JP3970263B2 - Aerodynamic sound source search system and aerodynamic sound source search method - Google Patents

Description

  The present invention relates to a system and method for analyzing a sound source distribution of aerodynamic sounds.

In recent years, the rate of contribution of aerodynamic sound to noise has increased due to the speedup of transportation means such as cars, railways, and aircraft.
For example, regarding the Shinkansen noise, the noise factors include vibrations generated by contact / vibration between rails and wheels, sparks generated by arcs generated when the pantograph is separated from the overhead line, and around the lower part of the vehicle. The aerodynamic sound generated by the turbulence of the airflow directly shaking the air can be considered. Among these, as the train speed increases, the contribution rate of aerodynamic noise to noise has increased rapidly.

  Conventionally, as a measure to reduce aerodynamic noise, it was a frustrating method to compare the radiated sound by a wind tunnel experiment using a model with different conditions for a phenomenon that is a problem in an actual vehicle. . About the method of measuring a radiated sound, it describes in the following patent documents 1, 2, for example.

JP 2001-31656 A JP 2002-267469 A

The method described above is an excellent method for solving real problems. However, it depends largely on the experience of the experimenter. Moreover, if the physical phenomenon is not correctly grasped, the direction of improvement will be wrong and an effective reduction effect cannot be expected. In addition, with the recent increase in the speed of the Shinkansen, the limit of the exploratory method for reducing aerodynamic noise based on empirical rules is becoming apparent.
Under such circumstances, there is an increasing expectation for an aerodynamic sound reduction countermeasure method based on the theory of fluid noise.

  The present invention has been made in view of such problems, and an object thereof is to provide an aerodynamic sound source search system and an aerodynamic sound source search method for analyzing a sound source distribution of aerodynamic sound based on the theory of fluid noise.

In order to solve the above problems, an aerodynamic sound source exploration system according to the present invention is an aerodynamic sound source exploration system for obtaining a sound source distribution of aerodynamic sound generated around an object located in a flow field, wherein the flow of the flow in the flow field is determined. A flow rate distribution calculating unit that calculates a distribution of velocity vectors, and a sound source calculating unit that calculates a sound source distribution using a calculation formula using a frequency as a parameter based on the distribution of the velocity vectors. .

  In addition, the aerodynamic sound source search system according to the present invention is characterized in that the sound source is calculated in consideration of only scattered sound. In the case of a low Mach number, the scattered sound is more dominant than the direct sound, so only the scattered sound needs to be considered.

The aerodynamic sound source exploration method according to the present invention is an aerodynamic sound source exploration method for obtaining a sound source distribution of aerodynamic sound generated around an object located in a flow field, and calculating a flow velocity vector distribution in the flow field. And a sound source calculation step of calculating a sound source distribution using a calculation formula using a frequency as a parameter based on the distribution of the velocity vector.

The aerodynamic sound source exploration program according to the present invention is a program for aerodynamic sound source exploration that causes a computer to execute processing for obtaining a sound source distribution of aerodynamic sound generated around an object located in a flow field, A flow velocity distribution calculating step for calculating a velocity vector distribution, and a sound source calculating step for calculating a sound source distribution using a calculation formula using a frequency as a parameter based on the velocity vector distribution. To do.

  ADVANTAGE OF THE INVENTION According to this invention, the aerodynamic sound source search system and the aerodynamic sound source search method which analyze the sound source distribution of aerodynamic sound based on the theory of fluid noise can be provided.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(First embodiment)

  First, the configuration of the aerodynamic sound source search system according to the first embodiment of the present invention will be described. FIG. 1 is a diagram schematically showing the overall configuration of an aerodynamic sound source exploration system 10. As shown in the figure, the aerodynamic sound source exploration system 10 includes a PC 21, a display 22 as display means, a keyboard 23 and a mouse 24 as input means.

  The PC 21 also includes an arithmetic unit 211 including a CPU for performing various calculations according to a program, a memory 212 including a semiconductor memory used as a work area for calculations, and an HDD for storing various data. And a storage device 213 including a (hard disk drive). The storage device 213 includes a program DB (database) 214 that stores various programs for realizing the functions of the aerodynamic sound source exploration system 10 described later.

  The aerodynamic sound source exploration system 10 having the above-described configuration is a system that analyzes the sound source distribution of aerodynamic sound based on the theory of fluid noise. Specifically, the velocity vector and sound around an object located in a flow field are analyzed. It is a system that calculates the distribution of sound sources around an object from the Green function that represents the nature of the field.

  Next, a process for calculating the sound source distribution of the dipolar sound by the aerodynamic sound source search system having the above configuration will be described. FIG. 2 is a flowchart showing a flow of processing for calculating a sound source distribution. As shown in the figure, first, in step 1 (S1), first, the arithmetic unit 211 obtains the distribution of the velocity vector u within a predetermined region of the flow field where the object exists (flow velocity distribution calculation function). The velocity vector u is calculated by setting predetermined parameters using numerical calculation such as the LES method. Further, the calculation process of the velocity vector u is realized by the calculation device 211 executing the velocity vector calculation program in the program DB 214. The numerical calculation by the LES method is explained in detail in “Hirohisa Omiya, Hiroshi Miyake, Toru Yoshizawa,“ Numerical fluid dynamics of turbulent flow-model and calculation method ”, University of Tokyo Press, January 1998. ing.

  Subsequently, in S2, the arithmetic unit 211 calculates the distribution of the vorticity vector ω from the distribution of the velocity vector u obtained in S1 by executing the vorticity vector calculation program in the program DB 214 (vorticity vector calculation). function). This vorticity vector calculation program calculates the vorticity vector ω by substituting the velocity vector u calculated in S1 into the equation ω = rot u.

In S3, the arithmetic unit 211 executes the sound source calculation program in the program DB 214 to calculate the sound source distribution of the dipolar sound (sound source calculation function). In this sound source calculation process, the time series data of the outer product ω × u of the velocity vector u calculated in S1 and the vorticity vector ω calculated in S2 is converted into a frequency domain value by Fourier transform, and the result is expressed by the following equation: Substituted in (1), the sound source is calculated.

Here, the vector x is the position vector of the observation point, the vector y is the position vector of the velocity vector u, and α is the angular frequency. The frequency space Green function G (x, y, α) is selected to satisfy the following equation (2) and conform to the object shape satisfying the following equation (3) on the boundary surface (object surface) S: It is.

In Equations (2) and (3), c ₀ is the sound velocity of the flow field, vector n (n _{i in} tensor display) is a unit normal vector of the object plane (boundary surface) S, and is outside the object. The direction of heading is positive, and δ is Dirac's delta function.
Thus, according to the aerodynamic sound source search system that calculates the sound source distribution using the above equation (1) in the frequency domain, it is possible to obtain the sound source distribution with high accuracy from the distribution of the velocity vector u.

Here, the calculation method of the above equation (1) used when calculating the sound source distribution from the velocity vector u and the vorticity vector ω will be described in detail below.
Howe derived the following equation (5) by approximating the Lighthill hydroacoustic fundamental equation expressed by the following equation (4) for a high Reynolds number flow with a small Mach number and small influence of viscosity.

However, B in the above equation (5) is defined by the following equation (6).

Here, the above equation (4) indicates that the non-uniformity of the sound field generated from a relatively small non-uniform region that occupies a part of the infinite spread of a uniform fluid having a constant sound velocity c ₀ and density ρ _0. It is a homogeneous wave equation. Ρ is the fluid density, and p is the instantaneous pressure fluctuation. T _ij is called a Lighthill stress tensor, and is expressed by Equation (7) where δ _ij is the Kronecker delta.

Further, τ _ij is a viscous stress tensor, and is expressed by the following equation (8) when the viscosity coefficient is μ.

Next, the boundary surface of the object placed in the flow field is S, the boundary surface at infinity is Σ _inf, and the region between them is Ω _all . In Σ _inf , the flow is assumed to be uniform. It is assumed that the object is stationary and the flow velocity at the boundary surface S is zero. When the observation point x is sufficiently far from the sound source region, the following equation (9) can be obtained for the sound pressure (Pa) at the observation point of the position vector x by expanding the equation (5) using the Green formula. .

However, the Green function G (x, y, t-τ) satisfies the following formula (10) and has a normal direction differential on the object plane S of 0, that is, the following shape (11). A suitable one is selected.

Next, the Fourier transform equations (12), (13), (14)
(9) is converted from the time domain to the frequency domain, the following formula (15) is obtained, where α is the angular frequency.

At this time, the Green function G (x, y, α) of the frequency space is expressed by the following equations (16) and (17) (the above equations (2) and (3) from the above equations (10) and (11). The one that matches the object shape satisfying the expression ()) is selected.

Here, when the spread of the sound source is sufficiently small compared to the wavelength, the difference in delay time depending on the position in the sound source region can be ignored, and this state is called that the sound source is compact (low frequency). . At this time, a low-frequency approximated green function G (x, y, t) that satisfies the above equations (10) and (11) is expressed by the following equation (18).

When this equation (18) is transformed into the frequency domain using the Fourier transform equation (14), the following equation (19) is obtained for the Green function G (x, y, α).

On the other hand, if compact approximation does not hold, equations (16) and (17) must be solved by some method. Here, the boundary element method (BEM = Boundary Element Method) is used.
First, the solution of the equation (16) that satisfies the equation (17) is defined as G _N (x, y, α). Moreover, when the free space Green function G ₀ (x, y, α) is expressed by the following equation (20),
Equation (20) is the basic solution of Equation (16), and the following Equation (21) holds.

From the green formula,
However, the vector z (z _{i in} tensor display) is a position vector on the boundary surface (object surface) S, and the vector n (n _{i in} tensor display) is a unit normal vector of the boundary surface S, and Ω _all The direction toward is positive. From the above equations (16), (17), and (21), equation (22) becomes the following equation (23).

For details on how to solve the above equation (23) using the boundary element method, see TWWu.
et al, 'Boundary Element Acoustics', WIT Press, 2000, etc.

By performing an extreme operation to bring the point y in the flow closer to the predetermined point z _p on the boundary surface S, the above equation (23) becomes the following equation (24).

By discretizing separately the interface element, G _N on the boundary surface (x, z _p, α) is obtained. Then, by substituting the equation (23), G _N in y any point in the flow (x, y, alpha) is determined.

Equation (23) describes how a point sound source placed at an arbitrary point y in the flow is scattered by the boundary surface S and reaches the observation point x. The first term on the right side of Equation (23) represents the direct sound propagation, and the second term on the right side of Equation (23) represents the propagation of the scattered sound from the boundary surface S. Therefore, G ⁱ (x, y, α) and G ^s (x, y, α) are defined by the following equations (25) and (26),

When G _N (x, y, α) is expressed by the following equation (27),
The above equation (15) becomes the following equation (28).

Here, a calculation example of G ^s (x, y, α) is shown in FIG. FIG. 3 shows a calculation example of G ^s (x, y, α) in the scattered field around the two-dimensional wing. FIG. 3A shows the case where the frequency of the sound source is 100 Hz. This shows a case where the frequency of the sound source is 3000 Hz.

Then, as in the above equation (25) and (26), in the following equation (29) and (30), defining a p _a ^s (x, α) and ^{_{p a i (x, α)}} .

Then, the sound pressure p _a at the observation point x (x, alpha) will be defined by the following equation (31).

As a result, the above equation ^{_{(29) p a s (x}} , α) defined by represents the scattered sound scattered by the boundary surface S, p _a ⁱ (x, defined by the above formula (30), alpha ) Represents the direct sound transmitted directly from the turbulence in the fluid. Also, the integrand term of equation (29),
Is the sound source of scattered sound, the integrand of equation (30),
Can be regarded as direct sound sources.

Here, regarding the above equation (32), the green function G ^{s in} the frequency space is defined by the following equation (26) with the coordinate of the point on the object plane S as the vector z, as described above.

The Green function G _N (x, z, α) is a vector n which is a vector normal to the sound velocity c ₀ , a unit normal vector of the object plane S and going outward, and a Dirac delta function δ. Is a solution of the following equation (2) that satisfies the following equation (3) on the object plane S:

The green function G ₀ (z, y, α) is a free space Green function expressed by the following equation (34).

Then, the following equation (1), which is the integrand of equation (15) described above, which is the sum of equations (32) and (33), can be regarded as a total sound source.

  As described above in detail, in the present embodiment, Equation (1) for obtaining the sound source distribution is obtained by developing the Lighthill hydroacoustic basic equation using the Green function in the frequency domain. It was. Therefore, according to the aerodynamic sound source exploration system 10 according to the present embodiment, the sound source distribution can be obtained with high accuracy based on the velocity vector of the flow field even when the sound source has a high frequency (when it is not compact). Is possible.

  In the case of a low Mach number, generally, the scattered sound of the equation (32) becomes dominant compared to the direct sound of the equation (33). Therefore, in the present embodiment, the sound source is calculated using the expression (1) that combines the scattered sound and the direct sound, but the sound source is calculated using the expression (32) of the scattered sound instead of the expression (1). You may comprise so that it may obtain | require. In particular, when calculating a sound source from a velocity vector in a finite region, it is preferable to use equation (32). Here, the low Mach number means a case where the Mach number M is sufficiently smaller than 1. Preferably, it means that the Mach number M is smaller than 0.3.

(Second Embodiment)
Next, a second embodiment of the present invention will be described. FIG. 4 is a diagram illustrating a configuration of an aerodynamic sound source search system 10 according to the second embodiment. The aerodynamic sound field exploration system according to the present embodiment measures a velocity vector in a finite region using a PIV system that measures a flow velocity distribution by a technique called PIV, and obtains a sound source distribution based on the measured value. It is.

  The PIV system is described in detail in, for example, “Visualization Society of Japan,“ PIV Handbook ”, Morikita Publishing Co., Ltd., July 2002”. In addition, the same number is attached | subjected to the same structure as the structure which concerns on 1st Embodiment, and detailed description is abbreviate | omitted.

  As shown in FIG. 4, the aerodynamic sound source search system 10 includes a smoke generation device 11, a sheet illumination device 12, a CCD camera 13, and a sound source analysis device 20. The sound source analysis device 20 includes a PC 21 and a display 22, and the PC 21 includes an arithmetic device and a recording device (not shown).

  As shown in FIG. 4, the measurement target of the aerodynamic sound source exploration system is a cylindrical model 14. The cylindrical model 14 is arranged with its upper and lower surfaces parallel to the ground, and its size is 50 mm in diameter and 600 mm in length. The aerodynamic sound source exploration system 10 is arranged in a wind tunnel device (not shown). When the wind tunnel device is operated, wind blows from the left side to the right side in the figure, and a flow field is formed around the cylindrical model 14. The wind speed of this wind tunnel device is 150km / h (41.7m / s). Due to this flow field, aerodynamic sound is generated around the cylindrical model 14, and the aerodynamic sound source exploration system 10 analyzes the spatial distribution of this aerodynamic sound source.

  The PC 21 is connected to the CCD camera 13, and an image photographed by the CCD camera 13 is stored in a recording device in the PC 21. The arithmetic device in the PC 21 is configured to perform processing / analysis on the image data stored in the recording device. The analysis result is displayed on the display 22.

  The sheet illumination device 12 illuminates a predetermined two-dimensional measurement region (see FIG. 4) of the flow field with a sheet-like illumination light at a cycle of 4 Hz, and the CCD camera 13 performs imaging in synchronization with this illumination. ing. The sheet illumination device 12 and the CCD camera 13 are synchronized by a synchronization device (not shown) connected thereto. Therefore, the recording device in the PC 21 stores a plurality of images taken in time series at minute time intervals.

  5 is a diagram showing the positional relationship between the CCD camera 13 and the cylindrical model 14, FIG. 5 (a) is a diagram showing the positional relationship seen from the front of FIG. 4, and FIG. 5 (b) is seen from the upper side of FIG. It is a figure which shows a positional relationship.

As shown in the figure, the CCD camera 13 is arranged at a position perpendicular to the measurement area plane and capable of photographing a predetermined measurement area around the cylindrical model 14. In the present embodiment, it is arranged at a position where the right side (downstream side) of the cylindrical model 14 can be photographed in the drawing. The origins of the x-axis, y-axis, and z-axis are set at positions near the center of gravity of the cylindrical model 14.
Next, an operation when the spatial distribution of the aerodynamic sound source is analyzed by the aerodynamic sound source search system 10 will be described.

  First, after operating the wind tunnel device, the smoke generator 11 generates smoke. The smoke generator 11 is installed on the left side, which is upstream of the flow from the cylindrical model 14 in the figure, and the generated smoke is mixed into the flow field around the cylindrical model 14. Thereby, the flow field is visualized. This smoke needs to contain particles that can follow the flow. This is because if the particle diameter is too large or the particle mass is too heavy, it becomes impossible to follow the flow.

  After the smoke is mixed, the sheet illumination device 12 irradiates the measurement area near the cylindrical model 14 with the sheet illumination light. Subsequently, an image of the flow field at the moment of illumination is taken by the CCD camera 13. An image photographed by the CCD camera 13 is transferred to the PC 21 of the sound source analyzer 20 and stored in a recording device in the PC 21.

Next, processing for analyzing an image stored in the recording device in the sound source analysis device 20 will be described with reference to FIG. 2 as in the first embodiment.
First, in S1, the PC 21 calculates the velocity vector distribution (flow velocity distribution) by analyzing the movement of the particles between two images adjacent in time series stored in the recording device (flow velocity distribution). Calculation function). In this image analysis, each image is divided into 35 × 38 = 1330 cells, and a velocity vector u is calculated for each cell. Since this processing is the same as the processing in the general PIV system described above, detailed description thereof is omitted.

  As the velocity vector obtained, for example, x = 100 mm, y = 150 mm, z = 0 mm, instantaneous flow velocity in x direction = 10 m / s, instantaneous flow velocity in y direction = −5 m / s, and x = 100 mm , Y = 100 mm, z = 0 mm, velocity vectors such as an instantaneous velocity in the x direction = 20 m / s and an instantaneous velocity in the y direction = 10 m / s can be obtained.

FIG. 6 is a diagram showing the distribution of the velocity vector u obtained by the image analysis of S1. FIG. 6A is a diagram showing the instantaneous velocity distribution at time t ₁ , and FIG. 6B is a diagram showing the instantaneous velocity distribution at time t ₂ . In FIG. 6, an arrow indicates a velocity vector, the length of the arrow indicates the size of the velocity vector, and the direction of the arrow indicates the direction of the velocity vector. In the figure, the magnitude of the velocity vector located at the upper and lower ends and facing the horizontal direction is the wind speed of 150 km / h of the wind tunnel device described above. From the velocity vector distribution shown in FIG. 6, it can be seen that Karman vortices are generated on the downstream side of the cylindrical model 14.

  Next, in S2, the arithmetic unit 211 executes the vorticity vector calculation program in the program DB 214 to obtain the vorticity vector ω distribution from the distribution of the velocity vector u obtained in S1 (vorticity vector calculation function). ). This vorticity vector calculation program calculates the vorticity vector ω by substituting the velocity vector u calculated in S1 into the equation ω = rot u.

In S3, the arithmetic unit 211 executes the sound source calculation program in the program DB 214 to calculate the sound source distribution of the dipolar sound (sound source calculation function). In this sound source calculation processing, the time series data of the outer product ω × u of the velocity vector u calculated in S1 and the vorticity vector ω calculated in S2 is converted into a frequency domain value by Fourier transform, and the result is described above. By substituting into the scattered sound equation (32), an aerodynamic dipole sound source is calculated.

  In the second embodiment, the velocity vector in the finite region is measured by the PIV system. In the case of a low Mach number, the scattered sound is more dominant than the direct sound, and therefore the scattered sound (32) is used. In addition, since scattered sound is hardly affected by the velocity vector outside the measurement area, the sound source can be obtained with high accuracy by substituting the velocity vector and vorticity vector within the measurement area by the PIV system into equation (32). Can be sought.

  According to the aerodynamic sound source exploration system according to the second embodiment, the same effect as that of the first embodiment is achieved, and the dipole sound source distribution is analyzed using the measurement value of the PIV system. Even if it is difficult to capture with high accuracy by theoretical methods such as numerical calculation of fluid, such as turbulent transition and boundary layer behavior near the wall, it is possible to analyze with sufficient accuracy. Further, by using the measured value of the PIV system, it is possible to accurately analyze a phenomenon such as a cavity sound in which the generated compression wave affects the behavior of the fluid.

  The first and second embodiments of the present invention have been described in detail above. However, the embodiments of the present invention are not limited to the above-described embodiments, and do not depart from the spirit of the present invention. Various modifications are possible.

  For example, each function of the aerodynamic sound source exploration system described above is realized by the arithmetic device executing a plurality of programs stored in the program DB, but all functions are realized by a single integrated program. It is good also as a simple structure. In addition, each function may not be realized by the execution of the program by the arithmetic unit, but an electronic circuit for realizing each function may be used. In other words, it may be configured so that the function of the aerodynamic sound source search system according to the present embodiment can be realized by appropriately combining software and hardware.

  In the second embodiment, the aerodynamic sound source distribution around the cylinder model is obtained for the sake of simplicity. However, the distribution of the aerodynamic sound is not limited to the cylinder model, and is not limited to the cylinder model. Any shape model may be used as long as it is an object to be analyzed.

1 is a diagram showing a schematic configuration of an aerodynamic sound source search system according to a first embodiment of the present invention. It is a flowchart which shows the flow of the process which calculates the sound source distribution which concerns on the 1st Embodiment of this invention. It is a figure which shows the example of posting of the Green function in the frequency space which concerns on the 1st Embodiment of this invention. It is a figure which shows schematic structure of the aerodynamic sound source search system which concerns on the 2nd Embodiment of this invention. It is a figure which shows the positional relationship of the CCD camera which concerns on the 2nd Embodiment of this invention, and a cylindrical model. It is a figure which shows distribution of the velocity vector calculated | required by the aerodynamic sound source search system which concerns on the 2nd Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Aerodynamic sound source exploration system 11 Smoke generator 12 Sheet illumination device 13 CCD camera 14 Cylindrical model 20 Sound source analyzer 21 PC
211 arithmetic device 212 memory 213 storage device 214 program DB
22 Display 23 Keyboard 24 Mouse

Claims (7)

An aerodynamic sound source exploration system for obtaining a sound source distribution of aerodynamic sound generated around an object located in a flow field,
A flow velocity distribution calculating means for calculating a distribution of flow velocity vectors in the flow field;
Sound source calculation means for calculating a sound source distribution using a calculation formula using a frequency as a parameter based on the distribution of the velocity vector;
An aerodynamic sound source exploration system characterized by comprising The calculation formula of the frequency domain is as follows: the velocity vector is the vector u, the vorticity vector is the vector ω, the observation point coordinates are the vector x, the velocity vector coordinates are the vector y, and the angular frequency is α. The aerodynamic sound source search system according to claim 1, wherein
However, the Green function G in the frequency space is defined as follows, where the velocity of sound is c ₀ , the vector normal to the object plane S and the vector positive from the object outward direction is a vector n, and the Dirac delta function is δ. A material that satisfies the equation (2) and that matches the object shape on the object surface S that satisfies the following equation (3) is selected.
  The aerodynamic sound source search system according to claim 1, wherein the sound source calculation unit calculates a sound source in consideration of only scattered sound. The calculation formula considering only the scattered sound is as follows: the velocity vector is vector u, the vorticity vector is vector ω, the observation point coordinates are vector x, the velocity vector coordinates are vector y, and the angular frequency is α. The aerodynamic sound source exploration system according to claim 3, wherein
However, the Green function G ^s in the frequency space is defined by the following equation (26) with the coordinates of the point on the object plane S as a vector z,
The Green function _GN is defined on the object plane S, where the sound velocity is c ₀ , a vector normal vector of the object plane S and a vector n that is positive in the direction outward from the object is a vector n, and the Dirac delta function is δ. The following equation (2) that satisfies the following equation (3):
The Green function G ₀ is a free space Green function expressed by the following equation (34).
An aerodynamic sound source exploration method for obtaining a sound source distribution of aerodynamic sound generated around an object located in a flow field,
A flow velocity distribution calculating step for calculating a flow velocity vector distribution in the flow field;
A sound source calculation step of calculating a sound source distribution using a calculation formula using a frequency as a parameter based on the distribution of the velocity vector;
An aerodynamic sound source exploration method characterized by comprising: 6. The aerodynamic sound source search method according to claim 5, wherein the sound source calculation step is a step of calculating a sound source in consideration of only scattered sound. An aerodynamic sound source exploration program that causes a computer to execute processing for obtaining a sound source distribution of aerodynamic sound generated around an object located in a flow field,
A flow velocity distribution calculating step for calculating a flow velocity vector distribution in the flow field;
A sound source calculation step of calculating a sound source distribution using a calculation formula using a frequency as a parameter based on the distribution of the velocity vector;
An aerodynamic sound source exploration program characterized by comprising