Two-stage turbine time sequence position optimization method based on wake transport model
By optimizing the timing position of the two-stage turbine using a wake transport model, the problems of high computational cost and positional deviation in traditional methods are solved, thereby improving the efficiency of low-pressure turbines and enabling their engineering applications.
Patent Information
- Application Number
- CN202511188147.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-25
- Publication Date
- 2025-12-19
AI Technical Summary
Traditional timing effect control methods are computationally expensive and fail to accurately describe the relationship between speed and wake deformation, resulting in deviations in the optimal timing position and making it difficult to improve the efficiency of low-pressure turbines under different speed conditions.
A time-series position optimization method for a two-stage turbine based on a wake transport model is established. By calculating the flow parameters and circumferential migration distance at the specified rotational speed, a mathematical model is constructed to predict the optimal time-series position, reducing the computational load and considering the influence of rotational speed on wake deformation.
It significantly reduces the computational load for predicting timing effects under multiple speed conditions, accurately determines the optimal timing position, achieves precise control of timing effects, and improves the efficiency of low-pressure turbines.
Smart Images
Figure CN121167916A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of turbine design of an aero-engine, and particularly relates to a two-stage turbine time sequence position optimization method based on a wake transport model, and is particularly suitable for improving the aerodynamic performance of an aero-engine with variable speed. BACKGROUND
[0002] In the aero-engine technology system, the low-pressure turbine is one of the key components of the engine, and its performance has a decisive influence on the overall performance of the engine. Nowadays, the turbine performance of modern aero-engines is usually maintained in the range of 85% to 92%. However, with the rapid development of aviation technology, the requirements for the performance of aero-engines are becoming more and more stringent, and further improving the efficiency of the low-pressure turbine has become a key technical bottleneck that needs to be overcome in the current aero-engine research field. Traditional measures to improve turbine efficiency, such as material improvement and aerodynamic shape optimization, have achieved remarkable results. However, in recent years, the traditional method of improving the efficiency of the low-pressure turbine has gradually shown the problem of diminishing returns. In recent years, time sequence effect has gradually attracted attention as a new way to improve the efficiency of the low-pressure turbine. Time sequence effect is to adjust the phase relationship between the same blade rows to change the flow path and pressure distribution of the airflow in the turbine, thereby reducing flow loss and improving turbine efficiency.
[0003] Traditional time sequence effect regulation mainly compares the performance parameters of the low-pressure turbine under different time sequence positions through CFD simulation of multiple time sequence positions, such as efficiency, power, etc., to find the optimal time sequence position.
[0004] The traditional method of finding the optimal time sequence position needs to be calculated and simulated separately for each working condition, which has high calculation cost, and full three-dimensional simulation calculation requires a lot of computing resources. The existing prediction model is based on the assumption of the design condition and does not fully consider the influence of the speed on the deformation of the wake. In the actual running process, the speed of the low-pressure turbine will change with the change of the engine working condition. The change of the speed will cause the deformation of the wake generated by the upstream blade row in the propagation process, and the shape, strength and position of the wake will change. The traditional model fails to accurately describe the relationship between the speed and the wake deformation, resulting in a deviation between the optimal time sequence position obtained based on the traditional model and the actual situation under different speed conditions, which cannot truly realize the optimal regulation of the time sequence effect, thereby limiting the improvement effect of the low-pressure turbine efficiency. The traditional time sequence effect regulation method does not establish a quantitative relationship between geometric parameters such as axial spacing and chord length and the best time sequence. In the design of the low-pressure turbine, the geometric parameters such as axial spacing and chord length are limited by many factors, so the results obtained may not be realized in the actual turbine structure, making it difficult to directly apply the time sequence effect regulation technology to engineering practice, and reducing its feasibility and effectiveness in actual engine design. SUMMARY
[0005] In view of this, this application provides a two-stage turbine timing position optimization method based on a wake transport model, which aims to solve the problem of large computational load in timing effect prediction under multiple speed conditions. By establishing an explicit mathematical relationship between speed and optimal timing position, the computational load in timing effect prediction under multiple speed conditions is greatly reduced, the efficiency of low-pressure turbine is improved, and the precise control and engineering application of timing effects are realized. This provides an efficient and feasible technical solution for improving the performance of low-pressure turbines in aero-engines.
[0006] This application provides the following technical solution: a two-stage turbine timing position optimization method based on a wake transport model, comprising: Based on the flight environment variables and flight requirements of the aero-engine, the operating parameters of the two-stage low-pressure turbine are obtained; Based on the operating parameters, the flow parameters of the two-stage low-pressure turbine at different speeds are calculated. These flow parameters include the axial velocity V1 at the cross-section where the first-stage stator wake core reaches the axial position of the first-stage moving blade leading edge, and the maximum axial velocity V at the cross-section where the first-stage stator wake core reaches the middle axial position of the first-stage moving blade surface. m The axial velocity V2 when the first stage stationary blade wake core detaches from the trailing edge of the first stage moving blade and the axial velocity V3 at the cross section where the first stage stationary blade wake core reaches the axial position of the leading edge of the second stage stationary blade. Based on the operating parameters and the flow parameters, the circumferential migration distance L1 when the first-stage stationary blade wake core reaches the first-stage moving blade, the circumferential migration distance L2 from the moment the first-stage stationary blade wake core reaches the first-stage moving blade until it detaches from the suction surface of the first-stage moving blade, and the circumferential migration distance L3 from the moment the first-stage stationary blade wake core detaches from the suction surface of the first-stage moving blade until it reaches the leading edge of the second-stage stationary blade are calculated respectively. Based on the circumferential migration distances L1, L2, and L3, the circumferential migration distance of the entire transport path when the core of the first-stage stator wake reaches the leading edge of the second-stage stator is calculated. Construct based on the circumferential migration distance Predicting the optimal timing position phase difference The mathematical model is used to determine the optimal timing position of the two-stage low-pressure turbine at different speeds.
[0007] According to one embodiment of this application, the method further includes: redesigning the optimal timing position phase difference between the first-stage stator and the second-stage stator based on the optimal timing positions of the two-stage low-pressure turbine at different speeds. Under the same boundary conditions, the low-pressure turbine efficiency before and after the redesign was calculated and compared to verify the mathematical model.
[0008] According to one embodiment of this application, the operating parameters include: Reynolds number, total inlet temperature and pressure, Mach number, and rotor speed of the two-stage low-pressure turbine during operation, as well as blade axial chord length, pitch, axial distance between the trailing edge of the first-stage stationary blade and the leading edge of the first-stage rotor blade, axial distance between the trailing edge of the first-stage rotor blade and the leading edge of the second-stage stationary blade, airflow angle at the outlet of the first-stage stationary blade, airflow angle at the outlet of the first-stage rotor blade, rotation radius of the first-stage rotor blade, rotation radius of the second-stage stationary blade, and number of blades of the second-stage stationary blade.
[0009] According to one embodiment of this application, the circumferential migration distance L1 when the core of the first-stage stationary blade wake reaches the first-stage moving blade is calculated using the following formula:
[0010] in, This indicates the axial distance between the trailing edge of the first-stage stationary blade and the leading edge of the first-stage moving blade. This indicates the airflow angle at the outlet of the first-stage stationary blade.
[0011] According to one embodiment of this application, the circumferential migration distance L2 of the first-stage stationary blade wake core from its arrival at the first-stage moving blade until it detaches from the suction surface of the first-stage moving blade is calculated using the following formula:
[0012] in, This indicates the radius of rotation of the first-stage moving blade. Indicates the rotational speed of the moving blade. This represents the time required for the core of the first-order still leaf wake to migrate a circumferential distance L1.
[0013] According to one embodiment of this application, the time required for the core of the first-stage stator wake to travel a circumferential migration distance L1 is calculated using the following formula. :
[0014] in, The axial velocity is the velocity at the cross section where the core of the first-stage stationary blade wake reaches the axial position of the first-stage moving blade leading edge. The maximum axial velocity at the cross section at the middle axial position of the first-stage stationary blade wake core reaching the surface of the first-stage moving blade. The first stage stator blade wake core reaches maximum axial velocity The axial distance from the leading edge of the first-stage moving blade. The axial velocity of the first-stage stationary blade wake core as it detaches from the trailing edge of the first-stage moving blade. It is the axial chord length of the first-stage moving blade.
[0015] According to an embodiment of the present application, the circumferential migration distance L3 of the first stage vane wake core from the start of shedding from the suction surface of the first stage moving blade to the arrival at the leading edge of the second stage vane is calculated by the following formula:
[0016] wherein, represents the radius of rotation of the first stage moving blade, represents the rotating speed of the moving blade, represents the time required for the first stage vane wake core to migrate circumferentially by the distance L3, represents the outlet flow angle of the first stage moving blade, represents the axial distance between the trailing edge of the first stage moving blade and the leading edge of the second stage vane.
[0017] According to an embodiment of the present application, the time required for the first stage vane wake core to migrate circumferentially by the distance L3 is calculated by the following formula
[0018] wherein, represents the axial distance between the trailing edge of the first stage moving blade and the leading edge of the second stage vane, V2 represents the axial speed of the first stage vane wake core when it is shed from the trailing edge of the first stage moving blade, and V3 represents the axial speed of the first stage vane wake core when it arrives at the axial position cross-section of the leading edge of the second stage vane.
[0019] According to an embodiment of the present application, the circumferential migration distance L1, the circumferential migration distance L2 and the circumferential migration distance L3 are sequentially added to obtain the circumferential migration distance of the entire transport line when the first stage vane wake core arrives at the leading edge of the second stage vane .
[0020] According to an embodiment of the present application, the mathematical model for predicting the phase difference of the optimal timing position based on the circumferential migration distance is represented as:
[0021] wherein, R2 represents the radius of rotation of the second stage vane, represents the number of blades of the second stage vane, and K represents an integer multiple.
[0022] Compared with the traditional method, the above at least one technical scheme adopted by the embodiments of the present specification can achieve the beneficial effects at least including: by establishing the display mathematical relationship between the rotation speed and the optimal timing position, the embodiments of the present application avoid the process of separately performing a large number of CFD simulations on each working condition by the traditional “trial and error method”, greatly reduce the calculation amount of timing effect prediction under multiple rotation speed conditions, significantly shorten the research and development cycle, and reduce the requirements on the computing device. The influence of rotation speed on wake deformation is fully considered, the relationship between rotation speed and wake deformation can be accurately described, so that the optimal timing position can be more accurately determined under different rotation speed conditions, the precise regulation and control of timing effect is realized, and the low-pressure turbine efficiency is effectively improved. The prediction model can quickly predict the optimal timing position, provides strong technical support for the design and optimization of the low-pressure turbine of the aero-engine, and improves the guiding significance of the timing effect in engineering application. BRIEF DESCRIPTION OF DRAWINGS
[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.
[0024] Figure 1 is a flow chart of a two-stage turbine timing position optimization method based on a wake transport model according to an embodiment of the present application; Figure 2 is a construction schematic diagram of a mathematical model according to an embodiment of the present application; Figure 3 is an entropy cloud diagram of the optimal timing position under the mathematical model of the second stage stator vane according to an embodiment of the present application; Figure 4 is a comparison schematic diagram of turbine efficiency corresponding to the optimal timing position under the mathematical model and original turbine efficiency according to an embodiment of the present application. DETAILED DESCRIPTION
[0025] The embodiments of the present application will be described in detail below with reference to the drawings.
[0026] Following, the embodiments of the present application are described through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the disclosure. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. The present application can also be implemented or applied by other different specific embodiments, and various modifications or changes can be made to the details in the specification without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.
[0027] As shown in the Figure 1 , the embodiment of the present application provides a double-stage turbine timing position optimization method based on a wake transport model, comprising: S101. According to the flight environment variables and flight requirements of the aero-engine, the working parameters of the double-stage low-pressure turbine are obtained; S102. According to the working parameters, the flow parameters of the double-stage low-pressure turbine under different rotating speeds are calculated, the flow parameters including the axial velocity V1 of the first-stage stator wake core arriving at the axial position section of the first-stage rotor leading edge, the maximum axial velocity V2 of the first-stage stator wake core arriving at the middle axial position section of the first-stage rotor blade surface, the axial velocity V3 of the first-stage stator wake core arriving at the axial position section of the second-stage stator leading edge, and the axial velocity V4 of the first-stage stator wake core arriving at the axial position section of the second-stage rotor leading edge; m S103. Based on the working parameters and the flow parameters, the circumferential migration distance L1 of the first-stage stator wake core arriving at the first-stage rotor, the circumferential migration distance L2 of the first-stage stator wake core from arriving at the first-stage rotor to falling off from the first-stage rotor suction surface, and the circumferential migration distance L3 of the first-stage stator wake core from falling off from the first-stage rotor suction surface to arriving at the second-stage stator leading edge are calculated respectively; S104. According to the circumferential migration distance L1, the circumferential migration distance L2 and the circumferential migration distance L3, the circumferential migration distance L4 of the first-stage stator wake core arriving at the second-stage rotor leading edge is calculated, and a mathematical model based on the circumferential migration distance L4 is constructed to predict the optimal timing position phase difference According to the mathematical model, the optimal timing position of the double-stage low-pressure turbine under different rotating speeds is determined.
[0028] In an embodiment of the present application, the method further comprises: based on the optimal timing position of the two-stage low-pressure turbine at different rotational speeds, redesigning the phase difference of the optimal timing position between the first-stage stator vane and the second-stage stator vane ; under the same boundary conditions, calculating and comparing the efficiencies of the low-pressure turbine before and after the redesign, respectively, to verify the mathematical model.
[0029] In an embodiment of the present application, the method for optimizing the timing position of the two-stage low-pressure turbine comprises the following steps:
[0030] In an embodiment of the present application, the method for optimizing the timing position of the two-stage low-pressure turbine comprises the following steps: Step 1, obtaining the working parameters of the two-stage low-pressure turbine According to the environmental variables (such as air flow temperature, speed, pressure, density, viscosity, etc.) and flight requirements (flight height, speed, etc.) of the engine during daily flight, the Reynolds number, inlet total temperature and pressure, Mach number, rotor speed (N), etc. parameters of the two-stage low-pressure turbine during work are obtained. And the blade design parameters (axial chord length, pitch, axial distance between the first-stage stator vane trailing edge and the first-stage rotor vane leading edge C1, axial distance between the first-stage rotor vane trailing edge and the second-stage stator vane leading edge C2, first-stage stator vane outlet flow angle , first-stage rotor vane outlet flow angle , first-stage rotor vane rotation radius, second-stage stator vane rotation radius, and second-stage stator vane number n, etc.).
[0031] Step 2, calculating the flow parameters of the two-stage low-pressure turbine at different rotational speeds In this embodiment, the internal flow parameters of the two-stage low-pressure turbine at the design rotational speed 900 rad / min, 80% design rotational speed 720 rad / min, and 120% design rotational speed 1080 rad / min without phase difference between the original first-stage stator vane and the second-stage stator vane are obtained by using the CFX simulation calculation based on the above boundary conditions (working parameters). The axial velocity V1 of the first-stage stator vane wake core reaching the axial position cross section of the first-stage rotor vane leading edge, the maximum axial velocity V m, the axial velocity V2 of the first stage vane wake core when it is shed from the first stage rotor trailing edge, and the axial velocity V3 of the first stage vane wake core when it reaches the axial position section of the second stage vane leading edge. Finally, the stage efficiency of the two-stage low-pressure turbine at different rotating speeds is obtained.
[0032] Step 3, construction of a mathematical model for predicting the optimal timing position based on wake transport mechanism This embodiment divides the transport process of the first stage wake into three stages: the wake reaches the first stage rotor; the wake is sheared, stretched, etc. by the rotor until it is shed from the suction surface of the first stage rotor; and the wake hits the leading edge of the second stage vane after being shed from the first stage rotor. According to the flow parameters of the three stages obtained by the CFX calculation, a mathematical relationship is established, and finally the phase difference of the optimal timing position is calculated. .
[0033] As shown in Figure 2 , Figure 2 is a schematic diagram of the transport process of the first stage vane wake. This embodiment divides the transport process of the wake into three stages: the wake reaches the first stage rotor; the wake is sheared, stretched, etc. by the rotor until it is shed from the suction surface of the first stage rotor; and the wake hits the leading edge of the second stage vane after being shed from the first stage rotor.
[0034] First stage: the wake generated by the first stage vane reaches the first stage rotor, that is, the wake of the upstream vane reaches position a in the figure, at this time the circumferential migration distance L1 of the wake can be calculated by formula (1):
[0035] wherein, represents the axial distance between the trailing edge of the first stage vane and the leading edge of the first stage rotor, represents the outlet flow angle of the first stage vane.
[0036] Second stage: the first stage vane wake is sheared, stretched, twisted and deformed by the first stage rotor, and then rotates with the rotor until the wake generated by the upstream guide vane enters the rotor passage and rotates with the rotor. When the vortex reaches position b, it will be shed from the suction surface of the first stage rotor. In this process, the circumferential migration distance L2 of the first stage vane wake can be calculated by formula (2):
[0037] wherein, represents the radius of rotation of the first stage rotor, represents the rotor rotating speed, represents the time required for the first stage vane wake core to migrate circumferentially by a distance L2. And The calculation of the first stage stator wake core passing through the axial velocity of the first stage rotor blade and the axial chord length can be calculated. Assuming that the axial velocity passing through the blade wake of the first stage rotor blade is linearly distributed, is the axial velocity of the first stage stator wake core passing through the axial position section of the leading edge of the first stage rotor blade, is the maximum axial velocity of the first stage stator wake core passing through the axial position section of the middle of the first stage rotor blade surface, is the axial distance from the first stage stator wake core to the maximum axial velocity to the leading edge point of the first stage rotor blade (wherein the parameters are obtained by numerical simulation through software CFX, by setting a monitoring line in the axial direction in the rotor passage, extracting the axial velocity distribution data of the first stage stator wake, and determining the axial distance between the velocity peak value and the leading edge point of the first stage rotor blade, is the axial velocity of the first stage stator wake core when it is shed from the trailing edge of the first stage rotor blade, is the axial chord length of the first stage rotor blade. Thus, the time required for the first stage stator wake core to pass through the circumferential migration distance L1 is calculated by formula (3):
[0038] The third stage: the first stage stator wake is separated from the first stage rotor and reaches the leading edge of the second stage stator. At this time, the distance L3 of the wake core moving circumferentially can be calculated by formula (4):
[0039] wherein, represents the radius of rotation of the first stage rotor, represents the rotational speed of the rotor, represents the time required for the first stage stator wake core to pass through the circumferential migration distance L3, represents the outlet flow angle of the first stage rotor, represents the axial distance between the trailing edge of the first stage rotor and the leading edge of the second stage stator.
[0040] The time for the first stage stator wake core to reach the leading edge of the second stage stator is , and the same assumption is made that the wake is linearly distributed along the way, and V3 is the axial velocity of the first stage stator wake core passing through the axial position section of the leading edge of the second stage stator blade. Thus, the time required for the third stage is calculated by formula (5):
[0041] wherein, is the axial distance between the first stage blade trailing edge and the second stage blade leading edge, V2 is the axial velocity of the first stage stator wake core when it is shed from the first stage blade trailing edge, and V3 is the axial velocity of the first stage stator wake core when it reaches the second stage stator blade leading edge axial position cross section.
[0042] The entire circumferential migration distance of the wake core of the upstream stator (the first stage stator) to the leading edge of the downstream stator (the second stage stator) can be obtained through the above calculation , and is calculated by formula (6):
[0043] To ensure that the wake transport of the upstream stator reaches the leading edge of the downstream stator, formula (7) must be satisfied, i.e., the mathematical model is expressed as: (7) wherein, is the relative circumferential distance between the leading edge of the downstream stator blade and the trailing edge of the upstream stator blade, R2 is the rotational radius of the second stage stator, is the number of blades of the second stage stator, and K is an integer multiple. Thus, the relative position of the downstream stator and the upstream stator can be calculated, and the optimal timing position is determined.
[0044] Step 4, verifying the prediction model According to the prediction model constructed in the third step, the optimal timing position under different rotational speeds can be obtained. Based on the optimal timing position predicted by the model, the phase difference between the first stage stator and the second stage stator is redesigned. Subsequently, under the same boundary conditions, CFX numerical simulation is performed under different rotational speed conditions, and the efficiency of the optimized phase difference scheme is compared with that of the original phaseless design, so as to verify whether the efficiency is improved.
[0045] As shown in Figure 3 , Figure 4 , Figure 3 is an entropy cloud diagram of the optimal timing position of the second stage stator blade surface, and the highlighted part represents the wake trajectory, which hits the leading edge of the downstream blade when the upstream wake is at the optimal timing position predicted by the prediction model. Figure 4 is a comparison diagram of the efficiency of the optimal timing position and the original timing position under different rotational speeds, which verifies that the timing position predicted by the prediction model has high efficiency, and the accuracy of the prediction model is verified.
[0046] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or replacements within the technical range disclosed in the present application can be easily thought of by those skilled in the art, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims
1. A two-stage turbine timing position optimization method based on a wake transport model, characterized in that, The application relates to a method for calculating the working parameters of a double-stage low-pressure turbine. According to the flight environment variables and flight requirements of an aero-engine, the working parameters of a double-stage low-pressure turbine are obtained; According to the working parameters, flow parameters of the double-stage low-pressure turbine at different rotating speeds are calculated, the flow parameters including axial velocity V1 of a first-stage stator blade wake core arriving at an axial position section of a first-stage rotor blade leading edge, maximum axial velocity V2 of the first-stage stator blade wake core when the first-stage stator blade wake core is separated from a first-stage rotor blade trailing edge, and axial velocity V3 of the first-stage stator blade wake core arriving at an axial position section of a second-stage stator blade leading edge. m , first-stage stator blade wake core from the first-stage rotor blade trailing edge, and the axial velocity V3 of the first-stage stator blade wake core arriving at the axial position section of the second-stage stator blade leading edge; Based on the working parameters and the flow parameters, the circumferential migration distance L1 of a first-stage static blade wake core when reaching a first-stage moving blade, the circumferential migration distance L2 of the first-stage static blade wake core from reaching the first-stage moving blade to falling off the suction surface of the first-stage moving blade, and the circumferential migration distance L3 of the first-stage static blade wake core from falling off the suction surface of the first-stage moving blade to reaching the leading edge of a second-stage static blade are respectively calculated. According to the circumferential migration distance L1, the circumferential migration distance L2 and the circumferential migration distance L3, a circumferential migration distance of the entire transport line is calculated when the first stage stator blade wake core reaches the leading edge of the second stage stator blade , a mathematical model based on the circumferential migration distance is constructed to predict the phase difference of the optimal timing position . According to the mathematical model, the optimal timing position of the double-stage low-pressure turbine at different rotating speeds is determined.
2. The two-stage turbo timing position optimization method of claim 1, wherein, The method further comprises: based on the optimal timing position of the double-stage low-pressure turbine at different rotation speeds, redesigning a phase difference of the optimal timing position between the first-stage static blade and the second-stage static blade ; and under the same boundary conditions, respectively calculating and comparing the efficiencies of the low-pressure turbine before and after the redesign to verify the mathematical model.
3. The dual stage turbo timing position optimization method of claim 1, wherein, The working parameters include the Reynolds number, the inlet total temperature and total pressure, the Mach number, the moving blade rotating speed, the blade axial chord length, the pitch, the axial distance between the first-stage static blade trailing edge and the first-stage moving blade leading edge, the axial distance between the first-stage moving blade trailing edge and the second-stage static blade leading edge, the first-stage static blade outlet flow angle, the first-stage moving blade outlet flow angle, the rotating radius of the first-stage moving blade, the rotating radius of the second-stage static blade and the number of the second-stage static blade.
4. The dual stage turbo timing position optimization method of claim 1, wherein, The circumferential migration distance L1 of the first-stage static blade wake core when reaching the first-stage moving blade is calculated by the following formula: wherein, denotes the axial distance between the first stage vane trailing edge and the first stage blade leading edge, denotes the first stage vane exit flow angle.
5. The dual stage turbo timing position optimization method of claim 1, wherein, The circumferential migration distance L2 of the first-stage static blade wake core from reaching the first-stage moving blade to falling off the suction surface of the first-stage moving blade is calculated by the following formula: wherein, R1 represents the rotational radius of the first stage rotor blade, ω1 represents the rotational speed of the rotor blade, T1 represents the time required for the first stage stator blade wake core to pass through the circumferential migration distance L2.
6. The dual stage turbo timing position optimization method of claim 5, wherein, The time required for the first stage vane wake core to traverse the circumferential distance LI is calculated by the equation : wherein, Vt1is the axial velocity of the first stage stator wake core at the axial location of the first stage rotor leading edge, Vt1is the maximum axial velocity of the first stage stator wake core at the axial location of the middle of the first stage rotor blade surface, Vt1is the axial distance from the first stage stator trailing edge to the axial location of the maximum axial velocity of the first stage stator wake core, Vt1is the axial distance from the first stage stator trailing edge to the axial location of the maximum axial velocity of the first stage stator wake core, Vt1is the axial velocity of the first stage stator wake core at the axial location of the first stage rotor leading edge, Vt1is the axial chord length of the first stage stator.
7. The dual stage turbo timing position optimization method of claim 1, wherein, The circumferential migration distance L3 of the first-stage static blade wake core from falling off the suction surface of the first-stage moving blade to reaching the leading edge of the second-stage static blade is calculated by the following formula: wherein, represents a rotational radius of the first stage moving blade, represents a moving blade rotational speed, represents a time required for the first stage stator wake core to pass through the circumferential migration distance L3, represents a first stage moving blade outlet flow angle, represents an axial distance between the first stage moving blade trailing edge and the second stage stator leading edge.
8. The dual stage turbo timing position optimization method of claim 7, wherein, The time required for the first stage vane wake core to traverse the circumferential distance L3 is calculated by the equation : wherein, wherein, δ represents the axial distance between the trailing edge of the first stage rotor blade and the leading edge of the second stage stator blade, V2 represents the axial velocity of the first stage stator wake core when it is shed from the trailing edge of the first stage rotor blade, and V3 represents the axial velocity of the first stage stator wake core when it reaches the axial location of the leading edge of the second stage stator blade.
9. The dual stage turbo timing position optimization method of claim 1, wherein, The circumferential migration distance L1, the circumferential migration distance L2 and the circumferential migration distance L3 are sequentially added to obtain the circumferential migration distance of the first stage stator vane wake core to the second stage stator vane leading edge .
10. The dual stage turbo timing position optimization method of claim 1, wherein, based on the circumferential migration distance the mathematical model representing the optimal timing position phase difference is represented by the mathematical model wherein R2 represents a rotational radius of the second stage vane, wherein N represents the number of vanes of the second stage vane, and K represents an integer multiple.