Reynolds Number Limit Analysis Method for Fan Blades with Whale Fin-like Wavy Leading Edges

Abstract

The present invention discloses a method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge. In the method, the design parameters of the whale fin-like wavy leading edge structure are used as design variables to establish three-dimensional models of a reference blade and multiple groups of fan blades with different whale fin-like wavy leading edges; a computational domain of the interference between the incoming flow turbulence and the fan blade is established, and the computational domain is meshed with set grid parameters; based on several preset different Reynolds numbers, the average velocity of the flow field at the inlet of the computational domain is changed, and the boundary conditions of the computational domain are set; the lift and drag coefficients of the reference blade and the fan blade with a whale fin-like wavy leading edge at different Reynolds numbers are calculated to determine the sensitive range of the aerodynamic performance of the fan blade to the Reynolds number; the surface pressure pulsation of the fan blade is collected as an equivalent dipole noise source to determine the sensitive range of the noise reduction of the fan blade with a whale fin-like wavy leading edge to the Reynolds number, and on the premise that the aerodynamic performance of the fan blade is not damaged, the whale fin-like structure with the best noise reduction effect is determined.

Description

Technical Field

[0001] The present invention belongs to the technical field of aero-engine aeroacoustics, and particularly relates to a method for analyzing the Reynolds number limit of a fan blade with a wave-shaped leading edge imitating a whale fin. Background Art

[0002] The Reynolds number is an important parameter used to characterize the flow characteristics of a fluid and is also a key parameter for distinguishing laminar and turbulent flows. The smaller the Reynolds number, the more significant the influence of the fluid viscous force. At different Reynolds numbers, the aerodynamic performance of an airfoil will vary greatly. As the altitude increases, the air density, pressure, and temperature decrease, and the kinematic viscosity coefficient increases, resulting in a significant reduction in the Reynolds number of the aero-engine fan during low-speed cruise of an aircraft, and the aerodynamic performance of the airfoil will deteriorate rapidly. Therefore, at high altitudes and low Reynolds numbers, the design technology of high-performance engine fans is one of the bottlenecks restricting the development of high-altitude aircraft.

[0003] Benefiting from the wave-shaped protrusion structure at the leading edge of the flipper, the huge humpback whale can hunt quietly. This bionic wave structure can not only improve the aerodynamic performance of the airfoil after stall but also effectively reduce the tonal and broadband noise generated by the airfoil. Therefore, the bionic wave-shaped leading edge structure is applicable to the design of aero-engine fans under high-altitude and low Reynolds number conditions from both the aerodynamic and aeroacoustic perspectives. However, the influence of the bionic whale fin wave-shaped leading edge structure on the blade aerodynamic performance varies with the Reynolds number. Therefore, on the premise of ensuring the aerodynamic performance of the engine fan rotor, analyzing the Reynolds number sensitivity limit of noise reduction of the bionic whale fin wave-shaped leading edge blade and optimizing the blade noise reduction design are of great significance for the design of aero-engine fans of high-altitude aircraft.

[0004] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present invention and may therefore include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention proposes a method for analyzing the Reynolds number limit of a fan blade with a wave-shaped leading edge imitating a whale fin. A series of fan blades with wave-shaped leading edges are constructed with different design parameters of the bionic whale fin wave-shaped leading edge. Within a certain range of Reynolds numbers, a calculation model of the interference between the incoming flow turbulence and the wave-shaped leading edge blade is established, and the aerodynamic parameters in the flow field are calculated through high-precision numerical simulation. The sensitivity of the aerodynamic performance of the fan blade with a wave-shaped leading edge imitating a whale fin to the Reynolds number is analyzed, the equivalent dipole sound sources on the blade surface are collected, and the far-field noise is solved in combination with the Ffowcs Williams-Hawkings equation. The sensitivity limit of the noise reduction effect of the fan blade with a wave-shaped leading edge imitating a whale fin to the Reynolds number is analyzed. On the premise of ensuring the aerodynamic performance, the wave-shaped leading edge design parameters with the best noise reduction effect are determined, and the noise reduction optimization design of the fan blade with a wave-shaped leading edge imitating a whale fin is carried out.

[0006] The object of the present invention is achieved through the following technical solutions. A method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge includes:

[0007] In the first step: taking the design parameters of the whale fin-like wavy leading edge structure as design variables, three-dimensional models of a reference blade and multiple groups of fan blades with different whale fin-like wavy leading edges are established;

[0008] In the second step: based on the three-dimensional models of the reference blade and the whale fin-like wavy leading edge blades of multiple groups of different fan blades, a computational domain of the interference between the incoming flow turbulence and the fan blades is established, and the computational domain is meshed with the set grid parameters;

[0009] In the third step: based on several preset different Reynolds numbers, the average velocity of the flow field at the inlet of the computational domain is changed, and the boundary conditions of the computational domain are set;

[0010] In the fourth step: based on the preset numerical calculation model, the full three-dimensional compressible Naiver-Stoke flow field control equation is solved, the lift and drag coefficients of the reference blade and the whale fin-like wavy leading edge blade at different Reynolds numbers are calculated, and the sensitive range of the aerodynamic performance of the fan blade to the Reynolds number is determined;

[0011] In the fifth step: the surface pressure pulsation of the fan blade is collected as an equivalent dipole noise source, and based on the Ffowcs Williams-Hawkings equation, the far-field sound pressure is solved to determine the sensitive range of the noise reduction of the fan blade with a whale fin-like wavy leading edge to the Reynolds number. On the premise that the aerodynamic performance of the fan blade is not damaged, the whale fin-like structure with the best noise reduction effect is determined.

[0012] In the method for analyzing the Reynolds number limit of the fan blade with a whale fin-like wavy leading edge, in the first step, taking the amplitude h from the wave crest to the wave trough and the wavelength λ of the whale fin-like wavy leading edge as design parameters, and taking the mean chord length as the chord length of the reference blade and the wavy leading edge blade, three-dimensional models of the reference blade and multiple groups of fan blades with different whale fin-like wavy leading edges are established. The distribution c(z) of the chord length of the whale fin-like wavy leading edge blade along the span z is: where z is the blade span, h is the amplitude from the wave crest to the wave trough of the whale fin-like wavy leading edge, λ is the wavelength from the wave crest to the wave trough of the whale fin-like wavy leading edge, is the mean chord length of the airfoil; the cross-sectional airfoils at different spanwise positions of the wavy leading edge blade are constructed by scaling the upstream thickness distribution at the position x of the maximum blade thickness max When the abscissa x of the control curve of the wavy leading edge airfoil s is less than the position x of the maximum thickness of the reference blade max , the wavy leading edge blade is the same as the reference blade. The specific construction method is:

[0013]

[0014] Among them, x max is the position of the maximum blade thickness, x s is the abscissa of the airfoil control curve of the wavy leading edge, x w is the position along the mean camber line of the wavy leading edge blade curve, y s and y w are the thicknesses of the reference blade and the wavy leading edge blade along the central axis, respectively.

[0015] In the Reynolds number limit analysis method of the whale fin-inspired wavy leading edge fan blade, in the second step, a cuboid computational domain is established based on the three-dimensional models of the reference blades and the whale fin-inspired wavy leading edge blades of multiple different fan blades. The origin of the computational domain coincides with the origin of the reference blade control curve. The width of the computational domain is consistent with the span z of the three-dimensional models of the reference blades and the whale fin-inspired wavy leading edge blades. The entrance of the computational domain is at a distance from the origin of the computational domain The exit of the computational domain is at a distance from the origin of the computational domain The upper and lower boundaries of the computational domain are both at a distance from the origin of the computational domain The computational domain model is meshed with the set mesh parameters.

[0016] In the Reynolds number limit analysis method of the whale fin-inspired wavy leading edge fan blade, in the second step, the set mesh parameters include the dimensionless distance y of the blade boundary layer grid wall + satisfies y + < 1, the grid height growth rate in the direction perpendicular to the blade wall is less than 1.2, ensuring that the grid skewness is less than 0.5 and the aspect ratio of the near-wall grid is less than 20.

[0017] In the Reynolds number limit analysis method of the whale fin-inspired wavy leading edge fan blade, in the third step, based on several preset different Reynolds numbers the average flow velocity at the entrance is changed to establish the corresponding computational model. Among them, Re i is the i-th group of Reynolds numbers, is the corresponding average flow velocity at the entrance of the i-th group, L is the blade characteristic length, and v is the kinematic viscosity of the fluid; the boundary condition at the entrance of the computational domain is set as a velocity inlet, the boundary condition at the exit is set as a pressure outlet, the left and right sides are set as cyclic boundary conditions, and the upper and lower sides are set as symmetric boundary conditions.

[0018] In the Reynolds number limit analysis method of the whale fin-inspired wavy leading edge fan blade, in the fourth step, the numerical computational model is a large eddy simulation turbulence model. Based on the large eddy simulation turbulence model, the fully three-dimensional compressible Navier-Stokes equations are solved to calculate the distributions of the pressure p and the velocity V in the computational domain in several computational models with different Reynolds numbers. Among them, the fully three-dimensional compressible Navier-Stoke equations are:

[0019]

[0020] wherein, T is the temperature, ρ is the fluid density, is the differential operator, V is the fluid velocity vector, is the material derivative, defined as V is the fluid flow velocity vector, p is the pressure, S M is the momentum source term, e is the internal energy per unit fluid, k is the thermal conductivity, Φ is the dissipation function, S e is the internal energy source term, μ is the dynamic viscosity coefficient;

[0021] Based on the surface pressure distributions p i of the whale fin-like wavy leading edge blades and the reference blades, the aerodynamic performance parameters are measured respectively. The aerodynamic performance parameters include the lift coefficient C il and the drag coefficient C id , wherein, the lift coefficient of the i-th group of blades is defined as C il = L / 2ρ 0 V 2 S, where L is the lift force on the blade, ρ 0 is the atmospheric density, V is the fluid flow velocity, and S is the blade reference area, defined as The drag coefficient of the i-th group of blades is defined as C id = D / 2ρ 0 V 2 S, where D is the drag force on the blade; Compare the differences in the lift coefficient and drag coefficient between the whale fin-like wavy leading edge blades and the reference blades under different Reynolds numbers, analyze the variation laws of the lift coefficient and drag coefficient with the Reynolds number, and determine the sensitive range of the aerodynamic performance of the wavy leading edge fan blades to the Reynolds number.

[0022] In the method for analyzing the Reynolds number limit of the whale fin-like wavy leading edge fan blades, in the fifth step, the surface pressure pulsations of the several groups of whale fin-like wavy leading edge fan blades with different Reynolds numbers are collected as the equivalent dipole noise source F i , and based on the Ffowcs Williams-Hawkings equation, the far-field noise ρ′ is solved. The Ffowcs Williams-Hawkings equation is:

[0023]

[0024] where ρ′ is the far-field noise, is the second-order partial derivative of ρ′, is the speed of sound, is the Laplace operator, x i , x jare coordinates in the Cartesian coordinate system, δ is the Dirac function, f is the wall function, and the equivalent dipole noise source F i is defined as: F i = ρn i - τ ij n j , where n i , n j represents the x i , x j direction component of the normal vector perpendicular to the blade surface, and τ ij is the stress tensor; the far-field sound pressure p' is calculated from the density fluctuation ρ' in the flow field: Calculate the acoustic field characteristics of the far-field noise of the whale fin-like blade at different Reynolds numbers respectively. According to the variation law of the acoustic field characteristics with the Reynolds number, determine the sensitive range of the noise reduction of the whale fin-like wavy leading-edge blade to the Reynolds number; compare the acoustic field characteristics of the far-field noise of the blades with different wavy leading-edge design parameters at different Reynolds numbers, and on the premise that the aerodynamic performance of the fan blade is not damaged, determine the whale fin-like structure with the best noise reduction effect and optimize the noise reduction design of the new fan rotor.

[0025] In the method for analyzing the Reynolds number limit of the whale fin-like wavy leading-edge fan blade, the sensitive range of the aerodynamic performance of the wavy leading-edge fan blade to the Reynolds number means that within the range of the Reynolds number, the variation amplitudes of the lift coefficient and the drag coefficient of the blade with the Reynolds number are within ±10%.

[0026] In the method for analyzing the Reynolds number limit of the whale fin-like wavy leading-edge fan blade, the acoustic field characteristics include the far-field sound pressure level, the sound power spectrum, and the sound directivity.

[0027] In the method for analyzing the Reynolds number limit of the whale fin-like wavy leading-edge fan blade, the sensitive range of the noise reduction effect of the whale fin-like wavy leading-edge blade to the Reynolds number means that within the range of the Reynolds number, the far-field sound pressure level and the peak value of the sound power spectrum generated by the interference between the whale fin-like wavy leading-edge blade and the turbulence are lower than the far-field sound pressure level and the peak value of the sound power spectrum of the reference blade under the same conditions.

[0028] Compared with the prior art, the present invention has the following advantages: The method for analyzing the Reynolds number limit of the whale fin-like wavy leading-edge fan blade of the present invention conducts a Reynolds number sensitivity analysis on the whale fin-like wavy leading-edge blades with different design parameters (amplitude, wavelength). By continuously changing the Reynolds number, it explores the influence trend of the whale fin-like blade on the aerodynamic performance and broadband noise of the fan rotor, clarifies the Reynolds number sensitivity limit, and realizes the optimization of the noise reduction design of the new fan rotor on the premise of ensuring the aerodynamic performance. Description of the Drawings

[0029] Upon reading the detailed description in the following preferred specific embodiments, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The accompanying drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts. Moreover, throughout the drawings, the same reference numerals are used to represent the same components.

[0030] In the drawings:

[0031] Figure 1 is a schematic flow chart of a method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to an embodiment of the present invention;

[0032] Figure 2 is a schematic diagram of design parameters of a method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to an embodiment of the present invention;

[0033] Figure 3 is a schematic diagram of the surface average pressure distribution of a method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to an embodiment of the present invention.

[0034] The present invention will be further explained below in conjunction with the accompanying drawings and embodiments. Specific Embodiments

[0035] The specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the specific embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present invention can be more thoroughly understood and the scope of the present invention can be fully conveyed to those skilled in the art.

[0036] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different terms to refer to the same component. The specification and claims do not use the difference in terms as a way to distinguish components, but use the difference in functions of components as a criterion for distinction. As used throughout the specification and claims, the term "comprising" or "including" is an open-ended term and should be interpreted as "including but not limited to". The subsequent description in the specification is for the purpose of describing the preferred embodiments of implementing the present invention, but the description is for the general purpose of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be defined by the appended claims.

[0037] For the convenience of understanding the embodiments of the present invention, the following will further explain with specific embodiments in conjunction with the accompanying drawings, and the accompanying drawings do not limit the embodiments of the present invention.

[0038] For better understanding, as Figures 1 to 3 shown, the Reynolds number limit analysis method for the whale fin-like wavy leading edge fan blade includes,

[0039] In the first step S1: Taking the design parameters of the whale fin-like wavy leading edge structure as design variables, establish three-dimensional models of the baseline blade and multiple groups of different whale fin-like wavy leading edge fan blades;

[0040] In the second step S2: Based on the three-dimensional models of the baseline blade and the whale fin-like wavy leading edge blade of multiple groups of different fan blades, establish a computational domain of the oncoming flow turbulence and the fan blade interference, and perform grid division of the computational domain with the set grid parameters;

[0041] In the third step S3: Based on several preset different Reynolds numbers, change the average velocity of the flow field at the inlet of the computational domain and set the boundary conditions of the computational domain;

[0042] In the fourth step S4: Based on the preset numerical calculation model, solve the fully three-dimensional compressible Naiver-Stoke flow field control equation, calculate the lift and drag coefficients of the baseline blade and the whale fin-like wavy leading edge blade at different Reynolds numbers, and determine the sensitive range of the fan blade aerodynamic performance to the Reynolds number;

[0043] In the fifth step S5: Collect the surface pressure pulsation of the fan blade as an equivalent dipole noise source, based on the FfowcsWilliams-Hawkings equation, solve the far-field sound pressure, determine the sensitive range of the noise reduction of the whale fin-like wavy leading edge fan blade to the Reynolds number, and on the premise that the aerodynamic performance of the fan blade is not damaged, determine the whale fin structure with the best noise reduction effect.

[0044] In the preferred embodiment of the Reynolds number limit analysis method for the whale fin-like wavy leading edge fan blade, in the first step S1, taking the amplitude h from the peak to the trough of the whale fin-like wavy leading edge and the wavelength λ as design parameters, and taking the mean chord length as the chord length of the baseline blade and the wavy leading edge blade, establish three-dimensional models of the baseline blade and multiple groups of different whale fin-like wavy leading edge fan blades. The distribution c(z) of the chord length of the whale fin-like wavy leading edge blade along the span z is: where z is the blade span, h is the amplitude from the peak to the trough of the whale fin-like wavy leading edge, λ is the wavelength from the peak to the trough of the whale fin-like wavy leading edge, is the mean chord length of the airfoil; the cross-sectional airfoils at different spanwise positions of the wavy leading edge blade are obtained by scaling the position x of the maximum blade thickness maxConstruct the upstream thickness distribution. When the abscissa x of the wave front airfoil control curve s is less than the position x of the maximum thickness of the reference blade max the wavy leading edge blade is the same as the reference blade. The specific construction method is as follows:

[0045]

[0046] Among them, x max is the position of the maximum thickness of the blade, x s is the abscissa of the wave front airfoil control curve, x w is the position of the wavy leading edge blade curve along the mean camber line, y s and y w are the thicknesses of the reference blade and the wavy leading edge blade along the central axis respectively.

[0047] In the preferred implementation of the Reynolds number limit analysis method of the whale fin-like wavy leading edge fan blade, in the second step S2, a cuboid calculation domain is established based on the three-dimensional models of the reference blades and the whale fin-like wavy leading edge blades of multiple different fan blades. The origin of the calculation domain coincides with the origin of the reference blade control curve. The width of the calculation domain is the same as the span z of the three-dimensional models of the reference blades and the whale fin-like wavy leading edge blades. The entrance of the calculation domain is at a distance from the origin of the calculation domain The exit of the calculation domain is at a distance from the origin of the calculation domain The upper and lower boundaries of the calculation domain are both at a distance from the origin of the calculation domain Mesh the calculation domain model with the set grid parameters.

[0048] In the preferred implementation of the Reynolds number limit analysis method of the whale fin-like wavy leading edge fan blade, in the second step S2, the set grid parameters include the dimensionless distance y of the blade boundary layer grid wall + satisfies y + <1, the grid height growth rate in the direction perpendicular to the blade wall is less than 1.2, ensuring that the grid skewness is less than 0.5 and the aspect ratio of the near-wall grid is less than 20.

[0049] In the preferred implementation of the Reynolds number limit analysis method of the whale fin-like wavy leading edge fan blade, in the third step (S3), based on several preset different Reynolds numbers change the average flow velocity at the entrance, and establish the corresponding calculation model. Among them, Re i is the i-th group of Reynolds numbers, is the corresponding average flow velocity at the entrance of the i-th group, L is the characteristic length of the blade, and v is the kinematic viscosity of the fluid; set the boundary condition at the entrance of the calculation domain as velocity inlet, the boundary condition at the exit as pressure outlet, the left and right sides are set as cyclic boundary conditions, and the upper and lower sides are set as symmetric boundary conditions.

[0050] In the preferred embodiment of the method for analyzing the Reynolds number limit of the whale fin-like wavy leading-edge fan blade, in the fourth step (S4), the preset numerical calculation model is a large eddy simulation turbulence model. Based on the large eddy simulation turbulence model, the fully three-dimensional compressible Naiver-Stokes equation is solved to calculate the distributions of pressure p and velocity V in the computational domain in several computational models with different Reynolds numbers. Among them, the fully three-dimensional compressible Naiver-Stoke equation is:

[0051]

[0052] where T is the temperature, ρ is the fluid density, is the differential operator, V is the fluid velocity vector, is the material derivative, defined as V is the fluid flow velocity vector, p is the pressure, S M is the momentum source term, e is the internal energy per unit fluid, k is the thermal conductivity, Φ is the dissipation function, S e is the internal energy source term, μ is the dynamic viscosity coefficient;

[0053] Based on the surface pressure distributions p i of the whale fin-like wavy leading-edge blade and the reference blade, the aerodynamic performance parameters are measured respectively. The aerodynamic performance parameters include the lift coefficient C il and the drag coefficient C id . Among them, the lift coefficient of the i-th group of blades is defined as C il =L / 2ρ 0 V 2 S, where L is the lift force on the blade, ρ 0 is the atmospheric density, V is the fluid flow velocity, S is the reference area of the blade, defined as The drag coefficient of the i-th group of blades is defined as C id =D / 2ρ 0 V 2 S, where D is the drag force on the blade; Compare the differences in the lift coefficient and drag coefficient between the whale fin-like wavy leading-edge blade and the reference blade at different Reynolds numbers, analyze the variation laws of the lift coefficient and drag coefficient with the Reynolds number, and determine the sensitive range of the aerodynamic performance of the wavy leading-edge fan blade to the Reynolds number.

[0054] In the preferred embodiment of the method for analyzing the Reynolds number limit of the whale fin-like wavy leading-edge fan blade, in the fifth step (S5), the surface pressure pulsations of the several whale fin-like wavy leading-edge fan blades with different Reynolds numbers are collected as the equivalent dipole noise source F i , and based on the Ffowcs Williams-Hawkings equation, the far-field noise ρ′ is solved. Among them, the Ffowcs Williams-Hawkings equation is:

[0055]

[0056] where ρ′ is the far - field noise, is the second - order partial derivative of ρ′, is the speed of sound, is the Laplace operator, x i , x j are the coordinates in the Cartesian coordinate system, δ is the Dirac function, f is the wall function, and the equivalent dipole noise source F i is defined as: F i = ρn i - τ ij n j , where n i , n j represent the x i , x j direction components of the normal vector perpendicular to the blade surface, τ ij is the stress tensor; the far - field sound pressure p′ is calculated from the density fluctuation ρ′ in the flow field: Calculate the acoustic field characteristics of the far - field noise of the whale - fin - like blade at different Reynolds numbers respectively. According to the variation law of the acoustic field characteristics with the Reynolds number, determine the sensitive range of the noise reduction of the whale - fin - like wavy leading - edge blade to the Reynolds number; compare the acoustic field characteristics of the far - field noise of the blades with different wavy leading - edge design parameters at different Reynolds numbers, and on the premise that the aerodynamic performance of the fan blade is not damaged, determine the whale - fin - like structure with the best noise reduction effect and optimize the noise reduction design of the new fan rotor.

[0057] In the preferred embodiment of the method for analyzing the Reynolds number limit of the whale - fin - like wavy leading - edge fan blade, the sensitive range of the aerodynamic performance of the wavy leading - edge fan blade to the Reynolds number means that within the Reynolds number range, the variation amplitudes of the lift coefficient and the drag coefficient of the blade with the Reynolds number are within ±10%.

[0058] In the preferred embodiment of the method for analyzing the Reynolds number limit of the whale - fin - like wavy leading - edge fan blade, the acoustic field characteristics include the far - field sound pressure level, the sound power spectrum, and the sound directivity.

[0059] In the preferred embodiment of the method for analyzing the Reynolds number limit of the whale - fin - like wavy leading - edge fan blade, the sensitive range of the noise reduction effect of the whale - fin - like wavy leading - edge blade to the Reynolds number means that within the Reynolds number range, the far - field sound pressure level and the peak value of the sound power spectrum generated by the interference between the whale - fin - like wavy leading - edge blade and the turbulence are lower than those of the reference blade under the same conditions.

[0060] In one embodiment, the method includes the following steps:

[0061] In the first step: Taking the design parameters of the whale fin-like wavy leading edge structure as design variables, three-dimensional models of the baseline blade and multiple groups of fan blades with different whale fin-like wavy leading edges are established.

[0062] In the second step: Based on the three-dimensional models of the several groups of whale fin-like wavy leading edge blades with different structural parameters and the baseline blade, a computational domain model of the interference between the incoming flow turbulence and the fan blade is established, and the computational domain grid is divided with the set grid parameters;

[0063] In the third step: Based on several preset different Reynolds numbers, the average velocity of the flow field at the inlet is changed, and the boundary conditions of the computational domain are set;

[0064] In the fourth step: Based on the preset numerical calculation model, the fully three-dimensional compressible Naiver-Stoke flow field control equation is solved, the lift and drag coefficients of the fan blade with a wavy leading edge at different Reynolds numbers are calculated, and the sensitivity limit of the aerodynamic performance of the fan blade with a wavy leading edge to the Reynolds number is determined;

[0065] In the fifth step: The surface pressure pulsation of the fan blade is collected as an equivalent dipole noise source. Based on the FfowcsWilliams-Hawkings equation, the far-field sound pressure is solved, the variation law of the noise reduction effect of the whale fin-like wavy leading edge with the Reynolds number is analyzed, the sensitivity limit of the noise reduction Reynolds number of the fan blade with a whale fin-like wavy leading edge is determined, and on the premise that the aerodynamic performance of the fan blade is not damaged, the whale fin-like structure with the best noise reduction effect is determined, and the noise reduction optimization design of the blade is carried out;

[0066] In the method described above, in the first step,

[0067] Taking the amplitude h from the peak to the trough of the whale fin-like wavy leading edge and the wavelength λ as design parameters, and taking the mean chord length as the chord length of the baseline blade and the wavy leading edge blade, three-dimensional models of the baseline blade and multiple groups of fan blades with different whale fin-like wavy leading edges are established. The specific fan blade parameters are shown in Table 1; among them, the distribution c(z) of the chord length of the whale fin-like wavy leading edge blade along the span z is: where z is the blade span, h is the amplitude from the peak to the trough of the whale fin-like wavy leading edge, λ is the wavelength from the peak to the trough of the whale fin-like wavy leading edge, is the mean chord length of the airfoil; the cross-sectional airfoils at different spanwise positions of the wavy leading edge blade are constructed by scaling the upstream thickness distribution at the position x max of the maximum blade thickness. When the abscissa x s of the control curve of the wavy leading edge airfoil is less than the position x max of the maximum thickness of the baseline blade, the wavy leading edge blade is the same as the baseline blade. The specific construction method is:

[0068]

[0069] Among them, x max is the position of the maximum blade thickness, x s is the abscissa of the control curve of the wavy leading-edge airfoil, x w is the position along the mean camber line of the wavy leading-edge blade curve, y s and y w are the thicknesses of the reference blade and the wavy leading-edge blade along the central axis, respectively.

[0070]

[0071] Among them, the No. 0 blade in Table 1 is the reference blade, and the remaining blades are whale fin-inspired wavy leading-edge fan blades with different design parameters. The design parameters of the reference blade and the wavy leading-edge are as Figure 2 shown;

[0072] In the said method, in the second step,

[0073] Based on the 3D models of several groups of whale fin-inspired wavy leading-edge blades with different structural design parameters and the reference blade, a cuboid computational domain is established. The origin of the computational domain coincides with the origin of the control curve of the reference blade. The width of the computational domain is consistent with the span z = 100 mm of the 3D models of the wavy leading-edge blade and the reference blade. The entrance of the computational domain is at a distance from the origin of the computational domain The exit of the computational domain is at a distance from the origin of the computational domain The upper and lower boundaries of the computational domain are both at a distance from the origin of the computational domain With the preset grid parameters, the computational domain model is meshed. Among them, the preset grid parameters include the dimensionless distance y of the blade boundary layer grid wall + satisfying y + < 1, the grid height growth rate in the direction perpendicular to the blade wall is less than 1.2, ensuring that the grid skewness is less than 0.5 and the aspect ratio of the near-wall grid is less than 20.

[0074] In the said method, in the third step,

[0075] In the Reynolds number range of 1×10 4 to 1×10 6 with a Reynolds number interval of 5×10 4 calculate the preset Reynolds number Change the average flow velocity at the entrance Establish the corresponding computational model. Among them, Re i is the i-th group of Reynolds numbers, is the corresponding average flow velocity at the entrance of the i-th group, L is the blade characteristic length, and v is the kinematic viscosity of the fluid; set the boundary condition at the entrance of the computational domain as velocity inlet, the boundary condition at the exit as pressure outlet, the left and right sides are set as cyclic boundary conditions, and the upper and lower sides are set as symmetric boundary conditions.

[0076] In the method, in the fourth step,

[0077] The numerical calculation model is a large eddy simulation turbulence model. Based on the large eddy simulation turbulence model, the fully three-dimensional compressible Navier-Stokes equations are solved to calculate the distributions of pressure p, velocity V in the calculation domains of several calculation models with different Reynolds numbers described in the third step respectively. Among them, the fully three-dimensional compressible Navier-Stokes equations are defined as:

[0078]

[0079] where T is the temperature, ρ is the fluid density, is the differential operator, V is the fluid velocity vector, is the material derivative, defined as V is the fluid flow velocity vector, p is the pressure, S M is the momentum source term, e is the internal energy per unit fluid, k is the thermal conductivity, Φ is the dissipation function, S e is the internal energy source term, μ is the dynamic viscosity coefficient, where Re = 2×10 5 The average pressure distribution on the surface of the wavy leading-edge blade is as Figure 3 shown; Based on the surface pressure distributions p i of the whale fin-inspired wavy leading-edge blade and the reference blade, the aerodynamic performance parameters are measured respectively. The aerodynamic performance parameters include the lift coefficient C il and the drag coefficient C id . Among them, the lift coefficient of the i-th group of blades is defined as C il = L / 2ρ 0 V 2 S, where L is the lift force on the blade, ρ 0 is the atmospheric density, V is the fluid flow velocity, and S is the reference area of the blade, defined as The drag coefficient of the i-th group of blades is defined as C id = D / 2ρ 0 V 2 S, where D is the drag force on the blade; Compare the differences in the lift coefficient and drag coefficient between the whale fin-inspired wavy leading-edge blade and the reference blade at different Reynolds numbers, analyze the variation laws of the lift coefficient and drag coefficient with the Reynolds number, and determine the sensitive range of the aerodynamic performance of the wavy leading-edge fan blade to the Reynolds number.

[0080] In the method, in the fifth step,

[0081] Collect the surface pressure pulsations of several groups of whale fin-inspired wavy leading-edge fan blades with different Reynolds numbers as the equivalent dipole noise source F i, based on the Ffowcs Williams-Hawkings equation, solve for the far-field noise p′, where the Ffowcs Williams-Hawkings equation is defined as:

[0082]

[0083] where ρ′ is the far-field noise, is the second-order partial derivative of ρ′, is the speed of sound, is the Laplace operator, x i , x j are the coordinates in the Cartesian coordinate system, δ is the Dirac function, f is the wall function, and the equivalent dipole noise source F i is defined as: F i = ρn i - τ ij n j where n i , n j represent the x i , x j direction components of the unit normal vector perpendicular to the blade surface, τ ij is the stress tensor; the far-field sound pressure ρ′ is calculated from the density fluctuation ρ′ in the flow field: Calculate the acoustic field characteristics of the far-field noise of the whale fin-like blade at different Reynolds numbers respectively. According to the variation law of the acoustic field characteristics with the Reynolds number, determine the sensitive range of the noise reduction of the whale fin-like wavy leading-edge blade to the Reynolds number; compare the acoustic field characteristics of the far-field noise of the blades with different wavy leading-edge design parameters at different Reynolds numbers, and on the premise that the aerodynamic performance of the fan blade is not damaged, determine the whale fin-like structure with the best noise reduction effect, and optimize the noise reduction design of the new fan rotor.

[0084] Although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, rather than restrictive. Those of ordinary skill in the art can also make many forms under the inspiration of this specification and without departing from the scope protected by the claims of the present invention, and these all belong to the scope of protection of the present invention.

Claims

1. A method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge, characterized in that, it includes the following steps, In the first step: taking the design parameters of the whale fin-like wavy leading edge structure as design variables, establish three-dimensional models of a reference blade and multiple groups of different fan blades with whale fin-like wavy leading edges; In the second step: based on the three-dimensional models of the reference blade and the whale fin-like wavy leading edge blades of multiple groups of different fan blades, establish a computational domain for the interference between the incoming flow turbulence and the fan blade, and perform grid division of the computational domain with set grid parameters; In the third step: based on several preset different Reynolds numbers, change the average velocity of the flow field at the inlet of the computational domain and set the boundary conditions of the computational domain; In the fourth step: based on a preset numerical calculation model, solve the full three-dimensional compressible Naiver-Stoke flow field control equation, calculate the lift and drag coefficients of the reference blade and the whale fin-like wavy leading edge blade at different Reynolds numbers, and determine the sensitive range of the aerodynamic performance of the fan blade to the Reynolds number; In the fifth step: collect the surface pressure pulsation of the fan blade as an equivalent dipole noise source, and based on the FfowcsWilliams-Hawkings equation, solve the far-field sound pressure to determine the sensitive range of the noise reduction of the fan blade with a whale fin-like wavy leading edge to the Reynolds number, and on the premise that the aerodynamic performance of the fan blade is not damaged, determine the whale fin-like structure with the best noise reduction effect; Among them, in the first step, the amplitude from the wave crest to the wave trough of the wavy leading edge imitating a whale fin and the wavelength are used as design parameters, and the mean chord length is used as the chord length of the reference blade and the wavy leading edge blade. Three-dimensional models of the reference and multiple groups of different whale fin-like wavy leading edge fan blades are established. The chord length of the whale fin-like wavy leading edge blade along the span distribution is: , where is the airfoil span, is the amplitude from the wave crest to the wave trough of the wavy leading edge imitating a whale fin, is the wavelength from the wave crest to the wave trough of the wavy leading edge imitating a whale fin, is the mean chord length of the airfoil; the cross-sectional airfoils at different spanwise positions of the wavy leading edge blade are constructed by scaling the thickness distribution upstream of the maximum thickness position of the blade. When the abscissa of the wavy leading edge airfoil control curve is less than the maximum thickness position of the reference blade, the wavy leading edge blade is the same as the reference blade. The specific construction method is: ， Among them, is the position of the maximum blade thickness, is the abscissa of the control curve of the wavy leading-edge airfoil, is the position along the mean camber line of the wavy leading-edge blade curve, and are the thicknesses of the reference blade and the wavy leading-edge blade along the central axis, respectively.

2. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 1, wherein, In the second step, a cuboid computational domain is established based on the three-dimensional models of the reference blades and the whale fin-like wavy leading edge blades of multiple groups of different fan blades. The origin of the computational domain coincides with the origin of the control curve of the reference blade; the width of the computational domain is consistent with the span length of the three-dimensional models of the reference blade and the whale fin-like wavy leading edge blade. The inlet of the computational domain is at a distance from the origin of the computational domain , and the outlet of the computational domain is at a distance from the origin of the computational domain . The upper and lower boundaries of the computational domain are both at a distance from the origin of the computational domain ; the computational domain model is meshed with the set mesh parameters.

3. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 2, wherein, In the second step, the set grid parameters include the dimensionless distance of the blade boundary layer grid wall surface Satisfy , the grid height growth rate in the direction perpendicular to the blade wall surface is less than 1.2, ensuring that the grid skewness is less than 0.5 and the aspect ratio of the near-wall grid is less than 20.

4. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 1, wherein, In the third step, based on several preset different Reynolds numbers , change the average velocity of the flow field at the inlet to establish the corresponding calculation model, where is the th group of Reynolds numbers, is the average velocity of the corresponding th group of the flow field at the inlet, is the characteristic length of the blade, is the kinematic viscosity of the fluid; set the boundary condition at the inlet of the calculation domain as velocity inlet, the boundary condition at the outlet as pressure outlet, the left and right sides as cyclic boundary conditions, and the upper and lower sides as symmetric boundary conditions.

5. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 4, wherein, In the fourth step, the numerical calculation model is a large eddy simulation turbulence model. Based on the large eddy simulation turbulence model, the fully three-dimensional compressible Navier-Stokes equations are solved to calculate the pressure in several calculation models with different Reynolds numbers respectively. , velocity distributions in the computational domain. Among them, the fully three-dimensional compressible Navier-Stokes equations are as follows: ， wherein, is the temperature, is the fluid density, is the differential operator, is the fluid velocity vector, is the material derivative, defined as , is the pressure, is the momentum source term, is the internal energy per unit fluid, is the thermal conductivity, is the dissipation function, is the internal energy source term, is the dynamic viscosity coefficient; Surface Pressure Distribution of Whale-Fin-Like Wavy Leading-Edge Blades and Baseline Blades , measure the aerodynamic performance parameters respectively, and the aerodynamic performance parameters include lift coefficient and drag coefficient . Among them, the lift coefficient of the th group of blades is defined as , where is the lift force received by the blade, is the atmospheric density, is the fluid flow velocity, is the blade reference area, defined as ; the drag coefficient of the th group of blades is defined as , where is the drag force received by the blade; compare the differences in lift coefficient and drag coefficient between the whale-fin-like wavy leading-edge blades and the baseline blades under different Reynolds numbers, analyze the variation laws of lift coefficient and drag coefficient with Reynolds number, and determine the sensitive range of the aerodynamic performance of the wavy leading-edge fan blades to Reynolds number.

6. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 5, wherein, In the fifth step, several groups of surface pressure pulsations of the whale fin-like wavy leading edge fan blades with different Reynolds numbers are collected as the equivalent dipole noise sources , and the far-field noise is solved based on the Ffowcs Williams-Hawkings equation , where the Ffowcs Williams-Hawkings equation is as follows: ， Among them, is the far-field noise, is the second-order partial derivative of, is the speed of sound, is the Laplace operator, , is the coordinate in the Cartesian coordinate system, is the Dirac function, is the wall function, the equivalent dipole noise source is defined as: , where , represents the in the direction of the normal vector perpendicular to the blade surface, direction component, is the stress tensor; the far-field noise is calculated from the density fluctuation in the flow field: ; Calculate the acoustic field characteristics of the far-field noise of the whale fin-like blade at different Reynolds numbers respectively. According to the variation law of the acoustic field characteristics with the Reynolds number, determine the sensitive range of the noise reduction of the whale fin-like wavy leading-edge blade to the Reynolds number; Compare the acoustic field characteristics of the far-field noise of the blades with different wavy leading-edge design parameters at different Reynolds numbers, and determine the whale fin-like structure with the best noise reduction effect on the premise that the aerodynamic performance of the fan blade is not damaged.

7. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 6, wherein, The sensitive range of the aerodynamic performance of the wavy leading-edge fan blade to the Reynolds number indicates that within the range of the Reynolds number, the variation amplitudes of the blade lift coefficient and drag coefficient with the Reynolds number are within or less.

8. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 6, wherein, the acoustic field characteristics include far-field sound pressure level, sound power spectrum, and sound directivity.

9. The method for analyzing the Reynolds number limit of a fan blade with a whale fin-like wavy leading edge according to claim 8, wherein, the sensitive range of the noise reduction effect of the fan blade with a whale fin-like wavy leading edge to the Reynolds number means that within the range of the Reynolds number, the far-field sound pressure level and the peak value of the sound power spectrum generated by the interference between the fan blade with a whale fin-like wavy leading edge and the turbulence are lower than those of the reference blade under the same conditions.

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