A design method for a casing treatment with stabilization and noise reduction functions

Abstract

This invention provides a design method for a casing treatment with stabilization and noise reduction functions. The method includes: constructing the wall impedance equation of the casing treatment using the equivalent distributed source method and the characteristic impedance model of porous materials; matching the perturbation continuity equation and momentum equation of the casing treatment section with the bladeless region of an axial compressor using the transfer element method; constructing the perturbation frequency characteristic equation of the axial compressor with casing treatment based on small perturbation theory; solving the perturbation frequency characteristic equation to obtain the perturbation frequency; determining the instability point of the axial compressor based on the imaginary part of the perturbation frequency; calculating the instability point of the axial compressor under different casing treatment parameters; and selecting the casing treatment parameters corresponding to the lowest instability point as the design parameters of the casing treatment. Implementing the technical solution of this invention can optimize the stabilization of the casing treatment. The casing treatment designed using the technical solution of this invention can achieve noise reduction due to the use of porous materials.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology, and in particular to a design method for casing treatment with stabilization and noise reduction functions. Background Technology

[0002] As one of the three core components of an engine, the compressor plays a decisive role in its performance. As a crucial performance parameter, the pressure ratio of modern aero engines reaches 30 for military use, while advanced civilian engines even approach 50. For compressors, this high pressure ratio design trend leads to increasingly severe flow stability problems for the compressor / fan, easily resulting in insufficient stability margins and thus rendering them unusable. In engineering, casing-type engines, with their advantages of simple structure and strong anti-distortion capabilities, have been applied to aircraft such as the JT-9D, the Su-27 using the A-31Φ engine, and the WP-13. Meanwhile, since the 1970s, when the United States made civil aircraft noise a mandatory airworthiness indicator, major aircraft companies have dedicated themselves to reducing civil aircraft noise over the past 50 years, with aero engine noise, as a major noise source, becoming a focal point. Currently, civil aero engines mainly adopt high bypass ratio designs to improve thrust-to-weight ratio and reduce jet noise; thus, fan noise becomes the primary noise source. Acoustic liners, as a well-developed noise reduction technology, are commonly used to reduce fan noise. These acoustic treatment structures are often installed in engine nacelles and ducts to reduce noise from the perspective of sound propagation. To meet the weight reduction requirements of engines, the length of the nacelle has been further reduced, leading to the development of transrotor acoustic liners. A type of open-cell foam metal with a cellular structure has been favored by NASA's Glenn Laboratory due to its ability to withstand high-intensity flow fields in the blade tip region, its high-temperature resistance, structural stability, and excellent sound absorption properties.

[0003] Patent No. ZL2017 1 0436118.2 discloses a casing treatment device with stabilization and noise reduction functions, combining casing treatment with foamed metal transrotor acoustic liner, such as... Figure 1 As shown, it includes a perforated plate 101, a rotor 102, and a back cavity 103, which can simultaneously achieve stabilization and noise reduction functions, and has good engineering application prospects. However, there is currently no method to guide the design of this type of casing treatment. Summary of the Invention

[0004] To address at least one technical problem in the prior art, the present invention provides a design method for casing treatment with stabilization and noise reduction functions.

[0005] The present invention provides a design method for casing treatment with stabilization and noise reduction functions, comprising:

[0006] The wall impedance equation of the casing treatment is constructed using the equivalent distributed source method and the characteristic impedance model of porous materials.

[0007] The perturbation continuity equation and momentum equation are matched between the casing processing section and the bladeless region of the axial compressor using the transfer unit method.

[0008] Based on the small perturbation theory, the perturbation frequency characteristic equation of the axial compressor with the aforementioned casing treatment is constructed.

[0009] The perturbation frequency is obtained by solving the characteristic equation of the perturbation frequency;

[0010] The instability point of the axial compressor is determined by the imaginary part of the disturbance frequency at different flow rates.

[0011] Calculate the instability point of the axial compressor under different casing treatment parameters, and select the casing treatment parameters corresponding to the lowest instability point as the design parameters for casing treatment.

[0012] Optionally, constructing the wall impedance equation for the casing treatment includes:

[0013] The equivalent distributed source method is used to determine the scattered pressure disturbance field generated in the compressor main duct and each back cavity due to the introduction of the casing treatment;

[0014] Based on the scattering pressure perturbation field, the impedance equation of the perforated plate is constructed;

[0015] The characteristic impedance model of the porous material is used to replace the air density and characteristic wavenumber in the scattered sound field of the back cavity filled with the porous material.

[0016] Based on the perforated plate impedance equation, the vibration velocity of the casing treatment surface is written as a function of the incident wave to obtain the wall impedance equation of the casing treatment.

[0017] Optionally, the scattering pressure perturbation field is:

[0018]

[0019] Where, p s This represents the scattered pressure disturbance field within the target area. Let represent the coordinates of the observation point, t represent the time of the observation point, T represent the upper limit of the time integration, and S() represent the integration surface at time τ. V represents the density of a gas. n G represents the vibration velocity of the vortex layer, and G represents the Green's function, which is related to the shape of the pipe and the shape of the target region and its two end boundaries. Let τ represent the flow derivative, τ represent the source time, and s represent the source integral surface. Indicates the coordinates of the source point;

[0020] The impedance equation for the perforated plate is:

[0021]

[0022] Where, p + and p - These represent the pressure disturbances on the outer and inner sides of the perforated plate, respectively. Z represents the velocity of the acoustic particles in the mainstream outward normal direction of the perforated plate, and Z represents the impedance of the perforated plate.

[0023] The characteristic impedance model of the porous material includes:

[0024]

[0025]

[0026] Where Z0 = 0c0 represents the characteristic impedance of air, c1 to c8 represent coefficients related to porous materials, f represents the real part of the incident frequency, j represents the imaginary unit, k0 represents the characteristic wavenumber of air, and σ represents the flow resistance of porous materials.

[0027] Optionally, the casing processing includes N layers of perforated plates, where N is an integer greater than or equal to 2, and the impedance equation of each perforated plate is established:

[0028]

[0029]

[0030]

[0031] in, This represents the pressure scattering field generated by the vibration of the small holes in the first perforated plate within the first back cavity. p represents the pressure scattering field generated by the vibration of the small holes in the second layer of perforated plate in the first back cavity. 1, Z represents the pressure scattering field generated by the vibration of the small holes in the first perforated plate in the main pipe; B and C represent the incident waves on the left and right surfaces of the casing processing area; and Z1 represents the impedance of the first perforated plate. This represents the pressure scattering field generated in the Nth back cavity by the vibration of the small holes in the Nth perforated plate. This represents the pressure scattering field generated in the N-1th back cavity by the vibration of the small holes in the N-1th perforated plate. This represents the pressure scattering field generated in the (N-1)th back cavity by the vibration of the small holes in the Nth layer of the perforated plate. Z represents the velocity of the acoustic particles in the mainstream outward normal direction of the Nth perforated plate, and Z represents the impedance of the Nth perforated plate.

[0032] Optionally, the scattered pressure pulsation field can be sinusoidally transformed and written as a series sum:

[0033]

[0034] Among them, z jk V represents the equivalent radiation impedance of the pipe. k The sine expansion coefficients represent the vibration velocity, j represents the order of the sine transformation, k represents the order of the axial sine expansion of the velocity, l represents the axial length of the geometric cavity, and p s denoted by scattering pressure pulsation field, x represents the axial coordinate of the observation point;

[0035] The specific expression for equivalent radiation impedance is:

[0036]

[0037] Where ρ0 represents the density of air, i represents the imaginary unit, ω represents the perturbation frequency, t represents the observation time, m and n represent the circumferential and radial mode numbers, and Φ m, It is the characteristic function, Γ m,n κ represents the orthogonal integral value of the characteristic function of the corresponding mode. m,n Let represent the characteristic value of the corresponding modal pipe, l represent the axial length of the geometric cavity, s(τ) represent the integral surface at time τ, ω represent the disturbance frequency, and U represent the axial average velocity of the main stream. Let x represent the forward and backward axial wavenumbers of modes m and n, x represent the axial coordinates of the observation point, x′ represent the axial coordinates of the source point, k represent the axial sine expansion order of the velocity, s represent the source point integral surface, and j represent the sine transformation order.

[0038] Based on the perforation plate impedance equation of the N-layer perforated plate, the normal vibration velocity sinusoidal within the small holes of each layer of perforated plate is expanded as follows:

[0039]

[0040]

[0041]

[0042] Where, k n The axial expansion order represents the velocity, and its subscript n = 1 to N indicates the nth perforated plate. The sinusoidal expansion coefficient represents the vibration velocity of the small holes in the nth layer of the perforated plate.

[0043] Solving the system of equations in claim 4 simultaneously yields the wall impedance equation for the casing processing section:

[0044]

[0045] in, Represents the characteristic impedance form of the scattered waves from each region. and the impedance Z of each perforated plate N The impedance combination formed, I j (B,C) represents the coefficients after the incident wave undergoes a sinusoidal transformation.

[0046] Optionally, the matching of the disturbance continuity equation and momentum equation between the casing processing section and the bladeless region of the axial compressor using the transfer unit method includes:

[0047] Construct matching equations for pressure disturbances and axial velocity disturbances on the left and right interfaces:

[0048] A l -B l -C l -p s,l =-p i,l

[0049] A l,V -B l,V -C l,V -p s,l,V =-p i,l,V

[0050] B r +C r +p s,r -C r =0

[0051] B r,V +C r,V +p s,r,V -D r,V =0

[0052] Where A represents the reflected wave at the left interface of the casing processing section, B represents the incident wave at the left interface, C represents the incident wave at the right interface, and D represents the transmitted wave at the right interface. The subscript l indicates the left interface, the subscript r indicates the right interface, and the subscript V indicates the velocity disturbance wave given by the axial momentum equation. i p represents the incident sound wave at the left interface. s The pressure disturbance wave introduced by the casing treatment is obtained by substituting the wall impedance equation of the casing treatment section into the mainstream scattered pressure disturbance field.

[0053] The matching equations described by the transfer unit method can be written in matrix form:

[0054]

[0055] Where ss represents the coefficient matrix, A n B n C n Dn Let A, B, C, and D represent the coefficients of the modal expansions, respectively. ω0 represents the back-transmission axial wavenumber, ω0 represents the disturbance frequency, U represents the axial average velocity, and n represents the mode expansion order.

[0056] Optionally, the characteristic equation of the disturbance frequency is:

[0057] ψ(ω)X mn =0

[0058] Where ψ represents the matching equation matrix of the compression system with the casing processing section, ω represents the disturbance frequency, and X mn A vector representing the combination of modal coefficients of pressure, axial, circumferential, and radial velocity pulsations related to the circumferential and radial modal numbers.

[0059] Optionally, determining the instability point of the axial compressor based on the imaginary part of the disturbance frequency at different flow rates includes:

[0060] Determine the imaginary part of the disturbance frequency. If the imaginary part is less than 0, the disturbance of the compression system amplifies exponentially with time, and the compression system becomes unstable.

[0061] The embodiments of this invention provide one or more technical solutions that utilize the equivalent distributed source method and the characteristic impedance model of porous materials to construct the wall impedance equation of the casing treatment. The transfer element method is used to match the perturbation continuity equation and momentum equation between the casing treatment section and the bladeless region of the axial compressor. Based on small perturbation theory, a perturbation frequency characteristic equation for the axial compressor with the casing treatment is constructed. This ensures that the perturbation frequency solution of the perturbation frequency characteristic equation accurately reflects the stability enhancement and noise reduction capabilities of the casing treatment device, making the determination of the instability point based on the perturbation frequency more accurate. Furthermore, this invention can determine optimized casing treatment parameters by utilizing the instability points of the axial compressor under different casing treatment parameters, achieving the optimization objective.

[0062] The wall impedance equation of this invention is related to casing processing parameters such as the number of casing processing layers, the flow resistance of porous material, the height of each casing processing layer, the axial length of casing processing, and the perforation rate of perforated plate. This allows the invention to optimize casing processing parameters such as the number of casing processing layers, the flow resistance of porous material, the height of each casing processing layer, the axial length of casing processing, and the perforation rate of perforated plate during the optimization design, resulting in more comprehensive parameter optimization.

[0063] The design method provided by this invention is essentially an analytical method with physical basis. It can calculate the instability point of a configuration within 2 to 5 minutes. The calculation speed is fast and it is supported by physical evidence.

[0064] This invention constructs the wall impedance equation of the casing treatment based on the characteristic impedance model of porous materials. The sound absorption characteristics of porous materials themselves enable the casing treatment designed according to the method of this invention to have the dual functions of sound absorption and noise reduction. Attached Figure Description

[0065] The accompanying drawings illustrate exemplary embodiments of the invention and, together with the description thereof, serve to explain the principles of the invention. These drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification.

[0066] Figure 1 A schematic diagram of a casing processing device with stabilization and noise reduction functions in the prior art is shown;

[0067] Figure 2 A flowchart is shown as a design method for a casing treatment with stabilization and noise reduction functions according to an exemplary embodiment of the present invention.

[0068] Figure 3 Another flowchart of a design method for a casing treatment with stabilization and noise reduction functions according to an exemplary embodiment of the present invention is shown;

[0069] Figure 4 A sub-flowchart of a design method for a casing treatment with stabilization and noise reduction functions according to an exemplary embodiment of the present invention is shown;

[0070] Figure 5 A schematic diagram illustrating a casing processing unit according to an exemplary embodiment of the present invention is shown;

[0071] Figure 6 The diagram illustrates an application example of the design method for casing treatment with stabilization and noise reduction functions according to an exemplary embodiment of the present invention in a low-speed single-unit compressor. Detailed Implementation

[0072] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the invention. It should be understood that the accompanying drawings and embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the invention.

[0073] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0074] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to". The term "based on" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first", "second", etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0075] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0076] The names of the messages or information exchanged between the multiple devices in the embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0077] The present invention will now be described with reference to the accompanying drawings:

[0078] See Figure 2 and Figure 3 A design method for a casing treatment with stabilization and noise reduction functions includes:

[0079] S201, using the equivalent distributed source method and the characteristic impedance model of porous materials, constructs the wall impedance equation for casing treatment.

[0080] See Figure 4 The wall impedance equation for the casing treatment can be constructed using the following steps:

[0081] S401, using the equivalent distributed source method, determines the scattered pressure disturbance field generated in the compressor main duct and each back cavity due to the introduction of casing treatment:

[0082]

[0083] Where, p s This represents the scattered pressure disturbance field within the target area. Let S(τ) represent the coordinates of the observation point, t represent the time of the observation point, T represent the upper limit of the time integration, and S(τ) represent the integration surface at time τ. Indicates gas density,

[0084] ′

[0085] V nG represents the vibration velocity of the vortex layer, and G represents the Green's function, which is related to the shape of the pipe and the shape of the target region and its two end boundaries. Let τ represent the flow derivative, τ represent the source time, and s represent the source integral surface. Indicates the coordinates of the source point;

[0086] S402, based on the scattering pressure perturbation field, construct the impedance equation of the perforated plate.

[0087] Using Howe's model, the impedance equation for the perforated plate is constructed as follows:

[0088]

[0089] Where, p + and p - These represent the pressure disturbances on the outer and inner sides of the perforated plate, respectively. Z represents the velocity of the acoustic particles in the mainstream outward normal direction of the perforated plate, and Z represents the impedance of the perforated plate. Z belongs to Figure 3 The parameters of the perforated plate in the diagram.

[0090] See Figure 5 When the number of layers processed by the casing is two as shown in the figure, the perforation plate impedance equations for the inner and outer perforated plates are constructed respectively:

[0091]

[0092]

[0093] in, This represents the pressure scattering field generated by the vibration of the small holes in the inner perforated plate in the first back cavity 1. p represents the pressure scattering field generated by the vibration of the small holes in the outer perforated plate in the first back cavity 1. 1, The diagram represents the pressure scattering field generated in the main pipe by the vibration of the small holes in the inner perforated plate. B and C represent the incident waves on the left and right surfaces of the casing processing area. Z1 represents the velocity of the acoustic particles in the mainstream outward normal direction of the inner perforated plate, and Z2 represents the impedance of the inner perforated plate. This represents the pressure scattering field generated by the vibration of the small holes in the outer perforated plate in the second back cavity 2. Z1 represents the velocity of the acoustic particles in the mainstream outward normal direction of the outer perforated plate, and Z2 represents the impedance of the outer perforated plate. It can be seen that the number of layers in the casing treatment is not necessarily the two layers shown in the diagram; three to more layers can be achieved. The number of layers in the casing treatment belongs to... Figure 3 The number of layers processed in the casing. (This is from...) Figure 5 It can be seen that the first back cavity 1 is the back cavity located between the inner perforated plate and the outer perforated plate, and the back cavity 2 is the back cavity located on the side of the outer perforated plate away from the inner perforated plate.

[0094] As we know, the casing treatment can have N layers, meaning the casing treatment includes N layers of perforated plates, where N is an integer greater than or equal to 2. We establish the perforated plate impedance equation for each layer:

[0095]

[0096] in, This represents the pressure scattering field generated by the vibration of the small holes in the first perforated plate within the first back cavity. p represents the pressure scattering field generated by the vibration of the small holes in the second layer of perforated plate in the first back cavity. 1, Z represents the pressure scattering field generated by the vibration of the small holes in the first perforated plate in the main pipe; B and C represent the incident waves on the left and right surfaces of the casing processing area; and Z1 represents the impedance of the first perforated plate. This represents the pressure scattering field generated in the Nth back cavity by the vibration of the small holes in the Nth perforated plate. This represents the pressure scattering field generated in the N-1th back cavity by the vibration of the small holes in the N-1th perforated plate. This represents the pressure scattering field generated in the (N-1)th back cavity by the vibration of the small holes in the Nth layer of the perforated plate. Z represents the velocity of the acoustic particles in the mainstream outward normal direction of the Nth perforated plate, and Z represents the impedance of the Nth perforated plate.

[0097] As we know, p represents the scattering pressure field, its first subscript indicates the Nth perforated plate, and its second subscript C N Or, main indicates that its scattering region is the back cavity N or the main channel, V f Z represents the velocity of the acoustic particles in the mainstream outward normal direction of the perforated plate, and V represents the impedance of the perforated plate. f And the subscript N of Z indicates the Nth layer of perforated plate.

[0098] As we know, the Nth back cavity is the back cavity corresponding to the Nth perforated plate.

[0099] The scattering pressure pulsation field is sinusoidally transformed and expressed as a series sum:

[0100]

[0101] Among them, z jk The equivalent radiation impedance of the pipe, V, varies with the shape of the scattering region and the main pipe, following different forms of the Green's function. k The sine expansion coefficients represent the vibration velocity, j represents the order of the sine transformation, k represents the order of the axial sine expansion of the velocity, l represents the axial length of the geometric cavity, and p s denoted as the scattering pressure pulsation field, and x represents the axial coordinate of the observation point.

[0102] The specific expression for equivalent radiation impedance is:

[0103]

[0104] Where ρ0 represents the density of air, i represents the imaginary unit, ω represents the perturbation frequency, t represents the observation time, m and n represent the circumferential and radial mode numbers, and Φ m, It is the characteristic function, Γ m,n k represents the orthogonal integral value of the characteristic function of the corresponding mode. m,n Let represent the characteristic value of the corresponding modal pipe, l represent the axial length of the geometric cavity, s(τ) represent the integral surface at time τ, ω represent the disturbance frequency, and U represent the axial average velocity of the main stream. Let represent the forward and backward axial wavenumbers of modes m and n, respectively; x represent the axial coordinates of the observation point; x′ represent the axial coordinates of the source point; k represent the axial sine expansion order of the velocity; s represent the source point integral surface; and j represent the sine transform order. See also Figure 3 , Γ m,n belong Figure 3 The parameters related to the height of each layer in the casing are denoted by l. Figure 3 The parameters in the text are the axial length of the casing.

[0105] S403 uses the characteristic impedance model of porous materials to replace the air density and characteristic wavenumber in the scattered sound field of the back cavity filled with porous materials.

[0106] The characteristic impedance model of porous materials is applied to the back cavity filled with porous materials, replacing the density and characteristic wavenumber in the scattered sound field of the back cavity. The characteristic impedance model of porous materials includes the characteristic impedance Z based on the porous properties of the material. c And the characteristic wavenumber k based on materials with porous properties. c Functions:

[0107]

[0108]

[0109] Where Z0 = 0c0 represents the characteristic impedance of air, c1 to c8 represent coefficients related to porous materials (obtained experimentally), f represents the real part of the incident frequency, j represents the imaginary unit, k0 represents the characteristic wavenumber of air, and σ represents the flow resistivity of the porous material. See also Figure 3 σ belongs to Figure 3 The flow resistance parameters of porous materials.

[0110] S404. Based on the perforated plate impedance equation, the vibration velocity of the casing treatment surface is written as a function of the incident wave to obtain the wall impedance equation of the casing treatment.

[0111] Specifically, the vibration velocity of the casing surface is the vibration velocity of the perforated plate holes caused by the introduction of the casing treatment. The expansion coefficient of the vibration velocity of the perforated plate holes caused by the introduction of the casing treatment can be written as a function of the incident wave to obtain the wall impedance equation of the casing treatment.

[0112] Specifically, with Figure 5 The given example of a double-layer structure can be written in the form of equivalent radiation impedance based on the impedance equations (3) and (4) of the inner and outer perforated plates:

[0113]

[0114]

[0115] Where k′ represents the order of the sinusoidal expansion of the vibration velocity of the small holes in the outer perforated plate, and k represents the order of the sinusoidal expansion of the vibration velocity of the small holes in the inner perforated plate. This represents the equivalent radiation impedance of the vibration velocity within the small hole of the outer perforated plate in cavity 1 at the inner observation point. This represents the equivalent radiation impedance of the vibration velocity within the small hole of the outer perforated plate in cavity 2 at the outer observation point. This represents the equivalent radiation impedance of the vibration velocity within the small hole of the inner perforated plate in cavity 1 at the inner observation point. The equivalent radiation impedance of the vibration velocity within the small hole of the outer perforated plate in cavity 1 at the outer observation point is represented by z. main, This represents the equivalent radiation impedance of the vibration velocity within the small holes of the inner perforated plate in the mainstream at the inner observation point. This represents the equivalent radiation impedance of the vibration velocity within the small hole of the inner perforated plate in cavity 1 at the outer observation point. The sinusoidal expansion coefficient representing the vibration velocity of the small holes in the outer perforated plate. This represents the sinusoidal expansion coefficient of the vibration velocity of the small holes in the inner perforated plate. The superscript 1 indicates the inner perforated plate, 2 indicates the outer perforated plate, and I... j Z1 represents the coefficients after the incident wave undergoes a sinusoidal transformation, Z2 represents the impedance of the inner perforated plate, and V represents the impedance of the outer perforated plate. j 1 This indicates the vibration velocity of the small holes in the inner perforated plate. This represents the vibration velocity of the small holes in the outer perforated plate. The normal vibration velocity within the small holes of both perforated plates is expanded sinusoidally as follows:

[0116]

[0117] Where, k n The axial expansion order represents the velocity, with subscripts n = 1 and 2 indicating the 1st and 2nd perforated plate layers, respectively. The sinusoidal expansion coefficient represents the vibration velocity of the small holes in the nth layer of the perforated plate.

[0118] Therefore, equation (9) is substituted into equations (3.1) and (4.1).

[0119] Therefore, by simultaneously solving the above system of equations (1) to (5), the wall impedance equation of the casing processing section is obtained:

[0120]

[0121] in, Represents the characteristic impedance form of the scattered waves from each region. and the impedance Z of each perforated plate N The wall impedance combination is formed, where n = 1, 2, I j (B,C) represents the coefficients after the incident wave undergoes a sinusoidal transformation.

[0122] The wall impedance combination formula for the casing treatment in this step is obtained based on the aforementioned functional equation, which involves the corresponding porous material flow resistance parameter σ, the axial length parameter l of the casing treatment, and the parameter Γ related to the height of each layer of the casing treatment. m,n The perforated plate parameter Z and the layer number parameters involved in the perforated plate impedance equation, these casing processing parameters affect the corresponding wall impedance equation, which in turn affects the corresponding disturbance frequency characteristic equation. Ultimately, they affect the disturbance frequency obtained by solving the disturbance frequency characteristic equation, so that the disturbance frequency covers the relevant parameter characteristics of the casing processing. This allows the stability capability to be accurately reflected based on the disturbance frequency, and thus the optimized design of the casing processing parameters can be obtained through calculation.

[0123] S202, using the transfer element method, matches the disturbance continuity equation and momentum equation between the casing processing section and the bladeless region of the axial compressor.

[0124] Specifically, matching equations are constructed for the pressure disturbance and axial velocity disturbance on the left and right interfaces:

[0125] A l -B l -C l -p s,l =-p i,l

[0126] A l,V -B l,V -C l,V -p s,l,V =-p i,l,V

[0127] B r +C r +p s,r -C r =0

[0128] B r,V +C r,V +p s,r,V -C r,V =0

[0129] Where A represents the reflected wave at the left interface of the casing processing section, B represents the incident wave at the left interface, C represents the incident wave at the right interface, and D represents the transmitted wave at the right interface. The subscript l indicates the left interface, the subscript r indicates the right interface, and the subscript V indicates the velocity disturbance wave given by the axial momentum equation. i p represents the incident sound wave at the left interface. s The pressure disturbance wave introduced by the casing treatment is obtained by substituting the wall impedance equation (10) of the casing treatment section into the mainstream scattered pressure disturbance field equation (1). The above equation is based on the assumption that the positive axial direction is to the right.

[0130] The equations can be written in matrix form by using the transitive element method:

[0131]

[0132] Where ss represents the coefficient matrix, A n B n C n D n Let A, B, C, and D represent the coefficients of the modal expansions, respectively. ω0 represents the back-transmission axial wavenumber, ω0 represents the disturbance frequency, U represents the axial average velocity, and n represents the mode expansion order.

[0133] S203, based on small perturbation theory, constructs the perturbation frequency characteristic equation of an axial compressor with casing treatment.

[0134] Specifically, based on the small perturbation theory, the perturbation frequency characteristic equation of an axial compressor with casing treatment can be constructed as follows:

[0135] ψ(ω)X mn =0(12)

[0136] Where ψ represents the matching equation matrix of the compression system with the casing processing section, ω represents the perturbation frequency, and X mn This represents a vector of modal coefficients related to the circumferential and radial modal numbers, encompassing pressure, axial, circumferential, and radial velocity pulsations. The matching equation matrix for the compression system with the casing treatment section is the complete matching equation matrix for the entire compression system plus the casing treatment section. Other matching equation matrices can be constructed using existing methods. Therefore, the matching equation matrix for the compression system with the casing treatment section can be constructed based on the matching equation for the casing treatment section mentioned above, which will not be described in detail in this invention.

[0137] S204, solve the characteristic equation of the disturbance frequency to obtain the disturbance frequency.

[0138] Solving the above equation yields the perturbation frequency ω = ω_min of the compression system. r + i Since any disturbance quantity w can be expressed as Form, when the imaginary part ω of the perturbation frequency i If the value is less than 0, the real part of the disturbance w will be exponentially amplified, meaning that the compression system with the casing processing section will become unstable. Therefore, the instability point of the axial compressor can be determined based on the imaginary part of the disturbance frequency.

[0139] S205, the instability point of the axial compressor is determined based on the imaginary part of the disturbance frequency at different flow rates.

[0140] Specifically, the imaginary part of the disturbance frequency of the compression system can be determined at different flow rates. When the flow rate decreases to a certain point, the imaginary part of the disturbance frequency of the compression system changes from positive to negative. This flow rate point is the instability point of the axial compressor.

[0141] S206 Calculate the instability point of the axial compressor under different casing treatment parameters, and select the casing treatment parameter corresponding to the lowest instability point as the design parameter of the casing treatment.

[0142] Within a given parameter range, the instability point of the axial compressor under different casing treatment parameters can be calculated through steps S201 to 205. A database can be constructed, and the casing treatment parameters corresponding to the lowest instability flow point of the compressor can be selected, which is the optimal design of the casing treatment.

[0143] For example, the design method of the present invention is applied to a single-stage low-speed compressor with an inner diameter of 0.6 m, a design speed of 2930 rpm, a rotor hub ratio of 0.6 to 0.8, and a stator hub ratio of 0.5. For a porous metal material with a flow resistance σ of 1102 Rayls / m, the initial depth h1 of the porous metal material is set to 3 mm, and the length L is 25 mm, designated as the FMT structure. First, according to the design method of the present invention, the overall depth h1+h2 of the casing is optimized to 20 mm, named the FM structure. Then, the back cavity depth h2 is optimized to 17 mm, i.e., the FMTB structure. Finally, FMTB-L is the structure with an optimized axial length L of the casing for 50 mm. Figure 6 The pressure rise characteristics presented were verified by steady-state throttling experiments based on the design method of this application. It was found that the optimized FMTB-L structure achieved a 32.6% increase in flow margin compared to the original FMT structure.

Claims

1. A design method for a casing treatment with stabilization and noise reduction functions, characterized in that, include: The wall impedance equation of the casing treatment is constructed using the equivalent distributed source method and the characteristic impedance model of porous materials. The perturbation continuity equation and momentum equation are matched between the casing processing section and the bladeless region of the axial compressor using the transfer unit method. Based on the small perturbation theory, the perturbation frequency characteristic equation of the axial compressor with the aforementioned casing treatment is constructed. The perturbation frequency is obtained by solving the characteristic equation of the perturbation frequency; The instability point of the axial compressor is determined by the imaginary part of the disturbance frequency at different flow rates. Calculate the instability point of the axial compressor under different casing treatment parameters, and select the casing treatment parameters corresponding to the lowest instability point as the design parameters for casing treatment; The construction of the wall impedance equation for the casing treatment includes: The equivalent distributed source method is used to determine the scattered pressure disturbance field generated in the compressor main duct and each back cavity due to the introduction of the casing treatment; Based on the scattered pressure disturbance field, the perforated plate impedance equation is constructed, wherein the casing treatment includes N layers of perforated plates, where N is an integer greater than or equal to 2. The perforated plate impedance equation for each layer of perforated plates is established as follows: in, This represents the pressure scattering field generated by the vibration of the small holes in the first perforated plate within the first back cavity. This represents the pressure scattering field generated by the vibration of the small holes in the second layer of perforated plate in the first back cavity. This represents the pressure scattering field generated by the vibration of the small holes in the first layer of perforated plate in the main pipe. This represents the incident waves on the left and right surfaces of the casing processing area. This indicates the impedance of the first layer of perforated plate. This represents the pressure scattering field generated in the Nth back cavity by the vibration of the small holes in the Nth perforated plate. This represents the pressure scattering field generated in the N-1th back cavity by the vibration of the small holes in the N-1th perforated plate. This represents the pressure scattering field generated in the (N-1)th back cavity by the vibration of the small holes in the Nth layer of the perforated plate. This represents the velocity of the acoustic particles in the mainstream outward normal direction of the Nth perforated plate. The impedance of the Nth layer perforated plate is represented by the impedance equation for perforated plates derived from Howe's equation. The characteristic impedance model of the porous material is used to replace the air density and characteristic wavenumber in the scattered sound field of the back cavity filled with the porous material. Based on the perforated plate impedance equation, the vibration velocity of the casing treatment surface is written as a function of the incident wave to obtain the wall impedance equation of the casing treatment.

2. The design method for a casing with stabilization and noise reduction functions according to claim 1, characterized in that, The scattering pressure disturbance field is: ； in, This represents the scattered pressure disturbance field within the target area. Indicates the coordinates of the observation point. Indicates the observation point time. Indicates the upper limit of time integration. express The integral surface at time t, Indicates gas density, Indicates the vibration velocity of the vortex layer. The Green's function represents the shape of the pipe and is related to the shape of the target region and its two end boundaries. Represents the flow derivative. Indicates the source time. Represents the source point integral surface. Indicates the coordinates of the source point; The impedance equation for the perforated plate is: ； in, and These represent the pressure disturbances on the outer and inner sides of the perforated plate, respectively. This represents the velocity of the acoustic particles in the mainstream outward normal direction of the perforated plate. Indicates the impedance of the perforated plate; The characteristic impedance model of the porous material includes: in, The characteristic impedance of air. ~ This represents a coefficient related to porous materials. Represents the real part of the incident frequency. Represents the imaginary unit. The wavenumber, representing the characteristic wavenumber of air, This indicates the flow resistance of porous materials.

3. The design method for a casing with stabilization and noise reduction functions according to claim 2, characterized in that, The scattering pressure pulsation field is sinusoidally transformed and expressed as a series sum: in, This represents the equivalent radiation impedance of the pipe. The sinusoidal expansion coefficient representing the vibration velocity. Indicates the order of the sine transform. Indicates the order of the sinusoidal expansion along the velocity axis. Indicates the axial length of the geometric cavity. This represents the scattering pressure pulsation field. Indicates the axial coordinates of the observation point; The specific expression for equivalent radiation impedance is: in, Indicates the density of air. Represents the imaginary unit. Indicates the frequency of the disturbance. Indicates the observation point time. Indicates the circumferential and radial modal numbers, It is a characteristic function. This represents the orthogonal integral value of the characteristic function of the corresponding mode. This represents the characteristic value of the corresponding modal pipeline. Indicates the axial length of the geometric cavity. express The integral surface at time t, Indicates the frequency of the disturbance. This represents the mainstream axial average velocity. express The forward and backward axial wavenumbers of the mode, Indicates the axial coordinates of the observation point. Indicates the axial coordinate of the source point. The order of the axial sine expansion of velocity. Represents the source point integral surface. Indicates the order of the sine transform; Based on the perforation plate impedance equation of the N-layer perforated plate, the normal vibration velocity sinusoidal within the small holes of each layer of perforated plate is expanded as follows: in, The axial expansion order of velocity is indicated by its subscript. Indicates the first Perforated plate Indicates the first The sinusoidal expansion coefficient of the vibration velocity of the small holes in the perforated plate; Solve the equation: in, Represents the characteristic impedance form of the scattered waves from each region. and the impedance of each perforated plate The impedance combination is formed. This represents the coefficients after the incident wave undergoes a sinusoidal transformation.

4. The design method for a casing with stabilization and noise reduction functions according to claim 2, characterized in that, The method of matching the casing processing section with the bladeless region of the axial compressor using the transfer unit method includes: Construct matching equations for pressure disturbances and axial velocity disturbances on the left and right interfaces: in, This indicates the reflected wave at the left interface of the casing processing section. This represents the incident wave at the left interface. This represents the incident wave at the right interface. Indicates the transmitted wave at the right interface, subscript Indicates the left interface, subscript Indicates the right side of the screen, subscript This represents the velocity perturbation wave given by the axial momentum equation. This represents the incident sound wave at the left interface. The pressure disturbance wave introduced by the casing treatment is obtained by substituting the wall impedance equation of the casing treatment section into the scattered pressure disturbance field; The matching equations described by the transfer unit method can be written in matrix form: in, Represents the coefficient matrix. They represent The coefficients of the modal expansion, Indicates the axial wavenumber of the back-transmission. Indicates the frequency of the disturbance. Indicates the axial average velocity. This indicates the modal expansion order.

5. The design method for a casing with stabilization and noise reduction functions according to claim 4, characterized in that, The characteristic equation for the disturbance frequency is: in, This represents the matching equation matrix of the compression system with the aforementioned casing processing section. Indicates the frequency of the disturbance. A vector representing the combination of modal coefficients of pressure, axial, circumferential, and radial velocity pulsations related to the circumferential and radial modal numbers.

6. The design method for a casing with stabilization and noise reduction functions according to claim 1, characterized in that, The method of determining the instability point of the axial compressor based on the imaginary part of the disturbance frequency at different flow rates includes: Determine the imaginary part of the disturbance frequency. If the imaginary part is less than 0, the disturbance of the compression system amplifies exponentially with time, and the compression system becomes unstable.

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