A method for constructing a high-load turbine loss correction model suitable for a wide range of operating conditions

Abstract

The present invention relates to a method for constructing a high-load turbine loss correction model suitable for a wide range of operating conditions, comprising the following steps: SS1, constructing a blade KO model based on blade profile parameters; SS2, combining the blade profile loss and trailing edge loss of the KO model into a total blade profile loss, and establishing a correction model to predict the total blade profile loss; SS3, obtaining the angle of attack factor in the KO model; SS4, defining a deviation coefficient = experimental value / KO model predicted value, and performing linear regression calculation on the angle of attack with the deviation coefficient; SS5, calculating the coupling factor of the negative angle of attack; SS6, calculating the coupling factor of the positive angle of attack; SS7, obtaining the total angle of attack coefficient. The present invention is suitable for a high-load wide-operating condition turbine blade profile loss correction model, and can more accurately predict the loss of the turbine under the conditions of a wide Reynolds number and a wide angle of attack, thereby better predicting the aerodynamic performance of the turbine, and providing important guidance for low-dimensional simulation, optimization and design.

Description

Technical Field

[0001] The present invention belongs to the field of aero-engine / gas turbine turbine technology, and specifically relates to a method for constructing a high-load turbine loss correction model applicable to a wide range of operating conditions. Background Art

[0002] As an impeller-type working machine, axial-flow turbines have been widely used in various energy and power fields. In order to achieve efficient axial-flow turbine design, accurate prediction of aerodynamic performance is necessary. People have successively developed loss prediction models, flow analysis, and three-dimensional numerical simulation methods to make numerical research more suitable for the strong three-dimensional unsteady viscous flow inside the turbine. Considering that turbine design has the characteristics of multi-parameter nonlinear coupling and the design process requires fine and repeated adjustments, loss prediction models are particularly important. They can provide important guidance for low-dimensional simulation, optimization and design, and greatly shorten the R&D cycle. There are usually four methods for turbine loss estimation, namely, estimating losses using loss models, estimating losses based on existing loss data, estimating losses through numerical simulation, and estimating losses through experiments. Among them, estimating losses using loss models can greatly save time. Therefore, many scholars at home and abroad have done a lot of work in the establishment, correction and improvement of loss models and achieved certain results. However, different loss models have different prediction accuracy and results, 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 the loss model prediction, so as to quickly and accurately estimate the loss. At the same time, the original loss model can be corrected through existing loss data or through numerical simulation and experimental methods.

[0003] However, the existing loss models differ in basic assumptions, calculation methods, loss prediction accuracy and scope of application. Studies have shown that the selection of different loss models has a great impact on the optimization design results. The traditional model itself is not adaptable to high-load and wide-operating turbines. Therefore, the pursuit of more accurate and better applicable loss prediction methods for high-load and wide-operating turbines has always been a key research topic for scholars at home and abroad.

[0004] For example, the Kacker-Okapuu (KO) model of the cascade is an empirical model for predicting and analyzing the flow losses inside the turbine blade passage. This model was proposed by Ajay Kacker and Marko Okapuu and is mainly used in the aerodynamic design and optimization process of blades in gas turbine engines. The KO model can provide designers with a relatively simple and effective tool to evaluate the impact of different design variables on the aerodynamic performance of the cascade, especially in predicting the total pressure loss inside the blade passage. The KO model is based on a large amount of experimental data and empirical relationships, and estimates the flow losses by considering the effects of blade geometry, flow conditions (such as Reynolds number and Mach number), and cascade configuration (such as blade spacing, angle of attack, etc.). It is particularly suitable for the preliminary design stage and can provide useful guidance and reference when different design options need to be quickly evaluated. The core of the model is that it can reasonably simplify complex flow phenomena, so that the aerodynamic performance of the cascade can be preliminarily evaluated without a complete numerical fluid dynamics (CFD) simulation. However, it should be noted that although the KO model is widely used in industry, it is still an empirical model, and its accuracy depends on the selection of model parameters and the scope of application.

[0005] It can be seen that in terms of blade loss alone, the traditional loss model is not well applicable within the scope of high-load wide-operating condition turbines, because the loss of high-load wide-operating condition turbines is different from that of traditional turbines. Therefore, a high-load wide-operating condition turbine blade loss correction model with angle of attack correction is imminent. Summary of the invention

[0006] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a method for constructing a high-load turbine loss correction model suitable for a wide range of operating conditions. Based on the existing experimental data, by adding a correction factor, the influence of the angle of attack on the loss is corrected, the traditional KO model is improved, and a more accurate prediction of the aerodynamic performance of the turbine is achieved.

[0007] The technical solution adopted by the present invention to solve its technical problems is:

[0008] A method for constructing a high-load turbine loss correction model applicable to a wide range of operating conditions of the present invention comprises the following steps:

[0009] SS1, based on the blade profile parameters, constructs the cascade KO model, as shown in formula (1):

[0010]

[0011] Among them, Y P is the leaf shape loss of the KO model, χ i is the attack angle correction factor of the KO model; Y′ P,AMis the blade loss in the AM model, k p is the Mach number correction factor, Y shock is the shock wave loss, Y′ TET is the trailing edge loss;

[0012] SS2, the blade loss and trailing edge loss of the KO model are combined into the total blade loss, and a modified model is established to predict the total blade loss, as shown in formula (2):

[0013]

[0014] Among them, Y P is the total blade loss of the modified model, K′ p is the new corrected Mach number factor, χ′ i is the angle of attack correction factor of the modified model, χ′ Re is the Reynolds factor of the modified model;

[0015] SS3, obtain the angle of attack factor in the KO model, as shown in formula (3):

[0016]

[0017] SS4, define the deviation coefficient = experimental value / KO model predicted value, and use the deviation coefficient to perform linear regression calculation on the angle of attack, as shown in formula (4):

[0018] χ=-4×10 5 ×(i) 3 -0.0019×(i) 2 +0.031×i+2.1408(i<0) (4)

[0019] SS5, calculation of the coupling factor of the negative angle of attack: Observing the residual, it is found that the negative angle of attack has been basically stable and has no relationship with the Reynolds number. Decoupling is achieved and it is only related to the positive angle of attack and the negative angle of attack. Therefore, the residual is regressed on the positive angle of attack and the negative angle of attack to obtain the coupling factor of the negative angle of attack, as shown in formula (5):

[0020]

[0021] SS6, calculation of the coupling factor of the positive angle of attack: The residual of the positive angle of attack still changes with the Reynolds number and the angle of attack simultaneously, so the Reynolds number is regressed first, and it is observed that the coupling factors of Re < 50k and Re > 50k are quite different; therefore, after being divided into two categories, the residual is regressed again on the positive angle of attack and the negative angle of attack, as shown in formulas (6) and (7):

[0022]

[0023]

[0024] SS7, the total angle of attack coefficient is obtained, as shown in formula (8):

[0025]

[0026] Preferably, the process of obtaining the angle of attack factor in the KO model in step SS3 is:

[0027] α 1 is the inlet airflow angle, β 1 is the imported metal angle, α 2 is the outlet airflow angle, β 2 is the exit metal angle, S refers to the grid pitch, and C refers to the chord length;

[0028] 55<α 1 <60 as an example,

[0029]

[0030]

[0031]

[0032] i=i s +Δi s .

[0033] Preferably, in the process of combining the blade profile loss and the trailing edge loss into the blade profile loss in step SS2, a blade profile factor is introduced, which includes a correction for the trailing edge loss.

[0034] Preferably, the coefficient of deviation defined in step SS4 is obtained by performing a linear regression analysis on the experimental data and the KO model prediction value by the least squares method.

[0035] Preferably, when calculating the coupling factor of the negative angle of attack in step SS5, it further includes analyzing the residual to determine the stability of the negative angle of attack, and based on this, determining the decoupling relationship between the negative angle of attack and the Reynolds number.

[0036] Preferably, when calculating the coupling factor of the positive angle of attack in step SS6, it further includes classifying the residuals of the positive angle of attack according to different ranges of Reynolds numbers, and performing regression analysis on the residuals in different Reynolds number ranges, so as to obtain the positive angle of attack coupling factors suitable for different Reynolds number ranges.

[0037] Preferably, step SS4 further comprises the following steps:

[0038] SS41. Collect a series of experimental data, including the turbine blade loss values ​​under different working conditions. And calculate the predicted value of the KO model through the formula in the KO model;

[0039] SS42, linear fitting of experimental data and KO model prediction values ​​was performed using the least squares method to determine the coefficients in the linear regression equation;

[0040] SS43. When performing linear regression analysis, taking into account the possible errors and deviations in the experimental data, the weighted least squares method is used to process the data to improve the accuracy and reliability of the regression equation;

[0041] SS44, obtain a mathematical model describing the relationship between the experimental value and the KO model predicted value, which can quantify the deviation between the two, namely the deviation coefficient;

[0042] SS45. The original KO model is modified using the obtained deviation coefficient to more accurately predict the loss of turbine blades under wide angle of attack conditions.

[0043] The advantages of the present invention compared with the prior art are as follows:

[0044] (1) The present invention provides a modified model for turbine blade loss under high load and wide operating conditions, which can more accurately predict turbine loss under wide Reynolds number and wide angle of attack conditions. The traditional turbine loss model has limited applicability under high load and wide operating conditions, while the present invention significantly improves the accuracy of prediction by introducing correction factors and coupling factors.

[0045] (2) The model of the present invention is not only applicable to conventional turbine design conditions, but also can cope with extreme conditions, such as high angle of attack and high Reynolds number. This wide applicability makes the model of the present invention highly practical in different types of turbine designs and can cope with various design challenges.

[0046] (3) Through the modified model of the present invention, the aerodynamic performance of the turbine can be predicted more accurately, which helps to reduce the number of design iterations, shorten the R&D cycle, reduce costs, and ultimately improve the overall performance and efficiency of the turbine.

[0047] (4) The present invention provides a deeper understanding of the turbine blade loss mechanism through an in-depth analysis of the coupling effects of angle of attack and Reynolds number. This understanding helps guide future research directions, promote the development of turbine aerodynamic design theory, and provide a theoretical basis for the design of new turbines.

[0048] (5) The present invention makes full use of the existing experimental data in the process of constructing the correction model. Through the least square method and linear regression analysis, the present invention can effectively extract useful information from the experimental data and convert it into the correction parameters of the model. By effectively utilizing the experimental data, the accuracy of the model is improved.

[0049] (6) The model of the present invention specifically considers the effect of the coupling effect of the angle of attack and the Reynolds number on the turbine blade loss. By calculating the coupling factors for negative and positive angles of attack respectively, the present invention can more accurately describe this coupling effect and incorporate it into the loss prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flow chart of a method for constructing a high-load turbine loss correction model applicable to a wide range of operating conditions according to the present invention;

[0051] Figure 2 This is a parameter diagram of a high-load turbine blade suitable for a wide angle of attack according to the present invention. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical scheme and advantages of the implementation of the present invention clearer, the technical scheme in the embodiment of the present invention will be described in more detail below in conjunction with the drawings in the embodiment 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 construed as limitations on the present invention. Based on the embodiments in 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 scheme of the present invention are further described in detail below in conjunction with the drawings, and an embodiment of the present invention is given.

[0053] A method for constructing a high-load turbine loss correction model applicable to a wide range of operating conditions of the present invention comprises the following steps:

[0054] SS1, based on the blade profile parameters, constructs the cascade KO model, as shown in formula (1):

[0055]

[0056] Among them, Y P is the leaf shape loss of the KO model, χ i is the attack angle correction factor of the KO model; Y′ P,AM is the blade loss in the AM model, k p is the Mach number correction factor, Y shock is the shock wave loss, Y′ TET is the trailing edge loss;

[0057] SS2, the blade loss and trailing edge loss of the KO model are combined into the total blade loss, and a modified model is established to predict the total blade loss, as shown in formula (2):

[0058]

[0059] Among them, Y P is the total blade loss of the modified model, K′ p is the new corrected Mach number factor, χ′ i is the angle of attack correction factor of the modified model, χ′ Re is the Reynolds factor of the modified model;

[0060] SS3, obtain the angle of attack factor in the KO model, as shown in formula (3):

[0061]

[0062] SS4, define the deviation coefficient = experimental value / KO model predicted value, and use the deviation coefficient to perform linear regression calculation on the angle of attack, as shown in formula (4):

[0063] χ=-4×10 5 ×(i) 3 -0.0019×(i) 2 +0.031×i+2.1408(i<0) (4)

[0064] SS5, calculation of the coupling factor of the negative angle of attack: By observing the residual, it is found that the negative angle of attack has been basically stable and has no relationship with the Reynolds number. Decoupling is achieved and it is only related to the positive angle of attack and the negative angle of attack. Therefore, the residual is regressed on the negative angle of attack and the positive angle of attack to obtain the coupling factor of the negative angle of attack, as shown in formula (5):

[0065]

[0066] SS6, calculation of the coupling factor of the positive angle of attack: The residual of the positive angle of attack still changes with the Reynolds number and the angle of attack simultaneously, so the Reynolds number is regressed first, and it is observed that the coupling factors of Re < 50k and Re > 50k are quite different; therefore, after being divided into two categories, the residual is regressed again on the positive angle of attack and the negative angle of attack, as shown in formulas (6) and (7):

[0067]

[0068]

[0069] SS7, the total angle of attack coefficient is obtained, as shown in formula (8):

[0070]

[0071] The process of obtaining the angle of attack factor in the KO model in step SS3 is as follows:

[0072] α 1 is the inlet airflow angle, β1 is the imported metal angle, α 2 is the outlet airflow angle, β 2 It is the exit metal angle.

[0073] 55<α 1 <60 as an example,

[0074]

[0075]

[0076]

[0077] i=i s +Δi s .

[0078] In summary, the present invention is based on the latest blade loss experimental data, uses the control variable regression and the coupling factor method to modify the original blade cascade Kacker-Okapuu (KO) model (blade parameters such as Figure 2 ) was optimized. Since the wake loss coefficient in the KO loss model is considered separately, and the experimental data obtained is the blade loss in a larger sense, that is, it includes the blade loss and trailing edge loss of the KO model. When the trailing edge loss and the blade loss are difficult to deal with separately, the blade loss and the trailing edge loss of the KO model are merged into the blade loss following the approach of Traupel, and a model is established to predict the blade loss. The angle of attack factor in the KO model is obtained, and then the deviation coefficient is defined as experimental value / KO model predicted value. Then the deviation coefficient is used to perform a linear regression on the angle of attack, and the residual is observed. It is found that the negative angle of attack has been basically stable and has nothing to do with the Reynolds number. Decoupling is achieved, and it is only related to the positive and negative angles of attack. Therefore, the residual is regressed on the positive and negative angles of attack to obtain the coupling factor of the negative angle of attack. The residual of the positive angle of attack still changes with the Reynolds number and the angle of attack. Therefore, we first regress the Reynolds number. After observing that the coupling factors of Re<50k and Re>50k are quite different, they are divided into two categories. Then, we regress the residual on the positive angle of attack and the negative angle of attack in turn, and then regress the angle of attack once more to get the total angle of attack coefficient.

[0079] In the process of combining the blade profile loss and the trailing edge loss into the blade profile loss in step SS2, a blade profile factor is introduced, which includes a correction for the trailing edge loss.

[0080] The deviation coefficient defined in step SS4 is obtained by performing linear regression analysis on the experimental data and the KO model prediction value using the least squares method.

[0081] Wherein, when calculating the coupling factor of the negative angle of attack in step SS5, it further includes analyzing the residual to determine the stability of the negative angle of attack, and based on this, determining the decoupling relationship between the negative angle of attack and the Reynolds number.

[0082] Among them, when calculating the coupling factor of the positive angle of attack in step SS6, it further includes classifying the residuals of the positive angle of attack according to different ranges of Reynolds numbers, and performing regression analysis on the residuals in different Reynolds number ranges respectively, so as to obtain the positive angle of attack coupling factors suitable for different Reynolds number ranges.

[0083] Wherein, step SS4 further comprises the following steps:

[0084] Collect a series of experimental data, including the turbine blade loss values ​​under different working conditions. And calculate the predicted value of the KO model through the formula in the KO model;

[0085] SS42, linear fitting of experimental data and KO model prediction values ​​was performed using the least squares method to determine the coefficients in the linear regression equation;

[0086] SS43. When performing linear regression analysis, taking into account the possible errors and deviations in the experimental data, the weighted least squares method is used to process the data to improve the accuracy and reliability of the regression equation;

[0087] SS44, obtain a mathematical model describing the relationship between the experimental value and the KO model predicted value, which can quantify the deviation between the two, namely the deviation coefficient;

[0088] SS45. The original KO model is modified using the obtained deviation coefficient to more accurately predict the loss of turbine blades under wide angle of attack conditions.

[0089] The advantages of the present invention compared with the prior art are as follows:

[0090] (1) The present invention aims at a high-load turbine loss correction model with a wide range of operating conditions, and can more accurately predict turbine losses under conditions of a wide Reynolds number and a wide angle of attack. The conventional turbine loss model has limited applicability under high-load and wide operating conditions, and the present invention significantly improves the accuracy of prediction by introducing correction factors and coupling factors.

[0091] (2) The model of the present invention is not only applicable to conventional turbine design conditions, but also can cope with extreme conditions, such as high angle of attack and high Reynolds number. This wide applicability makes the model of the present invention highly practical in different types of turbine designs and can cope with various design challenges.

[0092] (3) Through the modified model of the present invention, the aerodynamic performance of the turbine can be predicted more accurately, which helps to reduce the number of design iterations, shorten the R&D cycle, reduce costs, and ultimately improve the overall performance and efficiency of the turbine.

[0093] (4) The present invention provides a deeper understanding of the turbine blade loss mechanism through an in-depth analysis of the coupling effects of angle of attack and Reynolds number. This understanding helps guide future research directions, promote the development of turbine aerodynamic design theory, and provide a theoretical basis for the design of new turbines.

[0094] (5) The present invention makes full use of the existing experimental data in the process of constructing the correction model. Through the least square method and linear regression analysis, the present invention can effectively extract useful information from the experimental data and convert it into the correction parameters of the model. By effectively utilizing the experimental data, the accuracy of the model is improved.

[0095] (6) The model of the present invention specifically considers the effect of the coupling effect of the angle of attack and the Reynolds number on the turbine blade loss. By calculating the coupling factors for negative and positive angles of attack respectively, the present invention can more accurately describe this coupling effect and incorporate it into the loss prediction.

[0096] Through the above embodiments, the purpose of the present invention is fully and effectively achieved. Those skilled in the art can understand that the present invention includes but is not limited to the contents described in the drawings and the above specific embodiments. Although the present invention has been described with respect to the most practical and preferred embodiments currently considered, it should be understood that the present invention is not limited to the disclosed embodiments, and any modification that does not deviate from the functional and structural principles of the present invention will be included in the scope of the claims.

Claims

1. A method for constructing a high-load turbine blade loss correction model suitable for a wide range of operating 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 loss in the AM model, k p is the Mach number correction factor, Y shock is the shock wave loss, is the trailing edge loss; SS2, the blade loss and trailing edge loss of the KO model are combined into the total blade loss, and a modified model is established to predict the total blade loss, as shown in formula (2): (2) in, is the total blade 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 Reynolds factor of the modified model; SS3, obtain the angle of attack correction factor of the KO model, as shown in formula (3): (3) SS4, define the deviation coefficient = experimental value / KO model predicted value, and use the deviation coefficient to perform linear regression calculation on the angle of attack, as shown in formula (4): （4） SS5, calculation of the coupling factor of the negative angle of attack: Observing the residual, it is found that the negative angle of attack has been basically stable and has no relationship with the Reynolds number. Decoupling is achieved and it is only related to the positive angle of attack and the negative angle of attack. Therefore, the residual is regressed on the positive angle of attack and the negative angle of attack to obtain the coupling factor of the negative angle of attack, as shown in formula (5): (5) SS6, calculation of the coupling factor for positive angle of attack: The residual of the positive angle of attack still changes with the Reynolds number and the angle of attack simultaneously, so we first regress the Reynolds number, and observe that the coupling factors for Re<50k and Re>50k are quite different; therefore, after dividing them into two categories, we regress the residuals for positive and negative angles of attack again, as shown in formulas (6) and (7): (6) (7) SS7, the total angle of attack coefficient is obtained as shown in formula (8): (8) 。 2. The method for constructing a high-load turbine blade loss correction model applicable to a wide range of operating conditions according to claim 1, characterized in that: in, The process of obtaining the angle of attack factor in the KO model in step SS3 is as follows: obtain the airflow angle and the metal angle, where is the inlet airflow angle, It is imported metal angle. is the outlet airflow angle, is the exit metal angle, S is the grid pitch, and C is the chord length; Assumptions , then: 。 3. The method for constructing a high-load turbine blade loss correction model applicable to a wide range of operating conditions according to claim 2, characterized in that: In the process of combining the blade profile loss and the trailing edge loss into the blade profile loss in step SS2, the blade profile factor is introduced, which includes a correction for the trailing edge loss.

4. The method for constructing a high-load turbine blade loss correction model applicable to a wide range of operating conditions according to claim 3, characterized in that: The coefficient of deviation defined in step SS4 is obtained by performing a linear regression analysis of the experimental data and the KO model prediction value using the least squares method.

5. The method for constructing a high-load turbine blade loss correction model applicable to a wide range of operating conditions according to claim 4, characterized in that: When calculating the coupling factor of the negative angle of attack in step SS5, it further includes analyzing the residual to determine the stability of the negative angle of attack, and based on this, determining the decoupling relationship between the negative angle of attack and the Reynolds number.

6. The method for constructing a high-load turbine blade loss correction model applicable to a wide range of operating conditions according to claim 5, characterized in that: When calculating the coupling factor of the positive angle of attack in step SS6, it further includes classifying the residuals of the positive angle of attack according to different ranges of Reynolds numbers, and performing regression analysis on the residuals in different Reynolds number ranges respectively, so as to obtain the positive angle of attack coupling factors suitable for different Reynolds number ranges.

7. The method for constructing a high-load turbine blade loss correction model applicable to a wide range of operating conditions according to claim 6, characterized in that: Step SS4 further comprises the following steps: SS41. Collect a series of experimental data, including the turbine blade loss values ​​under different operating conditions, and calculate the predicted values ​​of the KO model through the formula in the KO model; SS42, linear fitting of experimental data and KO model prediction values ​​was performed using the least squares method to determine the coefficients in the linear regression equation; SS43. When performing linear regression analysis, taking into account the possible errors and deviations in the experimental data, the weighted least squares method is used to process the data to improve the accuracy and reliability of the regression equation; SS44, obtain a mathematical model describing the relationship between the experimental value and the KO model predicted value, which can quantify the deviation between the two, namely the deviation coefficient; SS45. The original KO model is modified using the obtained deviation coefficient to more accurately predict the loss of turbine blades under a wide range of operating conditions.

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