Method for quantitatively analyzing vortex intensity based on velocity gradient characteristics

Abstract

The invention belongs to the technical field of hydromechanics vortex recognition and analysis, and relates to a method for quantitatively analyzing vortex intensity based on velocity gradient characteristics, which comprises the following steps of: 1, inputting three-dimensional flow field velocity distribution data; 2, calculating the speed gradient tensor of each grid point; 3, solving a characteristic value and a characteristic vector of the velocity gradient tensor; 4, extracting a vortex core line of the flow field vortex, and a characteristic value and a characteristic vector of a velocity gradient tensor at the vortex core line; and 5, performing continuous quantitative analysis on the vortex intensity at the vortex core line by analyzing the characteristic value and the characteristic vector to obtain quantitative analysis of the vortex evolution process. According to the method, the technical defects of subjective misjudgment, pseudo vortex interference and incapability of quantizing intensity distribution caused by manual setting of an experience threshold in an existing vortex identification method are overcome, and threshold-independent objective identification and continuous intensity quantitative analysis of flow field vortexes are realized.

Description

Technical Field

[0001] This invention belongs to the field of fluid vortex identification and analysis technology, and relates to a method for quantitatively analyzing vortex intensity based on velocity gradient characteristics. Background Technology

[0002] Current vortex identification primarily relies on vorticity criteria (such as the vorticity criterion) (see Jeong & Hussain, JFM 1995), which uses a preset empirical threshold (such as Q>0.01) to binarize the region where vortices exist. However, this method has the following fundamental drawbacks:

[0003] (1) Subjectivity and instability: The selection of threshold lacks mathematical theoretical basis, and slight changes (such as Q>0.005→0.02) lead to a misjudgment rate of vortex structure >30% (Graftieaux et al., JFM 2001); (2) Lack of quantification function and poor analyzability: It can only mark the spatial range of vortex and cannot output continuous intensity index, resulting in poor quantification and analysis of vortex evolution process; (3) Insufficient anti-interference ability: In the strong shear environment such as the internal flow field of turbomachinery, the velocity gradient tensor is disturbed by the shear flow and is prone to generating pseudo vortices.

[0004] In view of this, this invention is hereby proposed. Summary of the Invention

[0005] The purpose of this invention is to overcome the technical defects of existing vortex identification methods, such as subjective misjudgment, pseudo-vortex interference, and inability to quantify intensity distribution caused by manually set empirical thresholds. This invention provides a quantitative analysis method for vortex intensity based on velocity gradient tensor feature analysis, so as to achieve threshold-independent objective identification and continuous intensity quantitative analysis of flow field vortices.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] This invention provides a method for quantitatively analyzing vortex intensity based on velocity gradient characteristics, comprising the following steps:

[0008] Step 1: Input the three-dimensional flow field velocity distribution data;

[0009] Step 2: Calculate the velocity gradient tensor for each grid point;

[0010] Step 3: Solve for the eigenvalues ​​and eigenvectors of the velocity gradient tensor;

[0011] Step 4: Extract the vortex core lines of the flow field vortices, and the eigenvalues ​​and eigenvectors of the velocity gradient tensor at the vortex core lines;

[0012] Step 5: Perform continuous quantitative analysis of vortex intensity at the vortex core line by analyzing eigenvalues ​​and eigenvectors to obtain a quantitative analysis of the vortex evolution process.

[0013] Furthermore, in step 4, the vortex core lines are extracted using the eigenmode analysis method of FieldView.

[0014] Furthermore, MATLAB was used to calculate the eigenvalues ​​and eigenvectors of the velocity gradient tensor at the vortex core line location.

[0015] Furthermore, in step 5, the intensity characteristics of the vortex are analyzed by combining the eigenvalues ​​of the linear velocity tensor along the vortex core and the variation of the axial velocity of the vortex core.

[0016] Furthermore, in step 5, the vortex development is divided into four stages. In the first stage of vortex development, v r >0, v cr <0, the angular velocity of the vortex core increases; in the second stage of vortex development, v r >0, v cr >0, the vortex core rotational angular velocity does not change significantly; in the third stage of vortex development, at the position where the axial velocity is zero, the vortex breaks up; in the fourth stage of vortex development, v r <0, v cr >0 indicates that the vortex core exhibits both axial and radial diffusion, and the vortex core's rotational angular velocity decreases rapidly.

[0017] Furthermore, the maximum rotational angular velocity of the vortex core is 117, the maximum axial dimensionless velocity is 1.527E-02, and the maximum axial acceleration is 3.165E+01.

[0018] Furthermore, the method for quantitatively analyzing vortex intensity based on velocity gradient characteristics is applicable to the quantitative assessment of vortex intensity in high angle-of-attack flow fields of aircraft and internal flow fields of turbomachinery.

[0019] Compared with the prior art, the present invention has the following beneficial effects:

[0020] 1. Threshold-independent objective identification: Vortex identification is achieved by extracting vortex core lines from the flow field, eliminating human intervention and resulting in high accuracy;

[0021] 2. Continuous intensity quantification capability: Constructs a continuous quantification analysis index for vortex intensity based on eigenvalues ​​and eigenvectors, outputs the distribution of vortex quantification eigenvalues ​​along the vortex core line, and accurately characterizes the vortex core quantification evolution process;

[0022] 3. Improved engineering applicability: Suppresses pseudo-vortices in strong shear flow fields (such as turbomachinery), supporting accurate analysis of vortex energy dissipation. Attached Figure Description

[0023] The accompanying drawings are incorporated in and form part of this specification, and together with the description serve to explain the principles of the invention.

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a distribution diagram of the dimensionless v velocity of the vortex core line in this invention;

[0026] Figure 2 This is a distribution diagram of the eigenvalues ​​of the vortex core linear velocity gradient tensor of the present invention. Detailed Implementation

[0027] Exemplary embodiments will now be described in detail. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples consistent with some aspects of the invention as detailed in the appended claims.

[0028] This invention provides a method for quantitatively analyzing vortex intensity based on velocity gradient characteristics, see appendix. Figure 1-2 As shown, it includes the following steps:

[0029] Step 1: Input the three-dimensional flow field velocity distribution data.

[0030] Step 2: Calculate the velocity gradient tensor for each grid point.

[0031] Step 3: Solve for the eigenvalues ​​and eigenvectors of the velocity gradient tensor.

[0032] Step 4: Extract the vortex core line of the flow field vortex, and the eigenvalues ​​and eigenvectors of the velocity gradient tensor at the vortex core line.

[0033] Specifically, the eigenmode analysis method of Fieldview is used to extract vortex cores, and the flow field variables such as the position, velocity, and velocity gradient tensor of the vortex cores are exported to a file.

[0034] Step 5: Perform continuous quantitative analysis of vortex intensity at the vortex core line by analyzing eigenvalues ​​and eigenvectors to obtain a quantitative analysis of the vortex evolution process.

[0035] Specifically, MATLAB was used to calculate the eigenvalues ​​and eigenvectors of the velocity gradient tensor at the vortex core line. The characteristics of the vortex were then analyzed by combining the eigenvalues ​​of the velocity tensor along the vortex core line with the variation of the vortex core axial velocity.

[0036] According to an embodiment of the present invention, the axial dimensionless velocity distribution and the vortex core linear velocity gradient tensor eigenvalue distribution are obtained. Figure 1-2 From this, we can see that in the first stage of vortex development, vr >0, v cr <0, the angular velocity of the vortex core increases; in the third stage of vortex development, v r >0, v r >0, the vortex core rotational angular velocity does not change significantly; in the fourth stage of vortex development, at the position where the axial velocity is zero, the vortex breaks up; in the fifth stage of vortex development, v r <0, v cr >0 indicates that the vortex core exhibits both axial and radial diffusion, and its rotational angular velocity decreases rapidly. The maximum rotational angular velocity of the vortex core is 117, the maximum dimensionless axial velocity is 1.527E-02, and the maximum axial acceleration is 3.165E+01.

[0037] The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics provided by this invention is applicable to the quantitative assessment of vortex intensity in high angle-of-attack flow fields of aircraft and internal flow fields of turbomachinery.

[0038] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.

[0039] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for quantitatively analyzing vortex intensity based on velocity gradient characteristics, characterized in that, Includes the following steps: Step 1: Input the three-dimensional flow field velocity distribution data; Step 2: Calculate the velocity gradient tensor for each grid point; Step 3: Solve for the eigenvalues ​​and eigenvectors of the velocity gradient tensor; Step 4: Extract the vortex core lines of the flow field vortices, and the eigenvalues ​​and eigenvectors of the velocity gradient tensor at the vortex core lines; Step 5: Perform continuous quantitative analysis of vortex intensity at the vortex core line by analyzing eigenvalues ​​and eigenvectors to obtain a quantitative analysis of the vortex evolution process.

2. The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics according to claim 1, characterized in that, In step 4, the vortex core lines are extracted using the eigenmode analysis method of FieldView.

3. The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics according to claim 1, characterized in that, The eigenvalues ​​and eigenvectors of the velocity gradient tensor at the location of the vortex core line are calculated using MATLAB.

4. The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics according to claim 1, characterized in that, In step 5, the intensity characteristics of the vortex are analyzed by combining the eigenvalues ​​of the linear velocity tensor along the vortex core and the variation of the axial velocity of the vortex core.

5. The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics according to claim 1, characterized in that, In step 5, the vortex development is divided into four stages. In the first stage of vortex development, v r >0, v cr <0, the angular velocity of the vortex core increases; in the second stage of vortex development, v r >0, v cr >0, the vortex core rotational angular velocity does not change significantly; in the third stage of vortex development, at the position where the axial velocity is zero, the vortex breaks up; in the fourth stage of vortex development, v r <0, v cr >0 indicates that the vortex core exhibits both axial and radial diffusion, and the vortex core's rotational angular velocity decreases rapidly.

6. The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics according to claim 1, characterized in that, The vortex core has a maximum rotational angular velocity of 117°, a maximum dimensionless axial velocity of 1.527E-02, and a maximum axial acceleration of 3.165E+01.

7. The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics according to any one of claims 1-6, characterized in that, The method for quantitatively analyzing vortex intensity based on velocity gradient characteristics is applicable to the quantitative assessment of vortex intensity in high angle-of-attack flow fields of aircraft and internal flow fields of turbomachinery.

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