A method for measuring wall friction spatiotemporal signal in turbulent field

Abstract

This invention belongs to the field of fluid measurement technology, specifically relating to a method for measuring the spatiotemporal signal of wall friction in a turbulent flow field. It includes: S1: acquiring a time-series particle image; S2: extracting near-wall region particle images from the time-series particle images; S3: determining a query window with spatiotemporal resolution; S4: using the query window with spatiotemporal resolution to obtain the velocity at each measurement point in the near-wall region; S5: fitting the near-wall region velocity distribution with spatiotemporal resolution; S6: using the velocity distribution fitting to obtain the spatiotemporal wall friction signal. This invention designs a method for measuring the spatiotemporal signal of wall friction in a flow field, possessing resolution in both space and time.

Description

Technical Field

[0001] This invention belongs to the field of fluid measurement technology, specifically relating to a method for measuring the spatiotemporal signal of wall friction in a turbulent flow field. Background Technology

[0002] In turbulent boundary layers, complex turbulent coherent structures exist, which generate significant velocity gradients at the flat plate wall, thus altering the wall friction at the boundary layer. Accurate measurement of frictional drag is crucial for research on turbulence and drag reduction control.

[0003] Currently, methods for measuring frictional resistance can be broadly categorized into two types: direct measurement and indirect measurement. Direct measurement methods utilize sensitive components to directly measure frictional resistance on the fluid surface. This method is simple to operate but requires high-quality components, and its accuracy is easily affected by mechanical manufacturing and installation. Indirect measurement methods rely on the strong shear force at the wall surface, measuring the influence of this shear force on physical quantities to indirectly deduce frictional resistance. The hot-wire method is a commonly used indirect method for measuring frictional resistance. This method offers high accuracy, but heat loss at the wall surface can affect the experiment, and it can also interfere with the flow field.

[0004] Currently, the near-wall velocity distribution calculated in the field of PIV particle image velocimetry has too low resolution, cannot reflect the complex velocity gradient in the near-wall region, and will produce huge errors. Existing algorithms also cannot guarantee that the spatial and temporal resolution of wall friction resistance is satisfied at the same time. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for measuring the spatiotemporal signal of wall friction in a turbulent flow field.

[0006] The present invention adopts the following technical solution: a method for measuring the spatiotemporal signal of wall friction in a turbulent field, comprising: S1: acquiring time-series particle images; S2: extracting near-wall region particle images from the time-series particle images; S3: determining a query window with spatiotemporal resolution; S4: using the query window with spatiotemporal resolution to obtain the velocity of each measurement point in the near-wall region; S5: fitting the near-wall region velocity distribution with spatiotemporal resolution; S6: using the velocity distribution fitting to obtain the spatiotemporal wall friction signal.

[0007] Step S1 is as follows:

[0008] The laser and high-speed camera are controlled synchronously using a signal synchronizer; the computer is equipped with a high-speed image acquisition card to connect to the camera and store data images, which are acquired through a particle image velocimeter; the high-speed camera captures the flow field region below the flat plate, and the computer uses the particle image velocimeter to send control signals to the laser and high-speed camera for exposure through the signal synchronizer. After acquiring the exposure data, the high-speed camera transmits the particle image back to the computer for storage.

[0009] Step S2 is as follows:

[0010] Select 0< The viscous subfield with a value <5 is considered as the near-wall region of the flow field, in which... This represents the dimensionless height of the wall normal at the internal scale, and Where y is the distance from the wall normal height, Indicates the wall friction speed. v It represents the kinematic viscosity of the fluid; the physical spatial information y is converted into corresponding pixel information in the image through pixel resolution and then extracted.

[0011] Step S3 is as follows:

[0012] S31: In the particle image of the near-wall region, set a query window and query area with spatiotemporal resolution according to the flow conditions in the flow field;

[0013] S32: Determine whether the query window contains sufficient particle grayscale information;

[0014] S33: If the query window meets the conditions, determine the spatiotemporal resolution of the query window;

[0015] If the query window does not meet the conditions, expand the spatial scale of the query window or increase the time scale and repeat steps S32 and S33 until the query window meets the conditions.

[0016] Expanding the query window spatial scale means increasing the flow distance and normal distance of the query window while maintaining the original image sequence, thereby increasing the query area of ​​the query window and increasing the particle information in that area;

[0017] Increasing the time scale, or increasing the number of image sequences, allows for the addition of particle information from multiple images in the query region while maintaining the original query region area unchanged.

[0018] In S32, sufficient particle grayscale information is obtained from 4-5 particles.

[0019] In S33, when the required flow field information emphasizes temporal resolution, the spatial size of the query window is enlarged, and a query window with a flow direction dimension much larger than the normal dimension is selected. This achieves the technical effect of sufficient particle information in the query area at high temporal resolution. When the required flow field information emphasizes spatial resolution, an image sequence is added, and the query window is set to the same position in each image of the image sequence. This achieves the technical effect of sufficient particle information at high spatial resolution. Furthermore, both methods can be used in combination to achieve particle information that achieves both high spatial and temporal resolution.

[0020] Step S4 is as follows:

[0021] Calculate the interval based on the defined spatiotemporal scale query window and query region. Image correlation values ​​of particle images in the flow direction and normal direction;

[0022] Based on the pixel position of the maximum value of the particle image correlation value , Find each query window in the near-wall region. displacement after motion ;

[0023] The actual displacement is obtained by matching the pixel with the actual physical space. ;

[0024] according to Calculate the speed of each query window .

[0025] The process of calculating image correlation values ​​is as follows:

[0026]

[0027] in That is, the image correlation value, representing the normalized cross-correlation coefficient, with a range of... The cross-correlation coefficient represents the degree of similarity between image sequences during image matching. When two images are completely identical, the correlation coefficient is 1; when the grayscale distributions of the two images are completely opposite, the correlation coefficient is -1. and These represent the pixel position and the past pixel position of the query window, respectively. The possible movement after and The position after, Indicates the displacement distance of the particle image flow direction. This represents the normal displacement distance of the particle image.

[0028] Step S5 is as follows:

[0029] The velocities in the near-wall flow field under different spatiotemporal resolution query windows were calculated, and the velocities of the query windows at the same flow direction position were arranged together according to the distance from the wall normal.

[0030] Remove defective pixels;

[0031] There are n velocity points at the same location with the same flow direction. , … Where n refers to the number of query windows in the normal space, u represents the flow velocity, and y represents the normal distance. Curve fitting is performed on these n data points.

[0032] Assume the function equation is in the form of: , and For the unknown, Substituting into the equation, we get: Then, it transforms: Similarly , It can be obtained The matrix formed is in the form of: ,set up For A, For T, For k,

[0033] but

[0034]

[0035]

[0036]

[0037] The velocity is fitted to a sloped line, and the slope k of this line is calculated to replace the velocity gradient. .

[0038] Step S6 is as follows:

[0039] In 0< <5 Near-wall region, wall frictional resistance The wall friction resistance at the spatiotemporal resolution can be obtained by calculating the velocity gradient.

[0040] in Represents the wall friction resistance. Represents the velocity gradient. The coefficient of dynamic friction of the fluid medium.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) For the measurement of wall friction in flow, the present invention designs a method for measuring the spatiotemporal signal of wall friction in flow field, which has resolution in both space and time;

[0043] (2) Based on the high-quality particle image time series data of the near wall of the flow field to determine the wall friction, the present invention obtains the spatiotemporal variation signal of the flow friction. It is a non-contact, non-destructive measurement that does not interfere with the flow field. The principle is clear and the data is reliable.

[0044] (3) The measurement method described in this invention has adjustable temporal and spatial resolution of the friction signal, and the spatiotemporal scale can be flexibly adjusted according to the actual needs of the customer to meet the requirements. Attached Figure Description

[0045] Figure 1 This is a schematic flowchart of a method for measuring spatiotemporal signals of wall friction in a turbulent field, as described in an embodiment of the present invention.

[0046] Figure 2 This is a schematic diagram of PIV experimental image acquisition as described in the embodiment;

[0047] Figure 3 This is a schematic diagram of the effect of a two-dimensional particle image and a magnified view of a part of it, provided as an embodiment of the present invention;

[0048] Figure 4 Flowchart of the algorithm for determining spatiotemporal resolution;

[0049] Figure 5 This is a schematic diagram of the spatiotemporal scale.

[0050] Figure 6 This is a schematic diagram of the velocity fitting curve in the near-wall region;

[0051] Figure 7 This is a schematic diagram illustrating the change in wall friction resistance.

[0052] Figure 8 This is a schematic diagram illustrating the correlation between the frictional resistance signals of two fixed-point walls. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] This embodiment provides a method for measuring the spatiotemporal signal of wall friction in a turbulent field, such as... Figure 1 As shown, it includes:

[0055] S1: Acquire time-series particle images.

[0056] For example, the process of acquiring time-series particle images is as follows:

[0057] like Figure 2 As shown, a signal synchronizer 4 is used to synchronize the control of laser 1 and high-speed camera 2. Computer 3 is equipped with a high-speed image acquisition card, which is used to connect the camera to store data images. The two are completed through a particle image velocimeter (PIV).

[0058] High-speed camera 2 captures the flow field region below the flat plate. Computer 3 uses the PIV system to synchronize the control signal to the exposure of laser 1 and high-speed camera 2 through signal synchronizer 4. After obtaining the exposure data, high-speed camera 2 transmits the particle image back to computer 3 and stores it.

[0059] The particle concentration in the particle image should be as high as possible to facilitate subsequent calculations and ensure the accuracy of the results.

[0060] S2: Extract near-wall region particle images from time-series particle images.

[0061] For example, the process of extracting near-wall region particle images from time-series particle images is as follows:

[0062] In this embodiment, images that match the near-wall region are extracted from the particle image, such as... Figure 3 As shown. The horizontal axis represents the horizontal position in the particle image, and the vertical axis represents the vertical position in the particle image. Figure 3 In the middle, the white line at the top is y + =0 represents the flat plate region; the area below the white line is the particle distribution region; the white dashed line represents y. + =5 position, the area between the flat plate region and the white dashed line is the near-wall flow field particle region.

[0063] In the classic wall-based turbulent stratification model, based on the stratified structure of turbulence in the flow field, the turbulent boundary layer can be divided into four layers according to the different normal heights from the wall: a viscous sublayer, a buffer layer, a logarithmic layer, and a wake layer. The dimensionless wall normal height and flow velocity at the internal scale are typically represented as... and Generally, the viscous underlayer is approximately 0 < <5. Here, the viscous bottom field of view is mainly selected as the near-wall region of the flow field. The physical space information y is converted into the corresponding pixel information in the image through pixel resolution and then extracted. On this basis, programming software is used to further filter and extract the required image.

[0064] in , y is the distance from the wall's normal height. Indicates the wall friction speed. v represents the kinematic viscosity of the fluid, and u represents the flow velocity.

[0065] S3: Determine a query window with spatiotemporal resolution.

[0066] For example, such as Figure 4 As shown in Figure 5, the process of determining the spatiotemporal resolution is as follows:

[0067] Particle image velocimetry is an intelligent detection method that employs optical, non-contact, and globally quantitative techniques. It ensures accurate acquisition of the spatiotemporal signal of frictional resistance, maximizing both spatial and temporal resolution while providing sufficient grayscale information. A query window and query area with spatiotemporal resolution are configured, with the query window size being x pixel × y pixel × n(t).

[0068] Where x pixel represents the pixel in the flow direction, y pixel represents the pixel in the normal direction, and n(t) represents the particle image sequence.

[0069] To determine the grayscale information of the experimentally captured images, it is advisable to aim for an image containing approximately 4-5 particles. If this requirement is not met, the spatiotemporal resolution is determined. Methods include:

[0070] (1) Expand the query window by x pixel × y pixel, sacrificing temporal resolution;

[0071] (2) Increase the time series n(t) at the expense of time resolution.

[0072] When measuring near-wall regions, because these regions contain large velocity gradients, it is common practice to choose a query window with a flow dimension much larger than the normal dimension when expanding the query window spatial scale. Simultaneously, when increasing the time scale n(t), the query window is set to the same x pixel × y pixel location in each image of the image sequence. For example... Figure 5 As shown, in the 1st, 3rd, and 5th... …… The same position in the particle image is selected in the query window of x pixel × y pixel, and the query area is at the 2nd, 4th, and 6th positions. …… Cross-correlation is performed at the same locations in the particle image.

[0073] S4: Use the spatiotemporal resolution query window to obtain the velocity of each measurement point in the near-wall region.

[0074] For example, based on the determined spatiotemporal scale of the query window and query region, the interval is calculated using a cross-correlation algorithm. Image correlation values ​​of particle images under particle flow direction displacement and particle normal displacement:

[0075]

[0076] in That is, the image correlation value, representing the normalized cross-correlation coefficient, with a range of... The cross-correlation coefficient represents the degree of similarity between image sequences during image matching. When two images are completely identical, the correlation coefficient is 1; when the grayscale distributions of the two images are completely opposite, the correlation coefficient is -1. and These represent the pixel position and the past pixel position of the query window, respectively. The possible movement after and The position after, Indicates the displacement distance of the particle image flow direction. This represents the normal displacement distance of the particle image. , This represents the average grayscale matrix of the particle images in the query window. , These represent the standard deviations of the grayscale matrix for each image;

[0077] Based on the pixel location of the maximum correlation value in the particle image, calculate each query window in the near-wall region. The actual physical displacement s of the subsequent motion, and then using Calculate the speed of each query window. .

[0078] S5: Fitting of near-wall velocity distribution with spatiotemporal resolution.

[0079] For example, the fitting process for the near-wall velocity distribution with spatiotemporal resolution is as follows:

[0080] The velocities in the near-wall flow field under different spatiotemporal resolution query windows were calculated. The velocities of the query windows at the same flow direction location were grouped together according to their distance from the wall normal. Bad points were eliminated according to the 3σ criterion. Using the least squares method, it was found that there were 20 velocity points at the same flow direction location. , … Where 20 refers to the number of query windows in the normal space, u represents the flow velocity, and y represents the normal distance. Curve fitting needs to be performed on these 20 data points. Observation shows that it approximates a linear function. Assume the function equation is in the form of: , and For the unknown, if we take Substituting into the equation, we get: Then, it transforms: Similarly For i=1,2…10, we can obtain Therefore, they can be combined into a matrix form:

[0081] Assuming For A, For T, For k

[0082]

[0083]

[0084]

[0085]

[0086] The velocity is fitted to a sloped line, and the slope k of this line is calculated to replace the velocity gradient. ;

[0087] in This represents the velocity gradient.

[0088] Figure 6 This is a schematic diagram of the near-wall region velocity distribution fitting process in an embodiment of this application. Figure 6 In the diagram, the vertical axis represents the normal distance from the wall, the horizontal axis represents the flow velocity, the black dots represent data points obtained using the measurement method of this embodiment, and the black line u=ky represents the fitted straight line. Figure 6 It can be seen that there is a good fit and consistency between the black dots and the black lines.

[0089] S6: Obtain the spatiotemporal wall friction signal by fitting the velocity distribution.

[0090] For example, the process of obtaining the spatiotemporal wall friction signal is as follows:

[0091] like Figure 7 The diagram shows the variation of wall friction. The horizontal axis indicates the flow direction. This represents the dimensionless representation of the flow direction distance, where x represents the flow direction distance. The vertical axis represents the boundary layer thickness, and the vertical axis represents the wall friction resistance ratio. This represents the dimensionless representation of wall friction. This represents the signal after subtracting the average friction. The signal represents the average friction resistance.

[0092] In a turbulent field, at 0 < In the near-wall region (<5), the velocity gradient follows a linear law. According to Newton's law of internal friction, the wall friction resistance is... The wall friction resistance at the spatiotemporal resolution can be obtained by calculating the velocity gradient.

[0093] in Represents the wall friction resistance. Represents the velocity gradient. This represents the coefficient of dynamic friction.

[0094] Figure 8 This is a schematic diagram for verifying the correlation signal of near-wall frictional resistance at two points in an embodiment of this application. Figure 8 In the diagram, the vertical axis represents the magnitude of the correlation coefficient, and the horizontal axis represents the time delay between signals. Figure 8 As can be seen, the signal delay between the two points near the wall friction resistance is t=0.25s. In this embodiment, the signal distance between the two points is s=0.021m. The migration speed of the two signals is calculated. Calculated =0.084m / s, the free flow velocity selected in this embodiment is... =0.158m / s, solving for = =0.53 falls within the range of 0.5-0.6 (the migration velocity of the main flow structure in the near-wall region of wall turbulence), indicating that the signal migration velocity in this embodiment is consistent with the migration velocity of the main flow structure near the wall, thus confirming the reliability of the data.

[0095] For example,

[0096] This method can also be used to measure the spatiotemporal signal of friction in laminar flow fields. The difference is in the definition of the near-wall region; in the laminar flow field, the near-wall region of the particle image should be the velocity gradient. It is a linear region.

[0097] The above description of the disclosed embodiments enables those skilled in the art to make or use 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. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for measuring the spatiotemporal signal of wall friction in a turbulent field, characterized in that, include: S1: Acquire time-series particle images; S2: Extract near-wall region particle images from time-series particle images; S3: Determine the query window with spatiotemporal resolution; Step S3 is as follows: S31: In the particle image of the near-wall region, set a query window and query area with spatiotemporal resolution according to the flow conditions in the flow field; S32: Determine whether the query window contains sufficient particle grayscale information; S33: If the query window meets the conditions, determine the spatiotemporal resolution of the query window; If the query window does not meet the conditions, expand the spatial scale of the query window or increase the time scale and repeat steps S32 and S33 until the query window meets the conditions. Expanding the query window spatial scale means increasing the flow distance and normal distance of the query window while maintaining the original image sequence, thereby increasing the query area of ​​the query window and increasing the particle information in that area; Increasing the time scale, or increasing the number of image sequences, allows for the addition of particle information from multiple images in the query region while maintaining the original query region area unchanged. In S33 When the required flow field information emphasizes temporal resolution, the spatial size of the query window is enlarged, and a query window with a flow direction size much larger than the normal dimension is selected; this achieves the technical effect of providing sufficient particle information in the query area under high temporal resolution. When the required flow field information focuses on spatial resolution, an image sequence is added and the query window is set to the same position in each image of the image sequence, so as to achieve the technical effect of sufficient particle information under high spatial resolution. S4: Calculate the velocity of each measurement point near the wall using a query window with spatiotemporal resolution; S5: Fit the near-wall velocity distribution with spatiotemporal resolution; S6: Obtain the spatiotemporal wall friction signal by fitting the velocity distribution.

2. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 1, characterized in that, Step S1 specifically involves: The laser (1) and the high-speed camera (2) are synchronously controlled by a signal synchronizer (4); the computer (3) is equipped with a high-speed image acquisition card, which is used to connect the camera to store data images and complete the acquisition through a particle image velocimeter. The high-speed camera (2) captures the flow field area below the flat plate. The computer (3) uses a particle image velocimeter to transmit control signals to the laser (1) and the high-speed camera (2) via a signal synchronizer (4). After the high-speed camera (2) acquires the exposure data, it transmits the particle image back to the computer (3) and stores it.

3. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 1, characterized in that, Step S2 specifically involves: Select 0< The viscous subfield with a value <5 is considered as the near-wall region of the flow field, in which... This represents the dimensionless height of the wall normal at the internal scale, and Where y is the distance from the wall normal height, Indicates the wall friction speed. v It represents the kinematic viscosity of the fluid; the physical spatial information y is converted into corresponding pixel information in the image through pixel resolution and then extracted.

4. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 1, characterized in that, In S32, sufficient particle grayscale information consists of 4-5 particles.

5. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 1, characterized in that, Step S4 specifically involves: Calculate the interval based on the defined spatiotemporal scale query window and query region. Image correlation values ​​of particle images in the flow direction and normal direction; Based on the pixel position of the maximum value of the particle image correlation value , Find each query window in the near-wall region. displacement after motion ; The actual displacement is obtained by matching the pixel with the actual physical space. ; according to Calculate the speed of each query window .

6. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 5, characterized in that, The process of calculating image correlation values ​​is as follows: in That is, the image correlation value, representing the normalized cross-correlation coefficient, with a range of... The cross-correlation coefficient represents the degree of similarity between image sequences during image matching. When two images are completely identical, the correlation coefficient is 1; when the grayscale distributions of the two images are completely opposite, the correlation coefficient is -1. and These represent the pixel position and the past pixel position of the query window, respectively. The possible movement after that and The position after This indicates the displacement distance of the particle image flow direction. This represents the normal displacement distance of the particle image.

7. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 1, characterized in that, Step S5 specifically involves: The velocities in the near-wall flow field under different spatiotemporal resolution query windows were calculated, and the velocities of the query windows at the same flow direction position were arranged together according to the distance from the wall normal. Remove defective pixels; There are n velocity points at locations with the same flow direction. , … Where n refers to the number of query windows in the normal space, u represents the flow velocity, and y represents the normal distance. Curve fitting is performed on these n data points. Assume the function equation is in the form of: , and For the unknown, Substituting into the equation, we get: Then, it transforms: Similarly , It can be obtained The matrix formed is in the form of: ,set up For A, For T, For k, but The velocity is fitted to a sloped line, and the slope k of this line is calculated to replace the velocity gradient. .

8. The method for measuring the spatiotemporal signal of wall friction in a turbulent field according to claim 1, characterized in that, Step S6 specifically involves: In 0< <5 Near-wall region, wall frictional resistance The wall friction resistance at the spatiotemporal resolution can be obtained by calculating the velocity gradient. in Represents the wall friction resistance. Represents the velocity gradient. The coefficient of dynamic friction of the fluid medium.

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