A method for predicting blade loss in high-load turbines suitable for low Reynolds number conditions

Abstract

The present invention relates to a high-load turbine blade loss prediction method suitable for low Reynolds number operating conditions, comprising the following steps: SS1, constructing a cascade KO model based on blade profile parameters; SS2, combining the blade loss and trailing edge loss of the KO model into total blade loss, and establishing a correction model to predict the total blade loss; SS3, defining a deviation coefficient = experimental value / KO model predicted value, and performing linear regression on the inlet Re; SS4, naming the intercept term blade factor, and after determining the model, optimizing it through enumeration; SS5, obtaining a total correction formula. The high-load turbine blade loss prediction method suitable for low Reynolds number operating conditions in the present invention can more accurately predict turbine losses under low Reynolds number and wide angle of attack conditions, thereby better predicting the turbine's aerodynamic performance.

Description

Technical Field

[0001] The present invention belongs to the field of aero-engine / gas turbine turbine technology and provides a high-load turbine blade loss prediction method suitable for low Reynolds number working conditions, which can achieve more accurate prediction of the turbine's aerodynamic performance. Background Art

[0002] Axial-flow turbines, as impeller-type working machines, have been widely used in various energy and power applications. To achieve efficient axial-flow turbine design, accurate prediction of aerodynamic performance is essential. Methods such as loss prediction models, flow analysis, and three-dimensional numerical simulation have been developed to better address the highly three-dimensional unsteady viscous flow within turbines. Given the multi-parameter, nonlinear coupling nature of turbine design and the need for meticulous and iterative adjustments in the design process, loss prediction models are particularly important. They provide crucial guidance for low-dimensional simulation, optimization, and design, significantly shortening the R&D cycle. Four common approaches to turbine loss estimation are: using loss models, estimating losses based on existing loss data, estimating losses through numerical simulation, and estimating losses through experiments. Using loss models to estimate losses can significantly save time, leading to extensive research and development efforts, including significant success, in establishing, refining, and improving loss models. However, the accuracy and results of different loss models are different, so it is necessary to study the loss model and find a suitable loss model or an appropriate correction method to improve the accuracy of loss model estimation, so as to estimate the loss quickly and accurately. At the same time, the original loss model can be corrected through existing loss data or through numerical simulation and experimental methods.

[0003] However, existing loss models differ in their underlying assumptions, calculation methods, loss prediction accuracy, and scope of application. Studies have shown that the choice of different loss models significantly impacts design optimization results. Furthermore, traditional models are inherently ill-suited for turbines operating under high loads and a wide range of operating conditions. Therefore, the pursuit of more accurate and applicable loss prediction methods for turbines operating under high loads and a wide range of operating conditions has been a key research topic for scholars both domestically and internationally.

[0004] Regarding blade losses alone, traditional loss models are not well-suited for turbines operating under low Reynolds numbers, high loads, and wide operating conditions. This is partly due to their inadequate consideration of low Reynolds numbers and partly due to differences between the losses of high-load, wide-operating turbines and those of traditional turbines. Therefore, it is urgent to develop a corrected blade loss model for turbines operating under low Reynolds numbers, high loads, and wide operating conditions. Summary of the Invention

[0005] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a method for predicting high-load turbine blade loss suitable for low Reynolds number conditions. Based on existing experimental data, by adding a correction factor, the influence of the Reynolds number on the loss is focused on correcting the effect, improving and refining the traditional KO model, and achieving more accurate prediction of the turbine's aerodynamic performance.

[0006] The technical solution adopted by the present invention to solve its technical problems is:

[0007] A method for predicting blade loss of a high-load turbine suitable for low Reynolds number working conditions comprises the following steps:

[0008] SS1, based on the blade profile parameters, constructs the cascade KO model, as shown in formula (1):

[0009] (1)

[0010] in, is the leaf shape loss of the KO model, is the attack angle correction factor of the KO model, is the blade profile loss in the AM model, is the Mach number correction factor, is the shock wave loss, is the trailing edge loss, Re is the inlet Reynolds number;

[0011] SS2, the blade profile loss and trailing edge loss of the KO model are combined into the total blade profile loss, and a modified model is established to predict the total blade profile loss, as shown in formula (2):

[0012] (2)

[0013] in, is the total blade profile loss of the modified model, is the new corrected Mach number factor, is the angle of attack correction factor of the modified model, is the modified Reynolds factor of the modified model;

[0014] SS3, define the deviation coefficient = experimental value / KO model predicted value, and perform linear regression on the inlet Reynolds number Re, as shown in formula (3):

[0015] (3)

[0016] in is the coefficient of deviation; is the leaf shape factor;

[0017]

[0018] in, is the modified Reynolds factor of the modified model;

[0019] SS4, named the intercept term as the leaf factor , which is related to the leading edge thickness and the trailing edge thickness. After the model is determined, the enumeration method is used to find the optimal formula (4):

[0020] (4)

[0021] Where, and are the leading edge thickness and trailing edge thickness of the blade respectively;

[0022] SS5, the overall correction formula is obtained, as shown in formula (5):

[0023] (5)

[0024] is the modified Reynolds factor for blade profile loss.

[0025] Preferably, in step SS5, Correction is made using the modified Reynolds factor for blade profile losses:

[0026] (6)

[0027] in, is the Reynolds factor for blade profile loss.

[0028] Preferably, step SS2 further comprises the following steps:

[0029] SS21, Combined Blade Profile and Trailing Edge Losses: Quantitative methods for determining trailing edge losses, including calculations of fluid dynamics and fitting of experimental data;

[0030] SS22, Adjust the KO model: Based on the characteristics of the trailing edge losses, adjust the KO model to include these additional losses, and redefine and calculate the model parameters;

[0031] SS23, Calculate new loss coefficient: Use the adjusted KO model to calculate the new blade loss coefficient, reflecting the combined effects of blade loss and trailing edge loss;

[0032] SS24, Determine the Reynolds Number Correction Factor: Determine the corrected Reynolds factor applicable to low Reynolds numbers through experimental data and theoretical analysis;

[0033] SS25, establish a total loss prediction model: combine all the above correction factors and basic blade loss to establish a comprehensive blade loss prediction model, namely formula (2).

[0034] Preferably, step SS3 further comprises the following steps:

[0035] SS31, Experimental Data Preparation: Collect experimental data on turbine blade loss at different Reynolds numbers. The experimental data includes the measured values of blade loss and the corresponding inlet Reynolds number Re.

[0036] SS32, calculate the coefficient of deviation: For each set of experimental data, use formula (3) to calculate the coefficient of deviation , generate a table of correspondence between coefficient of deviation and experimental conditions;

[0037] SS33, Performing Linear Regression: Using Statistical Tools, Entering the Coefficient of Variation and the inlet Reynolds number Re data, perform linear regression analysis; determine the parameters of the linear regression equation, including the slope and intercept;

[0038] SS34, modified KO model: Based on the results of linear regression analysis, the Reynolds number related terms in the KO model are modified; the modified Reynolds factor and blade shape factor are incorporated into the model to form a new modified model.

[0039] Preferably, step SS4 further comprises the following steps:

[0040] SS41, Establishing the relationship between blade shape factor and geometric parameters: Based on fluid mechanics principles and experimental data, establish the relationship between the blade shape factor σ and the leading edge thickness and trailing edge thickness of the blade;

[0041] SS42, Enumeration Optimization: After determining the relationship between the blade profile factor σ and the leading edge thickness and trailing edge thickness, an enumeration method is used to search for possible parameter combinations to find the optimal σ value;

[0042] SS43, determine the correction formula: determine the correction formula of the blade factor σ by finding the best parameter combination through enumeration method.

[0043] Preferably, step SS42 further includes:

[0044] SS421, Define parameter space: First, determine the range of values for the leading edge thickness and the trailing edge thickness, where the range is set based on design requirements, manufacturing limitations, or previous empirical data.

[0045] SS422, Setting Resolution and Step Size: In parameter space, set a resolution or step size for discretization in each dimension.

[0046] SS423, Initializing Performance Metrics: Select the accuracy of the predictions as the performance metric and use the mean squared error or coefficient of determination to assess the goodness of fit of the model.

[0047] SS424. Traverse Parameter Combinations: Traverse all possible leading-edge and trailing-edge thickness combinations in the parameter space, taking a set step size. For each parameter pair, calculate the blade profile factor σ and use the corresponding model to predict blade profile loss.

[0048] SS425. Evaluate Performance: For each parameter combination, evaluate the model's performance using an independent test dataset. Record the performance metrics for each parameter combination and identify the optimal parameter combination.

[0049] SS426. Comparison and Selection: After traversing all parameter combinations, compare the performance indicators of each parameter combination and select the best parameter combination as the final blade shape factor σ; this optimal parameter combination provides the model with the lowest error or highest goodness of fit when predicting blade shape loss.

[0050] The advantages of the present invention compared with the prior art are:

[0051] (1) The present invention provides a method for predicting blade losses in high-load turbines, particularly suitable for low Reynolds number operating conditions. Under low Reynolds number and wide angle of attack conditions, the method can more accurately predict turbine losses, thereby better predicting the turbine's aerodynamic performance. For turbines operating under specific operating conditions, the method can improve design accuracy and turbine performance.

[0052] (2) Based on the latest experimental data on blade profile losses, this paper optimizes the original Kacker-Okapuu (KO) blade cascade model by using a regression method with control variables and a coupling factor. This optimization makes the model more effective than the traditional KO model in estimating turbine losses, especially at low Reynolds numbers, and can effectively improve the accuracy of turbine design and analysis.

[0053] (3) The present invention not only provides a new prediction method, but also helps to better understand the influence of Reynolds number and blade shape on high-load and wide-operating-condition turbine losses by analyzing the new loss model, which helps to further optimize turbine design and improve turbine performance.

[0054] (4) By defining a deviation coefficient and performing linear regression analysis, this paper innovatively finds a function related to the Reynolds number to fit this deviation coefficient, thereby proposing the concept of blade factor. This method provides a new approach to the prediction of turbine blade loss and helps improve the accuracy and efficiency of prediction.

[0055] (5) Using the loss model of the present invention to estimate losses can significantly save time, provide important guidance for low-dimensional simulation, optimization and design, and greatly shorten the R&D cycle. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a flow chart of a method for predicting blade loss of a high-load turbine applicable to low Reynolds number working conditions according to the present invention;

[0057] Figure 2 This is a parameter diagram of the turbine blade profile suitable for a low Reynolds number, high load and wide operating conditions according to the present invention.

[0058] Figure 3 It is the linear regression diagram of the imported Re of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the implementation of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below in conjunction with the drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to be used to explain the present invention, and should not be understood as limiting the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The structure and technical solutions of the present invention are further described in detail below in conjunction with the drawings, and an embodiment of the present invention is given.

[0060] like Figure 1 As shown, a high-load turbine blade loss prediction method applicable to low Reynolds number working conditions of the present invention comprises the following steps:

[0061] SS1, based on the blade profile parameters, constructs the cascade KO model, as shown in formula (1):

[0062] (1)

[0063] in, is the leaf shape loss of the KO model, is the attack angle correction factor of the KO model, is the blade profile loss in the AM model, is the Mach number correction factor, is the shock wave loss, is the trailing edge loss, Re is the inlet Reynolds number;

[0064] SS2, the blade profile loss and trailing edge loss of the KO model are combined into the total blade profile loss, and a modified model is established to predict the total blade profile loss, as shown in formula (2):

[0065] (2)

[0066] in, is the total blade profile loss of the modified model, is the new corrected Mach number factor, is the angle of attack correction factor of the modified model, is the modified Reynolds factor of the modified model;

[0067] SS3, define the deviation coefficient = experimental value / KO model predicted value, and perform linear regression on the inlet Reynolds number Re, as shown in formula (3):

[0068] (3)

[0069] in, is the coefficient of deviation; is the leaf shape factor;

[0070]

[0071] in, is the modified Reynolds factor of the modified model;

[0072] SS4, named the intercept term as the leaf factor , which is related to the leading edge thickness and the trailing edge thickness. After the model is determined, the enumeration method is used to find the optimal formula (4):

[0073] (4)

[0074] Where, and are the leading edge thickness and trailing edge thickness of the blade respectively;

[0075] SS5, the overall correction formula is obtained, as shown in formula (5):

[0076] (5)

[0077] is the modified Reynolds factor for blade profile loss.

[0078] Preferably, in step SS5, Correction is made using the modified Reynolds factor for blade profile losses:

[0079] (6)

[0080] in, is the Reynolds factor for blade profile loss.

[0081] Wherein step SS2 further comprises the following steps:

[0082] SS21, Combined Blade Profile and Trailing Edge Losses: Quantitative methods for determining trailing edge losses, including calculations of fluid dynamics and fitting of experimental data;

[0083] SS22, Adjust the KO model: Based on the characteristics of the trailing edge losses, adjust the KO model to include these additional losses, and redefine and calculate the model parameters;

[0084] SS23, Calculate new loss coefficient: Use the adjusted KO model to calculate the new blade loss coefficient, reflecting the combined effects of blade loss and trailing edge loss;

[0085] SS24, Determine the Reynolds Number Correction Factor: Determine the corrected Reynolds factor applicable to low Reynolds numbers through experimental data and theoretical analysis;

[0086] SS25, establish a total loss prediction model: combine all the above correction factors and basic blade loss to establish a comprehensive blade loss prediction model, namely formula (2).

[0087] Wherein step SS3 further comprises the following steps:

[0088] SS31, Experimental Data Preparation: Collect experimental data on turbine blade loss at different Reynolds numbers. The experimental data includes the measured values of blade loss and the corresponding inlet Reynolds number Re.

[0089] SS32, calculate the coefficient of deviation: For each set of experimental data, use formula (3) to calculate the coefficient of deviation , generate a table of correspondence between coefficient of deviation and experimental conditions;

[0090] SS33, Performing Linear Regression: Using Statistical Tools, Entering the Coefficient of Variation and the inlet Reynolds number Re data, perform linear regression analysis; determine the parameters of the linear regression equation, including the slope and intercept;

[0091] SS34, modified KO model: Based on the results of linear regression analysis, the Reynolds number related terms in the KO model are modified; the modified Reynolds factor and blade shape factor are incorporated into the model to form a new modified model.

[0092] Wherein step SS4 further comprises the following steps:

[0093] SS41, Establishing the relationship between blade shape factor and geometric parameters: Based on fluid mechanics principles and experimental data, establish the relationship between the blade shape factor σ and the leading edge thickness and trailing edge thickness of the blade;

[0094] SS42, Enumeration Optimization: After determining the relationship between the blade profile factor σ and the leading edge thickness and trailing edge thickness, an enumeration method is used to search for possible parameter combinations to find the optimal σ value;

[0095] SS43, determine the correction formula: determine the correction formula of the blade factor σ by finding the best parameter combination through enumeration method.

[0096] Wherein step SS42 further includes:

[0097] SS421, Define parameter space: First, determine the range of values for the leading edge thickness and the trailing edge thickness, where the range is set based on design requirements, manufacturing limitations, or previous empirical data.

[0098] SS422, Setting Resolution and Step Size: In parameter space, set a resolution or step size for discretization in each dimension.

[0099] SS423, Initializing Performance Metrics: Select the accuracy of the predictions as the performance metric and use the mean squared error or coefficient of determination to assess the goodness of fit of the model.

[0100] SS424. Traverse Parameter Combinations: Traverse all possible leading-edge and trailing-edge thickness combinations in the parameter space, taking a set step size. For each parameter pair, calculate the blade profile factor σ and use the corresponding model to predict blade profile loss.

[0101] SS425. Evaluate Performance: For each parameter combination, evaluate the model's performance using an independent test dataset. Record the performance metrics for each parameter combination and identify the optimal parameter combination.

[0102] SS426. Comparison and Selection: After traversing all parameter combinations, compare the performance indicators of each parameter combination and select the best parameter combination as the final blade shape factor σ; this optimal parameter combination provides the model with the lowest error or highest goodness of fit when predicting blade shape loss.

[0103] In summary, the present invention uses the latest blade loss experimental data, uses the control variable regression and the coupling factor method to correct the original blade cascade Kacker-Okapuu (KO) model, namely formula (1), (blade parameters such as Figure 1) was optimized. Since the wake loss coefficient in the KO loss model is considered separately, the experimental data obtained is the blade loss in a broader sense, that is, it includes the blade loss and trailing edge loss of the KO model. In the case that the trailing edge loss and blade loss are difficult to be treated separately, it was decided to follow Traupel's approach and merge the blade loss and trailing edge loss of the KO model into blade loss. The next step is to establish a model to predict it. The overall formula is shown in formula (2).

[0104] Under low Reynolds number conditions, it was found that formula (2) corrected the KO model under low Reynolds number conditions. By comparing with experimental data, it was found that the estimated effect was better than the KO model, so the correction was made based on formula (2). First, the deviation coefficient was defined as experimental value / KO model predicted value. The next step was to find a function related to Reynolds number that could fit this deviation coefficient well. Therefore, a linear regression was performed on the inlet Re to obtain the following results: Figure 3 The regression results show that the intercept term varies with the blade shape, so the intercept term is named the blade shape factor. This blade shape factor is considered to be related to the leading edge thickness and trailing edge thickness. After determining the model, we use the enumeration method to find the optimal solution, and obtain formula (4). Finally, the overall revised formula (5) is obtained.

[0105] The advantages of the present invention compared with the prior art are:

[0106] (1) The present invention provides a method for predicting blade losses in high-load turbines, particularly suitable for low Reynolds number operating conditions. Under low Reynolds number and wide angle of attack conditions, the method can more accurately predict turbine losses, thereby better predicting the turbine's aerodynamic performance. For turbines operating under specific operating conditions, the method can improve design accuracy and turbine performance.

[0107] (2) Based on the latest experimental data on blade profile losses, this paper optimizes the original Kacker-Okapuu (KO) blade cascade model by using a regression method with control variables and a coupling factor. This optimization makes the model more effective than the traditional KO model in estimating turbine losses, especially at low Reynolds numbers, and can effectively improve the accuracy of turbine design and analysis.

[0108] (3) The present invention not only provides a new prediction method, but also helps to better understand the influence of Reynolds number and blade shape on high-load and wide-operating-condition turbine losses by analyzing the new loss model, which helps to further optimize turbine design and improve turbine performance.

[0109] (4) By defining a deviation coefficient and performing linear regression analysis, this paper innovatively finds a function related to the Reynolds number to fit this deviation coefficient, thereby proposing the concept of blade factor. This method provides a new approach to the prediction of turbine blade loss and helps improve the accuracy and efficiency of prediction.

[0110] (5) Using the loss model of the present invention to estimate losses can significantly save time, provide important guidance for low-dimensional simulation, optimization and design, and greatly shorten the R&D cycle.

[0111] The above embodiments fully and effectively achieve the objectives of the present invention. Those skilled in the art will appreciate that the present invention includes, but is not limited to, the contents described in the accompanying drawings and the above specific embodiments. Although the present invention has been described with reference to the embodiments currently considered to be the most practical and preferred, it should be understood that the present invention is not limited to the disclosed embodiments, and any modifications that do not deviate from the functional and structural principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A high-load turbine blade loss prediction method suitable for low Reynolds number conditions, characterized in that: The following steps are involved: SS1, based on the blade profile parameters, constructs the cascade KO model, as shown in formula (1): （1） in, is the leaf shape loss of the KO model, is the attack angle correction factor of the KO model, is the blade profile loss in the AM model, is the Mach number correction factor, is the shock wave loss, is the trailing edge loss, Re is the inlet Reynolds number; SS2, the blade profile loss and trailing edge loss of the KO model are combined into the total blade profile loss, and a modified model is established to predict the total blade profile loss, as shown in formula (2): （2） in, is the total blade profile loss of the modified model, is the new corrected Mach number factor, is the angle of attack correction factor of the modified model, is the modified Reynolds factor of the modified model; SS3, define the deviation coefficient = experimental value / KO model predicted value, and perform linear regression on the inlet Reynolds number Re, as shown in formula (3): （3） in is the coefficient of deviation; is the leaf shape factor; in, is the modified Reynolds factor of the modified model; SS4, named the intercept term as the leaf factor , which is related to the leading edge thickness and the trailing edge thickness. After the model is determined, the enumeration method is used to find the optimal formula (4): （4） Where, and are the leading edge thickness and trailing edge thickness of the blade respectively; SS5, the overall correction formula is obtained, as shown in formula (5): （5） is the modified Reynolds factor for blade profile loss.

2. The method for predicting blade loss of a high-load turbine suitable for low Reynolds number working conditions according to claim 1, characterized in that: In step SS5, Correction is made using the modified Reynolds factor for blade profile losses: （6） in, is the modified Reynolds factor for blade profile loss.

3. The method for predicting blade loss of a high-load turbine suitable for low Reynolds number working conditions according to claim 2, characterized in that: Wherein step SS2 further comprises the following steps: SS21, Combined blade profile losses and trailing edge losses: A quantitative method is needed to determine the trailing edge losses, including calculations of fluid dynamics and fitting of experimental data; SS22, Adjust the KO model: Based on the characteristics of the trailing edge losses, adjust the KO model to include these additional losses, and redefine and calculate the model parameters; SS23, Calculate new loss coefficient: Use the adjusted KO model to calculate the new blade loss coefficient, reflecting the combined effects of blade loss and trailing edge loss; SS24, Determine the Reynolds Number Correction Factor: Determine the corrected Reynolds factor applicable to low Reynolds numbers through experimental data and theoretical analysis; SS25, establish a total loss prediction model: combine all correction factors and basic blade loss to establish a comprehensive blade loss prediction model, namely formula (2).

4. The method for predicting blade loss of a high-load turbine suitable for low Reynolds number working conditions according to claim 3, characterized in that: Wherein step SS3 further comprises the following steps: SS31, Experimental Data Preparation: Collect experimental data on turbine blade loss at different Reynolds numbers. The experimental data includes the measured values of blade loss and the corresponding inlet Reynolds number Re. SS32, calculate the coefficient of deviation: For each set of experimental data, use formula (3) to calculate the coefficient of deviation , generate a table of correspondence between coefficient of deviation and experimental conditions; SS33, Performing Linear Regression: Using Statistical Tools, Entering the Coefficient of Variation and the inlet Reynolds number Re data, perform linear regression analysis; determine the parameters of the linear regression equation, including the slope and intercept; SS34, modified KO model: Based on the results of linear regression analysis, the Reynolds number related terms in the KO model are modified; the modified Reynolds factor and blade shape factor are incorporated into the model to form a new modified model.

5. The method for predicting blade loss of a high-load turbine suitable for low Reynolds number working conditions according to claim 4, characterized in that: Wherein step SS4 further comprises the following steps: SS41, Establishing the relationship between blade shape factor and geometric parameters: Based on fluid mechanics principles and experimental data, establish the relationship between the blade shape factor σ and the leading edge thickness and trailing edge thickness of the blade; SS42, Enumeration Optimization: After determining the relationship between the blade profile factor σ and the leading edge thickness and trailing edge thickness, the enumeration method is used to search for parameter combinations to find the optimal σ value; SS43, determine the correction formula: determine the correction formula of the blade factor σ by finding the best parameter combination through enumeration method.

6. The method for predicting blade loss of a high-load turbine suitable for low Reynolds number working conditions according to claim 5, characterized in that: Step SS42 further includes: SS421, Define parameter space: First, determine the range of leading edge thickness and trailing edge thickness. The range is set based on design requirements, manufacturing constraints, or previous empirical data. SS422, Setting Resolution and Step Size: In parameter space, set a resolution or step size for discretization in each dimension; SS423, Initialize Performance Indicator: Select the accuracy of the prediction as the performance indicator and use the mean squared error or coefficient of determination to assess the goodness of fit of the model; SS424. Traverse Parameter Combinations: Traverse all leading-edge and trailing-edge thickness combinations in the parameter space at a specified step size. For each parameter pair, calculate the blade profile factor σ and use the corresponding model to predict blade profile loss. SS425. Evaluating Performance: For each parameter combination, evaluate the model's performance using an independent test dataset. Record the performance metrics for each parameter combination and identify the optimal parameter combination. SS426. Comparison and Selection: After traversing all parameter combinations, compare the performance indicators of each parameter combination and select the best parameter combination as the final blade shape factor σ; this best parameter combination results in the model achieving the lowest error or highest goodness of fit when predicting blade shape loss.

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