CN114117318B - Pneumatic probe one-dimensional self-adaptive grid node measurement method based on least square method - Google Patents
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Abstract
The invention discloses a method for measuring one-dimensional self-adaptive grid nodes of a pneumatic probe based on a least square method, which comprises the steps of carrying out linear interpolation reconstruction on a one-dimensional flow field pressure preliminary distribution value to obtain an integral pressure distribution construction function of each pressure measurement hole on the pneumatic probe, then calculating residual errors between an actual measurement value of each measurement node and a linear interpolation predicted value obtained by utilizing the construction function one by using the least square method, removing the measurement node with the least influence on the residual errors one by one, reaching a final self-adaptive measurement grid node, carrying out final actual high-precision measurement, carrying out static measurement on each node on the grid, and forming integral pressure distribution by using the measurement value of each measurement node. According to the invention, in the self-adaptive process, the measurement points can be directly subjected to redistribution calculation, and meanwhile, the final measurement points can be determined after preliminary measurement and calculation, so that the self-adaptive calculation is not required to be performed again for the refined measurement results, and the measurement time can be further reduced.
Description
Technical Field
The invention relates to the technical field of gas turbine engine impeller machinery fine test, in particular to a pneumatic probe measuring method, which is a pneumatic probe one-dimensional self-adaptive grid node measuring method based on a least square method.
Background
Modern gas turbine engines have to be optimally designed for the performance of the impeller mechanical blades in the design stage in order to obtain as high efficiency as possible. To understand the flow characteristics of the vane flow channels to provide guidance for vane design, porous pneumatic probes are required to measure flow field parameters in the vane channels and downstream of the vanes. A sufficiently dense measurement grid is typically required for accurate capture of the flow structure, but this in turn increases the measurement time, so a balance often needs to be found in measurement accuracy and measurement time. If the number of measuring points is increased at the complex flowing position, the number of measuring points is reduced in the smooth flowing area, and the self-adaptive measuring grid mechanism can reduce the measuring time and can measure more working conditions in the blade grid and the stage under the condition that a certain measuring precision of a complex flowing structure is ensured.
The current research on the adaptive technology of the measurement grid is still in a preliminary stage internationally. Lenherr et al propose a two-dimensional measurement grid generation technique based on a coarse equidistant initial grid. The initial grid population must be thick enough so that the measurement time is short enough, while thin in the flow complex areas in order to capture important flow field information. Thereafter, during the fine rest measurement, the grid is gradually refined, overall from coarse to fine, according to specific detection criteria related to local gas flow angle and pressure gradient. Another approach, proposed by Franken and Ivey, also starts flow adaptive measurements by coarse equidistant grids in the circumferential and radial directions. Also provided that the coarse two-dimensional grid is sufficiently fine to contain the primary features of the flow field. After the preliminary measurement, the grid is refined, creating a grid with twice the density for probe measurement. In the next step, the previous mesh is interpolated by thin plate splines to a denser mesh spacing and the difference for each point on the mesh is calculated. The areas where the difference value between the two grids is larger than the minimum threshold are further refined.
Both methods do not involve adaptive redistribution of points, since they simply bisect the distance between two adjacent points if specified refinement criteria are met. Another feature is the need for grid refinement during the measurement process and calculation of the detection criteria for the flow parameters based on the stationary fine measurement results of the probe. These all make the measurement points of the measurement grid not more efficient to perform in refinement, and the overall measurement time is reduced to a limited extent, failing to fully exploit the characteristics of the adaptive measurement grid.
Disclosure of Invention
According to the problems, the invention provides the pneumatic probe one-dimensional self-adaptive grid node measuring method based on the least square method, the measuring points can be directly subjected to redistribution calculation in the self-adaptive process, meanwhile, the final measuring points can be determined after preliminary measurement and calculation, the self-adaptive calculation is not required to be performed on the refined measuring results, and the measuring time can be further reduced.
The technical scheme adopted by the invention for achieving the aim of the invention is as follows:
The method is characterized in that the measurement points can be directly subjected to redistribution calculation, and meanwhile, the final measurement points can be fixed after preliminary measurement and calculation, the adaptive calculation is not needed to be performed on the refined measurement results, and the measurement time can be further reduced, and the method at least comprises the following steps:
SS1. pretreatment: performing rapid front scanning and back scanning in a one-dimensional flow field by using a pneumatic probe, and performing phase correction to obtain the primary distribution of the pressure of the one-dimensional flow field;
SS2. Linear interpolation: based on the one-dimensional flow field pressure preliminary distribution value measured in the step SS1, carrying out linear interpolation reconstruction on each two adjacent measuring nodes to obtain an integral pressure distribution construction function of each pressure measuring hole on the pneumatic probe;
Ss3. remove the least-affected measurement node to the residual: calculating residual errors between an actual measured value of each measuring node and a linear interpolation predicted value obtained by using a constructor one by using a least square method, traversing all the measuring nodes, judging whether the residual error of each measuring node reaches a maximum preset threshold one by one, deleting a certain measuring node if the residual error of the measuring node is smaller than the maximum preset threshold, and reserving the measuring node if the residual error of the measuring node is larger than the maximum preset threshold;
SS4, repeating the steps SS 2-SS 3 until the residual errors of all reserved measurement nodes integrally reach a maximum preset threshold value to obtain a final self-adaptive measurement grid node, and entering the step SS5;
And SS5, performing final actual high-precision measurement by utilizing the self-adaptive measurement grid nodes obtained in the step SS4, performing stationary measurement on each node on the grid, wherein the total number of grid nodes is minimum at the moment, and enough measurement nodes can be ensured at the position with severe pressure change, so that the total pressure distribution measurement result has high fidelity, and finally the measured value of each measurement node can form the total pressure distribution.
Preferably, in step SS1, the pneumatic probe is a five-hole pneumatic probe.
Preferably, in step SS2, each two adjacent measurement nodes perform linear interpolation reconstruction by the following reconstruction function:
Where P j (τ) represents a linear interpolation constructor, τ represents an intermediate coordinate value, τ j represents a current measurement point coordinate value, τ j+1 represents a next measurement point coordinate value, y (τ j) represents a current point measurement value, and y (τ j+1) represents a next point measurement value.
Preferably, in the above step SS3, the residual RES between the actual measurement value of the measurement node and the linear interpolation prediction value obtained by using the constructor is calculated according to the following formula:
Where p k denotes the current measurement pressure port number, p 0 denotes the probe No. 0 measurement pressure port, p 4 denotes the probe No. 4 measurement pressure port, Representing the measurement value of the kth measurement pressure hole at the ith position measurement point,/>Representing the linear interpolation prediction of the kth measured pressure orifice at the ith position measurement point.
According to the method for measuring the one-dimensional self-adaptive grid nodes of the pneumatic probe based on the least square method, the rough spatial distribution of flow field pressure is rapidly measured through a pretreatment process. Then constructing a piecewise function by utilizing a least square principle, so that the constructed approximation function approximates to the actual measured value, wherein the least square principle formula is as follows:
in the formula (1), f represents an approximation function fitted according to the measurement points, v (f) represents approximation, y represents a function value of the measurement points, The independent variable of the selected measuring point is represented, i represents the number of the selected measuring point, and m represents the total number of the selected measuring points.
The method for constructing the function adopts a linear interpolation method for reconstruction, and the linear interpolation method still has a stable effect under the condition of less intermediate construction nodes. In the construction process, firstly, nodes are taken equidistantly, and the construction interpolation method is as follows:
In the formula (2), P j (τ) represents a linear interpolation constructor, τ represents an intermediate coordinate value, τ j represents a current measurement point coordinate value, τ j+1 represents a next measurement point coordinate value, y (τ j) represents a current point measurement value, and y (τ j+1) represents a next point measurement value.
After the construction is finished, when the construction function is subjected to iterative improvement, setting the residual error between the construction function and an actual measurement point as a standard, and defining as follows:
In the formula (3), RES represents the residual error between the construction function and the actual measurement point, p k represents the number of the current measurement pressure hole, p 0 represents the measurement pressure hole of the probe No. 0, p 4 represents the measurement pressure hole of the probe No. 4, Representing the measurement value of the kth measurement pressure hole at the ith position measurement point,/>Representing the linear interpolation prediction of the kth measured pressure orifice at the ith position measurement point.
And finally, carrying out iterative deletion on the nodes in the construction function, wherein each iterative process needs to traverse all the nodes to obtain the node with the least influence on residual errors after deleting the node, and deleting the node. And stopping deleting until the residual reaches the maximum threshold set by people, wherein the obtained node is the self-adaptive measurement grid point.
Compared with the prior art, the pneumatic probe one-dimensional self-adaptive grid node measuring method based on the least square method has the following characteristics:
1) The scheme is simple and easy to realize: the measuring equipment is the same as the original measuring equipment, and the measuring speed which is about 20 percent higher than that of the original measuring method can be realized only by adding the steps of quick measurement and least square method reconstruction calculation.
2) Good generalization: by measuring the pressure distribution of various objects, the self-adaptive scheme is adopted to measure the pressure and other parameters, and has higher measurement accuracy and certain speed improvement.
3) And the testing precision is high: the reconstruction value obtained by the self-adaptive scheme has high approximation degree with the original distribution, and the final measurement result obtained by self-adaptive measurement node distribution is ensured to have high accuracy.
Drawings
Fig. 1 is a schematic diagram of a five-hole pneumatic probe structure, in which,The total pressure probe hole is ①、③ -YAW, the left and right YAW probe holes are ②、④ -PITCH, and the upper and lower PITCH probe holes are provided.
Fig. 2 is a schematic diagram of the superposition result after the rapid front-sweep and back-sweep and the phase correction in the pretreatment process of the present invention.
FIG. 3 is a schematic diagram showing the result of the present invention after linear reconstruction of all the predicted pressure holes and point deletion.
Fig. 4 is a schematic diagram of the distribution of measurement nodes after the final adaptation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention become more apparent, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are intended to be illustrative of the invention and should not be construed as limiting the invention in any way. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
FIG. 1 shows a five-hole pneumatic probe used in the measurement process of the invention, wherein five pressure holes are respectively a total pressure probe hole, a left yaw probe hole, a right yaw probe hole, an upper pitch probe hole and a lower pitch probe hole, and the five-hole pneumatic probe performs one-dimensional measurement along the circumferential direction of the five-hole pneumatic probe, so that an adaptive measurement grid point is required to be obtained.
Fig. 2 shows the superposition result of the rapid front sweep and back sweep (i.e. the measurement is traversed from left to right and the transient measurement is traversed from right to left in the one-dimensional coordinate system) and the phase correction in the preprocessing process of the invention, which can provide a standard for the adaptive interpolation calculation in the next step.
Fig. 3 is a schematic result of the present invention after linear reconstruction of all pressure hole predicted pressures and point deletion.
Fig. 4 shows the distribution of the measurement nodes after the final adaptation.
The invention relates to a method for measuring one-dimensional self-adaptive grid nodes of a pneumatic probe based on a least square method, which mainly comprises the following steps:
1) And (5) pretreatment. And (3) performing rapid front scanning and back scanning (namely traversing measurement from left to right and traversing transient measurement from right to left in a one-dimensional coordinate system) in a flow field by using a five-hole pneumatic probe, and performing phase correction to obtain the primary distribution of flow field pressure. The reason for this is that the probe has a delayed response during the pressure-to-pressure step change during the transient continuous measurement, so that the measurement phase difference can be seen from fig. 2 (a) for the results of the front and back sweeps. In order to obtain correct pressure distribution, phase correction is needed, the specific method is that the same measuring point obtained by front scanning and back scanning carries out arithmetic average on the abscissa, namely the corrected abscissa position is obtained, and the corrected result is the preliminary distribution of flow field pressure;
2) And (3) using a linear interpolation method to carry out linear interpolation reconstruction calculation on the flow field pressure preliminary distribution value measured in the step (1) by using each two adjacent points to obtain an integral pressure distribution construction function of each pressure measurement point (p 0、p1、p2、p3、p4) on the probe, wherein each two adjacent points carry out linear interpolation reconstruction calculation by using the following reconstruction functions:
Where P j (τ) represents a linear interpolation constructor, τ represents an intermediate coordinate value, τ j represents a current measurement point coordinate value, τ j+1 represents a next measurement point coordinate value, y (τ j) represents a current point measurement value, and y (τ j+1) represents a next point measurement value;
3) The measurement node that has least impact on the residual is removed. Calculating residual RES between an actual measured value of each measuring node and a linear interpolation predicted value obtained by using a constructor one by using a least square method, traversing all the measuring nodes, judging whether the residual of each measuring node reaches a maximum preset threshold one by one, deleting a certain measuring node if the residual of the measuring node is smaller than the maximum preset threshold, and reserving the measuring node if the residual of the measuring node is larger than the maximum preset threshold, wherein the residual RES between the actual measured value of the measuring node and the linear interpolation predicted value obtained by using the constructor is calculated according to the following formula:
Where p k denotes the current measurement pressure port number, p 0 denotes the probe No. 0 measurement pressure port, p 4 denotes the probe No. 4 measurement pressure port, Representing the measured value/>, of the kth measured pressure hole at the ith position measurement pointA linear interpolation predicted value of a measurement point of a kth measurement pressure hole at an ith position is represented;
4) Repeating the steps 2) and 3) until the residual error of all reserved measurement nodes integrally reaches a maximum preset threshold value, and obtaining a final self-adaptive measurement grid node to enter the step 5);
5) And 3) carrying out final actual high-precision measurement by utilizing the self-adaptive measurement grid nodes obtained in the step 4), namely carrying out static measurement on each node on the grid. The total number of the grid nodes is relatively minimum, and enough measuring points can be ensured at the position with severe pressure change, so that the total pressure distribution measuring result has high fidelity. And finally, the measured value of each node can form the integral pressure distribution.
The object of the present invention is fully effectively achieved by the above-described embodiments. Those skilled in the art will appreciate that the present invention includes, but is not limited to, those illustrated in the drawings and described in the foregoing detailed description. While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims.
Claims (4)
1. The method is characterized in that the measurement points can be directly subjected to redistribution calculation, and meanwhile, the final measurement points can be fixed after preliminary measurement and calculation, the adaptive calculation is not needed to be performed on the refined measurement results, and the measurement time can be further reduced, and the method at least comprises the following steps:
SS1, pretreatment: performing rapid front scanning and back scanning in a one-dimensional flow field by using a pneumatic probe, and performing phase correction to obtain the primary distribution of the pressure of the one-dimensional flow field;
SS2. Linear interpolation: based on the one-dimensional flow field pressure preliminary distribution value measured in the step SS1, carrying out linear interpolation reconstruction on each two adjacent measuring nodes to obtain an integral pressure distribution construction function of each pressure measuring hole on the pneumatic probe;
SS3. Remove the least-affected measurement node to residual: calculating residual errors between an actual measured value of each measuring node and a linear interpolation predicted value obtained by using a constructor one by using a least square method, traversing all the measuring nodes, judging whether the residual error of each measuring node reaches a maximum preset threshold one by one, deleting a certain measuring node if the residual error of the measuring node is smaller than the maximum preset threshold, and reserving the measuring node if the residual error of the measuring node is larger than the maximum preset threshold;
SS4, repeating the steps SS 2-SS 3 until the residual error of all reserved measurement nodes integrally reaches a maximum preset threshold value to obtain a final self-adaptive measurement grid node, and entering a step SS5;
And SS5, carrying out final actual high-precision measurement by utilizing the self-adaptive measurement grid nodes finally obtained in the step SS4, carrying out static measurement on each node on the grid, and forming integral pressure distribution by the measured value of each measurement node.
2. The method for measuring a one-dimensional adaptive mesh node of a pneumatic probe based on the least square method according to claim 1, wherein in the step SS1, the pneumatic probe is a five-hole pneumatic probe.
3. The method for measuring the one-dimensional adaptive mesh node of the air probe based on the least square method according to claim 1, wherein in the step SS2, each two adjacent measurement nodes are linearly interpolated and reconstructed by the following reconstruction function:
In the method, in the process of the invention, Representing a linear interpolation constructor,/>Representing intermediate coordinate values,/>Representing the current measurement point coordinate value,/>Representing the next measurement point coordinate value,/>Representing the current point measurement value,/>Representing the next point measurement value.
4. The method for measuring a one-dimensional adaptive mesh node of a pneumatic probe based on the least square method according to claim 1, wherein in the step SS3, a residual error between an actual measurement value of the measurement node and a linear interpolation prediction value obtained by using a constructor is calculated according to the following formula:
In the method, in the process of the invention, Representing the current measured pressure hole number,/>Represents a probe number 0 measurement pressure hole,/>Represents a probe No. 4 measurement pressure hole,/>Representing the measurement value of the kth measurement pressure hole at the ith position measurement point,/>Representing the linear interpolation prediction of the kth measured pressure orifice at the ith position measurement point.
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| US4560873A (en) * | 1983-06-17 | 1985-12-24 | Lear Siegler, Inc. | Situ multi-channel combustion gas analyzer |
| CN110851929A (en) * | 2019-11-15 | 2020-02-28 | 中国科学院工程热物理研究所 | Two-dimensional leaf-type optimization design method and device based on self-adaptive grid |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4560873A (en) * | 1983-06-17 | 1985-12-24 | Lear Siegler, Inc. | Situ multi-channel combustion gas analyzer |
| CN110851929A (en) * | 2019-11-15 | 2020-02-28 | 中国科学院工程热物理研究所 | Two-dimensional leaf-type optimization design method and device based on self-adaptive grid |
Non-Patent Citations (2)
| Title |
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| 亚声速条件下五孔探针非线性插值计算方法研究;史远鹏;王佳璐;陆华伟;孔晓治;王宇;;风机技术;20200826(04);全文 * |
| 来流湍流度对超高负荷低压涡轮附面层流动控制手段的影响;孙爽;李伟;雷志军;卢新根;付宇;朱俊强;;航空动力学报;20160705(07);全文 * |
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