WO2019237284A1 - 一种微型燃气涡轮发动机起动过程建模方法 - Google Patents

一种微型燃气涡轮发动机起动过程建模方法 Download PDF

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WO2019237284A1
WO2019237284A1 PCT/CN2018/091091 CN2018091091W WO2019237284A1 WO 2019237284 A1 WO2019237284 A1 WO 2019237284A1 CN 2018091091 W CN2018091091 W CN 2018091091W WO 2019237284 A1 WO2019237284 A1 WO 2019237284A1
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gas turbine
speed
turbine engine
micro gas
engine
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French (fr)
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杜宪
马艳华
孙希明
彭凯
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Dalian University of Technology
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Dalian University of Technology
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Priority to US16/462,512 priority Critical patent/US20190384888A1/en
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02C—GAS-TURBINE PLANTS; AIR INTAKES FOR JET-PROPULSION PLANTS; CONTROLLING FUEL SUPPLY IN AIR-BREATHING JET-PROPULSION PLANTS
    • F02C7/00—Features, components parts, details or accessories, not provided for in, or of interest apart form groups F02C1/00 - F02C6/00; Air intakes for jet-propulsion plants
    • F02C7/26—Starting; Ignition
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2200/00—Mathematical features
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2250/00—Geometry
    • F05D2250/80—Size or power range of the machines
    • F05D2250/82—Micromachines
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2260/00—Function
    • F05D2260/81—Modelling or simulation

Definitions

  • the invention belongs to the technical field of engine modeling, and in particular relates to a method for modeling a starting process of a micro gas turbine engine.
  • a miniature gas turbine engine is a complex thermodynamic system consisting of a compressor, a combustion chamber, and a turbine.
  • a mathematical model of the micro gas turbine engine below the idling speed and calculate the starting performance can provide a reference for the control of the micro gas turbine engine during the starting process. Therefore, modeling the starting process of a micro gas turbine engine is very valuable.
  • the present invention is a method for modeling a micro gas turbine engine during the starting process in order to solve the problems of large amount of modeling data, low efficiency, and low modeling accuracy of the gas turbine engine during the prior art.
  • a method for modeling the starting process of a micro gas turbine engine includes the following steps:
  • the first step is to model the speed of the micro gas turbine engine
  • the second step is to model the relationship between the performance parameters and speed of the micro gas turbine engine
  • the third step is error analysis.
  • the first step is to model the speed of the micro gas turbine engine
  • Step 1 Analyze the starting process mechanism of the micro gas turbine engine, and use the engine rotor effect modeling method to build a gas turbine engine residual torque model by using the current value of the micro gas turbine engine starter motor and the micro gas turbine engine speed. On this basis, the steady-state fuel amount is calculated, and the relationship between the fuel amount of the micro gas turbine engine and the speed of the micro gas turbine engine is obtained by linear interpolation. The fuel amount and speed of the micro gas turbine engine are obtained by using a polynomial fitting method. Expression between
  • Step 2 According to the test data of the fuel quantity and engine speed of the micro gas turbine engine during the startup process, and compare it with the relationship between the steady state fuel quantity and the micro gas turbine engine speed established in step 1, get the fuel quantity during the startup process and Difference between steady state fuel quantities;
  • Step 3 The fuel quantity difference obtained in step 2 can make the micro gas turbine engine produce an acceleration effect. Since the relationship between the fuel quantity difference and the micro gas turbine engine speed is highly non-linear, a piecewise linearization method is used to Fit the relationship between the fuel amount difference and the speed of the micro gas turbine engine;
  • Step 4 The fuel quantity difference and the starter current work together to make the micro gas turbine engine accelerate, and the acceleration of the micro gas turbine engine is integrated to obtain the speed of the micro gas turbine engine;
  • the second step is to model the relationship between the performance parameters and speed of the micro gas turbine engine
  • Step 5 Because the relationship between the speed of the micro gas turbine engine and the gas performance parameters is very close, the polynomial fitting method is used to obtain the performance parameters of the micro gas turbine engine (compressor outlet pressure, compressor outlet temperature, combustion chamber outlet temperature, The relationship between the exit pressure of the combustion chamber, the exit temperature of the turbine and the exit pressure of the turbine, etc.) and the speed of the micro gas turbine engine;
  • Step 6 Since the calculation of the performance parameters of the gas turbine engine by the generated polynomial will slow down the model and may also cause the numerical calculation to be unstable, discretizing the polynomial and generating a one-dimensional interpolation table will help improve The real-time nature of the starting model.
  • the third step is error analysis.
  • Each performance parameter here refers to the compressor outlet pressure, compressor outlet temperature, combustion chamber outlet pressure, turbine outlet pressure, turbine Outlet temperature, micro gas turbine engine speed.
  • the existing modeling methods of micro gas turbine engines are mostly pure mechanism or machine learning methods. It is difficult to accurately describe the starting process of micro gas turbine engines, and machine learning requires a large amount of experimental data. In engineering practice, the pure mechanism currently used is complicated and inefficient, and the modeling accuracy is not high.
  • the invention provides a method for modeling the starting process of a micro gas turbine engine based on a combination of a mechanism and an identification method, which makes up for the shortcomings of the prior art.
  • the invention has simple operation, high accuracy, and can realize the modeling of the entire micro gas turbine engine. This method has certain expansibility and can be extended to other fields.
  • Figure 1 is a flowchart of modeling a micro gas turbine engine.
  • FIG. 2 is a graph showing the relationship between the residual torque and the fuel amount.
  • FIG. 3 is a graph showing the relationship between the fuel amount difference and the remaining torque.
  • Figure 4 is a comparison chart of the modeling error of the starting process, where: (a) the compressor outlet temperature error; (b) the compressor outlet pressure error; (c) the combustion chamber outlet pressure error; (d) the turbine outlet pressure error; (e) ) Turbine outlet temperature error; (f) Gas turbine speed error.
  • a method for modeling the starting process of a micro gas turbine engine includes the following steps:
  • Step 1 The starting process of the micro gas turbine engine is divided into 3 stages.
  • the engine speed is changed from zero to the speed at which the turbine starts to generate power, and the engine is completely accelerated by the starter.
  • the turbine starts to generate power. Turn off the speed from the starter;
  • the third stage turn off the speed from the starter to the idle speed;
  • the engine speed is from zero to the speed at which the turbine starts to generate power (that is, from zero speed to ignition speed), and the engine is completely accelerated by the starter, which satisfies the engine rotor motion equation, that is, formula (1).
  • M st K st ⁇ I st , where I st represents the current value of the starter, K st is the torque constant of the starter, and its value is different for different types of starters.
  • the starter referred to here is an electric starter.
  • ⁇ is the angular velocity of the micro gas turbine engine
  • J is the moment of inertia calculated on the shaft of the micro gas turbine engine, that is, the equivalent moment of inertia. According to the structure of different micro gas turbine engines, mechanical energy conservation is used for the calculation. Refer to the specific reduction formula (2)
  • J 1 is the moment of inertia of load 1 driven by the micro gas turbine engine shaft
  • ⁇ 1 is the angular velocity of load 1 driven by the micro gas turbine engine shaft
  • J 2 is the moment of inertia of load 2 driven by the micro gas turbine engine shaft
  • ⁇ 2 is the angular velocity of load 2 driven by the micro gas turbine engine shaft
  • J n is the moment of inertia of the load n driven by the micro gas turbine engine shaft
  • ⁇ n is the angular velocity of the load n driven by the micro gas turbine engine shaft.
  • the engine speed is changed from the ignition speed to the starter disengagement speed.
  • the engine is accelerated by the starter and the turbine, and the engine rotor motion equation is satisfied, that is, formula (3) is satisfied.
  • M gas M T -M C -M f
  • M T represents the torque generated by the turbine
  • M C represents the torque consumed by the compressor.
  • M f represents the torque consumption caused by friction, and is generally proportional to the square of the speed
  • M st is the torque provided by the electric starter, which is the same as in formula (1).
  • J has the same calculation process as formula (1), and ⁇ formula (1) is the same.
  • the engine accelerates the idling speed by disengaging the speed at the starter, which satisfies formula (4).
  • Step 2 Modeling of the first stage micro gas turbine engine speed
  • the torque value of the model is integrated by using the first-order Runge-Kutta method (Euler method) to obtain the model gas turbine engine speed to ensure the speed of the micro gas turbine engine and the gas turbine in the test data. Speed error is within 5%;
  • Step 3 Modeling of the second stage micro gas turbine engine speed
  • Step 3.2 On the basis of step 3.1, perform a polynomial fitting to obtain the relational expression between the turbine speed and the steady-state fuel quantity.
  • the relational expression is a three-term polynomial, and the specific polynomial coefficient varies with the type of fuel. There is a difference.
  • the fuel used here is natural gas, and its specific expression is shown in formula (5):
  • Step 3.3 The functional relationship between the residual torque of the micro gas turbine engine and the difference in fuel quantity is very complex, showing a high degree of non-linearity, and simplified it.
  • the piecewise linear function is used to characterize the complex relationship, assuming the remaining revolution of the gas turbine
  • the moment and the fuel quantity difference are piecewise linear functions, that is, the formula (6) is used for characterization.
  • k (n) and b (n) are coefficients, and the values of different gas turbine speeds are different, that is, the values of k (n) and b (n) are functions of the gas turbine speed n, (W f —W fss ) is the difference between the dynamic fuel quantity and the steady-state fuel quantity obtained by the polynomial, and the value is different for different gas turbine speeds;
  • Step 3.4 Sum the residual torque of the micro gas turbine engine and the torque of the starter on the gas turbine shaft, and then integrate it using the first-order Runge-Kutta method (Eulerian method) to obtain the model calculation
  • the speed of the micro gas turbine engine ensures that the error between the speed of the micro gas turbine engine and the gas turbine speed in the test data is within 5%;
  • Step 3.5 In order to ensure that "the error between the speed of the micro gas turbine engine and the speed of the gas turbine in the test data is within 5%" mentioned in step 3.4, the real time adjustment of the formula (6) according to the speed of the micro gas turbine engine is required. k (n), b (n), make the speed of the built micro gas turbine engine starting model approach the test speed as much as possible.
  • Step 4 Modeling of the third stage micro gas turbine engine speed
  • the equivalent moment of inertia of the engine is obtained through calculation (see formula (2) for details); using the equation of rotor motion and the amount of fuel, the torque value of the starter added to the shaft of the micro gas turbine engine is calculated according to formula (6).
  • the first-order Runge-Kutta method (Eulerian method) is used to integrate it to obtain the model's micro gas turbine engine speed, ensuring that the micro gas turbine engine speed and the gas turbine speed error in the test data are within 5%. ; It is necessary to adjust k (n) and b (n) in formula (6) in real time according to the speed of the micro gas turbine engine, so that the speed of the built micro gas turbine engine starting model can approach the test speed as much as possible.
  • Step 5 The relationship between the performance parameters of the micro gas turbine engine and the speed of the gas turbine engine is very close.
  • the performance parameters of the gas turbine engine mentioned here mainly include: compressor outlet temperature, compressor outlet pressure, and combustion chamber outlet pressure , Turbine outlet temperature, turbine outlet pressure, using MATLAB's own data fitting tool to fit the gas turbine engine performance parameters and gas turbine engine speed function expressions, namely:
  • T 2 is the temperature of the compressor outlet
  • K T is the temperature coefficient of the compressor outlet.
  • N g represents the speed of the micro gas turbine engine.
  • P 2 is the compressor outlet pressure
  • K P is the pressure coefficient of the compressor outlet.
  • N g represents the speed of the micro gas turbine engine.
  • P 3C is the outlet pressure of the combustion chamber
  • K c is the pressure coefficient of the combustion chamber.
  • N g represents the rotational speed of the micro gas turbine engine
  • T 4 is the turbine outlet temperature
  • K t is the temperature coefficient of the turbine outlet.
  • N g represents the speed of the micro gas turbine engine
  • N gt represents the micro gas turbine engine's speed.
  • Rated speed, N idle represents the idling speed of the micro gas turbine engine;
  • Step 6 Linearize and discretize the polynomial function relationship between the obtained performance parameters and speed of the gas turbine engine, that is, linearly discretize the formulas (7), (8), (9), (10), and (11)
  • the step size of the micro gas turbine engine speed is taken as 0.2% ⁇ N gt , and the discretized data is put into the corresponding one-dimensional linear interpolation table.

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Abstract

一种微型燃气涡轮发动机起动过程建模方法，步骤如下：微型燃气涡轮发动机转速的建模；微型燃气涡轮发动机的性能参数与转速的关系建模；误差分析。该微型燃气涡轮发动机起动过程建模方法基于机理和辨识方法相结合的微型燃气涡轮发动机起动过程建模方法，弥补了现有技术的不足，且操作简单，准确率高，并可实现整个微型燃气涡轮发动机的建模。该方法具有一定的拓展性，可推广到其它领域。

Description

一种微型燃气涡轮发动机起动过程建模方法 技术领域
本发明属于发动机建模技术领域，具体涉及一种微型燃气涡轮发动机起动过程建模方法。
背景技术
微型燃气涡轮发动机是一个复杂的热力学系统，由压气机、燃烧室和涡轮组成。在对微型燃气涡轮发动机起动的研究过程中，如何建立微型燃气涡轮发动机慢车转速以下的数学模型并进行起动性能的数值计算，能为微型燃气涡轮发动机起动过程的控制提供参考。因此，对微型燃气涡轮发动机的起动过程进行建模是非常有价值的。
在微型燃气涡轮发动机建模技术方面，国内外公开发表的文献较少，亦未有相关专利涉及此方面的内容。在已有文献中，多是利用支持向量机等方法对发动机起动过程进行建模，但是支持向量机需要大量的发动机起动过程数据，通过对输入输出数据的训练得到发动机的起动模型，然而对于新研发的微型燃气涡轮发动机而言，一般通过燃气涡轮发动机的设计参数得到起动过程的燃油计划，为了保证燃气涡轮发动机能成功起动，通过人工手动的方法完成微型燃气涡轮发动机的起动过程。通过人工起动得到的实验数据建立燃气涡轮发动机的起动模型，然后再通过起动模型进一步优化发动机起动过程的燃油计划，存在一定的局限性。
对于微型燃气涡轮发动机而言，当前的起动过程建模技术已经渐渐满足不了工程的实际需要。因此，探索出一种有效且适用于工程实践的高效建模方法成为一个亟需解决的问题。微型燃气涡轮发动机起动建模技术也因此具备了广阔的研究和应用前景。
发明内容
本发明是为了解决现有技术存在的燃气涡轮发动机起动过程建模数据要求量大，效率低下，建模精度不高的问题，而提出的一种微型燃气涡轮发动机起动过程建模方法。
一种微型燃气涡轮发动机起动过程建模方法，包括以下步骤：
第一步，微型燃气涡轮发动机转速的建模；
第二步，微型燃气涡轮发动机的性能参数与转速的关系建模；
第三步，误差分析。
现具体阐述如下：
第一步，微型燃气涡轮发动机转速的建模；
步骤1：分析微型燃气涡轮发动机起动过程机理，通过发动机转子效应建模方法，具体是通过微型燃气涡轮发动机起动电机的电流值和微型燃气涡轮发动机的转速值，建立燃气涡轮发动机剩余转矩模型，在此基础上计算得到稳态燃料量，从而通过线性插值的方法得到微型燃气涡轮发动机燃料量和微型燃气涡轮发动机转速之间的关系，运用多项式拟合的方法得到微型燃气涡轮发动机燃料量和转速之间的表达式；
步骤2：根据微型燃气涡轮发动机起动过程的燃料量和发动机转速的试验数据，并与步骤1所建的稳态燃料量和微型燃气涡轮发动机转速的关系式进行对比，得到起动过程的燃料量与稳态燃料量之间的差值；
步骤3：步骤2得到的燃料量差值能使微型燃气涡轮发动机产生加速效应，由于燃料量差值与微型燃气涡轮发动机转速之间的关系是高度非线性的，利用分段线性化的方法去拟合燃料量差值与微型燃气涡轮发动机转速之间的关系；
步骤4：燃料量差值和起动机电流共同作用，使微型燃气涡轮发动机产生加 速效应，通过对微型燃气涡轮发动机的加速度进行积分，从而得到微型燃气涡轮发动机的速度；
第二步，微型燃气涡轮发动机的性能参数与转速的关系建模；
步骤5：由于微型燃气涡轮发动机的转速与燃气性能参数之间的关系十分密切，采用多项式拟合的方法得到微型燃气涡轮发动机性能参数(压气机出口压力、压气机出口温度、燃烧室出口温度、燃烧室出口压力、涡轮后出口温度和涡轮后出口压力等)与微型燃气涡轮发动机转速之间的关系；
步骤6：由于通过生成的多项式计算燃气涡轮发动机性能参数会减慢模型的速度，同时也可能引起数值计算不稳定的现象，所以将多项式进行离散化，生成一维插值表的形式，有利于提高起动模型的实时性。
第三步，误差分析。
所建立的微型燃气涡轮发动机起动模型的各个性能参数与试验数据的误差均在5％以内，各个性能参数此处指压气机出口压力、压气机出口温度、燃烧室出口压力、涡轮出口压力、涡轮出口温度、微型燃气涡轮发动机转速。
本发明的有益效果：
现有微型燃气涡轮发动机建模方法多是利用纯机理或机器学习的方法，难以准确刻画微型燃气涡轮发动机的起动过程，而机器学习需要大量的试验数据。在工程实践中，目前普遍采用的纯机理操作繁复，效率低下，建模准确度不高。本发明提供了一种基于机理和辨识方法相结合的微型燃气涡轮发动机起动过程建模方法，弥补了现有技术的不足。本发明操作简单，准确率高，并可实现整个微型燃气涡轮发动机的建模。该方法具有一定的拓展性，可推广到其它领域。
附图说明
图1为微型燃气涡轮发动机建模流程图。
图2为剩余转矩与燃料量的关系图。
图3为燃料量差值与剩余扭矩关系图。
图4为起动过程建模误差对比图，其中，(a)压气机出口温度误差；(b)压气机出口压力误差；(c)燃烧室出口压力误差；(d)涡轮出口压力误差；(e)涡轮出口温度误差；(f)燃机转速误差。
具体实施方式
为了使本发明的目的、技术及优点更加清楚明白，以下结合附图及实例，对本发明进行进一步详细说明。
一种微型燃气涡轮发动机起动过程建模方法，包括以下步骤：
步骤1：微型燃气涡轮发动机的起动过程分为3个阶段，第一阶段，发动机转速由零到涡轮开始产生功率的转速，发动机完全由起动机带动加速；第二阶段，由涡轮开始产生功率的转速到起动机脱开；第三阶段，由起动机脱开转速至慢车转速；
按照发动机起动过程的各个阶段，对其进行建模；
第一阶段，发动机转速由零到涡轮开始产生功率的转速(即从零转速到点火转速)，发动机完全由起动机带动加速，满足发动机转子运动方程，即满足公式(1)。
Figure PCTCN2018091091-appb-000001
式中M st＝K st×I st，其中I st表示起动机电流值，K st为起动机转矩常数，针对不同类型的起动机，其值不同。此处所指的起动机为电起动机。ω为微型燃气涡轮发动机的角速度，J为归算到微型燃气涡轮发动机轴上的转动惯量，即等效转动惯量，针对不同的微型燃气涡轮发动机的结构，利用机械能守恒进行归算。具 体的归算公式参照(2)
Figure PCTCN2018091091-appb-000002
式中，J 1为微型燃气涡轮发动机轴带动的负载1的转动惯量，ω 1为微型燃气涡轮发动机轴带动的负载1的角速度；J 2为微型燃气涡轮发动机轴带动的负载2的转动惯量，ω 2为微型燃气涡轮发动机轴带动的负载2的角速度；J n为微型燃气涡轮发动机轴带动的负载n的转动惯量，ω n为微型燃气涡轮发动机轴带动的负载n的角速度。
第二阶段，发动机转速由点火转速到起动机脱开转速，发动机在起动机和涡轮的共同带动下进行加速，满足发动机转子运动方程，即满足公式(3)。
Figure PCTCN2018091091-appb-000003
式中，M gas就是点火后微型燃气涡轮发动机的剩余扭矩(M gas＝M T-M C-M f)，M T代表涡轮产生的转矩，M C代表压气机消耗的转矩，一般与压气机转速的平方成正比，M f表示摩擦引起的转矩消耗，一般与转速的平方成正比；M st是电起动机提供的转矩，与(1)式中相同。J与公式(1)计算过程相同，ω公式(1)相同。
第三阶段，发动机在剩余转速的作用下由发动机在起动机脱开转速加速慢车转速的过程，满足公式(4)。
Figure PCTCN2018091091-appb-000004
式中，J与公式(1)相同，ω公式(1)相同。M gas与公式(3)计算过程相同。
步骤2：第一阶段微型燃气涡轮发动机转速的建模
首先，通过计算得到发动机等效转动惯量(具体参见公式(2))；利用转子 运动方程式，结合起动机电流值，根据M st＝K st×I st计算得到起动机加在微型燃气涡轮发动机轴上的转矩值，利用一阶龙格-库塔方法(欧拉方法)对其进行积分，得到该模型的微型燃气涡轮发动机转速，保证该微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内；
步骤3：第二阶段微型燃气涡轮发动机转速的建模
步骤3.1：通过计算得到发动机等效转动惯量(具体参见公式(2))；利用转子运动方程式，结合起动机电流值，得到燃机剩余转矩值，燃机剩余转矩＝涡轮产生的转矩-压气机消耗的转矩-摩擦引起的转矩，筛选出燃机剩余扭矩绝对值为零的所有点，根据筛选出的燃机剩余扭矩绝对值为零的点，利用线性插值方法确认出各点相对应的燃料量，该燃料量即为对应点的“稳态燃料量”；
步骤3.2：在步骤3.1的基础上，进行多项式拟合，得到燃机转速和稳态燃料量之间的关系表达式，其关系式是一个三项多项式，具体的多项式系数因燃料种类的不同而有所差别，此处采用的燃料为天然气，其具体表达式参见公式(5)：
Figure PCTCN2018091091-appb-000005
步骤3.3：微型燃气涡轮发动机的剩余转矩和燃料量差值之间的函数关系十分复杂，呈现高度的非线性，对其进行简化，采用分段线性函数刻画该复杂关系，假设燃机剩余转矩与燃料量差值之间是分段一次函数关系，即采用公式(6)进行刻画。
M gas＝k(n)×(W f-W fss)+b(n)         (6)
式中，k(n)、b(n)为系数，不同的燃机转速，其值不相同，即k(n)、b(n)数值是燃机转速n的函数，(W f—W fss)为动态燃料量和多项式得到的稳态燃料量之间的差值，燃机转速不同，其值也不同；
步骤3.4：微型燃气涡轮发动机的剩余转矩与起动机作用在燃机轴上的转矩求和，再利用一阶龙格-库塔方法(欧拉方法)对其进行积分，得到该模型计算出的微型燃气涡轮发动机转速，保证该微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内；
步骤3.5：为了保证步骤3.4中提到的“微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内”，需要根据微型燃气涡轮发动机的转速来实时调整公式(6)中的k(n)、b(n)，使构建的微型燃气涡轮发动机起动模型的转速最大程度地接近试验转速。
步骤4：第三阶段微型燃气涡轮发动机转速的建模
首先，通过计算得到发动机等效转动惯量(具体参见公式(2))；利用转子运动方程式，结合燃料量，根据公式(6)计算得到起动机加在微型燃气涡轮发动机轴上的转矩值，利用一阶龙格-库塔方法(欧拉方法)对其进行积分，得到该模型的微型燃气涡轮发动机转速，保证该微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内；需要根据微型燃气涡轮发动机的转速来实时调整公式(6)中的k(n)、b(n)，使构建的微型燃气涡轮发动机起动模型的转速最大程度地接近试验转速。
步骤5：微型燃气涡轮发动机的性能参数与燃气涡轮发动机转速之间的关系十分密切，此处提到的燃气涡轮发动机的性能参数主要包括：压气机出口温度、压气机出口压力、燃烧室出口压力、涡轮出口温度、涡轮出口压力五个参数，利用MATLAB自带的数据拟合工具拟合出燃气涡轮发动机的性能参数和燃气涡轮发动机转速的函数表达式，即：
Figure PCTCN2018091091-appb-000006
式(7)中，T 2为压气机出口温度，K T为压气机出口的温度系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速；
Figure PCTCN2018091091-appb-000007
式(8)中，P 2压气机出口压力,K P为压气机出口的压力系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速；
Figure PCTCN2018091091-appb-000008
式(9)中，P 3C为燃烧室出口压力，K c为燃烧室的压力系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速；
P 4＝constant+k wp×N g            (10)
式(10)中，故涡轮出口压力P 4建模为常值+k wp×N g，常值为标准大气压强的1.03倍，k wp×N g与微型涡轮发动机工作转速有关，k wp随微型涡轮发动机转速的变化而变化；
Figure PCTCN2018091091-appb-000009
式(11)中，T 4为涡轮出口温度，K t为涡轮出口的温度系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速，N gt表示微型燃气涡轮发动机的额定转速，N idle表示微型燃气涡轮发动机的慢车转速；
步骤6：将所得的燃气涡轮发动机性能参数和转速之间的多项式函数关系进行线性化离散，即对公式(7)、(8)、(9)、(10)、(11)进行线性离散，为了保证离散精度，微型燃气涡轮发动机转速的步长值取为0.2％×N gt，将离散化处理后的数据放入相应的一维线性插值表。
误差分析：根据燃气涡轮发动机的试验数据，得到压气机出口压力、压 气机出口温度、燃烧室出口压力、涡轮出口压力、涡轮出口温度、微型燃气涡轮发动机转速等参数与燃机起动模型之间的差距均在5％以内，说明本发明所提出的微型燃气涡轮发动机起动过程的建模方法是有效的、可行的。

Claims (1)

  1. 一种微型燃气涡轮发动机起动过程建模方法，其特征在于，步骤如下：
    步骤1：微型燃气涡轮发动机的起动过程分为3个阶段，第一阶段，发动机转速由零到涡轮开始产生功率的转速，发动机完全由起动机带动加速；第二阶段，由涡轮开始产生功率的转速到起动机脱开；第三阶段，由起动机脱开转速至慢车转速；
    按照发动机起动过程的各个阶段，对其进行建模；
    第一阶段，发动机转速由零到涡轮开始产生功率的转速即从零转速到点火转速，发动机完全由起动机带动加速，满足发动机转子运动方程，即满足公式(1)：
    Figure PCTCN2018091091-appb-100001
    式中M st＝K st×I st，其中I st表示起动机电流值，K st为起动机转矩常数；ω为微型燃气涡轮发动机的角速度，J为归算到微型燃气涡轮发动机轴上的转动惯量，即等效转动惯量，针对不同的微型燃气涡轮发动机的结构，利用机械能守恒进行归算；具体的归算公式(2)
    Figure PCTCN2018091091-appb-100002
    式中，J 1为微型燃气涡轮发动机轴带动的负载1的转动惯量，ω 1为微型燃气涡轮发动机轴带动的负载1的角速度；J 2为微型燃气涡轮发动机轴带动的负载2的转动惯量，ω 2为微型燃气涡轮发动机轴带动的负载2的角速度；J n为微型燃气涡轮发动机轴带动的负载n的转动惯量，ω n为微型燃气涡轮发动机轴带动的负载n的角速度；
    第二阶段，发动机转速由点火转速到起动机脱开转速，发动机在起动机和涡轮的共同带动下进行加速，满足发动机转子运动方程，即满足公式(3)：
    Figure PCTCN2018091091-appb-100003
    式中，M gas是点火后微型燃气涡轮发动机的剩余扭矩M gas，M T代表涡轮产生的转矩；M C代表压气机消耗的转矩，与压气机转速的平方成正比；M f表示摩擦引起的转矩消耗，与转速的平方成正比；M st是电起动机提供的转矩，与公式(1)相同；J与公式(1)相同，ω与公式(1)相同；
    第三阶段，微型燃气涡轮发动机在剩余转速的作用下，由发动机在起动机脱开转速加速慢车转速的过程，满足公式(4)：
    Figure PCTCN2018091091-appb-100004
    式中，J与公式(1)相同，ω与公式(1)相同；M gas与公式(3)相同；
    步骤2：第一阶段微型燃气涡轮发动机转速的建模
    首先，通过计算得到发动机等效转动惯量，见公式(2)；利用转子运动方程式，结合起动机电流值，根据M st＝K st×I st计算得到起动机加在微型燃气涡轮发动机轴上的转矩值，利用一阶龙格-库塔方法对其进行积分，得到该模型的微型燃气涡轮发动机转速，保证该微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内；
    步骤3：第二阶段微型燃气涡轮发动机转速的建模
    步骤3.1：通过计算得到发动机等效转动惯量，见公式(2)；利用转子运动方程式，结合起动机电流值，得到燃机剩余转矩值，燃机剩余转矩＝涡轮产生的转矩-压气机消耗的转矩-摩擦引起的转矩，筛选出燃机剩余扭矩绝对值为零的所有点，根据筛选出的燃机剩余扭矩绝对值为零的点，利用线性插值方法确认出各点相对应的燃料量，该燃料量即为对应点的“稳态燃料量”；
    步骤3.2：在步骤3.1的基础上，进行多项式拟合，得到燃机转速和稳态燃 料量之间的关系表达式，其关系式是三项多项式，表达式(5)：
    Figure PCTCN2018091091-appb-100005
    步骤3.3：微型燃气涡轮发动机的剩余转矩和燃料量差值之间的函数关系十分复杂，呈现高度的非线性，对其进行简化，因此，采用分段线性函数刻画该复杂关系，假设燃机剩余转矩与燃料量差值之间是分段一次函数关系，即采用公式(6)进行简化
    M gas＝k(n)×(W f-W fs) s+b(    (6)
    式中，k(n)、b(n)为系数，不同的燃机转速，其值不相同，即k(n)、b(n)数值是燃机转速n的函数，(W f-W fss)为动态燃料量和多项式得到的稳态燃料量之间的差值，燃机转速不同，其值也不同；
    步骤3.4：微型燃气涡轮发动机的剩余转矩与起动机作用在燃机轴上的转矩求和，再利用一阶龙格-库塔方法对其进行积分，得到该模型计算出的微型燃气涡轮发动机转速，保证该微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内；
    步骤3.5：为了保证步骤3.4中提到的“微型燃气涡轮发动机的转速和试验数据中的燃机转速误差在5％以内”，需根据微型燃气涡轮发动机的转速来实时调整公式(6)中的k(n)、b(n)，使构建的微型燃气涡轮发动机起动模型的转速最大程度地接近实际的试验转速；
    步骤4：第三阶段微型燃气涡轮发动机转速的建模
    首先，通过计算得到发动机等效转动惯量，见公式(2)；利用转子运动方程式，结合燃料量，根据公式(6)计算得到起动机加在微型燃气涡轮发动机轴上的转矩值，利用一阶龙格-库塔方法对其进行积分，得到该模型的微型燃气涡轮发动机转速，保证该微型燃气涡轮发动机的转速和试验数据中的燃机转速误 差在5％以内；需根据微型燃气涡轮发动机的转速来实时调整公式(6)中的k(n)、b(n)，使构建的微型燃气涡轮发动机起动模型的转速最大程度地接近实际的试验转速；
    步骤5：微型燃气涡轮发动机的性能参数与燃气涡轮发动机转速之间的关系十分密切，燃气涡轮发动机的性能参数包括压气机出口温度、压气机出口压力、燃烧室出口压力、涡轮出口温度和涡轮出口压力五个参数，拟合燃气涡轮发动机的性能参数和燃气涡轮发动机转速的函数表达式，即：
    Figure PCTCN2018091091-appb-100006
    式(7)中，T 2为压气机出口温度，K T为压气机出口的温度系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速；
    Figure PCTCN2018091091-appb-100007
    式(8)中，P 2压气机出口压力,K P为压气机出口的压力系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速；
    Figure PCTCN2018091091-appb-100008
    式(9)中，P 3C为燃烧室出口压力，K c为燃烧室的压力系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速；
    P 4＝constant+k wp×N g (10)
    式(10)中，故涡轮出口压力P 4建模为常值+k wp×N g，常值为标准大气压强的1.03倍，k wp×N g与微型涡轮发动机工作转速有关，k wp随微型涡轮发动机转速的变化而变化；
    Figure PCTCN2018091091-appb-100009
    式(11)中，T 4为涡轮出口温度，K t为涡轮出口的温度系数，不同的起动运行过程，其参数不同，N g表示微型燃气涡轮发动机的转速，N gt表示微型燃气涡轮发动机的额定转速，N idle表示微型燃气涡轮发动机的慢车转速；
    步骤6：将所得的燃气涡轮发动机性能参数和转速之间的多项式函数关系进行线性化离散，即对公式(7)、(8)、(9)、(10)、(11)进行线性离散，为了保证离散精度，微型燃气涡轮发动机转速的步长值取为0.2％×N gt，将离散化处理后的数据放入相应的一维线性插值表。
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CN112906322A (zh) * 2021-03-17 2021-06-04 中国航空发动机研究院 一种燃气涡轮发动机盘腔内部参数的计算方法
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