One-dimensional prediction method for multi-stage axial-flow transonic turbine characteristics based on dimensionless numbers

Abstract

The purpose of this invention is to provide a one-dimensional prediction method for the characteristics of a multi-stage axial-flow transonic turbine based on dimensionless numbers, comprising the following steps: turbine characteristic calculation; angle-of-attack loss calculation; total pressure loss calculation using a loss model; lag angle calculation using a lag angle model; transonic position determination; transonic cross-sectional characteristic parameter calculation; iterating the above process until the required accuracy is met, thus completing the characteristic prediction at the operating point. This invention's one-dimensional prediction method for the aerodynamic characteristics of a multi-stage axial-flow transonic turbine based on dimensionless numbers can plot turbine characteristic curves using turbine inlet velocity, inlet mass flow rate, and total expansion ratio as the abscissas; it can predict turbine design and non-design operating conditions; the method simultaneously considers the influence of angle of attack and lag angle, and incorporates a loss model; this method can simultaneously predict the characteristics of subsonic and transonic turbines; furthermore, this invention improves the accuracy of turbine characteristic prediction and shortens the design cycle of axial-flow turbines.

Description

Technical Field

[0001] The present invention relates to a design method for an axial flow turbine of a gas turbine, specifically a method for predicting the characteristics of a multi-stage axial flow transonic turbine. Background Technology

[0002] Among the main components of an aero-engine, the turbine plays a crucial role, providing power to the gas turbine. Aerodynamic design is the most critical part of turbine design; a high-performance turbine inevitably possesses a high level of aerodynamic design. In the early stages of turbine design, only basic design parameters such as inlet total temperature, total pressure, and expansion ratio are typically provided, lacking detailed geometric and aerodynamic parameters. Therefore, making reasonable predictions of turbine characteristics using limited design parameters to guide the overall turbine design is particularly important.

[0003] Turbines are mainly classified into four types according to the flow direction of the working fluid: axial flow, radial flow, oblique flow, and mixed flow. Among them, axial flow turbines are widely favored due to their large flow rate and high efficiency. The aerodynamic design of axial flow turbines is a process of gradual optimization from low-dimensional to high-dimensional design. The rationality of the selection of one-dimensional design parameters will directly affect the three-dimensional design results; therefore, parameter selection is crucial in the preliminary design. Turbine design must consider not only the performance at the design point but also the performance under non-design conditions. The design condition is determined based on the operating conditions under which the turbine operates normally, and the losses under the design condition are often minimal, resulting in the best performance. However, in actual operation, turbines often deviate from the design condition, requiring the prediction of the turbine's non-design characteristics.

[0004] To explore the selection rules of one-dimensional parameters for multi-stage axial-flow transonic turbines, determine the selection range of one-dimensional parameters for transonic turbines, and study the influence of one-dimensional parameters on turbine characteristics, thereby improving the overall turbine performance, shortening the turbine design cycle, and saving computational resources. Summary of the Invention

[0005] The purpose of this invention is to provide a one-dimensional prediction method for the characteristics of a multi-stage axial-flow transonic turbine based on dimensionless numbers, which allows for rapid prediction of the aerodynamic characteristics of a multi-stage axial-flow transonic turbine at a one-dimensional level.

[0006] The objective of this invention is achieved as follows:

[0007] This invention relates to a one-dimensional prediction method for the characteristics of multi-stage axial-flow transonic turbines based on dimensionless numbers, characterized by:

[0008] (1) Calculate the dimensionless speed coefficient of the turbine stage inlet and the equivalent speed coefficient of the turbine rotor by using the rotational speed and the inlet flow rate;

[0009] (2) Solve the stator blade exit characteristic parameters by establishing mass conservation and continuity equations through the 0-1 section: By setting the initial values ​​of the stator blade velocity coefficient and the exit airflow angle, the stator blade characteristic parameters calculated for the first time are obtained. The stator blade loss model uses the results to calculate the new stator blade velocity coefficient. The lag angle is calculated through the lag angle model. The above process is repeated until the accuracy is met, and the dimensionless velocity coefficient and exit airflow angle parameters of the turbine stage stator blade are obtained.

[0010] (3) Solving for the inlet parameters of the moving blade: Calculate the relative airflow angle and relative velocity of the moving blade using the outlet parameters of the stationary blade and the rotational speed of the moving blade.

[0011] (4) Solve the stator blade exit characteristic parameters by establishing mass conservation and continuity equations through the 0-2 section: By setting the initial values ​​of the blade velocity coefficient and the outlet airflow angle, the blade characteristic parameters calculated for the first time are obtained. The blade loss model uses this result to calculate the new blade velocity coefficient. The lag angle is calculated through the lag angle model. The above process is repeated until the accuracy is met, and the turbine stage blade exit relative parameters are obtained.

[0012] (5) Solve for the inlet parameters of the moving blade: Calculate the absolute airflow angle and absolute velocity at the outlet of the moving blade using the above results;

[0013] (6) Calculation of the next stage characteristic parameters: Solve the dimensionless velocity coefficient of the next stage stator inlet by the flow continuity equation, and repeat steps (2) to (5) to obtain the characteristic parameters of the stage.

[0014] (7) Repeat steps (2) to (6) above, and calculate the turbine stage characteristic parameters of any stage by applying the derived turbine inlet and turbine stage inlet flow continuity equations, and finally obtain the turbine overall characteristic parameters.

[0015] The present invention may also include:

[0016] 1. In steps (2) and (3), different lag angle models and total pressure loss models are used depending on whether the speed is subsonic or transonic.

[0017] 2. Based on the maximum allowable mass flow rate of each stage and section of the turbine as the criterion for judging whether the fluid can pass through the turbine stage section, adjust the inlet flow rate and complete the turbine characteristic calculation at that speed.

[0018] The advantages of this invention are:

[0019] 1. The one-dimensional prediction method for the aerodynamic characteristics of a multi-stage axial-flow transonic turbine based on dimensionless numbers proposed in this invention can provide various forms of turbine characteristic curve plotting. It can plot turbine characteristic curves with turbine inlet velocity coefficient, turbine inlet flow rate, total temperature ratio, and total expansion ratio as the abscissa and turbine total efficiency as the ordinate; as well as plot the relationship curves between turbine inlet velocity and characteristics such as total temperature ratio and total expansion ratio.

[0020] 2. The one-dimensional prediction method for the aerodynamic characteristics of a multi-stage axial-flow transonic turbine based on dimensionless numbers proposed in this invention simultaneously considers the changes in angle of attack, total pressure loss, and lag angle. It can quickly predict the subsonic and transonic characteristics of the turbine and can calculate the turbine under both design and non-design conditions. Attached Figure Description

[0021] Figure 1 This is a flowchart of the present invention;

[0022] Figure 2 This is a schematic diagram of the velocity triangle;

[0023] Figure 3a For comparison of the relative velocities at the blade inlet, Figure 3b The relative error is the relative velocity of the moving blade inlet.

[0024] Figure 4a For comparison of the relative velocities at the blade exit, Figure 4b This refers to the relative error of the relative velocity at the blade exit.

[0025] Figure 5a For comparison of the overall inflation ratio at each level. Figure 5b The relative error of the total expansion ratio at each level;

[0026] Figure 6a For comparison of total temperature ratios at each level, Figure 6b This represents the relative error of the total temperature ratio at each level;

[0027] Figure 7 Relationship between dimensionless import velocity and total-total expansion ratio;

[0028] Figure 8 The relationship between the rate of imports without factorial change and total-total efficiency. Detailed Implementation

[0029] The invention will now be described in more detail with reference to the accompanying drawings:

[0030] Combination Figure 1-8 The process of this invention includes the following parts:

[0031] (1) Dimensionless velocity coefficient of turbine stage inlet and equivalent speed coefficient of turbine rotor: Both are calculated by speed and inlet flow rate;

[0032] (2) Solve the stator blade exit characteristic parameters by establishing mass conservation and continuity equations through the 0-1 section: By setting the initial values ​​of the stator blade velocity coefficient and the exit airflow angle, the stator blade characteristic parameters calculated for the first time are obtained. The stator blade loss model uses the results to calculate the new stator blade velocity coefficient. The lag angle is calculated through the lag angle model. The above process is repeated until the accuracy is met, and the turbine stage stator blade exit dimensionless velocity coefficient and exit airflow angle are obtained.

[0033] (3) Solving for the inlet parameters of the moving blade: Calculate the relative airflow angle and relative velocity during winter nights using the outlet parameters of the stationary blade and the rotational speed of the moving blade.

[0034] (4) Solve the stator blade exit characteristic parameters by establishing mass conservation and continuity equations through section 0-2: Similar to the calculation method of parameters in section 0-1, by setting the initial values ​​of the blade velocity coefficient and the outlet airflow angle, the blade characteristic parameters calculated for the first time are obtained. The blade loss model uses this result to calculate the new blade velocity coefficient, and the lag angle is calculated through the lag angle model. Repeat the above process until the accuracy is met, and obtain the turbine stage blade exit relative parameters.

[0035] (5) Solve for the inlet parameters of the moving blade: Calculate the absolute airflow angle and absolute velocity at the outlet of the moving blade using the above results;

[0036] (6) Calculation of the next stage characteristic parameters: Solve the dimensionless velocity coefficient of the next stage stator inlet by the flow continuity equation, and repeat the process (2) to (5) to obtain the characteristic parameters of the stage.

[0037] (7) Repeat steps (2) to (6) above, and calculate the turbine stage characteristic parameters of any stage by applying the derived turbine inlet and turbine stage inlet flow continuity equations, and finally obtain the turbine overall characteristic parameters.

[0038] This invention presents a one-dimensional prediction method for the characteristics of a multi-stage axial-flow transonic turbine based on dimensionless numbers. It derives the parameter relationships of each cross-section based on the fundamental flow equations and energy equations of fluid mechanics, and completes the calculation of turbine stage-related parameters, thereby realizing turbine characteristic calculation. In the following formulas: k represents the adiabatic index; P and T represent the pressure and temperature of each cross-section, respectively; A represents the area of ​​each cross-section; G represents the mass flow rate through each cross-section; the superscript "*" indicates the stagnation parameter; the subscripts "0, 1, 2" represent cross-sections 0, 1, and 2 of stage, respectively; m is a constant; λ0 is the dimensionless velocity coefficient at the turbine inlet; λ c1 λ is the dimensionless velocity coefficient at the stator blade exit. w2 λ is the dimensionless velocity coefficient at the blade exit. u1 λ is the dimensionless circumferential velocity coefficient at the blade inlet; 0,i Let λ be the dimensionless velocity coefficient at the turbine stage stator inlet; q(λ) is the hydrodynamic function; the formulas for solving the above parameters are as follows:

[0039] The dimensionless velocity coefficient λ0 at the turbine inlet:

[0040]

[0041] dimensionless velocity coefficient λ at the stator exit c1 :

[0042]

[0043] dimensionless velocity coefficient λ at the blade exit w2 :

[0044]

[0045] The dimensionless speed coefficient λ of the turbine rotor u1 :

[0046]

[0047] Fluid aerodynamic function:

[0048]

[0049]

[0050]

[0051] Formula for calculating constant m:

[0052]

[0053] (1) Establish the continuous flow equations at the turbine inlet and the stator outlet:

[0054] The flow equation at the turbine inlet is:

[0055]

[0056] The flow equation at the stationary vane outlet is:

[0057]

[0058] According to the law of conservation of mass, the mass flow rate at the turbine inlet should be equal to the mass flow rate at the stator outlet, therefore:

[0059] G0 = G1

[0060]

[0061] When the working fluid remains constant: m0 = m1, according to the enthalpy-entropy diagram...

[0062] After simplifying equation (11), we get:

[0063]

[0064] In the formula: σ V (λ c1 ) represents the stator vane restitution coefficient; q(λ0) represents the turbine inlet equivalent flow rate; q(λ) c1 The value is the equivalent flow rate at the stationary blade outlet. The specific calculation formula is as follows:

[0065]

[0066]

[0067]

[0068] Substituting equations (13), (14), and (15) into equation (12), we get:

[0069]

[0070] The above formula can be simplified to a simpler form:

[0071] X(λ0,k)=B1Y1(λ c1 ,k,φ) (17)

[0072] In the formula:

[0073] X and Y1 are newly constructed functions, and their definitions are as follows:

[0074]

[0075]

[0076] Based on the changes in the values ​​of λ and k, X(λ,k) and Y1(λ,k,φ) can be plotted as curves, which facilitates the calculation of turbine characteristics.

[0077] (2) Establish the continuous flow equations for the turbine inlet and the moving blade outlet:

[0078] The flow equation at the moving blade outlet is:

[0079]

[0080] According to the law of conservation of mass, the mass flow rate at the turbine inlet should be equal to the mass flow rate at the blade outlet, therefore:

[0081] G0 = G2 (21)

[0082]

[0083] When the working fluid remains constant: m0 = m2.

[0084] After simplifying equation (22), we get:

[0085]

[0086] Further simplification yields:

[0087]

[0088] In the formula: q(λ) W2 ) represents the equivalent flow rate at the turbine blade outlet; σ B (λ W2 ) represents the blade pressure recovery coefficient.

[0089] The specific calculation formula is as follows:

[0090]

[0091]

[0092]

[0093] Substituting equations (25), (26), (27), and (20) into equation (24), we get:

[0094]

[0095] The above formula can be simplified to a simpler form:

[0096]

[0097] Where:

[0098] Y2 is a newly constructed function, defined as follows:

[0099]

[0100] According to λ c1 , λ w2 , λ u ,φ, And the change in the value of k, It can be used to create graphs, making it easy to observe the characteristics of the turbine.

[0101] (3) Establish the continuous flow equations for the turbine inlet and each stage inlet:

[0102] G0 = G 0,i (31)

[0103]

[0104]

[0105] Expanding further:

[0106]

[0107] The outlet of the previous stage of the turbine is the inlet of the next stage, that is, the 2-section of the (i-1)th stage is the 0-section of the i-th stage (2,i-1 = 0,i), where:

[0108]

[0109]

[0110] In the same turbine stage:

[0111]

[0112]

[0113]

[0114]

[0115] Equation (34) can be rearranged into a simpler form:

[0116]

[0117] Y3 is a new aerodynamic function, where:

[0118] According to the law of conservation of mass, the mass flow rate at the turbine inlet is equal to that at each stage inlet. By decomposing the mass flow rate formula, the relationship between the turbine inlet and the inlet parameters at each stage can be obtained, as shown in equation (41). Based on the established flow relationship between the stator inlet (0 section), the stator outlet (1 section), and the moving blade outlet (2 section, which is also the 0 section of the next stage), the flow calculation of the entire turbine can be realized through equation (34). Thus, the establishment of the method for predicting the characteristics of a multi-stage axial flow transonic turbine stage based on dimensionless numbers is completed.

[0119] By conserving mass and making the parameters dimensionless, the flow equations for calculating turbine characteristics stage by stage are established, and the analysis is further simplified, resulting in the following set of equations:

[0120]

[0121] Given that the dimensionless velocity coefficients of each cross section of any turbine stage have been determined, turbine characteristic parameters such as total temperature ratio, total expansion ratio, and total efficiency can be easily obtained.

[0122]

[0123]

[0124] Turbine-stage thermal reaction:

[0125]

[0126] Turbine total-to-total temperature ratio:

[0127]

[0128] Turbine static total temperature ratio:

[0129]

[0130] Turbine total expansion ratio:

[0131]

[0132] Turbine static expansion ratio:

[0133]

[0134] Turbine isentropic total temperature ratio:

[0135]

[0136] Turbine overall efficiency:

[0137]

[0138] Turbine overall static efficiency:

[0139]

[0140] Total losses of the cascade:

[0141] The total loss of the AMDC model is based on the relationship of the Ainlye & Mathies model, which assumes that the blade shape is related to the secondary flow loss and the Reynolds number, and that the trailing edge coefficient is related to the trailing edge thickness and chord length.

[0142]

[0143] In the formula: Y P For blade shape loss; Y S For secondary flow loss; Y TL For gap leakage loss; χ Te This is the trailing edge correction factor.

[0144] Leaf shape loss:

[0145] Y p = [1 + 60(M-1)] 2 ]χ i ·Y P(i＝0)(54)

[0146]

[0147]

[0148] In the formula: M is the exit Mach number; Y P(i＝0) Zero angle of attack blade loss coefficient; The airfoil loss coefficient for small-angle blade cascades; α is the airfoil loss coefficient for large-angle blade cascades; t is the maximum blade thickness; c is the airfoil chord length; α in The inlet airflow angle; α out This is the outlet airflow angle.

[0149] Secondary flow loss:

[0150] Dunham & Came's research revealed that the secondary flow loss model in the Ainley & Mathieson loss model is not entirely applicable to the calculation of turbine losses with small aspect ratios. Through the study of numerous experimental results, they incorporated the influence of aspect ratio into the secondary flow loss relationship and simplified the dimensionless velocity coefficient λ. The specific relationship is as follows:

[0151]

[0152] In the formula: h is the toroidal height (when the gap is 0, it is equal to the blade height).

[0153] Tip clearance leakage loss:

[0154] The Ainley & Mathieson model assumes a linear relationship between tip clearance leakage loss and tip clearance. In contrast, the Donham & Came model considers tip clearance leakage loss to be a power function of tip clearance, with the specific relationship expressed as follows:

[0155]

[0156] In the formula: τ is the leaf tip gap; B is the correction coefficient, which is 0.37 when the leaf has a crown and 0.47 when the leaf does not have a crown.

[0157] In the one-dimensional characteristic prediction of turbines, the ability to accurately determine the location of blockages in the gas flow through the turbine blades is crucial for accurate prediction of turbine characteristics. Therefore, accurate determination of blockage locations is of paramount importance. This paper uses the maximum allowable mass flow rate of the divided cross-sections (sections 0, 1, and 2) as the criterion for determining whether fluid can pass through a certain turbine stage cross-section. If the turbine inlet mass flow rate is less than the maximum allowable mass flow rate for all sections, the fluid passes smoothly through all sections of the turbine. If the turbine inlet mass flow rate is equal to the maximum allowable mass flow rate for a certain section, the fluid passes smoothly through that section, and the calculation continues for the next section's maximum allowable mass flow rate until the turbine outlet section. Conversely, if the turbine inlet mass flow rate is greater than the maximum allowable mass flow rate for a certain section, the fluid cannot pass smoothly through that section and is blocked. The program then returns to the previous step, increases the inlet flow rate by half, recalculates the relevant aerodynamic parameters, and continues to determine whether the fluid can pass through the maximum allowable mass flow rate for that section. If the turbine inlet mass flow rate is less than the maximum allowable mass flow rate for that section, the process continues for the next section. If the reduced turbine inlet mass flow rate is still greater than the maximum allowable mass flow rate for that section, the turbine inlet mass flow rate is further reduced to half of the previous value until it is less than or equal to the maximum allowable mass flow rate for that section. The process continues for the next section's condition until the turbine outlet.

[0158] Example:

[0159] The main differences between various analytical methods for plotting characteristic curves lie in the selection of the independent variable (the coordinates of the characteristic curve) and the method of calculating the losses. To simplify the analytical plotting of characteristic curves, this paper uses a given turbine equivalent speed coefficient λ. u The turbine operating state is determined by the dimensionless velocity coefficient λ0 at the turbine inlet. The turbine characteristic calculation results are obtained through step-by-step calculations, and the turbine characteristic calculation process is as follows:

[0160] (1) Given the dimensionless velocity coefficient λ0 at the turbine inlet and the dimensionless rotational speed coefficient λ at the blade inlet u1 .

[0161] λ u1 Determination:

[0162]

[0163] In the formula: D1 is the average diameter at the inlet of the moving blade; the unit is m; For converted speed α cr R is the critical speed of sound, expressed in m / s, and R is the gas constant.

[0164] (2) Formula for calculating the relative airflow angle at the inlet of the moving blade (section 1):

[0165]

[0166] (3) Solve for λc1 in the first equation of the equation set derived from the continuity equation of the flow rate at section 0-1.

[0167] X(λ0,k)=B1Y1(λ c1 ,k,φ) (61)

[0168] (4) Similarly, by deriving the continuity equation for the flow rate at section 0-2, the second equation in the system of equations is solved to obtain λw2.

[0169]

[0170] (5) Formula for calculating the absolute airflow angle at the outlet of the moving blade (section 2):

[0171]

[0172] (6) Solving the flow continuity equation for the dimensionless velocity coefficient λ0,i+1 at the turbine stage stator inlet.

[0173]

[0174] (7) By cyclically using the first, second, and third basic equations of the continuous equation set of turbine inlet and turbine stage inlet flow that have been derived, repeat the above steps (1) to (6) to complete the calculation of turbine stage characteristic parameters of any stage and realize the prediction of turbine overall characteristics.

[0175] Taking a certain type of multi-stage axial flow turbine as an example:

[0176] Given the turbine design parameters and the velocity coefficients of the stationary and moving blades, new stationary and moving blade velocity coefficients are calculated using a loss model. The increase in inlet flow rate is achieved through the continuous increase in inlet velocity. The main parameters for the one-dimensional turbine calculation are shown in Table 1 below:

[0177] Table 1. Main parameters for one-dimensional calculation

[0178]

[0179]

[0180] To verify the reliability of the method proposed in this paper, relevant parameters in the turbine characteristic calculation process, such as the expansion ratio of each stage, temperature ratio, absolute velocity of the stator inlet, and relative velocity of the moving blade inlet, were compared with experimental data. The comparison of parameter results between one-dimensional calculation and experimental stages is shown in Figure 3-6. The absolute value of the relative error of parameters such as total pressure, total temperature, and static temperature at the outlet of each stage does not exceed 10%.

[0181] Table 2 Comparison of Calculation Results of Technical Parameters

[0182] parameter One-dimensional results Reference value Relative error (%) Turbine total static expansion ratio 3.350 3.460 3.179 Turbine total expansion ratio 3.238 3.380 2.876 Turbine total-to-total temperature ratio 0.728 0.756 3.636 Turbine Total Efficiency 0.944 0.915 3.137

[0183] The calculated results of the technical parameters are shown in Table 2. The relative error of the total-total temperature ratio is 3.636%, the relative error of the total-total expansion ratio is 2.876%, and the relative error of the total-total efficiency is 3.137%. The absolute value of the relative error of each technical parameter does not exceed 4%.

[0184] The method for rapid prediction of multi-stage turbine characteristics based on dimensionless numbers proposed in this invention has a certain degree of versatility. It is not only applicable to turbines of ship gas turbines, but also to turbines of aero engines and gas turbines of power plants, as well as the calculation of turbine characteristics of various industrial gas turbines.

Claims

1. A one-dimensional prediction method for the characteristics of multi-stage axial-flow transonic turbines based on dimensionless numbers, characterized by: (1) Calculate the dimensionless speed coefficient of the turbine stage inlet and the equivalent speed coefficient of the turbine rotor by using the rotational speed and the inlet flow rate; (2) Solve the stator blade exit characteristic parameters by establishing mass conservation and continuity equations through the 0-1 section: By setting the initial values ​​of the stator blade velocity coefficient and the exit airflow angle, the stator blade characteristic parameters calculated for the first time are obtained. The stator blade loss model uses the results to calculate the new stator blade velocity coefficient. The lag angle is calculated through the lag angle model. The above process is repeated until the accuracy is met, and the dimensionless velocity coefficient and exit airflow angle parameters of the turbine stage stator blade are obtained. (3) Solving for the inlet parameters of the moving blade: Calculate the relative airflow angle and relative velocity of the moving blade using the outlet parameters of the stationary blade and the rotational speed of the moving blade. (4) Solve the stator blade exit characteristic parameters by establishing mass conservation and continuity equations through the 0-2 section: By setting the initial values ​​of the blade velocity coefficient and the outlet airflow angle, the blade characteristic parameters calculated for the first time are obtained. The blade loss model uses this result to calculate the new blade velocity coefficient. The lag angle is calculated through the lag angle model. The above process is repeated until the accuracy is met, and the turbine stage blade exit relative parameters are obtained. (5) Solve for the inlet parameters of the moving blade: Calculate the absolute airflow angle and absolute velocity at the outlet of the moving blade using the above results; (6) Calculation of the next stage characteristic parameters: Solve the dimensionless velocity coefficient of the next stage stator inlet by the flow continuity equation, and repeat steps (2) to (5) to obtain the characteristic parameters of the stage. (7) Repeat steps (2) to (6) above, and calculate the turbine stage characteristic parameters of any stage by using the derived turbine inlet and turbine stage inlet flow continuity equations to finally obtain the turbine overall characteristic parameters. The dimensionless velocity coefficient λ0 at the turbine inlet: dimensionless velocity coefficient λ at the stator exit c1 : dimensionless velocity coefficient λ at the blade exit w2 : The dimensionless speed coefficient λ of the turbine rotor u1 : The hydrodynamic function q(λ) is: Formula for calculating constant m: Wherein, the superscript "*" indicates the stagnation parameter; the subscripts "0, 1, 2" represent sections 0, 1, and 2 respectively; P and T represent the pressure and temperature of each section respectively; A represents the area of ​​each section; G represents the mass flow rate through each section; R is the gas constant; and k represents the adiabatic index. By conserving mass and making the parameters dimensionless, the flow equations for calculating turbine characteristics stage by stage are established, and the analysis is further simplified, resulting in the following set of equations: Among them, functions X, Y1, and Y2 are: The derivation process is as follows: Establish the continuous flow equations for the turbine inlet and each stage inlet: G0=G 0,i Expanding further: The outlet of the previous stage of the turbine stage is the inlet of the next stage; that is, the section 2 of the (i-1)th stage is the section 0 of the i-th stage. In the same turbine stage: Equation (34) can be rearranged into a simpler form:

2. The one-dimensional prediction method for multi-stage axial-flow transonic turbine characteristics based on dimensionless numbers according to claim 1, characterized in that: In steps (2) and (3), different lag angle models and total pressure loss models are used depending on whether the speed is subsonic or transonic.

3. The one-dimensional prediction method for multi-stage axial-flow transonic turbine characteristics based on dimensionless numbers according to claim 1, characterized in that: Based on the maximum allowable mass flow rate of each stage and section of the turbine as the criterion for judging whether the fluid can pass through the turbine stage section, the inlet flow rate is adjusted and the turbine characteristics at that speed are calculated.

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