Method for optimizing guide vane of water turbine by fitting quadratic function

Abstract

The invention discloses a method for optimizing a guide vane of a water turbine by fitting a quadratic function. The method aims at improving the efficiency of the water turbine through numerical simulation and mathematical modeling. First, in computer-aided design software UG, different numbers of guide vanes are modeled to generate a plurality of geometric configurations. Then, STAR-CCM + software is used for conducting fluid dynamic simulation on each configuration, and efficiency data of the guide vane under different working conditions are collected; the relation between the number of the guide vanes and the efficiency is obtained through data processing, quadratic function fitting is carried out through a scientific calculation library in Python, and the target is to determine optimal function parameters a, b and c. And carrying out optimization analysis according to a fitting result, and finally finding out the optimal number of the guide vanes capable of maximizing the efficiency of the water turbine. The method not only provides a scientific and efficient optimization means for the design of the water turbine, but also has a good application prospect in the design and optimization of other fluid equipment.

Description

Technical Field

[0001] The invention belongs to the technical field of hydroelectric power generation systems, and in particular relates to a method for optimizing turbine guide vanes by using a fitted quadratic function. Background Art

[0002] Turbine guide vanes play a vital role in hydropower generation systems and directly affect the performance, efficiency and reliability of turbines. Reasonable design and optimized guide vanes can improve turbine operating efficiency, reduce energy loss, and extend equipment life, thereby better meeting the needs of energy production. Summary of the invention

[0003] The present invention aims to solve the technical problems existing in the background technology and provides a method for optimizing turbine guide vanes by fitting a quadratic function.

[0004] In order to solve the technical problem, the technical solution of the present invention is:

[0005] A method for optimizing a turbine guide vane by fitting a quadratic function, the method comprising:

[0006] S1: Construct the geometric model of turbines with different numbers of guide vanes in UG software;

[0007] S2: Import the guide vane geometry model generated in UG, perform numerical simulation in STAR-CCM+, and use numerical simulation to obtain performance data under different numbers of guide vanes;

[0008] S3: Analyze the collected data, determine the characteristics and change patterns of the data, and select effective data sets;

[0009] S4: Use the collected data set to build a quadratic function model f(x)=ax 2 +bx+c, where x is the number of blades and f(x) is the efficiency.

[0010] S5: Determine the optimal quadratic function parameters by minimizing the sum of squared errors between the actual efficiency and the fitted efficiency, and use the optimization algorithm to find the optimal parameters a, b, and c.

[0011] Further, the step S1 comprises:

[0012] Start UG software;

[0013] Create a new part file;

[0014] Use sketch tools to draw the geometry of the guide vanes on a plane, including outlines and shapes;

[0015] Modeling can be performed by setting the number of guide vanes to different values ​​as needed;

[0016] Parametric design of each model for quick subsequent adjustment and modification;

[0017] After completing the modeling, check the integrity of the geometry to ensure there are no overlaps or errors.

[0018] Further, the step S2 comprises:

[0019] Open the STAR-CCM+ software and create a new project;

[0020] Import the guide vane model created in UG into STAR-CCM+;

[0021] Set up the computational domain and define the flow boundary conditions, including inflow and outflow conditions;

[0022] Mesh the guide vanes using the automatic meshing tool, ensuring that the mesh is fine enough to capture the characteristics of the flow;

[0023] Select an appropriate physical model and define the physical properties of the fluid;

[0024] Configure the solver parameters to ensure simulation stability;

[0025] Run numerical simulations and collect output data to record turbine efficiency data for different numbers of guide vanes.

[0026] Further, the step S3 comprises:

[0027] Export data: export the performance data obtained from simulation to Excel or CSV file;

[0028] Data cleaning: remove outliers, format data, and check data integrity;

[0029] Data analysis: Use statistical software to read the data set, generate preliminary charts, observe the performance trend under different guide vane parameters, and save the processed data set, including the number of guide vanes and their corresponding efficiency values.

[0030] Further, the step S5 comprises:

[0031] Import the quadratic function fitting model into relevant mathematical tool libraries, using NumPy or SciPy in Python, and then use these tools to define the quadratic function and estimate the parameters based on the collected data set to find the optimal parameter values ​​(a, b, and c) so that the function can fit the actual data well;

[0032] Based on the obtained fitting parameters, the quality of the fit was evaluated by calculating the mean squared error (MSE) and the coefficient of determination (R). 2to measure the effect of fitting, MSE is used to quantify the error between the predicted value and the actual value; and R 2 The value indicates the proportion of the explanatory variable to the dependent variable variation. The closer the value is to 1, the better the fitting effect.

[0033] Adjust the fit: Based on the evaluation results, if the fit is not good, for example, the MSE is high or the R 2 If the value is low, consider adjusting it by:

[0034] Increase the order of the function, using cubic functions or higher-order polynomials;

[0035] Re-estimate parameters and find the optimal solution to ensure that the model can better capture the patterns of the data;

[0036] Finally, to verify the applicability and accuracy of the fitted model, the fitted quadratic function or the adjusted function is applied to a new data set, the actual efficiency values ​​associated with these new data are collected and compared with the model predictions, and the MSE and R are calculated again. 2 value to confirm the model's fitting effect on the new data set and thus test its universality.

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] The present invention has the following advantages: 1. Simplified optimization process: Fitting the guide vane optimization law into a quadratic function can simplify the optimization process, reduce the calculation complexity, and improve the optimization efficiency. 2. Clear mathematical expression: The quadratic function is simple and clear in form, and the parameters are easy to understand and adjust, which is conducive to engineers and researchers to understand the characteristics of the guide vane optimization law. 3. Local optimal solution: The quadratic function can better fit the guide vane optimization law within a certain range, which helps to find the local optimal solution and improve the performance of the guide vane design. 4. Flexibility: The quadratic function has a certain flexibility and can adapt to different guide vane design requirements by adjusting the coefficient to achieve customized guide vane design. 5. Convenient mathematical analysis: The quadratic function has good mathematical properties, which is convenient for mathematical analysis and derivation, and is conducive to in-depth research on the optimization process of guide vane design. 6. Wide application in engineering: As a common mathematical model, the quadratic function is widely used in the engineering field. Fitting the guide vane optimization law into a quadratic function is conducive to application and promotion in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 , a main flow chart of a method for optimizing turbine guide vanes by fitting a quadratic function according to the present invention. DETAILED DESCRIPTION

[0040] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0041] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0042] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0043] Embodiment 1:

[0044] The technical solution of the present invention is as follows: 1. Collect data: First, collect data on the optimization law of the guide vane. These data are the results obtained based on numerical simulation. 2. Understand the data: Analyze the collected data to determine the characteristics and change laws of the data. This helps to determine whether the data can be fitted by a quadratic function. 3. Select an appropriate quadratic function form: The general form of a quadratic function is f(x)=ax 2 +bx+c. Determining the values ​​of a, b, and c is a critical step. 4. Fitting the data: Use appropriate software (NumPy or SciPy library in Python) to fit a quadratic function to the data and find the quadratic function that best fits the data. 5. Evaluate the quality of the fit: After fitting, evaluate the quality of the fit and determine the degree of error in the fit. Use indicators such as Mean Squared Error and coefficient of determination to evaluate the quality of the fit. 6. Adjust the fit: Based on the evaluation results, if the fit is not good, you can try to adjust the parameters of the quadratic function, or consider other higher-order functions to better fit the data. 7. Verify the fitted model: Finally, apply the fitted quadratic function to other data sets of the guide vane optimization law to verify the applicability and accuracy of the model.

[0045] Key points of the present invention: 1. Data collection and processing: The key is to collect enough guide vane design data, including performance indicators and geometric features under different parameters. These data need to be effectively processed and cleaned to ensure the accuracy and reliability of the data. 2. Quadratic function fitting: Selecting a suitable quadratic function model for fitting is a key step. This involves determining the coefficients and constant terms of the quadratic term to best fit the actual data and maintain the smoothness of the curve. 3. Definition of optimization objectives: The optimization objectives of the guide vane design need to be clearly defined during the fitting process, which helps to guide the fitting and optimization process of the quadratic function. 4. Model verification: It is crucial to verify the fitted quadratic function model, and the accuracy and reliability of the model can be verified by comparing with actual data or using methods such as cross-validation. 5. Parameter adjustment and optimization: According to actual needs and optimization goals, adjusting and optimizing the parameters of the quadratic function is a key technical link. The guide vane design is optimized by adjusting the coefficients to achieve optimal performance. 6. Flexibility and versatility: Designing a flexible and universal quadratic function model can adapt to different types of guide vane optimization problems, thereby improving the scope of application and practicality of this method.

[0046] In summary, data processing, model fitting, verification, parameter optimization and other links are the key technical points for fitting the guide vane optimization law into a quadratic function. Effectively handling these key points can ensure the optimization effect and feasibility of the guide vane design.

[0047] Embodiment 2:

[0048] like Figure 1 As shown, the present invention mainly comprises the following steps:

[0049] A method for optimizing a turbine guide vane by fitting a quadratic function, the method comprising:

[0050] S1: Construct the geometric model of turbines with different numbers of guide vanes in UG software;

[0051] S2: Import the guide vane geometry model generated in UG, perform numerical simulation in STAR-CCM+, and use numerical simulation to obtain performance data under different numbers of guide vanes;

[0052] S3: Analyze the collected data, determine the characteristics and change patterns of the data, and select effective data sets;

[0053] S4: Use the collected data set to build a quadratic function model f(x)=ax 2 +bx+c, where x is the number of blades and f(x) is the efficiency.

[0054] S5: Determine the optimal quadratic function parameters by minimizing the sum of squared errors between the actual efficiency and the fitted efficiency, and use the optimization algorithm to find the optimal parameters a, b, and c.

[0055] Further, the step S1 comprises:

[0056] Start UG software;

[0057] Create a new part file;

[0058] Use sketch tools to draw the geometry of the guide vanes on a plane, including outlines and shapes;

[0059] Modeling can be performed by setting the number of guide vanes to different values ​​as needed;

[0060] Parametric design of each model for quick subsequent adjustment and modification;

[0061] After completing the modeling, check the integrity of the geometry to ensure there are no overlaps or errors.

[0062] Further, the step S2 comprises:

[0063] Open the STAR-CCM+ software and create a new project;

[0064] Import the guide vane model created in UG into STAR-CCM+;

[0065] Set up the computational domain and define the flow boundary conditions, including inflow and outflow conditions;

[0066] Mesh the guide vanes using the automatic meshing tool, ensuring that the mesh is fine enough to capture the characteristics of the flow;

[0067] Select an appropriate physical model and define the physical properties of the fluid;

[0068] Configure the solver parameters to ensure simulation stability;

[0069] Run numerical simulations and collect output data to record turbine efficiency data for different numbers of guide vanes.

[0070] Further, the step S3 comprises:

[0071] Export data: export the performance data obtained from simulation to Excel or CSV file;

[0072] Data cleaning: remove outliers, format data, and check data integrity;

[0073] Data analysis: Use statistical software to read the data set, generate preliminary charts, observe the performance trend under different guide vane parameters, and save the processed data set, including the number of guide vanes and their corresponding efficiency values.

[0074] Further, the step S5 comprises:

[0075] Import the quadratic function fitting model into relevant mathematical tool libraries, using NumPy or SciPy in Python, and then use these tools to define the quadratic function and estimate the parameters based on the collected data set to find the optimal parameter values ​​(a, b, and c) so that the function can fit the actual data well;

[0076] Based on the obtained fitting parameters, the quality of the fit was evaluated by calculating the mean squared error (MSE) and the coefficient of determination (R). 2 to measure the effect of fitting, MSE is used to quantify the error between the predicted value and the actual value; and R 2 The value indicates the proportion of the explanatory variable to the dependent variable variation. The closer the value is to 1, the better the fitting effect.

[0077] Adjust the fit: Based on the evaluation results, if the fit is not good, for example, the MSE is high or the R 2 If the value is low, consider adjusting it by:

[0078] Increase the order of the function, using cubic functions or higher-order polynomials;

[0079] Re-estimate parameters and find the optimal solution to ensure that the model can better capture the patterns of the data;

[0080] Finally, to verify the applicability and accuracy of the fitted model, the fitted quadratic function or the adjusted function is applied to a new data set, the actual efficiency values ​​associated with these new data are collected and compared with the model predictions, and the MSE and R are calculated again. 2 value to confirm the model's fitting effect on the new data set and thus test its universality.

[0081] Embodiment 3:

[0082] The present invention provides a specific case for illustration:

[0083] First, the modeling of different numbers of guide vanes is performed in UG software, and then grid division and numerical simulation are performed in STAR CCM+ to collect data. Then the data is processed to obtain the corresponding efficiency, as shown in Table 1; then the code is run in Pycharm to obtain the values ​​of a, b, and c in the quadratic function, as shown in Table 2; f(x) = -0.0047336x^2+0.0576415x+-0.1342714.

[0084] Steps to determine the parameters of a quadratic function in PyCharm:

[0085] 1. Prepare the environment:

[0086] Start the Python development environment PyCharm and make sure that the necessary libraries, such as NumPy and SciPy, are installed. If they are not installed yet, you can use Python package management tools such as pip to install them:

[0087] 2. Data preparation:

[0088] Collect the efficiency data obtained from the STAR-CCM+ simulation and save it as a CSV file. The file should contain two columns, one for the number of guide vanes and the other for the corresponding efficiency values. For example, you can name the file data.csv.

[0089] 3. Write Python script:

[0090] Create a new Python file in PyCharm (e.g. fit_function.py).

[0091] Write the code in the file as follows:

[0092] Import the necessary libraries:

[0093] Use NumPy for mathematical calculations, use SciPy's curve fitting function to fit quadratic functions, and use Pandas to read CSV files.

[0094] Define the quadratic function model:

[0095] Define a method that accepts an input parameter (the number of guide vanes) and an output parameter (a quadratic function of the efficiency).

[0096] Reading data:

[0097] Use the Pandas library to read the data in the CSV file and store the number of guide vanes and efficiency values ​​in variables respectively.

[0098] Perform a curve fit:

[0099] Use SciPy's curve_fit function to pass in the number of guide vanes and efficiency values, and select the defined quadratic function model.

[0100] This function will return the fitted parameters a, b and c.

[0101] Output:

[0102] Print the fitted parameters to view the specific values ​​obtained.

[0103] The following is a text description of the structure and logic of the sample code:

[0104] Import the library:

[0105] First, we need to import NumPy, SciPy, and Pandas. These libraries provide the necessary functions for numerical calculations and data processing.

[0106] Reading data:

[0107] Use the pandas.read_csv() function to read the CSV file and store the number of guide vanes and the corresponding efficiency values ​​as two NumPy arrays.

[0108] Define a quadratic function:

[0109] Create a function called quadratic_func with the input variable x (the number of guide vanes) and the output as a linear combination of a, b, and c, i.e. f(x) = ax2 + bx + c.

[0110] Fitting data:

[0111] Call the curve_fit function, provide the quadratic function model and the guide vane number and efficiency value data read from the CSV file, and return the optimal fitting parameters and their covariance.

[0112] Output:

[0113] The values ​​of the fitting parameters a, b, and c are output on the console for further analysis and use.

[0114] UG software (now known as Siemens NX) is a powerful computer-aided design (CAD) and computer-aided engineering (CAE) tool widely used in product design, engineering analysis and manufacturing.

[0115] STAR-CCM+ is a computational fluid dynamics (CFD) software developed by Siemens Digital Industries Software. It is widely used in the field of engineering simulation, especially in the multi-physics coupling analysis of fluid mechanics, heat conduction, chemical reaction, etc.

[0116] Table 1

[0117] Number of blades efficiency 3 0.002974926 4 0.000805848 5 0.050126676 6 0.046838463 7 0.026720658 8 0.027086003

[0118] Table 2

[0119] a b c -0.0047336 0.0576415 -0.1342714

[0120] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0121] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A method for optimizing turbine guide vanes by fitting a quadratic function, characterized in that: The method comprises: S1: Construct the geometric model of turbines with different numbers of guide vanes in UG software; S2: Import the guide vane geometry model generated in UG, perform numerical simulation in STAR-CCM+, and use numerical simulation to obtain performance data under different numbers of guide vanes; S3: Analyze the collected data, determine the characteristics and change patterns of the data, and select effective data sets; S4: Use the collected data set to build a quadratic function model f(x)=ax 2 +bx+c; S5: Determine the optimal quadratic function parameters by minimizing the sum of squared errors between the actual efficiency and the fitted efficiency, and use the optimization algorithm to find the optimal parameters a, b, and c.

2. The method for optimizing turbine guide vanes by fitting a quadratic function according to claim 1, characterized in that: The step S1 comprises: Start UG software; Create a new part file; Use sketch tools to draw the geometry of the guide vanes on a plane, including outlines and shapes; Modeling can be performed by setting the number of guide vanes to different values ​​as needed; Parametric design of each model for quick subsequent adjustment and modification; After completing the modeling, check the integrity of the geometry to ensure there are no overlaps or errors.

3. The method for optimizing turbine guide vanes by fitting a quadratic function according to claim 1, characterized in that: The step S2 comprises: Open the STAR-CCM+ software and create a new project; Import the guide vane model created in UG into STAR-CCM+; Set up the computational domain and define the flow boundary conditions, including inflow and outflow conditions; Mesh the guide vanes using the automatic meshing tool, ensuring that the mesh is fine enough to capture the characteristics of the flow; Select an appropriate physical model and define the physical properties of the fluid; Configure the solver parameters to ensure simulation stability; Run numerical simulations and collect output data to record turbine efficiency data for different numbers of guide vanes.

4. The method for optimizing turbine guide vanes by fitting a quadratic function according to claim 1, characterized in that: The step S3 comprises: Export data: export the performance data obtained from simulation to Excel or CSV file; Data cleaning: remove outliers, format data, and check data integrity; Data analysis: Use statistical software to read the data set, generate preliminary charts, observe the performance trend under different guide vane parameters, and save the processed data set, including the number of guide vanes and their corresponding efficiency values.

5. The method for optimizing turbine guide vanes by fitting a quadratic function according to claim 1, characterized in that: The step S5 comprises: Import the quadratic function fitting model into relevant mathematical tool libraries, using NumPy or SciPy in Python, and then use these tools to define the quadratic function and estimate the parameters based on the collected data set to find the optimal parameter values ​​(a, b, and c) so that the function can fit the actual data well; Based on the obtained fitting parameters, the quality of the fit was evaluated by calculating the mean squared error (MSE) and the coefficient of determination (R). 2 to measure the effect of fitting, MSE is used to quantify the error between the predicted value and the actual value; and R 2 The value indicates the proportion of the explanatory variable to the dependent variable variation. The closer the value is to 1, the better the fitting effect. Adjust the fit: Based on the evaluation results, if the fit is not good, for example, the MSE is high or the R 2 If the value is low, consider adjusting it by: Increase the order of the function, using cubic functions or higher-order polynomials; Re-estimate parameters and find the optimal solution to ensure that the model can better capture the patterns of the data; Finally, to verify the applicability and accuracy of the fitted model, the fitted quadratic function or the adjusted function is applied to a new data set, the actual efficiency values ​​associated with these new data are collected and compared with the model predictions, and the MSE and R are calculated again. 2 value to confirm the model's fitting effect on the new data set and thus test its universality.

Images