CN117494566A - One-dimensional model modeling and correcting method for axial flow compressor - Google Patents

Abstract

The invention discloses a one-dimensional model modeling and correction method of an axial flow compressor. Firstly, a one-dimensional model of the axial flow compressor is established through the medium diameter method for step-by-step cascades. Then, based on the design point backward angle and reference loss model, the polynomial fitting method is used to establish the non-design point backward angle and non-design point loss model. Finally, the PSO algorithm is used The established one-dimensional model of the axial flow compressor is corrected step by step to align the model calculation results with the test data. A one-dimensional model of an axial flow compressor was established and corrected using the above method. After simulation verification and comparison, the maximum error between the compressor characteristic calculation results and the test results did not exceed 6%. The compressor model was embedded into the entire turbine engine. Simulation verification was carried out in the machine performance model, and the maximum error did not exceed 4%, which verified the effectiveness of this method.

Description

A one-dimensional model modeling and correction method of axial flow compressor

Technical field

The invention relates to the technical field of aerospace engines, and mainly relates to a one-dimensional model modeling and correction method of an axial flow compressor.

Background technique

The mathematical model of aerospace engines is the premise and basis for carrying out engine performance analysis and prediction, control plan design and optimization. With the continuous development of aviation science and technology, the requirements for mathematical models of aerospace engines are becoming higher and higher. The axial flow compressor is a key component that determines the performance of the entire aircraft engine. Traditional modeling methods rely too much on the characteristics of test components and are currently unable to meet the calculation needs for variable guide vanes and variable tip clearances of the compressor. However, the CFD-based compressor Full three-dimensional numerical simulation calculations are very time-consuming and are not suitable for dynamic real-time calculations of the entire engine model.

Therefore, it is necessary to further study the method of establishing a one-dimensional mechanism model of the axial flow compressor based on the characteristics of the compressor test components, so as to realize the one-dimensional refinement of the axial flow compressor under working conditions such as variable guide vanes and variable tip clearances. Modeling requires the model to have high simulation accuracy. At present, there are few studies on one-dimensional model modeling methods for axial flow compressors in China. In existing studies, one-dimensional model performance calculation methods are mainly used for preliminary aerodynamic design and performance estimation of compressors, with more emphasis on calculation results and experiments. The trend of the results is consistent. Even if the model is partially corrected, the overall simulation accuracy is still not high, making it difficult to adapt to the high-precision simulation of the overall engine performance.

Contents of the invention

Purpose of the invention: In view of the problems existing in the above background technology, the present invention first uses the pitch diameter method to establish a one-dimensional performance model of the axial flow compressor, and uses the polynomial fitting method to correct the non-design point lagging angle and non-design point loss model based on the design point data. ; On this basis, a step-by-step correction scheme for the axial flow compressor based on the PSO algorithm is proposed to improve the calculation accuracy of the one-dimensional performance model of the axial flow compressor and meet the needs of high-precision simulation of the overall engine performance.

Technical solution: In order to achieve the above objects, the technical solution adopted by the present invention is:

A one-dimensional model modeling and correction method of an axial flow compressor, including the following steps:

(1) Establish a one-dimensional model of the axial flow compressor based on the medium diameter method and the geometric parameters of the axial flow compressor. The one-dimensional model of the axial flow compressor includes multiple single cascade models, and the axial flow is calculated through multiple single cascade models. Compressor characteristics;

(2) Use polynomial fitting method to establish non-design point lagging angle and non-design point loss models based on the design point lagging angle and reference loss model;

(3) Use the PSO algorithm to correct the one-dimensional compressor model step by step. First, correct the empirical coefficients of the reference loss model to align the airflow parameters of each section of the compressor design point, and then correct the non-design point lagging angle and non-design point loss. model to calibrate compressor characteristics.

Preferably, the implementation process of step (1) is as follows:

Step1.1: Use the outlet airflow parameters of the previous stage cascade model as the inlet airflow parameters of the current stage cascade model. The inlet airflow parameters include the axial speed C _1a , absolute speed C ₁ , and absolute angle α of the inlet airflow. _1. Relative speed W ₁ , relative angle β ₁ , mass flow rate m, total pressure P ₁ ^* , static pressure P ₁ , total temperature T ₁ ^* , static temperature T ₁ ; according to the inlet airflow velocity triangle and the current stage cascade model The structure and the characteristics of the current stage cascade model are used to calculate the angle of attack i and lagging angle δ. The relative speed W ₁ , absolute speed C ₁ and implicated speed U ₁ are the three sides of the inlet airflow velocity triangle, and C _1a is the inlet airflow. For the height of the velocity triangle, the angle between C _1a and W ₁ is the relative angle β ₁ , and the angle between C _1a and C ₁ is the absolute angle α ₁ ;

Step1.2: Preliminarily guess the axial velocity C _2a of the exit airflow of the current stage cascade model, and calculate the exit airflow velocity triangle, including calculating the absolute speed C ₂ , absolute angle α ₂ , and relative velocity W ₂ of the exit airflow of the current stage cascade model. , relative angle β ₂ ; the relative velocity W ₂ , absolute velocity C ₂ and implicated velocity U ₂ of the outlet airflow of the current stage cascade model are the three sides of the outlet airflow velocity triangle, C _2a is the height of the outlet airflow velocity triangle, C The angle between _2a and W ₂ is the relative angle β ₂ , and the angle between C _2a and C ₂ is the absolute angle α ₂ ;

Step1.3: Calculate the outlet airflow parameters of the current stage cascade model, including calculating the total outlet airflow pressure P ₂ ^* , static pressure P ₂ , total temperature T ₂ ^* , and static temperature T ₂ ;

Step1.4: Calculate the rim work L _u and loss work L _f based on the inlet air flow velocity triangle, outlet air flow velocity triangle and loss model;

Step1.5: Calculate the isentropic change work _Li according to the thermodynamic state parameters;

Step1.6: Determine whether the work balance equation L _u =L _i +L _f is established. If it is established, output the outlet airflow parameters of the current stage cascade model. If it is not established, update C _2a and return to Step1.2.

Preferably, the non-design point backward angle model and non-design point loss model modeling methods in step (2) are as follows:

Step2.1: Calculate critical angle of attack:

In the formula, Ma ₁ is the relative Mach number of the inlet airflow, k ₁ and k ₂ are correction coefficients, and i ₀ is the design angle of attack;

Construct a non-design point trailing angle model:

In the formula, δ ₀ is the reference lagging angle, k ₃ , k ₄ , k ₅ are correction coefficients;

Step2.2: The reference loss model uses the Denton/Traupel loss model to calibrate and correct the Denton/Traupel loss model:

First, calculate the loss coefficient of a single cascade model:

ζ＝ζ _profile +ζ _trailing +ζ _shock +ζ _tip +ζ _axial (3)

In the formula, ζ _profile is the profile loss coefficient, ζ _trailing is the wake loss coefficient, ζ _shock is the shock loss coefficient, ζ _tip is the tip clearance loss coefficient, and ζ _axial is the axial torus loss coefficient;

Calculate the rotor work loss:

L' _f ＝ζW ₁ ² /2 (4)

Calculate the work lost by the stator:

The calculation formula of non-design point loss coefficient is as shown in Equation (6):

In the formula, k ₆ , k ₇ , k ₈ are correction coefficients.

Preferably, the correction method based on the PSO algorithm in step (3) is as follows:

First, the PSO algorithm is used to correct the empirical coefficients of the reference loss model. The cross-sectional parameters of the design points calculated by the reference loss model are aligned with the simulation results of the three-dimensional model of the axial flow compressor. After the design points are aligned, the correction coefficients are optimized through the PSO algorithm. The value enables the non-design point performance of the axial flow compressor to be aligned with the test data.

Beneficial effects:

The present invention proposes a one-dimensional performance model modeling and correction method of an axial flow compressor. It establishes a one-dimensional performance model of the axial flow compressor based on the medium diameter method and the polynomial method, and corrects the one-dimensional performance model step by step through the PSO algorithm. Compared with the existing technology, it has the following beneficial effects:

1) For modeling of the entire aircraft engine, compared to the traditional compressor model that relies on component characteristic diagrams, the one-dimensional compressor performance model established by this method has more functions, such as calculating variable guide vanes and variable tip clearances. resulting changes in characteristics;

2) A step-by-step correction method for the one-dimensional performance model of the axial flow compressor is proposed, which improves the simulation accuracy of the one-dimensional performance model and has engineering applicability.

Description of the drawings

Figure 1 is the calculation flow chart of a single cascade;

Figure 2 shows the error diagram of the import and export parameters before and after the design point correction;

Figure 3 shows the compressor guide vane adjustment plan;

Figure 4 is a comparison chart between the calculated characteristics and experimental characteristics of the modified model;

Figure 5 is an error diagram between the simulation and test data of the corrected engine model.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

The present invention provides a one-dimensional model modeling and correction method of an axial flow compressor. The specific modeling method is shown in Figure 1.

Step (1): Establish a one-dimensional model of a single cascade based on the pitch diameter method and the geometric parameters of the compressor. The input of the cascade model is the airflow parameters output by the upper-level cascade model. The entire compressor is completed through the step-by-step calculation of the cascade model. Calculation of machine characteristics;

Step (2), use the polynomial fitting method to establish the non-design point lagging angle and non-design point loss model based on the design point lagging angle and reference loss model;

Step (3): Use the PSO algorithm to correct the one-dimensional compressor model step by step. First, correct the empirical coefficients of the reference loss model to align the airflow parameters of each section of the compressor design point, and then correct the non-design point backward angle and non-design point. Point loss model to align compressor characteristics.

The process of establishing a one-dimensional model of a single cascade according to step (1) is as follows:

Step1: Use the airflow parameters at the outlet of the previous stage cascade as the input parameters of the current stage cascade inlet, such as the inlet airflow axial speed C _1a , absolute speed C ₁ , absolute angle α ₁ , relative speed W ₁ , relative angle β ₁ , Mass flow rate m, total pressure P ₁ ^* , static pressure P ₁ , total temperature T ₁ ^* , static temperature T ₁ . Calculate the angle of attack i and lagging angle δ based on the inlet velocity triangle and the cascade structure and characteristics;

Step2: Preliminarily guess the axial velocity C _2a of the blade outlet airflow, and calculate the outlet airflow velocity triangle, including the absolute outlet airflow velocity C ₂ , absolute angle α ₂ , relative velocity W ₂ , and relative angle β ₂ ;

Step3: Calculate the airflow parameters at the blade outlet including the total outlet airflow pressure P ₂ ^* , static pressure P ₂ , total temperature T ₂ ^* , and static temperature T ₂ ;

Step4: Calculate the rim work L _u and loss work L _f based on the inlet and outlet velocity triangle and loss model;

Step5: Calculate the isentropic change work _Li according to the thermodynamic state parameters;

Step6: Determine whether the work balance equation _Lu = _Li + L _f is established. If it is established, output the current cascade outlet cross-section airflow parameters. If it is not established, update C _2a and return to Step 2.

Step (2) The non-design point backward angle model and non-design point loss model modeling methods are as follows:

Step (2.1) The lagging angle is greatly affected by the angle of attack and the relative Mach number of the inlet airflow. Combined with the blade cascade characteristic line and referring to the classic non-design point lagging angle model, this paper divides the non-design point lagging angle calculation into two parts based on the angle of attack.

First, calculate the critical angle of attack

In the formula, Ma ₁ is the relative Mach number of the inlet airflow, k ₁ and k ₂ are correction coefficients, and i ₀ is the design angle of attack.

According to the critical angle of attack, the calculation of the non-design point lagging angle is divided into two parts.

In the formula, δ ₀ is the reference lagging angle, k ₃ , k ₄ , and k ₅ are correction coefficients.

(2.2) The reference loss model adopts the Debton/Traupel loss model, which considers several different loss mechanisms and avoids the use of a large amount of empirical data. It has a wide range of applications, but requires calibration and correction of the model.

First, calculate the critical angle of attack

In the formula, Ma ₁ is the relative Mach number of the inlet airflow, k ₁ and k ₂ are correction coefficients, and i ₀ is the design angle of attack.

According to the critical angle of attack, the calculation of the non-design point lagging angle is divided into two parts.

In the formula, δ ₀ is the reference lagging angle, and k ₃ , k ₄ , and k ₅ are correction coefficients.

(2.2) The reference loss model adopts the Debton/Traupel loss model, which considers several different loss mechanisms and avoids the use of a large amount of empirical data. It has a wide range of applications, but requires calibration and correction of the model.

First, calculate the loss coefficient:

ζ＝ζ _profile +ζ _trailing +ζ _shock +ζ _tip +ζ _axial (19)

In the formula, ζ _profile is the profile loss coefficient, ζ _trailing is the wake loss coefficient, ζ _shock is the shock loss coefficient, ζ _tip is the tip clearance loss coefficient, and ζ _axial is the axial torus loss coefficient.

Calculate the rotor work loss:

L' _f ＝ζW ₁ ² /2 (20)

Calculate the work lost by the stator:

When the blade cascade deviates from the design point, it will cause airflow separation at the trailing edge, which will lead to an increase in flow loss. Therefore, the non-design point loss model in this article is based on the reference model and considers the impact of the angle of attack and inlet Mach number on the loss coefficient. The calculation formula of non-design point loss coefficient is as shown in Equation 22:

In the formula, k ₆ , k ₇ , k ₈ are correction coefficients.

Step (3) The step-by-step model correction method based on the PSO algorithm is as follows:

First, the reference loss model empirical coefficients are corrected through the PSO algorithm, and the cross-sectional parameters of the design points calculated by the model are aligned with the three-dimensional model simulation results. After the design point is aligned, the PSO algorithm is used to optimize the value of the correction coefficient k so that the compressor non-design point performance is aligned with the test data. At this time, the reference loss model can be modified in a small range. This processing method reduces the particle dimensions involved in a single optimization process of the PSO optimization algorithm, greatly improving the optimization speed and optimization effect.

In order to verify the effectiveness of the one-dimensional model modeling and correction method of the axial flow compressor, a five-stage transonic axial flow compressor was selected for modeling. This compressor contains zero-stage adjustable guide vanes and the first two stages of stator cascades. Adjustable. The one-dimensional model of the axial flow compressor is established and corrected according to the above method. First, the PSO optimization algorithm is used to correct the empirical coefficients in the reference loss model to align with the design point, and the one-dimensional model calculation results of the airflow parameters of the rotor inlet and outlet sections at the front and rear design points are corrected. The numerical simulation error with the three-dimensional model is shown in the figure. As can be seen from Figure 2, the calculation error of the one-dimensional compressor model before correction is within an acceptable range, indicating that the reference loss model has strong applicability to the established axial flow compressor. After correction, the rotor inlet and outlet cross-section error is within 2%, the design point pressure ratio error is 0.2%, the isentropic efficiency error is 1.8%, and the design point parameter alignment effect is good.

The adjustment rules of the zero-stage guide vane and the first two rows of stator vanes of this type of axial flow compressor at different rotational speeds are shown in Figure 3. Input the adjustment rule of the compressor guide vanes in the figure into the one-dimensional compressor model after the design point correction. Based on the corrected reference loss model, continue to apply the PSO optimization algorithm to the correction coefficient (k ₁ ... k ₈ ) Optimization is performed to correct the non-design point backward angle model and non-design point loss model, thus completing all corrections to the one-dimensional model.

The comparison between the calculated results of the modified one-dimensional compressor model characteristics and the test results is shown in Figure 4. Compared with the test results of the one-dimensional compressor model established and revised in this article, the maximum relative error in pressure ratio occurs at 95% rotational speed, which is 5.7%; the maximum relative error in isentropic efficiency occurs at 100% rotational speed, which is 2.6%. . Overall, the calculated results are not only consistent with the experimental results, but also have smaller errors, and the accuracy is significantly higher than most current one-dimensional compressor model programs.

Taking a certain type of turboshaft engine as an example, on the basis of the one-dimensional model of the axial flow compressor, a model of typical engine components is established, which mainly includes: inlet, centrifugal compressor, combustion chamber, gas turbine, power turbine, tail jet Pipes and other six components ultimately form a performance calculation model of the turboshaft engine. Among them, the centrifugal compressor, gas turbine and power turbine all use test component characteristics to establish mathematical models, and the axial flow compressor components use the one-dimensional performance model established in this article.

The test conditions of the complete engine are sea level standard days, and the fuel quantity is the design value. Change the power turbine speed np to 85% and 100% of the design value respectively. At the same time, adjust the axial flow compressor guide vane angle for bench testing and record the overall engine performance data. The error comparison between the calculation results of the complete engine model and the measured parameters of the engine bench test, such as output power Ne, gas generator speed ng, and total power turbine inlet temperature T ₄₅ , is shown in the figure. From Figure 5, it can be seen that the embedded axial flow compressor The simulation error of the one-dimensional turboshaft engine performance model does not exceed 4%, which meets the error accuracy requirements of the engine performance simulation.

Claims (4)

1. A method for modeling and modifying a one-dimensional model of an axial flow compressor, which is characterized by including the following steps: (1) Establish a one-dimensional model of the axial flow compressor based on the medium diameter method and the geometric parameters of the axial flow compressor. The one-dimensional model of the axial flow compressor includes multiple single cascade models, and the axial flow is calculated through multiple single cascade models. Compressor characteristics; (2) Use polynomial fitting method to establish non-design point lagging angle and non-design point loss models based on the design point lagging angle and reference loss model; (3) Use the PSO algorithm to correct the one-dimensional compressor model step by step. First, correct the empirical coefficients of the reference loss model to align the airflow parameters of each section of the compressor design point, and then correct the non-design point lagging angle and non-design point loss. model to calibrate compressor characteristics. 2. A one-dimensional model modeling and correction method of an axial flow compressor according to claim 1, characterized in that the implementation process of step (1) is as follows: Step1.1: Use the outlet airflow parameters of the previous stage cascade model as the inlet airflow parameters of the current stage cascade model. The inlet airflow parameters include the axial speed C _1a , absolute speed C ₁ , and absolute angle α of the inlet airflow. _1. Relative speed W ₁ , relative angle β ₁ , mass flow rate m, total pressure P ₁ ^* , static pressure P ₁ , total temperature T ₁ ^* , static temperature T ₁ ; according to the inlet airflow velocity triangle and the current stage cascade model The structure and the characteristics of the current stage cascade model are used to calculate the angle of attack i and lagging angle δ. The relative speed W ₁ , absolute speed C ₁ and implicated speed U ₁ are the three sides of the inlet airflow velocity triangle, and C _1a is the inlet airflow. For the height of the velocity triangle, the angle between C _1a and W ₁ is the relative angle β ₁ , and the angle between C _1a and C ₁ is the absolute angle α ₁ ; Step1.2: Preliminarily guess the axial velocity C _2a of the exit airflow of the current stage cascade model, and calculate the exit airflow velocity triangle, including calculating the absolute speed C ₂ , absolute angle α ₂ , and relative velocity W ₂ of the exit airflow of the current stage cascade model. , relative angle β ₂ ; the relative velocity W ₂ , absolute velocity C ₂ and implicated velocity U ₂ of the outlet airflow of the current stage cascade model are the three sides of the outlet airflow velocity triangle, C _2a is the height of the outlet airflow velocity triangle, C The angle between _2a and W ₂ is the relative angle β ₂ , and the angle between C _2a and C ₂ is the absolute angle α ₂ ; Step1.3: Calculate the outlet airflow parameters of the current stage cascade model, including calculating the total outlet airflow pressure P ₂ ^* , static pressure P ₂ , total temperature T ₂ ^* , and static temperature T ₂ ; Step1.4: Calculate the rim work L _u and loss work L _f based on the inlet air flow velocity triangle, outlet air flow velocity triangle and loss model; Step1.5: Calculate the isentropic change work _Li according to the thermodynamic state parameters; Step1.6: Determine whether the work balance equation L _u =L _i +L _f is established. If it is established, output the outlet airflow parameters of the current stage cascade model. If it is not established, update C _2a and return to Step1.2. 3. A one-dimensional model modeling and correction method of an axial flow compressor according to claim 2, characterized in that in the step (2), the non-design point backward angle model and the non-design point loss model modeling method as follows: Step2.1: Calculate critical angle of attack: In the formula, Ma ₁ is the relative Mach number of the inlet airflow, k ₁ and k ₂ are correction coefficients, and i ₀ is the design angle of attack; Construct a non-design point trailing angle model: In the formula, δ ₀ is the reference lagging angle, k ₃ , k ₄ , k ₅ are correction coefficients; Step2.2: The reference loss model uses the Denton/Traupel loss model to calibrate and correct the Denton/Traupel loss model: First, calculate the loss coefficient of a single cascade model: ζ＝ζ _profile +ζ _trailing +ζ _shock +ζ _tip +ζ _axial (3) In the formula, ζ _profile is the profile loss coefficient, ζ _trailing is the wake loss coefficient, ζ _shock is the shock loss coefficient, ζ _tip is the tip clearance loss coefficient, and ζ _axial is the axial torus loss coefficient; Calculate the rotor work loss: L' _f ＝ζW ₁ ² /2 (4) Calculate the work lost by the stator: The calculation formula of non-design point loss coefficient is as shown in Equation (6): In the formula, k ₆ , k ₇ , k ₈ are correction coefficients. 4. A one-dimensional model modeling and correction method of an axial flow compressor according to claim 3, characterized in that the correction method based on the PSO algorithm in step (3) is as follows: First, the PSO algorithm is used to correct the empirical coefficients of the reference loss model. The cross-sectional parameters of the design points calculated by the reference loss model are aligned with the simulation results of the three-dimensional model of the axial flow compressor. After the design points are aligned, the correction coefficients are optimized through the PSO algorithm. The value enables the non-design point performance of the axial flow compressor to be aligned with the test data.