Wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division

Through the wind tunnel PIV velocity field measurement method based on quadtree adaptive meshing, the problem of low measurement accuracy in large gradient velocity gradient flow is solved and more accurate velocity field measurement is achieved.

CN119124551BActive Publication Date: 2025-01-24AVIC SHENYANG AERODYNAMICS RES INST
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Patent Information

Application Number
CN202411585457.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-11-08
Publication Date
2025-01-24
Estimated Expiration
2044-11-08

AI Technical Summary

Technical Problem

When the existing PIV technology measures the flow of large gradient velocity gradients, it is difficult to set a globally unified fixed-side length query domain window, resulting in the calculation results losing flow details or the speed vector cannot be calculated correctly.

Method used

The wind tunnel PIV velocity field measurement method based on quad-tree adaptive meshing is used, the displacement vector field is calculated through the quad-tree adaptive mesh displacement vector field method, and the velocity field is calculated based on the calibration coefficient and the pulse laser light emission time interval.

Benefits of technology

Effectively solve the problem of liquidity details caused by the size of the fixed search domain in the large gradient flow measurement. The problem of loss and vector computing error can be used to adjust the size of the measurement domain according to the local vector displacement of the particles and improve the measurement accuracy.

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Abstract

The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division belongs to the field of wind tunnel measurement technology. In order to solve the wind tunnel PIV velocity field measurement of large gradient velocity gradient flow, the present invention builds a wind tunnel velocity field measurement system; optical path adjustment; after determining the installation position of the sheet laser head, the laser sheet light thickness is adjusted by adjusting the lens distance inside the sheet laser head to adjust the laser intensity of the dual-cavity pulse laser to adjust the image shooting effect; turn on the dual-cavity pulse laser and the dual-frame camera, and adjust the pulse laser first cavity light output and the pulse laser second cavity light output to be respectively distributed in the dual-frame exposure of the dual-frame camera; measure calibration parameters; collect dual-frame camera test images of time series; use the quadtree adaptive grid displacement vector field method to calculate the displacement vector field of the processed dual-frame camera test images; calculate the velocity field based on the displacement vector field and the calibration coefficient, and the interval between the pulse laser first cavity light output time and the pulse laser second cavity light output time.
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Description

Technical Field

[0001] The invention belongs to the technical field of wind tunnel measurement, and in particular relates to a wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division. Background Art

[0002] As a high-precision flow field measurement technology, PIV uses photography and particle tracing technology in a non-invasive way to capture the image of particle motion in the wind tunnel flow field, and then calculates and analyzes the velocity distribution in the flow field. This technology can capture the velocity field at a very high spatial and temporal resolution, which is crucial for analyzing details such as turbulent structure, vortex motion, and velocity gradient in the flow. Existing PIV technology mainly calculates the velocity field through two consecutive frames of images taken by the camera. The conventional method is to set an interrogation domain window with a fixed side length and grid the two frames of images. The estimated side length of the interrogation domain window is generally related to the displacement length of the particle in the image, which is usually 4-5 times the particle displacement. The displacement length of the particle in the image depends on the trigger interval of the dual-cavity laser set when the test system is built, and the conversion relationship between pixels and actual space length.

[0003] Under conventional velocity gradient, a globally unified fixed-length interrogation domain window can calculate the velocity field more accurately. However, in the case of flows with large velocity gradients, it is difficult to set a globally unified fixed-length value to satisfy the local particle displacement length, which makes it difficult to calculate accurately. That is, if the interrogation domain window is set too large, the calculated result will lose flow details, and if the interrogation domain window is too small, the velocity vector cannot be calculated correctly. Summary of the invention

[0004] The problem to be solved by the present invention is to solve the wind tunnel PIV velocity field measurement of large gradient velocity gradient flow, and a wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division is proposed.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division includes the following steps:

[0007] S1. Build a wind tunnel velocity field measurement system: including setting a sheet optical head above the test area of ​​the wind tunnel test section, the sheet optical head is connected to a dual-cavity pulse laser, setting a dual-frame camera at the optical observation window position of the wind tunnel test section, and setting a particle generator and a signal generator at the entrance position of the wind tunnel test section, the signal generator is used to control the dual-cavity pulse laser to emit laser;

[0008] S2. Adjustment of optical path: After determining the installation position of the laser head, adjust the thickness of the laser light sheet by adjusting the lens distance inside the laser head, and adjust the image shooting effect by adjusting the laser intensity of the dual-cavity pulse laser;

[0009] S3. Timing adjustment: Turn on the dual-cavity pulse laser and the dual-frame camera, and adjust the light output from the first cavity of the pulse laser and the light output from the second cavity of the pulse laser to be distributed in the dual-frame exposure of the dual-frame camera respectively;

[0010] S4. Measurement and calibration parameters: Place a steel ruler in the test area of ​​the wind tunnel test section. Keep the steel ruler and the laser sheet light overlapped and within the field of view of the dual-frame camera. Use the dual-frame camera to capture the steel ruler image. Measure the conversion relationship between the steel ruler scale and pixels in the steel ruler image to obtain the calibration coefficient. k ;

[0011] S5. Image acquisition: Turn on the dual-frame camera, dual-cavity pulse laser and particle generator, start the wind tunnel test, and start image acquisition after the flow field stabilizes. n A time series of dual-frame camera test images;

[0012] S6. Collected in step S5 n The time series of dual-frame camera test images are pre-processed to obtain the processed n A time series of dual-frame camera test images;

[0013] S7. The processed data obtained in step S6 n A time series of dual-frame camera test images is used to calculate the displacement vector field using a quadtree adaptive grid displacement vector field method;

[0014] S8. Based on the displacement vector field obtained in step S7 and the calibration coefficient measured in step S4 k , the interval between the pulse laser first cavity light emission time and the pulse laser second cavity light emission time set in step S3, and the velocity field is calculated.

[0015] Furthermore, in step S1, the imaging chip array captured by the dual-frame camera is set to be a square.

[0016] Furthermore, in step S2, the light thickness of the laser sheet in the area to be measured is adjusted to be less than 1 mm.

[0017] Furthermore, in step S3, the exposure time of the double-frame camera is set to m, the pulse laser first cavity light emission time is set to a through the signal generator, and the interval between the pulse laser first cavity light emission time and the pulse laser second cavity light emission time is dt.

[0018] Further, step S5 collects n Time series of dual-frame camera test images ,in, For the A frame time series image collected by a time series dual-frame camera, For the B-frame time series images collected by a time series dual-frame camera.

[0019] Furthermore, the specific implementation method of step S6 includes the following steps:

[0020] S6.1. n Time series of dual-frame camera test images , calculate the average image of the time series of frame A and the average image of the time series of frame B , , the calculation formula is:

[0021] ;

[0022] ;

[0023] S6.2. Yes , Corresponding minus , get , , then , Use the image histogram equalization algorithm to enhance the image and obtain the processed , ;

[0024] S6.3. n The time series of dual-frame camera test images are processed using the method in step S6.2 to obtain the processed n A time series of dual-frame camera test images.

[0025] Furthermore, the specific implementation method of step S7 includes the following steps:

[0026] S7.1. Collect the data obtained in step S6 , ;

[0027] S7.2. Based on the initial spatial computational domain, the calculation results obtained in step S7.1 are , Divide the domain into four equal parts to obtain four equally divided sub-computational domains and set the minimum threshold , minimum subdivision limit of space ;

[0028] S7.3. In the four sub-computational domains, the displacement lengths in the sub-computational domains are calculated sequentially by using the image cross-correlation algorithm. The image cross-correlation algorithm is to set the existing image and ,image and The expression of the mutual correlation coefficient matrix is:

[0029] ;

[0030] in, is a two-dimensional correlation matrix, in which the highest peak is the most relevant position. is the two-dimensional fast Fourier transform FFT, is the conjugate of the result after two-dimensional fast Fourier transform, is the two-dimensional inverse fast Fourier transform iFFT, is the side length of the image;

[0031] The deviation vector of the center origin position of the two-dimensional correlation matrix is ​​set as the horizontal displacement vector and the vertical displacement vector;

[0032] S7.4. Determine whether the size of the current sub-domain is smaller than the minimum spatial subdivision limit set in step S7.2 If the answer is no, then continue to execute step S7.5. If the answer is yes, then save the displacement length in the sub-computational domain to the displacement vector field, terminate the recursive segmentation, and stop the computational domain subdivision.

[0033] S7.5. Determine whether the displacement length of the current sub-computational domain obtained in step S7.3 is less than the minimum threshold set in step S7.2 If the judgment is no, save the displacement length in the sub-computational domain to the displacement vector field, terminate the recursive segmentation, and stop subdividing the computational domain. If the judgment is yes, divide the current sub-computational domain into four equal parts again and return to step S7.3;

[0034] S7.6. Determine whether all recursive sub-domain calculations are completed. If it is not, return to step S7.3. If it is, output the displacement vector field. , is the horizontal component of the displacement field, is the vertical component of the displacement field.

[0035] Furthermore, the calculation formula of step S8 is:

[0036] ;

[0037] ;

[0038] ;

[0039] in, For the i The horizontal component of the time series velocity vector, For the i The vertical component of the time series velocity vector, For the i The length of the time series velocity vector;

[0040] Then traverse the calculation , and obtain all the internal transient velocity field results of the time series.

[0041] Beneficial effects of the present invention:

[0042] The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division described in the present invention can adaptively adjust the query domain size according to the local vector displacement of the particle image, effectively solving the problem of flow detail solution loss and vector calculation error caused by fixed query domain size in large gradient flow measurement. At the same time, the velocity measurement can be carried out in a targeted manner according to the relaxation degree of the set threshold condition. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a structural schematic diagram of the wind tunnel velocity field measurement system of the present invention;

[0044] Figure 2 This is a schematic diagram of the timing control of the pulse laser and the dual-frame camera in the experiment;

[0045] Figure 3 It is a flowchart of the adaptive mesh partitioning solution algorithm based on quadtree partitioning;

[0046] Figure 4 A dynamic diagram of image adaptive meshing;

[0047] Figure 5 It is a flow chart of a wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to the present invention;

[0048] Figure 1 In the middle, 1 is the optical head, 2 is the dual-frame camera, 3 is the dual-cavity pulse laser, 4 is the signal generator, 5 is the particle generator, and 6 is the wind tunnel test section. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0050] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0051] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 -Attached Figure 5 The detailed instructions are as follows:

[0052] Embodiment 1:

[0053] A wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division includes the following steps:

[0054] S1. Build a wind tunnel velocity field measurement system: including setting a sheet optical head above the test area of ​​the wind tunnel test section, the sheet optical head is connected to a dual-cavity pulse laser, setting a dual-frame camera at the optical observation window position of the wind tunnel test section, and setting a particle generator and a signal generator at the entrance position of the wind tunnel test section, the signal generator is used to control the dual-cavity pulse laser to emit laser;

[0055] Furthermore, in step S1, the imaging chip array captured by the dual-frame camera is set to be a square.

[0056] S2. Adjustment of optical path: After determining the installation position of the laser head, adjust the thickness of the laser light sheet by adjusting the lens distance inside the laser head, and adjust the image shooting effect by adjusting the laser intensity of the dual-cavity pulse laser;

[0057] Furthermore, in step S2, the thickness of the laser sheet in the area to be tested is adjusted to be less than 1 mm; particles are appropriately placed in the area to be tested, the scattering intensity of the particles in the image taken by the dual-frame camera is observed, and the laser dual-cavity light output energy is adjusted accordingly, so that the particles in the image will not be overexposed, and the brightness will not be too low to reduce the signal-to-noise ratio.

[0058] S3. Timing adjustment: Turn on the dual-cavity pulse laser and the dual-frame camera, and adjust the light output from the first cavity of the pulse laser and the light output from the second cavity of the pulse laser to be distributed in the dual-frame exposure of the dual-frame camera respectively;

[0059] Further, in step S3, the exposure time of the double-frame camera is set to m, the time when the pulse laser first cavity emits light is set to a through the signal generator, and the interval between the time when the pulse laser first cavity emits light and the time when the pulse laser second cavity emits light is dt; the timing relationship diagram is shown in Figure 2 shown.

[0060] S4. Measurement and calibration parameters: Place a steel ruler in the test area of ​​the wind tunnel test section. Keep the steel ruler and the laser sheet light overlapped and within the field of view of the dual-frame camera. Use the dual-frame camera to capture the steel ruler image. Measure the conversion relationship between the steel ruler scale and pixels in the steel ruler image to obtain the calibration coefficient. k ;

[0061] S5. Image acquisition: Turn on the dual-frame camera, dual-cavity pulse laser and particle generator, start the wind tunnel test, and start image acquisition after the flow field stabilizes. n A time series of dual-frame camera test images;

[0062] Further, step S5 collects n Time series of dual-frame camera test images ,in, For the A frame time series image collected by a time series dual-frame camera, For the B frame time series images collected by a time series dual-frame camera;

[0063] Furthermore, after the data is collected and saved locally, the wind tunnel, particle generator, dual-cavity pulse laser and dual-frame camera are turned off.

[0064] S6. Collected in step S5 n The time series of dual-frame camera test images are pre-processed to obtain the processed n A time series of dual-frame camera test images;

[0065] Furthermore, the specific implementation method of step S6 includes the following steps:

[0066] S6.1. n Time series of dual-frame camera test images , calculate the average image of the time series of frame A and the average image of the time series of frame B , , the calculation formula is:

[0067] ;

[0068] ;

[0069] S6.2. Yes , Corresponding minus , get , , then , Use the image histogram equalization algorithm to enhance the image and obtain the processed , ;

[0070] S6.3. n The time series of dual-frame camera test images are processed using the method in step S6.2 to obtain the processed n A time series of dual-frame camera test images.

[0071] S7. The processed data obtained in step S6 n A time series of dual-frame camera test images is used to calculate the displacement vector field using a quadtree adaptive grid displacement vector field method;

[0072] Furthermore, the specific implementation method of step S7 includes the following steps:

[0073] S7.1. Collect the data obtained in step S6 , ;

[0074] S7.2. Based on the initial spatial computational domain, the calculation results obtained in step S7.1 are , Divide the domain into four equal parts to obtain four equally divided sub-computational domains and set the minimum threshold , minimum subdivision limit of space ;

[0075] S7.3. In the four sub-computational domains, the displacement lengths in the sub-computational domains are calculated sequentially by using the image cross-correlation algorithm. The image cross-correlation algorithm is to set the existing image and ,image and The expression of the mutual correlation coefficient matrix is:

[0076]

[0077] in, is a two-dimensional correlation matrix, in which the highest peak is the most relevant position. is the two-dimensional fast Fourier transform FFT, is the conjugate of the result after two-dimensional fast Fourier transform, is the two-dimensional inverse fast Fourier transform iFFT, is the side length of the image;

[0078] The deviation vector of the center origin position of the two-dimensional correlation matrix is ​​set as the horizontal displacement vector and the vertical displacement vector;

[0079] S7.4. Determine whether the size of the current sub-domain is smaller than the minimum spatial subdivision limit set in step S7.2 If the answer is no, then continue to execute step S7.5. If the answer is yes, then save the displacement length in the sub-computational domain to the displacement vector field, terminate the recursive segmentation, and stop the computational domain subdivision.

[0080] S7.5. Determine whether the displacement length of the current sub-computational domain obtained in step S7.3 is less than the minimum threshold set in step S7.2 If the judgment is no, save the displacement length in the sub-computational domain to the displacement vector field, terminate the recursive segmentation, and stop subdividing the computational domain. If the judgment is yes, divide the current sub-computational domain into four equal parts again and return to step S7.3;

[0081] S7.6. Determine whether all recursive sub-domain calculations are completed. If it is not, return to step S7.3. If it is, output the displacement vector field. , is the horizontal component of the displacement field, is the vertical component of the displacement field;

[0082] S8. Based on the displacement vector field obtained in step S7 and the calibration coefficient measured in step S4 k , the interval between the pulse laser first cavity light emission time and the pulse laser second cavity light emission time set in step S3, and the velocity field is calculated.

[0083] Furthermore, the calculation formula of step S8 is:

[0084] ;

[0085] ;

[0086] ;

[0087] in, For the i The horizontal component of the time series velocity vector, For the i The vertical component of the time series velocity vector, For thei The length of the time series velocity vector;

[0088] Then traverse the calculation , and obtain all the internal transient velocity field results of the time series.

[0089] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0090] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division, characterized in that: The steps include: S1. Build a wind tunnel velocity field measurement system: including setting a sheet optical head above the test area of ​​the wind tunnel test section, the sheet optical head is connected to a dual-cavity pulse laser, setting a dual-frame camera at the optical observation window position of the wind tunnel test section, and setting a particle generator and a signal generator at the entrance position of the wind tunnel test section, the signal generator is used to control the dual-cavity pulse laser to emit laser; S2. Adjustment of optical path: After determining the installation position of the laser head, adjust the thickness of the laser light sheet by adjusting the lens distance inside the laser head, and adjust the image shooting effect by adjusting the laser intensity of the dual-cavity pulse laser; S3. Timing adjustment: Turn on the dual-cavity pulse laser and the dual-frame camera, and adjust the light output from the first cavity of the pulse laser and the light output from the second cavity of the pulse laser to be distributed in the dual-frame exposure of the dual-frame camera respectively; S4. Measurement and calibration parameters: Place a steel ruler in the test area of ​​the wind tunnel test section. Keep the steel ruler and the laser sheet light overlapped and within the field of view of the dual-frame camera. Use the dual-frame camera to capture the steel ruler image. Measure the conversion relationship between the steel ruler scale and pixels in the steel ruler image to obtain the calibration coefficient. k ; S5. Image acquisition: Turn on the dual-frame camera, dual-cavity pulse laser and particle generator, start the wind tunnel blowing test, and start image acquisition after the flow field stabilizes. n A time series of dual-frame camera test images; S6. Collected in step S5 n The double-frame camera test images of the time series are pre-processed to obtain the processed n A time series of dual-frame camera test images; S7. The processed data obtained in step S6 n A time series of dual-frame camera test images is used to calculate the displacement vector field using a quadtree adaptive grid displacement vector field method; S8. Based on the displacement vector field obtained in step S7 and the calibration coefficient measured in step S4 k , the interval between the pulse laser first cavity light emission time and the pulse laser second cavity light emission time set in step S3, and the velocity field is calculated.

2. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 1 is characterized in that: In step S1, the imaging chip array captured by the dual-frame camera is set to be a square.

3. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 2 is characterized in that: In step S2, the thickness of the laser sheet in the area to be measured is adjusted to be less than 1 mm.

4. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 3 is characterized in that: In step S3, the exposure time of the double-frame camera is set to m, the pulse laser first cavity light emission time is set to a through the signal generator, and the interval between the pulse laser first cavity light emission time and the pulse laser second cavity light emission time is dt.

5. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 4 is characterized in that: Step S5: Collection n Time series of dual-frame camera test images ,in, For the A frame time series image collected by a time series dual-frame camera, For the B-frame time series images collected by a time series dual-frame camera.

6. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 5 is characterized in that: The specific implementation method of step S6 includes the following steps: S6.

1. n Time series of dual-frame camera test images , calculate the average image of the time series of frame A and the average image of the time series of frame B , , the calculation formula is: ; ; S6.

2. Yes , Corresponding minus , get , , then , Use the image histogram equalization algorithm to enhance the image and obtain the processed , ; S6.

3. n The time series of dual-frame camera test images are processed using the method in step S6.2 to obtain the processed n A time series of dual-frame camera test images.

7. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 6 is characterized in that: The specific implementation method of step S7 includes the following steps: S7.

1. Collect the data obtained in step S6 , ; S7.

2. Based on the initial spatial computational domain, the calculation results obtained in step S7.1 are , Divide the domain into four equal parts to obtain four equally divided sub-computational domains and set the minimum threshold , minimum subdivision limit of space ; S7.

3. In the four sub-computational domains, the displacement lengths in the sub-computational domains are calculated sequentially by using the image cross-correlation algorithm. The image cross-correlation algorithm is to set the existing image and ,image and The expression of the mutual correlation coefficient matrix is: ; in, is a two-dimensional correlation matrix, in which the highest peak is the most relevant position. is the two-dimensional fast Fourier transform FFT, is the conjugate of the result after two-dimensional fast Fourier transform, is the two-dimensional inverse fast Fourier transform iFFT, is the side length of the image; The deviation vector of the center origin position of the two-dimensional correlation matrix is ​​set as the horizontal displacement vector and the vertical displacement vector; S7.

4. Determine whether the size of the current sub-domain is smaller than the minimum spatial subdivision limit set in step S7.2 If the answer is no, then continue to step S7.

5. If the answer is yes, then save the displacement length in the sub-computational domain to the displacement vector field, terminate the recursive segmentation, and stop the computational domain subdivision. S7.

5. Determine whether the displacement length of the current sub-computational domain obtained in step S7.3 is less than the minimum threshold set in step S7.2 If the judgment is no, save the displacement length in the sub-computational domain to the displacement vector field, terminate the recursive segmentation, and stop subdividing the computational domain. If the judgment is yes, divide the current sub-computational domain into four equal parts again and return to step S7.3; S7.

6. Determine whether all recursive sub-domain calculations are completed. If it is not, return to step S7.

3. If it is, output the displacement vector field. , is the horizontal component of the displacement field, is the vertical component of the displacement field.

8. The wind tunnel PIV velocity field measurement method based on quadtree adaptive grid division according to claim 7 is characterized in that: The calculation formula of step S8 is: ; ; ; in, For the i The horizontal component of the time series velocity vector, For the i The vertical component of the time series velocity vector, For the i The length of the time series velocity vector; Then traverse the calculation , and obtain all the internal transient velocity field results of the time series.

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