JPH06123671A - Method of indicating flow trace from flow field data - Google Patents

Abstract

PURPOSE:To indicate a flow trace at a short time by a method wherein a flow function of a plurality of circumferences is calculated from the integration of a speed and two of the obtained function values which have the same edge values are adjusted to calculate a flow function of a flow field. CONSTITUTION:It is assumed that parallel lines which are located perpendicularly to each other by the same intervals in a region to be analyzed in which the intersection points are made to be grid points. Next, flow speed data of a prescribed range of flow speed measuring points is extracted from the grid points to be interporated. In the case that the number of the extracted data does not reach a prescribed number, a radius of the extracting region is enlarged to extract once again. One combination from three pieces of data taken from (n) pieces of data is used for the execution of interporating calculation. A center value is obtained by means of a statically operation. Thus, interporating grid points are set sequentially and the interporating calculations are repeated until when the calculations for all of the grid points of the interporation region are completed. A flow function is calculated by utilizing the interporated grid point data to obtain various types of physical values of a flow field.

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 flow trace from flow field data, and more particularly to calculating the velocity of a visualization space by tracing the tracer particle from a visualized image visualized by the tracer particle, It is suitable for use in a method of calculating and displaying a flow trace in a two-dimensional cross section from the result of interpolation at a grid point.

[0002]

2. Description of the Related Art As is well known, conventionally, in order to calculate the flow velocity of a fluid, for example, a laser velocity meter is used for measurement,
Alternatively, the measurer determines the measurement point in advance in the two-dimensional cross section of the measurement space and measures it.

The above-mentioned measurement points are determined as grid points at equal intervals or arbitrary non-uniform intervals, and the flow field is measured by measuring the velocity at each grid point. According to this measurement, the inflow / outflow amount of the fluid at the element formed by the four grid points is stored, and the flow function or excess can be easily measured from the velocity measurement result.

[0004]

However, in the conventional technique as described above, it takes a huge amount of time to measure the flow velocity in the flow field. In order to solve this problem, there is an attempt to use a technique of image processing from an image visualized by tracer particles and simultaneously measure a visualized space at multiple points using an algorithm based on a tracer particle tracking method.

This method is described, for example, in the paper "Journal of the Japan Society of Mechanical Engineers (B) Vol. 55, 509 (1989-1), 1".
There are methods disclosed on pages 07-114. In the above method, the tracer particles mixed in the fluid in advance are irradiated with light using a light emitting device such as a strobe, and the locus thereof is subjected to image processing.

However, in such a flow visualization method, since the measurement data at the same time are arbitrarily present in the visualization space, it is difficult to perform a flow function or excessive measurement in the visualization space. SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and an object of the present invention is to enable the trace of a flow field to be obtained and displayed in a short time.

[0007]

According to the method for displaying a flow track from flow field data of the present invention, a velocity field is measured from a visualized image of a flow by a tracer tracking method, and the obtained velocity field is interpolated at grid points. In the method of displaying a flow trace from flow field data, in which a flow function is calculated from the result of interpolation calculation and displayed, the flow function φ of four circumferences is calculated from the integral of velocity, and the end of the obtained flow function value is Corrects the flow function values of two identical circles and analyzes the elliptical Poisson equation to calculate and display the flow function of the flow field.

Another feature of the present invention is that
The contour lines are calculated and displayed from the values of the obtained stream function.

Another feature of the present invention is that the grid points having regularity are set as intersections of a plurality of straight lines which are orthogonal to each other and are equally spaced or unequal spaced.

Further, in the present invention, the grid point having the regularity is set as an intersection of a plurality of concentric circles and a radial line.

[0011]

In the method for displaying a trace of flow field data according to the present invention, since the measured data can be interpolated once at the grid points and the flow function can be calculated only from the flow velocity data at the interpolated grid points, It becomes unnecessary to input the flow function value of the circumference. Also, since the stream function is calculated only from the velocity field, even if there is a complicated obstacle in the visualization space, the stream function can be calculated and displayed from the velocity field in the visualization space in a short time. Will be easier.

[0012]

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

In order to perform data interpolation, as shown in FIG. 2, first, in step S10, a grid point sequence is created in the area to be analyzed. FIG. 3 shows an example of grid points. In this example, straight lines that are orthogonal to each other at equal intervals are assumed, and the intersections thereof are grid points. Also, in this example, the straight lines are equidistant, but they may be unequal. For example, the lattice spacing may be changed between the part of interest and its surroundings, or polar coordinates composed of concentric circles and radial lines may be assumed.

Next, in step S11, as shown in FIG. 4, the flow velocities of the flow velocity measuring points K, L, M, N, ... Data (n
Individual). In this case, the radius L is, for example, 6 times the distance between grid points. n is a fixed number P sequentially taken out from the measurement points near the interpolation point G (a number exceeding 3; for example, 10)
And

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 step S13 is performed.
Repeat 11 again. In step S13, the value of P may be sequentially reduced to, for example, 8, 6, ...

Next, in step S14, grid point data is interpolated using one set of _n C ₃ combinations in total obtained by extracting 3 data from the _n 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 u, and the flow velocity data of the measurement point K is u _k , (dx) _k , (dy) _k , and the grid point G and the measurement point K are used.
If the distances between and, du / dx and du / dy are velocity gradients at the grid point G,

[0017]

[Equation 1]

[0018] The other two measurement points L, M (flow velocity data u _L , u _M , distances (dx) _L , (dx) _M , (d
y) _L and (dy) _M ), if the same linear form is given, the interpolated data u to be obtained can be obtained from the simultaneous equations of Equation 2 below.

[0019]

[Equation 2]

The interpolated value calculated in step S14 is 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} =
The median value of 1 to _n C ₃ ) is calculated by statistical processing. This statistical processing may be, for example, average value calculation Σu _i / _n C ₃ . Alternatively, as shown in FIG. 5, the frequency N of the value u _i may be obtained, and statistical calculation may be performed to obtain the median value by Gaussian approximation or binomial approximation.

Next, the next interpolation grid point is set in step S17, and steps S11 to S are executed until the completion of interpolation calculation for all grid points in the interpolation area is detected in step S18.
The process of 17 is repeated.

As described above, the flow velocity vector on the grid point as shown in FIG. 6 can be interpolated and calculated. Then, the interpolated grid point data can be used to calculate the flow function, and further various physical quantities of the flow field can be obtained based on the flow function.

Next, an example of the procedure for calculating the flow function values of all the lattice points will be described with reference to the flowchart of FIG. As shown in FIG. 1, first, initial setting is performed in step S1. This is performed by setting φ _{(1, 1) to} φ ₍ ε _xpI, ε _XPJ) to 0 as shown in the calculation procedure explanatory diagram of FIG. 7.

Next, from φ _{(1, 1)} = 0, φ
_{(2, 1)} , φ ₍₃ , ₁₎・ ・ ・ φ ₍ ε _{xpI, 1)} , φ ₍ ε _{xpI, 2)}・
_{·· φ (ε xpI, ε xpJ} ) calculating a (step S2), phi accordance unit _{(2) (1, 2)} , φ (1, 3) ··· φ
_(1, ε _xpI) , φ _(2, ε _xpI) ... φ ₍ ε _xpI, ε _xpJ) are calculated (step S3).

[0025]

[Equation 3]

Then, in step S4, the correction coefficient α is calculated from the value obtained in step S2. That is, the correction coefficient α is obtained from the equation α = φ _{B (} ε _xpI, ε _xpJ) / φ _{A (} ε _xpI, ε _xpJ) .

Then, the process proceeds to step S5 and step S5.
Φ _{(1, 2)} = φ _{(1, 2)} / α φ _{(1, 3)} = φ _{(1, 3)} / α · · · · φ _(1, ε _{xpJ )} = Φ _(1, ε _xpJ) / α _··· φ ₍ ε _xpI, ε _xpJ) = φ ₍ ε _xpI, ε _xpJ) / α to correct the φ value of the circumference of the means (2). Next, in step S6, Formula 4 is developed.

[0028]

[Equation 4]

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

Next, in step S7, ψ 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 Equation 4. Next, in step S8, the value of ψ ² _{I, J} is calculated for each grid using the value of ψ ¹ _{I, J} calculated in step S7.

Next, in step S9, the above-mentioned calculation is repeated, and ψ ⁿ _{I, J} −ψ ^{n + 1} _{I, J in} each lattice.
The calculation is repeated until the maximum absolute value of becomes less than 10 ^-5 . After that, the process proceeds to step S10, it is determined whether or not ψ of all grid points has been calculated, and if not calculated, the process returns to step S9.

When ψ of all grid points is calculated, the process proceeds to step S11, and contour lines are calculated and displayed from the obtained values of grid points. As a result, contour lines as shown in FIG. 9 are displayed. As is apparent from FIG. 9, the contour lines of the stream function well represent the lattice point velocity field.

FIG. 10 shows the contour lines of the stream function by the integral calculation from the velocity in the grid, and the stream function distribution on the right side of the cylinder (indicated by ● in the figure) due to the velocity interpolation error to the grid points. It turns out that something is wrong.

[0034]

As described above, according to the present invention, the flow trace is calculated and displayed. Therefore, it is not necessary to set the flow function of the circumference of the visualization space from the velocity field interpolated at the grid point. , The flow function value can be accurately calculated only from the velocity data, and good display can be performed. Therefore, for example, even if an obstacle such as a cylinder exists in the visualization space, it is possible to easily calculate and display the flow function by forming an equidistant grid, and to grasp the physical quantity of the flow field in a short time. You can do it with precision.

[Brief description of drawings]

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

FIG. 2 is a flowchart for explaining 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 velocity distribution map on grid points obtained by interpolation processing.

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

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

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

FIG. 10 is a diagram showing contour lines of a stream function by an integral calculation from velocities in a lattice.

[Explanation of symbols]

 φ Stream function α Correction value ψ Lattice point

Claims (4)

[Claims] 1. 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 at grid points, and calculating and displaying a flow function from the result of the interpolation computation. In the flow display method from, the flow function φ of the four circumferences is calculated from the integral of the velocity, and the flow function values of the two circumferences with the same end among the obtained flow function values are corrected, and the elliptical Poisson A flow trace display method from flow field data, characterized in that a flow function of a flow field is calculated and displayed by analyzing an equation. 2. The flow trace display method from flow field data according to claim 1, wherein contour lines are calculated and displayed from the values of the obtained stream function. 3. The trace from the flow field data according to claim 1, wherein the grid points having regularity are set as intersections of a plurality of straight lines which are orthogonal to each other and are equally spaced or unequal spaced. Display method. 4. The flow trace display method from flow field data according to claim 1, wherein the grid points having regularity are set as intersections of a plurality of concentric circles and radial lines.