A method for calculating two design points of a compression system based on one-dimensional inverse-positive-inverse problem

Abstract

This application provides a dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem, belonging to the field of gas turbine engine technology. The method includes obtaining the boundary conditions and blade geometry parameters of the first design point; performing a one-dimensional inverse problem analysis to obtain the one-dimensional design parameters of the first design point and transferring them to the second design point; obtaining the compression system's speed, flow rate, and pressure ratio at the second design point; performing a one-dimensional forward problem analysis to obtain the current flow rate at the second design point; performing another one-dimensional inverse problem analysis; calculating whether the pressure ratio and efficiency at the second design point meet the requirements based on the current flow rate; if not, adjusting according to a step-by-step process until the pressure ratio and efficiency at the second design point meet the requirements; and calculating the one-dimensional design parameters of the compression system at the second design point to obtain the one-dimensional key performance influencing parameters at both the first and second design points. This application improves the accuracy and efficiency of dual-design-point calculation for compression systems, and enhances its versatility and flexibility.

Description

Technical Field

[0001] This application relates to the field of gas turbine engine technology, and in particular to a dual design point calculation method for compression systems based on a one-dimensional inverse-forward-inverse problem. Background Technology

[0002] The inlet airflow temperature of the power compressor components in high-speed aircraft increases dramatically with increasing Mach number. When the flight Mach number reaches Ma3, the temperature at the compressor inlet will be heated to approximately 600K. At this point, limited by the strength limit of the blade disk, the rotor's physical speed cannot exceed the design speed by much, causing the compressor system to operate at a relatively low relative conversion speed during high-speed flight. To simultaneously achieve performance at both the high conversion speed design point and the low conversion speed operating point, the high-efficiency region of the compressor system needs to be widened from the traditional 0.8-1.0 relative conversion speed range to an ultra-wide relative conversion speed range of 0.5-1.0.

[0003] The main methods used in the aerodynamic design of compression systems are the one-dimensional average streamline method, the two-dimensional flow path method, and the three-dimensional CFD method. Among them, the one-dimensional average streamline method (also known as the one-dimensional inverse problem design method) is one of the most important aspects of compression system design. Once the one-dimensional design determines the flow path, number of stages, and distribution of the average parameters of each row of blades along the flow direction, the upper limit of its performance parameters is also basically determined.

[0004] Future high-speed aircraft propulsion systems require compression systems to operate efficiently across an ultra-wide relative conversion speed range. Conventional one-dimensional inverse problem design methods can only calculate performance evaluation parameters such as diffusion factor, reaction force, and load coefficient at a given single design point. This cannot simultaneously consider the high conversion speeds during ground flight and the extremely low conversion speeds during high-speed flight in the initial one-dimensional design phase. If the conventional single-design-point method is used, focusing solely on optimal high conversion speed performance during ground flight as the target for one-dimensional matching adjustments, the performance of the compression system at extremely low conversion speeds during high-speed flight will drastically degrade, failing to meet the requirement of efficient operation across an ultra-wide relative conversion speed range. Therefore, it is urgently necessary to conduct dual-design-point evaluations during the initial one-dimensional design phase of high-speed propulsion compression systems, taking into account performance at both high and extremely low conversion speeds.

[0005] Conventional one-dimensional inverse problem design methods for compression systems require recalculating the second design point, which necessitates re-assigning parameters such as load and reaction force at each stage. This leads to changes in the one-dimensional geometry of the compression system during the evaluation of the second design point compared to the geometric parameters at the first design point, rendering the evaluation of the second design point ineffective. Consequently, it becomes difficult to achieve the goal of improving and guiding the design parameters of the operating point at low conversion speeds of high-speed power compression systems during the initial design phase. Summary of the Invention

[0006] To address the problem that conventional one-dimensional methods with a single design point cannot meet the high-efficiency requirements of compression systems over an ultra-wide range, this application provides a dual-design-point calculation method for compression systems based on a one-dimensional inverse-forward-inverse problem. This method can guide designers during the initial one-dimensional design of the compression system, ensuring efficient operation over an ultra-wide range of relative conversion speeds.

[0007] This application provides a method for calculating the dual design points of a compressed system based on a one-dimensional inverse-forward-inverse problem. The method includes:

[0008] Step 1: Obtain the first boundary conditions and blade geometry parameters of the aero-engine compression system at the first design point. The first boundary conditions include the total inlet temperature, total inlet pressure, inlet flow rate, rotational speed, inlet airflow angle, and outlet airflow angle of the compression system.

[0009] Step 2: Based on the first boundary conditions and blade geometric parameters, the one-dimensional average streamline method is used to perform a one-dimensional inverse problem analysis of each stage of the blades until the last stage blade, to obtain the one-dimensional design parameters of the compression system at the first design point. The one-dimensional design parameters include the rotor blade geometric parameters and the stator blade geometric parameters.

[0010] Step 3: Transfer the one-dimensional design parameters to the second design point, obtain the rotational speed, flow rate and pressure ratio of the compression system at the second design point, perform one-dimensional forward problem analysis of each stage of the blades until the last stage blade, and obtain the current flow rate of the compression system at the second design point.

[0011] Step 4: Perform a one-dimensional inverse problem analysis again. Calculate whether the pressure ratio and efficiency at the second design point meet the requirements based on the current flow rate. If not, adjust according to the step-by-step process, repeating steps 1 to 3 until the pressure ratio and efficiency at the second design point meet the requirements. The step-by-step process includes the following steps in sequence: stage adjustment, average tangential velocity adjustment, tangential velocity distribution adjustment, load distribution adjustment, axial velocity distribution adjustment, and counterforce adjustment. If the requirements are met, calculate the one-dimensional design parameters of the compression system at the second design point.

[0012] Step 5: Output the aerodynamic design-related parameters for the first and second design points to obtain the one-dimensional key performance parameters for the first and second design points.

[0013] According to a specific implementation of an embodiment of this application, the step of using a one-dimensional average streamline method to perform a one-dimensional inverse problem analysis of each stage of the blades until the last stage blade, to obtain the one-dimensional design parameters of the compression system at the first design point, includes:

[0014] For the current stage rotor blades, the one-dimensional average streamline method is used to calculate the rotor inlet parameters, rotor outlet parameters, rotor Mach number, rotor diffusion factor, and rotor loss in sequence.

[0015] Perform iterative processing of the current stage rotor isentropic compression efficiency until the rotor isentropic compression efficiency converges.

[0016] For the current stage stator blade, the one-dimensional average streamline method is used to calculate the stator inlet parameters, stator outlet parameters, stator Mach number, stator diffusion factor, and stator loss in sequence.

[0017] Perform iterations on the current level of the stator restoration coefficients until the stator restoration coefficients converge.

[0018] For the current stage rotor and stator, calculate the blade geometry parameters to obtain the rotor blade geometry parameters and stator blade geometry parameters;

[0019] If the current stage stator blade is the last stage blade, the one-dimensional design parameters of the compression system at the first design point are output. If the current stage stator blade is not the last stage blade, the outlet parameters are transferred to the next stage rotor to perform parameter calculations for the new stage.

[0020] According to a specific implementation of an embodiment of this application, the calculation of the rotor inlet parameters includes:

[0021] Calculate the total enthalpy of the airflow at the rotor inlet based on the total temperature at the rotor inlet;

[0022] The total rotor inlet velocity is calculated based on the rotor inlet airflow angle and the initial rotor inlet axial velocity.

[0023] The static enthalpy at the rotor inlet is calculated based on the total velocity at the rotor inlet and the total enthalpy of the airflow at the rotor inlet.

[0024] The rotor inlet static temperature is obtained based on the rotor inlet static enthalpy;

[0025] Based on the relationship between total temperature and total pressure and static temperature and static pressure, the rotor inlet static pressure is calculated, and then the rotor inlet static density is obtained.

[0026] The rotor inlet area is calculated based on the rotor inlet static density, the given flow rate, and the rotor inlet axial velocity.

[0027] Adjust the rotor inlet axial speed until the calculated rotor inlet area is the same as the given rotor inlet area to obtain the final rotor inlet area;

[0028] Based on the final rotor inlet area, the mean diameter ratio is obtained. Based on the mean diameter ratio, the rotor inlet tangential velocity and rotor inlet relative velocity are obtained, and then the rotor inlet relative airflow angle is obtained.

[0029] According to a specific implementation of an embodiment of this application, the calculation of the rotor outlet parameters includes:

[0030] Based on the given load factor, tangential velocity, and total enthalpy of the rotor inlet airflow, the total enthalpy of the rotor outlet airflow, the total temperature of the rotor outlet airflow, and the stagnation state entropy of the rotor outlet airflow are calculated sequentially.

[0031] The isentropic work and the total isentropic enthalpy at the rotor outlet are calculated based on the initial value of the rotor efficiency, and then the total pressure at the rotor outlet is obtained.

[0032] The rotor outlet circumferential velocity is calculated based on the circumferential component of the absolute velocity of the airflow at the rotor inlet, the rotor power, and the circumferential velocity at the mid-diameter of the rotor blades.

[0033] Calculate the relative airflow angle and the total velocity at the rotor outlet based on the circumferential velocity at the rotor outlet.

[0034] Based on the total velocity at the rotor outlet and the total enthalpy of the airflow at the rotor outlet, the static enthalpy at the rotor outlet, the static temperature at the rotor outlet, and the static pressure at the rotor outlet are calculated sequentially.

[0035] The rotor outlet area is calculated based on the rotor outlet axial velocity, rotor outlet static pressure, rotor outlet static temperature, and given flow rate.

[0036] Adjust the rotor outlet axial velocity until the calculated rotor outlet area is the same as the given rotor outlet area to obtain the final rotor outlet area.

[0037] Based on the final rotor inlet area, the hub radius and pitch diameter ratio of the rotor outlet are obtained.

[0038] According to a specific implementation of this application, the formula for calculating the rotor Mach number is as follows:

[0039] ,

[0040] ,

[0041] ,

[0042] ,

[0043] Where Ma is the rotor inlet Mach number, λ1 is the rotor inlet velocity coefficient, k is the adiabatic index, W1 is the rotor inlet relative velocity, and a cr,w This is the critical speed of sound. H is the relative total enthalpy at the rotor inlet. cr,w This is the enthalpy value corresponding to the critical total temperature. U is the total enthalpy of the airflow at the rotor inlet. cp1C is the circumferential velocity at the inlet mid-diameter of the rotor blade. 1u This represents the circumferential component of the absolute velocity of the airflow at the rotor inlet;

[0044] The formula for calculating the rotor diffusion factor is:

[0045] ,

[0046] ,

[0047] Among them, D pk σ is the rotor diffusion factor. pk For the consistency, β1 is the relative airflow angle at the rotor inlet, β2 is the relative airflow angle at the rotor outlet, and C 1a C is the axial velocity at the rotor inlet. 2a This refers to the axial velocity at the rotor outlet.

[0048] The formula for calculating the rotor loss is:

[0049] ,

[0050] ,

[0051] Where ω is the rotor loss, θ th Let μ be the momentum thickness, μ be the loss exponent, and σ be the loss coefficient. pk When μ < 1, μ = 0.25, σ pk When μ is ≥1, μ = 0.7.

[0052] According to a specific implementation of an embodiment of this application, the step of performing a one-dimensional forward problem analysis of each stage of the blades until the last stage blade, to obtain the current flow rate of the compression system at the second design point, includes:

[0053] For the current stage rotor blades, a one-dimensional forward problem analysis method is used to sequentially calculate the rotor inlet aerodynamic parameters at the second design point, the rotor outlet lag angle at the second design point, the rotor loss at the second design point, and the rotor outlet aerodynamic parameters at the second design point based on the rotor outlet lag angle and the rotor loss at the second design point.

[0054] For the current stage stator blade, a one-dimensional forward problem analysis method is used to sequentially calculate the aerodynamic parameters of the stator inlet at the second design point, the stator lag angle at the second design point, the stator loss at the second design point, and the aerodynamic parameters of the stator outlet at the second design point based on the stator lag angle and the stator loss at the second design point.

[0055] Determine whether the current stage stator blade is the last stage. If it is not the last stage, pass the parameters of this stage to the next stage rotor blade and perform parameter calculations. If it is the last stage, obtain the current flow rate of the compression system at the second design point.

[0056] According to a specific implementation of an embodiment of this application, the calculation of the rotor inlet aerodynamic parameters at the second design point includes:

[0057] Calculate the total enthalpy of the airflow at the rotor inlet at the second design point based on the total rotor inlet temperature at the second design point.

[0058] Calculate the total velocity at the rotor inlet at the second design point based on the rotor inlet airflow angle at the second design point and the initial axial velocity at the rotor inlet at the second design point.

[0059] Calculate the static enthalpy of the rotor inlet at the second design point based on the full velocity of the rotor inlet at the second design point and the total enthalpy of the airflow at the rotor inlet at the second design point.

[0060] The static temperature at the rotor inlet at the second design point is calculated based on the static enthalpy at the rotor inlet at the second design point.

[0061] Based on the relationship between total temperature and total pressure and static temperature and static pressure, the rotor inlet static pressure at the second design point is calculated, and then the rotor inlet static density at the second design point is obtained.

[0062] The rotor inlet area at the second design point is calculated based on the static density at the rotor inlet at the second design point, the given flow rate at the second design point, and the axial velocity at the rotor inlet at the second design point.

[0063] Adjust the rotor inlet axial velocity at the second design point until the calculated rotor inlet area at the second design point is the same as the rotor inlet area calculated at the first design point, and obtain the final rotor inlet area at the second design point.

[0064] Based on the final rotor inlet area at the second design point, the mid-diameter ratio at the second design point is obtained. Based on the mid-diameter ratio at the second design point, the tangential velocity at the rotor inlet at the second design point and the relative velocity at the rotor inlet at the second design point are obtained, and then the relative airflow angle at the rotor inlet at the second design point is obtained.

[0065] Calculate the Mach number at the rotor inlet at the second design point based on the aerodynamic parameters at the rotor inlet at the second design point.

[0066] According to a specific implementation of an embodiment of this application, the calculation of the rotor outlet lag angle at the second design point includes:

[0067] The reference angle of attack is calculated based on the reference angle of attack of a 10% thick blade without curvature, the influence factor of thickness distribution, the calculation factor of the angle of attack slope, the influence factor of the relative position of the maximum deflection of the blade on the angle of attack slope, and the difference between the inlet and outlet geometric angles of the blade.

[0068] The reference lag angle is calculated based on the influence factors of blade shape on lag angle, thickness influence coefficient, reference lag angle of blade shape with 0 curvature and 10% thickness, lag angle curvature slope factor, consistency, influence factor of relative position of maximum deflection on curvature, and the difference between blade inlet and outlet geometric angles.

[0069] The rotor outlet lag angle at the second design point is calculated based on the reference angle of attack, the reference lag angle, the relative airflow angle at the rotor inlet at the second design point, and the relative airflow angle at the rotor outlet at the second design point.

[0070] According to a specific implementation of this application, the formula for calculating the reference angle of attack of the 10% thickness and non-curved blade cascade is as follows:

[0071] ,

[0072] Among them, i 0,10 σ is the reference angle of attack for a 10% thickness, non-curved blade cascade. pk For consistency, β 1_sec The relative airflow angle at the rotor inlet is the second design point.

[0073] The formula for calculating the thickness distribution influence factor is as follows:

[0074] ,

[0075] Among them, K ic To account for the influence of thickness distribution factors, This represents the maximum relative thickness of the leaf shape.

[0076] The formula for calculating the angular slope factor of the angle of attack is as follows:

[0077] ,

[0078] , ,

[0079] ,

[0080] Where n is the angular slope calculation factor for the angle of attack, and K a λ is the bending angle influence coefficient. f is the consistency influence coefficient, and q is the consistency influence factor;

[0081] The formula for calculating the influence factor of the relative position of the maximum deflection of the airfoil on the bending angle slope factor is as follows:

[0082] ,

[0083] Among them, Kif The influence factor of the relative position of the maximum deflection of the airfoil on the bending angle slope factor, x f Location of maximum deflection;

[0084] The formula for calculating the reference angle of attack is:

[0085] ,

[0086] Among them, i ref For reference angle of attack, K i,sh θ is the shape correction factor, and θ is the difference between the inlet and outlet geometric angles of the blade;

[0087] The formula for calculating the reference lag angle of the airfoil with 0 camber and 10% thickness is as follows:

[0088] ,

[0089] Where, δ 0,10 The reference lag angle for a blade profile with 0 camber and 10% thickness;

[0090] The formula for calculating the influence coefficient of the thickness is:

[0091] ,

[0092] Among them, K δ,c The influence coefficient of thickness;

[0093] For the NACA65 series airfoil, the formula for calculating the lag angle slope factor is:

[0094] ,

[0095] For the C4 series and BC10 series airfoils, the formula for calculating the lag angle slope factor is as follows:

[0096] ,

[0097] Where m is the slope factor of the backward angle;

[0098] The formula for calculating the influence factor of the relative position of the maximum deflection on the bending angle is as follows:

[0099] ,

[0100] Among them, K δ,f β is the influence factor of the relative position of maximum deflection on the bending angle. 2_sec The relative airflow angle at the rotor outlet is the second design point.

[0101] The formula for calculating the reference lag angle is:

[0102] ,

[0103] ,

[0104] Where, δ ref For reference, the lagging angle, K δ,sh μ is the influence factor of leaf shape on the lag angle. sec It is an exponential factor for consistency;

[0105] The formula for calculating the rotor outlet lag angle at the second design point is:

[0106] ,

[0107] Where, δ sec Let f(x) be the rotor outlet lag angle at the second design point, and f(x) be the calculation coefficient for the lag angle under the current airflow angle at the angle of attack.

[0108] In the formula ,

[0109] When x≥0 ,

[0110] When x < 0 ,

[0111] Where x is an intermediate function and i is the angle of attack of the current airflow angle.

[0112] According to a specific implementation of this application, the formula for calculating the rotor loss at the second design point is as follows:

[0113] When Ma W1_sec When <0.6, ;

[0114] When 0.6≤Ma W1_sec When ≤0.95,

[0115] ;

[0116] When Ma W1_sec When >0.95,

[0117] ;

[0118] When ω sec >2ω cr When, ω sec =2ω cr ;

[0119] Among them, Ma W1_sec ω is the rotor inlet Mach number at the second design point. esc For the rotor loss at the second design point, ω crTo account for the losses caused by the speed coefficient and the maximum thickness of the blade, ω cr The expression is as follows:

[0120] ,

[0121] λ 1_sec When K < 0.53, λ_sec =1,

[0122] λ 1_sec When ≥0.53, ,

[0123] When K < 0.06, c_sec =1,

[0124] When ≥0.06, ,

[0125] Where ω is the rotor loss, K λ_sec K is the loss correction factor for the velocity coefficient at the second design point. c_sec λ is the loss correction factor for the maximum thickness at the second design point. 1_sec D is the rotor inlet speed coefficient at the second design point. pk_sec This is the diffusion factor at the second design point.

[0126] Beneficial effects:

[0127] The dual-design-point calculation method for compressed systems based on a one-dimensional inverse-forward-inverse problem in this application has the following advantages:

[0128] To address the requirement that the compression system of future high-speed aircraft can operate efficiently over an ultra-wide relative conversion speed range, a one-dimensional dual-design-point method is proposed, which takes into account the performance of compression systems with high conversion speeds on the ground and low conversion speeds under high-speed flight conditions.

[0129] To address the issue that conventional one-dimensional inverse problem design methods require re-defining parameters such as loads and counterforces at each stage, leading to changes in the one-dimensional geometry of the compression system compared to the first design point during the second design point evaluation, thus rendering the second design point evaluation ineffective, a "reverse-forward-reverse" one-dimensional dual design point method is proposed. This method adds the evaluation of the second design point while ensuring that the one-dimensional geometry of the compression system remains unchanged. This solves the problem that conventional one-dimensional compression system design methods cannot complete dual design point evaluation.

[0130] The one-dimensional dual-design-point method can quickly guide designers to identify problems in each row of blades at the two design points in the early stages of compression system design, and can better take into account the performance of the dual design points under a wide range of conditions.

[0131] Taking into account the sensitivity of the second design point and its impact on the overall scheme, a step-by-step adjustment process for improving the second design point of the compressor using the "reverse-positive-reverse" one-dimensional dual design point method is summarized. This process can quickly improve the performance of the dual design point of the compression system. Attached Figure Description

[0132] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0133] Figure 1 This is a schematic diagram illustrating the definition of the average streamline according to an embodiment of the present invention;

[0134] Figure 2 A flowchart of a one-dimensional inverse problem design method according to an embodiment of the present invention;

[0135] Figure 3 This is a flowchart of a dual-design-point calculation method for a compression system based on a one-dimensional "inverse-forward-inverse" problem according to an embodiment of the present invention.

[0136] Figure 4 This is a comparison diagram of dimensionless flow-pressure ratio characteristics after stage adjustment and evaluation according to an embodiment of the present invention;

[0137] Figure 5 A comparison diagram of dimensionless flow efficiency characteristics after stage adjustment and evaluation according to an embodiment of the present invention;

[0138] Figure 6 A comparison diagram of dimensionless flow-pressure ratio characteristics after adjustment and evaluation of average tangential velocity according to an embodiment of the present invention;

[0139] Figure 7 A comparison diagram of dimensionless flow efficiency characteristics after adjustment and evaluation of average tangential velocity according to an embodiment of the present invention;

[0140] Figure 8 A comparison diagram of dimensionless flow-pressure ratio characteristics after tangential velocity distribution adjustment and evaluation according to an embodiment of the present invention;

[0141] Figure 9 A comparison diagram of dimensionless flow efficiency characteristics after tangential velocity distribution adjustment and evaluation according to an embodiment of the present invention;

[0142] Figure 10 This is a comparison diagram of dimensionless flow-pressure ratio characteristics after load distribution adjustment and evaluation according to an embodiment of the present invention;

[0143] Figure 11 A comparison diagram of dimensionless flow efficiency characteristics after load distribution adjustment and evaluation according to an embodiment of the present invention;

[0144] Figure 12 A comparison diagram of dimensionless flow-pressure ratio characteristics after axial velocity distribution adjustment and evaluation according to an embodiment of the present invention;

[0145] Figure 13 A comparison diagram of dimensionless flow efficiency characteristics after axial velocity distribution adjustment and evaluation according to an embodiment of the present invention;

[0146] Figure 14 This is a comparison diagram of the dimensionless flow-pressure ratio characteristics after counterforce adjustment and evaluation according to an embodiment of the present invention;

[0147] Figure 15 This is a comparison diagram of the dimensionless flow efficiency characteristics after counterforce adjustment and evaluation according to an embodiment of the present invention. Detailed Implementation

[0148] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0149] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0150] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0151] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0152] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0153] The technical terminology used in the one-dimensional inverse problem design in this application will be explained below.

[0154] The one-dimensional inverse problem design method is based on assumptions such as one-dimensionality, steady state, inviscidity, adiabatic walls, and ideal gas properties, and is carried out through three fundamental equations. The fundamental equations include: the continuity equation, the energy equation, and the ideal gas equation.

[0155] The continuity equation, as shown in equation (2-1), represents that the flow rate remains equal at different cross-sections of the compression system. In equation (2-1), subscripts 1 and 2 represent the rotor inlet cross-section and rotor outlet cross-section, respectively. The static density at the rotor inlet. The axial velocity at the rotor inlet. The rotor inlet area; The static density at the rotor outlet. The rotor outlet axial velocity, This represents the rotor outlet area.

[0156] (2-1)

[0157] The energy equation is shown in equation (2-2), representing the energy conservation at different cross-sections of the compression system, where C is the velocity of the airflow (C1 is the total velocity at the rotor inlet, and C2 is the total velocity at the rotor outlet), and h is the enthalpy of a unit mass of airflow. Enthalpy of unit mass airflow at the rotor inlet. (where L is the enthalpy of the unit mass airflow at the rotor outlet), with subscripts 1 and 2 representing the rotor inlet and outlet cross-sections, respectively. u For the exchange of mechanical work, its definition in the compressor is shown in equation (2-3).

[0158] (2-2)

[0159] Where L u The calculation method is shown in (2-3), where C 2uU1 represents the circumferential velocity at the rotor outlet (the circumferential component of the absolute velocity of the airflow at the rotor outlet), U2 represents the tangential velocity at the rotor outlet mid-diameter, and C represents the circumferential velocity at the rotor outlet mid-diameter. 1u U1 represents the circumferential velocity at the rotor inlet (the circumferential component of the absolute velocity of the airflow at the rotor inlet), and U1 represents the tangential velocity at the middle diameter of the rotor inlet.

[0160] (2-3)

[0161] The ideal gas equation is shown in equation (2-4). In the equation, p represents pressure. R represents density, and R is the ideal gas constant.

[0162] (2-4)

[0163] The calculations for the one-dimensional inverse problem design method are generally performed at the mean streamline and are based on the one-dimensional flow assumption, neglecting the radial variation of aerodynamic parameters. The mean streamline is a special streamline specified on the meridional surface of the compressor, and its radius is generally defined as shown in equation (2-5), where R... m R h R t These represent the radius of the mean streamline, the radius of the root, and the radius of the tip, respectively.

[0164] (2-5)

[0165] Figure 1 The average streamline of a certain stage of the compressor is given, where 1, 2, 3, and 4 represent the rotor inlet, rotor outlet, stator inlet, and stator outlet, respectively.

[0166] Based on the above, this paper proposes a dual-design-point calculation method for compression systems, based on a one-dimensional inverse-forward-inverse problem, to address the requirement that compression systems for future high-speed aircraft power systems operate efficiently across an ultra-wide relative conversion speed range. This method considers the performance of compression systems operating at high conversion speeds on the ground and low conversion speeds during high-speed flight. The dual-design-point calculation method for compression systems based on a one-dimensional inverse-forward-inverse problem provided in this application refers to... Figure 3 This includes the following steps:

[0167] Step 1: Obtain the first boundary conditions and blade geometry parameters of the aero-engine compression system at the first design point. The first boundary conditions include the total inlet temperature, total inlet pressure, inlet flow rate, rotational speed, inlet airflow angle, and outlet airflow angle of the compression system.

[0168] Step 2: Based on the first boundary conditions and blade geometric parameters, the one-dimensional average streamline method is used to perform a one-dimensional inverse problem analysis of each stage of the blades until the last stage blade, to obtain the one-dimensional design parameters of the compression system at the first design point. The one-dimensional design parameters include the rotor blade geometric parameters and the stator blade geometric parameters.

[0169] Step 3: Transfer the one-dimensional design parameters to the second design point, obtain the rotational speed, flow rate and pressure ratio of the compression system at the second design point, perform one-dimensional forward problem analysis of each stage of the blades until the last stage blade, and obtain the current flow rate of the compression system at the second design point.

[0170] Step 4: Perform a one-dimensional inverse problem analysis again. Calculate whether the pressure ratio and efficiency at the second design point meet the requirements based on the current flow rate. If not, adjust according to the step-by-step process, repeating steps 1 to 3 until the pressure ratio and efficiency at the second design point meet the requirements. The step-by-step process includes the following steps in sequence: stage adjustment, average tangential velocity adjustment, tangential velocity distribution adjustment, load distribution adjustment, axial velocity distribution adjustment, and counterforce adjustment. If the requirements are met, calculate the one-dimensional design parameters of the compression system at the second design point.

[0171] Step 5: Output the aerodynamic design-related parameters for the first and second design points to obtain the one-dimensional key performance parameters for the first and second design points.

[0172] This embodiment proposes a novel one-dimensional "inverse-forward-inverse" problem-based method for calculating the dual design points of a compression system. Building upon conventional one-dimensional inverse problem methods, it employs an "inverse-forward-inverse" approach, adding an evaluation of the second design point while maintaining the one-dimensional geometry of the compression system. After calculating the first design point, the geometric parameters of the entire compression system are derived and combined with the rotational speed, flow rate, and pressure ratio conditions of the second design point. Considering the sensitivity of the second design point and its impact on the overall scheme, a step-by-step adjustment process is summarized to quickly improve the performance of the compression system at both design points. Then, the one-dimensional inverse problem method is used to calculate key one-dimensional performance parameters such as the diffusion factor, flow coefficient, and load coefficient at the second design point of the compression system. Finally, the aerodynamic evaluation results of the compression system at both design points are output. This method can guide designers to consider the performance of the compression system at both design points under a wide range of conditions from the early stages of compression system design. Therefore, by accurately calculating various parameters at both design points, this method effectively improves the adaptability and stability of the compression system under a wide range of operating conditions. Compared to traditional one-dimensional inverse problem design methods, the method in this embodiment not only considers the performance requirements of the first design point, but also achieves a more comprehensive optimization of the overall performance of the compression system by introducing the evaluation and adjustment of the second design point. Furthermore, the proposed step-by-step adjustment strategy allows designers to more effectively improve the performance of the compression system, significantly increasing design efficiency and accuracy.

[0173] In practice, the one-dimensional design parameters are read in, including boundary conditions such as inlet total temperature, inlet total pressure, inlet flow rate, rotational speed, and inlet / outlet airflow angle under the first design point condition, as well as the radii, load coefficients, and reaction forces of the inlet and outlet blade tips and roots for each row of blades. Based on the read-in one-dimensional design parameters, a one-dimensional inverse problem analysis is conducted.

[0174] In one embodiment, refer to Figure 2 The method employs a one-dimensional average streamline approach to perform a one-dimensional inverse problem analysis on each stage of the blades, up to the last stage, to obtain the one-dimensional design parameters of the compression system at the first design point, including:

[0175] For the current stage rotor blades, the one-dimensional average streamline method is used to calculate the rotor inlet parameters, rotor outlet parameters, rotor Mach number, rotor diffusion factor, and rotor loss in sequence.

[0176] Perform iterative processing of the current stage rotor isentropic compression efficiency until the rotor isentropic compression efficiency converges.

[0177] For the current stage stator blade, the one-dimensional average streamline method is used to calculate the stator inlet parameters, stator outlet parameters, stator Mach number, stator diffusion factor, and stator loss in sequence.

[0178] Perform iterations on the current level of the stator restoration coefficients until the stator restoration coefficients converge.

[0179] For the current stage rotor and stator, calculate the blade geometry parameters to obtain the rotor blade geometry parameters and stator blade geometry parameters;

[0180] If the current stage stator blade is the last stage blade, the one-dimensional design parameters of the compression system at the first design point are output. If the current stage stator blade is not the last stage blade, the outlet parameters are transferred to the next stage rotor to perform parameter calculations for the new stage.

[0181] In this embodiment, a one-dimensional inverse problem analysis was performed at the first design point. Using the one-dimensional average streamline method, a detailed inverse problem analysis was conducted on each stage of the blades, comprehensively considering the airflow characteristics within the compression system from rotor inlet parameters to stator outlet parameters. This process not only calculated key parameters such as Mach number, diffusion factor, and losses for each stage of the blades, but also ensured the convergence of the rotor isentropic compression efficiency and stator restitution coefficient through iterative calculations, thus obtaining accurate one-dimensional design parameters. This approach effectively captures the complex flow phenomena within the compression system while maintaining computational accuracy, providing a solid foundation for subsequent performance evaluation and optimization at two design points. Furthermore, through stage-by-stage blade analysis, designers can gain a clearer understanding of the impact of each stage on overall performance, enabling targeted adjustments and optimizations, thereby improving design efficiency and accuracy.

[0182] Furthermore, the calculation of the rotor inlet parameters includes:

[0183] Calculate the total enthalpy of the airflow at the rotor inlet based on the total temperature at the rotor inlet;

[0184] The total rotor inlet velocity is calculated based on the rotor inlet airflow angle and the initial rotor inlet axial velocity.

[0185] The static enthalpy at the rotor inlet is calculated based on the total velocity at the rotor inlet and the total enthalpy of the airflow at the rotor inlet.

[0186] The rotor inlet static temperature is obtained based on the rotor inlet static enthalpy;

[0187] Based on the relationship between total temperature and total pressure and static temperature and static pressure, the rotor inlet static pressure is calculated, and then the rotor inlet static density is obtained.

[0188] The rotor inlet area is calculated based on the rotor inlet static density, the given flow rate, and the rotor inlet axial velocity.

[0189] Adjust the rotor inlet axial speed until the calculated rotor inlet area is the same as the given rotor inlet area to obtain the final rotor inlet area;

[0190] Based on the final rotor inlet area, the mean diameter ratio is obtained. Based on the mean diameter ratio, the rotor inlet tangential velocity and rotor inlet relative velocity are obtained, and then the rotor inlet relative airflow angle is obtained.

[0191] In practice, the calculation of rotor inlet parameters includes the following:

[0192] Based on the above conditions, the aerodynamic parameters of the rotor inlet are calculated, and the total enthalpy of the rotor inlet airflow is obtained from the total rotor inlet temperature using equation (2-6). :

[0193] (2-6)

[0194] In equation (2-6) The isobaric heat capacity of air. This is the total temperature at the rotor inlet.

[0195] Based on the rotor inlet airflow angle α1 and the initial rotor inlet axial velocity C 1a The full rotor inlet speed C1 can be obtained:

[0196] C1=C 1a / sin(α1)(2-7)

[0197] Based on the rotor inlet full speed C1 and the rotor inlet airflow total enthalpy The rotor inlet static enthalpy H1 can be obtained as follows:

[0198] (2-8)

[0199] Based on the rotor inlet static enthalpy H1, the rotor inlet static temperature T1 is calculated using formula (2-9):

[0200] (2-9)

[0201] The rotor inlet static pressure can be calculated based on the relationship between total temperature and total pressure and static temperature and static pressure, and then the rotor inlet static density ρ1 can be obtained. Then, according to equation (2-10), the rotor inlet area A1 can be obtained from the given flow rate G.

[0202] A1=G / (ρ1C 1a (2-10)

[0203] Since the outer diameter is given, the inner diameter can be obtained from the rotor inlet area A1, and then the mean diameter ratio can be obtained.

[0204] Adjust the rotor inlet axial velocity until the calculated rotor inlet area A1 is the same as the given area. Based on the pitch diameter ratio, U1 (representing the rotor inlet tangential velocity) and W1 (representing the rotor inlet relative velocity) at the pitch diameter can be calculated, thereby determining the rotor inlet relative airflow angle β1.

[0205] Furthermore, the calculation of the rotor outlet parameters includes:

[0206] Based on the given load factor, tangential velocity, and total enthalpy of the rotor inlet airflow, the total enthalpy of the rotor outlet airflow, the total temperature of the rotor outlet airflow, and the stagnation state entropy of the rotor outlet airflow are calculated sequentially.

[0207] The isentropic work and the total isentropic enthalpy at the rotor outlet are calculated based on the initial value of the rotor efficiency, and then the total pressure at the rotor outlet is obtained.

[0208] The rotor outlet circumferential velocity is calculated based on the circumferential component of the absolute velocity of the airflow at the rotor inlet, the rotor power, and the circumferential velocity at the mid-diameter of the rotor blades.

[0209] Calculate the relative airflow angle and the total velocity at the rotor outlet based on the circumferential velocity at the rotor outlet.

[0210] Based on the total velocity at the rotor outlet and the total enthalpy of the airflow at the rotor outlet, the static enthalpy at the rotor outlet, the static temperature at the rotor outlet, and the static pressure at the rotor outlet are calculated sequentially.

[0211] The rotor outlet area is calculated based on the rotor outlet axial velocity, rotor outlet static pressure, rotor outlet static temperature, and given flow rate.

[0212] Adjust the rotor outlet axial velocity until the calculated rotor outlet area is the same as the given rotor outlet area to obtain the final rotor outlet area.

[0213] Based on the final rotor inlet area, the hub radius and pitch diameter ratio of the rotor outlet are obtained.

[0214] In practice, the calculation of rotor outlet parameters includes the following:

[0215] Given the rotor outlet outer diameter, rotor outlet inner diameter, rotor initial efficiency, and load factor, first calculate the total enthalpy of the airflow at the rotor outlet based on the load factor and tangential velocity. , , where H z The rotor power is calculated from the load factor and tangential velocity. The total temperature of the airflow at the rotor outlet. The entropy of the stagnant airflow at the rotor outlet can be calculated from the total temperature at the rotor outlet.

[0216] From the initial value of the rotor efficiency, the isentropic work can be obtained, the isentropic total enthalpy at the rotor outlet can be obtained, and the total pressure at the rotor outlet can be calculated. Specifically: ,

[0217] in, H is the isentropic total enthalpy at the rotor outlet.z,ad The isentropic work applied to the rotor, and the isentropic processing amount after taking into account the effect of efficiency; The rotor outlet total temperature is calculated based on an isentropic process. This is the rotor outlet stagnation state entropy calculated using an isentropic process. Total pressure at rotor outlet This refers to the total pressure at the rotor inlet. The entropy of the stagnation state of the airflow at the rotor inlet.

[0218] The formula for calculating the rotor outlet circumferential velocity is: , where C 2u C represents the circumferential velocity at the rotor outlet. 1u H represents the circumferential velocity at the rotor inlet. z U is the power added to the rotor. cp This is the tangential velocity at the mid-diameter of the rotor blade.

[0219] The formula for calculating the relative airflow angle β2 at the rotor outlet is: In the formula, Given the initial rotor outlet axial velocity, U cp2 C is the circumferential velocity at the mid-diameter of the rotor blade exit. 2u This represents the circumferential component of the absolute velocity of the airflow at the rotor outlet.

[0220] The formula for calculating the rotor outlet velocity C2 is: From this, the rotor outlet static enthalpy H2 is obtained. Further calculations are then performed on the rotor outlet static temperature T2 and rotor outlet static pressure P2, specifically: , where S2 is the rotor outlet static entropy.

[0221] Finally, the rotor outlet area A2 can be obtained, and the calculation formula is as follows: ,in Adjust the rotor outlet axial velocity to determine the flow amplification factor at that location. Continue until the calculated area matches the given area. Based on the outlet area, geometric parameters such as the rotor outlet hub radius and pitch diameter ratio can be obtained.

[0222] Furthermore, parameters such as the rotor Mach number and the D-factor (diffusion factor) are calculated. The formula for calculating the rotor Mach number is as follows:

[0223] ,

[0224] ,

[0225] ,

[0226] ,

[0227] Where Ma is the rotor inlet Mach number, λ1 is the rotor inlet velocity coefficient, k is the adiabatic index (specific heat ratio), W1 is the rotor inlet relative velocity, and a cr,w This is the critical speed of sound. H is the relative total enthalpy at the rotor inlet. cr,w This is the enthalpy value corresponding to the critical total temperature. U is the total enthalpy of the airflow at the rotor inlet. cp1 C is the circumferential velocity at the inlet mid-diameter of the rotor blade. 1u This represents the circumferential component of the absolute velocity of the airflow at the rotor inlet;

[0228] The formula for calculating the rotor diffusion factor is:

[0229] (2-11)

[0230] (2-12)

[0231] Among them, D pk σ is the rotor diffusion factor. pk For the consistency, β1 is the relative airflow angle at the rotor inlet, β2 is the relative airflow angle at the rotor outlet, and C 1a C is the axial velocity at the rotor inlet. 2a This refers to the axial velocity at the rotor outlet.

[0232] The formula for calculating the rotor loss is:

[0233] (2-13)

[0234] (2-14)

[0235] Where ω is the rotor loss, θ th Let μ be the momentum thickness, μ be the loss exponent, and σ be the loss coefficient. pk When μ < 1, μ = 0.25, σ pk When μ is ≥1, μ = 0.7.

[0236] In practice, the relative total enthalpy at the rotor inlet is first calculated. This allows us to obtain the relative total temperature at the rotor inlet. Rotor inlet relative entropy Rotor inlet relative to total pressure Critical relative total temperature Critical speed of sound H cr,wThe enthalpy value corresponding to the critical total temperature is used to obtain the rotor inlet velocity coefficient λ1. Based on the relationship between the rotor velocity coefficient and the Mach number, the rotor Mach number at the first design point is calculated. D-factor (diffusion factor) solution: The diffusion factor is related to consistency and airflow angle. The relative airflow angles at the rotor inlet and outlet have been determined. The consistency σ is calculated using formula (2-12). pk The values ​​are assigned, the diffusion factor is calculated based on the consistency, the momentum thickness is calculated based on the diffusion factor, and the rotor loss is calculated based on the momentum thickness, consistency, and the relative airflow angle at the rotor outlet.

[0237] Furthermore, the rotor isentropic compression efficiency is iterated. The actual total pressure at the rotor outlet is obtained through the loss coefficient, and then the outlet entropy function is obtained. Based on the entropy function, the new isentropic compression efficiency value is solved. The difference between the isentropic compression efficiency obtained in this iteration and the isentropic compression efficiency of the previous iteration is calculated. If both are less than the given error, the iteration ends; otherwise, it returns to use the current calculation efficiency for a new round of calculation.

[0238] Furthermore, the calculations of stator inlet parameters, stator outlet parameters, stator Mach number, stator diffusion factor, and stator loss can all refer to the calculations of rotor inlet parameters, rotor outlet parameters, rotor Mach number, rotor diffusion factor, and rotor loss, which will not be repeated in this embodiment. The actual total pressure at the stator outlet is obtained through the loss coefficient. Based on the total inlet and outlet pressures, a new recovery coefficient value is calculated. The difference between the current recovery coefficient value and the recovery coefficient from the previous iteration is calculated. If both are less than a given error, the iteration ends; otherwise, a new round of calculation is performed using the currently calculated recovery coefficient.

[0239] Furthermore, the geometric parameters such as the blade bend angle and aspect ratio of the rotor and stator are calculated. The angle of attack and lag angle are calculated using the NACA (National Advisory Committee for Aeronautics) method. Based on the angle of attack, lag angle, and parameters such as the airflow angle, aspect ratio, and consistency at the rotor / stator blade inlet and outlet, the blade inlet geometric angle β is determined. 1K Exit geometric angle β 2K Calculation of parameters such as the number of blades.

[0240] After completing the geometric parameter calculation, determine whether it is the last stage. If it is the last stage, output one-dimensional design parameters; otherwise, pass the output parameters to the next row of rotors to start the calculation of a new stage.

[0241] After completing the one-dimensional inverse problem analysis, the entire rotor and stator geometric parameters obtained from the one-dimensional inverse problem analysis at the first design point are transferred, and the rotational speed, flow rate, and pressure ratio conditions at the second design point are input. Then, a one-dimensional forward problem analysis is performed. The specific process of the one-dimensional forward problem analysis is explained in detail below.

[0242] In one embodiment, performing a one-dimensional forward problem analysis of each stage of the blades until the last stage blade, to obtain the current flow rate of the compression system at the second design point, includes:

[0243] For the current stage rotor blades, a one-dimensional forward problem analysis method is used to sequentially calculate the rotor inlet aerodynamic parameters at the second design point, the rotor outlet lag angle at the second design point, the rotor loss at the second design point, and the rotor outlet aerodynamic parameters at the second design point based on the rotor outlet lag angle and the rotor loss at the second design point.

[0244] For the current stage stator blade, a one-dimensional forward problem analysis method is used to sequentially calculate the aerodynamic parameters of the stator inlet at the second design point, the stator lag angle at the second design point, the stator loss at the second design point, and the aerodynamic parameters of the stator outlet at the second design point based on the stator lag angle and the stator loss at the second design point.

[0245] Determine whether the current stage stator blade is the last stage. If it is not the last stage, pass the parameters of this stage to the next stage rotor blade and perform parameter calculations. If it is the last stage, obtain the current flow rate of the compression system at the second design point.

[0246] In this embodiment, during the one-dimensional forward problem analysis, detailed aerodynamic parameter calculations, lag angle calculations, and loss calculations are performed on the rotor and stator for each stage of blades. This step-by-step analysis fully considers the unique characteristics of each stage of blades, making the calculation results closer to reality and greatly improving the accuracy of the calculations. Furthermore, the parameter transfer direction is determined by whether it is the last stage of blades. If it is not the last stage, the parameters of this stage are transferred to the next stage of rotor blades for further calculation. If it is the last stage, the current flow rate of the compression system at the second design point is obtained. This process design is logically clear and well-organized, enabling efficient completion of the calculation tasks for the entire compression system at both design points. Finally, this method comprehensively utilizes one-dimensional inverse and one-dimensional forward problems to analyze the compression system from different perspectives, fully considering the impact of various factors on system performance. This provides a reliable and comprehensive basis for the design and optimization of the compression system, contributing to improving the overall performance and operating efficiency of the compression system.

[0247] Furthermore, the calculation of the rotor inlet aerodynamic parameters at the second design point includes:

[0248] Calculate the total enthalpy of the airflow at the rotor inlet at the second design point based on the total rotor inlet temperature at the second design point.

[0249] Calculate the total velocity at the rotor inlet at the second design point based on the rotor inlet airflow angle at the second design point and the initial axial velocity at the rotor inlet at the second design point.

[0250] Calculate the static enthalpy of the rotor inlet at the second design point based on the full velocity of the rotor inlet at the second design point and the total enthalpy of the airflow at the rotor inlet at the second design point.

[0251] The static temperature at the rotor inlet at the second design point is calculated based on the static enthalpy at the rotor inlet at the second design point.

[0252] Based on the relationship between total temperature and total pressure and static temperature and static pressure, the rotor inlet static pressure at the second design point is calculated, and then the rotor inlet static density at the second design point is obtained.

[0253] The rotor inlet area at the second design point is calculated based on the static density at the rotor inlet at the second design point, the given flow rate at the second design point, and the axial velocity at the rotor inlet at the second design point.

[0254] Adjust the rotor inlet axial velocity at the second design point until the calculated rotor inlet area at the second design point is the same as the rotor inlet area calculated at the first design point, and obtain the final rotor inlet area at the second design point.

[0255] Based on the final rotor inlet area at the second design point, the mid-diameter ratio at the second design point is obtained. Based on the mid-diameter ratio at the second design point, the tangential velocity at the rotor inlet at the second design point and the relative velocity at the rotor inlet at the second design point are obtained, and then the relative airflow angle at the rotor inlet at the second design point is obtained.

[0256] Calculate the Mach number at the rotor inlet at the second design point based on the aerodynamic parameters at the rotor inlet at the second design point.

[0257] In practice, the rotor inlet aerodynamic parameters are calculated based on the rotational speed, flow rate, pressure ratio, and geometric conditions of the rotor and stator blades at the second design point. This includes the following:

[0258] The total enthalpy of the airflow at the rotor inlet at the second design point can be obtained from the total temperature at the rotor inlet at the second design point according to equation (5-1):

[0259] (5-1)

[0260] In equation (5-1), Where X is the first intermediate function. The total rotor inlet temperature at the second design point. The total enthalpy of the rotor inlet airflow at the second design point.

[0261] Based on the rotor inlet airflow angle at the second design point and the initial rotor inlet axial velocity at the second design point, the total rotor inlet velocity C at the second design point can be obtained. 1_sec :

[0262] C 1_sec =C 1a_sec / sin(α 1_sec(5-2)

[0263] C 1a_sec Let α be the rotor inlet axial velocity at the second design point. 1_sec The rotor inlet airflow angle is the second design point.

[0264] Based on the rotor inlet full speed C at the second design point 1_sec and the total enthalpy of the rotor inlet airflow at the second design point The static enthalpy H at the rotor inlet at the second design point can be obtained. 1_sec :

[0265] (5-3)

[0266] Based on the rotor inlet static enthalpy at the second design point, the rotor inlet static temperature T at the second design point is calculated using equation (5-4). 1_sec In the formula X2 is the second intermediate function.

[0267] (5-4)

[0268] The static pressure can be calculated based on the relationship between total temperature and total pressure and static temperature and static pressure, and then the static density ρ at the rotor inlet at the second design point can be obtained. 1_sec Then according to A 1_sec =G _sec / (ρ 1_sec C 1a_sec The rotor inlet area A at the second design point is obtained. 1_sec G _sec Specify the flow rate for the second design point. Adjust the rotor inlet axial velocity at the second design point until the calculated rotor inlet area A is reached. 1_sec The area is calculated to be the same as the area obtained from the first design point. The U at the mid-diameter can be calculated based on the mid-diameter ratio. 1_sec (The rotor inlet tangential velocity at the second design point) and W 1_sec (Relative velocity of rotor inlet at the second design point), thereby determining the relative airflow angle β at the rotor inlet at the second design point. 1_sec The rotor inlet Mach number is calculated based on the aerodynamic parameters at the rotor inlet. Ma W1_sec The calculation process for the rotor inlet Mach number at the second design point is basically the same as that for the first design point.

[0269] Furthermore, the calculation of the rotor outlet lag angle at the second design point includes:

[0270] The reference angle of attack is calculated based on the reference angle of attack of a 10% thick blade without curvature, the influence factor of thickness distribution, the calculation factor of the angle of attack slope, the influence factor of the relative position of the maximum deflection of the blade on the angle of attack slope, and the difference between the inlet and outlet geometric angles of the blade.

[0271] The reference lag angle is calculated based on the influence factors of blade shape on lag angle, thickness influence coefficient, reference lag angle of blade shape with 0 curvature and 10% thickness, lag angle curvature slope factor, consistency, influence factor of relative position of maximum deflection on curvature, and the difference between blade inlet and outlet geometric angles.

[0272] The rotor outlet lag angle at the second design point is calculated based on the reference angle of attack, the reference lag angle, the relative airflow angle at the rotor inlet at the second design point, and the relative airflow angle at the rotor outlet at the second design point.

[0273] In practice, the reference angle of attack and reference lag angle are first determined: the reference state refers to the operating state with the minimum loss coefficient in the entire working state of the blade cascade. However, in reality, the relationship between the loss coefficient and the angle of attack is relatively flat near the reference state of the blade cascade, making it difficult to determine the minimum loss point. Therefore, a simplified definition is defined: for a flat relationship graph, the state at the midpoint between twice the minimum loss is the reference state, and the angle of attack at this point is called the reference angle of attack.

[0274] Furthermore, the formula for calculating the reference angle of attack of the 10% thickness and non-curved blade cascade is as follows:

[0275] (5-5),

[0276] Among them, i 0,10 σ is the reference angle of attack for a 10% thickness, non-curved blade cascade. pk For consistency, β 1_sec The relative airflow angle at the rotor inlet is the second design point.

[0277] The formula for calculating the thickness distribution influence factor is as follows:

[0278] (5-6),

[0279] Among them, K ic To account for the influence of thickness distribution factors, This represents the maximum relative thickness of the leaf shape.

[0280] The formula for calculating the angular slope factor of the angle of attack is as follows:

[0281] (5-7),

[0282] (5-8), (5-9),

[0283] (5-10),

[0284] Where n is the angular slope calculation factor for the angle of attack, and K a λ is the bending angle influence coefficient. f is the consistency influence coefficient, and q is the consistency influence factor;

[0285] The formula for calculating the influence factor of the relative position of the maximum deflection of the airfoil on the bending angle slope factor is as follows:

[0286] (5-11),

[0287] Among them, K if The influence factor of the relative position of the maximum deflection of the airfoil on the bending angle slope factor, x f Location of maximum deflection;

[0288] The formula for calculating the reference angle of attack is:

[0289] (5-12),

[0290] Among them, i ref The reference angle of attack is θ, which is the difference between the inlet and outlet geometric angles of the blade; K i,sh For the NACA65 series leaf shape, K is the shape correction factor. i,sh The value is 1.0; for the C4 series blade type, K i,sh The value is 1.1; for the BC10 series airfoil, K i,sh The value is 1.05;

[0291] The calculation of the reference lag angle first involves calculating the reference lag angle for an airfoil with 0 camber and 10% thickness. The formula for calculating the reference lag angle for the airfoil with 0 camber and 10% thickness is as follows:

[0292] (5-13),

[0293] Where, δ 0,10 The reference lag angle for a blade profile with 0 camber and 10% thickness;

[0294] The formula for calculating the influence coefficient of the thickness is:

[0295] (5-14),

[0296] Among them, K δ,c The influence coefficient of thickness;

[0297] For the NACA65 series airfoil, the formula for calculating the lag angle slope factor is:

[0298] (5-15),

[0299] For the C4 series and BC10 series airfoils, the formula for calculating the lag angle slope factor is as follows:

[0300] (5-16),

[0301] Where m is the slope factor of the backward angle;

[0302] The formula for calculating the influence factor of the relative position of the maximum deflection on the bending angle is as follows:

[0303] (5-17),

[0304] Among them, K δ,f β is the influence factor of the relative position of maximum deflection on the bending angle. 2_sec The relative airflow angle at the rotor outlet is the second design point.

[0305] The formula for calculating the reference lag angle is:

[0306] (5-18),

[0307] (5-19),

[0308] Where, δ ref For reference, the lagging angle, K δ,sh K is the influence factor of leaf shape on the lag angle. δ,sh The value of K is referenced. i,sh μ sec It is an exponential factor for consistency;

[0309] The formula for calculating the rotor outlet lag angle at the second design point is:

[0310] (5-20),

[0311] Where, δ sec Let f(x) be the rotor outlet lag angle at the second design point, and f(x) be the calculation coefficient for the lag angle under the current airflow angle at the angle of attack.

[0312] In the formula ,

[0313] When x≥0 ,

[0314] When x < 0 ,

[0315] Where x is an intermediate function and i is the angle of attack of the current airflow angle.

[0316] Furthermore, for the calculation of rotor losses at the second design point, the calculation of the reference loss is first performed. The calculation of the reference loss is the same as that at the first design point, and will not be repeated here. Then, the rotor loss at the second design point is calculated based on the reference angle of attack, the reference loss, and the current inlet airflow angle. The formula for calculating the rotor loss at the second design point is:

[0317] When Ma W1_sec When <0.6, ;

[0318] When 0.6≤Ma W1_sec When ≤0.95,

[0319] ;

[0320] When Ma W1_sec When >0.95,

[0321] ;

[0322] When ω sec >2ω cr When, ω sec =2ω cr ;

[0323] Among them, Ma W1_sec ω is the rotor inlet Mach number at the second design point. esc For the rotor loss at the second design point, ω cr To account for the losses caused by the speed coefficient and the maximum thickness of the blade, ω cr The expression is as follows:

[0324] ,

[0325] λ 1_sec When K < 0.53, λ_sec =1,

[0326] λ 1_sec When ≥0.53, ,

[0327] When K < 0.06, c_sec =1,

[0328] When ≥0.06, ,

[0329] Where ω is the rotor loss, K λ_sec K is the loss correction factor for the velocity coefficient at the second design point. c_sec λ is the loss correction factor for the maximum thickness at the second design point. 1_secD is the rotor inlet speed coefficient at the second design point. pk_sec This is the diffusion factor at the second design point.

[0330] Furthermore, based on the loss at the second design point and the lag angle at the rotor outlet at the second design point, the total pressure, static pressure, total temperature, static temperature, Mach number, and rotor pressure ratio and efficiency at the rotor outlet at the second design point are calculated.

[0331] Furthermore, after completing the calculation of the rotor-related parameters at the second design point, the stator inlet parameters, stator outlet lag angle, stator loss, and stator outlet parameters at the second design point are calculated sequentially. The stator outlet parameters at the second design point are calculated based on the stator loss and stator outlet lag angle at the second design point, including the total pressure, static pressure, total temperature, static temperature, Mach number, and stator recovery coefficient at the stator outlet. The calculation of the stator inlet parameters, stator outlet lag angle, and stator loss at the second design point is based on the calculation of the rotor inlet parameters, rotor outlet lag angle, and rotor loss at the second design point, respectively, and will not be elaborated further here.

[0332] Further determine if the current stage is the last stage. If not, pass the parameters of this stage to the next stage and perform the calculation for the next stage. If it is the last stage, determine whether the pressure ratio converges. Specifically, determine whether the pressure ratio and efficiency calculated under the current flow rate meet the requirements. If not, adjust according to the step-by-step process: stage adjustment → evaluation and screening → average tangential velocity adjustment → evaluation and screening → tangential velocity distribution adjustment → evaluation and screening → load distribution adjustment → evaluation and screening → axial velocity distribution adjustment → evaluation and screening → reaction force adjustment → evaluation and screening. If the pressure ratio and efficiency calculated at the first and second design points meet the requirements, calculate the aerodynamic design parameters for the second design point. After completing the calculation, calculate the one-dimensional performance key influencing parameters such as diffusion factor, load coefficient, flow coefficient, and reaction force at the second design point. Output the one-dimensional performance key influencing parameters of the first and second design points for reference in subsequent designs.

[0333] The embodiments of this application propose a one-dimensional dual-design-point method to address the requirement that the compression system of future high-speed aircraft must operate efficiently across an ultra-wide relative conversion speed range, taking into account the performance of the compression system under both high conversion speeds on the ground and low conversion speeds during high-speed flight. To address the problem that conventional one-dimensional inverse problem design methods require re-defining parameters such as loads and counterforces at each stage, leading to changes in the one-dimensional geometry of the compression system compared to the first design point during the evaluation of the second design point, thus rendering the evaluation of the second design point ineffective, a "reverse-forward-reverse" one-dimensional dual-design-point method is proposed. This method adds the evaluation of the second design point while ensuring that the one-dimensional geometry of the compression system remains unchanged, thus solving the problem that conventional one-dimensional compression system design methods cannot complete dual-design-point evaluation.

[0334] This method can quickly guide designers to identify problems in each row of blades at two design points in the early stages of compression system design, and can better take into account the performance of the two design points under a wide range of conditions.

[0335] In one specific embodiment, Table 1 shows the evaluation results of one-dimensional parameters for a certain fan at two design points. The table indicates that the main reason for the low efficiency at the second design point is the reduction in the efficiency of R1 and the decrease in the total pressure recovery coefficient of S2. Given that both the diffusion factor and velocity coefficient of R1 are reduced, the main reason for the increased loss is the excessive angle of attack. Similarly, given that both the diffusion factor and velocity coefficient of S2 are reduced, the main reason for the increased loss is the excessively negative angle of attack.

[0336] Table 1. Output results of the fan dual design point calculation method for the one-dimensional "inverse-forward-inverse" problem before improvement.

[0337]

[0338] Therefore, in the subsequent improved design, the load on R1 was reduced, which can alleviate the problem of a sharp increase in losses caused by the excessive angle of attack of R1 at the second design point; at the same time, the throat area of ​​S2 was increased to reduce the losses of S2. Table 2 shows the evaluation results of the one-dimensional parameters of a certain fan at the dual design points after the improvement. Under the premise that the efficiency at high speed is not reduced, the efficiency at low conversion speed is improved by 2 percentage points.

[0339] Table 2. Output results of the improved calculation method for the dual design point of the fan in the one-dimensional "inverse-forward-inverse" problem.

[0340]

[0341] One-dimensional design already involves numerous parameters, and the addition of a second design point evaluation further increases the number of target parameters in the dual-design-point calculation method. This significantly increases the difficulty of directly optimizing and adjusting all input parameters. This invention comprehensively considers the sensitivity of the second design point performance and its impact on the overall scheme, summarizing a step-by-step adjustment process for improving the compressor's second design point using a "reverse-positive-reverse" one-dimensional dual-design-point method. First, the number of compressor stages is adjusted. Conventional compressor stage determination only considers the influence of the high-speed first design point, largely ignoring the influence of the low-speed second design point. Furthermore, changing the number of stages has a significant impact on the entire compressor scheme. Therefore, considering the performance of both the high-speed first design point and the low-speed second design point, the number of compressor stages is determined first. After determining the number of compressor stages, the average tangential velocity is adjusted. The adjustment of the average tangential velocity directly affects the compressor's Mach number. A lower average tangential velocity can reduce the relative Mach number of each stage, increasing the usable range of each stage, thereby increasing the flow rate and efficiency at the second design point. After determining the average tangential velocity, the tangential velocity distribution of each stage of the compressor can be adjusted. Reducing the outlet stage tangential velocity can further reduce the relative Mach number of the compressor outlet stage, increasing its usable range and further improving the flow rate and efficiency at the second design point. After determining the tangential velocity distribution, the load distribution of each stage of the compressor can be adjusted. A lower inlet stage load is more conducive to increasing the overall compressor flow rate at low speeds. After determining the load of each stage, the axial velocity distribution can be adjusted. A lower outlet axial velocity can increase the outlet stage area, which is beneficial for alleviating the blockage of the downstream stages in the low-speed "surge and blockage" state. Finally, the reaction force is adjusted. Considering that the current design system's experience is based on the first design point, the parameters of the first design point are adjusted throughout the step-by-step adjustments. The impact on the characteristics of both the first and second design points is then comprehensively considered. As more data from the second design point accumulates, adjustments can be gradually made specifically for the second design point.

[0342] Considering the sensitivity of the second design point and its impact on the overall scheme, a step-by-step adjustment process for improving the compressor's second design point using the "reverse-forward-reverse" one-dimensional dual design point method is summarized. This process can quickly improve the dual design point performance of the compression system. The detailed adjustment process is as follows: stage adjustment → evaluation and screening → average tangential velocity adjustment → evaluation and screening → tangential velocity distribution adjustment → evaluation and screening → load distribution adjustment → evaluation and screening → axial velocity distribution adjustment → evaluation and screening → counterforce adjustment → evaluation and screening. The changes in the calculated characteristics at each step are shown in [the table below]. Figures 4 to 15 .

[0343] The results for the first and second design points are shown in Table 3. After the adjustment, the flow rate at the first design point decreased by 0.4% and the efficiency decreased by 1.1 percentage points. The flow rate at the second design point increased by nearly 10% and the efficiency increased by 3 percentage points. Under the premise that the performance at the first design point slightly decreased, the flow rate and efficiency at the second design point were significantly improved.

[0344] Table 3 Comparison of results for the first and second design points

[0345]

[0346] The embodiments provided by this invention propose a dual-design-point calculation method for compression systems based on a one-dimensional inverse-forward-inverse problem, which has significant advantages and practicality. First, by introducing the concept of dual design points, this method effectively solves the problem that traditional one-dimensional design methods cannot simultaneously consider high and low speed performance under a wide range of operating conditions. Especially in future high-speed aircraft propulsion systems, this method can ensure that the compression system can operate efficiently over an ultra-wide relative conversion speed range, thereby meeting the stringent requirements of the propulsion system. Second, the "inverse-forward-inverse" design process adopted in this method adds an evaluation step for the second design point while ensuring the one-dimensional geometry of the compression system remains unchanged. This innovation not only solves the problem of second design point evaluation failure in conventional one-dimensional design methods but also enables designers to quickly identify problems in each row of blades at the two design points in the early stages of design, thereby allowing for targeted optimization and improvement.

[0347] Furthermore, this method provides designers with a systematic and scientific optimization solution through a detailed step-by-step adjustment process. From level adjustment to counter-force adjustment, each step is accompanied by evaluation and screening, ensuring that designers can make the best decisions based on the actual situation. This step-by-step adjustment process not only improves design efficiency but also significantly enhances the performance of the compression system at both design points.

[0348] Through verification using specific embodiments, this method has achieved significant results in practical applications. In the improved one-dimensional parameter evaluation results for the fan's dual design points, low-speed efficiency was significantly improved, while high-speed efficiency remained stable. This achievement fully demonstrates the practicality and superiority of this method, providing strong technical support for the design of future compression systems.

[0349] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for calculating dual design points of a compressed system based on a one-dimensional inverse-forward-inverse problem, characterized in that, The method includes: Step 1: Obtain the first boundary conditions and blade geometry parameters of the aero-engine compression system at the first design point. The first boundary conditions include the total inlet temperature, total inlet pressure, inlet flow rate, rotational speed, inlet airflow angle, and outlet airflow angle of the compression system. Step 2: Based on the first boundary conditions and blade geometric parameters, the one-dimensional average streamline method is used to perform a one-dimensional inverse problem analysis of each stage of the blades until the last stage blade, to obtain the one-dimensional design parameters of the compression system at the first design point. The one-dimensional design parameters include the rotor blade geometric parameters and the stator blade geometric parameters. Step 3: Transfer the one-dimensional design parameters to the second design point, obtain the rotational speed, flow rate and pressure ratio of the compression system at the second design point, perform one-dimensional forward problem analysis of each stage of the blades until the last stage blade, and obtain the current flow rate of the compression system at the second design point. Step 4: Perform a one-dimensional inverse problem analysis again. Calculate whether the pressure ratio and efficiency at the second design point meet the requirements based on the current flow rate. If not, adjust according to the step-by-step process, repeating steps 1 to 3 until the pressure ratio and efficiency at the second design point meet the requirements. The step-by-step process includes the following steps in sequence: stage adjustment, average tangential velocity adjustment, tangential velocity distribution adjustment, load distribution adjustment, axial velocity distribution adjustment, and counterforce adjustment. If the requirements are met, calculate the one-dimensional design parameters of the compression system at the second design point. Step 5: Output the aerodynamic design-related parameters for the first and second design points to obtain the one-dimensional key performance parameters for the first and second design points.

2. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 1, characterized in that, The method employs a one-dimensional average streamline approach to perform a one-dimensional inverse problem analysis on each stage of the blades, up to the last stage, to obtain the one-dimensional design parameters of the compression system at the first design point, including: For the current stage rotor blades, the one-dimensional average streamline method is used to calculate the rotor inlet parameters, rotor outlet parameters, rotor Mach number, rotor diffusion factor, and rotor loss in sequence. Perform iterative processing of the current stage rotor isentropic compression efficiency until the rotor isentropic compression efficiency converges. For the current stage stator blade, the one-dimensional average streamline method is used to calculate the stator inlet parameters, stator outlet parameters, stator Mach number, stator diffusion factor, and stator loss in sequence. Perform iterations on the current level of the stator restoration coefficients until the stator restoration coefficients converge. For the current stage rotor and stator, calculate the blade geometry parameters to obtain the rotor blade geometry parameters and stator blade geometry parameters; If the current stage stator blade is the last stage blade, the one-dimensional design parameters of the compression system at the first design point are output. If the current stage stator blade is not the last stage blade, the outlet parameters are transferred to the next stage rotor to perform parameter calculations for the new stage.

3. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 2, characterized in that, The calculation of the rotor inlet parameters includes: Calculate the total enthalpy of the airflow at the rotor inlet based on the total temperature at the rotor inlet; The total rotor inlet velocity is calculated based on the rotor inlet airflow angle and the initial rotor inlet axial velocity. The static enthalpy at the rotor inlet is calculated based on the total velocity at the rotor inlet and the total enthalpy of the airflow at the rotor inlet. The rotor inlet static temperature is obtained based on the rotor inlet static enthalpy; Based on the relationship between total temperature and total pressure and static temperature and static pressure, the rotor inlet static pressure is calculated, and then the rotor inlet static density is obtained. The rotor inlet area is calculated based on the rotor inlet static density, the given flow rate, and the rotor inlet axial velocity. Adjust the rotor inlet axial speed until the calculated rotor inlet area is the same as the given rotor inlet area to obtain the final rotor inlet area; Based on the final rotor inlet area, the mean diameter ratio is obtained. Based on the mean diameter ratio, the rotor inlet tangential velocity and rotor inlet relative velocity are obtained, and then the rotor inlet relative airflow angle is obtained.

4. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 3, characterized in that, The calculation of the rotor outlet parameters includes: Based on the given load factor, tangential velocity, and total enthalpy of the rotor inlet airflow, the total enthalpy of the rotor outlet airflow, the total temperature of the rotor outlet airflow, and the stagnation state entropy of the rotor outlet airflow are calculated sequentially. The isentropic work and the total isentropic enthalpy at the rotor outlet are calculated based on the initial value of the rotor efficiency, and then the total pressure at the rotor outlet is obtained. The rotor outlet circumferential velocity is calculated based on the circumferential component of the absolute velocity of the airflow at the rotor inlet, the rotor power, and the circumferential velocity at the mid-diameter of the rotor blades. Calculate the relative airflow angle and the total velocity at the rotor outlet based on the circumferential velocity at the rotor outlet. Based on the total velocity at the rotor outlet and the total enthalpy of the airflow at the rotor outlet, the static enthalpy at the rotor outlet, the static temperature at the rotor outlet, and the static pressure at the rotor outlet are calculated sequentially. The rotor outlet area is calculated based on the rotor outlet axial velocity, rotor outlet static pressure, rotor outlet static temperature, and given flow rate. Adjust the rotor outlet axial velocity until the calculated rotor outlet area is the same as the given rotor outlet area to obtain the final rotor outlet area. Based on the final rotor inlet area, the hub radius and pitch diameter ratio of the rotor outlet are obtained.

5. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 4, characterized in that, The formula for calculating the rotor Mach number is: ， ， ， ， Where Ma is the rotor inlet Mach number, λ1 is the rotor inlet velocity coefficient, k is the adiabatic index, W1 is the rotor inlet relative velocity, and a cr,w This is the critical speed of sound. H is the relative total enthalpy at the rotor inlet. cr,w This is the enthalpy value corresponding to the critical total temperature. U is the total enthalpy of the airflow at the rotor inlet. cp1 C is the circumferential velocity at the inlet median diameter of the rotor blade. 1u This represents the circumferential component of the absolute velocity of the airflow at the rotor inlet; The formula for calculating the rotor diffusion factor is: ， ， Among them, D pk σ is the rotor diffusion factor. pk For the consistency, β1 is the relative airflow angle at the rotor inlet, β2 is the relative airflow angle at the rotor outlet, and C 1a C is the axial velocity at the rotor inlet. 2a The rotor outlet axial velocity; The formula for calculating the rotor loss is: ， ， Where ω is the rotor loss, θ th Let μ be the momentum thickness, μ be the loss exponent, and σ be the loss coefficient. pk When μ < 1, μ = 0.25, σ pk When μ is ≥1, μ = 0.

7.

6. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 1, characterized in that, The step-by-step one-dimensional forward problem analysis of the blades, up to the last blade, is performed to obtain the current flow rate of the compression system at the second design point, including: For the current stage rotor blades, a one-dimensional forward problem analysis method is used to sequentially calculate the rotor inlet aerodynamic parameters at the second design point, the rotor outlet lag angle at the second design point, the rotor loss at the second design point, and the rotor outlet aerodynamic parameters at the second design point based on the rotor outlet lag angle and the rotor loss at the second design point. For the current stage stator blade, a one-dimensional forward problem analysis method is used to sequentially calculate the aerodynamic parameters of the stator inlet at the second design point, the stator lag angle at the second design point, the stator loss at the second design point, and the aerodynamic parameters of the stator outlet at the second design point based on the stator lag angle and the stator loss at the second design point. Determine whether the current stage stator blade is the last stage. If it is not the last stage, pass the parameters of this stage to the next stage rotor blade and perform parameter calculations. If it is the last stage, obtain the current flow rate of the compression system at the second design point.

7. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 6, characterized in that, The calculation of the rotor inlet aerodynamic parameters at the second design point includes: Calculate the total enthalpy of the airflow at the rotor inlet at the second design point based on the total rotor inlet temperature at the second design point. Calculate the total velocity at the rotor inlet at the second design point based on the rotor inlet airflow angle at the second design point and the initial axial velocity at the rotor inlet at the second design point. Calculate the static enthalpy of the rotor inlet at the second design point based on the full velocity of the rotor inlet at the second design point and the total enthalpy of the airflow at the rotor inlet at the second design point. The static temperature at the rotor inlet at the second design point is calculated based on the static enthalpy at the rotor inlet at the second design point. Based on the relationship between total temperature and total pressure and static temperature and static pressure, the rotor inlet static pressure at the second design point is calculated, and then the rotor inlet static density at the second design point is obtained. The rotor inlet area at the second design point is calculated based on the static density at the rotor inlet at the second design point, the given flow rate at the second design point, and the axial velocity at the rotor inlet at the second design point. Adjust the rotor inlet axial velocity at the second design point until the calculated rotor inlet area at the second design point is the same as the rotor inlet area calculated at the first design point, and obtain the final rotor inlet area at the second design point. Based on the final rotor inlet area at the second design point, the mid-diameter ratio at the second design point is obtained. Based on the mid-diameter ratio at the second design point, the tangential velocity at the rotor inlet at the second design point and the relative velocity at the rotor inlet at the second design point are obtained. Then, the relative airflow angle at the rotor inlet at the second design point is obtained. Calculate the Mach number at the rotor inlet at the second design point based on the aerodynamic parameters at the rotor inlet at the second design point.

8. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 7, characterized in that, The calculation of the rotor outlet lag angle at the second design point includes: The reference angle of attack is calculated based on the reference angle of attack of a 10% thick blade cascade without curvature, the thickness distribution influence factor, the angle of attack slope calculation factor, the influence factor of the relative position of the maximum deflection of the blade on the angle of attack slope factor, and the difference between the inlet and outlet geometric angles of the blade. The reference lag angle is calculated based on the influence factors of blade shape on lag angle, thickness influence coefficient, reference lag angle of blade shape with 0 curvature and 10% thickness, lag angle curvature slope factor, consistency, influence factor of relative position of maximum deflection on curvature, and the difference between blade inlet and outlet geometric angles. The rotor outlet lag angle at the second design point is calculated based on the reference angle of attack, the reference lag angle, the relative airflow angle at the rotor inlet at the second design point, and the relative airflow angle at the rotor outlet at the second design point.

9. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 8, characterized in that, The formula for calculating the reference angle of attack of the 10% thickness, non-curved blade cascade is as follows: ， Among them, i 0,10 σ is the reference angle of attack for a 10% thickness, non-curved blade cascade. pk For consistency, β 1_sec The relative airflow angle at the rotor inlet is the second design point. The formula for calculating the thickness distribution influence factor is as follows: ， Among them, K ic To account for the influence of thickness distribution factors, This represents the maximum relative thickness of the leaf shape. The formula for calculating the angular slope factor of the angle of attack is as follows: ， ， ， ， Where n is the angular slope calculation factor for the angle of attack, and K a λ is the bending angle influence coefficient. f is the consistency influence coefficient, and q is the consistency influence factor; The formula for calculating the influence factor of the relative position of the maximum deflection of the airfoil on the bending angle slope factor is as follows: ， Among them, K if The influence factor of the relative position of the maximum deflection of the airfoil on the bending angle slope factor, x f Location of maximum deflection; The formula for calculating the reference angle of attack is: ， Among them, i ref For reference angle of attack, K i,sh θ is the shape correction factor, and θ is the difference between the inlet and outlet geometric angles of the blade; The formula for calculating the reference lag angle of the airfoil with 0 camber and 10% thickness is as follows: ， Where, δ 0,10 The reference lag angle for a blade profile with 0 camber and 10% thickness; The formula for calculating the influence coefficient of the thickness is: ， Among them, K δ,c The influence coefficient of thickness; For the NACA65 series airfoil, the formula for calculating the lag angle slope factor is: ， For the C4 series and BC10 series airfoils, the formula for calculating the lag angle slope factor is as follows: ， Where m is the slope factor of the backward angle; The formula for calculating the influence factor of the relative position of the maximum deflection on the bending angle is as follows: ， Among them, K δ,f β is the influence factor of the relative position of maximum deflection on the bending angle. 2_sec The relative airflow angle at the rotor outlet is the second design point. The formula for calculating the reference lag angle is: ， ， Where, δ ref For reference, the lagging angle, K δ,sh μ is the influence factor of leaf shape on the lag angle. sec It is an exponential factor for consistency; The formula for calculating the rotor outlet lag angle at the second design point is: ， Where, δ sec Let f(x) be the rotor outlet lag angle at the second design point, and f(x) be the calculation coefficient for the lag angle under the current airflow angle at the angle of attack. In the formula , When x≥0 , When x < 0 , Where x is an intermediate function and i is the angle of attack of the current airflow angle.

10. The dual-design-point calculation method for a compression system based on a one-dimensional inverse-forward-inverse problem as described in claim 9, characterized in that, The formula for calculating rotor loss at the second design point is: When Ma W1_sec When <0.6, ; When 0.6≤Ma W1_sec When ≤0.95, ； When Ma W1_sec When >0.95, ； When ω sec > 2ω cr then, ω sec = 2ω cr ; Among them, Ma W1_sec ω is the rotor inlet Mach number at the second design point. esc For the rotor loss at the second design point, ω cr To account for the losses caused by the speed coefficient and the maximum thickness of the blade, ω cr The expression is as follows: ， λ 1_sec When K < 0.53, λ_sec =1, λ 1_sec When ≥0.53, , When K < 0.06, c_sec =1, When ≥0.06, , Where ω is the rotor loss, K λ_sec K is the loss correction factor for the velocity coefficient at the second design point. c_sec λ is the loss correction factor for the maximum thickness at the second design point. 1_sec D is the rotor inlet speed coefficient at the second design point. pk_sec This is the diffusion factor at the second design point.

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