KR100788212B1 - Creation method for airpalne's gas turbine engine - Google Patents

Abstract

A method for producing a performance curve diagram of a gas turbine engine for an aircraft is provided to simply reduce the cost for and the risk of development of an engine by producing the performance curve diagram of a component using approximate experimental data. A method for producing a performance curve diagram of a gas turbine engine for an aircraft includes the steps of: obtaining a reduced scale factor by using performance data for heights given from an engine manufacturer(S1); calculating an RPM corrected according to a temperature and a height(S2); calculating the pressure ratios, flux functions, and efficiencies for heights by using the corrected RPM(S3); obtaining a performance curve diagram by displaying the pressure ratios, flux functions, and efficiencies for heights with a linear graph at a predetermined RPM using a reduced scale factor(S4); producing an initial group using an arbitrary initialization method(S5); normalizing the suitability value using a scaling window method(S6); forming a mating supply source based on the suitability value using a reproduction operator; and setting a number of households.

Description

Creation Method for Airpalne's Gas Turbine Engine

The present invention relates to a method of generating a performance diagram of a gas turbine engine for an aircraft, and more particularly, by simulating the performance of a gas turbine engine used in an aircraft by using a system identification method and a genetic algorithm, the development risk is reduced and the development cost is reduced. And it relates to a method of generating a performance diagram of a gas turbine engine for an aircraft to be used for diagnosis of the state of the engine.

In general, a gas turbine engine, as shown in FIG. 1, includes a gas generator 2 composed of a compressor 22, a combustor 24, a compressor turbine 26, a power turbine 4, and a generator 6. It is composed.

Performance simulation of the gas turbine engine is to predict the accurate engine performance under various conditions by using the performance diagram and the thermodynamic relationship that express the performance characteristics of the above components.

This performance simulation can replace many expensive and risky tests and serves as the basis for diagnosing and controlling the condition of the engine.

In order to simulate the performance, it is very important to obtain the correct performance diagram because the engine must satisfy the constraint that the performance of each component must follow its own performance diagram.

However, these performance diagrams are produced by the engine manufacturer through a lot of research and testing and are not usually disclosed to the buyers.

However, when the engine is purchased, the engine manufacturer provides a software called the performance deck, which is used to interpret the performance of the engine's operating conditions and changes in the input parameters determined by temperature, pressure, power, non-fuel consumption rate. The analysis results of the same parameters can be seen.

However, since the performance deck does not disclose the performance of the internal algorithms and the components used at all, it is impossible to modify or supplement the user's convenience.

Therefore, in order to use the performance analysis result and the state diagnosis desired by the user, it is necessary to develop the performance analysis code, and for this, it is very important to obtain the component performance diagram.

Most people studying performance simulation and diagnostics use some of the published performance plots by scaling them based on design points.

The most commonly used scale of performance diagram is the scale equation used in the DYNGEN program developed by NASA, which scales the overall performance data by the performance ratio of the component performance diagram to the design point performance of the engine. .

However, this scale equation has a merit that it is possible to simply obtain a performance diagram, but there is a condition that the scale ratio is close to 1, so that the performance ratio of the research engine is comparable with the existing performance diagram. The disadvantage is that it does not match the performance of the actual engine.

It is also very difficult to obtain a performance map that is relatively well consistent with the component characteristics of the engine under study.

Many studies have been presented to effectively represent the performance of components. Hormouziadis and Herbig (1974) have introduced glass functions and elliptic approximations to describe velocity curves and efficiency contours to represent various aspects of compressor performance curves.

Dobryanskii and Martyanova (1989) proposed a method to store performance diagram data using a look-up table and to define the value of a variable at any point on the performance diagram using linear or Lagrangian interpolation.

El-Gammal (1991) developed criteria and algorithms for linear models of compressors, which allows the objective selection of the most appropriate model from well-known performance data.

Sieros et al. (1997) use analytical functions to represent nonlinear representations of compressor and turbine performance plots.

Orkisz and Stawarz (1997) proposed a method of functionally expressing the relationship between the variables (flow rate, pressure ratio, efficiency, and rotational speed) of the axial compressor and turbine performance curves.

Kurzke et al. (2000) presented a method of constructing a new performance diagram by statistically analyzing the performance curves of many compressors and defining the highest efficiency area, the flow-speed relationship, and the shape of the velocity diagram.

However, the above-described conventional scaling method requires a large amount of data on the performance diagram, and thus has a disadvantage in that it is difficult to use when the performance data data is small.

In general, design point performance, such as the engine's maximum takeoff conditions, is disclosed, allowing the use of thermodynamic equations to calculate the approximate performance of each component.

The scale factor value of the performance diagram is calculated by using the pressure ratio, air flow rate, and efficiency of the component calculated as described above.

If performance data such as power and specific fuel consumption can be obtained under conditions other than the design point through engine experiments or engine manufacturers, scale values under other conditions can also be obtained.

If we reconstruct the component performance diagram by numerically analyzing the scale values of the various conditions, we can obtain the performance diagram that is closer to the actual engine than the component performance diagram obtained by the scale value of only one design point.

The present invention provides a method for generating a performance diagram of an aircraft gas turbine engine capable of reducing engine development cost and risk by obtaining a performance diagram of an engine close to actual engine performance by a genetic algorithm and a system identification method. There is this.

The object of the present invention described above,

A first step of obtaining a scale factor value using performance data of each altitude given from an engine manufacturer, a second step of calculating a revised speed according to temperature and altitude, a pressure ratio of each altitude using the corrected speed, System identification consisting of three steps of calculating the flow rate function and efficiency, and four steps to obtain the performance diagram by displaying the pressure ratio, flow rate function and efficiency value for each altitude in a linear graph at the specific speed revised using the scale factor value. A performance lead calculation process by;

Five steps to generate initial population using random initialization, six steps to normalize goodness-of-fit values using scaling window technique, seven steps to set number of households, and cross-feeding sources based on goodness-of-fit values using reproduction operator 8-1 step of forming a step, and 8-2 steps of applying a modified simple crossover (Modified Simple Crossover) and dynamic mutation (Dynamic Mutation), characterized in that it comprises a process of calculating the performance diagram by a genetic algorithm The performance line of the gas turbine engine for an aircraft can be achieved by the method.

According to the present invention, by analyzing the engine performance diagram by genetic algorithm and system identification, the error rate of the compressor performance diagram is much smaller than that of other techniques, and the component performance diagram can be simplified simply by the approximate experimental data without the existing performance diagram. This can reduce the engine development costs and risks.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

2 is a flowchart illustrating a performance diagram generating process of a gas turbine engine according to the present invention.

Referring to FIG. 2, it can be seen that a method for generating a performance diagram of an aircraft gas turbine engine according to the present invention is largely composed of a performance diagram calculating process (I) based on system identification and a performance diagram calculating process (G) using a genetic algorithm. have.

The performance diagram calculation process (I) based on the system identification may include a first step of obtaining a scale factor value using performance data for each altitude given from an engine manufacturer, and a second step of calculating a revised speed according to temperature and altitude; 3, calculating the pressure ratio, flow rate function, and efficiency for each altitude using the corrected rotation speed; and linearizing the pressure ratio, flow rate function, and efficiency value for each altitude at a specific rotation speed corrected using the scale factor value. It is composed of four steps to obtain a performance diagram by displaying it in a graph.

More specifically,

Stage 1

The engine manufacturer receives performance data for ground stop standard atmosphere and performance data for altitudes of 10000ft, 20000ft, and 30000ft.

Tier 2

The corrected speed of the engine is obtained by calculating the correction temperature and the actual speed.

That is, the calculation formula for calculating the correction temperature θ is

이다.

to be.

Where T ₁ is the temperature at the time of the experiment and 288.25 is the standard atmospheric temperature.

The formula for calculating the correction rotation speed CN is defined as follows.

----------- (1)

----------- (One)

Tier 3

Scale factors such as pressure ratio, flow rate function, and efficiency for each altitude are calculated using the corrected rotation speed.

First, substitute the values of the design points for the pressure ratio, flow rate function, and efficiency provided by the engine manufacturer in the following formulas (1), (2), and (3) to obtain the pressure ratio, flow rate function, and efficiency for the disclosed arbitrary points. .

: 효율을 의미한다.In the above formula, PR: pressure ratio, MFP: flow rate function,

: Means efficiency.

Table 1 below shows the scale factor values calculated by the above formulas (1), (2) and (3).

: 효율Note) PR: Pressure Ratio, MFP: Flow Function,

: efficiency

Meanwhile, the pressure ratio, flow rate function, and efficiency of the present invention are calculated through the following formulas (4), (5), and (6).

…………………(4)

… … … … … … … (4)

…………………(5)

… … … … … … … (5)

…………………(6)

… … … … … … … (6)

: 비열비 ><P ₁ : Inlet pressure, P ₂ : Outlet pressure, m: Air flow rate T ₁ : Inlet temperature T ₂ : Outlet temperature

: Specific heat ratio>

Each scale factor obtained at these four elevations is used to obtain four sets of component performance plots.

Here, it is assumed that the pressure ratio, the flow rate function, and the efficiency have the following linear function with respect to the correction rotation speed.

Where y is the pressure ratio, the flow rate function and the efficiency, and x is the correction speed.

The coefficients a and b of the polynomials were calculated using the polyfit built into the commercial program MATLAB.

Polyvals were used to derive polynomials from each β-line.

The β-line means each horizontal line in the following [Table 2], 1, 2, 3… from the top. , Up to 20 times.

[Table 2] below is a table comparing 100% RPM performance data and component performance of the compressor obtained by using the conventional performance scale method, and 100% RPM performance data of the compressor obtained by the system identification method.

In the data according to the system identification method of the present invention on the right in [Table 2], the left column represents the pressure ratio, the middle column represents the flow rate function, and the right column represents the efficiency.

In addition, as described above, the horizontal line means β-line, the uppermost β-line is number 1, and the lowermost β-line is 20 times.

In Table 2, β-line No. 12 is data on the pressure ratio, the flow rate function, and the efficiency at the design point.

4 steps

The performance diagram is obtained by displaying the pressure ratio, the flow rate function, and the efficiency of the compressor, the compressor turbine, and the power turbine with respect to the corrected rotation speed obtained through the above-described process.

3A to 3C are performance diagrams of components according to the system identification method according to the present invention, FIG. 3A is a performance diagram for a compressor, FIG. 3B is a performance diagram for a compressor turbine, and FIG. 3C is a power turbine. It is a performance diagram.

In each figure, the solid line is the component performance figure obtained by the system identification method of this invention, and the dotted line is the performance figure calculated | required by the conventional method.

The rotational speed was expressed in RPM, and was set at 70, 80, 90, 100, and 110%, of which 100% RPM was a diagram showing the performance of the design point.

Therefore, the conventional method was able to obtain only the performance at the design point, but according to the present invention, various performances for each component can be obtained by variously obtaining the corrected rotation speed and obtaining the pressure ratio, flow rate function, and efficiency using the corresponding scale factor. Can be obtained.

Genetic algorithms, on the other hand, are probabilistic search methods that model the natural phenomena of genetic inheritance and survival competition in the form of algorithms.

Genetic inheritance mimics the genetic process of producing new offspring for each generation, and survival competition mimics Darwin's evolution of grouping from generation to generation.

Genetic operators such as reproduction, mating, and mutations are used to maintain and improve the populations that are likely to be harmful to implement breeding and selection of these species.

Genetic operators are used to select individuals and to promote information formation and exchange among them, thereby improving the population and conducting searches in different directions. In particular, the strengths and weaknesses of individuals in their selection are distinguished by their fitness.

)의 함수관계를 다음과 같이 정의 하였다. Rotation speed (N), pressure ratio (PR), flow rate function (MFP), efficiency (

) Is defined as the following.

First, the flow rate function is a function of the pressure ratio and the rotational speed and is expressed by Equation 10 below.

MFP _N = aPR ³ + bPR ² + cPR + d ........... (10)

In addition, the efficiency is as Equation (11) as a function of the flow rate function and the rotation speed.

_n = aMFP³ + bMFP² + cMFP + d .................(11)

_n = aMFP ³ + bMFP ² + cMFP + d ... (11)

Here, six revolutions of the compressor revolutions of 65000, 70000, 75000, 80000, 85000, and 90000 RPM were selected.

Therefore, knowing the values of the coefficients a, b, c, and d in Equations 10 and 11, the respective values according to the rotation speeds can be obtained and component performance diagrams can be generated.

In the present invention, a simple genetic algorithm is applied to obtain the non-coefficients a, b, c, and d.

Through calculation under various conditions, 'n' data groups are formed from the equation (10) and the absolute value of the object function (Objectfuc) as follows is minimized.

............(12)

............ (12)

"Error" in Equation 12 is a percentage error for any a, b, c, d.

Referring back to FIG. 2, the performance diagram calculation process using the genetic algorithm according to the present invention includes five steps of generating an initial group using a random initialization method, and six steps of normalizing a fitness value using a scaling window method. , 7 steps to set the number of generations, 8-1 steps to form a cross-feeding source based on the goodness-of-fit value using the reproduction operator, and to apply Modified Simple Crossover and Dynamic Mutation. It consists of 8-2 steps.

More specifically,

5 steps

We generated 1000 initial populations using random initialization and 4 real chromosomes since 4 unknowns.

6 steps

The entity is evaluated using the objective function and the scaling window technique is used to normalize the goodness-of-fit values.

7 steps

The number of households is set to 100 to 999, and the non-coefficient range is set to -1200 to 1200. When the number of generations is reached, the process ends after generating a component performance characteristic equation (S9).

Step 8-1

When the number of generations in step 7 is not reached, the reproduction operator is used to select individuals in the group and form a breeding source based on the fitness values.

The reproduction algorithm uses Gradient-like selectors proposed by Pham and Jin to maintain genetic diversity of the population and to select optimal individuals.

Step 8-2

Modified Simple Crossover and Dynamic Mutation were applied to fit the real chromosome. The mating rate and the mutation rate were set to 0.9 and 0.1, respectively, and the above six steps were performed.

4 is a view comparing the flow rate value calculated by the genetic algorithm of the present invention with the reference data value, in which the objective function value of Equation 12 converges to "0" at 100% rotational speed. Is showing.

Looking at the results, it can be seen that the three flow rate functions (mfp1 to mfp3) calculated by the genetic algorithm are almost equal to the reference data value (Object Fun).

This means that the genetic algorithm correctly found the unknown values a, b, c, and d that satisfy the three pairs of flow function-pressure ratio functions.

The relationship between the flow rate function and the pressure ratio of RPM 60%, 70%, 80%, and 90% was also calculated in this way.

% RPM a b c d 60 -5.628 59.151 -205.21 240.498 70 -13.675 160.731 -626.19 815.302 80 -17.90 219.90 -895.80 1119.0 90 -15.00 187.60 -777.30 1077.40 100 -6.186 77.442 -322.41 454.25

5 is a diagram showing a newly produced compressor using a genetic algorithm in the present invention.

As shown in Figure 5, it is possible to obtain the performance diagram for the compressor pressure ratio / flow rate function under the conditions of RPM 60, 70, 80, 90, 100%.

The result of comparing the method using the genetic algorithm with the performance value of the conventional program GASTURB 9.0 and the performance deck program provided by the engine manufacturer are described below.

Steady-state performance analysis of gas generator rotation speed, altitude, and flying Mach number was performed using GASTURB 9.0, a commercial program.

In the analysis, the compressor performance and the GASTURB standard performance scale shown in Fig. 5 were used, respectively, based on the design point. The performance of axial horsepower according to the flight Mach number change was compared.

Compressor turbine performance diagram and power turbine performance diagram were used for NASAGV61 engine and NASAGV68 engine, respectively, provided by GASTURB.

6A to 6C are diagrams illustrating a comparison result between an air flow rate ratio, a fuel flow rate ratio, a performance deck program diagram of an output, a genetic algorithm diagram, and a GASTURB diagram with respect to the change of the gas generator rotor rotational speed in the ground stop state.

That is, Figure 6a is a comparison result between the change of the gas generator rotor rotational speed and the air flow rate, Figure 6b is a comparison result between the change of the gas generator rotor rotational speed and the fuel flow rate, Figure 6c is a change and output of the gas generator rotor rotational speed The comparison result.

In the figure, EEPP is a performance deck program diagram, GAs is a genetic algorithm diagram, and GASTURB is a diagram of commercial program GASTURB 9.0.

As can be seen in Figures 6a to 6c, the results of the comparison of the performance analysis results according to the gas generator rotation rate when using the standard performance diagram provided by GASTURB scaled out that the error suddenly increases as the deviation from the design point RPM 100% Can be.

7A to 7C are diagrams showing a performance analysis comparison result between a performance deck program diagram according to an altitude change in a 100% gas generator rotor rotational speed and a flight Mach number 0, and a genetic algorithm diagram and a GASTURB diagram.

That is, FIG. 7A illustrates the correlation between the air flow rate ratio and the altitude, FIG. 7B illustrates the correlation between the fuel flow rate ratio and the altitude, and FIG. 7C illustrates the correlation between the output and the altitude.

Referring to the results of FIGS. 7A to 7C, it can be seen that the performance deck analysis result (EEPP) is closer to the performance deck analysis result obtained by using the genetic algorithm.

1 is a view showing a schematic configuration of a gas turbine engine for an aircraft applied to the present invention.

2 is a flowchart illustrating a process of generating a performance diagram of a gas turbine engine for an aircraft according to the present invention.

3a to 3c is a performance diagram of the components according to the system identification method according to the present invention, Figure 3a is a performance diagram for the compressor, Figure 3b is a performance diagram for the compressor turbine, Figure 3c is a performance diagram for the power turbine to be.

4 is a view comparing the flow rate value calculated by the genetic algorithm of the present invention with the reference data value, showing that the objective function value of Equation (12) converges to "0" at 100% rotational speed. have.

5 is a diagram of a newly compressor performance using the genetic algorithm in the present invention.

6A to 6C are graphs showing the results of comparing the airflow rate ratio, fuel flow rate ratio, performance deck program diagram of the generator, and the genetic algorithm diagram and the GASTURB diagram with respect to the change of the gas generator rotor rotational speed in the ground stop state.

7A to 7C are diagrams illustrating a performance analysis result between a performance deck program diagram according to an altitude change at a 100% gas generator rotor rotation speed and a flight Mach number 0, and a genetic algorithm diagram and a GASTURB diagram.

Claims (9)

Step 1, which calculates the scale factor using each altitude performance data from the engine manufacturer, 2 steps to calculate the revised speed based on temperature and altitude, Pressure ratio for each altitude using the corrected rotation speed (

), Flow function (

), efficiency(

Step 3), A performance diagram calculation process comprising a four-step system identification step for obtaining a performance diagram by displaying a pressure graph, a flow rate function, and an efficiency value for each altitude at a specific rotation speed corrected using the scale factor value; 5 steps to create an initial population using random initialization; 6 steps to normalize goodness-of-fit values using scaling window techniques, 7 steps of forming a cross-feed source based on the goodness-of-fit value using the reproduction operator; Process of calculating performance leads by genetic algorithm consisting of 8 steps to set generation number Performance lead generation method of a gas turbine engine for an aircraft comprising a. The method of claim 1, 2 step The formula for calculating the correction speed CN is

remind

Is the actual rotational speed,

Calibrate temperature Method of generating a performance diagram of an aircraft gas turbine engine, characterized in that defined as. The method of claim 2, The correction temperature

The equation to find is

Is, T ₁ is the temperature at the time of experiment, 288.25 is the standard atmospheric temperature Method of generating a performance diagram of an aircraft gas turbine engine, characterized in that defined as. The method of claim 3, wherein The pressure ratio (

The formula for calculating)

ego, Wherein P ₁ : inlet pressure, P ₂ : the performance diagram generation method of a gas turbine engine for an aircraft, characterized in that defined by the outlet pressure. The method of claim 3, wherein The flow rate function (

The formula for calculating)

ego, Where m is the air flow rate, T _{1 is the} inlet temperature, and P _{1 is the} inlet pressure. The method of claim 3, wherein The efficiency (

The formula for calculating)

Is, P ₁ : inlet pressure, P ₂ : outlet pressure, m: air flow rate, T ₁ : inlet temperature T ₂ : outlet temperature,

: Method of generating performance diagram of a gas turbine engine for an aircraft, characterized by a specific heat ratio. The method of claim 1, In the seventh step, the number of households is set to 100 to 999, and the non-coefficient range is set to -1200 to 1200. Upon reaching this, the aircraft gas turbine is finished after performing the step of generating a component performance characteristic equation. How to create a performance map of the engine. The method according to claim 1 or 7, When the number of generations in step 7 is not reached, the reproduction operator is used to select individuals in the group based on the goodness-of-fit values and form a breeding source. The reproduction algorithm maintains the genetic diversity of the group and selects the optimal individual. Method for generating a performance diagram of a gas turbine engine for an aircraft, characterized by further comprising 8-1 steps in which the Gradient-like selector proposed by Pham and Jin is used. The method of claim 8, After Step 8-1, Modified Simple Crossover and Dynamic Mutation were applied to fit the real chromosome, and the mating rate and the mutation rate were set to 0.9 and 0.1, respectively. Method for generating a performance diagram of a gas turbine engine for an aircraft, characterized in that it further comprises the step 8-2.

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