Engine performance design method based on thermodynamic parameters

Abstract

The present invention discloses an engine performance design method based on thermal parameters, and relates to the field of aviation technology. Based on the dynamic characteristics of an engine system, the present invention adopts a random analysis method to construct a random analysis model for robust design of engine performance facing the influence of uncertainty, and flexibly considers and analyzes the random response distribution characteristics of thermal parameters of engine components and performance parameters of the whole machine under various uncertainties. The present invention solves the problems in traditional performance design methods, such as insufficient or difficult consideration of uncertainty analysis, cumbersome calculations, high design costs, weak adaptability to operating conditions, and insufficient mining of candidate design space.

Description

Technical Field

[0001] The invention relates to the technical field of aviation engines, and in particular to an engine performance design method based on thermal parameters. Background Art

[0002] The performance design of aircraft engines is a key technology to determine the key thermal parameters and performance parameters of engines under new configurations and new mission requirements. The complex mechanical structure and wide adaptability bring more uncertainties to the engine performance design, which will reduce the performance advantages of the engine system to a certain extent. At present, robust design has been applied to the performance design stage of the engine, which aims to maximize the possibility of selecting high-quality candidate designs that meet all performance requirements, while minimizing the risks brought by uncertainty, making the design results less sensitive to the impact of uncertainty.

[0003] At present, the performance design methods of aircraft engines are mainly divided into two categories. One is a mechanism model established based on the mechanism equation of the engine working process. By setting the uncertainty magnitude of different component parameters and system parameters, simulation calculation and optimization methods are used to obtain the performance response characteristics of components and systems, thereby determining the design parameters of the engine.

[0004] The main problems of this method are: (1) the mechanism modeling itself inevitably has modeling uncertainty, and its corresponding performance design results are inevitably affected by uncertainty; (2) the internal uncertainty of the engine system (such as component performance degradation) and external uncertainty (such as intake disturbance, actuator actuation, etc.) are difficult to fully consider in the process of mechanism modeling; (3) the candidate designs based on optimization are limited, and it is difficult to carry out a large number of simulation experiments, so the performance design results are usually suboptimal. The other type is based on the influence of uncertainty on thermal parameters and performance parameters of simulation methods. Commonly used methods include probability method, interval analysis method and proxy model method, that is, analyzing the distribution interval of thermal parameters under a certain uncertainty interval to achieve engine performance design. The main problems of this type of method are: (1) cumbersome calculation process, high calculation cost, and lengthy calculation time limit the number of candidate designs that can be explored; (2) it can only adapt to specific working conditions, and needs to be remodeled for variable working conditions, which makes it difficult to fully explore the candidate design space and increases expensive redesign work.

[0005] Both of the above-mentioned methods have great limitations in the application of aero-engine performance design, and it is difficult to comprehensively achieve the optimal treatment of the impact of multi-source uncertainties on performance in aero-engines in terms of design efficiency and design effect. Summary of the invention

[0006] The object of the present invention is to provide an engine performance design method based on thermodynamic parameters to solve the problems in the background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] The engine performance design method based on thermal parameters includes the following steps:

[0009] Step 1: Based on the rotational inertia equation and thermodynamic equation of the aircraft engine composed of key components such as the fan, compressor, combustion chamber, high-pressure turbine, low-pressure turbine, and tail nozzle, the time-varying nonlinear dynamic equation of the engine system is constructed as follows:

[0010]

[0011] Among them, x(t) represents the state vector of the engine thermal parameters; h(t, x) represents the nonlinear characteristics of the engine system; g(t, x) represents the input function related to the engine state; e(t) represents the system input vector. Due to manufacturing and assembly errors, long-term operation wear of the actuator, and degradation of component performance, the input of the engine system usually has a certain degree of randomness, which in turn leads to randomness in the system state parameters, which directly affects the working performance of the engine system. In a certain steady state, the state parameter x(t) and the system input e(t) can be expressed as:

[0012] x=x0+Δxe=e0+Δe

[0013] Among them, Δe is the random input disturbance, Δx is the random response of the state parameter, and (x0, e0) is the stable operating point under a certain condition;

[0014] Step 2: Assuming that h(t, x) and g(t, x) are differentiable at the stable working point, expand the h(t, x) and g(t, x) polynomials in the neighborhood U(x0, e0) of (x0, e0) and substitute them into the nonlinear dynamic equations, then:

[0015]

[0016] make Then we have:

[0017]

[0018] Right now

[0019] The above equation describes the random response Δx of the state parameters under random excitation Δe, and the coefficient matrices A, B, and F describe the nonlinear characteristics of the engine system;

[0020] Step 3: Use the equivalent linearization method to transform the nonlinear stochastic differential equation into an equivalent linear stochastic differential equation. For the above nonlinear state space differential equation, the linear stochastic differential equation of the jth state variable is:

[0021]

[0022] Among them, A j and V j is the j-th row element in A and B. Based on the minimum mean square error coefficient criterion, the statistical characteristics of the equivalent linearization process are:

[0023]

[0024] Let α = [α jk ], which can be obtained by iterative calculation of the above statistical characteristics;

[0025] Step 4: Combine the covariance definition of random disturbance and random response;

[0026] Step 5: Define the impact indicators FAT and FDT of random disturbance on the random response of thermal parameters;

[0027] Step 6: Based on the random response variance of the thermal parameters obtained from the above analysis, the 3σ criterion is used to consider the impact of the random response variance on the value range of the thermal parameters, and a robust optimization method for performance parameters is established;

[0028] Step 7: Based on the full-state working characteristics of the aircraft engine, the steady-state working points under different working states are identified, and the robust optimization of the engine design parameters of steps 1 to 6 is carried out for different steady-state working points to obtain the engine performance design parameter sets under different steady-state working states;

[0029] Step 8: Based on the full-state operating characteristics of the engine and the performance requirements under different operating states, a design parameter group that can meet the full-state performance requirements is selected from the engine performance design parameter set as the full-state performance design parameters of the aircraft engine.

[0030] 2. The engine performance design method based on thermodynamic parameters according to claim 1 is characterized in that in the step 3, a linear differential equation of the statistical characteristics of the random response of the state parameters can be further obtained:

[0031]

[0032] Let z(t) = Δx, w(t) = Δe, B = g(t, x0). Stationary random sample vector combined with random excitation:

[0033] w(t)=RS(t),

[0034] Among them, S(t) is a stationary random sample vector, and R is the observation matrix of the random sample vector.

[0035] 3. The engine performance design method based on thermodynamic parameters according to claim 2 is characterized in that the above stochastic differential equation can be converted into:

[0036]

[0037] Combining the covariance definitions of random disturbances and random responses, we have:

[0038]

[0039] The above covariance differential equation describes the variance and covariance of the random response of the thermodynamic parameters.

[0040] It can be used to analyze the random response distribution characteristics of the system's thermal parameters and performance parameters under random disturbances.

[0041] 4. The engine performance design method based on thermodynamic parameters according to claim 1 is characterized in that, in step 4, the covariance definition of random disturbance and random response is combined, and then:

[0042]

[0043] The above covariance differential equation describes the variance and covariance of the random response of the thermodynamic parameters.

[0044] It can be used to analyze the distribution characteristics of the random response of the system's thermal parameters and performance parameters under random disturbances.

[0045] 5. The engine performance design method based on thermal parameters according to claim 1, characterized in that, in step 5, the influence indexes FAT and FDT of random disturbance on the random response of thermal parameters are defined as follows:

[0046]

[0047] in,

[0048] represents the peak value of variance, FAT is the first arrival time of the peak value of thermal parameter variance, and FDT is the first duration of random disturbance influence;

[0049] In the optional solution: In step 6, a robust optimization method for performance parameters is established as follows:

[0050] Optimization target: π total ,B r ,T4,T7

[0051] Objective function:

[0052] lb≤[π total ,B r ,T4,T7]≤ub

[0053] Constraint: Para0-3σ≤Paras≤Para0+3σ

[0054] Paras=[P 13 , P3, P 45 , T 45 , T5, T7].

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) Ability to flexibly consider system internal and external uncertainties in engine performance design;

[0057] (2) Be able to fully analyze the impact of uncertainty on the random response distribution characteristics of thermal parameters and performance parameters;

[0058] (3) It can quickly obtain the random response distribution characteristics of the component cross-section thermal parameters and the overall performance parameters. Based on the maximum probability density of the distribution characteristics, the design parameters of the engine can be quickly determined, significantly reducing the calculation cost;

[0059] (4) The performance design model based on stochastic dynamics under different working conditions has strong analogy and does not require re-modeling. It can quickly realize the performance design of all working conditions, fully explore the candidate design space and the number of candidate designs, and reduce expensive redesign work. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The overall technical framework diagram of the invention.

[0061] Figure 2 It is an indicator diagram of the variance of the random response of the thermal parameters in the invention changing with time.

[0062] Figure 3 This is an analysis diagram of the impact of the uncertainty in the invention on the random response of the thermal parameters of the engine system.

[0063] Figure 4 Schematic diagram of the robust optimization fitness function value in the invention.

[0064] Figure 5 It is a distribution characteristic diagram of the performance design parameters of the turbofan engine in the invention. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the invention more clearly understood, the invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0066] In one embodiment, Figure 1-Figure 5 As shown, the engine performance design method based on thermal parameters includes the following steps:

[0067] Step 1: Based on the dual-rotor rotation inertia equation and component thermodynamic equation of a typical turbofan engine configuration consisting of key components such as fan, compressor, combustion chamber, high-pressure turbine, low-pressure turbine, tail nozzle, etc., construct the time-varying nonlinear dynamic equation of the turbofan engine system:

[0068]

[0069] Among them, x(t) represents the engine dynamic state vector, such as the dual rotor speed, component cross-sectional temperature and pressure, fuel quantity and tail nozzle area, etc.; h(t, x) represents the nonlinear characteristics of the engine system; g(t, x) represents the input function related to the engine working state; e(t) represents the system input vector, such as fuel quantity, tail nozzle area, fan guide vane angle and compressor inlet adjustable guide vane angle, etc. Due to manufacturing and assembly errors, long-term operation wear of the actuator, and component performance degradation, the input of the engine system usually has a certain degree of randomness, which in turn leads to randomness in the system state parameters, which directly affects the working performance of the engine system. In a certain steady state, the state parameter x(t) and the system input e(t) can be expressed as:

[0070] x=x0+Δx e=e0+Δe where Δe is the random input disturbance, Δx is the random response of the state parameter, (x0, e0) is the stable operating point under a certain working condition, and represents the working state of the engine system under ideal conditions.

[0071] Step 2: Assuming that h(t, x) and g(t, x) are differentiable in the neighborhood U(x0, e0) of the stable working point (x0, e0), expand the h(t, x) and g(t, x) polynomials and substitute them into the nonlinear dynamic equations, we have:

[0072]

[0073] Considering the strong nonlinear characteristics of the turbofan engine system, let

[0074] To represent the nonlinearity of the system, we have:

[0075]

[0076] Right now

[0077] The above equations describe the random response Δx of the system state parameters under the action of random excitation Δe. The coefficient matrices A, B and F describe the nonlinear characteristics of the engine system. The coefficient matrices can be obtained through the dynamic model of the turbofan engine system and the small perturbation method.

[0078] Step 3: Use the equivalent linearization method to transform the nonlinear stochastic differential equation into an equivalent linear stochastic differential equation. For the above nonlinear state space differential equation, the linear stochastic differential equation of the jth state parameter can be expressed as:

[0079]

[0080] Among them, A j and B j is the j-th row element in A and B. Based on the minimum mean square error coefficient criterion, the statistical characteristics of the equivalent linearization process are:

[0081]

[0082] Let α = [α jk ], which can be obtained by iterative calculation under the constraints of the above statistical characteristics. Further, the linear differential equation of the statistical characteristics of the random response of the state parameters can be obtained:

[0083]

[0084] Let z(t) = Δx, w(t) = Δe, B = g(t, x0). Stationary random sample vector combined with random excitation:

[0085] w(t)=RS(t),

[0086] Among them, S(t) is a stationary random sample vector, and R is the observation matrix of the random sample vector, which can represent the magnitude of random uncertainty. Further, the above stochastic differential equation can be transformed into:

[0087]

[0088] Step 4: Combining the covariance definitions of random disturbance and random response, we have:

[0089]

[0090] The above covariance differential equation describes the variance of the random response of the thermal parameters, where the main diagonal elements of V(t) represent the variance of the random response of the thermal parameters. Based on the variance, the random response characteristics of the thermal parameters and performance parameters of the system under random disturbances can be analyzed, such as Figure 2 .

[0091] Step 5: Define the impact indicators FAT and FDT of random disturbance on the random response of thermal parameters as follows:

[0092]

[0093] Among them, Var-Peak represents the peak value of variance, FAT is the first arrival time of the peak value of thermal parameter variance, and FDT is the first duration of random disturbance influence. Figure 2 The results can be used to analyze the FAT and FDT of each thermal parameter, such as Figure 3 .

[0094] Step 6: Based on the random response variance of the thermal parameters obtained from the above analysis, the 3σ criterion is used to consider the impact of the random response variance on the value range of the thermal parameters, and a robust optimization method for performance parameters is established as follows:

[0095] Optimization target: π total ,B r ,T4,T7

[0096] Objective function:

[0097] lb≤[π total ,B r ,T4,T7]≤ub

[0098] Constraint: Para0-3σ≤Paras≤Para0+3σ

[0099] Paras=[P 13 , P3, P 45 , T 45 , P5, P7]

[0100] Among them, the design parameter is the total pressure ratio π total , bypass ratio B r , the main combustion chamber outlet temperature T4, the afterburner outlet temperature T7. ω1 and ω2 represent the weights of thrust Thur and fuel consumption rate SFC. The following table ori and opt represent the original and optimized performance parameters. lb and ub represent the boundary constraints of the design parameters, and Paras represents the thermodynamic parameter vector at the steady-state operating point. The engine design parameters at the steady-state operating point are obtained through optimization. The results of the robust optimization fitness function are as follows: Figure 4 .

[0101] Step 7: Based on the full-state working characteristics of the aircraft engine, the clustering method is used to identify the steady-state working points under different working conditions. The robust optimization of the engine design parameters from step 1 to step 6 is carried out for different steady-state working points to obtain the engine performance design parameter set under different steady-state working conditions.

[0102] Step 8: Based on the full-state operating characteristics of the engine and the performance requirements under different operating states, select a design parameter group that can meet the full-state performance requirements from the engine performance design parameter set as the full-state performance of the aircraft engine

[0103] The above-mentioned embodiment discloses an engine performance design method based on thermal parameters. Aiming at the problems existing in the existing robust design method for aircraft engine performance, the present invention, based on the dynamic characteristics of the engine system, adopts a random analysis method to construct a random analysis model for robust design of engine performance facing the influence of uncertainty, flexibly considers and analyzes the random response distribution characteristics of the thermal parameters of engine components and the performance parameters of the whole machine under various uncertainties, and quickly determines the performance design parameters under different working conditions based on the probability density distribution of the random response, fully explores the candidate design space under all conditions, and realizes the robust design of aircraft engine performance under all conditions. The present invention solves the problems of insufficient or difficult consideration of uncertainty analysis, cumbersome calculation, high design cost, weak adaptability to operating conditions, and insufficient exploration of candidate design space in traditional performance design methods.

[0104] The above is only a specific implementation of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present disclosure, which should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.

Claims

1. An engine performance design method based on thermodynamic parameters, characterized in that: The following steps are involved: Step 1: Based on the rotational inertia equation and thermodynamic equation of the aircraft engine composed of key components such as the fan, compressor, combustion chamber, high-pressure turbine, low-pressure turbine, and tail nozzle, the time-varying nonlinear dynamic equation of the engine system is constructed as follows: Among them, x(t) represents the state vector of the engine thermal parameters; h(t, x) represents the nonlinear characteristics of the engine system; g(t, x) represents the input function related to the engine state; e(t) represents the system input vector. Due to manufacturing and assembly errors, long-term operation wear of the actuator, and degradation of component performance, the input of the engine system usually has a certain degree of randomness, which in turn leads to randomness in the system state parameters, which directly affects the working performance of the engine system. In a certain steady state, the state parameter x(t) and the system input e(t) can be expressed as: x=x0+Δx e=e0+Δe Among them, Δe is the random input disturbance, Δx is the random response of the state parameter, and (x0, e0) is the stable operating point under a certain condition; Step 2: Assuming that h(t, x) and g(t, x) are differentiable at the stable working point, expand the h(t, x) and g(t, x) polynomials in the neighborhood U(x0, e0) of (x0, e0) and substitute them into the nonlinear dynamic equations, then: make Then we have: Right now The above equations describe the random response Δx of the state parameters under random excitation Δe, and the coefficient matrices A, B, and F describe the nonlinear characteristics of the engine system; Step 3: Use the equivalent linearization method to transform the nonlinear stochastic differential equation into an equivalent linear stochastic differential equation. For the above nonlinear state space differential equation, the linear stochastic differential equation of the jth state variable is: Among them, A j and B j is the j-th row element in A and B. Based on the minimum mean square error coefficient criterion, the statistical characteristics of the equivalent linearization process are: Let α = [α jk ], which can be obtained by iterative calculation of the above statistical characteristics; Step 4: Combine the covariance definition of random disturbance and random response; Step 5: Define the impact indicators FAT and FDT of random disturbance on the random response of thermal parameters; Step 6: Based on the random response variance of the thermal parameters obtained from the above analysis, the 3σ criterion is used to consider the impact of the random response variance on the value range of the thermal parameters, and a robust optimization method for performance parameters is established; Step 7: Based on the full-state working characteristics of the aircraft engine, the steady-state working points under different working states are identified, and the robust optimization of the engine design parameters of steps 1 to 6 is carried out for different steady-state working points to obtain the engine performance design parameter sets under different steady-state working states; Step 8: Based on the full-state operating characteristics of the engine and the performance requirements under different operating states, a design parameter group that can meet the full-state performance requirements is selected from the engine performance design parameter set as the full-state performance design parameters of the aircraft engine.

2. The engine performance design method based on thermodynamic parameters according to claim 1, characterized in that: In step 3, the linear differential equation of the statistical characteristics of the random response of the state parameters can be further obtained: Let z(t) = Δx, w(t) = Δe, B = g(t, x0); Stationary random sample vector combined with random excitation: w(t)=RS(t), Among them, S(t) is a stationary random sample vector, and R is the observation matrix of the random sample vector.

3. The engine performance design method based on thermodynamic parameters according to claim 2, characterized in that: The above stochastic differential equation can be transformed into: Combining the covariance definitions of random disturbances and random responses, we have: The above covariance differential equation describes the variance and covariance of the random response of the thermodynamic parameters. It can be used to analyze the random response distribution characteristics of the system's thermal parameters and performance parameters under random disturbances.

4. The engine performance design method based on thermodynamic parameters according to claim 1, characterized in that: Step 4: Combining the covariance definitions of random disturbance and random response, we have: The above covariance differential equation describes the variance and covariance of the random response of the thermodynamic parameters. It can be used to analyze the distribution characteristics of the random response of the system's thermal parameters and performance parameters under random disturbances.

5. The engine performance design method based on thermodynamic parameters according to claim 1, characterized in that: Step 5: Define the impact indexes FAT and FDT of random disturbance on the random response of thermal parameters as follows: in, represents the peak value of variance, FAT is the first arrival time of the peak value of thermal parameter variance, and FDT is the first duration of random disturbance influence; In the optional solution: In step 6, a robust optimization method for performance parameters is established as follows: Optimization target: π total , B r , T4, T7 Objective function: lb≤[π total ,B r ,T4,T7]≤ub Constraint: Para0-3σ≤Paras≤Para0+3σ Paras=[P 13 ,P3,P 45 ,T 45 ,P5,P7]。

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