CN117494566A - One-dimensional model modeling and correcting method for axial flow compressor - Google Patents
One-dimensional model modeling and correcting method for axial flow compressor Download PDFInfo
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Abstract
The invention discloses a one-dimensional model modeling and correcting method for an axial flow compressor. Firstly, a one-dimensional model of the axial flow compressor is built through a pitch diameter method step by step blade cascade, then, a non-design point lag angle and a non-design point loss model are built through a polynomial fitting method based on a design point lag angle and a reference loss model, and finally, the built one-dimensional model of the axial flow compressor is corrected step by step through a PSO algorithm, so that a model calculation result is aligned with test data. By means of the method, a corrected one-dimensional model of the axial-flow compressor is built and completed, and through simulation verification comparison, the maximum error of the compressor characteristic calculation result compared with the test result is not more than 6%, the compressor model is embedded into the whole machine performance model of the turboshaft engine to carry out simulation verification, the maximum error is not more than 4%, and the effectiveness of the method is verified.
Description
Technical Field
The invention relates to the technical field of aero-engines, in particular to a one-dimensional model modeling and correcting method for an axial flow compressor.
Background
The mathematical model of the aeroengine is a premise and a foundation for developing the analysis and prediction of the whole engine performance and the design and optimization of a control plan. With the continuous development of aviation science and technology, the requirements on the mathematical model of the aero-engine are also higher and higher. The axial flow compressor is a key component for determining the overall performance of the aeroengine, the traditional modeling method excessively depends on the characteristics of test components, the calculation requirements of the compressor on the aspects of changing guide vanes, changing blade tip gaps and the like cannot be met at present, the full three-dimensional numerical simulation calculation of the compressor based on CFD is huge in time consumption, and the method is not suitable for dynamic real-time calculation of an overall engine model.
Therefore, a method for establishing a one-dimensional mechanism model of the axial flow compressor is further researched on the basis of the characteristics of the test parts of the compressor, one-dimensional fine modeling of the axial flow compressor under the working conditions of variable guide vanes, variable blade tip clearances and the like is realized, and meanwhile, the model is required to have higher simulation precision. The current one-dimensional model modeling method for the axial flow compressor is less in research, and in the existing research, the one-dimensional model performance calculation method is mainly used for preliminary pneumatic design and performance estimation of the compressor, and further emphasizes the consistency of calculation results and test result trends, and even if the model is partially corrected, the overall simulation precision is still not high, so that the method is difficult to adapt to high-precision simulation of the overall performance of the engine.
Disclosure of Invention
The invention aims to: aiming at the problems in the background technology, firstly, a one-dimensional performance model of the axial flow compressor is established by adopting a pitch diameter method, and a non-design point lag angle and a non-design point loss model are corrected by adopting a polynomial fitting method based on design point data; on the basis, a PSO algorithm-based step-by-step correction scheme of the axial flow compressor is provided, the calculation accuracy of a one-dimensional performance model of the axial flow compressor is improved, and the requirement of high-accuracy simulation of the overall performance of the engine is met.
The technical scheme is as follows: in order to achieve the above purpose, the invention adopts the following technical scheme:
a one-dimensional model modeling and correcting method of an axial flow compressor comprises the following steps:
(1) Establishing an axial flow compressor one-dimensional model based on a pitch diameter method and geometric parameters of the axial flow compressor, wherein the axial flow compressor one-dimensional model comprises a plurality of single blade grid models, and calculating the characteristics of the axial flow compressor through the plurality of single blade grid models;
(2) Establishing a non-design point lag angle and a non-design point loss model on the basis of the design point lag angle and a reference loss model by utilizing a polynomial fitting method;
(3) And correcting the one-dimensional model of the compressor step by using a PSO algorithm, firstly correcting the empirical coefficient of a reference loss model so as to aim at the airflow parameters of each section of the design point of the compressor, and then correcting the lag angle of the non-design point and the loss model of the non-design point so as to aim at the characteristics of the compressor.
Preferably, the implementation process of the step (1) is as follows:
step1.1: taking the outlet airflow parameter of the previous stage blade grid model as the inlet airflow parameter of the current stage blade grid model, wherein the inlet airflow parameter comprises the axial speed C of inlet airflow 1a Absolute speed C 1 Absolute angle alpha 1 Relative velocity W 1 Relative angle beta 1 Mass flow m, total pressure P 1 * Static pressure P 1 Total temperature T 1 * Static temperature T 1 The method comprises the steps of carrying out a first treatment on the surface of the Calculating an attack angle i and a lag angle delta according to the inlet airflow velocity triangle, the structure of the current stage cascade model and the characteristics of the current stage cascade model, wherein the phasesFor velocity W 1 Absolute speed C 1 And a dragging speed U 1 Three sides of the triangle of inlet air flow velocity, C 1a Is the high of the inlet air flow velocity triangle, C 1a And W is 1 Is included by a relative angle beta 1 ，C 1a And C 1 Is an absolute angle alpha 1 ；
Step1.2: initial guess of axial velocity C of outlet airflow of cascade model of current stage 2a Calculating an outlet airflow velocity triangle including calculating an absolute velocity C of the current stage cascade model outlet airflow 2 Absolute angle alpha 2 Relative velocity W 2 Relative angle beta 2 The method comprises the steps of carrying out a first treatment on the surface of the Relative velocity W of the current stage cascade model outlet airflow 2 Absolute speed C 2 And a pulling speed U 2 Three sides of the triangle of outlet air flow velocity, C 2a Is the high of the outlet air flow velocity triangle, C 2a And W is 2 Is included by a relative angle beta 2 ，C 2a And C 2 Is an absolute angle alpha 2 ；
Step1.3 calculating the current stage cascade model outlet airflow parameters including calculating the total outlet airflow pressure P 2 * Static pressure P 2 Total temperature T 2 * Static temperature T 2 ；
Step1.4: calculating the rim work L according to the inlet airflow speed triangle, the outlet airflow speed triangle and the loss model u And loss work L f ；
Step1.5 calculating isentropic Change work L according to thermodynamic State parameters i ；
Step1.6 judging the work balance equation L u ＝L i +L f If yes, outputting the outlet airflow parameters of the current stage cascade model, and if not, updating C 2a Returning to Step1.2.
Preferably, the modeling method of the non-design point lag angle model and the non-design point loss model in the step (2) is as follows:
step2.1: calculating a critical attack angle:
wherein Ma 1 For inlet gas flow relative Mach number, k 1 、k 2 To correct the coefficient, i 0 To design the attack angle;
constructing a non-design point lag angle model:
in delta 0 For reference to the falling angle, k 3 、k 4 、k 5 Is a correction coefficient;
step2.2: the reference loss model adopts a Denton/Traupel loss model, and the Denton/Traupel loss model is calibrated and corrected:
first, the loss coefficients of the individual cascade model are calculated:
ζ＝ζ profile +ζ trailing +ζ shock +ζ tip +ζ axial (3)
in zeta profile Zeta is the section loss coefficient trailing Zeta is the wake loss coefficient shock Zeta is the loss factor of shock wave tip Zeta is the tip clearance loss coefficient axial Is the loss coefficient of the axial annulus;
calculating the loss work of the rotor:
L' f ＝ζW 1 2 /2 (4)
calculating stator loss work:
the calculation formula of the non-design point loss coefficient is shown as (6):
wherein k is 6 、k 7 、k 8 Is a correction coefficient.
Preferably, the correction method based on the PSO algorithm in the step (3) is as follows:
firstly, correcting an empirical coefficient of a reference loss model through a PSO algorithm, aligning each section parameter of a design point calculated by the reference loss model with a simulation result of a three-dimensional model of the axial flow compressor, and optimizing a value of the correction coefficient through the PSO algorithm after aligning the design point so as to align the performance of a non-design point of the axial flow compressor with test data.
The beneficial effects are that:
the invention provides a modeling and correcting method for a one-dimensional performance model of an axial flow compressor, which is based on a pitch diameter method and a polynomial method, and corrects the one-dimensional performance model step by step through a PSO algorithm, and has the following beneficial effects compared with the prior art:
1) Aiming at the whole aircraft engine modeling, compared with a compressor model established by the traditional dependence component characteristic diagram, the one-dimensional performance model of the compressor established by the method has more functions, such as calculating characteristic changes caused by variable guide vane and variable blade tip clearances;
2) The step-by-step correction method for the one-dimensional performance model of the axial flow compressor improves the simulation precision of the one-dimensional performance model and has engineering applicability.
Drawings
FIG. 1 is a single cascade calculation flow diagram;
FIG. 2 is a graph of design point correction front and back import and export parameter errors;
FIG. 3 is a compressor vane adjustment plan view;
FIG. 4 is a graph comparing the calculated characteristics of the model after correction with the experimental characteristics;
FIG. 5 is a graph of simulation and test data errors for a modified engine complete machine model.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
The invention provides a one-dimensional model modeling and correcting method of an axial flow compressor, and the specific modeling method is shown in figure 1.
Step (1), establishing a single cascade one-dimensional model based on a pitch diameter method and geometric parameters of the compressor, wherein the input of the cascade model is the airflow parameters output by the last stage of cascade model, and the characteristic calculation of the whole compressor is completed through the step-by-step calculation of the cascade model;
step (2), establishing a non-design point lag angle and a non-design point loss model based on the design point lag angle and a reference loss model by utilizing a polynomial fitting method;
and (3) correcting the one-dimensional model of the compressor step by utilizing a PSO algorithm, firstly correcting the empirical coefficient of a reference loss model so as to aim at the airflow parameters of each section of the design point of the compressor, and then correcting the lag angle of the non-design point and the loss model of the non-design point so as to aim at the characteristics of the compressor.
The single blade cascade one-dimensional model building process according to the step (1) comprises the following steps:
step1, taking the outlet airflow parameters of the previous stage blade cascade as the input parameters of the inlet of the current stage blade cascade, such as the axial speed C of the inlet airflow 1a Absolute speed C 1 Absolute angle alpha 1 Relative velocity W 1 Relative angle beta 1 Mass flow rate m total pressure P 1 * Static pressure P 1 Total temperature T 1 * Static temperature T 1 And (3) carrying out the process of (1) carrying out the process of (2. Calculating an attack angle i and a lag angle delta according to the inlet speed triangle and the blade grid structure and characteristics;
step2, first guess of the axial velocity C of the airflow at the blade cascade outlet 2a Calculating an outlet airflow velocity triangle including an outlet airflow absolute velocity C 2 Absolute angle alpha 2 Relative velocity W 2 Relative angle beta 2 ；
Step3 calculating the cascade outlet airflow parameters including the total outlet airflow pressure P 2 * Static pressure P 2 Total temperature T 2 * Static temperature T 2 ；
Step4: calculating the rim work L according to the inlet and outlet speed triangle and the loss model u And loss work L f ；
Step5, calculating according to thermodynamic state parametersIsentropic change work L i ；
Step6, judging the work balance equation L u ＝L i +L f If yes, outputting the current blade grid outlet section airflow parameters, and if not, updating C 2a Returning to Step2.
The modeling method of the non-design point falling angle model and the non-design point loss model in the step (2) is as follows:
step (2.1) of calculating the non-design point falling angle according to the magnitude of the attack angle by referring to a classical non-design point falling angle model in combination with the cascade characteristic line and combining the attack angle and the relative Mach number of the inlet airflow.
First, a critical attack angle is calculated
Wherein Ma 1 For inlet gas flow relative Mach number, k 1 ，k 2 To correct the coefficient, i 0 To design the angle of attack.
The calculation of the non-design point lag angle is divided into two parts according to the critical attack angle,
in delta 0 For reference to the falling angle, k 3 ，k 4 ，k 5 Is a correction coefficient.
(2.2) reference loss model Debton/Traupel loss model, which takes into account several different loss mechanisms and avoids the use of a large amount of empirical data, has a wide range of applications, but requires calibration corrections to the model.
First, a critical attack angle is calculated
Wherein Ma 1 To get inRelative Mach number, k of the mouth flow 1 、k 2 To correct the coefficient, i 0 To design the angle of attack.
The calculation of the non-design point lag angle is divided into two parts according to the critical attack angle,
in delta 0 For reference to the falling angle, k 3 、k 4 、k 5 Is a correction coefficient.
(2.2) reference loss model Debton/Traupel loss model, which takes into account several different loss mechanisms and avoids the use of a large amount of empirical data, has a wide range of applications, but requires calibration corrections to the model.
First, a loss coefficient is calculated:
ζ＝ζ profile +ζ trailing +ζ shock +ζ tip +ζ axial (19)
in zeta profile Zeta is the section loss coefficient trailing Zeta is the wake loss coefficient shock Zeta is the loss factor of shock wave tip Zeta is the tip clearance loss coefficient axial Is the loss coefficient of the axial annulus.
Calculating the loss work of the rotor:
L' f ＝ζW 1 2 /2 (20)
calculating stator loss work:
the separation of the flow at the trailing edge is caused when the cascade deviates from the design point, which in turn leads to an increase in flow losses, so that the non-design point loss model herein considers the influence of angle of attack and inlet mach number on the loss coefficient on the basis of the reference model. The non-design point loss coefficient calculation formula is shown as 22:
wherein k is 6 、k 7 、k 8 Is a correction coefficient.
The step model correction method based on PSO algorithm in the step (3) is as follows:
firstly, correcting experience coefficients of a reference loss model through a PSO algorithm, and aligning parameters of each section of a design point calculated by the model with simulation results of the three-dimensional model. When the design points are aligned, optimizing the value of the correction coefficient k through a PSO algorithm, so that the performance of the non-design points of the air compressor is aligned with the test data, and the reference loss model can be corrected in a small range. The processing mode reduces the particle dimension involved in the single optimizing process of the PSO optimizing algorithm, and greatly improves the optimizing speed and optimizing effect.
In order to verify the effectiveness of the one-dimensional model modeling and correction method of the axial flow compressor, a certain five-stage transonic axial flow compressor is selected for modeling, the compressor comprises zero-stage adjustable guide vanes, and the front two stages of stator blade cascades are adjustable. According to the method, a one-dimensional model of the axial flow compressor is established and corrected, firstly, experience coefficients in a reference loss model are corrected by using a PSO optimization algorithm to align design points, and the calculation results of the one-dimensional model and the numerical simulation errors of the three-dimensional model of rotor inlet and outlet section airflow parameters of the design points before and after correction are shown in the figure. As can be seen from fig. 2, the calculation error of the one-dimensional model of the compressor before correction is within an acceptable range, which indicates that the reference loss model has strong applicability to the established axial flow compressor. The error of the inlet and outlet section of the rotor after correction is within 2%, the error of the design point-pressure ratio is 0.2%, the error of isentropic efficiency is 1.8%, and the design point parameter alignment effect is good.
The adjustment rule of the zero-order guide vanes and the first two rows of guide vanes of the axial flow compressor is shown in figure 3 under different rotating speeds. Inputting the regulation rule of the guide vane of the air compressor in the graph to a one-dimensional model of the air compressor after the design point correction, and continuously applying a PSO optimization algorithm to the correction coefficient (k) on the basis of the corrected reference loss model 1 ...k 8 ) Optimizing to correct off-design point lag angle modelAnd (3) a non-design point loss model, so that all correction on the one-dimensional model is completed.
The pair of the corrected one-dimensional model characteristic calculation result and the test result of the compressor is shown in fig. 4. Compared with the test result, the calculated result of the one-dimensional model of the air compressor established and corrected in the method has the maximum relative error of the pressure ratio of 5.7 percent when the speed of rotation is 95 percent; the maximum relative error in isentropic efficiency occurs at 100% rotational speed at 2.6%. In general, the calculated result and the test result have the same trend, the error is smaller, and the precision is obviously higher than that of the one-dimensional model program of most of the current compressors.
Taking a certain type of turboshaft engine as an example, on the basis of a one-dimensional model of an axial flow compressor, a typical part model of the engine is built in a supplementary mode, and the method mainly comprises the following steps: six parts including an air inlet channel, a centrifugal compressor, a combustion chamber, a gas turbine, a power turbine and a tail nozzle are finally formed into a complete machine performance calculation model of the turboshaft engine. The centrifugal compressor, the gas turbine and the power turbine all adopt the characteristics of test parts to build mathematical models, and the axial flow compressor part adopts the one-dimensional performance model built in the process.
The test working condition of the whole engine is sea level standard day, and the fuel quantity is a design value. The rotating speed np of the power turbine is changed to be 85% and 100% of the design value respectively, meanwhile, the angle of the guide vane of the axial flow compressor is adjusted to conduct bench test run, and the performance data of the whole engine is recorded. The calculation result of the whole engine model and the actual measurement parameters of the engine bench test run such as output power Ne, gas generator rotating speed ng and total inlet temperature T of the power turbine 45 As shown in the error comparison graph, the simulation error of the whole turbine performance model of the turboshaft engine embedded with the one-dimensional model of the axial flow compressor is not more than 4% and the error precision requirement of the whole turbine performance simulation of the engine is met.
Claims (4)
1. The one-dimensional model modeling and correcting method for the axial flow compressor is characterized by comprising the following steps of:
(1) Establishing an axial flow compressor one-dimensional model based on a pitch diameter method and geometric parameters of the axial flow compressor, wherein the axial flow compressor one-dimensional model comprises a plurality of single blade grid models, and calculating the characteristics of the axial flow compressor through the plurality of single blade grid models;
(2) Establishing a non-design point lag angle and a non-design point loss model on the basis of the design point lag angle and a reference loss model by utilizing a polynomial fitting method;
(3) And correcting the one-dimensional model of the compressor step by using a PSO algorithm, firstly correcting the empirical coefficient of a reference loss model so as to aim at the airflow parameters of each section of the design point of the compressor, and then correcting the lag angle of the non-design point and the loss model of the non-design point so as to aim at the characteristics of the compressor.
2. The method for modeling and correcting a one-dimensional model of an axial flow compressor according to claim 1, wherein the implementation process of the step (1) is as follows:
step1.1: taking the outlet airflow parameter of the previous stage blade grid model as the inlet airflow parameter of the current stage blade grid model, wherein the inlet airflow parameter comprises the axial speed C of inlet airflow 1a Absolute speed C 1 Absolute angle alpha 1 Relative velocity W 1 Relative angle beta 1 Mass flow m, total pressure P 1 * Static pressure P 1 Total temperature T 1 * Static temperature T 1 The method comprises the steps of carrying out a first treatment on the surface of the Calculating an attack angle i and a lag angle delta according to the inlet airflow velocity triangle, the structure of the current stage cascade model and the characteristics of the current stage cascade model, wherein the relative velocity W 1 Absolute speed C 1 And a dragging speed U 1 Three sides of the triangle of inlet air flow velocity, C 1a Is the high of the inlet air flow velocity triangle, C 1a And W is 1 Is included by a relative angle beta 1 ，C 1a And C 1 Is an absolute angle alpha 1 ；
Step1.2: initial guess of axial velocity C of outlet airflow of cascade model of current stage 2a Calculating an outlet airflow velocity triangle including calculating an absolute velocity C of the current stage cascade model outlet airflow 2 Absolute angle alpha 2 Relative velocity W 2 Relative angle beta 2 The method comprises the steps of carrying out a first treatment on the surface of the Relative velocity W of the current stage cascade model outlet airflow 2 Absolute speed C 2 And a pulling speed U 2 Three sides of the triangle of outlet air flow velocity, C 2a Is the high of the outlet air flow velocity triangle, C 2a And W is 2 Is included by a relative angle beta 2 ，C 2a And C 2 Is an absolute angle alpha 2 ；
Step1.3 calculating the current stage cascade model outlet airflow parameters including calculating the total outlet airflow pressure P 2 * Static pressure P 2 Total temperature T 2 * Static temperature T 2 ；
Step1.4: calculating the rim work L according to the inlet airflow speed triangle, the outlet airflow speed triangle and the loss model u And loss work L f ；
Step1.5 calculating isentropic Change work L according to thermodynamic State parameters i ；
Step1.6 judging the work balance equation L u ＝L i +L f If yes, outputting the outlet airflow parameters of the current stage cascade model, and if not, updating C 2a Returning to Step1.2.
3. The method for modeling and correcting a one-dimensional model of an axial compressor according to claim 2, wherein the modeling method for the non-design-point lag angle model and the non-design-point loss model in the step (2) is as follows:
step2.1: calculating a critical attack angle:
wherein Ma 1 For inlet gas flow relative Mach number, k 1 、k 2 To correct the coefficient, i 0 To design the attack angle;
constructing a non-design point lag angle model:
in delta 0 For reference to the falling angle, k 3 、k 4 、k 5 Is a correction coefficient;
step2.2: the reference loss model adopts a Denton/Traupel loss model, and the Denton/Traupel loss model is calibrated and corrected:
first, the loss coefficients of the individual cascade model are calculated:
ζ＝ζ profile +ζ trailing +ζ shock +ζ tip +ζ axial (3)
in zeta profile Zeta is the section loss coefficient trailing Zeta is the wake loss coefficient shock Zeta is the loss factor of shock wave tip Zeta is the tip clearance loss coefficient axial Is the loss coefficient of the axial annulus;
calculating the loss work of the rotor:
L' f ＝ζW 1 2 /2 (4)
calculating stator loss work:
the calculation formula of the non-design point loss coefficient is shown as (6):
wherein k is 6 、k 7 、k 8 Is a correction coefficient.
4. The method for modeling and correcting a one-dimensional model of an axial compressor according to claim 3, wherein the correction method based on the PSO algorithm in the step (3) is as follows:
firstly, correcting an empirical coefficient of a reference loss model through a PSO algorithm, aligning each section parameter of a design point calculated by the reference loss model with a simulation result of a three-dimensional model of the axial flow compressor, and optimizing a value of the correction coefficient through the PSO algorithm after aligning the design point so as to align the performance of a non-design point of the axial flow compressor with test data.
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