JP2002358473A - Gas flow simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To elucidate a flow of gas around a sphere moving in the gas without making an actual body by trial. SOLUTION: A spherical model which has at least one recessed part or convex part or a groove part or a projection part is set by a computer and a space part is set around the spherical model; and the surface part of the spherical model and the space part are divided into blocks and many grating sections are formed of grating points. While gas is made to flow to the spherical model from one direction of the space part and the gas flows in the space part and passes on the surface of the spherical model, motion elements operating on the flow of the gas are computed by each grating section or each grating point to analyze the flow of the gas around the spherical model.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of simulating gas flow, and more particularly, to a method of setting a sphere model having a concave portion or a groove portion on its surface, and when the sphere model flies while rotating in gas. This is to analyze the behavior of the gas flow passing on the model.

[0002]

2. Description of the Related Art It is known that turbulence of airflow such as separation of gas occurs during flight around an object flying in a gas such as a sphere used in ball games. In particular, when the surface shape changes or when the sphere flies while rotating,
The turbulence of the airflow is further complicated. Such airflow turbulence affects the flight performance of an object, and particularly has a great effect on the flight distance of a sphere such as a ball used in ball games.

For example, in the case of a golf ball, a large number of dimples (recesses) provided on the ball surface greatly affect the aerodynamic characteristics of the ball. It is important to recognize the relationship. In addition, as an advanced player, it is often the case that a backspin is intentionally applied to a ball. In particular, it is important to grasp the aerodynamic characteristics when the golf ball rotates.

[0004] When actually evaluating how the flight characteristics change due to differences in dimples and the like provided on a golf ball, many types of golf balls having various dimple specifications are prototyped, and a hitting test of each prototype golf ball is performed. Is performed and the aerodynamic characteristics of the ball are determined by actually measuring the flight distance and the like. In recent years, instead of hitting experiments, a method has been proposed in which a prototype golf ball is placed in a wind tunnel to measure a lift coefficient, an efficiency coefficient, and the like to analyze aerodynamic characteristics of a golf ball. Various devices, methods, and the like have been proposed in order to analyze data.

For example, in JP-A-6-194242,
A drag and lift measurement method and apparatus for analyzing aerodynamic characteristics of a ball using a wind tunnel have been proposed. As shown in FIG. 21, the measuring device 1 arranged together with the golf ball in the wind tunnel rotates the aluminum shaft 2 for attaching the measurement target T such as a golf ball to the upper end by the motor 3, and
The distortion of the aluminum shaft 2 is detected by a strain-type central three-component force detector 4 arranged around the aluminum shaft 2. When the measuring object T is rotated in the airflow generated in the wind tunnel, the object T becomes in a simulated state with the actual flight state, and the drag or lift applied to the measuring object T is derived from the measured value of the distortion amount of the aluminum shaft 2 and measured. The flight characteristics of the object T are analyzed. In this measurement, airflows under various conditions are created in the wind tunnel, and aerodynamic characteristics can be measured under various conditions.

[0006]

However, Japanese Patent Application Laid-Open No. 6-194242 proposes an experimental method in which a rotating sphere is provided with irregularities in order to easily and effectively select a dimple shape. Also, there is a problem that a real model needs to be created, and a lot of cost and time are required for trial production.

[0007] In the above-described hitting test of a prototype ball or the like or measurement by a wind tunnel test, when there is a concave portion or a groove portion on the surface of an object to be measured, the trial production is difficult and the arrangement of the concave portion or the groove portion is difficult. -It is practically difficult to create a measurement object of various patterns with changed sizes and the like and accumulate measurement data. Therefore, there is a problem that it is not possible to know in detail how the shape, size, arrangement, etc. of the individual dimples provided on the surface of the golf ball affect the gas flow.

As described above, according to the conventional method for evaluating aerodynamic characteristics, only the resulting characteristics of the changed airflow can be determined, and the causal relationship between the newly designed dimple shape and the aerodynamic characteristics cannot be clearly associated. Therefore, a newly designed golf ball often does not always have the desired finish, and it is necessary to redesign and to recreate a prototype golf ball every time to check the aerodynamic characteristics. However, there is a problem that a large amount of time and cost are spent in total, and an efficient design cannot be performed.

Although aerodynamic characteristics are also evaluated by simulation using a computer without performing a trial production, the motion of an object rotating and flying in a gas is accurately represented by a simulation, and the aerodynamic characteristics are evaluated. There is a problem that cannot be grasped. In particular, it is difficult to accurately express the movement of a sphere having irregularities on the surface of a golf ball or the like while flying while rotating.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-described problems, and has been made to elucidate the flow of gas around a sphere moving while rotating in a gas such as a golf ball without trial production of a real object. And analyze how the shape of the sphere surface affects the flow of gas around the sphere,
The objective is to make it possible to visually evaluate the gas flow around a rotating sphere, and to improve the efficiency of development and design.

[0011]

In order to solve the above-mentioned problems, the present invention sets a spherical model having at least one concave or convex portion, or a groove or a projecting portion by a computer, and sets a space around the spherical model. Set the surface part of the spherical model and the space part to form a large number of grid sections by grid points, assuming a state in which the spherical model is rotating, near the surface of the spherical model or near the spherical model The grid section of the space is set, and gas flows from one direction of the space toward the sphere model.In a state where the gas flows through the space and the gas passes through the surface of the sphere model,
A gas flow simulation method is provided, wherein a motion element relating to a gas flow in the space is calculated for each of the lattice sections, and a gas flow around the spherical model is analyzed.

As described above, according to the present invention, a spherical model having a concave portion or a groove portion corresponding to a dimple or the like of a golf ball is set in a virtual space on a computer, and a space is formed around the spherical model. The surface of the sphere model or the space near the sphere model is divided into blocks, and grid points and grid sections are set and calculated. Therefore, by simulating the gas flow continuously flowing into the space by the computer, it is possible to analyze the flow of the gas around the spherical model having the concave portion or the groove portion. Therefore, it is possible to easily understand the influence of the concave portion and the groove portion on the flow of gas during flight.

The grid section of the surface of the spherical model or the space near the spherical model is set on the assumption that the spherical model is rotating. This makes it possible to easily understand the influence of the rotation of the sphere, such as the rotation speed of the sphere model, on the flow of gas around the sphere during flight.
In the case of a sphere, the rotation axis can be set in any way, so by appropriately setting the direction in which the gas flows and the direction in which the rotation of the sphere is considered, the rotation around the sphere can be performed for any rotation. It is possible to analyze the gas flow such as gas separation. Therefore, it is possible to grasp the aerodynamic characteristics when various spheres such as golf balls to which the backspin is applied fly while rotating.

The shapes and sizes of the concave portions and convex portions, or the groove portions and projecting portions provided in the spherical model can be variously configured, and can be a combination of these.
The surface shape of the sphere to be analyzed can be appropriately set.
Further, in the rotation of the sphere, since the rotation axis can be determined in any manner, the rotation axis can be arbitrarily set according to the surface shape of the sphere or the content of analysis.

[0015] The motion element related to the gas flow in the space is calculated for each grid section. Calculating for each grid section means for each grid, for each grid point of each grid, for each center of the grid,
This refers to calculating a motion element for each grid section by various methods, such as for each grid plane, each side of a grid connecting grid points, or any point between grid points.

It is preferable that the space is divided into blocks. Setting the space in the divided blocks makes it easy to set the grid section, and can facilitate the calculation.

Preferably, the grid section is a structured grid. Although it is possible to analyze even an unstructured grid, a highly accurate simulation result can be obtained by using a structured grid. Particularly for simulation of a relatively simple shape such as the surface shape of a golf ball, the structural grid has a high calculation accuracy and is useful. Note that it is also possible to use a combination of a structured grid and an unstructured grid, and it can be set as appropriate according to an analysis model or analysis contents.

In this simulation, it is possible to analyze the state in which the sphere model is flying at the flight speed V while rotating, taking into account the relative speed. It can also be analyzed assuming that it is the same as the state in which the air at the speed V passes where it is.

In a state where the spherical model is rotating,
When the gas passes through the sphere model surface and flows through the space, the motion elements related to the flow of the gas in the space are calculated for each grid section, but in the present invention, the rotation is performed by the method described below. It enables analysis of spherical models.

In the present invention, the rotation of the sphere model is expressed and analyzed using one of the following three methods or a combination thereof.

A method of rotating a lattice near a sphere. In the present method, the grid section of the space is divided into a plurality of regions. For example, the region is divided into a region 1 including a spherical model and a region 2 in the outer peripheral space of the region 1. The rotation of the region 1 itself indicates the rotation of the sphere model. In the vicinity of the interface between the two regions, the flow of the gas is calculated by mathematically interpolating physical quantities such as velocity and pressure (inflow mass, momentum, etc.). Is transmitted between the respective regions to calculate. In addition, it can be divided into a plurality of blocks such as four blocks and six blocks, and these blocks can be connected in an overlapping manner, so that modeling and calculation can be easily performed even in the entire space area. For the above-mentioned interpolation, it is preferable to arrange the grid sections so as to overlap each other near the interface between the areas. In addition, the lattice sections of the space may be arranged in combination such that a plurality of areas overlap without being divided into one space.

Specifically, it is preferable that the region 1 be circular in order to rotate around the spherical model. The outer region 2 may be square for fixing. Assuming that the region 2 is circular, the calculation of the rotational movement increases as the distance from the sphere model to the outside of the space increases. Therefore, the calculation time is shorter when the shape is square. In addition, it is preferable that the region 2 is set to be wide in a space portion on the downstream side of the spherical model (on the gas flow side after passing through the surface of the spherical model). Thereby, the turbulence of the airflow after passing through the spherical model surface and the grid section for analyzing the behavior are widened, so that the behavior and the turbulence of the airflow can be analyzed with high accuracy.

If the diameter of the circle of the cross section of the sphere model is D, it is preferable that the cross-sectional shape of the region 1 is the same as the circle of the cross section and the center and the radius is 1D or more and 5D or less. The reason for the above range is that if the radius of the region 1 is smaller than 1D, the distance between the region 2 and the sphere becomes short, and the accuracy of analysis near the surface of the sphere deteriorates due to the influence of the transfer between the region 1 and the region 2. This is because if the radius of the region 1 is larger than 5D, the calculation becomes complicated. Region 2
Means that the distance between the center of the sphere model and the end of region 2 is 20D
The shape is preferably as follows. If it is larger than 20D, the calculation becomes complicated and the calculation takes a long time.

The interpolation of the physical quantity at each region interface as described above will be described in detail. When the grid section is divided or overlapped into several pieces, or when the area interface periodically coincides, it is necessary to interpolate physical quantities such as speed and pressure in the vicinity of the area interface. In this interpolation method, any interpolation method such as primary linear interpolation, secondary linear interpolation, and spline interpolation may be used. In this way, by interpolating, it is possible to eliminate the deviation of the physical quantity such as speed and pressure between the regions caused by the rotation, and to accurately transmit the physical amount between the regions, and accurately evaluate the rotational movement. can do.

A method in which a lattice near a sphere is deformed. In this method, after the grid section is rotated, the position of the grid section after rotation is predicted, and the rotation is expressed by deforming the grid section to represent the shape at that position. Is what you do. Thus, the rotational movement can be accurately evaluated.

A method of giving rotation as a boundary condition. In this method, in order to more easily represent the rotation, the surface of the spherical model is set to have the speed of the rotation speed component as a boundary condition. That is, the speed of the rotating body is set to be relatively 0 with respect to the flow of air, and the surface of the spherical model is given a speed rω in order to consider rotation (r: distance from the rotation axis to the point, ω: Rotational angular velocity). Thus, the rotational movement can be accurately evaluated.

The surface portion and the space portion of the sphere model are divided into blocks to form a large number of grid sections. The grid sections may be tetrahedral, pentahedral, or a combination thereof.
Alternatively, a combination of these and a hexahedron is preferable. Although it is possible to analyze only the hexahedron, the combination as described above allows the grid sections to be densely packed only where it is desired to analyze finely, making it easier to handle the rotation of the spherical model, and improving the analysis accuracy. Better.

The motion elements acting on the gas flow are the velocity of the gas flow in each axial direction of the three-dimensional spatial coordinate system, the direction of the gas flow, and the pressure of the gas flow on the surface of the object. The calculation is performed every minute time by a gas flow mass conservation equation such as a continuous equation and a gas flow momentum conservation equation such as a motion equation and Navier Stokes equation.

As a specific simulation method,
Using the continuous equation discretized for each grid section into which the space is divided and the Navier-Stokes equation discretized, the calculation is performed for each minute time to calculate the numerical value of each motion element, and the calculation for each grid section is performed. By simulating the gas flow over the entire space by combining the results, a change in the gas flow can be analyzed. Also, when analyzing changes in airflow over time and airflow conditions in different time zones, it is also possible to analyze the change in gas flow in the required time zone by calculating the above formula by advancing the time every minute time. .

In considering the rotation of the spherical model, when the equations are discretized, it is necessary to change the denominator of the above two equations at each time interval according to the rotation. When the sphere model does not rotate, the denominator of the above two equations is always constant because the grid section is constant in an arbitrary grid section. However, when the sphere model rotates, the denominator Is required to correspond to the movement of the position of the grid section, and it is required to refer to the coordinates and physical quantities at the position after the movement of the grid section, and accordingly, the denominator in the equation is changed.

Based on the result of the above calculation, the flow direction and the flow velocity of the gas flow around the spherical model are visualized and analyzed by the vector direction and the vector length. Similarly, from the above calculation results, the pressure distribution applied to the flow of the gas around the sphere model is visualized by isobars or isosurfaces of pressure, and the vorticity distribution is visualized by isolines or isosurfaces of vorticity. Each is analyzed. By substituting the numerical value of the calculation result obtained in this way with a vector, an isobar, or the like, it is possible to visualize various movements of the gas flow.

Through such visualization, it is possible to clearly grasp the change in the gas flow due to the recesses and grooves of the rotating sphere model, and to determine the causal relationship between the recesses and grooves of the rotating object and the aerodynamic characteristics. it can. In addition, the visualization of the gas flow around the sphere model is based on the calculation results other than the above,
It is also possible to support trajectory, particle trace, volume rendering, etc., and input the numerical value of the calculation result of the gas flow into a dedicated visualization program or commercially available general-purpose visualization software etc. The situation can be visualized according to the purpose. Note that volume rendering refers to color-coding a space by physical quantities (pressure, density, and the like) at its coordinates, and indicates that a difference in pressure level or density is represented by a color difference.

The shape of each grid section obtained by dividing the surface portion or space portion of the spherical model as described above can be formed in various polyhedral shapes such as hexahedron, pentahedron, and tetrahedron. May be appropriately combined to form a grid.

As a method of cutting and discretizing a smoothly continuous equation for each of the divided grid sections, any one of a finite difference method, a finite volume method, a boundary element method, a finite element method and the like can be used. The above calculation may be performed for each grid point, each grid center, each section, etc.

In the calculation at a relatively low speed, the gas may be treated as incompressible, so that the calculation may be performed with the gas density kept constant. Further, density may be treated as a variable in consideration of compressibility, and in this case, it is necessary to consider an energy conservation equation.

The calculation may be directly performed by substituting numerical values into the above-described discrete equation and Navier-Stokes equation, and using a gas flow as a turbulence model and substituting a velocity value taking turbulence velocity into consideration. May be calculated. Further, in such an operation, the velocity of the gas flowing in contact with the surface of the spherical model is set to zero, that is, v is the rotational speed of the spherical body, and the pressure condition on the surface is calculated. The speed and pressure conditions on the outer surface of the region are appropriately set so that the internal flow is not stagnated. Further, as described above, in consideration of the rotation of the spherical model, the gas velocity in contact with the surface of the object may be set to a value equivalent to the rotational speed component of the object.

The dimension of the space from the surface of the spherical model to the end of the space is 10 times or more and 10000 times or less of the depth of the recess or groove (height of the projection or protrusion). It is set to become. As a result, it is possible to realize a simulation with high accuracy and excellent operation efficiency. The dimension of the space in the direction away from the surface of the spherical model outward is required to be at least 10 times the depth of the recess or groove, in order to analyze the influence of the surrounding gas such as the recess or groove. As an upper limit, in order to avoid the time required for the calculation within a range where the gas flow is uniform without being affected by the concave portion or the groove portion, etc.,
It is optimal that the depth is 10,000 times the depth of the concave portion or the groove portion.

Outward from the surface of the spherical model (edge of space)
Toward 1 / Re ^0.5 (Re is Reynolds number, Re
= Representative velocity × Representative length / Kinematic viscosity of gas) The thickness of each grid section of the space located in the range of 1 / (100
The value is set so as to increase outward from the surface of the sphere model in the range of not less than 0 · Re ^0.5 ) and not more than 1 / Re ^0.5 . When considering sphere rotation, the thickness of the grid section refers to the length in the direction perpendicular to the rotation axis of the sphere model, the height of the grid section refers to the length in the rotation axis direction of the sphere model, The width of the section indicates the length of the spherical model in the rotation direction.

Since the vicinity of the surface of the sphere model becomes a boundary layer and the flow velocity of the gas changes greatly, the lattice section of the space within 1 / Re ^0.5 from the surface of the sphere model is fine as described above. By dividing the gas flow, the gas flow can be simulated in detail, and the relationship between the concave portion or the groove and the change in the gas flow can be analyzed in detail. In addition, when leaving the vicinity of the surface of the sphere model, the change in the flow velocity becomes gentle, so that the grid section is largely divided as described above to reduce the number of calculations, increase the calculation efficiency, and reduce the time required for the simulation. .

The width and height of each grid section are set to 4 (the diameter if the concave portion is a circle) of the concave portion or the groove portion so that the influence of the concave portion or the groove portion can be surely confirmed. It is preferable that the size be about one-less or less. In addition, since the above-mentioned space part and the grid section are set in the non-dimensional space, the numerical value is a non-dimensional number and the unit is not added.However, when performing the gas flow simulation based on an actual golf ball or the like, the dimensional space is used. It is necessary to return, and a unit corresponding to a numerical value in the dimensionless space is added to perform evaluation.

Further, when a more detailed simulation is performed, a velocity distribution or a turbulence condition of the gas flow may be added to the gas flow as the gas inflow condition, and when the space on the surface of the spherical model is sufficiently large, etc. Alternatively, conditions such as setting the inflow velocity to a uniform velocity may be set. In addition, the flow direction of the flowing gas can be set as appropriate with respect to the rotating sphere in accordance with the purpose evaluated by the simulation method. In addition, since the influence of the recesses or grooves is weakened above the space part far from the spherical model surface, the pressure on the spherical model surface is zero, and the inflow and outflow speeds are simulated at a uniform flow velocity. Can be performed.

The sphere model is applied to a sphere having a concave portion, a groove, or the like, such as a golf ball having a dimple, and a simulation result of a gas flow around the sphere model can be used for designing a dimple of the golf ball. This can be useful for designing a golf ball that flies in a gas with rotation such as backspin.

More specifically, when the gas flow around the spherical model having the concave portion, the convex portion, the groove portion, and the projection portion is simulated and visualized by the computer as described above, the state of the flow around the concave portion, the groove portion, and the like, and It is possible to determine at a glance whether the effect of the recesses and grooves has occurred due to the transition of the gas flow into the intrusion, and easily evaluate whether the size, arrangement, arrangement, etc. of the designed recesses and grooves are optimal. it can. Moreover, in the simulation method of the present invention, the drag coefficient, the lift coefficient, and the moment coefficient can be obtained. In particular, since the moment coefficient can be obtained, the evaluation accuracy can be further improved. In particular, the dimple effect of a golf ball is to reduce the gas resistance by actively turbulently flowing the boundary layer, which is the gas flow on the ball surface, and moving the separation point of the flow backward from the ball surface. Therefore, the analysis result as described above can be effectively used. As a result, the golf ball can be evaluated without performing a trial production and an experiment of the golf ball, and the waste relating to the design can be eliminated, which can contribute to speeding up the development of the golf ball and greatly reduce the development cost.

The analysis result of this simulation is as follows.
The present invention can be used not only for the golf ball described above but also for elucidating the flow of gas on the surface of a sphere when a sphere having a concave portion or a groove on the surface of a tennis ball or the like flies while rotating in the gas.

In the above-described method of simulating a gas flow, the computer program is stored in a storage medium such as a CD or DVD in the form of a program, and the computer is read out of the recorded CD or DVD by a general-purpose computer. It can function as a flow simulation device.

[0046]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a simulation apparatus 10 according to the gas flow simulation method of the present invention,
A computer including a main unit 10a having a CPU, a storage device, and the like, a display 10b, and the like is used as hardware. In terms of software, a program according to the simulation method of the present invention is stored in a storage device of the main body 10a, and various gas flow simulations are enabled by executing the simulation program.

FIG. 2 shows a flow of a method of simulating a program incorporated in the simulation apparatus 10. First, the simulation apparatus 10 is included in the program as shown in FIG. A sphere model 20 is created three-dimensionally in a virtual space of a computer as an object to be simulated by drawing software. In the above drawing software, various shapes of the surface can be created, such as providing irregularities on the surface of the created object.

In the present embodiment, the surface 2 of the spherical model 20
390 recesses 20b are provided over the entire surface of Oa. The sphere model 20 is assumed to be a golf ball,
b assumes a dimple. Thus, the sphere model 20 to be simulated is set.

Next, as shown in FIGS. 4 to 7, a space 21 is set around the spherical model 20 in order to model a space to be simulated for gas flow. At this time, the dimension from the surface 20a of the spherical model 20 to the end of the space 21 is reduced so that the state of the change of the airflow due to the concave portion 20b of the surface 20a of the spherical model 20 can be sufficiently evaluated in consideration of the calculation efficiency. 1 of the depth dimension of 20b
It is set appropriately within the range of 0 to 100 times.

Then, the space 21 is divided into blocks to form a large number of grid sections 22.
The entirety of the surface portion 20c is divided into blocks to form a large number of lattice sections 23. The grid sections 22 and 23 are hexahedrons and are unstructured grids. Further, assuming that the sphere model 20 is rotating around its rotation axis i, the grid sections 22 and 23 of the surface part 20c of the sphere model 20 or the space part near the sphere model 20 are set as follows. are doing. It should be noted that grid sections 22, 23 are provided for the entire space 21 and the surface 20c of the sphere model 20.
However, for convenience of display, in FIG. 7, only the space 21 and a part of the surface 20 c of the sphere model 20 are shown in a lattice shape.

As shown in FIG. 8, the grid section 22 of the space section 21 is divided into two sections: a region 1 including the spherical model 20 and a region 2 in the outer peripheral space of the region 1. When the region 1 itself rotates, the spherical model 20
Represents the rotation of. In the vicinity of the interface between the two regions, physical quantities such as velocity and pressure (inflow mass, momentum, etc.) are mathematically calculated as 2
By interpolating by the next linear interpolation, the flow of gas is transmitted between the respective regions and calculation is performed. The area 1 is spherical for rotation around the spherical model 20, and the outer area 2 is spherical accordingly. Further, assuming that the diameter of the circle of the cross section of the sphere model 20 is D, the region 1 has the same center as the circle of the cross section and has a spherical shape with a radius of 1D. Region 2
Is appropriately set in a range where the distance between the center of the circle of the cross section of the sphere model and the end of the region 2 is 20D or less. In this simulation, the number of nodes constituting the grid section was 1179300, and the area 1 was 81 in the radial direction L1.
The mesh and region 2 are divided into 100 meshes in the radial direction L2, the regions 1 and 2 are divided into 362 meshes in the circumferential direction W, and the sphere model 20 is also divided into meshes.
For convenience of display, the number of lines is smaller than the actual number of meshes in the figure. ).

The size of the grid section 22 which divides the space portion 21 can be variously set, and the size of each section can be partially different. In FIG. 9, in consideration of the fact that the vicinity of the surface 20 a of the sphere model 20 having the concave portion 20 b having the depth t becomes a boundary layer, the change of the gas flow is large, and the change of the gas flow is small above the sphere model 20. Surface 2
In the vicinity of 0a, the thickness of the grid section 22 is divided into small pieces,
The thickness gradually increases outward. Specifically, 1 / Re moves outward from the surface 22a of the spherical model 22.
^0.5 (Re is Reynolds number, Re = representative velocity × representative length / kinematic viscosity of gas)
The thickness dh of 2 is set to be uniform in the present embodiment in order to improve calculation accuracy. Also, from the surface 20a of the sphere model 20, 1 / Re ^{0 .} The thickness h of each of the grid sections 22 located outside of ⁵ is set to be larger than 1 / Re ^{0.5 in} order to shorten the calculation time while maintaining the calculation accuracy, and gradually increases toward the outside. Is set to The representative speed is a ball flight speed, and the representative length is a sphere diameter. The surface 2 of the spherical model 22
The thickness dh of each lattice section 22 located in a range of 1 / Re ^0.5 or less outward from 2a is 1 / (1000 · Re ^0.5 ) or more and 1 / Re ^0.5 or less in relation to the number of Reynolds nozzles. May be set so as to gradually increase in the outer peripheral direction in the range of.

The shape of each grid section 22 is shown in FIG.
As shown, it is formed in a hexahedron and
Sphere model in the space 21
Direction perpendicular to the surface 20a of the
X for matching direction₁Direction, x ₁Orthogonal on the same plane as the direction
X direction₂Direction, x₁Direction and x₂Surface formed by direction
Is the vertical direction (the direction of the rotation axis i of the sphere model 20) as x₃
The direction is set.

As described above, the space 21 and the grid section 2
2, the simulation program causes the gas (air) T to flow toward the surface 20 a of the sphere model 20 from the one surface 21 a side of the space 21 as shown in FIG. 20a is passed through the space 21 in the direction of the arrow in the figure. Such a motion related to the flow of the gas T is represented by a continuous equation (1) corresponding to a general law of conservation of mass in the motion of a general object and a Navier-Stokes equation (1) corresponding to a general law of conservation of momentum of a general object. 2). In this simulation, considering the relative speed, the state in which the sphere model is flying at the flight speed V while rotating is the state in which the air at the velocity V passes while the sphere model is rotating at a fixed position. Are considered the same. When the compressibility is considered, it is necessary to consider the energy conservation equation of equation (α) in addition to equations (1) and (2).

[0055]

(Equation 1)

Equations (1) and (2) are expressed in tensor format.
Where ρ is the density of the gas, v is the velocity, and K is the
External force acting per unit mass, P is stress tensor acting on gas
Le, t is time, E_tIs the total energy per unit mass,
Θ is the heat flow vector, Q is the calorific value per unit mass, and V is
The volume, S, indicates the area. It should be noted that the external force K includes gravity and
The buoyancy corresponds to the pressure t
And shear components. Also, P_ij(I, j = 1,
2, 3) is the above-mentioned x₁x₂x₃Three-dimensional space
A matrix of 3 rows and 3 columns is shown below based on 9 numbers in the reference frame.
It can be expressed by Equation (3). P₁₁ P₁₁ P₁₃  P₂₁ P₂₂ P₂₃  P₃₁ P₃₂ P₃₃ … (3)

In the above-described simulation in which the gas T flows continuously around the spherical model 20, the flow of air is analyzed by calculation for each grid section 22 of the space 21. The above two equations (1) and (2) are used in this calculation, and the two equations are discretized and the calculation is performed in accordance with the division of the space portion 21 by the grid sections 22. The simulation method is performed by appropriately selecting a finite difference method, a finite volume method, a boundary element method, a finite element method, or the like in consideration of simulation conditions and the like.

In the case of using the finite difference method, the calculation by the above-mentioned discretized two equations is performed, for example, in each grid section 22.
At each intersection of minute time dt, a gas velocity, which is a kinetic element related to gas flow at a specific time,
By calculating the flow direction and the gas pressure on the object surface, and combining the calculation results at these intersections, the motion of the gas flow in the entire space 21 can be quantified. Thereafter, the same calculation as described above is performed every elapse of the minute time dt, and the motion of the gas flow in each time zone is digitized. Further, the above-described calculation may be performed at the center of each grid section 22 or on the grid surface, instead of being performed at the intersection of each grid section 22.

Each numerical value relating to the motion of the gas flow obtained as described above is visually displayed using dedicated or general-purpose visualization software, and the result of the simulation is determined. In the case of visualization, for example, only the direction and magnitude of the speed are displayed as a vector to indicate how the speed of the object surface and surroundings are, or isobaric lines connecting the same pressure value to the object surface, etc. Various factors related to the gas flow are visually shown, for example, by displaying the pressure distribution on the pressure surface. In this way, it is possible to visualize how the shape of the spherical model surface affects the flow of the surrounding gas, which is useful for designing the surface shape of the object. In this embodiment, in order to visualize the motion of air, commercially available visualization software (FIELD VIEW: Intelligen, USA) is used based on the calculated values.
(T Light) is used to visualize the air flow situation.

More specifically, FIG. 12 shows the vorticity distribution state of the eddy current around the spherical model 20 at a certain time on the vorticity isosurface. Further, a pressure (Pressure) distribution on the surface of the spherical model 20 is also shown. in this way,
By using the visualization software, it is possible to confirm that a vortex having a thin structure is generated in the downstream part of the sphere model 20, and that the vortex is separated from the ball.

FIGS. 13 and 14 show the flow of air around the sphere model 20 at a certain time using streamlines (velocity Velocity). This allows
It can be confirmed that the flow immediately after the ball is complicated. FIG. 15 shows a pressure distribution on the surface of the sphere model 20. Thus, it is possible to confirm that the pressure has a distribution even in one recess. Specifically, the pressure distribution is visualized by color-coding the surface of the ball according to the pressure distribution status. Further, in FIG. 15, on the surface of the spherical model 20 (pressure distribution, A high → E low), the upper pressure is lower than the lower pressure in the drawing (the upper pressure region E is lower in the drawing). Often). Thus, by visualizing the pressure distribution, it is possible to confirm that a lift is generated.

The vorticity distribution and pressure distribution may be visualized by vorticity and pressure isolines. In addition to the above, based on the calculated values, the flow velocity and flow direction, stream line,
Trajectory lines, particle traces, and the like can also be visualized by line segments, color coding, and the like. The flow direction of the air T is made to coincide with the velocity direction obtained by combining the components for each of the three-dimensional orthogonal coordinates by the above calculation.

As described above, by using the simulation method of the present invention, the flow of air around the sphere when the sphere model having the concave portion is rotating around the rotation axis can be analyzed. The state of the flow can be evaluated. Therefore, the state of air flow around a rotating sphere such as a golf ball having dimples is grasped, and it is determined how the rotation of the concave portion such as a dimple or the sphere influences the state of the air flow. Making it possible.

In the above embodiment, the area 1 and the area 2
Are both spherical in shape, but as shown in FIGS. 16 and 17, in setting the grid section 52 of the space 51,
The area 1 is spherical for rotation around the sphere model 20, and the outer area 2 is a rectangular parallelepiped for fixation. On the downstream side of the sphere model, the turbulence of the airflow after passing through the surface of the sphere model 20 is reduced. In order to analyze the behavior, the area of the grid section 52 on the downstream side may be set wide.

In the above embodiment, the concave portion 20b is provided over the entire surface 20a of the spherical model 20, but instead of the concave portion 20b, the surface 30a of the spherical model 30 is changed as shown in FIG. The spherical model 30 to be simulated may be set by providing the convex portion 30b over the entire surface. Also, as shown in FIG. 18B, a groove 30b ′ may be provided on the surface 30a ′ of the spherical model 30 ′ to set the spherical model 30 ′ to be simulated, or FIG. 18C. As shown in FIG. 5, a projection 30b "may be provided on the surface 30a" of the spherical model 30 ". The arrangement configuration and the number of recesses or grooves on the surface of the spherical model 30" are not particularly limited. Various arrangements for which simulation evaluation is desired, such as a combination of.

The gas flow simulation method described above can be variously modified in accordance with simulation conditions and the like. For example, the following equations (1) and (2) representing the gas flow are shown below. The integral equations (4) and (5)
May be applied. When compressibility is considered, it is necessary to consider the energy conservation equation of equation (β) in addition to equations (4) and (5). When a turbulence model is used as the gas flow, these equations (1) and (2)
(4) In (5), the turbulence velocity v ″ of the turbulence component may be added to the average gas velocity v ′, and the value v ′ + v ″ may be calculated as the velocity component.

[0067]

(Equation 2)

Furthermore, the velocity of the gas flow on the surface of the sphere model, which is a boundary condition of the gas flow, is set to the gas velocity v = 0, usually considering no slip, but if the velocity of the sphere surface is set to zero, Instead, the tangential component of the surface of the spherical model may be calculated as the speed on the surface of the spherical model at the rotational speed of the spherical model. That is, a value obtained by adding the rotation speed component v ″ to the gas speed v in consideration of the rotation speed component v ″ of the spherical model surface may be calculated as the speed component.

The shape of the lattice section 22 is not limited to the hexahedron, but may be a lattice section 2 shown in FIGS. 19 (A), (B) and (C).
2 ', 22 ", and 22'", it is possible to form a triangular pyramid, a quadrangular pyramid, a triangular prism, and the like. Further, as shown in FIG. The space 21 ′ can also be partitioned. Such various kinds of lattice-shaped sections of the space are appropriately determined in consideration of the shape and conditions of the object to be simulated.

In addition to the condition of the gas flowing into and out of the space 21 being a uniform flow velocity, a velocity distribution and a turbulence condition of the gas flow may be added to the flow velocity as a component in accordance with simulation conditions. .

Hereinafter, an experimental example of a sphere simulation using the gas flow simulation method of the present invention will be described in detail.

(Experimental Example 1) By a method similar to that of the first embodiment, a sphere model (golf ball) having a diameter of 42.7 mm rotates around the sphere model at a speed of 55 m / s while rotating. A simulation of gas flow was performed.

The diameter of the sphere (golf ball) surface is
2.0-4.5mm, depth 0.12-0.18mm
390 concave portions (dimples) were provided. In addition, each grid
The thickness of the image is a dimensionless number, and this dimensionless number is
The size corresponding to the case where dh is replaced by
The result is as follows. That is, the kinematic viscosity ν of air is 1
5.01 × 10^-6m²/ S and the representative length D
Is 42.5 mm in diameter of the golf ball, and at the representative speed V
If the speed of a certain sphere model is set to 55 m / s, the ray
The Nords number Re (Re = V · D / ν) is 150,000.
The thickness of the grid section in the space immediately adjacent to the spherical model surface
(X₃Direction) is 1 / 10Re^0.5The representative length D
1.083 × 10^-2mm
Was. Also, the width and height dimensions of the grid section are vertical and horizontal.
Direction (x₂And x ₃Direction) and within the recess (dimple)
The width of the recess so that changes in airflow in the
The dimensions were set to at least 10 × 10. air
Inflow velocity v₁Means that the velocity V of the spherical model 20 is 55 m / s
In order to simulate under the condition₁Also 5
At 5 m / s, the sphere model 20 flies at this speed
Created a situation similar to what you are doing. In addition, speed
At constant velocity, treat air as incompressible, and maintain constant density ρ
And the surface of the spherical model
The velocity component on the Dell surface was also zero.

The rotation speed during rotation is 1000 rpm (SP
= 0.0407), 4000 rpm (SP = 0.162)
A simulation was performed for the two types of 6). Assuming that the diameter of the golf ball is d [m], the flight speed of the golf ball is U [m / s], and the number of rotations is N [rps], the spin parameter SP is πNd / U, which is obtained from each simulation result. FIG. 20 shows the relationship between the drag coefficient Cd, the lift coefficient Cl, and the spin parameter SP.

FIG. 20 is a graph showing the aerodynamic characteristics of a golf ball rotating at a high speed in a wind tunnel airflow. A golf ball was actually manufactured, and the flight speed of the golf ball was 35 to 80 m / s.
Parameters and drag coefficient C during wind tunnel test assuming the
The relationship between d and the lift coefficient Cl is plotted and shown. Although not shown, the moment coefficient can also be calculated. As shown in FIG. 20, the simulation results (Experimental Example 1) are in good agreement with the results of the wind tunnel test that was actually performed, and the simulation analysis is consistent with the actual golf ball flight phenomena. Was confirmed. As described above, by changing the number of revolutions and the surface shape of the rotating sphere, it was confirmed that the gas flow during the rotating flight can be predicted by the present simulation for golf balls having various patterns.

[0076]

As is apparent from the above description, according to the present invention, the flow of the airflow around the spherical model can be grasped, and the change of the gas flow due to the concave portion or the groove provided in the spherical model can be analyzed. can do. In addition, various types of models can be easily created on a computer with respect to the size, shape, arrangement, etc. of the concave portions or the groove portions, and how these various concave portions or the groove portions affect the surrounding gas flow. Can be evaluated objectively and visually with visualization software, taking into account the drag coefficient, lift coefficient and the like. It is also possible to grasp changes in the flow of gas around the sphere model, drag coefficient, lift coefficient, and moment coefficient due to the difference in rotation speed. Therefore, the behavior of the air around the rotating sphere model can be easily grasped.

Further, since various conditions of the gas flow can be set, it is possible to simulate a sphere model with rotation under all conditions, and it is possible to simulate a conventional wind tunnel using a wind tunnel to generate wind. Thus, evaluation of far more gas flow conditions can be performed in a short time.

Further, since the influence of the concave portion and the groove portion of the sphere model to be evaluated on the air flow is performed only by simulation on a computer, it is not necessary to carry out an experiment by actually producing many types of test pieces as in the prior art. The time and cost required for product development and design can be significantly reduced.

More specifically, this can be reflected in the design of a rotating sphere such as a golf ball having dimples on its surface, and the development of an efficient golf ball with respect to the arrangement of dimples can be promoted. In particular, since the behavior of the gas generated around the golf ball and various flow patterns such as gas separation can be predicted, the behavior of the golf ball when the golf ball flies while rotating by the back spin is analyzed. It can be used for product development.

[Brief description of the drawings]

FIG. 1 is a schematic diagram of a computer according to a gas flow simulation method of the present invention.

FIG. 2 is a flowchart of a gas flow simulation method according to the present invention.

FIG. 3 is a diagram showing a sphere model to be simulated;

FIG. 4 is a diagram showing a surface state of a sphere model.

FIG. 5 is a diagram illustrating a state of a spherical model and a mesh in a space portion.

FIG. 6 is a diagram showing a state of a mesh in a space portion.

FIG. 7 is a schematic diagram showing a setting state of a spherical model and a space.

FIG. 8 is a schematic sectional view of an X ₁ X ₂ plane (a plane passing through the center of the spherical model) of a space including the spherical model.

FIG. 9 is a schematic view of a grid section in a space.

FIG. 10 is a detailed view of a main part of a lattice section in a space.

FIG. 11 is a schematic diagram showing a state of a gas flow in a space.

FIG. 12 is a diagram showing a vorticity distribution state of a vortex around a sphere model and a pressure distribution on the surface of the sphere model.

FIG. 13 is a diagram showing a state of air flow around a spherical model using streamlines.

FIG. 14 is a diagram showing a state of air flow around a spherical model and a pressure distribution on the surface of the spherical model.

FIG. 15 is a diagram showing a pressure distribution on the surface of a spherical model.

FIG. 16 is a cross-sectional view of a modified example of a setting state of a space including a sphere model.

FIG. 17 is a schematic diagram showing a modified example of a setting state of a sphere model and a space.

FIGS. 18A, 18B, and 18C are schematic diagrams illustrating shapes of modified examples of the spherical model.

FIGS. 19A, 19B, and 19C are schematic diagrams showing modified shapes of lattice sections, and FIGS. 19D and 19D are schematic diagrams of modified sections in a space.

FIG. 20 is a diagram showing a relationship between a spin parameter, a lift coefficient, and a drag coefficient.

FIG. 21 is a schematic view of a conventional measuring device.

[Explanation of symbols]

 Reference Signs List 20 sphere model 20a surface 20b recess 21 space 22 grid section

 ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Kazuhiro Fujisawa 3-6-9, Wakihama-cho, Chuo-ku, Kobe City, Hyogo Prefecture Within Sumitomo Rubber Industries, Ltd. (72) Inventor Takahiro Sashima Wakihama, Chuo-ku, Kobe City, Hyogo Prefecture 3-6-9 Machi Sumitomo Rubber Industries Co., Ltd. F-term (reference) 2G023 AB27 AC01 5B046 AA00 DA02 JA04

Claims (13)

[Claims] 1. A sphere model having at least one concave or convex portion, or a groove or a projection is set by a computer, a space is set around the sphere model, and a surface portion of the sphere model and the space are set. A large number of grid sections are formed by grid points, and a grid section of the surface of the sphere model or a space section near the sphere model is set assuming a state in which the sphere model is rotating. The gas flows into the space from the sphere model, the gas flows through the space, and the gas passes through the surface of the sphere model. And analyzing the flow of gas around the spherical model. 2. The gas flow simulation method according to claim 1, wherein the space is divided into blocks. 3. The gas flow simulation method according to claim 1, wherein the grid section is formed by a structural grid. 4. The moving element according to the gas flow is a velocity of the gas flow in each axial direction of the three-dimensional spatial coordinate system, a direction of the gas flow, and a pressure of the gas flow on the surface of the object. The gas flow simulation method according to any one of claims 1 to 3, wherein the elements are calculated at every minute time by a gas flow mass conservation formula and a momentum conservation formula. 5. The space according to claim 1, wherein the grid section formed in the space is divided into a plurality of regions, and a space on the downstream side of the sphere model is set large. The described gas flow simulation method. 6. The method according to claim 1, wherein a flow direction and a flow velocity of the gas flow around the spherical model are visualized and analyzed based on a vector direction and a vector length based on a result of the calculation. 2. The gas flow simulation method according to claim 1. 7. A pressure distribution applied to a gas flow around the sphere model based on a result of the calculation is visualized and analyzed by an isobar or a pressure isosurface.
The gas flow simulation method according to claim 1. 8. A vorticity distribution applied to a gas flow around the spherical model based on a result of the calculation and visualized and analyzed by vorticity isolines or isosurfaces. The gas flow simulation method according to claim 1. 9. The method according to claim 1, wherein a streamline, a trajectory, a particle trace, or a volume rendering relating to a gas flow around the spherical model is visualized and analyzed based on a result of the calculation. 2. The gas flow simulation method according to claim 1. 10. The gas flow simulation method according to claim 1, wherein a drag coefficient, a lift coefficient, and a moment coefficient of the spherical model are calculated based on a result of the calculation. 11. The space portion has a dimension from the surface of the spherical model to an end of the space portion that is at least 10 times as large as the depth of the concave portion or the groove portion (the height of the convex portion or the projection portion) and is 10,000. The gas flow simulation method according to any one of claims 1 to 10, wherein the value is set to be twice or less. 12. The space located in a range of 1 / Re ^0.5 (Re is Reynolds number, Re = representative velocity × representative length / kinematic viscosity of gas) or less outward from the surface of the spherical model. The thickness of each grid section of the part is 1 / (1000 · R
from e ^0.5) or 1 ^{/ Re 0.5} the surface of a sphere model in the following range is increased toward the outside, the space located above the 1 ^{/ Re 0.5} from the surface of the spherical model The thickness of each grid section is 1 / Re ^0.5
The gas flow simulation method according to any one of claims 1 to 11, wherein the value is set to be larger. 13. The gas according to claim 1, wherein the sphere is a golf ball and the recess is a dimple, and the flow of gas around the dimple of the golf ball is analyzed. Flow simulation method.