JP2010276448A - Physical quantity measuring method and physical quantity measuring apparatus around object - Google Patents

Abstract

Even if the boundary surface of an object placed in a fluid has a curved surface or when the boundary of the object is displaced in time in the fluid, the pressure and velocity of the fluid around the object Provided is a physical quantity measuring method capable of measuring a physical quantity such as temperature with high accuracy and simplicity.
A physical quantity measurement method according to the present invention visualizes a surrounding space of a curved object with a predetermined visualization medium, captures the visualized surrounding space and the curved object, and acquires image data including a cross-sectional image of the curved object. And dividing the surrounding space in the image data into a plurality of lattice spaces, obtaining physical quantities at each lattice point of the plurality of lattice spaces from the image data of each lattice space, The peripheral space is divided into a plurality of lattice spaces so that the periphery of the cross-sectional image is surrounded by and in contact with the outer edges by a plurality of lattice spaces having outer edges shaped along the outer periphery of the cross-sectional image.
[Selection] FIG.

Description

  The present invention relates to a physical quantity measurement method and a measurement apparatus around an object, and in particular, the physical quantity around the object is visualized by a visualization medium, and the pressure, velocity, temperature, etc. of the fluid around the object are visualized from the captured image of the visualized physical quantity. The present invention relates to a physical quantity measuring method and a physical quantity measuring apparatus for measuring a physical quantity.

  The behavior of physical quantities such as fluid pressure, fluid velocity, and temperature around an object when an object such as a cylindrical structure is placed in the fluid is important in various fields.

  Not only cylindrical structures, but if structures (cars, airplanes, etc.) are placed in the fluid, a wake is formed behind them. However, when the flow is fast, the wake is almost always turbulent. . In such a wake area, the area behind the structure has a lower pressure than the surrounding area. Therefore, the structure has a flow difference due to the pressure difference between the front and back (the front part where the flow collides and the rear part on the opposite side). It will receive an external force in the downstream direction, which will greatly affect the performance of cars and airplanes.

  Even in fluid-related vibrations in a cylindrical structure, vortices are repeatedly formed in the wake of the cylindrical structure, and the load fluid force generated by the vortex formed in the wake of the cylindrical structure causes the self-excited vibration of the cylindrical structure. Plays an important role in maintaining. The region behind the cylindrical structure repeatedly undergoes large pressure fluctuations along with the formation of vortices, and the force due to the pressure gradient acts on the cylindrical structure. Understanding the pressure distribution around objects is also important.

  There are various methods for measuring pressure. For example, a pressure gauge that can measure dynamic pressure, such as a Pitot tube, is attached to the wall of a cylindrical structure or in the fluid. However, there is only one measurement point in the experimental space that can be measured with a single Pitot tube, and many measurement points must be provided when measuring pressure distribution. In addition, the Pitot tube itself may disturb the fluid and affect the measured value.

  There are various methods for measuring and using pressure in surface measurement instead of point measurement. Among them, the method for estimating pressure from velocity information by PIV (Particle Image Velocimetry) analysis is that PIV is not suitable for the measurement target space. Since a large number of measurement points can be provided in contact and spatially in the form of a plane, research is actively conducted as a pressure measurement means capable of effective non-contact and surface measurement.

On the other hand, taking the divergence of the Navier-Stokes equation, which is the governing equation of the flow field, and combining it with the continuous equation, the following Poisson equation (Equation 1) relating to the pressure p is obtained.

  (Expression 1) means that the spatial distribution of pressure does not depend on time and can be obtained from a certain instantaneous velocity field. Here, the instantaneous velocity field can be obtained from PIV analysis (see, for example, Patent Document 1). By applying an appropriate boundary condition and solving the differential equation of (Equation 1), the pressure field at the same time Can be obtained. The velocity field obtained by PIV analysis is mostly two-dimensional. In this case, the above equation cannot be solved three-dimensionally based on velocity field information obtained from PIV analysis. However, it is useful to obtain information about the correlation between the velocity field and the pressure field, even if it is qualitative information, as long as various conditions such as boundary conditions are clarified.

JP 2007-10524 A

  However, generally, when performing PIV analysis, a space is divided into fine lattice spaces, and a velocity vector is obtained for each divided lattice space. At this time, if the outer edge of the lattice space and the boundary of the structure (wall surface of the cylindrical structure, etc.) are not parallel and do not match, the velocity data obtained by the PIV analysis is directly put into the Poisson equation to calculate the pressure distribution. It is very difficult to do.

  In PIV analysis, in order to obtain one velocity vector information, a lattice space image is used as a basic pattern image, and pattern matching between this basic pattern image and an image obtained from a correlation window having the same shape and the same size as the lattice space is performed. And a method for calculating the amount of movement of the correlation window is taken.

  In a general PIV analysis performed conventionally, a square or rectangular lattice space and a correlation window are used. For this reason, when the outer edge of the lattice space into which the space is divided when performing PIV analysis and the boundary of the cylindrical structure placed in the space are not parallel and inconsistent, the lattice space in the vicinity of the structure, or The phenomenon that the image of the structure inside the boundary is included in the correlation window occurs. The tracer particles mixed with the fluid change their positions according to the flow of the fluid, but do not enter the inside of the wall surface. However, if the boundary between the outer edge of the lattice space and the structure does not match, the image pattern of the structure inside the boundary other than the tracer particles is also reflected in the basic pattern image in the lattice space near the wall surface. Unlike the tracer particle, the image pattern of the structure is a fixed pattern that does not change its position with time. Since the movement amount of the correlation window is calculated by pattern matching of the tracer particle image, if the image pattern of the structure becomes more dominant than the tracer particle in the lattice space or the image pattern of the correlation window, the structure is fixed. The pattern causes a calculation error in performing the PIV analysis.

  Further, it is necessary to set boundary conditions when solving the aforementioned Poisson equation. The boundary condition includes a Dirichlet boundary condition that defines a value on the boundary and a Neumann boundary condition that defines a gradient value of the value on the boundary. In particular, there are “sliding wall boundary” and “fixed wall boundary” on the wall surface where fluid does not go in and out, the former is a boundary condition with a velocity parallel to the wall surface, and the latter has zero velocity on the wall surface. Is on such a boundary. Even when the pressure distribution around a cylindrical structure is solved numerically, it is necessary to set an appropriate boundary condition in the area corresponding to the end of the calculation area. However, the outer edge of the lattice space used in PIV analysis and the boundary of the structure do not match. In this case, it is not possible to simply set the boundary condition. For example, a method of estimating one boundary condition from a plurality of boundary values by interpolation processing is required, which not only increases the calculation cost but also causes an error in the estimated boundary condition. It becomes a factor to mix.

  Furthermore, even when the position of the boundary of the structure changes due to a phenomenon such as the vibration of the structure in the fluid, the above-described problem of mismatch between the outer edge of the lattice space and the boundary of the structure occurs.

  The present invention has been made in view of the above circumstances, and even when the boundary surface of an object placed in a fluid has a curved surface, the boundary of the object is displaced in time in the fluid. Even if it exists, it aims at providing the physical quantity measuring method and physical quantity measuring apparatus which can measure a physical quantity, such as the pressure of the fluid around an object, speed, temperature, etc. accurately and simply.

  In order to solve the above-described problem, the physical quantity measurement method according to the present invention visualizes the surrounding space of a curved object with a predetermined visualization medium, images the visualized surrounding space and the curved object, and obtains a cross-sectional image of the curved object. Obtaining the physical quantity at each lattice point of the plurality of lattice spaces from the image data of each of the lattice spaces, dividing the surrounding space in the image data into a plurality of lattice spaces, And in the step of dividing into the lattice space, the surrounding space is such that the periphery of the cross-sectional image is surrounded by and in contact with the outer edges by a plurality of lattice spaces having outer edges shaped along the outer periphery of the cross-sectional image. Is divided into a plurality of lattice spaces.

  In order to solve the above problems, the physical quantity measuring device according to the present invention captures a fluid mixed with tracer particles together with a curved object placed in the fluid and includes image data including a cross-sectional image of the curved object. An image analysis unit that obtains a velocity vector of the fluid from the image data based on a particle image flow velocity measurement technique, and the image analysis unit has a shape along the outer periphery of the cross-sectional image The space surrounding the curved surface object is divided into a plurality of lattice spaces so that the periphery of the cross-sectional image is surrounded by the plurality of lattice spaces having outer edges of Using image data and second image data captured after a predetermined frame time from the imaging time, the position of the lattice space of the first image data, and the tracer particles of the lattice space From the difference between the position of the correlation window corresponding to the tracer particle image of the second image data showing the strongest correlation with the image and the frame time, the velocity vector of the fluid at each lattice point in the plurality of lattice spaces is obtained. It is characterized by that.

  According to the physical quantity measuring method and the physical quantity measuring device according to the present invention, even when the boundary surface of the object placed in the fluid has a curved surface, the boundary of the object is displaced in time in the fluid. Even so, physical quantities such as pressure, speed, and temperature of the fluid around the object can be measured with high accuracy and simplicity.

The figure which shows the structural example of the physical quantity measuring apparatus which concerns on one Embodiment of this invention. The figure which shows notionally the method of measuring the physical quantity (in this case, speed distribution and pressure distribution) of the fluid which flows around an object. The figure which illustrates a typical PIV analysis method typically. The figure which shows typically the behavior of the fluid field when a prismatic or cylindrical curved object is placed in the fluid. The 1st figure explaining the problem of the conventional PIV analysis method. The 2nd figure explaining the problem of the conventional PIV analysis method. The figure which shows the processing concept of the physical quantity measuring method which concerns on a 1st Example. The basic flowchart which shows the process example of the physical quantity measurement method which concerns on a 2nd Example. The detailed flowchart which shows the process example of the physical quantity measurement method which concerns on a 2nd Example. The 1st figure explaining the processing concept of the physical quantity measuring method which concerns on a 2nd Example. The 2nd figure explaining the processing concept of the physical quantity measuring method which concerns on a 2nd Example. The 3rd figure explaining the processing concept of the physical quantity measuring method which concerns on a 2nd Example. The figure which shows the example of a division | segmentation of the object surrounding space when a lattice space is made into an unstructured lattice. The figure explaining the processing concept of the physical quantity measuring method which concerns on a 3rd Example.

  A physical quantity measuring method and a physical quantity measuring apparatus 1 according to an embodiment of the present invention will be described with reference to the accompanying drawings.

  The physical quantity measuring device 1 visualizes a physical quantity in the surrounding space of an object with a visualization medium, images the visualized physical quantity in the surrounding space with an imaging camera, analyzes the obtained image data, and measures the physical quantity in the surrounding area of the object. Device. In particular, the physical quantity measuring device 1 according to the present embodiment is an apparatus that can measure a physical quantity in a space close to the outer periphery of an object with high accuracy.

  Hereinafter, the velocity distribution and pressure distribution of the fluid flowing around the object will be described as an example of the physical quantity to be measured by the physical quantity measuring device 1. The PIV analysis method is well known as a method for measuring the fluid velocity distribution, and the physical quantity measuring apparatus 1 is also based on the PIV analysis method as a method for measuring the fluid velocity distribution.

  In PIV analysis, fine particles called tracer particles are mixed into a fluid as a visualization medium, and the spatial distribution of the velocity vector of the fluid is obtained from the amount of movement of the tracer particles per unit time. Further, as described above, by applying the velocity vector obtained by the PIV analysis and a predetermined boundary condition to the pressure Poisson equation (Equation 1), the pressure distribution of the fluid flowing around the object can be obtained.

  However, the physical quantity to be measured by the physical quantity measuring apparatus 1 is not limited to the velocity distribution or the pressure distribution. For example, the temperature distribution in the surrounding space of the object, the concentration distribution of a specific chemical substance, and the like are also measured. .

  For example, the temperature distribution of the surrounding space of the object can be obtained by mixing a dye or the like whose reflection characteristics change depending on the temperature into the surrounding space as a visualization medium and acquiring the spatial distribution of the amount of light reflected from the dye as image data. Can be measured.

  For chemical substances that reflect light of a specific wavelength, the concentration distribution of chemical substances can be determined by obtaining the spatial distribution of the amount of reflected light of chemical substances dissolved in the fluid as image data. Can be measured.

  As described above, if the physical quantity of the surrounding space of the object can be visualized by any method, the visualized physical quantity is acquired as image data, and the physical quantity measuring apparatus 1 and the physical quantity measuring method according to the present embodiment are applied to the object. The physical quantity of the space adjacent to the outer periphery of the can be measured with high accuracy.

(1) PIV Analysis Method First, the outline of the PIV analysis method that is the basis of the physical quantity measurement method according to the present embodiment and the basic configuration of the physical quantity measurement device 1 will be described.

  FIG. 1 is a diagram illustrating a configuration example of the physical quantity measuring device 1. FIG. 2 is a diagram conceptually showing a method of measuring the physical quantity (in this case, velocity distribution and pressure distribution) of the fluid 200 flowing around the object 201 using the physical quantity measuring apparatus 1.

  The physical quantity measuring device 1 has a configuration including at least an imaging unit 10 and an image analysis unit 20. The imaging unit 10 is, for example, a high-resolution high-speed video camera. The image analysis unit 20 is a device that analyzes the image data captured by the imaging unit 10, and is realized by, for example, a personal computer.

  The fluid to be measured is, for example, water or air, and is forcedly circulated in a closed space that houses the object 201 by a pump (not shown). Since water and air cannot be imaged as they are, minute particles called tracer particles (visualization medium) are mixed in the fluid. A sheet-like laser beam emitted from the laser light source 100 is scattered by the tracer particles. By imaging the scattered light with the imaging unit 10, the movement of the fluid can be visualized as the movement of the tracer particles. The tracer particles are required to have high followability to the fluid, and are appropriately selected according to the type of fluid. When the fluid is water, for example, a tracer (ORGASOL) having a particle size of about 20 μm and a density ratio with water of 1.02 is suitable.

  In the PIV analysis, an image obtained by capturing tracer particles is divided into a number of lattice spaces, and a velocity vector is obtained for each lattice space. Accordingly, the velocity vector is obtained as a multipoint spatial distribution instead of one point, and the spatial resolution of the velocity vector coincides with the size of the lattice space.

  FIG. 3 is a diagram schematically illustrating a typical PIV analysis method. In order to obtain the velocity vector from the image data of the tracer particles, at least two pieces of image data captured at different times are required.

FIG. 3A illustrates the first image data captured at time t = t ₀ , and FIG. 3B illustrates the second image data captured at time t = t ₀ + Δt. FIG. Δt is not particularly limited, but is, for example, the frame time of the imaging unit 10. The first and second image data are divided into a plurality of lattice spaces having a predetermined pixel size. In the example of FIG. 3, the measurement target space is divided into 12 lattice spaces of 3 × 4.

The PIV analysis, rather than follow the tracer particles each motion, and distribution of tracer particles in the lattice space at time t = t _0, the pattern matching between the distribution state of the tracer particles at time t = t 0 ₊ Δt performed ing. Specifically, a cross-correlation function R _{t0 + Δt / 2} (Δx, Δy) shown in (Expression 2) is obtained.

On the other hand, I _{t0 + Δt} (x + Δx, y + Δy) (x = −n to + n, y = −n to + n: n is an integer) is a luminance value of each pixel of the correlation window at time t = t ₀ + Δt. The target lattice space and the correlation window have the same shape and the same size, and Δx and Δy are the displacement amounts of the correlation window with respect to the target lattice space (see FIG. 3B).

For the image data at time t = t ₀ + Δt, the cross-correlation function R _{t0 + Δt / 2} (Δx, Δy) is calculated while shifting the correlation window in the x-axis direction and the y-axis direction (that is, changing Δx, Δy). The correlation window displacement amounts Δxm and Δym that maximize the cross-correlation function R _{t0 + Δt / 2} (Δx, Δy) are further obtained. Cross-correlation function _{R t0 + Δt / 2 (Δx} , Δy) is Δxm since the maximum, "as a whole" in the tracer particles time _t = t ₀ + Δt in the lattice space at time t = _{t 0} in the x-axis direction, y It can be estimated that it has moved by Δym in the axial direction.

  If the displacement amounts Δxm and Δym are obtained, velocity vectors (Vx = Δxm / Δt, Vy = Δym / Δt) at the lattice points (see FIG. 3D) of the lattice space of interest are obtained. By performing the same processing for all the lattice spaces, the velocity vectors of the lattice points corresponding to the respective lattice spaces are obtained as a spatial distribution as shown in FIG.

  In the conceptual description shown in FIG. 3, a case where no object exists in the fluid is described as an example. In contrast, in the physical quantity measuring device 1 according to the present embodiment, as shown in FIGS. 4A and 4B, a fluid field when a curved object such as a prism or a cylinder is placed in the fluid. (The spatial distribution of the velocity vector of the fluid and the spatial distribution of the pressure, or their temporal changes) are also measured.

  In particular, measuring the velocity distribution and pressure distribution of the fluid in the vicinity of the object surface and analyzing the influence of the fluid on the object from these measurement results are extremely important in practice as described above.

  In a conventional PIV analysis, an arbitrary point (for example, one point on the lower left of the image data) of the captured image data is set as the origin regardless of the shape, orientation, and position of the object placed in the fluid. The image data is divided into a rectangular lattice space. When the imaging camera (imaging unit 10) is installed horizontally and imaged, the horizontal direction is the X axis. For this reason, the following problems have arisen when speed and pressure are obtained from image data in a lattice space close to the surface of the object.

  5A and 5B are diagrams for explaining this problem. In this example, a prism is placed in the fluid, and the hatched areas shown in FIGS. 5A and 5B show cross-sectional images of the prism. As shown in FIGS. 5 (a) and 5 (b), there is a problem in the case where each side of the cross section of the prism is installed in the fluid in a state where it is inclined from the vertical horizontal position.

  The first problem is that the velocity vector value near the outer periphery of the prism obtained from the PIV analysis has an error.

  In the conventional PIV analysis method, the lattice space is rectangular and its outer edge is set to be horizontal and vertical. For this reason, the image data of the lattice space close to the outer periphery of the prism does not only include the tracer particle image in the fluid, but also includes a cross-sectional image of the prism.

As described above, in the PIV analysis method, the luminance value of each pixel (pixel) in the target lattice space (the space surrounded by the thick solid line in FIG. 5A) at time t = t ₀ and the time t = t Using the cross-correlation function with the luminance value of each pixel in the correlation window (space surrounded by a thick broken line in FIG. 5B) at ₀ + Δt, the displacement amount of the tracer particle moving at Δt is obtained. .

  The fluid (and tracer particles mixed in the fluid) do not enter the inside of the object (rectangular column), and an image inside the object is unnecessary in the PIV analysis. However, in the conventional PIV analysis method, the cross-sectional image of the prism is included in the image of the attention lattice space close to the outer periphery of the prism and the correlation window corresponding thereto. For this reason, the cross-correlation function includes not only the luminance value of the tracer particle image but also the luminance value of the prismatic cross-sectional image. As a result, the displacement amounts Δxm and Δym of the tracer particles obtained from the cross-correlation function are not purely displacement amounts of the tracer particles, but are displacement amounts having an error influenced by the luminance value of the prismatic cross-sectional image. The velocity vector obtained from Δxm and Δym also has an error. This error increases as the ratio of the object cross-sectional image in the lattice space increases.

  The second problem is that when the velocity vector obtained by the PIV analysis is applied to the pressure Poisson equation (Equation 1) to obtain the pressure, the lattice point of the lattice space and the boundary of the object do not coincide with each other. The calculation load increases and the obtained pressure includes an error.

  As described above, in the PIV analysis, a velocity vector is obtained at each lattice point in the lattice space. That is, the velocity vector is obtained as a spatial distribution of discrete positions in space (that is, the positions of the lattice points). On the other hand, in order to obtain the pressure distribution near the object by applying the spatial distribution of the velocity vector to the pressure Poisson equation (Equation 1) which is a differential method, the boundary condition of the object (pressure or velocity on the object surface, or Need to enter these gradients).

  If the boundary of the object and the grid point do not match, the boundary condition at one or more points on the boundary of the object near the grid point must be converted to the boundary condition at the grid point position by interpolation processing, etc. The calculation load required for this interpolation processing increases. In addition, even if the boundary condition at the grid point position is obtained by interpolation processing, the value is only an estimated value, so that it includes some error compared to the boundary condition when the grid point and the boundary completely match. Become.

  The two problems described above also occur when the object is a curved object such as a cylinder. 6 (a) and 6 (b) are diagrams showing this, and the hatched area in the figure corresponds to a circular cross-sectional circle. As shown in FIGS. 6A and 6B, the lattice space and correlation window image data used in the conventional PIV analysis method include not only tracer particle images but also cylindrical cross-sectional images in the vicinity of the outer periphery of the cylinder. It is. For this reason, as in the case of the prism, it is affected by the luminance value of the cylindrical section, and the obtained velocity vector value includes an error.

  In addition, since the lattice points do not coincide with the outer circumference of the cylinder, when the boundary condition is applied to the pressure Poisson equation, the calculation load increases as described above, which causes an error.

(2) First Example In order to solve the above two problems, in the physical quantity measuring device 1 and the physical quantity measuring method (first example) according to this embodiment, as shown in FIG. The space around the object is divided by the lattice space so that the outer edge of the lattice space around the object is parallel and coincides with the outer peripheral surface of the prism.

  In the conventional PIV analysis, the space around the prism is divided into a lattice space regardless of the orientation of the prism by an orthogonal coordinate system having horizontal and vertical X and Y axes. On the other hand, in the first embodiment, the image data expressed in the orthogonal coordinate system is rotated and translated so that the outer edge of the lattice space is parallel and coincides with the outer peripheral surface of the prism. It is divided in a lattice space.

  By dividing the object periphery in the lattice space as shown in FIG. 7 (b), the lattice space around the prism does not include the image of the cross section of the prism. It becomes possible to eliminate the influence. As a result, the first problem described above is solved, and the velocity vector of the fluid around the object can be obtained with high accuracy.

  Further, since the outer edge of the lattice space on the outer periphery of the prism is coincident with the outer peripheral surface of the prism, the boundary condition required in the pressure Poisson equation can be directly applied to the position of the lattice point. Therefore, interpolation processing is unnecessary, not only the calculation load is reduced, but also the fluid pressure near the object obtained from the pressure Poisson equation can be obtained with high accuracy.

  As described above, the captured image data may be rotated / translated to align the outer edge of the lattice space with the outer periphery of the prism, but the image capturing camera (imaging unit 10) itself can be rotated / translated to rotate the lattice. The outer edge of the space may coincide with the outer periphery of the prism.

(3) Second Example The first example is an effective method for an object (such as a prism) whose surface is flat. However, since the shape of the lattice space is square, the outer periphery of the cross section is curved. For a curved surface object such as a cylinder, the outer edge of the lattice space and the outer periphery of the object cross section cannot be completely matched.

  The second embodiment provides a method that can also be applied to a curved object having a circular cross-section outer periphery.

  FIG. 8 is a flowchart illustrating a processing example of the physical quantity measurement method according to the second embodiment. Also in the second embodiment, the physical quantity to be measured is the fluid velocity vector and pressure.

  In step ST1 and step ST2, the fluid in the surrounding space of the cylinder is visualized by the tracer particles, the visualized surrounding space and the cylinder are imaged, and image data including a cross-sectional image of the cylinder is acquired.

  In step ST3, the peripheral space is divided into a plurality of lattice spaces so that the periphery of the cross-sectional image is surrounded by the plurality of lattice spaces having outer edges shaped along the outer periphery of the cross-sectional image.

  In step ST4, the physical quantity (velocity vector and pressure) at each lattice point is obtained from the image data of the divided lattice space.

  FIG. 9 is a flowchart showing a more specific processing example of step ST3 and step ST4. The processing from step ST10 to step ST13 is a specific example of step ST3 in FIG. 8, and the processing of steps ST14 and ST15 is a specific example of step ST4 in FIG.

  In step ST10, the outer circumference circle of the cross-sectional image of the cylinder is obtained from the image data. Specifically, since the cross-sectional image of the cylinder has a higher brightness value than the surrounding space, the center position of the area having a brightness value higher than a predetermined threshold is the center position of the cylinder cross-section (circular). The outer circumference circle of the cross-sectional image is obtained by drawing a circle with a known cylinder radius with respect to the center position.

  In step ST11, the surrounding space of the cylindrical object is divided into a plurality of arcuate lattice spaces by a plurality of radial straight lines extending radially from the center of the outer circumference circle and a plurality of concentric circles drawn outside the outer circumference circle of the cross-sectional image. .

  FIG. 10A shows division by a rectangular lattice space used in the conventional PIV analysis (the same division method as in FIG. 6), and FIG. 10A shows an arcuate lattice space used in the second embodiment. Shows the division by.

  In the second embodiment, the shape of the lattice space is an arcuate shape. In each lattice space surrounding the outer periphery of the cylinder, the outer edges (arcs) facing the outer periphery of the cylinder all coincide with the outer periphery of the cylinder. For this reason, the image data of each lattice space surrounding the outer periphery of the cylinder does not include the cross-sectional image of the cylinder, but includes only the tracer particle image in the fluid. As a result, the velocity vector obtained from the image data of each lattice space is not affected by the cross-sectional image of the cylinder.

  In addition, since the boundary of the outer periphery of the cylinder is on the lattice point of each lattice space surrounding the outer periphery of the cylinder, the position of the boundary condition applied to the pressure Poisson equation can be exactly matched to the position of the lattice point.

In step ST12, the pixel position of the image data is converted from the orthogonal coordinate system (XY coordinate system) to the polar coordinate system (θ, r) with the center of the concentric circle as the origin, corresponding to the shape of the arcuate lattice space. To do. As shown in FIG. 10B, θ is a polar coordinate declination, and r is a moving radius. In step ST12, the luminance _{Im, n} at the pixel position (θ _m , r _n ) when expressed in polar coordinates is obtained as follows.

First, the pixel position of the orthogonal coordinates corresponding to the pixel position (θ _{m, r n)} and _{(x mn, y mn),} expressed by the following equation (θ _{m, r n).}

Next, the surrounding four pixels closest to the pixel position (x _mn , y _mn ) are searched, and their luminance values are set as I ₁ , I ₂ , I ₃ , and I ₄ as shown in FIG. Further, the distances between these four pixels and (x _mn , y _mn ) are obtained and are set as r ₁ , r ₂ , r ₃ , and r ₄ , respectively. Then, I _{m, n} at the pixel position (θ _m , r _n ) expressed in polar coordinates is obtained from the following equation.

  Next, in step ST13, the image data expressed in polar coordinates is developed into coordinates whose horizontal axis is the declination angle θ and whose vertical axis is the moving radius r (hereinafter, these coordinates are referred to as θ · r coordinates).

  FIG. 12A is a diagram in which image data (cylindrical cross-sectional image and tracer particle image) expressed in orthogonal coordinates are superimposed on a coordinate axis expressed in polar coordinates and an arcuate lattice space. On the other hand, FIG. 12B is a diagram schematically showing image data expressed in polar coordinates and further developed into θ · r coordinates.

In FIG. 12B, the horizontal axis declination θ ranges from 0 to 2π, and the vertical axis radial radius r ranges from the radius R _inner of the outer circumferential circle of the cylinder to the radius Rmax of the maximum concentric circle indicating the maximum measurement range. It is.

In the next step ST14, PIV analysis is performed on the image data developed in the θ · r coordinate, and the velocity vector of each lattice point is obtained. Specifically, the velocity vector of each grid point is obtained from two image data of time t = t ₀ and time t = t ₀ + Δt developed in the θ · r coordinate.

  The arcuate lattice space set in step ST11 (see FIG. 12 (a)) has different declination lengths depending on the radius r, but the lattice space after the expansion into the θ · r coordinates is as shown in FIG. As shown in (b), all are rectangular lattice spaces of the same size. This means that conventional PIV analysis software using the XY coordinate system can be used as it is as PIV analysis software in the second embodiment.

  However, in the square lattice space in the second embodiment, the influence of the cross-sectional image of the cylinder is completely eliminated even in the lattice space close to the outer periphery of the cylinder, which is greatly different from the conventional PIV analysis.

  Finally, in step ST15, the pressure in the space around the object is calculated by applying the obtained boundary condition between the velocity vector and the outer peripheral surface of the cylinder to the pressure Poisson equation. Also in this case, the setting position of the boundary condition coincides with the lattice point of the rectangular lattice space expanded to the θ · r coordinate.

  The second embodiment described above provides a method of dividing an object surrounding space by a lattice space having an optimal shape (curved lattice space) for a curved object having a circular cross section.

  This is further expanded to illustrate a lattice space in which the outer edge of the lattice space coincides with the outer periphery of the cross-sectional image along the outer periphery of the cross-sectional image with respect to a curved object having an arbitrary cross-sectional shape, ie, illustrated in FIG. The surrounding space of the object may be divided by a so-called unstructured grid.

  By dividing the surrounding space of the object with an unstructured grid, it is possible to match the outer edge of the lattice space to the outer periphery of the cross section of a curved object with an arbitrary cross-sectional shape. The velocity vector distribution and the pressure distribution can be obtained with high accuracy.

(4) Third Example When an object is placed in a fluid, the position of the object may change due to vibration or the like due to the influence of the fluid. In such a case, as schematically shown in FIG. 14A, the outer edge of the lattice space set in the first and second embodiments does not coincide with the outer periphery of the object.

  Therefore, in the third embodiment, before the object periphery is divided in the lattice space, the outer periphery of the object is estimated from image data, and the lattice space is set so that the outer edge is in contact with the determined outer periphery. . In other words, when the outer peripheral position of the object changes, the lattice space is dynamically set according to the change.

  For example, when the object is a cylinder, as shown in FIG. 14 (b), the circumference position of the cylinder is first determined from the image data, and then the surroundings in a polar coordinate system lattice space in which the outer edge is in contact with the determined outer circumference of the cylinder Divide the space. According to this method, even when the position of the object constantly changes due to the influence of the fluid, the velocity vector and pressure around the object can be obtained with high accuracy from the image data in which the influence of the object cross-sectional image is always excluded. .

  The method for obtaining the position of the outer periphery of the object is not particularly limited. For example, when the radius of the cross-sectional circle of the cylindrical object is known, the center position of the cross-sectional circle is estimated from the image data of the cross-sectional circle, and the estimated center position is known. It is possible to determine the outer circle of the object by drawing a circle with a radius of. Further, when a cross-sectional circle image is clearly captured in the captured image data, the position of the outer circumference circle can be determined directly from the captured image. For an object having an arbitrary cross-sectional shape, the position of one or more specific points in the cross-sectional image is obtained from the image data, and the position of the object is determined from the relative positional relationship between the obtained position of the specific point and the outer cross-section of the object. You may make it estimate a cross-sectional outer periphery.

  As described above, according to the physical quantity measuring device 1 and the physical quantity measuring method according to the present embodiment, even if the boundary surface of the object placed in the fluid has a curved surface, the boundary of the object is Even in the case of temporal displacement in a fluid, physical quantities such as pressure, velocity, temperature, etc. of the fluid around the object can be measured with high accuracy and simplicity.

  Note that the present invention is not limited to the above-described embodiments as they are, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. In addition, various inventions can be formed by appropriately combining a plurality of constituent elements disclosed in the embodiment. For example, some components may be deleted from all the components shown in the embodiment. Furthermore, the constituent elements over different embodiments may be appropriately combined.

DESCRIPTION OF SYMBOLS 1 Physical quantity measuring apparatus, 10 imaging part, 20 Image analysis part.

Claims (10)

Visualize the surrounding space of the curved object with a predetermined visualization medium,
Imaging the surrounding space and the curved object visualized to obtain image data including a cross-sectional image of the curved object;
Dividing the surrounding space in the image data into a plurality of lattice spaces;
A physical quantity at each lattice point of the plurality of lattice spaces is determined from the image data of each of the lattice spaces.
Has steps,
In the step of dividing into the lattice space,
Dividing the peripheral space into a plurality of lattice spaces so that the periphery of the cross-sectional image is surrounded by and in contact with the outer edges by a plurality of lattice spaces having outer edges shaped along the outer periphery of the cross-sectional image;
A physical quantity measuring method characterized by the above. In the visualization step, the fluid around the curved object is visualized by tracer particles,
In the step of obtaining the physical quantity, the first image data captured at a certain time and the second image data captured after a predetermined frame time from the imaging time are used, and a grid of the first image data is used. From the difference between the position of the space and the position of the correlation window corresponding to the tracer particle image of the second image data showing the strongest correlation with the tracer particle image of the lattice space, and the frame time, Find the velocity vector of the fluid,
The physical quantity measuring method according to claim 1, wherein: Applying the determined velocity vector to the Poisson equation that defines the relationship between the spatial distribution of pressure and the spatial distribution of velocity vector, to determine the fluid pressure around the curved object,
The physical quantity measuring method according to claim 2, further comprising a step. The curved object is an object having a circular cross section,
The cross-sectional image included in the image data is circular,
In the step of dividing into the lattice space,
Dividing the surrounding space into a plurality of arcuate lattice spaces by a plurality of straight lines extending radially from the center of the circle and a plurality of concentric circles drawn on the outer circumference and the outside of the cross-sectional image;
The physical quantity measuring method according to claim 3. The physical quantity measurement method according to claim 4, wherein the coordinates of the first and second image data are expressed by polar coordinates having the center of the circle as an origin. In the step of obtaining the velocity vector,
The first and second image data expressed in the polar coordinates are expanded into θ · r coordinates where the horizontal axis is expressed by the declination θ and the vertical axis is expressed by the radius r, and are expanded into the θ · r coordinates. 6. The physical quantity measuring method according to claim 5, wherein the velocity vector is obtained based on the first and second image data. The curved object is an object whose position can be displaced in the fluid,
Estimating the outer periphery of the cross-sectional image from the image data, further comprising:
In the step of dividing into the lattice space,
Dividing the surrounding space into a plurality of lattice spaces based on the estimated outer periphery of the cross-sectional image;
The physical quantity measuring method according to claim 2, wherein the physical quantity is measured. The lattice space is a lattice space generated by an unstructured lattice.
The physical quantity measuring method according to claim 1, wherein: An imaging unit that captures a fluid mixed with tracer particles together with a curved object placed in the fluid and acquires image data including a cross-sectional image of the curved object;
Based on a particle image flow velocity measurement technique, an image analysis unit for obtaining a velocity vector of the fluid from the image data;
With
The image analysis unit
Dividing the peripheral space of the curved object into a plurality of lattice spaces so that the periphery of the cross-sectional image is surrounded by the plurality of lattice spaces having outer edges shaped along the outer periphery of the cross-sectional image;
Using the first image data captured at a certain time and the second image data captured after a predetermined frame time from the imaging time, the position of the lattice space of the first image data, and the lattice From the difference between the position of the correlation window corresponding to the tracer particle image of the second image data showing the strongest correlation with the tracer particle image of the space, and the frame time, the fluid at each lattice point of the plurality of lattice spaces Find the velocity vector,
A physical quantity measuring device characterized by that. The curved object is an object having a circular cross section,
The cross-sectional image included in the image data is circular,
The image analysis unit
The surrounding space is divided into a plurality of arcuate lattice spaces by a plurality of straight lines extending radially from the center of the circle and a plurality of concentric circles drawn on the outer circumference circle and the outside of the cross-sectional image, and the first, second The coordinates of the image data are expressed by polar coordinates with the center of the circle as the origin.
The physical quantity measuring device according to claim 9.

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