JP4825099B2 - Blade airfoil design method - Google Patents

Description

The present invention relates to a blade airfoil design how to design a wing of a helicopter rotor blade.

FIG. 3 is a diagram for explaining the present invention. However, with reference to FIG. 3, the rotor blade of the helicopter (hereinafter simply referred to as “blade”) is accompanied by rotation in the direction of arrow A , It is moving forward in the flight direction B. Therefore, when the helicopter is moving forward, the air speed of the blade varies depending on the angular position of the blade. The airspeed of the blade is different between the hub-side blade root and the tip-side blade tip.

  Further, FIG. 4 is a view for explaining the present invention. Referring to FIG. 4, when the helicopter is moving forward, the lift force is balanced between the forward side and the backward side. It is necessary to change the angle of attack α, also called the pitch angle of the blade, during one rotation. Therefore, the blade is moving in an environment where the angle of attack α and the airspeed constantly change.

  As for the blade shape of such a blade, candidate shapes were designed based on empirical rules, performance was evaluated and confirmed by wind tunnel tests, and shapes that satisfy the required performance were selected. Since the wind tunnel test requires large-scale wind tunnel facilities, an analysis based on computational fluid dynamics (CFD) is used in place of the wind tunnel test in order to evaluate and confirm the performance. In addition, when using CFD analysis, the airfoil is automatically designed by the automatic optimization design method in which the airfoil is evaluated and the parameters for determining the airfoil are modified by the optimization algorithm and optimized by the CFD analysis. Has been.

Blades are required to have high maximum lift, high speed limits for helicopter flight speed, and small pitch moment characteristics. Since these performances have mutually contradictory aspects, it is difficult to design a blade airfoil that satisfies all the performances even with an optimization algorithm design method that utilizes CFD analysis. In addition, the design method using an optimization algorithm that uses CFD analysis results in low accuracy depending on how the evaluation is performed in CFD analysis, and requires an enormous amount of time for computation. Even further one blade, in the vicinity of the blade root and near the blade tip, since performance required is different for a plurality of sites, it is necessary to design each the site, difficulties in airfoil design Hasa et al It was.

  For example, Patent Document 1 discloses a method for optimally designing the shape of a blade provided in a cascade of an axial compressor by a multi-purpose genetic algorithm. However, as described above, there are specific performance requirements for the helicopter blade, and even if the design method disclosed in Patent Document 1 is used as it is, it is not possible to suitably design the airfoil of the helicopter blade. Thus, there is no design method suitable for designing the helicopter blade airfoil, and a suitable design method is desired.

JP 2002-70504 A

An object of the present invention can be suitably designed airfoil of helicopter rotor blades, is to provide a blade airfoil design how suitable for airfoil design helicopter rotor blades.

The present invention is to design a parameter representing an airfoil in a design apparatus comprising input means for inputting information on parameters defining the airfoil and arithmetic means for executing operations for airfoil evaluation and design. A method of designing a helicopter rotor blade airfoil using a multi-objective optimization algorithm that obtains a Pareto solution by evaluating design variables for multiple objective functions that represent the performance required for the rotor blade airfoil as variables. There,
An initial setting step in which the calculation means sets airfoil parameters including a blade thickness, a camber, a chord length, and a leading edge radius, using information representing initial values of parameters defining the airfoil input by the input means ; ,
After the initial setting step, the calculation means defines an airfoil according to the set airfoil parameters, and an airfoil definition step,
After the airfoil definition step, an evaluation analysis step in which the computing means evaluates the defined airfoil by a static analysis with respect to a plurality of objective functions;
After the evaluation and analysis step, calculating means obtains a Pareto solution based on the evaluation result of the airfoil in the evaluation analysis step, seen including a determination step of determining whether or not Pareto solutions is mature,
The plurality of objective functions includes low speed performance and medium speed performance,
In the evaluation analysis step, the calculation means uses a predetermined value in a predetermined low speed range as an airspeed of the rotor blade, and gradually increases the angle of attack from the zero lift angle of attack, thereby increasing the resistance coefficient to 0.03. Calculate the lift coefficient at the angle, evaluate the low-speed performance using the calculated lift coefficient, and further use the predetermined value in the predetermined medium speed range as the airspeed of the rotor blade, from the zero lift angle of attack to the angle of attack The blade airfoil in a design apparatus is characterized in that a lift coefficient at an angle of attack with a resistance coefficient of 0.03 is calculated by gradually increasing the lift coefficient, and medium speed performance is evaluated using the calculated lift coefficient It is a design method.

Or the present invention, the plurality of objective function further comprises a high-speed performance,
In the evaluation analysis step, the calculation means fixes the angle of attack to a zero lift angle of attack, calculates the Mach number at which the resistance coefficient is 0.03 by gradually changing the Mach number from a predetermined value, and calculates the Mach number. By gradually changing the number, a Mach number at which the absolute value of the variation amount of the pitching moment coefficient from the pitching moment coefficient at a predetermined Mach number becomes 0.02 is calculated. Of the two calculated Mach numbers The high-speed performance is evaluated using the Mach number limit expressed by the smaller of the two.

Or the present invention, the multi-objective optimization algorithm, characterized in that it is a versatile genetic algorithm.

Further, the present invention is characterized in that the computing means further includes a step of evaluating by dynamic analysis the Pareto solution obtained by evaluating the design variable by static analysis.

  According to the present invention, a plurality of performances required for the blade shape of the rotor blade are represented as objective functions, respectively, and an optimum Pareto solution of the blade shape is obtained while evaluating with the plurality of objective functions. As a result, the airfoils evaluated with respect to a plurality of performances are automatically designed, and the airfoils suitable for the helicopter rotor blade can be designed. In addition, among the multiple airfoils obtained as Pareto solutions, there are multiple airfoils suitable for each part of the rotor blade, from the airfoil facing the root of the rotor blade to the airfoil facing the tip of the blade. ing. Therefore, multiple blade types suitable for each part from the blade root to the blade tip of the rotor blade can be designed by a single design calculation, design efficiency is improved, and the blade shape is designed in a short time and at low cost. be able to.

According to the present invention, the objective function, slow performance, include medium speed performance and high-speed performance, airfoil each of these performance was evaluated is designed. As a result, a suitable airfoil can be designed as the airfoil of the helicopter rotor blade.
According to the present invention, a multipurpose genetic algorithm is used as the multipurpose optimization algorithm. The multi-objective genetic algorithm is an algorithm that can be suitably used to obtain an optimal Pareto solution while evaluating a plurality of objective functions. Therefore, an airfoil suitable for a helicopter rotor blade can be suitably designed.

  Further, according to the present invention, it is possible to design a suitable airfoil evaluated by both static analysis and dynamic analysis.

  FIG. 1 is a flowchart showing a blade airfoil design method (hereinafter simply referred to as “design method”) according to an embodiment of the present invention. FIG. 2 is a block diagram showing a design apparatus 20 that executes the design method of FIG. FIG. 3 is a plan view showing the airspeed distribution of the rotor blade (hereinafter simply referred to as “blade”) 11 during the forward flight of the helicopter 10. FIG. 4 is a graph showing the angle of attack distribution of the blade 3. The helicopter 10 is provided with a plurality of blades 11 which are blades, but only one blade 11 is virtually shown in FIG.

Of the variables used in the following description, typical ones are as follows.
V _ad : helicopter forward speed V _T : airspeed when the blade is rotating α: angle of attack α ₀ : zero lift angle of attack = angle of attack where lift is 0 φ: azimuth angle = rear angle position The angular position of the blade 11 representing 0 degrees and the rotational direction A as positive ω ₁ : rotational angular velocity of the blade (rotor) q: dynamic pressure = 0.5 × air density × airspeed ²
C _D : Resistance coefficient = resistance / (dynamic pressure × reference area)
C _L : lift coefficient = lift / (dynamic pressure x reference area)
C _L300 : Lift coefficient at an angle of attack where the resistance coefficient reaches 0.03; hereinafter referred to as “index lift coefficient”.
C _LMAX : Maximum lift coefficient C _Lbuff : Lift coefficient at the angle of attack at which the aerodynamic force begins to oscillate (Buffet) C _m : Pitching moment coefficient = pitching moment / (dynamic pressure x reference area x reference length)
C _m0 : Pitching moment coefficient at zero lift angle of attack; hereinafter referred to as “zero lift moment coefficient”.
C _mmin : minimum pitching moment coefficient in one cycle during dynamic analysis; hereinafter referred to as “minimum moment coefficient”.
ΔC _m : Pitching moment fluctuation from zero lift moment coefficient C _m0 M: Mach number = airspeed / sonic velocity M _lim : Mach number limit M _DD : Resistance divergence Mach number

  Here, in the case of a two-dimensional airfoil, the “reference area” refers to the area of a wing having a chord length and a span length of a unit length.

In the case of a two-dimensional airfoil, the “reference length” uses the chord length.
“Mach number limit” means that when the Mach number of the flow increases, shock waves are generated in the vicinity of the wing, causing a sudden increase in resistance and a sudden change in moment, and there is a limit that cannot be operated at a higher Mach number. This is called the Mach number limit.

  “Resistance divergence Mach number” is one of the calculation methods of the Mach number limit, and indicates the Mach number at which the resistance rapidly increases. Although there are several definition methods, a point increased by 0.002 from the resistance coefficient of Mach number M = 0.6 is used.

  For example, the airfoil of the blade 11 of the helicopter 10, which is a high-performance helicopter, uses an analysis based on computational fluid dynamics (abbreviated as CFD) (hereinafter referred to as “CFD analysis”) and is automatically called a numerical optimization method. Designed by optimal design method. This automatic optimum design method is a method of designing an optimum airfoil by repeating evaluation of the performance of the airfoil, for example, several tens to thousands of times while correcting parameters defining the airfoil. For example, there are a single-objective optimization algorithm and a multi-objective optimization algorithm as optimization algorithms called optimization engines used in the automatic optimization design method.

  In the single-objective optimization algorithm, when there are a plurality of objective functions, the objective functions are apparently converted into single-objective functions by weighting and adding the objective functions. In such a single-objective optimization algorithm, there is a problem that the optimal solution obtained differs depending on the weighting method of each objective function, and the accuracy is lowered. On the other hand, in the multi-objective optimization algorithm, each objective function is evaluated individually, and a design variable having a point superior to the others with respect to at least one objective function is a Pareto solution. A Pareto solution obtained by such a multi-objective optimization algorithm includes a plurality of design variables according to the importance of the objective function, and includes an optimal solution with high accuracy.

  In the design method according to the present invention, a parameter representing the airfoil is used as a design variable, and a plurality of objective functions representing the performance required for the airfoil of the blade 11 are optimized while evaluating the design variable by a multi-objective optimization algorithm. Find the Pareto solution. The airfoil obtained as the Pareto solution includes a plurality of airfoils in accordance with the importance of different performance depending on the flight conditions of the helicopter, the part of the blade 11 and the like.

The blade 11 of the helicopter 10 moves forward in the flight direction B at a forward speed V _ad which is a speed at which the helicopter 10 moves forward, for example, while rotating in the rotational direction A counterclockwise when viewed from above, and the pitch angle It is a complex movement that changes the angle of attack α, also called as. When it is assumed that there is no wind, the air speed (= relative speed to the atmosphere) V _{T at} a certain position of the blade 11 is a directional component (rotational direction) perpendicular to the blade of the rotational speed Rω ₁ and the forward speed V _ad. Component) and V _ad sinφ (= Rω ₁ + V _ad sinφ). R is the distance from the center of rotation. In the hovering state, the flight speed V _ad is 0, and the air speed V _T is the rotational speed Rω ₁ regardless of the angular position of the blade 11.

An example of the air speed V _T is indicated by the Mach number M. In the hovering state, for example, the air speed V _T of the blade root 12 is M = 0.2, and the air speed V _T of the blade tip 13 is M. = 0.6. When the flight speed V _ad is M = 0.2, the airspeed V _T of the blade tip 13 of the blade 11 is M = 0 at an angular position where the forward azimuth angle φ is 90 ° during one rotation. .8, and M = 0.4 when the azimuth angle φ on the reverse side is 270 °. In this embodiment, by using the evaluation index that can be used over the entire such extensive airspeed V _T, and evaluate the performance of the airfoil, to design the airfoil. In the present embodiment, M = 0.4 or less is a low speed region, M = 0.7 or more is a high speed region, and a middle speed region is between the low speed region and the high speed region. Hereinafter, in terms of airspeed V _T, sometimes simply show only Mach number M.

  In the present invention, the relatively high speed region means a relatively high speed region including the high speed region (M ≧ 0.7), and is not limited to the high speed region, and M = approximately 0.6. It means the above area. In the present invention, the relatively low speed region means a relatively low speed region including the low speed region (M ≦ 0.4), and is not limited to the low speed region. An area of less than 6 is meant.

  The design apparatus 20 shown in FIG. 2 includes an input unit 21, a storage unit 22, an external recording unit 23, a calculation unit 24, and an output unit 25. The design device 20 is realized using a computer called a computer such as a super computer. The input means 21 is a means for inputting information including parameter information defining the airfoil and command information for instructing the evaluation and design of the airfoil, such as a keyboard.

  The storage means 22 is a means for storing information in a medium provided inside the computer, such as a hard disk drive and a semiconductor memory, for example, an arithmetic program for executing the design method and evaluation method of the present invention, and an arithmetic program Data necessary for the calculation by is stored. The external recording means 23 is means for recording information on a removable recording medium such as a compact disc (abbreviated CD) and a digital versatile disc (abbreviated DVD) and reproducing the information recorded on the recording medium, for example, An arithmetic program for executing the design method and the evaluation method of the present invention, data necessary for arithmetic operations by the arithmetic program, and the like are stored. An information holding means for holding information such as a calculation program and data is configured including the storage means 22 and the external recording means 23.

  The arithmetic means 24 is realized by, for example, a central arithmetic processing unit (abbreviated as CPU), and based on command information input by the input means 21, an optimal design arithmetic program, CFD, or the like is obtained from either the storage means 22 or the external recording means 23. A calculation program and data including an analysis calculation program are read, and calculation for evaluation and design of the airfoil is executed using the parameter information input by the input means 21. The output unit 25 is a unit that outputs a calculation result by the calculation unit 24, and is, for example, a display device. The calculation result by the calculation unit 24 may be output by being recorded on a recording medium by the external recording unit 23. Therefore, a result output means for outputting the calculation result is configured including the output means 25 and the external recording means 23.

  Specifically, the design method is executed by the design device 20, specifically, by the calculation unit 24. In this embodiment, a multi-objective genetic algorithm (abbreviated as MOGA) using static CFD analysis is used for this design method. Hereinafter, one airfoil may be referred to as an individual.

  When the information indicating the initial value of the parameter defining the airfoil is input by the input unit 21 and the command information for instructing the design of the airfoil is given to the calculation unit 24, as shown in FIG. The design is started and the process proceeds to step s1. In the initial setting step of step s1, the calculating means 24 initializes parameters that define the blade shape of the blade 11. The parameter is a value representing an airfoil, and includes, for example, a blade thickness, a camber, a chord length, a leading edge radius, and the like. For example, a random number such as a random number algorithm or a random number table is used, and the random number is set as a parameter. In this embodiment, parameters for 60 individuals are set.

  When the parameter initialization in step s1 ends, the process proceeds to step s2. In the airfoil definition step of step s2, the calculation means 24 defines the airfoil according to the set parameters. In this embodiment, 60 airfoils are defined. When the definition of the airfoil in step s2 ends, the process proceeds to step s3.

In the moment adjustment step of step s3, the computing means 24 corrects the camber for the defined airfoil, and adjusts so that the absolute value | C _m0 | of the zero lift moment coefficient C _m0 becomes small. The pitching moment is a moment in the pitching direction with respect to the blade, and includes a torsional moment.

The blade 11 of the helicopter 10 is an elongated wing and has low torsional rigidity. Therefore, when a large torsional moment due to aerodynamic force is applied, torsional deformation occurs, and the expected aerodynamic characteristics may not be obtained. By reducing the absolute value | C _m0 | of the zero lift moment coefficient C _m0 , torsional deformation of the blade 11 can be prevented. When the adjustment of the zero lift moment coefficient C _m0 in step s3 is completed, the process proceeds to step s4.

In the analysis evaluation process of step s4, the calculation means 24 evaluates a plurality of objective functions representing the performance of the blade with respect to the defined airfoil based on the static CFD analysis. The multiple objective functions include low speed performance, medium speed performance, high speed performance, maximum blade thickness and pitching moment performance. Although the configuration may be such that evaluation is performed with respect to objective functions related to performance other than this, in the present embodiment, evaluation is performed with respect to these five objective functions.
Table 1 shows the objective function.

The low speed performance represents a low speed performance limit, and is represented by an index lift coefficient C _L300 when the airspeed V _T of the blade 11 is M = 0.4. This low-speed performance is hereinafter referred to as “low-speed index lift coefficient” and expressed as “C _L300 @ M = 0.4”. The lower the low speed index lift coefficient C _L300 @ M = 0.4, the higher the low speed performance is evaluated.

Medium speed performance, medium speed performance limit, represents the hovering performance near the blade tip 13, airspeed _{V T} of the blade 11 is represented by an index lift coefficient _{C L300} in the case of M = 0.6. This medium speed performance is hereinafter referred to as “medium speed index lift coefficient” and is described as “C _L300 @ M = 0.6”. It is evaluated that the medium speed performance is higher as the medium speed index lift coefficient C _L300 @ M = 0.6 increases.

Fast performance represents a fast limit, and the Mach number of drag coefficient _{C D} is greater than 0.03, the value of the moment coefficient _{C m} in the case of M = 0.6, the moment coefficient _{C m} is 0.02 change (increase ) Represents the smaller Mach number. This high-speed performance is hereinafter referred to as “Mach number limit” and described as “M _lim @ α ₀ ”. It is evaluated that the higher the Mach number limit M _lim @ α ₀ is, the higher the high speed performance is.

The maximum blade thickness represents the maximum value of the thickness dimension of the blade, and is described as “Tmax”. The larger the maximum blade thickness is, the higher the performance related to the maximum blade thickness is evaluated, and 15% cord length or more is considered sufficiently large.

The pitching moment performance represents the absolute value | C _m0 | of the zero lift moment coefficient C _m0 when the airspeed V _T of the blade 11 is M = 0.6. This pitching moment performance is hereinafter referred to as “specified moment coefficient” and is described as “| C _m0 |@M=0.6”. It is evaluated that the pitching moment performance is higher as the specified moment coefficient | C _m0 |@M=0.6 becomes smaller, and 0.01 or less is considered to be sufficiently small.

Regardless of pitching moment performance as an objective function, | C _m0 | is adjusted in step s3. The moment adjustment in step s3 is performed by a simple (non-viscous, incompressible) method. In general, the value is different from the value obtained by the CFD analysis at the time of objective function evaluation. In step s3, there is a case where the moment is small, but there is a case where it is not so in the CFD analysis.

  When the evaluation in step s4 ends, the process proceeds to step s5. In the determination step of step s5, the calculation means 24 obtains a Pareto solution based on the evaluation result of the airfoil in the analysis evaluation step of step s4, and determines whether or not the Pareto solution is mature. In this embodiment, since a multi-objective genetic algorithm is used as an optimization algorithm, instead of converging to a single optimal solution, a Pareto solution as a set of a plurality of non-inferior solutions matures. The optimal Pareto solution. In step s5, it is determined whether or not this optimal Pareto solution is obtained. If it is determined in step s5 that the Pareto solution is not mature, the process proceeds to step s6. If it is determined that the Pareto solution is mature, the process proceeds to step s7.

The parameter modification process in step s6, the arithmetic unit 24, for example selected, mating, modify parameters such as by mutation, change, and generate the next generation of individuals, the process proceeds to step s2. Thus, when it determines with not having matured in the determination process of step s5, the said parameter is corrected and set again, and the process from the said airfoil definition process of step s2 to the determination process of step s5 is repeated. Thus, the process of repeating the second and subsequent steps from step s2 to step s5 is a so-called repetition process.

  When the airfoil design process by MOGA using static CFD analysis is configured including the processes from step s1 to step s6, and it is determined in step s5 that the Pareto solution is mature, the Pareto The solution is output as a solution in the process of airfoil design by MOGA using static CFD analysis. Such processes of steps s1 to s6 are procedures of a so-called automatic optimum design method.

  In step s7, the calculation means 24 performs dynamic CFD analysis on the airfoil of the optimal Pareto solution obtained by determining that the Pareto solution is mature in step s5, and the dynamic performance of the airfoil is determined. And proceeds to step s8. In step s8, the computing means 24 determines whether or not the dynamic performance obtained in step s7 is good, specifically, whether or not the required performance is satisfied. The required performance related to the dynamic performance determined in step s8 is input by the input unit 21 together with the initial value of the parameter, for example, before starting the design operation. If it is determined in step s8 that the dynamic performance is good, the process proceeds to step s9. If it is determined that the dynamic performance is not good, the process proceeds to step s1.

  In step s9, the calculation means 24 defines a three-dimensional rotor using the airfoil of the optimal Pareto solution, and proceeds to step s10. In step s10, the computing means 24 performs a three-dimensional CFD analysis on the rotor defined in step s9, obtains the three-dimensional performance of the rotor, and proceeds to step s11. In step s11, the calculation means 24 determines whether or not the three-dimensional performance obtained in step s10 is good, specifically, whether or not the required performance is satisfied. The required performance related to the three-dimensional performance determined in step s11 is input by the input means 21 together with the initial value of the parameter, for example, before starting the design operation. If it is determined in step s11 that the three-dimensional performance is good, the process proceeds to step s12. If the design operation is terminated and it is determined that the three-dimensional performance is not good, the process proceeds to step s1.

  When the process proceeds from step s8 or step s11 to step s1, the parameter initialization in step s1 may be the same initialization as when the design operation is started and the parameters are initialized first, or from step s8. When shifting, the initial value may be newly calculated based on the result of step s7. When shifting from step s11, the initial value is newly calculated based on the result of step s10. You may do it.

  As described above, in this embodiment, in addition to the static CFD analysis, the performance is confirmed by the dynamic CFD analysis and the three-dimensional CFD analysis in steps s7 to s11. Therefore, a more suitable airfoil can be designed. it can. The process of steps s7 to s11 is not an essential configuration, and may be a configuration without steps s7 to s11 as another embodiment of the present invention.

  Hereinafter, this embodiment will be described in more detail. The design method according to the present invention makes it possible to obtain a blade airfoil that satisfies the numerical goal of no performance degradation during level flight, for example at a speed of 300 km / h, and for example a maximum speed of 250 km / h Although it is good, the goal is to enable automatic design to meet new design targets, such as increasing the hovering capability as much as possible. This design method can be used not only for blades 11 but also for airfoil designs of various aircraft and aerodynamic machines. By accumulating know-how on each element, it is flexible enough to respond immediately to new design goals. It is possible to optimize the design of the airfoil.

  The CFD analysis will be described below. The use of dynamic aerodynamic phenomena with velocity fluctuations in blade design is a pillar of the present invention. It is almost impossible to reproduce the dynamic aerodynamic phenomenon by experiment. Therefore, a dynamic aerodynamic phenomenon is simulated using CFD analysis. In order to analyze dynamic physical phenomena, dynamic unsteady analysis is also performed in CFD analysis. For dynamic analysis, even if a computer called the current fastest workstation is used with about 200,000 steps, it takes about 1 day, and it takes a long time for calculation. Since optimization design requires tens to thousands of iterations, it is difficult to use dynamic analysis as it is for optimization design. Thus, by analyzing and evaluating the objective function as described above, it is possible to dynamically design with sufficient performance even if only static analysis is performed.

The basics of CFD analysis will be described below. In CFD analysis, two-dimensional RANS (
The airfoil is analyzed by the CFD analysis method based on the Reynolds Averaged Navier-Stokes) equation. The basic equation is expressed by the following equation (1).
_Qt + _Ex + _Fy = _Rx + _Sy + H (1)

Here, Q _t , E _x , F _y , R _x , and S _y are conserved variables, inviscid flux in the x and y directions, viscous flux in the x and y directions, and H is fixed to the airfoil, respectively. This is a vector quantity of four variables each indicating an inertial force term due to translation and rotation of the coordinate system. The external boundary condition is also changed unsteady with the movement of the wing.

  The following is used as a numerical analysis method. First, MUSCL (Monotone Upstream-biased Scheme for Conservation Laws) and SHUS (Simple High Resolution Upwind Scheme) are used for spatial discretization. Second, MFGS (Matrix Free Gauss-Seidel) implicit method is used for time integration. A secondary accuracy center difference is used for the viscosity term.

A turbulent flow model is required to analyze the high Reynolds number turbulent flow field used by the blade airfoil, but here it is handled by RANS, and the Spalart-Allmaras model is used as the RANS turbulent model. The transition condition from laminar to turbulent flow is all-field turbulent. Time integration is first order accuracy
The Euler implicit method is used, but two internal iterations are performed to correct the nonlinearity of the implicit method in order to compensate for the linearization and Jacobian simplification associated with the MFGS implicit method. In each internal iteration,
Perform 20 Gauss-Seidel iterations.

FIG. 5 is a diagram showing a lattice 30 used for analysis. The lattice set around the airfoil for the CFD analysis is an airfoil O-type structural lattice as shown in FIG. 5 , and the number of lattice points is 263 in the circumferential direction and 60 in the radial direction. The minimum lattice spacing is 1 × 10 ⁻⁵ × (chord length). In the case of the static analysis, H = 0 is set in Equation (1), and the calculation time is shortened by using a local time method which is a general acceleration method for convergence to a steady solution.

The simulation of the movement of the blade 11 will be described below. Attention is paid to one blade section on the rotating blade 11 as described above. Airspeed V _T of the blade section, as described above, can be expressed by the following equation (2).
V _T = Rω ₁ + V _ad sin φ (2)

Here, when time is t, φ is expressed by the following equation (3).
φ = ω ₁ t (3)
The system represented by Formula (2) and Formula (3) is defined as the first system.

Separately from the first system, a two-dimensional wing that moves forward and backward in a uniform flow is considered, and this is the second system. When the forward / backward amplitude is A, the uniform flow velocity is V _unif , and the forward / backward angular velocity is ω ₂ , the relative velocity V _rel to the airflow is expressed by the following equation (4).
V _rel = V _unif + Aω ₂ sinω ₂ t (4)

Here, the sound speed, chord length, and kinematic viscosity coefficient of the first system are a ₁ , C ₁ , ν _1, and the sound speed, chord length, and kinematic viscosity coefficient of the second system are a ₂ , C ₂ , ν ₂ , the average peripheral speed Mach number M _R in equation (5), the advance ratio m in equation (6), the dimensionless angular velocity (Reduced Frequency) k in equation (7), and the Reynolds number in equation (8). by matching the four dimensionless parameters Re _2, to simulate the first system by the second system. However, the average peripheral speed Rω ₁ is used as the reference speed of the dimensionless angular speed.

  Although it is possible in principle to realize a second system in which a two-dimensional blade moves back and forth with fluctuations in the angle of attack in a uniform flow, it is possible to achieve a high speed condition in which the dynamic stall on the reverse side becomes significant. In reality, it is quite difficult to achieve this, apart from the Reynolds number, which is difficult in general wind tunnel tests. For example, to simulate the flight of a typical medium-sized helicopter at a speed of 250 km / h, the chord length is 0.33 m, the amplitude A = 1.78 m, and the period in a uniform flow with M = 0.6. It is necessary to vibrate the model back and forth at T = 0.16 sec. Although details are omitted, the amplitude A decreases in proportion to the model size, but the period T is also shortened, so that the simulation is not easy even if the reduced model is used.

  In the present embodiment, the movement of the blade 11 is simulated by two-dimensional CFD analysis as follows. First, paying attention to a position near the blade tip 13 of the blade 11 that is important for rotor characteristics, for example, a blade shape at a position in the blade length direction of 95%, data on the angle of attack and airspeed in one cycle are extracted. The blade length direction position is a position in the longitudinal direction of the blade 11 expressed as a percentage where the rotation center is 0 and the end surface of the blade tip 13 is 100.

  Second, the pitch motion is simulated by rotating around a 25% chord position. The chord position is a position expressed as a percentage in the chord direction where the leading edge is 0 and the trailing edge is 100. Third, speed fluctuation is simulated by reciprocating back and forth in a uniform flow with the rotation center as a reference point. The peripheral speed corresponds to the uniform flow speed, and the maximum forward / backward speed corresponds to the forward speed of the helicopter.

  The angle of attack variation will be described below. The blade 11 of the helicopter 10 operates to change the angle of attack α called a cyclic pitch in synchronization with the rotation of the rotor. Since this operation is driven by the swash plate and the pitch link, it includes a high frequency component rather than a simple sine wave operation. Therefore, in general, the angle of attack α for the uniform flow is expressed by Expression (9).

In the present embodiment, approximation as shown in Expression (10) is performed as a first-order approximation.
α = α ₀ −α ₁ sin ωt (10)

The aerodynamic coefficients of the peripheral speed dynamic pressure reference and the local dynamic pressure reference will be described below. In order to display the aerodynamic force acting on the blade 11, a dimensionless coefficient expressed by the equations (11) to (14) is used.
Lift coefficient C _L = lift / (reference area × dynamic pressure) (11)
Resistance coefficient C _D = resistance / (reference area × dynamic pressure) (12)
Pitching moment coefficient C _m = 25% Moment around cord position
/ (Reference length x reference area x dynamic pressure) (13)
Dynamic pressure = (density × speed ² ) / 2 (14)

In the dynamic analysis handled in the present embodiment, the air pressure V _T differs depending on the azimuth angle φ, so there is not one dynamic pressure. In the present embodiment, the following two reference dynamic pressures are selectively used depending on the purpose.

  The first is the dynamic pressure based on the peripheral speed dynamic pressure. The dynamic pressure based on the peripheral speed dynamic pressure is non-dimensionalized by the dynamic pressure using the peripheral speed of the rotor = the average speed of the dynamic analysis regardless of the azimuth angle φ. Since the same dynamic pressure is used at all azimuth positions φ, the absolute values of the force and moment can be obtained by multiplying the aerodynamic coefficient by a constant. For example, the moment based on the peripheral speed dynamic pressure is directly connected to the torsional deformation of the blade and the load on the pitch link.

The second is dynamic pressure based on local dynamic pressure. Dynamic local dynamic reference is dependent azimuth angle phi, is obtained by dimensionless by dynamic pressure using local airspeed V _T. Since the aerodynamic coefficient of static characteristics at each Mach number is equivalent to using the local air speed, the local dynamic pressure standard is appropriate for checking the performance limit of the airfoil.

  The performance evaluation method and design goals for blade airfoils are described below. First, a conventional performance evaluation method will be described below. During forward flight, the airfoil of the blade 11 is exposed to an airflow from a high speed low angle of attack (advanced side) to a low speed high angle of attack (retreated side) while the rotor makes one round. At the blade tip 13 where the dynamic pressure is large and most of the rotor lift (and the forward component becomes the propulsive force) and its vicinity (hereinafter referred to as “tip portion”), The critical condition of the blades, in which a super-velocity flow and a shock wave are generated, and separation of the flow accompanying a large angle of attack occurs on the receding side, is a severe situation that is repeated in a short time.

Furthermore, the blade 11 is very long and the rigidity in the direction of pitching (twisting up and down) is not so high. Also, even if the blade 11 itself has sufficiently high rigidity, the load due to the movement in the pitching direction is supported only by the pitch link at the blade root 12 and its vicinity (hereinafter referred to as “root part”). Therefore, the load limit of the pitch link may become the performance limit of the helicopter. Therefore, the pitching moment coefficient C _m giving air force in the pitching direction to the blade 11 must be kept small value. Therefore, conventionally, the following three points have been considered in the design of the airfoil of the blade 11.

The first point is the maximum lift coefficient C _LMAX at low speed. As described above, the angle of attack on the reverse side increases during high-speed forward flight. It is necessary that separation does not occur even at a high angle of attack, that is, the maximum lift coefficient C _{LMAX at} a low speed (M <0.4) on the receding side is increased. Further, the lift generation capability in a hovering state at a forward speed of 0 is indispensable for increasing the maximum take-off weight and improving the high-air performance. At the time of hovering, the vicinity of the blade tip 13 is about M = 0.6, and the maximum lift coefficient C _LMAX in the medium speed range is also an important evaluation item. At the angle of attack α near the maximum lift coefficient C _LMAX generation, even at low and medium speeds, the flow may accelerate to supersonic speeds near the leading edge of the blade 11, and the compressive effect will be effective. The value of the maximum maximum lift coefficient C _LMAX varies, and the balance varies depending on the airfoil.

The second point is the resistance divergence Mach number M _DD at a low angle of attack. On the forward side during high-speed forward flight, M> 0.8, and the lift is close to zero. Therefore, the resistance divergence Mach number M _DD is used as an index of high-speed characteristics. The drag divergence Mach number _{M DD,} had there are how to define several, typically 0.002 drag coefficient _{C D} at a certain lift coefficient _{C L} is higher than the value when the M = 0.6 ( = 20 Drag count) is defined as an increasing Mach number. Since the resistance coefficient C _D is approximately 100 counts at low angle of attack, resistance is meant that Mach number begins to increase slightly.

The third point is the absolute value | C _m0 | of the zero lift moment coefficient C _m0 so that | C _m0 | <0.01. It is necessary to reduce the pitching moment coefficient _{C m,} as described above, the absolute value of the pitching moment coefficient at zero lift An index _{| C m0} | is less than _{0.01 (| C m0 | <0.01} ) in Judge that it is small enough. Although the value varies depending on the Mach number M due to the compressive effect, a value at a low speed (M = 0.3) is often used. The absolute value | C _m0 | of the zero lift moment coefficient C _m0 does not change greatly until around M = 0.6.

  The inventors of the present invention review these indices by conducting tests and the like, and in the present embodiment, adopt indices that replace them. The index used in the present embodiment will be described below.

First, an index lift coefficient C _L300 that replaces the maximum lift coefficient C _LMAX will be described. In the speed range where M> 0.6, a clear maximum lift coefficient C _LMAX is not generated, and the lift coefficient C _L may gradually increase as the angle of attack increases. However, even if the increased lift coefficient C _L is, such a high angle of attack not actually available. When the angle of attack exceeds a certain angle of attack, the resistance increases rapidly and the aerodynamic force becomes unsteady, and the blade 11 starts to vibrate (buffet). Practically, the lift coefficient C _{L at} which _buffet is generated is a limit, and _this is called a _buffet generated lift coefficient C _Lbuff . As a result of the tests conducted by the present inventors on various types of airfoils, the resistance increases rapidly and the resistance coefficient C _D is 0 at both the maximum lift coefficient C _{L at} medium and low speeds and the _buffet- generated lift coefficient C _{Lbuff at} medium and high speeds. It was found that the wing usage limit was around 0.03 (300 counts). Based on this point, the index lift coefficient _{CL 300} is used as a new index.

The use of the index lift coefficient C _L300 has the following advantages. First, it can be evaluated with the same index from a low speed region to a medium high speed region. Secondly, when CFD analysis is used, the maximum lift coefficient C _{L MAX} may not be obtained depending on the turbulence model used, and the resistance coefficient C _D may not be obtained. The increase in the frequency is reproduced, the difference due to the turbulence model is small, and the analysis is reliable. Third, the index lift coefficient C _L300 means a point where the resistance rapidly increases, and the rapid increase in resistance is an important aerodynamic phenomenon. In addition, as described in relation to the maximum lift coefficient C _{L MAX} , various points of the wing, such as the point where the resistance increases rapidly, the lift gradually increased until then, and the pitching moment coefficient C _m changes abruptly. This is also an important indicator in the sense that non-linearity occurs in various characteristics. Fourth, as described later, it can also be used for performance evaluation on the high speed limit.

Next, an index lift coefficient C _L300 that replaces the resistance divergence Mach number M _DD will be described. In the case of a fixed wing aircraft, the resistance divergence Mach number M _DD has the important meaning that cruising in the vicinity is most efficient. The efficiency of a jet engine improves as the speed increases, and the air resistance increases rapidly above the resistance divergence Mach number M _DD . As a result, the overall fuel efficiency is maximized in the vicinity of the resistance divergence Mach number M _DD where the resistance starts to increase slightly. However, in the airfoil of the blade 11 is not to be constantly operated in drag divergence Mach near number M _DD, situation quite different. Even if the resistance coefficient C _D increases slightly beyond the resistance divergence Mach number M _DD , the impact on the performance is small in a moment.

In addition, the blade 11 having a resistance divergence Mach number M _DD of a forward side Mach number M = 0.845 or more at the time of horizontal flight at a speed of 300 km / h, which is one example of a target in the present embodiment, is extremely thin. It is impossible without wings. Such extreme thin blades are not suitable for operation at low speeds and high angles of attack, and cannot be applied to helicopter wings. Therefore, operation at the resistance divergence Mach number M _DD or more is inevitable on the highest speed side.

Similar to the situation in the middle / low speed range, the index lift coefficient C _L300 can be applied as an index of non-linear characteristics due to the transonic phenomenon in the high speed range. Transonic phenomena are phenomena in which subsonic and supersonic regions coexist in the flow field near the wing, and various nonlinear phenomena occur due to the generation of shock waves. The index lift coefficient C _L300 is different from the maximum lift coefficient C _LMAX in that it does not change the angle of attack α by fixing the Mach number M, but changes the Mach number M by fixing the angle of attack α or lift. However, the meaning is the same in terms of the combination of the lift coefficient _CL and the Mach number M, where the resistance coefficient _CD is 0.03.

Drag divergence Mach number _{M DD} is, M = 0.6 the resistance coefficient _{C D} is the point at which increasing 20 counts, is the drag coefficient _{C D} at M = 0.6, so about 100 counts, index lift coefficient _{C L300} the resistance coefficient C _D is that approximately 200 counts increased points. In the resistance divergence Mach number M _DD , shock wave resistance starts to be generated, but it can still be used, whereas the index lift coefficient C _L300 indicates the use limit.

Next, the evaluation of the low pitching moment coefficient (low C _m ) by unsteady analysis in consideration of shock waves and separation will be described. At a low angle of attack in the medium / low speed range, the pitching moment coefficient C _m does not change significantly from the zero lift moment coefficient C _m0 . However, availability nonlinear reduced such detachment and the forward side at high speeds of the shock wave generation during the backward side high angle of attack is changed greatly, the absolute value of the pitching moment coefficient C _m at low speed and low angle of attack | C _{m |} small airfoil necessarily Even in such a limit situation, it is not guaranteed that the absolute value | C _m | of the pitching moment coefficient C _m is small.

In particular, on the high speed forward side, the dynamic pressure is large and the load is large, and the twisting by the head-lowering moment there is a risk of causing blade control divergence due to positive feedback to the aerodynamic force. That is, what should be suppressed from the viewpoint of high speed performance is not the pitching moment coefficient C _m at low load, but the maximum value at high speed. Of course, it should be good that the pitching moment coefficient _Cm is small in the entire region, but it should be determined from the balance in the actual operation conditions. Therefore, in the present embodiment, pitching moment coefficient C _m is also Sankounisuru is, the final selection, close to the actual operation, the magnitude of the transient analysis result moment evaluation. Here, the head-lowering moment refers to a moment in which the leading edge portion of the blade 11 is twisted downward and the angle of attack of the blade is reduced toward the rotor end by elastic deformation.

The aerodynamic performance necessary for realizing level flight at a speed of 300 km / h will be described. Figure 6 is a graph showing the relationship between Mach number M and the lift coefficient C _L of each position in the blade 11. Figure 7 is a graph showing the relationship between Mach number M and the lift coefficient C _L of the existing airfoil. FIG. 6 shows the lift coefficient C _L for each position of the blade 11 when the medium-sized civil helicopter flies horizontally at 160 kt (about 296 km / h) predicted by the rotor performance calculation program. Show. In FIG. 6, the solid line indicates the lift coefficient C _L at a blade length direction position of 96%, the dashed line indicates the lift coefficient C _L at a blade length direction position of 77%, and the broken line indicates 52% of the blade length direction position. The lift coefficient _CL is shown.

The aerodynamic characteristics of the airfoil, since the flame correct target for achieving a high lift coefficient C _L with high Mach numbers, as the required performance in the upper right in FIG. 6, the design is difficult to achieve this. Therefore, it is most difficult to design the airfoil of the tip portion located at the upper right in FIG. Therefore, in the present embodiment, the focus is on the design of the airfoil at the position in the blade length direction of 95% of the tip portion.

If the index lift coefficient C _L300 of the static CFD analysis result exceeds the required lift coefficient C _L at each Mach number M shown in FIG. It is confirmed that the index lift coefficient C _L300 at each Mach number M exceeds the necessary lift coefficient C _L. However, as can be seen by comparing FIG. 6 and FIG. 7, there is no existing airfoil that satisfies this requirement.

The optimization design method will be described below.
“Optimization” is a Japanese translation of “Optimization”, and means, in applied mathematics, finding the maximum and minimum values of a function and the variable values that give them. Except for very simple functions, this problem cannot be solved analytically. Thus, many numerical methods have been proposed for obtaining the maximum and minimum values, including cases where functions cannot be expressed easily. If a parameter representative of design is taken as a variable and the objective function is considered as a performance index, the parameter that gives the best performance, that is, the design can be selected from the range that can be expressed by the parameter. Such a method is a method called optimum design or optimization design.

For example, in aerodynamic design, an airfoil is represented by some real parameters (for example, maximum blade thickness and leading edge radius, etc.), and any aerodynamic characteristics (for example, maximum lift coefficient) of the airfoil represented by the parameters are represented by CFD analysis. If it can be calculated, formally, the maximum lift coefficient C _{L MAX} can be expressed by design parameters. In other words, the contents of the objective function evaluation are actually quite complicated analysis operations including grid generation, CFD analysis, and post-processing of calculation results.

  Since a design is expressed by a plurality of variables, a set of parameters expressing one design is called a “parameter sequence”. There are many optimization methods, but it is a common feature that the parameter sequence that produces the next improved result is calculated from the result of the objective function of multiple parameter sequences, and the design is gradually improved. .

  Such an optimized design consists of the following three independent elements. First, the “expression method by parameter sequence” of design. Second, the “performance (objective function) evaluation method” of the design. Third, an “optimization engine” that calculates the next parameter sequence that is predicted to be improved from the parameter sequence and performance evaluation. The optimization engine is also called an optimization algorithm.

  When these three factors are determined, an optimization design method can be defined. The first and second elements are necessary items not only in the optimization design but also in the general design. If these two stages are realized on the design apparatus 20 (computer), the design parameter string and the performance are obtained. The great merit of the optimized design is that a better design can be calculated without considering on the surface the physical process that links the indices, for example, the process of generating a shock wave due to the increase in resistance at high speed. However, it is only in the optimization engine that there is no need to hesitate in the physical process, and it goes without saying that the parameter expression and performance evaluation method must be set with a deep understanding of the characteristics of the design object and the physical process. Yes.

  A method of airfoil expression using a parameter sequence will be described. The parameter expression method is selected in consideration of the following items. First, reduce the number of parameters as much as possible. Since the number of parameters is the number of dimensions of the design space to be searched, the number of points to be searched increases dramatically as the parameters increase. Second, as much as possible, a smooth and practical airfoil can be expressed with a wide range of parameters. Thirdly, a wide range of airfoils can be expressed.

  The following method was selected as a method satisfying these. FIG. 8 is a graph showing how to define an airfoil. FIG. 9 is a graph showing camber. FIG. 10 is a graph showing the blade thickness distribution. The airfoil takes the chord line connecting the trailing edge, which is the point of the sharp tip, and the leading edge, which is the farthest from the trailing edge, on the X axis, and takes the Y axis perpendicular to this, leading the leading edge And the trailing edge, and the chord length is 1, and is expressed in XY coordinates. In FIG. 8, the broken line indicates the camber line, the solid line indicates the upper surface of the airfoil, and the alternate long and short dash line indicates the lower surface of the airfoil.

  An airfoil is defined by a camber line and a blade thickness distribution, and both of these are expressed by Bezier curves. A Bezier curve has the advantage of always giving a curve having a degree corresponding to the number of points and having sufficient smoothness throughout. The camber is defined by six Bezier curves, and the X coordinate of each point is fixed at 0.0, 0.05, 0.2, 0.5, 0.8, and 1.0. As for the Y coordinate, the X coordinate is fixed at 0 at the two points of the leading edge and the trailing edge of 0.0 and 1.0, and the remaining Y coordinates of the middle four points are used as design parameters.

  The blade thickness distribution is defined by 7 Bezier curves, and the X coordinate of each point is fixed at 0.0, 0.0, 0.05, 0.2, 0.5, 0.8, and 1.0. To do. Regarding the Y coordinate, the leading edge is fixed to 0, the trailing edge is fixed to 0.01, and the Y coordinates of the remaining five intermediate points are used as design parameters. A round leading edge is expressed by superimposing the X coordinates of the two points on the leading edge side to zero. As in the optimization design case described later, it is possible to fix some parameters to limit the shape range.

As a more specific airfoil expression method, an airfoil expression method in the case of fixing the maximum airfoil thickness will be described. The blade thickness T is expressed as a percentage, where the chord length is 100. As an initial value, an input point Y coordinate at X = 0 of a Bezier curve giving a blade thickness distribution is fixed to 0.05, and blade coordinates are generated. Due to the nature of the Bezier curve, the maximum blade thickness Tmax may not be exactly 10% depending on the value of other design variables. Therefore, the positions of all control points except the trailing edge point are scaled in the Y direction. The scaling at which the blade thickness is 10% is obtained by repeated calculation. Since one point is fixed, the blade thickness distribution parameter is reduced by one to four.

As another specific airfoil expression method, an airfoil expression method in the case where the zero lift moment coefficient C _{m0 is} designated will be described. In order to change the inclination of the trailing edge, the Bezier input point for camber line at the second position from the trailing edge and at the X coordinate of 0.8 is controlled so that the zero lift moment coefficient C _m0 becomes the specified value. To do. Therefore, the design parameter of the camber line is reduced by 1 to 3 pieces. As a method, an aerodynamic characteristic is obtained by solving a two-dimensional inviscid potential flow by a panel method for the generated airfoil, and iterative calculation is performed so that the zero lift moment coefficient C _m0 becomes a specified value. Find the parameters. Since the panel method ends in a few seconds, the computational load does not increase. In the present embodiment, in the step s3 in FIG. 1, the camber line is corrected by operating the second point from the trailing edge.

The performance evaluation method and objective function to be applied will be described. The maximum blade thickness Tmax is used as the first objective function. The blade thickness is a dimension in a direction parallel to the Y axis of the airfoil, and the maximum blade thickness Tmax is the maximum value of the blade thickness of the airfoil. The maximum blade thickness Tmax is extracted from shape data defined by a Bezier curve as shown in FIG. Thin blades with small shock wave resistance are superior in resistance at high speed and low angle of attack. However, considering the mechanical strength and the like, thick blades are desirable from the structural viewpoint, so the maximum blade thickness Tmax is added to the evaluation.

As the second objective function, the absolute value | C _m0 | of the zero lift moment coefficient C _m0 is used. CFD analysis is performed under the conditions of M = 0.6 and Reynolds number Re = 4.61 × 10 ⁶ , and the angle of attack at which the lift coefficient C _L = 0 is obtained by iterative calculation with the angle of attack α = 0 ° as an initial condition. And a pitching moment coefficient C _m is obtained as a zero lift moment coefficient C _m0 . In the optimization design, the absolute value | C _m0 | <0.01 of the zero lift moment coefficient C _m0 is sufficiently small. In order to evaluate whether or not the absolute value | C _m0 | of the zero lift moment coefficient C _m0 is less than 0.01, max (| C _m0 |, 0.01) can be used as the evaluation value.

As the third objective function, the low speed index lift coefficient C _L300 @ M = 0.4 is used. The low speed index lift coefficient C _L300 @ M = 0.4 is the index lift coefficient C _L300 at M = 0.4. In M = 0.4, the zero lift angle of attack alpha _0, the drag coefficient _{C D} is 0. 0 until 3 is reached, thus C _D ≧ 0. The angle of attack α is gradually increased in increments of 1 ° until reaching 0 3. Once reached, the resistance coefficient C _D = 0... By linear interpolation with the value at the previous angle of attack. The lift coefficient C _L at the angle of attack α that becomes 0 3 is calculated. This low speed index lift coefficient C _L300 @ M = 0.4 corresponds to the maximum lift coefficient at low speed.

A medium speed index lift coefficient C _L300 @ M = 0.6 is used as the fourth objective function. The medium speed index lift coefficient C _L300 @ M = 0.6 is the index lift coefficient C _L300 at M = 0.6. In M = 0.6, the zero lift angle of attack alpha _0, the drag coefficient _{C D} is 0. 0 until 3 is reached, thus C _D ≧ 0. The angle of attack α is gradually increased in increments of 1 ° until reaching 0 3. Once reached, the resistance coefficient C _D = 0... By linear interpolation with the value at the previous angle of attack. The lift coefficient C _L at the angle of attack α that becomes 0 3 is calculated. This low speed index lift coefficient C _L300 @ M = 0.6 corresponds to the maximum lift coefficient in the hovering state.

As the fifth objective function, the Mach number limit M _lim @ α ₀ is used. The angle of attack α is fixed to zero lift angle of attack α ₀ and the Mach number M is gradually increased in steps of 0.01 from M = 0.7, and the smaller of the following two is the Mach number limit M _lim @ Α ₀ .

FIG. 11 is a graph showing an example of the Mach number limit M _lim @ α ₀ . The value of this graph varies depending on the airfoil and is merely an example shown in the Mach number limit M _lim @ α ₀ . In FIG. 11, the vertical axis shows the aerodynamic coefficient, and the aerodynamic coefficient includes a lift coefficient C _L , a resistance coefficient C _D , and a pitching moment coefficient C _m . The broken line 31 indicates the resistance coefficient C _D = 0. 0 3 and the broken line 32 indicates | ΔC _m | ≧ 0.02. The solid line 33 shows the drag coefficient _{C D,} a solid line 34 represents the pitching moment coefficient _{C m,} a solid line 35 shows the lift coefficient _{C L.} 36 indicates the lift limit, and 37 indicates the moment limit.

The first Mach number limit is the lift limit ( _{CL 300} limit). Resistance coefficient C _D ≧ 0. The Mach number M is increased in increments of 0.01 until reaching 03. Once reached, C _D = 0... By linear interpolation with the value at the previous Mach number M. The Mach number M that becomes 0 3 is calculated. This Mach number is the lift limit Mach number. The second Mach number limit is the moment limit. From pitch moment coefficient _{C m} at M = 0.6, the variation of pitch moment coefficient _{C m} and [Delta] C _m. The Mach number M is increased until the absolute value of the variation amount | ΔC _m | ≧ 0.02. When it reaches, the Mach number that satisfies | ΔC _m | = 0.02 is calculated by linear interpolation with the value at the previous Mach number. This Mach number is the moment limit Mach number.

  In the description with reference to FIG. 1, it has been described that these first to fifth objective functions are used. In addition, 80% code position blade thickness T @ 80% is used as the sixth objective function. . The 80% code position blade thickness T @ 80% is the blade thickness T at the code position of 80%, and is extracted from the shape data defined by the Bezier curve. As a result of experience, a wing advantageous in terms of aerodynamic characteristics is a very thin wing in the vicinity of the trailing edge, and may be included in the objective function. In comparison with the existing blade, it is judged that a blade thickness of 3% is sufficient, and in order to evaluate whether the blade thickness T at the cord position of 80% is 3% or more, min (T @ 80%, 0.03) can be the actual evaluation value.

  The performance evaluation value necessary to enable horizontal flight at a speed of 300 km / h will be described. When designing an airfoil that enables horizontal flight at a speed of 300 km / h, an evaluation value is set for each of the aforementioned target functions. This evaluation value varies depending on the design target, and an example is shown here.

The maximum blade thickness Tmax is not set. A smaller absolute value | C _m0 | of the zero lift moment coefficient C _m0 is better. The low speed index lift coefficient C _L300 @ M = 0.4 is set to C _L300 @ M = 0.4> 1.55 from the condition shown in FIG. The medium speed index lift coefficient C _L300 @ M = 0.6 is set to C _L300 @ M = 0.6> 0.95 from the condition shown in FIG. The Mach number limit M _lim @ α ₀ is set to M _lim @ α ₀ > 0.845 from the condition shown in FIG. By setting in this way, it is possible to design an airfoil that satisfies the required performance for enabling horizontal flight at a speed of 300 km / h shown in FIG.

  The types of optimization engines (optimization algorithms) will be described. The optimization engine is not limited to the one described below, but here, a typical optimization engine will be described.

  The first is the gradient method. Starting from one initial value, an objective function change rate (gradient) due to a change in parameter sequence is calculated by a method such as difference. The design is improved by gradually changing the parameter sequence in the direction in which the objective function is maximized (or minimized). The BFGS method that estimates the maximum (minimum) value by skillfully using the gradient information at a plurality of points is representative. Although the search efficiency is high, the solution obtained is limited to the maximum value that can be traced from the initial value, and there is no guarantee that this is the global maximum value. Therefore, a countermeasure is taken in which the initial value is randomly assigned in the search range and a plurality of trials are performed. When there are a plurality of objective functions, it is necessary to use each objective function after converting it into a single objective by weighting and adding the objective functions.

  The second is the downhill simplex (abbreviation DS) method. Define an N + 1 vertex simplex (triangle in 2D, tetrahedron in 3D) for an N-dimensional parameter space, and gradually move and transform the simplex using the evaluation results at the vertex To improve the design. Assuming the linearity of the objective function in the simplex, it is similar to the gradient method in that it uses the gradient determined by N + 1 evaluations. Although the convergence is inferior to that of BFGS, if the initial N + 1 distributions are sufficiently wide in the calculation space, there is a high possibility of reaching the maximum value in the distribution. Like the gradient method, it is basically a single-purpose optimization method.

  The third is a genetic algorithm (GA). This is a method of simulating the evolution of organisms due to genetic changes. It is characterized in that the evaluation at evaluation points sufficiently larger than the number of dimensions in the parameter space is repeated. In the example of a living organism, an evaluation point is called an individual, a repetition count is called a generation, and a parameter string is called a gene. Using the genetic evolution mechanism by DNA and Darwin's theory of evolution, the evolution calculation is performed in the following steps.

  First, the objective function is evaluated for the initial population. Next, the better the evaluation, the higher the probability of leaving the next generation (surviving the right person). Furthermore, in the generation of the next generation, a new gene is generated (mating) by randomly interpolating the genes of two individuals. Furthermore, random noise is added to the gene with a certain probability (mutation). Furthermore, evaluation of objective functions, survival of the right person, mating, and mutation are repeated for the new generation.

  Since GA uses a large number of evaluation points and does not use gradient information, there is little risk of convergence to a local maximum value. Since it is necessary to evaluate the objective function of the number of individuals × generation, it is a drawback that the calculation amount of evaluation becomes enormous. However, since the evaluation for the number of individuals can be executed completely in parallel, the parallelization efficiency on a parallel computer in which many computers are connected is very good. Moreover, GA alone is basically a single-purpose optimization method.

  The fourth is a multi-purpose genetic algorithm (abbreviated as MOGA). In the evolution of organisms, they do not converge on one optimal trait, and various species inhabit at the same time according to subtle environmental changes. That is, when there are a plurality of properties that favor survival, the importance of each property varies depending on the environment, so even if it says survival of the right person, it is not a kind. In this case, the Pareto optimal concept is convenient for comparing superiority and inferiority for each character. An individual that is Pareto optimal is referred to as a Pareto solution, but if it is a Pareto solution, it means that there is a possibility of becoming an optimal solution depending on weighting. Returning to the story of living things, there is a possibility that it may become the optimal trait depending on the environment. A Pareto rank is set, each individual is assigned to a Pareto rank, and a set of non-inferior solutions belonging to the highest Pareto rank is defined as a Pareto solution.

  FIG. 12 is a graph showing an image of a Pareto solution. FIG. 12 shows an example where there are two objective functions, for example, low speed performance and Mach number limit, ◯ indicates the first generation and second generation, and ● indicates the third generation. In addition, the Pareto solution is denoted by reference numeral “40”. The Pareto rank is determined by the following procedure. Initially, the rank of all individuals is initialized to 0 (highest rank). Compare all individuals with all other individuals except for yourself in terms of objective function. If you encounter an individual with a higher evaluation than yourself in all objective functions, drop your rank by one. In this way, all individuals are ranked with a Pareto rank. Individuals remaining in the rank of 0 (highest rank) have at least one advantage when compared to any other individual. That is, there is not one individual with the highest Pareto rank. In principle, there can be countless numbers. The set of individuals with the highest rank is the Pareto solution.

  In the case of FIG. 12, the Pareto solution is a set of solutions that are substantially on a single curve in the upper right. A line connecting this set is called a Pareto edge or a trade-off curve. In MOGA, the Pareto edge is gradually advanced to the upper right by overlapping generations. When mature, the rise of the Pareto edge stops and the optimal Pareto solution is reached. As shown in FIG. 12, an objective function important near the blade tip 13 (tip portion), for example, the Mach number limit, and an objective function important near the blade root 12 (portion near the hub), such as low speed performance, are evaluated. The Pareto solution obtained includes an airfoil suitable for the vicinity of the blade tip 13 and an airfoil suitable for the vicinity of the blade root 12. That is, an airfoil suitable for each part from the blade root 12 to the blade tip 13 of the blade 11 can be obtained by one design.

  In MOGA, this rank (Pareto rank) is used as an evaluation value inside MOGA. In GA, evolutionary computation is originally performed using many individuals, so this MOGA procedure can be introduced naturally and easily by simply changing the evaluation part from GA.

  Multi-objective optimization will be described. As described above, in the design of the airfoil of the blade 11, it is necessary to simultaneously improve about 5 to 6 evaluation items (items corresponding to the objective function). Moreover, it is unclear what weight the various objective functions can realize before the start of design. Therefore, the single-objective optimization method for the weighted average of the objective function is difficult to apply.

  Therefore, in this embodiment, MOGA, which is a multi-purpose optimization engine, is used as the optimization engine. The procedure for designing the airfoil of the blade 11 using MOGA is as shown in the flowchart of FIG. In the case of MOGA, even if design calculation progresses, it does not converge to a single optimum shape. Even if generations are repeated, what stands out in the Pareto solution does not appear and the advance of the Pareto edge stops corresponds to convergence and can be said to be mature.

  Hereinafter, the airfoil designed in the design direction of the present embodiment will be described. FIG. 13 is a graph showing an example of an airfoil designed by the design method according to the present invention. FIG. 14 is a graph showing another example of an airfoil designed by the design method according to the present invention. FIG. 15 is a graph showing still another example of an airfoil designed by the design method according to the present invention. FIG. 16 is a graph showing still another example of an airfoil designed by the design method according to the present invention. FIG. 17 is a graph showing an example of an existing airfoil. FIG. 18 is a graph showing another example of an existing airfoil. FIG. 19 is a graph showing still another example of an existing airfoil. In FIG. 13 to FIG. 19, the chord line is taken as the X axis, the Y axis is taken perpendicularly thereto, and the chord length is set to 1 as the XY coordinates. Moreover, in FIGS. 13-16, the line U shows an upper surface and the line L shows a lower surface.

  Hereinafter, for convenience, the airfoil of model number Case5-No50 in FIG. 13 is referred to as a first example airfoil, the airfoil of model number Case5-No178 in FIG. 14 is referred to as second example airfoil, and the model number in FIG. The airfoil of Case5-No142 is referred to as a third embodiment airfoil, and the airfoil of model number Case5-No195 in FIG. 16 is referred to as a fourth embodiment airfoil. In addition, the airfoil of model number NACA23012 in FIG. 17 is referred to as a first existing airfoil, the airfoil of model number NACA23008 in FIG. 18 is referred to as a second existing airfoil, and the airfoil of model number AK100D in FIG. It is called an airfoil.

  Table 2 shows the coordinate data of the first embodiment airfoil of FIG. Table 3 shows the coordinate data of the first embodiment airfoil of FIG. Table 4 shows the coordinate data of the third embodiment airfoil of FIG. Table 5 shows the coordinate data of the airfoil of the fourth embodiment shown in FIG. In Tables 1 to 4, XU is the X coordinate of the line U indicating the upper surface, YU is the Y coordinate of the line U indicating the upper surface, XL is the X coordinate of the line L indicating the lower surface, and YL Is the Y coordinate of the line L indicating the lower surface. XU and YU associated with the number (No.) are coordinates (XU, YU) that define the upper surface, and XL and YL associated with the number (No.) are the coordinates (XL) that define the lower surface. , YL). A line U connecting points of coordinates (XU, YU) in order from numbers (No.) 1 to 100 defines the upper surface, and a line L connecting points of coordinates (XL, YL) in order from numbers (No.) 1 to 100 Defines the top surface.

  Table 6 shows the performance of the first to fourth embodiment airfoils and the first to third existing airfoils.

  The first to fourth embodiment airfoils are airfoils included in the Pareto solution obtained by optimization while evaluating the first to sixth objective functions. These first to fourth embodiment airfoils have the following characteristics. The airfoil of the first embodiment shown in FIG. 13 is an airfoil suitable for a portion close to the blade root 12 in the blade 11, and is suitable, for example, as an airfoil of a portion from the position in the blade length direction of 80% to the blade root 12. . 14 to 16 are airfoils suitable for a portion of the blade 11 near the blade tip 13, for example, 80% of the blade length direction position to the blade tip 13. Suitable as an airfoil.

Further, the airfoil of the second embodiment shown in FIG. 14 has the best average lift / drag characteristics due to dynamic characteristics, the absolute value of the zero lift moment coefficient | C _m0 | is smaller than any of the first to third existing blades, and the speed It has the performance that the efficiency in horizontal flight at 300 km / h is the best. The third embodiment airfoil of FIG. 15 is slightly inferior in absolute value of zero lift moment coefficient | C _m0 |, but in all other items, the third existing airfoil is said to be the best aerofoil. It has better performance than the airfoil. The airfoil of the fourth embodiment shown in FIG. 16 has the smallest variation in pitching moment, and this airfoil is the best when the minimum moment coefficient C _mmin is an operational limitation in consideration of the torsional rigidity. Can be an airfoil.

  All of the airfoils designed by the design method according to the present invention including the first to fourth embodiment airfoils have a relatively small leading edge radius and a relatively strong leading edge droop. This is because the small leading edge radius is suitable for mitigating the supersonic region and shock wave generated near the maximum lift in the medium speed range (near M = 0.6), and the low speed maximum lift that is reduced by it. This is because it is effective to cover with the leading edge droop. In order to cancel out the moment caused by the leading edge droop, which is a camber that is convex upward, the camber is convex downward in the latter half. It is relatively thin and has high performance.

  With the design method according to the present invention, a large number of airfoils including these airfoils can be designed at one time. Therefore, a plurality of airfoils having various excellent performances can be designed, and from these airfoils, an airfoil suitable for each part of the blade 11 can be selected. Therefore, even if only one blade is used, the airfoil of the blade 11 of the helicopter 10 having different required performance depending on the position can be designed at one time. That is, it is possible to design from the airfoil suitable for the vicinity of the blade root 12 to the airfoil suitable for the vicinity of the blade tip 13 in one time.

FIG. 20 is a graph showing the airfoil Pareto solution designed by the design method according to the present invention, organized by the Mach number limit. The first to fourth embodiment airfoils of FIGS. 13 to 16 are included in this Pareto solution. In FIG. 20, “C _L300 ” is described as “CL300”, and “M _lim @ α ₀ ” is described as “Mlim”. As apparent from FIG. 20, the smaller the Mach number limit Mlim @ alpha _0, lift represented by the low speed indicator lift coefficient _{C L300} @ M = 0.4 and medium speed indicator lift coefficient _{C L300} @ M = 0.6 The airfoil has a large limit and is suitable for the part closer to the blade root 12. As apparent from FIG. 20, it is possible to design from the airfoil suitable for the vicinity of the blade root 12 to the airfoil suitable for the vicinity of the blade tip 13 in one time.

FIG. 21 is a graph showing moment characteristics by dynamic analysis of the airfoil of the second embodiment shown in FIG. FIG. 22 is a graph showing moment characteristics by dynamic analysis of the third existing airfoil of FIG. 21 and FIG. 22, the abscissa indicates the air speed VT that changes with the rotation of the blade in terms of Mach number M, and the ordinate indicates the moment coefficient of the head-down moment. "S tandard q base" on the ordinate represents the non-dimensional values in the above peripheral speed reference dynamic, "L ocal q base" indicates dimensionless value local reference dynamic pressure. As is clear from comparison between the circled regions of FIGS. 21 and 22, it can be seen that the airfoil of the second embodiment has a small head-lowering moment on the high speed side and is excellent in high speed performance. .

FIG. 23 is a graph showing resistance characteristics by dynamic analysis of the airfoil of the second embodiment shown in FIG. FIG. 24 is a graph showing resistance characteristics by dynamic analysis of the third existing airfoil of FIG. 23 and 24, the horizontal axis indicates the airspeed V _T which varies with the rotation of the blade Mach number M, the vertical axis shows the resistance coefficient C _D. 23 and, as apparent from the comparison area circled in FIG. 24, the second embodiment airfoil, medium speed indicator lift coefficient _{C L300} @ M = 0.6 is large, M = 0.6 near It can be seen that this is an excellent airfoil that can keep the resistance at low.

As is clear from the above description, in the design method according to the present invention, a plurality of performances required for the airfoil of the blade 11 are represented as objective functions, respectively, and are optimized by MOGA while evaluating with the plurality of objective functions. The airfoil optimum Pareto solution is required. The objective function includes low speed performance, medium speed performance, high speed performance, maximum blade thickness and pitching moment performance, and an airfoil in which each of these performances is evaluated is designed. In this way, the airfoil evaluated with respect to a plurality of performances is automatically designed, so that the airfoil suitable for the blade 11 of the helicopter 10 can be designed. Moreover, among the plurality of airfoils obtained as a Pareto solution, a plurality of airfoils suitable for each part of the blade 11, from the airfoil suitable for the vicinity of the blade root 12 of the blade 11 to the airfoil suitable for the vicinity of the blade tip 13. The type is included. Therefore, it is possible to design a plurality of airfoils suitable for each part from the blade root 12 to the blade tip 13 of the blade 11 by a single design calculation, increasing the design efficiency, and reducing the airfoils in a short time and at a low cost. Can be designed.

  Also, as shown as step s3 in FIG. 1, since the camber is corrected, it is possible to design an airfoil with improved pitching moment performance. The camber is corrected by changing the position of a point defining a Bezier curve defining the camber in the Y-axis direction.

  FIG. 25 is a diagram illustrating a camber correction method. FIG. 25 shows an example in which a camber is defined by a 4-point Bezier curve. When correcting the camber, as shown in FIGS. 25 (1) and 25 (2), if the position of the point 44 at the trailing edge is changed, the remaining points 42 and 43 are changed even if the point 41 at the leading edge is fixed. Design point. As shown in FIG. 25, when a 4-point Bezier curve is used, the two points 42 and 43 are design points. On the other hand, if the two points 41 and 44 on the leading edge and the trailing edge are fixed and the position of the second point 43 from the trailing edge is changed and corrected, the design point becomes one point 42 and the design point is changed. Can reduce points. In the present embodiment, by changing the position of the second point from the trailing edge, the camber can be corrected, design points can be reduced, and correction can be facilitated.

FIG. 26 is a graph showing the Pareto solution when the zero lift moment coefficient C _m0 is adjusted to 0, organized by the Mach number limit. FIG. 27 is a graph showing the Pareto solution when the zero lift moment coefficient C _m0 is adjusted to be −0.02, organized by the Mach number limit. In FIG. 26 and FIG. 27, “C _L300 ” is described as “CL300”, and “M _lim @ α0” is described as “Mlim”. FIG. 26 and FIG. 27 are graphs for showing the influence of the adjustment of the zero lift moment coefficient C _m0 , and are obtained by a design calculation executed separately from the design calculation obtained the Pareto solution shown in FIG. Pareto solution is shown. 26, as apparent from FIG. 27, zero than lift moment coefficient C _m0 to modify the camber to be 0, who zero lift moment coefficient C _m0 to modify the camber to be -0.02 but it is understood that the airfoil lift limit represented by low speed indicators lift coefficient _{C L300} @ M = 0.4 and medium speed indicator lift coefficient _{C L300} @ M = 0.6 is large is obtained. That modification of the camber is zero lift moment coefficient C _m0 is not 0, 0 around and 0 yo Ri small value, for example, by adjusting so as to about -0.015, becomes airfoil having a positive camber, An airfoil having good performance other than the zero lift moment coefficient C _m0 can be obtained.

  In addition, as described above, the airfoil designed by the design method of the present embodiment is a suitable airfoil for the helicopter 10 blade. The blade 11 having this airfoil is a blade having high speed, economy, and high comfort. In this way, a high-performance blade 11 can be realized.

  The above-described embodiment is merely an example of the present invention, and the configuration of the present invention can be changed. For example, the objective function may be different from the first to sixth objective functions described above, and it is not necessary to evaluate all the first to sixth objective functions, and any one may be selected and used. . The optimization algorithm is not limited to MOGA, and may be another multi-objective optimization algorithm.

It is a flowchart which shows the blade airfoil design method of one Embodiment of this invention. It is a block diagram which shows the design apparatus 20 which performs the design method of FIG. 3 is a plan view showing an airspeed distribution of the rotor blade 11 when the helicopter 10 is flying forward. FIG. 3 is a graph showing the angle of attack distribution of a blade 3. It is a figure which shows the grating | lattice 30 used for an analysis. It is a graph showing the relationship between Mach number M and the lift coefficient C _L of each position in the blade 11. It is a graph showing the relationship between Mach number M and the lift coefficient C _L of the existing airfoil. It is a graph which shows how to define an airfoil. It is a graph which shows a camber. It is a graph which shows blade | wing thickness distribution. It is a graph showing an example of a Mach number limit _{M lim} @ _{α 0.} It is a graph which shows the image of a Pareto solution. It is a graph which shows an example of the airfoil designed by the design method according to the present invention. It is a graph which shows the other example of the airfoil designed with the design method according to this invention. It is a graph which shows the further another example of the airfoil designed with the design method according to this invention. It is a graph which shows the further another example of the airfoil designed with the design method according to this invention. It is a graph which shows an example of the existing airfoil. It is a graph which shows the other example of the existing airfoil. It is a graph which shows the other example of the existing airfoil. It is a graph which shows the Pareto solution of the airfoil designed by the design method according to the present invention, arranged by the Mach number limit.

It is a graph which shows the moment characteristic by the dynamic analysis of 2nd Example airfoil of FIG. It is a graph which shows the moment characteristic by the dynamic analysis of the 3rd existing airfoil of FIG. It is a graph which shows the resistance characteristic by the dynamic analysis of the 2nd Example airfoil of FIG. It is a graph which shows the resistance characteristic by the dynamic analysis of the 3rd existing airfoil of FIG. It is a figure which shows the correction method of a camber. It is a graph which shows the Pareto solution at the time of adjusting so that the zero lift moment coefficient _Cm0 may be set to 0, arranged by the Mach number limit. It is a graph which shows the Pareto solution at the time of adjusting zero lift moment coefficient _Cm0 so that it may become -0.02, arranged in a Mach number limit.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Helicopter 11 Blade 12 Blade root 13 Blade tip 20 Design apparatus 21 Input means 22 Storage means 23 External recording means 24 Calculation means 25 Output means

Claims (4)

In a design apparatus comprising input means for inputting information on parameters defining an airfoil and arithmetic means for executing operations for airfoil evaluation and design, a parameter representing the airfoil is used as a design variable, and the rotor A method of designing a helicopter rotor blade airfoil by a multi-objective optimization algorithm that obtains a Pareto solution by evaluating design variables with respect to a plurality of objective functions representing performance required for the blade airfoil,
An initial setting step in which the calculation means sets airfoil parameters including a blade thickness, a camber, a chord length, and a leading edge radius, using information representing initial values of parameters defining the airfoil input by the input means ; ,
After the initial setting step, the calculation means defines an airfoil according to the set airfoil parameters, and an airfoil definition step,
After the airfoil definition step, an evaluation analysis step in which the computing means evaluates the defined airfoil by a static analysis with respect to a plurality of objective functions;
After the evaluation and analysis step, calculating means obtains a Pareto solution based on the evaluation result of the airfoil in the evaluation analysis step, seen including a determination step of determining whether or not Pareto solutions is mature,
The plurality of objective functions includes low speed performance and medium speed performance,
In the evaluation analysis step, the calculation means uses a predetermined value in a predetermined low speed range as an airspeed of the rotor blade, and gradually increases the angle of attack from the zero lift angle of attack, thereby increasing the resistance coefficient to 0.03. Calculate the lift coefficient at the angle, evaluate the low-speed performance using the calculated lift coefficient, and further use the predetermined value in the predetermined medium speed range as the airspeed of the rotor blade, from the zero lift angle of attack to the angle of attack The blade airfoil in a design apparatus is characterized in that a lift coefficient at an angle of attack with a resistance coefficient of 0.03 is calculated by gradually increasing the lift coefficient, and medium speed performance is evaluated using the calculated lift coefficient Design method. The plurality of objective functions further includes high speed performance;
In the evaluation analysis step, the calculation means fixes the angle of attack to a zero lift angle of attack, calculates the Mach number at which the resistance coefficient is 0.03 by gradually changing the Mach number from a predetermined value, and calculates the Mach number. By gradually changing the number, a Mach number at which the absolute value of the variation amount of the pitching moment coefficient from the pitching moment coefficient at a predetermined Mach number becomes 0.02 is calculated. Of the two calculated Mach numbers The blade airfoil design method for a design apparatus according to claim 1 , wherein high-speed performance is evaluated using a Mach number limit expressed by a smaller one of the two . 3. The blade airfoil design method according to claim 1, wherein the multi-objective optimization algorithm is a multi-objective genetic algorithm. The design apparatus according to any one of claims 1 to 3 , further comprising a step in which a computing unit evaluates the Pareto solution obtained by evaluating the design variable by static analysis by dynamic analysis. blade airfoil design method in.

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