CN114117665A - Method for calibrating empirical model of axial flow compressor under S2 flow surface frame - Google Patents

Method for calibrating empirical model of axial flow compressor under S2 flow surface frame Download PDF

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CN114117665A
CN114117665A CN202111344337.0A CN202111344337A CN114117665A CN 114117665 A CN114117665 A CN 114117665A CN 202111344337 A CN202111344337 A CN 202111344337A CN 114117665 A CN114117665 A CN 114117665A
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王春雪
张明亮
王大磊
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Beijing Power Machinery Institute
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Abstract

A calibration method for an empirical model of an axial flow compressor under an S2 flow surface frame belongs to the technical field of pneumatic analysis of compressors. The method can calibrate various empirical models of a plurality of blade rows on different spanwise positions on the meridian plane under various working conditions, so that the calibrated models can realize high-precision performance analysis basically consistent with test data. The required data volume and the calibration difficulty are reduced according to a physical mechanism, and all data can be completely obtained from a component test; the method has the advantages of simple operation, short calibration process period, easy calling of the calibrated model and the like, can consider the influence of the span-wise position, and is suitable for multiple working condition points.

Description

Method for calibrating empirical model of axial flow compressor under S2 flow surface frame
Technical Field
The invention relates to an empirical model calibration method for an axial flow compressor under an S2 flow surface frame, belongs to the technical field of pneumatic analysis of the axial flow compressor, and particularly relates to model calibration, high-precision performance analysis, test data analysis and the like for S2 flow surface analysis problems based on a streamline curvature method or other related methods.
Background
In a typical axial flow compressor design system, the design and analysis of one-dimensional and S2 flow surfaces occupy important positions in the design system, so the accuracy of the analysis of the low-dimensional means greatly influences the calculation accuracy of the multi-stage axial flow compressor.
Low dimensional analysis is generally based on flow and enthalpy conservation, while axial and circumferential momentum equations are omitted, the impact of which is taken into account by empirical loss and lag angle models; meanwhile, in low-dimensional analysis, the viscosity of the fluid is generally ignored, the viscosity influence of the blade surface is considered in a loss model, and the viscosity influence of the end wall is mostly expressed as thickening of the boundary layer of the end wall and can be considered by introducing a blocking factor. Obviously, these empirical loss, drop angle and blockage factor models directly determine the accuracy of the calculations, and therefore the accuracy of the empirical model is critical in the compressor 1D/S2 analysis.
The empirical model used in axial flow compressors is a multifactor, strongly coupled, nonlinear system. Firstly, the blade geometric parameters of the axial flow compressor are not uniform. In the early stage, traditional leaf types such as NACA 65, C4, BC6 and the like are mostly adopted; the Double Circular Arc (DCA) and (MCA) leaf profiles were introduced later; with the increase of the calculation level, the controllable diffusion leaf profile (CDA) is widely applied; at present, based on the popularization of computer optimization, obtaining a computer-generated leaf profile based on an optimization technology in the industry becomes a standard practice. These profiles have different profile coordinates and overall geometric characteristics such as maximum relative thickness, consistency, chord length, bend angle, stagger angle, and leading and trailing edge thickness. To fully define a profile, sometimes as many as 30 parameters are required. Such high geometric complexity poses significant difficulties for modeling. Secondly, the performance of the blade profile is closely related to the operating conditions. The loss and the clearance angle of the airfoil are affected by parameters such as Re, Ma, and the angle of attack. Under different working conditions, these parameters are different, so that the blade profile performance (loss, drop clearance, working range, etc.) is also greatly different. In addition, the flow mechanism of the vane is complicated and changeable. The inlet and outlet conditions directly affect the blade profile loss, such as inlet blockage B, axial velocity-density ratio (AVDR), etc.; complex secondary flow and turbulent mixing exist in the blade all the time, and different influences are brought to blade profiles at different spanwise positions; the interaction of main flows and leakage flows of tip clearances, end wall boundary layers, upstream blade trails, non-uniform incoming flows, twisted boundary layers and the like can make the accurate modeling of blade flow extremely difficult.
With the development of Computational Fluid Dynamics (CFD), researchers have increasingly understood the flow inside the blade, but even the most advanced and complex flow models, such as the unsteady Navier-Stokes equation or the large vortex simulation (LES), cannot be said to fully describe the flow map of the blade, let alone the simplified empirical model applied in low-dimensional modeling.
The pneumatic design of the axial flow compressor is a process from low dimension to high dimension, from simple to complex and gradual, and the reasonable simplification of the blade flow model in the low dimension becomes more critical to obtain the available empirical model. The complexity of modeling and the limited availability of data make existing models difficult to generalize, i.e., there is no universally available empirical model with engineering accuracy.
Disclosure of Invention
In order to solve the problem of calibrating an empirical model in the analysis of the positive problem of the S2 flow surface of the multistage axial flow compressor, the problems that a standard empirical model is low in precision, difficult to adjust and incapable of being used in multiple working conditions are solved. A method for calibrating an empirical model of a multistage axial-flow compressor under an S2 flow surface frame is provided. The method is a simple and comprehensive model calibration method, and can calibrate different empirical models at different blade rows and different spanwise positions on the meridian under different working conditions, so that the calibrated model can realize high-precision performance analysis basically consistent with test data.
The technical scheme adopted by the invention is as follows: a calibration method for an empirical model of an axial flow compressor under a two-dimensional flow surface frame comprises the following steps:
(1) defining a reference flow mrefAnd a reference rotational speed nrefThe method is used for non-dimensionalization of flow and rotating speed in the calibration process;
in the whole calibration process, the dimensionless flow is measured
Figure BDA0003353428040000031
And dimensionless rotational speed
Figure BDA0003353428040000032
Determining the working condition point of each blade profile section;
(2) calibration of end wall plugging factor B
For a certain operating point, the end wall blockage factor B at any one computing station iiThe calibration process is as follows:
firstly, inputting the blade row loss and the falling angle data obtained by the test under the working condition, and inputting the static pressure or the average meridian speed of the end wall of the casing on the ith station; the result meeting the static pressure of the end wall of the casing is obtained by adjusting the blocking factor of the station and combining with the complete radial balance equation to solve, and the blocking factor is the corresponding value B of the test statei，exp；
Secondly, calculating to obtain a corresponding model blocking factor B by adopting a standard end wall boundary layer model on the calculation stationi，modObtaining the correction quantity delta B of the blocking factor under the working conditioni；
Thirdly, the calibration process is carried out under different working conditions, and the change relation of the correction quantity of the blocking factor along with the working conditions is obtained:
Figure BDA0003353428040000033
when the working condition is determined, obtaining the corresponding correction quantity of the blocking factor according to the correction relation;
(3) calibration of loss and drop angle
For a certain working condition, the loss and the fall angle of the jth flow line of the blade row n are corrected as follows: firstly, an experience model is adopted to calculate the experience loss under the working condition
Figure BDA0003353428040000034
And empirical drop angle deltanj，calA value; ② according to the test, the obtained test loss
Figure BDA0003353428040000035
And test drop angle deltanj，expValue, calculating the correction amount of the corresponding loss and the falling angle
Figure BDA0003353428040000036
And deltanj；
And thirdly, carrying out the process on different working conditions to obtain the current blade row loss and the change of the correction of the fall angle along with the working conditions:
Figure BDA0003353428040000037
Figure BDA0003353428040000038
wherein
Figure BDA0003353428040000039
Representing the spanwise position, representing the influence of the streamline position;
after the calibration of the end wall blocking factor B and the loss and the drop clearance angle is finished, the whole model calibration process is finished;
(4) application of calibrated model
A certain operating condition
Figure BDA0003353428040000041
At the outlet of the blade row n, corresponding to the calculation station i and the streamline position
Figure BDA0003353428040000042
The correction of the empirical model is obtained by the following relation:
Figure BDA0003353428040000043
Figure BDA0003353428040000044
Figure BDA0003353428040000045
for plugging factor correction, at any operating point pair
Figure BDA0003353428040000046
Carrying out bilinear interpolation;
due to losses and drop clearance concerns
Figure BDA0003353428040000047
An independent variable for starting all the working points
Figure BDA0003353428040000048
Is interpolated and then converted into
Figure BDA0003353428040000049
Figure BDA00033534280400000410
Then to
Figure BDA00033534280400000411
And carrying out bilinear interpolation processing to finish the application of the calibrated model.
The method solves the problem of model parameter coupling by step calibration in combination with the physical working characteristics of the cascade, considers the data requirement of the S2 flow surface analysis problem and the test data obtained by the test of the compressor part or high-precision numerical calculation, integrates the common numerical solving technology (taking a streamline curvature method as an example, the method is also suitable for other solving methods such as a matrix method, a time propulsion method and the like), and comprehensively provides the mathematical definition and the calibration flow of the calibration problem of the compressor empirical model.
In the calculation process of the positive flow surface problem of the multistage axial flow compressor S2 (see the attached figure 2), 3 empirical models are involved, namely: loss model, lag angle model and end wall boundary layer blockage model, so the total pressure loss coefficient of the object calibrated by the model, namely the blade row
Figure BDA00033534280400000412
A drop angle δ, and a plugging factor B. While
Figure BDA00033534280400000413
And δ is a quantity related to the cascade characteristic, and the endwall boundary layer plugging factor is related to only endwall region flow conditions, so these 3 parameters can be calibrated in two steps to reduce the non-linear effect between the calibrated dependent parameters and the calibrated parameters.
For any operating condition, the specific calibration process (see fig. 3) is as follows: (1) in the S2 flow front problem, the total pressure loss and the lagging angle distribution obtained by inputting test data or high-precision simulation are used for determining the correction quantity delta B of the end wall plugging factoriWhere i is the computing station number; (2) in the S2 flow front problem, the calibrated B is inputiDetermining correction of loss and drop angle
Figure BDA0003353428040000051
And
Figure BDA0003353428040000052
where n is the blade row designation and j is the streamline designation. And (4) carrying out the calibration process on each working condition point to obtain the change of all correction data along with the working condition.
If the calibrated empirical model is used, only correction data of different working conditions are needed to be added, the structure of an original calculation program is not needed to be changed, and unified operation can be performed. When the calculated working condition is not the calibrated working condition, bilinear interpolation is carried out according to the rotating speed and the flow rate, and then the corresponding correction quantity can be determined.
The invention has the following effects:
in the prior art, calibration researches on empirical models are few, and few researches are mainly based on one-dimensional models, influence factors of all models are coupled together and considered uniformly, and optimization techniques are generally used for obtaining optimized model parameters. The method is difficult to be popularized to a two-dimensional situation (such as an S2 flow surface), so that a plurality of flow lines exist at the moment, the optimization not only needs data quantity which exceeds the actual acquirable quantity, but also the optimization time is greatly prolonged, and even an optimization result can not be obtained. The method adopts a step-by-step calibration method, reduces the required data volume and the calibration difficulty according to a physical mechanism, can completely obtain all data from a component test, has the advantages of simple operation, short calibration process period, easy calling of a calibrated model and the like, can consider the influence of the span-wise position, and is suitable for multiple working condition points.
Drawings
FIG. 1 is an aerodynamic design flow of an axial compressor.
Fig. 2 is a grid and numbering system for the S2 flow surface.
Fig. 3 is a flow surface model calibration process of S2.
FIG. 4 is a loss calibration for blade row R1.
FIG. 5 is a drop angle calibration of blade row R1.
FIG. 6 is a comparison of total pressure ratios before and after calibration of a two-stage compressor model.
FIG. 7 is a comparison of adiabatic efficiency before and after calibration for a two-stage compressor model.
Detailed Description
The following describes the use of the model calibration method of the present invention by taking a certain two-stage compressor as an example. The three aspects of the input data, the calibration process and the use of the calibrated model will be introduced.
Inputting data
Because the calibration is mainly carried out on the calculation of the S2 positive problem, the input data comprises two parts, one part is the data of a flow channel required by the calculation of the S2 flow surface, the geometric data of the blades (such as geometric characteristic parameters of inlet and outlet blade angles, maximum thickness, consistency, radius change and the like at different spread positions of each row of blades), the boundary conditions of working conditions and the like; the other part of the test data is test data for model calibration or high-precision numerical simulation data, including total temperature, total pressure, static pressure, meridional velocity, total velocity and the like, and the parameters can be converted into total pressure loss coefficients, drop relief angles and the like by combining geometric parameters of the blades, and the plugging factors corresponding to the test working conditions can be obtained through parameters of static pressure of the end wall or average meridional velocity and the like.
The calibration data may be experimental data or data obtained by processing high dimensional results (e.g. 3 DCFD). The requirements for calibration data are to cover all operating conditions, to take into account radial distribution, and to be as accurate as possible. The experimental data are used as an example to illustrate that the high-dimensional numerical simulation results are similar.
Calibration process
(1) First, a reference flow m is definedrefAnd a reference rotational speed nrefFor non-dimensionalization of flow and speed during calibration, so that non-dimensional flow is obtained during the entire calibration
Figure BDA0003353428040000061
And dimensionless rotational speed
Figure BDA0003353428040000062
The operating point of each profile section is determined.
(2) Calibration of end wall plugging factor B
As mentioned above, the invention adopts a step calibration method to reduce the influence factors and the nonlinearity degree of calibration. Since the general test is difficult to directly measure the plugging factor, the plugging factor under the test condition is obtained by calculation. For a certain operating point, the end wall blockage factor B at any one computing station iiThe calibration process is as follows: firstly, inputting all the blade row loss and fall angle data obtained by the test under the working condition, thus eliminatingThe coupling effect of the loss and the drop clearance angle and the blocking factor is realized; the static pressure (or average meridional velocity, and other relevant parameters) at the end wall of the casing at station i is input. According to the normal calculation process of the S2 positive problem, the calculated casing and the given value may be unequal, at the moment, the result meeting the static pressure of the casing can be obtained by adjusting the blocking factor of the station and combining with the complete radial balance equation to solve, and the blocking factor at the moment is the corresponding value B of the test statei，exp. Secondly, a standard end wall boundary layer model is adopted on the computing station, and a corresponding blocking factor B can be obtained through calculationi，calSo as to obtain the blocking factor correction quantity delta B under the working conditioni. Thirdly, the process is carried out under different working conditions, and the change relation of the correction quantity of the blocking factor along with the working conditions can be obtained
Figure BDA0003353428040000071
When the working condition is determined, the corresponding correction quantity of the blocking factor can be obtained according to the correction relation.
(3) Calibration of loss and drop angle
After the calibration of the blocking factor is completed, the calibration of the loss and lag angle models can be performed, and the correction quantity of the blocking factor is used all the time in the calibration process. For a certain working condition, the loss and the fall angle of the jth flow line of the blade row n are corrected as follows: firstly, an empirical model is adopted to calculate the loss under the working condition
Figure BDA0003353428040000072
And the clearance angle deltanj，calThe value is obtained. ② losses from tests
Figure BDA0003353428040000073
And the clearance angle deltanj，expValue, calculating corresponding loss and fall angle correction
Figure BDA0003353428040000074
And deltanj. Carrying out the above process for different working conditionsThe current blade row loss and the falling angle correction can be changed along with the working condition
Figure BDA0003353428040000075
Figure BDA0003353428040000076
Wherein
Figure BDA0003353428040000077
Representing the spanwise position, the effect of the streamline position is shown.
After the above process is completed, the whole model calibration process is completed.
(4) Use of calibrated model
After the model is calibrated, corresponding correction data can be generated, and the data can be stored as a data file and used when the calibrated model is required to be called subsequently. To a certain working condition
Figure BDA0003353428040000078
At the outlet of the blade row n, corresponding to the calculation station i and the streamline position
Figure BDA0003353428040000079
The correction of the empirical model can be obtained by the following relation:
Figure BDA00033534280400000710
Figure BDA00033534280400000711
Figure BDA00033534280400000712
for the factor of cloggingCorrection, at any operating point, to
Figure BDA0003353428040000081
Carrying out bilinear interpolation; since the loss and the fall angle relate to 3 independent variables, all working points can be firstly processed
Figure BDA0003353428040000082
Is interpolated, thus converting into
Figure BDA0003353428040000083
Figure BDA0003353428040000084
Interpolation similar to the occlusion factor correction can be used.
The calibration effect of the model calibration process applied to a certain two-stage compressor is shown in fig. 4 to 7. The corrected characteristic line is closer to the experimental result, so that the engineering requirement can be met, and the universality and the effectiveness of the invention are fully explained.

Claims (1)

1. A calibration method for an empirical model of an axial flow compressor under an S2 flow surface frame is characterized by comprising the following steps:
(1) defining a reference flow mrefAnd a reference rotational speed nrefThe method is used for non-dimensionalization of flow and rotating speed in the calibration process;
in the whole calibration process, the dimensionless flow is measured
Figure FDA0003353428030000011
And dimensionless rotational speed
Figure FDA0003353428030000012
Determining the working condition point of each blade profile section;
(2) calibration of end wall plugging factor B
For a certain operating point, the end wall blockage factor B at any one computing station iiThe calibration process is as follows:
firstly, inputting the blade row loss and the falling angle data obtained by the test under the working condition, and inputting the static pressure or the average meridian speed of the end wall of the casing on the ith station; the result meeting the static pressure of the end wall of the casing is obtained by adjusting the blocking factor of the station and combining with the complete radial balance equation to solve, and the blocking factor is the corresponding value B of the test statei，exp；
Secondly, calculating to obtain a corresponding model blocking factor B by adopting a standard end wall boundary layer model on the calculation stationi，modObtaining the correction quantity delta B of the blocking factor under the working conditioni；
Thirdly, the calibration process is carried out under different working conditions, and the change relation of the correction quantity of the blocking factor along with the working conditions is obtained:
Figure FDA0003353428030000013
when the working condition is determined, obtaining the corresponding correction quantity of the blocking factor according to the correction relation;
(3) calibration of loss and drop angle
For a certain working condition, the loss and the fall angle of the jth flow line of the blade row n are corrected as follows:
firstly, an experience model is adopted to calculate the experience loss under the working condition
Figure FDA0003353428030000014
And empirical drop angle deltanj，calA value;
② according to the test, the obtained test loss
Figure FDA0003353428030000015
And test drop angle deltanj，expValue, calculating the correction amount of the corresponding loss and the falling angle
Figure FDA0003353428030000016
And deltanj；
And thirdly, carrying out the process on different working conditions to obtain the current blade row loss and the change of the correction of the fall angle along with the working conditions:
Figure FDA0003353428030000021
Figure FDA0003353428030000022
wherein
Figure FDA0003353428030000023
Representing the spanwise position, representing the influence of the streamline position;
after the calibration of the end wall blocking factor B and the loss and the drop clearance angle is finished, the whole model calibration process is finished;
(4) application of calibrated model
A certain operating condition
Figure FDA0003353428030000024
At the outlet of the blade row n, corresponding to the calculation station i and the streamline position
Figure FDA0003353428030000025
The correction of the empirical model is obtained by the following relation:
Figure FDA0003353428030000026
Figure FDA0003353428030000027
Figure FDA0003353428030000028
for plugging factor correction, at any operating point pair
Figure FDA0003353428030000029
Carrying out bilinear interpolation;
due to losses and drop clearance concerns
Figure FDA00033534280300000210
An independent variable for starting all the working points
Figure FDA00033534280300000211
Is interpolated and then converted into
Figure FDA00033534280300000212
Figure FDA00033534280300000213
Then to
Figure FDA00033534280300000214
And carrying out bilinear interpolation processing to finish the application of the calibrated model.
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