WO2019155656A1

WO2019155656A1 - Propeller, propeller designing method, propeller designing method program, and information storage medium

Info

Publication number: WO2019155656A1
Application number: PCT/JP2018/027481
Authority: WO
Inventors: 嶋　英志; 誠司堤; 圭一郎藤本
Original assignee: 国立研究開発法人宇宙航空研究開発機構
Priority date: 2018-02-08
Filing date: 2018-07-23
Publication date: 2019-08-15
Also published as: JP6979205B2; JP2019138195A

Abstract

[Problem] To provide a propeller which is configured to be lightweight, maintains a loop shape during rotation, and has low noise, a propeller designing method, a propeller designing method program, and an information storage medium. [Solution] A propeller comprising a rotating blade connected around a rotating shaft, and including: a first rotating blade portion which includes a first blade upper surface and a first blade lower surface and has a sweepback angle; and a second rotating blade portion which includes a second blade upper surface and a second blade lower surface and has an advance angle. The second blade upper surface is continuous with the first blade lower surface. The second blade lower surface is continuous with the first blade upper surface. The first rotating blade portion and the second rotating blade portion form a loop shape. When the rotating blade rotates about the rotating shaft, at least a part of a central line of the rotating blade has a shape, formed in at least a partial arbitrary position, corresponding to the shape of a catenary line such that a tension and a centrifugal force acting in a first direction of the rotating blade are balanced, and such that a tension and a centrifugal force acting in a second direction of the rotating blade are balanced.

Description

Propeller, propeller design method, propeller design method program, and information storage medium

The present invention relates to a propeller, a propeller design method, a propeller design method program, and an information storage medium.

Propellers are widely used in air supply and aircraft propulsion engines. Some propeller blades have a loop shape for the purpose of improving the efficiency of the propeller (see, for example, Patent Document 1).

Special table 2016-507410 gazette

However, the external force acting on the propeller in the air is mainly centrifugal force, and the loop shape cannot be maintained at the time of rotation with a lightweight configuration unless appropriate consideration is given to the centrifugal force. Furthermore, the propeller is also required to reduce noise.

In view of the circumstances as described above, an object of the present invention is to provide a propeller, a propeller design method, a propeller design method program, and an information storage medium that are configured to be lightweight, maintain a loop shape during rotation, and have a low noise. is there.

In order to achieve the above object, a propeller according to an embodiment of the present invention includes a rotating shaft and a rotating blade. The rotor blade is connected around the rotation axis, and has a first rotor blade portion having a first blade upper surface and a first blade lower surface and having a receding angle, and has a second blade upper surface and a second blade lower surface and moves forward. A second rotor blade having a corner. The upper surface of the second blade is connected to the lower surface of the first blade, the lower surface of the second blade is connected to the upper surface of the first blade, and a loop shape is formed by the first rotating blade portion and the second rotating blade portion. When the direction perpendicular to the axial direction of the rotating shaft and from the rotating shaft toward the tip of the loop shape is the first direction, and the direction orthogonal to the axial direction and the first direction is the second direction, the rotor blade is centered on the rotating shaft. At least a part of the center line of the rotor blade formed when the rotor blade is rotated, the tension acting in the first direction of the rotor blade and the centrifugal force are in harmony, and the rotor blade second A catenary shape in which the tension acting in the direction and the centrifugal force are harmonized.

According to such a propeller, at least a part of the catenary line shape in which the centrifugal force acting on the rotor blades during rotation and the tension in the rotor blades balance becomes a loop shape, so that the rotor blades are deformed by the centrifugal force. It becomes difficult.

In the above-described propeller, the connecting portion where the first rotating blade portion is connected to the rotating shaft and the connecting portion where the second rotating blade portion is connected to the rotating shaft are shifted in the axial direction, and the first connecting portion is the second connecting portion. You may locate in the downstream of the flow direction of air rather than a connection location.

According to such a propeller, the second rotating blade portion is less likely to hit the weak region emitted by the first rotating blade portion, and the rotating blade tends to rotate efficiently without receiving a load.

In the above-described propeller, the first rotating blade portion and the second rotating blade portion may have the same angle of attack with respect to a plane orthogonal to the rotation axis.

According to such a propeller, the magnitudes of the twisting force of the first rotating blade received from the air and the twisting force of the second rotating blade received from the air are substantially the same, and they are offset. Thereby, it exists in the tendency for a rotary blade to become difficult to deform | transform at the time of rotation.

In the above-described propeller, the chord line and the camber line in the rotor blade may coincide with each other at the tip of the loop shape.

According to such a propeller, no lift is generated in the vicinity of the tip of the rotor blade, and it tends to be difficult to be deformed even if its width is narrowed.

In the above propeller, a plurality of rotor blades may be arranged around the rotation axis, and a plurality of rotor blades may be arranged at equal intervals.

Such propellers tend to exert large wind power because they have multiple rotor blades.

In the above propeller, the rotor blade may be made of a flexible material.

According to such a propeller, even if the rotor blade is deformed by impact during rotation, the rotor blade tends to be restored to its original shape.

As described above, according to the present invention, there are provided a propeller, a propeller design method, a propeller design method program, and an information storage medium that are light in weight, maintain a loop shape during rotation, and have a low noise.

It is a typical perspective view showing an example of a propeller concerning this embodiment. FIG. 1A is a schematic top view showing an example of a propeller according to the present embodiment. Fig. (B) is a schematic side view showing an example of a propeller according to the present embodiment. It is an example of the flowchart of the propeller design method which concerns on this embodiment. It is a schematic diagram which shows an example of the propeller design method which concerns on this embodiment. FIG. 5A is a graph showing an example of a loop-shaped imaginary line projected onto the XY axis plane. FIG. 5B is a graph showing an example of a loop-shaped virtual line projected on the YZ axis plane. It is a schematic diagram of the wake area | region which a general rotor blade emits. It is a schematic diagram which shows the concept of the method of determining the cross section of a rotary blade. It is a schematic diagram which shows the concept of the method of correcting the camber line of a blade cross section definition cross section. It is a typical perspective view which shows the propeller of the 1st modification of this embodiment. It is a typical perspective view which shows the propeller of the 2nd modification of this embodiment. It is a typical perspective view which shows the propeller of the 3rd modification of this embodiment. It is a typical perspective view which shows the propeller of the 4th modification of this embodiment. It is a typical perspective view which shows the propeller of the 5th modification of this embodiment. It is a typical perspective view which shows the propeller of the 6th modification of this embodiment.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. In each drawing, XYZ axis coordinates may be introduced.

(Outline of propeller)

FIG. 1 is a schematic perspective view showing an example of a propeller according to the present embodiment.
FIG. 2A is a schematic top view showing an example of a propeller according to the present embodiment.
FIG. 2B is a schematic side view showing an example of a propeller according to the present embodiment.

In the present embodiment, as the XYZ axis coordinates, the axial direction of the rotary shaft 10 is the Z-axis direction, the direction orthogonal to the Z-axis direction and from the rotary shaft 10 toward the tip 201 of the rotary blade 20 is the X-axis direction (first direction), A direction orthogonal to the Z-axis direction and the X-axis direction is defined as a Y-axis direction (second direction).

The propeller 100 of the present embodiment includes a rotating shaft 10 and a pair of rotating blades 20 connected to the rotating shaft 10. The pair of rotary blades 20 are arranged on a point target, for example, with the central axis 10c of the rotary shaft 10 as the center. In the propeller 100, the pair of rotary blades 20 constitutes an 8-shaped blade. The rotating shaft 10 is rotated counterclockwise about the central axis 10c by an external drive system (not shown), and the pair of rotary blades 20 are rotated counterclockwise about the rotating shaft 10. The pair of rotor blades 20 is made of, for example, a polyamide-based resin and has light weight and flexibility.

Each of the pair of rotor blades 20 includes a rotor blade portion 21 (first rotor blade portion) and a rotor blade portion 22 (second rotor blade portion). The rotary blade portion 21 has a blade upper surface 211 (first blade upper surface) and a blade lower surface 212 (first blade lower surface). The rotary blade portion 22 has a blade upper surface 221 (second blade upper surface) and a blade lower surface (second blade lower surface) 222. The rotary blade portion 21 has a receding angle that gradually recedes along a concentric circle with the rotating shaft 10 as the center. The rotary blade portion 22 has an advance angle that gradually advances along a concentric circle centered on the rotary shaft 10.

In the rotary blade 20, a loop shape is formed by the rotary blade portion 21 and the rotary blade portion 22. That is, in the rotary blade 20, the distance between the rotary blade portion 21 and the rotary blade portion 22 gradually increases as the distance from the rotary shaft 10 increases, and the distance becomes narrow after the distance has once reached the maximum. The rotary blade portion 21 and the rotary blade portion 22 that are divided into two branches from the rotary shaft 10 are connected at the tip 201 of the rotary blade 20. In the rotary blade 20, the blade main surface is twisted back in the vicinity of the loop-shaped tip 201, the blade upper surface 221 is connected to the blade lower surface 212, and the blade lower surface 222 is connected to the blade upper surface 211.

In the propeller 100, when the rotor blade 20 rotates, a pressure difference is generated between the blade upper surface 211 and the blade lower surface 212 near the rotor blade 21, and the blade surface 22 near the blade upper surface 221 and the blade lower surface 222. A pressure difference occurs. As a result, lift is generated in the rotor blade 20, and the propeller 100 moves in a direction opposite to the direction in which air flows.

However, at the same time as the lift force is generated in the rotary blade 20, the rotary blade portion 21 having the receding angle receives a torsional aerodynamic force (torsion moment), and the rotary blade portion 22 having the forward angle is twisted from the air. Receives increased aerodynamics.

However, in the propeller 100, the rotary blade portion 21 and the rotary blade portion 22 are connected by the tip 201 of the rotary blade 20. Further, on the XY axis plane, the center line 21L of the rotary blade part 21 and the center line 22L of the rotary blade part 22 are arranged line-symmetrically with respect to the central axis 20c of the rotary blade 20. Thus, the torsional aerodynamic force and the torsional aerodynamic force cancel each other out in the rotor blade 20, and even if the rotor blade 20 has a thin and light structure, the rotor blade 20 is not deformed by aerodynamic force. It is hard to get up.

For example, the rotary blade 21 and the rotary blade 22 have the same angle of attack with respect to an XY axis plane (rotary surface) orthogonal to the rotary shaft 10. Thereby, the magnitude | size of the torsional force of the rotary blade part 21 received from air and the torsional force of the rotary blade part 22 received from air become substantially the same, and they cancel.

It should be noted that the rotor blade can be made of a strong rigid body that is not subject to torsional deformation. However, the rotor blade having such rigidity inevitably increases in weight and cannot be reduced in weight.

Further, when the propeller 100 rotates in the air, the centrifugal force acts on the rotor blade 20 more strongly than the aerodynamic force. The propeller 100 is desired to have a configuration in which the rotor blade 20 is not easily deformed even by centrifugal force. In the propeller 100 according to the present embodiment, a suspended line shape in which a centrifugal force acting on the rotary blade 20 during rotation and a tension in the rotary blade 20 is balanced is introduced as a loop shape.

For example, the shape of at least a part of the

center lines

21L and 22L formed when the rotor blade 20 rotates about the rotation shaft 10 is at an arbitrary position of at least a part of the

center lines

21L and 22L. A tension acting in the X-axis direction and a centrifugal force acting in the X-axis direction are harmonized, and a tension line shape in which the tension acting in the Y-axis direction of the rotor blade 20 and the centrifugal force acting in the Y-axis direction are harmonized. Thereby, the propeller 100 has a lightweight structure in which a bending moment does not work.

Moreover, in the propeller 100, the connection location 11 (1st connection location) where the rotary blade part 21 was connected to the rotating shaft 10, and the connection location 12 (2nd connection location) where the rotary blade part 21 was connected to the rotary shaft 10 were used. Are displaced in the axial direction of the rotary shaft 10. Further, in the propeller 100, in the rotation direction R, a rotary blade portion 22 having an advancing angle is disposed behind the rotary blade portion 21 having a receding angle. That is, the connection location 11 is located downstream of the connection location 12 in the air flow direction. As a result, during rotation, the weak region emitted by the rotary blade portion 21 is positioned below the rotary blade portion 22, and the rotary blade portion 22 is less likely to hit the weak region emitted by the rotary blade portion 21.

(Determination of rotor blade shape)

In the present embodiment, the shape of at least a part of the loop-shaped

center lines

21L and 22L formed when the rotary blade 20 rotates about the rotation shaft 10 is an arbitrary part of at least a part of the

center lines

21L and 22L. At the position, the tension acting in the X-axis direction of the rotor blade 20 and the centrifugal force acting in the X-axis direction are harmonized, and the suspension force in which the tension acting in the Y-axis direction of the rotor blade 20 and the centrifugal force acting in the Y-axis direction are harmonized. Adopted from line shape.

For example, in order to obtain the

centerlines

21L and 22L of the

rotor blades

21 and 22, a differential equation in which the centrifugal force acting on the rotor blade 20 and the tension in the rotor blade 20 are harmonized is established and the differential equation is integrated. Thus, the loop shapes of the

center lines

21L and 22L are obtained.

FIG. 3 is an example of a flowchart of the propeller design method according to the present embodiment.
FIG. 4 is a schematic diagram illustrating an example of a propeller design method according to the present embodiment.

First, as shown in FIG. 3, the radius R of the propeller 100, the diameter R1 of the rotating shaft 10 (hub) of the propeller 100, the airfoil (blade cross-sectional shape) at each radial position, the chord length, and the rotation plane are formed. An angle (attack angle) is determined in advance (step S101). Establish the following differential equation.

For example, FIG. 4 shows an example in which the rotary blade 21 is regarded as a cable. Here, in the XY axis plane, a vector extending from the center axis 10c of the rotating shaft 10 to the center line 21L of the rotating blade portion 21 is represented by r. Further, the position parameter in the X-axis direction is x, the position parameter in the Y-axis direction is y, and the position parameter in the Z-axis direction is z.

Further, the angular velocity at which the rotary blade portion 21 rotates around the central axis 10c of the rotary shaft 10 is ω, the material density of the rotary blade 20 is ρ, the linear density of the rotary blade 20 is ρ _line , and it is cut perpendicular to the vector r. Let S be the area of the blade cross-section definition plane 21w of the rotary blade section 21 and ξ be the angle between the blade cross-section definition plane 21w and the line direction of the cable (center line 21L). The blade cross-section definition plane 21w is a plane that is parallel to the rotation axis 10 and arranged orthogonally.

Here, a minute volume v (portion with a dot) composed of a blade cross-section definition plane 21w having an area S and a height h is represented by v = S · h, and the weight of the minute volume v is ρ • v (= ρ · S · h). Furthermore, when the differential amount of the length along the line direction of the cable is ds, h is expressed by ds · sinξ. Thereby, the linear density ρ _line in the ds direction is expressed by ρ · S · sinξ. Note that ds corresponds to an integration step value, which will be described later, and is set to ds <0.01R (step S102).

Next, from the balance of tension and centrifugal force at Cartesian coordinates (x, y, z), the following ordinary differential equation is established. Here, T is a tension acting in the rotary blade portion 21.

... (1)

... (2)

... (3)

... (4)

... (5)

Here, the left sides of (1), (2), and (3) are forces acting per unit length of the X-axis, Y-axis, and Z-axis, and correspond to fx, fy, and fz.

Further, from the above equation (3), the tension T _{z in the} Z-axis direction is set as an initial value in advance.

... (6)
Is guided.

From the above formulas (1) to (6), by determining an appropriate initial value, the following simultaneous ordinary differential equation is established, and the loop shape is obtained using, for example, the Runge-Kutta method.

... (7)

... (8)

... (9)

(10)

(11)

(12)

For example, R is a distance from the central axis 10c of the rotation axis 10 to the loop-shaped tip 201 on the XY axis plane. Further, T _z is a tension acting in the Z-axis direction. The position of (x, y, z) = (R, 0, 0) is the initial value (s = 0) of the starting point of line integration. Let (x, y, z) = (0, 0, 0) be the end point in line integration. Q ₀ (initial value) is a tension acting in the Y-axis direction at s = 0 (step S103). Where the initial condition for line integration is

(13)

(14)
(Step S104, Step S105).

Further, from the symmetry of the loop shape, dx / ds = 0 can be set when s = 0. Further, in consideration of the airfoil (blade cross-sectional shape), the chord length, and the angle formed with the rotating surface, the linear density ρ _line (material density in the direction along the loop-shaped line) of the rotor blade 20 is set to a desired value. A value is set (step S106).

These simultaneous ordinary differential equations (6) to (12) are line-integrated from the start point to the end point for s using, for example, the Runge-Kutta method, and the relationship between x and y on the XY axis plane is obtained. For example, in this integration, only the length corresponding to ds is integrated (step S107). Next, it is determined whether or not the end point position (arrival position) is inside the diameter R1 of the rotating shaft 10 (step S108). When the position of the end point reaches the rotation axis 10, the integration is finished. If the position of the end point is not inside the diameter R1 of the rotating shaft 10, the rotor blade goes back to the front of step S106 and takes into consideration the airfoil (blade cross-sectional shape), blade chord length, and the angle formed by the rotating surface. The operation of setting the line density ρ _{line of} 20 to a desired value is repeated. Thereby, a loop-shaped imaginary line is obtained.

FIG. 5A is a graph showing an example of a loop-shaped imaginary line projected onto the XY axis plane. FIG. 5B is a graph showing an example of a loop-shaped imaginary line projected onto the YZ axis plane.

Here, when Q ₀ and T _z are regarded as tension parameters, Q ₀ and T _z have a degree of freedom. From Q ₀ and T _z to a desired value in the Y-axis direction or the Z-axis direction by the Newton iteration method or the like. The shape of the cable (swelling in the Y-axis direction or Z-axis direction) can be determined.

For example, as shown in FIG. 5A, when Q ₀ is set large, the angle θ formed by the X-axis direction and the cable line direction can be set large, and by setting Q ₀ small, the angle θ can be set small. After determining whether the angle θ is the target value (step S109), if the angle θ is not the target value, Q ₀ is corrected by the Newton method (step S110), and before step S104. Going back, the corrected Q ₀ becomes the initial value, and the integration by the Runge-Kutta method is performed again.

Further, since the center line 21L of the rotor blade 21 and the center line 22L of the rotor blade 22 are arranged symmetrically with respect to the center axis 20c, the first miracle of the center line 21L is obtained after obtaining the miracle. By drawing a virtual line drawn in the quadrant and a line that is symmetrical with the X axis in the fourth quadrant, the virtual line of the center line 22L of the rotor blade 22 is also determined.

In the present embodiment, at least a part of the loop-shaped imaginary line derived from the differential equation is set as the

center lines

21L and 22L of the rotor blade 20.

On the other hand, as shown in FIG. 5B, by adjusting T _z , it is possible to adjust the shift amount (shift amount) Z ₁ between the center line 21L and the center line 22L in the Z-axis direction. For example, by setting a large Tz, it is possible to set large displacement amount Z ₁ between the center line 21L and the center line 22L in the Z-axis direction. Further, by setting smaller the T _z, it can be set small displacement amount Z ₁ between the center line 21L and the center line 22L in the Z-axis direction. After displacement amount _{Z 1} is made a determination whether the target value (step S 111), when the deviation amount _{Z 1} is not a target value, due Newton method, is corrected displacement amount _{Z 1} (step S112 ), the deviation amount _{Z 1} fixed becomes the initial value, integration by Runge-Kutta method is performed again.

Here, the desired displacement amount Z _1, it is preferable to set at equal intervals as possible wake region emanating from a plurality of rotor blades.

FIG. 6 is a schematic diagram of a wake region generated by a general rotor blade.

Generally, there may be a spiral wake region WR generated by friction between the rotating blade BL and air or the like in the wake of the rotating blade BL (the wake of the rotation direction R) during rotation.

In the wake region WR, the velocity energy of the air decreases, and in the rotation direction R, when the wake region generated by the previous rotor blade hits the rotor blade that comes later, it becomes a load for the rotor blade that comes later. Therefore, it is desirable that each rotor blade be arranged so as to avoid a wake region that arises from the rotor blade that rotates first.

For example, if the average velocity of the air flow in the rotor blade is V, the air travel distance L during one round of the rotor blade is

(15)
It is represented by

Accordingly, when the number of rotor blades in the propeller is B, if each rotor blade is arranged so that the wake area interval in the Z-axis direction is L / B, each rotor blade is less likely to hit the wake area during rotation.

For example, in the propeller 100, since each of the pair of rotor blades 20 includes two pairs of

rotor blade portions

21 and 22, the blades are substantially four blades. Therefore, the optimum value of the wake area interval in the Z-axis direction is L / 4.

When the plurality of rotor blades BL are arranged at a constant angle in the rotation direction R (in the case of four rotor blades BL, an interval of π / 2), each of the plurality of rotor blades BL is shifted in the Z-axis direction. Without (shift amount Z ₁ = 0), by arranging the plurality of rotor blades BL on the XY axis plane, L / 4 is maintained in the case of four rotor blades with the optimum wake interval.

On the other hand, when the plurality of rotor blades BL are at the same position in the rotation direction R, in order to set the wake region interval to L / B, it is necessary to shift each of the plurality of rotor blades BL by L / B in the Z-axis direction. is there.

Intervals in the XY-axis plane of the rotor blades BL is the case of the intermediate angle phi (rad), the optimal value of Z ₁ is expressed by the following equation. Here, 0 <φ <π / 2.

... (16)

Propeller 100 is not limited to two pairs of

rotary blades

21 and 22, if they have a B 'group of the rotating wings, the optimum value of Z ₁ is expressed by the following equation.

... (17)

Unlike the straight blade, in the propeller 100 in which the rotary blade 20 is configured by a curve, the wake interval differs depending on the position from the central axis 10c. For this reason, in the present embodiment, the wake region interval is optimized so that the width of the rotary wing part 21 (rotary wing part 22) becomes the maximum (position 70% of the distance R from the central axis 10c). Determine the amount (Z ₁ ). For example, the shift amount (Z ₁ ) may be determined based on the tension parameter T _z .

Thus, the bulges (the magnitude of θ) of the

center lines

21L and 22L and the shift amount Z ₁ of the

center lines

21L and 22L are determined using (Q ₀ , T _z ). The above design procedure is automatically executed by a computer program using a computer. Further, the propeller design method program is stored in an information storage medium such as a hard disk, an optical disk, a USB memory, or a memory card.

Next, after determining the center line of the loop shape, the sections are arranged along the center line.

FIG. 7 is a schematic diagram showing the concept of a method for determining the cross section of the rotor blade. FIG. 7 also shows a coordinate system (inside the broken line) when the rotary blade 21 is viewed toward the vector r.

After the

center lines

21L and 22L are determined, the rotor blade 20 is determined by arranging two-dimensional blade cross sections along the

center lines

21L and 22L.

The blade cross section is defined as a two-dimensional shape in the X''Y '' axis plane using the X '' axis, which is the air flow direction in the blade cross section, and the Y '' axis perpendicular to the X '' axis. The In this embodiment, the blade cross section is defined by the unit vector x ′, y ′ after the blade cross section is rotated on the X ”Y” axis plane by a predetermined torsion angle α and rotated by α. 20s is introduced.

For example, x ′ is defined as a unit vector that is perpendicular to the vector r and has an angle α with the propeller rotation plane (XY plane). Note that the X ″ axis is parallel to the XY plane. Next, let l ′ be a unit vector indicating the direction of the center line 21L. Further, a unit vector perpendicular to x ′ and l ′ is defined as y ′ as follows. Note that an axis parallel to the unit vector x ′ is an X ′ axis, and an axis parallel to the unit vector y ′ is a Y ′ axis.

... (18)

The blade section defining section 20s is determined using the unit vectors x ′ and y ′, and the blade section defining section 20s is arranged so that the center of gravity of the blade section defining section 20s passes through the

center lines

21L and 22L (step S113). Thereby, the cross-sectional shape of the rotor blade 20 having a loop shape is determined. That is, by using the unit vector x ′ orthogonal to the vector r and the unit vector y ′ orthogonal to the unit vector x ′ and the unit vector l ′, even if the rotor blade 20 draws a loop shape, the

center line

21L , 22L and the cross section perpendicular to 22L is determined by (x ′, y ′). Note that n ′ is a normal vector of the blade cross section defining cross section 20s.

Next, the camber line of the blade cross section defining cross section 20s created using the unit vectors x ′ and y ′ is corrected.

8 (a) to 8 (e) are schematic diagrams showing the concept of a method for correcting the camber line of the blade cross section definition cross section.

As shown in FIG. 8A, the camber C of the blade cross section defining cross section 20s includes a camber line CL (line obtained by averaging the lines of the blade upper surface and the blade lower surface) and the chord line (blade cross section defining cross section 20s). The distance from the leading edge to the trailing edge). In the present embodiment, the X ′ axis corresponds to the chord line. Therefore, the camber C is a distance from an arbitrary point on the camber line CL from the X ′ axis. Therefore, the camber C becomes a function of x ′ and can be expressed by C = C (x ′). The distance from the camber line CL to the blade upper surface is the thickness t / 2, and the distance from the camber line CL to the blade lower surface is the thickness t / 2. As a result, the line on the blade upper surface of the blade cross section defining section 20s is C (x ′) + t / 2, and the line on the blade lower surface of the blade cross section defining section 20s is C (x ′) − t / 2. The distance from 0 on the X ′ axis to the intersection of the X ′ axis and the camber line CL corresponds to the chord length.

In this embodiment, the inner product of the vector r and the normal vector n ′ of the blade cross section defining cross section 20s is multiplied by C (x) to correct the camber along the center line (step S114). The corrected camber is represented by C = (r · n ′) · C (x).

For example, at the position P1 of the rotor blade 20 shown in FIG. 8B, r and n ′ are substantially in the same direction, and (r · n ′) is “1”. As a result, the camber line is not corrected and C = C (x) (FIG. 8C). On the other hand, at the position P2 of the rotary blade 20, r and n ′ are orthogonal to each other and (r · n ′) is “0”. As a result, the camber becomes “0” (FIG. 8D). That is, at the tip 201 of the loop shape, the camber is a straight line, and the chord line and the camber line in the rotary blade 20 coincide. As a result, no lift is generated in the vicinity of the tip 201 of the rotor blade 20, and it is difficult to deform even if its width is narrowed. Further, at the position P3 of the rotor blade 20, (r · n ′) is approximately “−1”, and the camber has a shape in which the camber at the position P1 is arranged symmetrically about the X ′ axis (FIG. 8). (E)).

Also, how to arrange the sections along the center line and the correction of the camber are automatically executed by a computer program using a computer. Further, this program is also stored in the information storage medium.

Also, assuming that the rotor blade 20 is a cable, the local velocity of the transverse wave running in the rotor blade 20 is

... (19)
Given in. Since the stress due to the centrifugal force is proportional to the density, the speed of the transverse wave is proportional to the peripheral speed, and the frequency is proportional to the rotational speed. Therefore, the shape is stable at any speed as long as it is stable at a certain rotational speed.

For example, the shape stability of the rotor blade 20 is similar to the shape stability of the jump rope when the jump rope is rotated, the shape stability of the lasso, and the like. For example, even if a jumping rope jumps to the ground and deforms greatly, it immediately returns to its original shape. Therefore, the rotary blade 20 can be made of a material that maintains a suspended shape when rotating, even if it is not suspended when not rotating (for example, when stationary).

Further, it is shown that the propeller 100 can significantly reduce high-frequency sound from the analysis result by the FW & H (Ffowcs. Williams-Hawkings) equation.

On the other hand, low frequency sound close to the fundamental frequency can be reduced by phase difference synchronous rotation. This cancels aerodynamic sound by the interference of waves generated from a propeller that rotates synchronously in the same direction with a phase difference. When the number of rotor blades arranged at equal intervals is B, the basic angular frequency Is in principle the same as increasing B times.

However, since wave interference is used, the waves may strengthen in some places, but at low frequencies, the wavelength is sufficiently long compared to the size of the propeller. As a result, even if the angle is different, the phase does not change greatly and is canceled over a wide range.

For example, the Fourier component of aerodynamic sound generated from a propeller having B rotor blades and an angular frequency ω can be expressed as follows in a complex number display.

... (20)

Where i is an imaginary unit.

In contrast, a propeller that rotates synchronously while maintaining the phase difference of the angle φ can be regarded as rotating at a time shifted by φ / ω, so its Fourier component is

(21)
It becomes.

Suppose that m rotor blades have a phase difference of equal intervals.

(22)
It is.

Therefore, the Fourier component of the synthesized sound is:

... (23)
It is.

Where n = m · l + j and 0 ≦ j ≦ m−1 (j: remainder when n is divided by integer m)

... (24)
It becomes.

Since the second term on the right side is 0 except when j = 0, all the harmonics other than integer multiples of m are canceled. That is, the sound emitted from the propeller 100 is extremely small.

(Modification 1)

FIG. 9 is a schematic perspective view showing a propeller of a first modified example of the present embodiment.

A propeller 101 shown in FIG. 9 includes a cylindrical duct member 30 in addition to the propeller 100. The propeller 100 is provided in the duct member 30. The central axis 10 c of the propeller 100 coincides with the central axis 30 c of the duct member 30.

With such a configuration, when the propeller 100 rotates, the air flow generated from the propeller 100 is rectified in the direction of the central axis 30c of the duct member 30. This increases the energy efficiency of the wind power. Further, since the duct member 30 surrounds the propeller 100, leakage of sound emitted from the propeller 100 is suppressed.

(Modification 2)

FIG. 10 is a schematic perspective view showing a propeller of a second modified example of the present embodiment.

The number of the rotary blades 20 is not limited to two around the rotary shaft 10 and may be three or more. For example, in the propeller 102 shown in FIG. 10, three rotor blades 20 are arranged at equal intervals.

With such a configuration, the wind power generated by the propeller 102 increases as compared to the propeller 100 due to the increase in the number of the rotor blades 20.

(Modification 3)

FIG. 11 is a schematic perspective view showing a propeller of a third modified example of the present embodiment.

In the propeller 103 shown in FIG. 11, the displacement between the connection location 11 and the connection location 12 in the Z-axis direction is smaller than that of the propeller 100. For example, the connection location 11 and the connection location 12 are located on the same XY axis plane.

Even in such a configuration, the rotary blade 20 is designed based on a catenary line in which centrifugal force and tension are balanced, so that the loop shape is maintained during rotation.

(Modification 4)

FIG. 12 is a schematic perspective view showing a propeller of a fourth modified example of the present embodiment.

In this embodiment, since the suspended line shape is applied to at least a part of the center line of the loop shape, a part of the loop shape may be a rigid body part. By including such a rigid body part in the loop shape, the rotor blade 20 is less susceptible to the bending moment. For example, in the propeller 104 shown in FIG. 12, an extending portion 204 that also functions as a counterweight is provided near the tip portion 201.

(Modification 5)

FIG. 13 is a schematic perspective view showing a propeller of a fifth modification of the present embodiment.

The rigid body portion may be a flat portion 205 like a propeller 105 shown in FIG. With such a configuration, the propeller 105 has the same effect as the propeller 104. Furthermore, when the propeller 105 is attached to the duct member 30, since the tip portion 201 is configured by the flat portion 205, the shape affinity with the duct member 30 is improved.

(Modification 6)

FIG. 14 is a schematic perspective view showing a propeller of a sixth modified example of the present embodiment.

FIG. 14 shows the periphery of the rotating shaft 10. The rigid body portion may be provided not near the tip portion 201 of the rotary blade 20 but near the rotating shaft 10. With such a configuration, the root portion of the rotor blade 20 having a large cross-sectional area and high rigidity becomes a rigid body portion, and the mechanical strength of the rotor blade 20 increases.

As mentioned above, although embodiment of this invention was described, this invention is not limited only to the above-mentioned embodiment, Of course, a various change can be added. Each embodiment is not necessarily an independent form, and can be combined as much as technically possible.

DESCRIPTION OF SYMBOLS 10 ... Rotary shaft 10c ...

Center axis

11, 12 ... Connection location 20 ...

Rotary blade

20c, 30c ...

Central shaft

21, 22 ...

Rotary blade part

21L, 22L ... Center line 21w ... Blade cross-section definition plane 20s ... Blade cross-section definition cross-section 30 ...

Duct member

100, 101, 102, 103, 104, 105 ... Propeller 201 ... Tip 204 ...

Extension part

205, 206 ...

Flat part

211, 221 ... Blade

upper surface

212, 222 ... Blade lower surface

Claims

A rotation axis;
Connected around the rotating shaft, having a first rotating blade portion having a first blade upper surface and a first blade lower surface and having a receding angle, and having a second blade upper surface and a second blade lower surface and having a forward angle. A second rotor blade portion, the second blade upper surface is connected to the first blade lower surface, the second blade lower surface is connected to the first blade upper surface, the first rotor blade and the second rotor blade And a rotor blade having a loop shape formed by the portion,
When the first direction is a direction perpendicular to the axial direction of the rotation axis and toward the tip of the loop shape from the rotation axis, and the second direction is a direction orthogonal to the axial direction and the first direction,
The shape of at least a part of the center line of the rotary blade formed when the rotary blade rotates about the rotary shaft acts in the first direction of the rotary blade at any position of the at least part. A propeller having a catenary line shape in which tension and centrifugal force are harmonized, and tension and centrifugal force acting in the second direction of the rotor blade are harmonized.
The propeller according to claim 1,
The connection location where the first rotary blade portion is connected to the rotary shaft and the connection location where the second rotary blade portion is connected to the rotary shaft are displaced in the axial direction,
The propeller, wherein the first connection location is located downstream of the second connection location in the air flow direction.
The propeller according to claim 1 or 2,
The propeller, wherein the first rotating blade portion and the second rotating blade portion have the same angle of attack with respect to a plane orthogonal to the rotation axis.
A propeller according to any one of claims 1 to 3,
The propeller in which the chord line and the camber line in the rotary blade coincide with each other at the tip of the loop shape.
The propeller according to any one of claims 1 to 4,
A plurality of the rotating blades are arranged around the rotating shaft, and the plurality of rotating blades are arranged at equal intervals.
A propeller according to any one of claims 1 to 5,
The rotor blade is a propeller made of a flexible material.
A rotating shaft, a first rotating blade portion connected around the rotating shaft and having a first blade upper surface and a first blade lower surface and having a receding angle; a second blade upper surface and a second blade lower surface; A second rotating blade portion having an advancing angle, wherein the second blade upper surface is connected to the first blade lower surface, the second blade lower surface is connected to the first blade upper surface, and the first rotating blade portion and the A propeller design method comprising a rotor blade having a loop shape formed by a second rotor blade portion,
The axial direction of the rotation axis is the Z-axis direction, the direction orthogonal to the Z-axis direction and from the rotation axis toward the tip of the loop shape is the X-axis direction, and the direction orthogonal to the Z-axis direction and the X-axis direction is Y If it is axial,
The shape of at least a part of the center line of the rotor blade formed when the rotor blade rotates about the rotation axis acts in the X direction of the rotor blade at any position of the at least part. A method for designing a propeller, in which tension and a centrifugal force acting in the X direction are harmonized, and a suspension line shape in which a tension acting in the Y direction and a centrifugal force acting in the Y direction of the rotor blade are harmonized.
A method for designing a propeller according to claim 7,
(A) x is a positional parameter in the X-axis direction, y is a positional parameter in the Y-axis direction, z is a positional parameter in the Z-axis direction, ω is an angular velocity at which the rotating blade rotates around the rotational axis, The material density of the rotor blade is ρ, the linear density of the rotor blade is ρ line , the area of the blade cross-section definition plane of the rotor blade cut in a direction parallel to and orthogonal to the rotation axis is S, and the blade cross-section definition Assuming that the angle formed by the plane and the line direction of the loop shape is ξ, the tension acting in the rotor blade is T,

... (A1)

... (A2)

... (A3)

... (A4)

... (A5)
Establishing an ordinary differential equation of
(B) From the above formulas (A1) to (A5), T z is a tension acting in the Z-axis direction,

... (A7)

... (A8)

... (A9)

... (A10)

... (A11)

... (A12)
Establishing a simultaneous ordinary differential equation of
(C) R is a distance from the central axis of the rotation axis to the tip of the loop shape, and (x, y, z) = (R, 0, 0) is a starting point (s = 0) in line integration, (X, y, z) = (0, 0, 0) is the end point in line integration, Q 0 is the tension in the Y-axis direction at the start point, and the initial condition is

... (A13)

... (A14)
Using the Runge-Kutta method, the above-mentioned simultaneous ordinary differential equations (A7) to (A12) are line-integrated from the start point to the end point with respect to s, and the relationship between x and y on the XY axis plane is obtained. To determine the loop-shaped virtual line,
(D) adopting at least a part of the imaginary line as a center line of the rotor blade.
A method for designing a propeller according to claim 7 or 8,
A shift amount in the axial direction between a connection location where the first rotary blade portion is connected to the rotary shaft and a connection location where the second rotary blade portion is connected to the rotary shaft is determined based on the T z. Propeller design method.
A propeller design method program for causing a computer to execute the propeller design method according to claim 8 or 9.
An information storage medium storing the propeller design method program according to claim 10.