expansion;

[0146] In practical applications, the expansion of the shaft will not only change its own mechanical structural parameters, but also affect the convective heat transfer characteristics of the fluid around it. If the shaft expands, its surface area will increase, and the surface laminar state may change, causing the local heat transfer coefficient to change. Therefore, when the shaft is heated, it will expand axially and radially, causing the contact area between the coolant and the shaft to change, while affecting the boundary layer thickness of the fluid, thereby changing the convective heat transfer coefficient;

[0147] In this embodiment, in order to accurately evaluate the thermal expansion effect of the shaft due to the temperature increase during operation, and the effect of thermal expansion on the cooling effect, it is first necessary to obtain the initial length and initial temperature rise of the shaft. These parameters are not only the basic data for calculating the thermal expansion of the shaft, but also the key input for adjusting the dynamic boundary conditions in the finite element thermal model. The initial length of the shaft determines the extent of its geometric change under high-temperature operation, while the initial temperature rise is used to evaluate the contribution of the thermal expansion of the material to the overall structural deformation;

[0148] Specifically, the axial strain of the shaft is monitored in real time by the fiber grating sensor, and the thermal expansion of the shaft is calculated in combination with the thermal expansion coefficient of the material. The fiber grating sensor can accurately measure the axial strain without interfering with the normal operation of the pump body, and decouple the influence of mechanical load through strain data to extract the deformation component caused only by thermal expansion;

[0149] The thermal expansion calculation formula is:

[0150] ,

[0151] in, Indicates the thermal expansion of the shaft, is the coefficient of thermal expansion, Indicates the initial length of the shaft. Indicates the initial temperature rise of the shaft, represents the axial stress, represents the elastic modulus, represents Poisson's ratio;

[0152] Furthermore, after the thermal expansion amount is obtained, its effect on the heat exchange efficiency of the coolant needs to be further calculated. The thermal expansion of the shaft may lead to an increase in the heat exchange surface area, thereby improving the heat exchange efficiency, but on the other hand, if the expansion of the shaft causes the cooling channel to shrink, it may increase the flow resistance and reduce the flow rate of the coolant, thereby affecting the local heat exchange effect. Therefore, in this embodiment, based on the real-time measured thermal expansion data, the convective heat transfer coefficient in the finite element thermal model is dynamically adjusted to reflect the heat exchange capacity of the coolant under actual working conditions. Specifically, combined with the calculated thermal expansion amount of the shaft, the fluid-solid heat exchange boundary conditions are corrected so that it can dynamically adapt to the geometric changes caused by thermal expansion and contraction, thereby ensuring the stability of the heat exchange efficiency;

[0153] The calculation formula of the convective heat transfer coefficient is:

[0154] ,

[0155] in, represents the corrected convective heat transfer coefficient, represents the initial convective heat transfer coefficient, represents the experience adjustment coefficient, Indicates the thermal expansion of the shaft, Indicates the radius of the rotating shaft;

[0156] S4.1.2: Obtain the dielectric constant of the matrix material of the finite element model, calculate the volume fraction of the nanoparticles, and update the equivalent thermal conductivity of the coolant based on the volume fraction;

[0157] In this embodiment, in order to improve the heat exchange capacity of the coolant and optimize the thermal conductivity of the coolant in a complex flow field, it is necessary to calculate the volume fraction of the nanoparticles in real time and update the equivalent thermal conductivity of the coolant based on this. The thermal conductivity of the coolant determines its overall heat exchange efficiency for the pump body to a large extent. Especially under high-temperature operating conditions, changes in the thermal conductivity of the coolant will directly affect the heat dissipation effect of the windings, bearings and shafts. Therefore, this embodiment uses an interdigital electrode sensor to measure the dielectric properties of the coolant, and infers the concentration and volume fraction of the nanoparticles in the coolant through its change trend;

[0158] Specifically, the dielectric constant of the coolant is first measured using an interdigital electrode sensor, and the volume fraction of nanoparticles in the coolant is calculated based on the known dielectric constant of the matrix material. This process enables the system to dynamically obtain the actual concentration of nanoparticles during operation without relying on laboratory testing, thereby achieving online monitoring.

[0159] The volume fraction of nanoparticles is calculated as:

[0160] ,

[0161] in, represents the volume fraction of nanoparticles, represents the equivalent dielectric constant of the coolant, represents the dielectric constant of the matrix material, represents the dielectric constant of the nanoparticles;

[0162] Furthermore, after calculating the volume fraction of the nanoparticles, the equivalent thermal conductivity of the coolant needs to be further corrected to ensure that the thermal model can accurately describe the heat transfer performance of the coolant. The addition of nanoparticles will change the microscopic heat transfer mechanism of the coolant, allowing heat to be transferred more effectively through the solid-liquid interface. However, since the distribution state of nanoparticles in the fluid is not fixed, they may present different dispersion or agglomeration states under different flow rates, shear stresses and temperature gradients. Therefore, when calculating the equivalent thermal conductivity, it is necessary to consider the dynamic behavior of nanoparticles under actual flow conditions.

[0163] This embodiment establishes a dynamic correction model of nanoparticle volume fraction and coolant equivalent thermal conductivity by combining fluid flow rate, temperature and particle size. When the coolant flow rate is high, the dispersion of the particles is better, and the improvement effect of equivalent thermal conductivity is more obvious. However, at low flow rate or turbulent state, the particles may affect the overall heat transfer capacity due to collision or agglomeration effect. Therefore, when calculating the equivalent thermal conductivity, the Brownian motion of nanoparticles, the thermal resistance of the particle-liquid interface and the particle agglomeration effect are comprehensively considered to ensure that the calculation results can accurately reflect the actual working conditions.

[0164] The calculation formula of the equivalent thermal conductivity of the coolant is:

[0165] ,

[0166] in, represents the corrected equivalent thermal conductivity of the coolant, represents the thermal conductivity of the matrix material, represents the thermal conductivity of the nanoparticles, n represents the particle shape factor, It represents the correction factor related to flow velocity, which determines the influence of flow state (laminar or turbulent) on thermal conductivity. Reynolds number, describing the state of fluid flow, represents the temperature correction factor, which describes the effect of temperature gradient on nanoparticle distribution and heat transfer. Indicates local temperature change, Indicates the average temperature of the coolant;

[0167] The specific steps of S4.3 are as follows:

[0168] S4.3.1: Discretize the three-dimensional transient temperature field by discrete heat conduction control equations, wherein the discretization includes spatial discretization and temporal discretization;

[0169] In this embodiment, the spatial discretization uses the finite element method to divide the internal structure of the digital pump into multiple finite volume grid units, each unit represents an independent calculation area, and its heat conduction behavior is jointly determined by the state of the surrounding adjacent units. When dividing the grid, it is preferred to use non-uniform adaptive grid refinement technology to increase the grid density in areas where the temperature gradient changes drastically (such as the junction of windings, bearings and coolant) to improve the accuracy of local heat transfer calculations, and use coarser grids in areas where the temperature field is relatively uniform to improve calculation efficiency;

[0170] In this embodiment, time discretization also adopts an implicit time stepping method. By introducing a dynamic step adjustment strategy, the time step size is automatically adjusted according to the different temperature change rates. A smaller time step is used in the rapid heating stage to improve the calculation accuracy, and the time step is appropriately increased when the temperature changes slowly to reduce the amount of calculation.

[0171] S4.3.2: After the spatial discretization is completed, a heat balance equation is established on each grid cell, and the temperature evolution trend of the temperature field is gradually solved according to the time discretization result. In each time step, the heat balance equation is updated according to the temperature evolution trend of the previous time step;

[0172] In this embodiment, the establishment of the heat balance equation is based on the principle of energy conservation, taking into account the heat transfer, heat source terms and boundary heat dissipation of each grid unit;

[0173] Specifically, the heat change of each grid unit is jointly affected by the heat conduction and convection heat transfer of the adjacent units and its own heat source term. Therefore, when establishing the heat balance equation, it is necessary to comprehensively consider the multi-physics field coupling effect, including the Joule heat of the winding, the convection heat transfer of the fluid, and the thermal expansion effect caused by the axial strain;

[0174] In this embodiment, each time step will update the heat transfer coefficient, heat source term strength and boundary heat dissipation conditions of the grid unit based on the current temperature distribution, so that the temperature evolution process can reflect the dynamic operation state of the digital pump in real time. Through this iterative solution method, the calculation accuracy can be effectively improved, and the physical consistency of the temperature distribution can be ensured, avoiding the accumulation of calculation errors caused by too large time steps or fixed parameters.

[0175] S4.3.3: Apply a unit change to each heat source term according to the heat balance equation, calculate the temperature contribution of the heat source term based on the change results, and generate a sensitivity matrix;

[0176] In this embodiment, in order to accurately capture the influence of the heat source term on the temperature field, the perturbation analysis method is used to numerically differentiate the heat balance equation, gradually adjust the size of the heat source term, and observe its influence on the temperature change of each grid unit to construct a mapping relationship between the heat source term and the temperature distribution. Since the heat source term has different influences on the temperature field at different locations, the sensitivity matrix needs to finely distinguish the influence range of different heat source terms on the temperature to ensure that it can accurately reflect the spatial distribution characteristics of the heat conduction path;

[0177] Furthermore, in order to improve the accuracy of sensitivity calculation, the adjoint matrix optimization method is used to perform weighted calculation on the areas with stronger influence of the heat source term, so that the sensitivity matrix can not only reflect the direct contribution of the heat source term, but also quantify the diffusion characteristics of heat in the local area.

[0178] S4.3.4: Map the row index and column index of the sensitivity matrix to the three-dimensional coordinates of the grid cell, and convert each element of the matrix into a sensitivity tensor using Fourier's law according to the mapping result;

[0179] In this embodiment, in order to expand the two-dimensional sensitivity matrix to the three-dimensional heat flux density field, it is first necessary to establish a mapping relationship between the sensitivity matrix and the finite element grid coordinates. This process determines the position distribution of each element of the sensitivity matrix in the three-dimensional grid by numbering the grid cells and combining their spatial coordinate information;

[0180] Furthermore, based on Fourier's law, the heat flux is calculated using the temperature gradient and corrected in combination with the sensitivity matrix to obtain a more accurate heat flux distribution. The adaptive gradient optimization method is used to perform local optimization on areas with large temperature gradients to reduce discrete errors and ensure the accuracy of heat flux calculation.

[0181] S4.3.5: Calculate the heat flux density of each grid according to the sensitivity tensor and the temperature gradient corresponding to the grid unit, aggregate all the heat flux densities, and generate a three-dimensional transient heat flux density field;

[0182] In this embodiment, in order to ensure that the calculation results of the heat flux density field are consistent with physical reality, the sensitivity tensor is first normalized to eliminate the influence of the weight difference between different heat source terms on the calculation results;

[0183] Furthermore, when calculating the heat flux, the spatial variation of thermal conductivity is taken into account, especially in the case of non-uniform distribution of materials, and the local thermal conductivity is dynamically adjusted to reflect the real heat conduction characteristics;

[0184] Furthermore, in order to optimize the temporal continuity of the heat flux density field, a time series filtering algorithm is used to smooth the heat flux density data of continuous time steps to reduce the numerical oscillation caused by calculation errors. Finally, through global aggregation, the heat flux densities of all grid cells are synthesized to obtain a complete three-dimensional transient heat flux density field, providing accurate input data for the subsequent local overheating area positioning.

[0185] The specific steps of S4.4 are as follows:

[0186] S4.4.1: Analyze the distribution of heat flux density, identify the concentrated areas and flow abnormalities in the heat flow direction, and screen out the heat accumulation points;

[0187] S4.4.2: Based on the heat accumulation point, calculate the difference between the input heat flow and the output heat flow of the area to determine whether there is a heat flow imbalance;

[0188] S4.4.3: If heat flow imbalances exist, mark them as areas of local overheating.

[0189] Example 2

[0190] See also Figure 4 , the present invention provides an embodiment: a digital pump operation system, the system comprising a data generation module, a model training module, a regional positioning module and a cooling control module;

[0191] The data generation module is used to generate winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters according to the collected digital pump sensor data;

[0192] The model training module is used to train the finite element thermal model. The training includes performing finite element meshing on the geometric structure of the digital pump, constructing initial boundary conditions, and inputting thermal power data under different thermal load conditions to generate a training data set. The model training module is also used to iteratively optimize the finite element thermal model, adjust heat source terms, boundary conditions and meshing until the model meets convergence conditions;

[0193] The regional positioning module is used to input the winding temperature gradient distribution, axial strain and coolant dielectric property parameters into a preset finite element thermal model, correct the boundary conditions through the adjoint matrix method, reconstruct the three-dimensional transient heat flux density field, and locate the local overheating area;

[0194] The cooling control module is used to receive the local overheating area information output by the area positioning module, and select a cooling strategy that adapts to the current operating state from a predefined cooling mode library.

[0195] The regional positioning module includes:

[0196] The temperature field calculation unit is used to calculate the three-dimensional transient temperature field according to the modified boundary conditions and the winding temperature gradient distribution in combination with the finite element thermal model, and iteratively solve the temporal evolution process of the temperature field using the time stepping method;

[0197] The sensitivity analysis unit is used to generate a sensitivity matrix using the heat source term perturbation method after the temperature field calculation is completed, and to evaluate the contribution of the heat source term to the temperature field;

[0198] The heat flux density field calculation unit is used to reconstruct the sensitivity matrix based on Fourier's law, and calculate the heat flux density of each grid in combination with the temperature gradient of the grid unit to generate a three-dimensional transient heat flux density field;

[0199] The overheating area identification unit is used to analyze the time-series changes of the heat flux density field, extract the areas with large heat flux density gradient, and calculate the equilibrium state of the input heat flux and output heat flux of the local grid unit. If the heat flux input of a certain area is much greater than the output, the area is marked as a potential overheating area.

[0200] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A digital pump operation method, characterized in that: The operation method comprises: Generate winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters based on the collected digital pump sensor data; The winding temperature gradient distribution, axial strain and coolant dielectric property parameters are input into the preset finite element thermal model, the boundary conditions are corrected by the adjoint matrix method, the three-dimensional transient heat flux density field is reconstructed, and the local overheating area is located; Select cooling mode from predefined mode library and generate operation control instructions; The training process of the finite element thermal model includes: Refining the geometry of the digital pump into a finite element model with a mesh distribution; According to the preset heat load operating conditions, the temperature distribution under each operating condition is recorded by inputting different heat powers to generate multiple sets of data sets; Initialize heat source terms and boundary conditions of the finite element model according to the plurality of data sets; The finite element model is adjusted through iterative optimization until the number of iterations reaches a preset number or the model reaches a convergence condition; The method of locating the local overheating area comprises: The boundary conditions are modified according to the axial strain and the dielectric characteristic parameters of the coolant; Calculate the three-dimensional transient temperature field based on the corrected boundary conditions and the winding temperature gradient distribution; Discretizing the three-dimensional transient temperature field, calculating the sensitivity matrix of the heat source term, reconstructing the sensitivity matrix by Fourier's law, and calculating the three-dimensional transient heat flux density field; The local overheating area is located according to the three-dimensional transient heat flux density field.

2. A digital pump operation method according to claim 1, characterized in that: The generating of winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters includes: The real-time temperature value of each thermocouple is collected according to the distributed temperature sensor network, and a two-dimensional temperature field is generated through a spatial interpolation algorithm. The temperature changes of adjacent measuring points are calculated to generate the winding temperature gradient distribution. The axial wavelength data of the rotating shaft and the winding parts are collected according to the fiber grating sensor chain, and the axial wavelength data is decoupled to generate the axial strain; The dielectric characteristic signal of the coolant is collected according to the interdigital electrode sensor, and the dielectric constant, loss factor and conductivity are calculated.

3. A digital pump operation method according to claim 1, characterized in that: The step of adjusting the finite element model by iterative optimization includes: According to the initialized heat source terms and boundary conditions, the heat conduction equations corresponding to multiple sets of data are calculated by the finite element method; Evaluate the energy conservation of the heat conduction equation and calculate the transmission loss value of the heat flux between the grid units of the finite element model; Determining whether the number of iterations reaches a preset number or whether the transmission loss value reaches a convergence condition; If neither is achieved, the heat flux density change rate is calculated according to the loss distribution of the transfer loss value, the mesh division of the finite element model is adjusted according to the heat flux density change rate, and the evaluation is re-performed.

4. A digital pump operation method according to claim 1, characterized in that: The modifying of the boundary conditions according to the axial strain and the dielectric characteristic parameters of the coolant includes: Obtain the initial length and initial temperature rise of the shaft of the finite element model, and calculate the thermal expansion of the shaft; updating the convection heat transfer coefficient according to the thermal expansion amount; Obtain the dielectric constant of the matrix material of the finite element model and calculate the volume fraction of nanoparticles; The equivalent thermal conductivity of the coolant is updated according to the volume fraction.

5. A digital pump operation method according to claim 1, characterized in that: The method of calculating the three-dimensional transient heat flux density field comprises: The three-dimensional transient temperature field is discretized by using a discrete heat conduction control equation, wherein the discretization includes spatial discretization and temporal discretization; After the spatial discretization is completed, the heat balance equation is established on each grid unit, and the temperature evolution trend of the temperature field is gradually solved according to the time discretization result. In each time step, the heat balance equation is updated according to the temperature evolution trend of the previous time step; A unit change is applied to each heat source term according to the heat balance equation, and the temperature contribution of the heat source term is calculated based on the change result to generate a sensitivity matrix; Map the row index and column index of the sensitivity matrix to the three-dimensional coordinates of the grid unit, and convert each element of the matrix into a sensitivity tensor through Fourier's law according to the mapping result; The heat flux density of each grid is calculated according to the sensitivity tensor and the temperature gradient corresponding to the grid unit, and all the heat flux densities are aggregated to generate a three-dimensional transient heat flux density field.

6. A digital pump operation method according to claim 1, characterized in that: Locating a local overheating area according to the three-dimensional transient heat flux density field includes: Analyze the distribution of heat flux density, identify the concentrated areas and abnormal flow areas of heat flow direction, and screen out heat accumulation points; Calculating the difference between the input heat flow and the output heat flow of the area corresponding to the heat accumulation point to determine whether there is heat flow imbalance; If there is an imbalance in heat flow, it is marked as a local overheating area.

7. A digital pump operation system, used to implement a digital pump operation method as claimed in any one of claims 1 to 6, characterized in that: The system includes a data generation module, a model training module, a regional positioning module and a cooling control module; The data generation module is used to generate winding temperature gradient distribution, axial strain and coolant dielectric characteristic parameters according to the collected digital pump sensor data; The model training module is used to train the finite element thermal model. The training includes performing finite element meshing on the geometric structure of the digital pump, constructing initial boundary conditions, and inputting thermal power data under different thermal load conditions to generate a training data set. The model training module is also used to iteratively optimize the finite element thermal model, adjust heat source terms, boundary conditions and meshing, until the model meets convergence conditions; The regional positioning module is used to input the winding temperature gradient distribution, axial strain and coolant dielectric property parameters into a preset finite element thermal model, correct the boundary conditions through the adjoint matrix method, reconstruct the three-dimensional transient heat flux density field, and locate the local overheating area; The cooling control module is used to receive the local overheating area information output by the area positioning module, and select a cooling strategy that adapts to the current operating state from a predefined cooling mode library.

8. A digital pump operation system according to claim 7, characterized in that: The regional positioning module includes: The temperature field calculation unit is used to calculate the three-dimensional transient temperature field according to the modified boundary conditions and the winding temperature gradient distribution in combination with the finite element thermal model, and iteratively solve the temporal evolution process of the temperature field using the time stepping method; The sensitivity analysis unit is used to generate a sensitivity matrix using the heat source term perturbation method after the temperature field calculation is completed, and to evaluate the contribution of the heat source term to the temperature field; The heat flux density field calculation unit is used to reconstruct the sensitivity matrix based on Fourier's law, and calculate the heat flux density of each grid in combination with the temperature gradient of the grid unit to generate a three-dimensional transient heat flux density field; The overheating area identification unit is used to analyze the distribution of heat flux density, identify the concentrated area and flow abnormality area of ​​the heat flow direction, and screen out the heat accumulation points; calculate the difference between the input heat flux and the output heat flux in the area corresponding to the heat accumulation point, and determine whether there is heat flow imbalance; if there is heat flow imbalance, mark it as a local overheating area.

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