High-precision high-temperature centrifugal pump performance index prediction method and device, electronic equipment

Abstract

This invention discloses a high-precision method, device, and electronic equipment for predicting the performance indicators of a high-temperature centrifugal pump. The method includes: constructing a density coupling function between medium density and temperature / pressure based on the ideal gas law and the Tammann equation; embedding the density coupling function into the FLUENT solver via a user-defined function (UDF) to dynamically correct the medium properties of the computational unit in real time during unsteady numerical simulation, obtaining corrected property parameters; performing unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump under test using FLUENT based on the corrected property parameters, obtaining input shaft power, internal flow field pressure, velocity, and transient flow field data; and calculating the head and efficiency based on the input shaft power, pressure, velocity, and fluid inlet / outlet head. This method enables accurate prediction of pump performance indicators.

Description

Technical Field

[0001] This application relates to the field of fluid machinery numerical simulation and performance prediction technology, and in particular to a high-precision method and device for predicting the performance indicators of a high-temperature centrifugal pump, as well as electronic equipment. Background Technology

[0002] High-temperature centrifugal pumps are core equipment in nuclear, chemical, and solar thermal power generation systems. The media they transport (such as molten salt and liquid metal) typically operate under high-temperature (>300℃) and high-pressure environments. Under these extreme conditions, the medium density is no longer a constant, but rather a strong function of temperature (T) and pressure (p). Significant changes in the medium's physical properties directly alter the flow structure within the pump, energy conversion efficiency, and fluid excitation force, thus decisively impacting the pump's performance and reliability.

[0003] Currently, the performance prediction of high-temperature centrifugal pumps in engineering projects generally has the following limitations: 1) Simplification of physical properties: Most simulations still use simple empirical formulas that only consider the effect of temperature or average density, failing to fundamentally couple the combined effects of temperature and pressure; 2) Theoretical gaps: There is a lack of property prediction models with a solid thermodynamic foundation, especially in the supercritical or highly compressible regions, where the ideal gas law has large deviations, while relying entirely on the real gas law is too complex and the parameters are difficult to obtain. 3) Predicting chain breakage: Most existing methods stop at predicting external characteristics and fail to establish a complete analysis chain from accurate flow field to structural vibration. Summary of the Invention

[0004] To address the aforementioned issues, this application provides a method, apparatus, and electronic device for predicting the performance indicators of a high-precision high-temperature centrifugal pump. The core of this method is to couple the ideal gas law with the Tammann equation to construct a density coupling function, and then deeply integrate it into the FLUENT simulation to achieve accurate prediction of the pump's performance under all operating conditions, from external characteristics to internal flow field.

[0005] According to a first aspect of the embodiments of this application, a method for predicting the performance indicators of a high-precision high-temperature centrifugal pump is provided, comprising: Based on the ideal gas law and the Tammann equation, a density coupling function is constructed for the medium density ρ and temperature T and pressure p: ; in, The corrected density of the medium; α is the fitting coefficient introduced by correcting the theoretical deviation between the two equations; p is the liquid phase constant. c and T c These are the liquid phase pressure and temperature coefficient, respectively. It is the critical temperature coefficient; The density coupling function is embedded into the FLUENT solver through a user-defined function (UDF) to dynamically correct the medium properties of the computational unit in real time during the unsteady numerical simulation process, thereby obtaining the corrected property parameters. Based on the corrected physical property parameters, FLUENT was used to perform unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump to be predicted, and the input shaft power, internal flow field pressure, velocity and transient flow field data were obtained. The head and efficiency are calculated based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads.

[0006] Optionally, the simultaneous equation of state for the ideal gas and the Tammann equation is as follows: The Tammann equation is considered as a compensation and correction term for the ideal gas equation of state under high pressure and high temperature conditions. Through dimensional analysis and coefficient comparison, the two equations are integrated into the density coupling function.

[0007] Optionally, the optimal value of the fitting coefficient is determined by minimizing the root mean square error between the calculated value of the density coupling function and the experimentally measured density values ​​under different (T, p) conditions.

[0008] Optionally, the dynamic correction is achieved by real-time monitoring of the local temperature T of each computational unit in the flow field. i and local pressure p i It then calls the UDF to calculate its corresponding real-time density ρ. m (T i , p i This is achieved through ).

[0009] Optionally, based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads, the head and efficiency are calculated, including: Substitute the pressure, velocity, and fluid inlet and outlet head into the head calculation formula to calculate the head at each operating point. Based on the input shaft power, combined with the head, flow rate, and density, the efficiency at each operating point is calculated using the efficiency formula.

[0010] According to a second aspect of the embodiments of this application, a high-precision high-temperature centrifugal pump performance index prediction device is provided, comprising: The module is used to construct a density coupling function between the medium density ρ and temperature T and pressure p, based on the ideal gas law and the Tammann equation. ; in, The corrected density of the medium; α is the fitting coefficient introduced by correcting the theoretical deviation between the two equations; p is the liquid phase constant. c and T c These are the liquid phase pressure and temperature coefficient, respectively. It is the critical temperature coefficient; The correction module is used to embed the density coupling function into the FLUENT solver through a user-defined function (UDF) to dynamically correct the medium properties of the computational unit in real time during the unsteady numerical simulation process, and obtain the corrected property parameters. The simulation module is used to perform unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump to be predicted using FLUENT based on the corrected physical property parameters, and obtain the input shaft power, internal flow field pressure, velocity and transient flow field data. The curve generation module is used to calculate the head and efficiency based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads.

[0011] According to a third aspect of the embodiments of this application, an electronic device is provided, comprising: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors perform the method as described in the first aspect.

[0012] According to a fourth aspect of the embodiments of this application, a computer-readable storage medium is provided that stores computer instructions thereon, which, when executed by a processor, implement the steps of the method as described in the first aspect.

[0013] The technical solutions provided by the embodiments of this application may include the following beneficial effects: 1) Strong theoretical innovation: For the first time, the ideal gas law and the Tammann equation are effectively integrated, creating a density coupling function with clear physical meaning, high accuracy and wide applicability, providing a new approach for the calculation of high-temperature fluid properties.

[0014] 2) High prediction accuracy: This density coupling function fundamentally improves the accuracy of physical property calculation, reducing the prediction error of head and efficiency across the entire operating range from 8% of the traditional method to less than 3%.

[0015] 3) Good engineering practicality: The density coupling function has few parameters and is easy to determine. It has high computational efficiency and is easy to integrate into mainstream commercial software through UDF. It has good promotion value and engineering application prospects.

[0016] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0017] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0018] Figure 1 This is a flowchart illustrating a high-precision method for predicting the performance indicators of a high-temperature centrifugal pump according to an exemplary embodiment.

[0019] Figure 2 This is a schematic diagram illustrating the optimization process for determining the correction coefficient α according to an exemplary embodiment.

[0020] Figure 3 This is a comparison chart of the head-flow rate curves obtained by simulation using the method of the present invention and conventional methods, and experimental values, according to an exemplary embodiment.

[0021] Figure 4 This is a cloud map of the vortex distribution of the impeller under different operating conditions, predicted by the method of the present invention according to an exemplary embodiment.

[0022] Figure 5 This is a block diagram illustrating a high-precision high-temperature centrifugal pump performance index prediction device according to an exemplary embodiment. Detailed Implementation

[0023] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0024] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0025] Figure 1 This is a flowchart illustrating a high-precision high-temperature centrifugal pump performance index prediction method according to an exemplary embodiment, such as... Figure 1 As shown, the method may include the following steps: S1: Based on the ideal gas law and the Tammann equation, construct the density coupling function of the medium density ρ with temperature T and pressure p: The expression for the density coupling function is as follows:

[0026] in, The corrected density of the medium; α is the fitting coefficient introduced by correcting the theoretical deviation between the two equations; p is the liquid phase constant. c and T c These are the liquid phase pressure and temperature coefficient, respectively. It is the critical temperature coefficient; Specifically, the ideal gas law ( The Tammann equation (ρ=ρ0(1 +α)) describes the behavior of an ideal gas; it is simple in form but applicable to low-pressure, high-temperature conditions. p p - α T The ideal gas law (T) is often used to describe the compressibility of liquids and dense gases, which are more sensitive to pressure changes. Both describe the property changes from different perspectives, but neither can accurately characterize the actual state of the medium inside a high-temperature centrifugal pump on its own. This application couples the ideal gas law and the Tammann equation to construct a density coupling function, and deeply integrates it into the FLUENT simulation to achieve accurate prediction of the pump under all operating conditions, from external characteristics to internal flow field.

[0027] The process of combining the ideal gas law and the Tammann equation is as follows: the Tammann equation is regarded as a compensation and correction term for the ideal gas law under high pressure and high temperature conditions (pressure above 5 MPa, temperature above 150 degrees Celsius). Through dimensional analysis and coefficient comparison, the two equations are integrated into the density coupling function.

[0028] Simultaneous equations: For ideal gases With the Tammann equation ρ=ρ0(1 +α) p p - α T T) serves as the basis for construction. ρ is the density of the medium, ρ0 is the reference density, and α p α is the isothermal compressibility coefficient, p is the absolute pressure of the medium, and α T Where is the coefficient of thermal expansion, and T is the absolute temperature of the medium.

[0029] Coefficient matching and function derivation: Through dimensional analysis and coefficient comparison, a critical coefficient p is introduced. c , T c By normalizing the terms in the Tammann equation and solving it simultaneously with the ideal gas law, the form of the density coupling function is derived.

[0030] Parameter determination: Taking sulfolane as an example, a set of basic parameters is determined by consulting property handbooks or conducting experiments: p c =1779 kPa, Tc = 0.5, R l = 0.25.

[0031] The optimal value of the fitting coefficient α is determined by minimizing the root mean square error between the calculated value of the density coupling function and the experimentally measured density values ​​under different (T, p) conditions. (See attached...) Figure 2 As shown, the optimal value of the correction coefficient α is determined through the following specific process: Experimental data acquisition: For the target high-temperature medium, its temperature at a series of different temperatures (T1, T2, ..., T) is measured using a high-temperature and high-pressure experimental setup (such as a standard PVT experimental system). m ) and different pressures (p1, p2, ..., p n The actual density values ​​under various operating conditions are used to form a set of experimental data points covering the actual operating range of the pump { (T i , p i ), ρ exp}

[0032] Parameter initialization: Determine other key parameters in the density coupling function (p c , T c , R l The initial values ​​of the medium can be obtained in advance by consulting the physical property handbook or by fitting partial experimental data.

[0033] Error calculation and iterative optimization: Within the set range of α values ​​(e.g., 0.50, 0.51, ..., 0.60), each candidate α value is substituted into the density coupling function in turn.

[0034] For each candidate α value, the function is used to calculate all experimental operating points (T). i , p i The corresponding density prediction value ρ pre (α). Calculate the root mean square error (RMS) between the predicted and experimental values ​​at this α value, as an indicator to evaluate the model's accuracy:

[0035] When α = 0.55, the RMS is minimized, therefore this is determined to be the optimal value. The final density coupling function is:

[0036] S2: The density coupling function is embedded into the FLUENT solver through a user-defined function UDF to dynamically correct the medium properties of the computing unit in real time during the unsteady numerical simulation process, and obtain the corrected property parameters. Specifically, the dynamic correction is achieved by real-time monitoring of the local temperature T of each computational unit in the flow field. i and local pressure p i It then calls the UDF to calculate its corresponding real-time density ρ. m (T i , p i This is achieved through ).

[0037] The optimal density coupling function determined in S1:

[0038] The density coupling function was written in C language and compiled into a user-defined function (UDF) dynamic link library. This compiled UDF dynamic link library was then loaded into ANSYS FLUENT using either the Interpreted or Compiled method. Subsequently, in the material property settings panel, the density property of the medium was changed from the default "constant" or "piecewise linear" model to "user-defined," and the loaded function was selected from the drop-down menu. This means that FLUENT will no longer use fixed density values ​​in subsequent calculations, but will instead call the provided function to calculate the density in real time. At each time step and each iteration step of the unsteady numerical simulation, the FLUENT solver automatically provides the local temperature T of the current computational cell. i and local pressure p i The value of T is passed as an input parameter to the UDF. The UDF function is then called, utilizing the received T value. i and p i The value of ρ is calculated in real time based on the density coupling function described above, determining the dielectric density ρ of the element under the current local conditions and at the current moment. m (T i , p i The calculated density value ρ m It is immediately returned to the FLUENT solver to update the physical properties of the computational unit in the current iteration step and to participate in the subsequent solving of the momentum and energy equations.

[0039] This design overcomes the shortcomings of traditional CFD simulations, which typically treat medium density as a constant or a simple function dependent only on temperature. This neglects the sensitivity of high-temperature, high-pressure fluid density to pressure and fails to reflect local property changes caused by flow and heat transfer. It accurately characterizes the nonlinearity of physical properties, reflects local effects, achieves a significant improvement in prediction accuracy, enhances the fidelity of flow field simulations, and strengthens the predictive ability for complex flow phenomena.

[0040] S3: Based on the corrected physical property parameters, FLUENT is used to perform unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump to be predicted, and the input shaft power, internal flow field pressure, velocity and transient flow field data are obtained. Specifically, taking a high-temperature molten salt pump as an example, a three-dimensional geometric model of the entire flow field, including the inlet extension section, impeller, volute, and outlet extension section, is established. The impeller uses a high-precision structured hexahedral mesh, while complex areas such as the volute use unstructured tetrahedral meshes. Its design parameters are: flow rate Q... d =505.7 m³ / h, head H d =157 m, rotational speed n=2980 rpm. Boundary conditions were set: the inlet pressure was set to 1 atm (total pressure), the reference atmospheric pressure was 1 atm, the outlet pressure was set to mass flow, the impeller domain was set to the rotating fluid domain, and the rotational speed was 2980 rpm. A high-fidelity unsteady simulation (transient) was performed, using the SST k-ω turbulence model and the time step set to the time required for the impeller to rotate 2°. After the simulation reached a steady state, transient flow field data (pressure field, velocity field, vorticity field contour plots, etc.) for at least 10 impeller rotation cycles were collected for analyzing the time-averaged flow structure. The pump's input shaft power P was obtained from the simulation. After the unsteady simulation reached a steady period, the pressure (p) at the pump inlet and outlet surfaces at multiple flow rate points was extracted from the FLUENT post-processor. in , p out ), velocity (v) in , v out ), fluid inlet and outlet head (z) out , z in ).

[0041] This design aims to accurately capture the dynamic physical processes inside the high-temperature centrifugal pump, revealing dynamic property corrections only in unsteady conditions and simultaneously exposing transient flow structures. This design also seeks to achieve unprecedented insight into the internal flow field and predictive reliability.

[0042] S4: Calculate the head and efficiency based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads; Specifically, the pressure, velocity, and fluid inlet and outlet heads mentioned above are substituted into the head calculation formula to calculate the head H at each operating point.

[0043] H = (p out - p in ) / (ρ m * g) + (v out - v in ) / (2g) + (z out - z in ); Where, ρ mThe density is calculated based on the average operating conditions of the inlet and outlet, and g is the gravitational acceleration.

[0044] Simultaneously, the pump's input shaft power P is obtained from the simulation, combined with the calculated head H, flow rate Q, and density ρ. m Through the efficiency formula η= (ρ m * g * Q * H) / P calculates the efficiency at each operating point.

[0045] Effect verification: Pumps for conveying sulfolane (Q d =505.7 m³ / h, H d For example, (=157 m, n=2980 rpm), refer to Figure 3 By calculating the head at a series of flow points, a complete head-flow performance curve can be generated. The efficiency value at each operating point is calculated using the efficiency formula, thus generating the efficiency-flow performance curve. Comparing the head-flow performance curve and the efficiency-flow performance curve with experimental values ​​shows a high degree of agreement, with a maximum error of less than 3%, significantly outperforming the prediction results of traditional models using constant density or considering only temperature.

[0046] Table 1:

[0047] A high-temperature centrifugal pump (Q) for conveying sulfolane d =505.7 m³ / h, H d =157 m, n=2980 rpm) is an example. After prediction using the method of the present invention, referring to Table 1, the results show that the head-flow performance curve and the efficiency-flow performance curve are in high agreement with the experimental values, with a maximum error of less than 3%.

[0048] The following diagram was created using transient flow field data. Figure 4 The vorticity distribution cloud map shown (where T represents the time period in seconds) can intuitively predict and evaluate the transient flow structure inside the pump. For example, under low flow conditions (0.6Q), d Under these conditions, the backflow vortex at the impeller inlet was successfully predicted; under high flow rate conditions (1.4Q), the backflow vortex was successfully predicted. d Under these conditions, the backflow phenomenon at the volute outlet is predicted. The precise capture of these phenomena reveals a flow instability mechanism that traditional methods cannot detect. Corresponding to the aforementioned embodiments of the high-precision high-temperature centrifugal pump performance index prediction method, this application also provides embodiments of a high-precision high-temperature centrifugal pump performance index prediction device.

[0049] Figure 5This is a block diagram illustrating a high-precision high-temperature centrifugal pump performance index prediction device according to an exemplary embodiment. (Refer to...) Figure 5 The device includes: Module 1 is used to construct a density coupling function between the medium density ρ and temperature T and pressure p, based on the ideal gas law and the Tammann equation. ; in, The corrected density of the medium; α is the fitting coefficient introduced by correcting the theoretical deviation between the two equations; p is the liquid phase constant. c and T c These are the liquid phase pressure and temperature coefficient, respectively. It is the critical temperature coefficient; Correction module 2 is used to embed the density coupling function into the FLUENT solver through a user-defined function UDF, and to perform real-time dynamic correction of the medium properties of the computing unit during unsteady numerical simulation to obtain the corrected property parameters. Simulation module 3 is used to perform unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump to be predicted using FLUENT based on the corrected physical property parameters, and obtain the input shaft power, internal flow field pressure, velocity and transient flow field data. The curve generation module 4 is used to calculate the head and efficiency based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads.

[0050] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0051] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0052] Accordingly, this application also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the high-precision high-temperature centrifugal pump performance index prediction method described above.

[0053] Accordingly, this application also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, implement the high-precision high-temperature centrifugal pump performance index prediction method described above.

[0054] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0055] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for predicting the performance indicators of a high-precision high-temperature centrifugal pump, characterized in that, include: Based on the ideal gas law and the Tammann equation, a density coupling function is constructed for the medium density ρ and temperature T and pressure p: ； in, The corrected density of the medium; α is the fitting coefficient introduced by correcting the theoretical deviation between the two equations; p is the liquid phase constant. c and T c These are the liquid phase pressure and temperature coefficient, respectively. It is the critical temperature coefficient; The density coupling function is embedded into the FLUENT solver through a user-defined function (UDF) to dynamically correct the medium properties of the computational unit in real time during the unsteady numerical simulation process, thereby obtaining the corrected property parameters. Based on the corrected physical property parameters, FLUENT was used to perform unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump to be predicted, and the input shaft power, internal flow field pressure, velocity and transient flow field data were obtained. The head and efficiency are calculated based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads.

2. The method according to claim 1, characterized in that, The process of combining the ideal gas law and the Tammann equation is as follows: The Tammann equation is considered as a compensation and correction term for the ideal gas equation of state under high pressure and high temperature conditions. Through dimensional analysis and coefficient comparison, the two equations are integrated into the density coupling function.

3. The method according to claim 1, characterized in that, The optimal value of the fitting coefficient is determined by minimizing the root mean square error between the calculated value of the density coupling function and the experimentally measured density values ​​under different (T, p) conditions.

4. The method according to claim 1, characterized in that, The dynamic correction is realized by monitoring the local temperature T i and local pressure p i of each calculation unit in the flow field in real time, and calling the UDF to calculate the corresponding real-time density p m (T i , p i ).

5. The method according to claim 1, characterized in that, Based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads, the head and efficiency are calculated, including: Substitute the pressure, velocity, and fluid inlet and outlet head into the head calculation formula to calculate the head at each operating point. Based on the input shaft power, combined with the head, flow rate, and density, the efficiency at each operating point is calculated using the efficiency formula.

6. A high-precision high-temperature centrifugal pump performance index prediction device, characterized in that, include: The module is used to construct a density coupling function between the medium density ρ and temperature T and pressure p, based on the ideal gas law and the Tammann equation. ； in, The corrected density of the medium; α is the fitting coefficient introduced by correcting the theoretical deviation between the two equations; p is the liquid phase constant. c and T c These are the liquid phase pressure and temperature coefficient, respectively. It is the critical temperature coefficient; The correction module is used to embed the density coupling function into the FLUENT solver through a user-defined function (UDF) to dynamically correct the medium properties of the computational unit in real time during the unsteady numerical simulation process, and obtain the corrected property parameters. The simulation module is used to perform unsteady numerical simulation of the entire flow field of the high-temperature centrifugal pump to be predicted using FLUENT based on the corrected physical property parameters, and obtain the input shaft power, internal flow field pressure, velocity and transient flow field data. The curve generation module is used to calculate the head and efficiency based on the input shaft power, pressure, velocity, and fluid inlet and outlet heads.

7. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-5.

8. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the method as described in any one of claims 1-5.

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