JP2881359B2 - Trace display method from flow field data - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for displaying a trail from flow field data, and more particularly, to calculating a velocity in a visualization space by tracking the tracer particle from a visualized image visualized by the tracer particle, This method is suitable for use in a method of calculating and displaying a trajectory in a two-dimensional cross section from the result of interpolation at lattice points.

[0002]

2. Description of the Related Art As is well known, conventionally, the flow velocity of a fluid is calculated by using, for example, a laser anemometer or the like.
Alternatively, a measurer determines a measurement point in advance in a two-dimensional cross section of the measurement space and performs measurement.

[0003] The above-mentioned measurement points are determined as grid points having equal intervals or arbitrary unequal intervals, and the flow field is measured by measuring the velocity at each grid point. According to this measurement, the inflow and outflow of the fluid at the elements formed by the four grid points are stored, and the flow function and the vorticity are easily measured from the speed measurement results.

[0004]

However, in the above-mentioned prior art, an enormous amount of time is required for measuring the flow velocity in the flow field. In order to solve this, there is an attempt to use an image processing technique from an image visualized by tracer particles and simultaneously measure a visualization space at multiple points using an algorithm based on a tracer particle tracking method.

[0005] This method is described in, for example, the paper "Transactions of the Japan Society of Mechanical Engineers (B), Vol. 55, 509 (1989-1),
There are methods disclosed on pages 07-114. In the above method, the tracer particles previously mixed in the fluid are irradiated with light using a light emitting device such as a strobe, and the trajectory is image-processed.

However, in such a flow visualization method, since the measurement data at the same time is arbitrarily present in the visualization space, it is difficult to measure the flow function and the vorticity in the visualization space. is there. By the way, the vorticity is ζ = (∂v
/ ∂x)-(∂u / ∂y), plane (xy plane), vertical
Fluid distortion about the linear axis (z). SUMMARY OF THE INVENTION In view of the above problems, an object of the present invention is to make it possible to obtain and display a trace of a flow field in a short time.

[0007]

According to the present invention, a method for displaying a flow trace from flow field data is to measure a velocity field from a visualized image of a flow by a tracer tracking method, and to interpolate the obtained velocity field into grid points. And a flow trace display method from flow field data for calculating and displaying a flow function from the result of the interpolation operation, wherein the four corners in a rectangular visualization space provided with a plurality of regular grid points are provided. An arbitrary corner is defined as a starting point, and a corner facing the starting point is defined as an end point. The starting point is defined from the starting point through the four outermost peripheries of the rectangular visualization space. The flow function φ is calculated from the integral of the velocity for each of the two routes leading to, the flow function value of one of the two calculated flow function values is selected, and the flow function value of the selected one is selected. A correction coefficient for correcting the flow function value of the other route that did not have the same value as the flow function value of the selected one route is calculated, and the correction coefficient is selected using the calculated correction coefficient. The flow function value of the other route was corrected, and the flow function of the flow field was calculated and displayed by analyzing the elliptic Poisson equation for each of the plurality of lattice points. And

Another feature of the present invention is that
Contour lines are calculated and displayed from the obtained values of the flow function.

Another feature of the present invention is that the regular lattice points are set as intersections of a plurality of straight lines at regular or irregular intervals that are orthogonal to each other.

Further, in the present invention, the regular lattice points are set as intersections of a plurality of concentric circles and radial straight lines.

[0011]

According to the method of displaying a flow trace from flow field data of the present invention, the measured data is once interpolated to grid points, and the flow function can be calculated only from the flow velocity data at the interpolated grid points. It is not necessary to input the value of the peripheral flow function. Also, since the flow function is calculated only from the velocity field, even if there is a complicated obstacle in the visualization space, the flow function should be calculated and displayed from the velocity field in the visualization space in a short time. Becomes easier.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a method for displaying a trail from flow field data according to the present invention will be described below with reference to the drawings. FIG. 1 is a flowchart showing a method of displaying a trail from the speed of a regular grid point according to an embodiment of the present invention, and FIG. 2 is a flowchart showing an algorithm of data interpolation.

In order to perform data interpolation, first, as shown in FIG. 2, a grid point sequence is created in a region to be analyzed in step S10. FIG. 3 shows an example of a grid point. In this example, straight lines orthogonal to each other at regular intervals are assumed, and the intersection point is set as a grid point. In this example, the straight lines are equally spaced, but may be irregularly spaced. For example, the lattice spacing may be changed between the part of interest and its surroundings, or polar coordinates consisting of concentric circles and radial straight lines may be assumed.

Next, in step S11, as shown in FIG. 4, the flow rates at the flow rate measuring points K, L, M, N,... Within a certain range (circle of radius L) from the grid point G to be interpolated. Data (n
). In this case, the radius L is, for example, six times the distance between lattice points. n is a fixed number P (number exceeding 3; for example, 10) sequentially taken out from measurement points close to the interpolation point G
And Increase the size of the circle (interpolation area) to 6 times
Also considers the spatial velocity gradient in Equation 1
So basically, the result is the same. However, it is a linear expression
Therefore, when the interpolation area becomes large, an error of the secondary accuracy occurs.
Will be.

Next, in step S12, the number of extracted data n
If it is determined that P has not reached P, the radius L of the extraction range is increased in step S13 and the
Perform step 11 again. In step S13, the value of P may be sequentially reduced, for example, to eight, six,....

Next, in step S14, grid point data is interpolated and calculated using one set of a total of _n C ₃ combinations obtained by extracting three pieces from the n pieces of data. The interpolation is performed by linear interpolation with a constant velocity gradient in the extraction circle. That is, in FIG. 4, the flow velocity (vector) of the grid point G to be interpolated is represented by u, and the flow velocity data of the measurement point K is _represented by u _k , (dx) _k , and (dy) _k by the lattice point G and the measurement point K.
Let du / dx, du / dy be the velocity gradient at the grid point G.

[0017]

(Equation 1)

## EQU1 ## The other two measurement points L, M (flow velocity data u _L , u _M , distance (dx) _L , (dx) _M , (d
y) _L and (dy) _M ), the same linear form is given, and the interpolation data u to be obtained can be obtained from the simultaneous equations of the following equation (2).

[0019]

(Equation 2)

The interpolation value calculated in step S14 is represented by u _i
And for all combinations of _n C ₃ , i = 1, 2,
... calculate up to _n C _3. Then, when the interpolation calculation of all the combinations is determined that ended in step S15, then in step S16, data of _n C ₃ u _{i (i} =
1 to _n C ₃ ) are obtained by statistical processing. This statistical processing may be, for example, an average value calculation Σu _i / _n C ₃ . Alternatively, seeking frequency N values u _i, as shown in FIG. 5 may be performed a statistical calculation for determining the median value by Gaussian approximation or binary approximation.

Next, the next interpolation grid point is set in step S17, and steps S11 to S11 are performed until the end of interpolation calculation for all the grid points in the interpolation area is detected in step S18.
Step 17 is repeated.

As described above, the flow velocity vector on the grid point as shown in FIG. 6 can be calculated by interpolation. The flow function can be calculated using the interpolated grid point data, and various physical quantities of the flow field can be obtained based on the flow function.

Next, an example of the procedure for calculating the stream function values of all the grid points will be described with reference to the flowchart of FIG. As shown in FIG. 1, first, initialization is performed in step S1. This is performed by setting φ _(1,1) to φ _{(n, m)} to 0, as shown in the calculation procedure explanatory diagram of FIG.

The grid point information calculated in this way includes:
When the flow function is calculated due to an error due to interpolation, the flow function behind the cylinder becomes strange as shown in paragraph [0033]. This is because errors at the time of grid point interpolation are accumulated by integration in the calculation of the stream function. In order to prevent such inconvenience, in the present embodiment, the circumference information is correctly predicted in advance (paragraphs [0026] to
[0027]), using the obtained value of φ at the grid point on the circumference and the velocity value at the internal grid point (the grid point excluding the grid point on the circumference in FIG. 7), φ at the internal internal grid point Is calculated by analyzing the Poisson equation. The circumference information referred to here is φ _(1,1) , φ in FIG.
_(2,1) , φ _{(3,1). . .} φ _{(n, 1)} , φ
_{(N, 2). . .} φ _{(n, m)} , φ _{(n−1, m)} , φ
_{(N-2, m). . .} φ _{(1, m)} ,
φ _{(1, m-1)} , φ _{(1, m-2). . .} φ
_{(1, 1)} . Next, a method of correctly predicting the circumference information will be described. In the present embodiment, the circumference information is predicted according to the means (1) and the means (2). Here, the means (1) is a function of calculating the upper grid points in FIG. 7 in order from the left to the right, and calculating the rightmost grid points, and calculating the right grid points in order from the top. That is, first, φ _(1,1) = 0 and φ
The value of _(2,1) is calculated from φ _(1,1) by “Equation 3”. Next, the value of φ _(3,1) is calculated from φ _(2,1) by “ _Equation 3”. After performing such calculations up to φ _{(n, 1)} , φ _{(n, 2). . .} By performing this for φ _{(n, m)} , the value of φ at the upper grid point and the right grid point in FIG. 7 is calculated (step S2). The means (2) is a function of calculating the grid points on the left side in FIG. 7 in order from top to bottom, and calculating the grid points on the lowermost side, and calculating the grid points on the lower side in order from left to right. Yes, φ
The value of _{(1, 2)} is calculated from φ _{(1, 1)} by “Equation 3”. Next, the value of φ _(1,3) is calculated from φ _(1,2) by “Equation 3”. After performing such calculations up to φ _{(1, m)} , φ _{(2, m). . .} By performing the same for φ _{(n, m)} , the value of φ at the grid points on the left and lower circumferences in FIG. 7 is calculated (step S3). In the above calculation, the value of φ _{(n, m)} is calculated in both step S2 and step S3. In step S2, the integration direction is calculated using the velocity information on the grid points of the upper and right circumferences. In contrast, in step S3, the speed information on the left and lower grid points is used. Therefore, the value of φ _{(n, m)} calculated in step S2 is different from the value of φ _{(n, m)} calculated in step S3. This is the paragraph [0
023] in the grid point interpolation. In order to correct this error, paragraphs [0024] to [0026]
Is corrected by The value of φ _(1,1) is obtained by estimating the value on the circumference and calculating the internal point from the value by Poisson equation. Therefore, the value of φ _(1,1) is an arbitrary value. For example, φ _(1,1) may be set to 10.

[0025]

(Equation 3)

Then, the process proceeds to step S4, where the correction coefficient α is obtained from the values obtained in steps S2 and S3.
Is calculated. Here, in step S2, each grid (φ
_(2,1) , φ _(3,1) ... φ _{(N, 1)} , φ
_{(N, 2)} ... Φ _{(N, M))} is calculated.
ing. In step S3, each grid (φ
₍₁ , ₂₎ , φ _{(1, 3)} ... φ _{(1, M)} , φ
_{(2, M)} ... φ The value of φ in _{(N, M,)} is calculated
ing. Therefore, the relation obtained by either one of the means
The numerical value φ _{(N, M)} was selected and not selected
The function value obtained according to the means is corrected. For example, means
The function value obtained in (1) is selected, and the function value obtained in (2) is selected.
Is corrected, the correction coefficient α is obtained by α = means (2).
Φ _{(N, M)} / φ _{(N, M)} obtained by means (1 ₎
It is calculated from the formula.

Next, the process proceeds to step S5, where
Using the correction coefficient α obtained in ₍₄₎ , φ _(1,2) = φ _(1,2) / αφ _(1,3) = φ _(1,3) / αφ _{(1, m)} = φ ₍ The value of φ around the means (2) is corrected by _{( 1, m)} / αφ _{(n, m)} = φ _{(n, m)} / α. Next, in step S6, equation 4 is developed.

[0028]

(Equation 4)

Here, β in Equation 4 is defined as β = ΔI / ΔJ. Note that ΔI and ΔJ are as shown in FIG. Further, ω in Equation 4 takes a value of ω = 1.4 to 1.7.

Next, in step S7, 展開¹ _{I, J} is calculated for each grid by using the value of ψ at the n = 0th time with respect to the expansion formula of Expression 4. Then, in step S8, the calculated [psi ¹ _I at step _S7, by using the value of _J [psi ² _I, the value of _J is calculated at each lattice.

Next, the process proceeds to step S9, and the above calculation is repeated, and 、 ⁿ _{I, J} −ψ ^{n + 1} _{I, J} at each lattice.
The calculation is repeated until the maximum value of the absolute value of is not more than 10 ^-5 . Thereafter, the process proceeds to step S10, where it is determined whether or not ψ has been calculated for all grid points. If ψ has not been calculated, the process returns to step S9.

If ψ has been calculated for all grid points, the process proceeds to step S11, where contour lines are calculated from the obtained grid point values and displayed. Thereby, the contour lines as shown in FIG. 9 are displayed. As is apparent from FIG. 9, the contour lines of the stream function express the lattice point velocity field well.

FIG. 10 shows contour lines of the flow function by integral calculation from the velocity at the grid point .
It can be seen that the flow function distribution on the right side ( shown by the attached circles ) is strange.

[0034]

According to the present invention, the flow trajectory is calculated and displayed as described above. Therefore, it is not necessary to set the flow function around the visualization space from the velocity field interpolated and calculated at the grid points. The flow function value can be calculated with high accuracy only from the speed data, and a good display can be performed. Therefore, even if there is an obstacle such as a cylinder in the visualization space, for example, an evenly-spaced grid can be formed and the flow function can be easily calculated and displayed, and the physical quantity of the flow field can be grasped quickly. You can do it with precision.

[Brief description of the drawings]

FIG. 1 is a flowchart showing a calculation / display procedure according to an embodiment of the present invention.

FIG. 2 is a flowchart illustrating an interpolation algorithm.

FIG. 3 is a diagram of an interpolation area showing grid points to be interpolated;

FIG. 4 is a diagram of grid points and measurements for explaining an interpolation algorithm.

FIG. 5 is a graph showing an example of statistical processing during interpolation calculation.

FIG. 6 is a flow velocity distribution diagram on a grid point obtained by interpolation processing.

FIG. 7 is a diagram illustrating each grid point in a visualization space.

FIG. 8 is an explanatory diagram of constants in Expression 4.

FIG. 9 is a diagram showing contour lines of a stream function.

FIG. 10 is a diagram showing contour lines of a flow function by integral calculation from velocities in a grid.

[Explanation of symbols]

 φ stream function α correction value 格子 grid point

Claims (4)

(57) [Claims] 1. A flow field data for measuring a velocity field from a visualized image of a flow by a tracer tracking method, interpolating the obtained velocity field to grid points, and calculating and displaying a flow function from the result of the interpolation operation. In the method of displaying a trail from a rectangle, a rectangular shape with a plurality of grid points with regularity is provided.
Depart from any of the four corners in the visualization space
Points as well as the corners facing the starting point
It is determined as the end point and passes through the four outer circumferences of the above rectangular visualization space.
Each of the two routes from the starting point to the end point
For this, the flow function φ is calculated from the integral of the velocity, and one of the two calculated flow function values is calculated.
And the flow function value of the other route not selected is
The same value as the flow function value of one of the selected routes
The correction coefficient for the correction is calculated as described above, and the other
The flow function of the route is corrected, and the flow function of the flow field is calculated and displayed by analyzing the elliptic Poisson equation for each of the plurality of lattice points. Trace display method from flow field data. 2. The method according to claim 1, wherein contour lines are calculated from the obtained flow function values and displayed. 3. The flow from the flow field data according to claim 1, wherein the regular grid points are set as intersections of a plurality of straight lines at equal or unequal intervals that are orthogonal to each other. Trace display method. 4. The method according to claim 1, wherein the regular grid points are set as intersections of a plurality of concentric circles and radial lines.