Gas compressor instability sensitivity analysis method and device, electronic equipment and storage medium

Abstract

The invention relates to the technical field of aviation compressors, in particular to a compressor instability sensitivity analysis method and device, electronic equipment and a storage medium, and aims at solving the problems that in the prior art, a design method depends on experience, so that the iteration speed is low, and universality is not achieved. Flow field parameters on the meridian plane of the target gas compressor are obtained; determining a first characteristic value parameter of the target gas compressor according to the flow field parameter and a Navier-Stokes equation, and determining a corresponding global mode according to the first characteristic value parameter; determining an adjoint equation and a sensitivity analysis equation according to a Lagrange function and a Navier-Stokes equation; and solving the adjoint equation according to the flow field parameter and the first characteristic value parameter to obtain an adjoint mode. The gas compressor instability sensitivity analysis method and device, the electronic equipment and the storage medium are used for analyzing the stability of the gas compressor.

Description

Technical Field

[0001] The present disclosure relates to the technical field of aviation compressors, and in particular to a method, device, electronic equipment and storage medium for analyzing the instability sensitivity of a compressor. Background Art

[0002] Once the compressor of an aircraft engine stalls, the engine cannot generate enough thrust, which affects the safe flight of the aircraft. Engine designers are more concerned about what design methods can be used to give the engine a larger stall margin, so as to ensure that it can work safely while pursuing high-efficiency engines.

[0003] The current stabilization methods mainly include casing processing, blade shaping and blade tip jet, etc. The action positions and related parameters in the above stabilization methods often depend on the designer's design experience, and this design method is not universal. This empirical design method has no solid theoretical basis, which seriously slows down the design process of the compressor and is not conducive to the rapid iteration of the aero-engine design stage. At the same time, it will also result in a large consumption of human, material, financial and other resources.

[0004] Therefore, how to solve the problems of narrow scope and slow design in the prior art is one of the important issues to be solved urgently in this field. Summary of the invention

[0005] In view of this, the present disclosure relates to the field of aviation compressor technology, and in particular to a compressor instability sensitivity analysis method, device, electronic device and storage medium, so as to solve the problem that the design method in the prior art relies on experience, resulting in slow iteration speed and lack of universal applicability.

[0006] According to one aspect of the present disclosure, a method for analyzing compressor instability sensitivity is provided, comprising:

[0007] After performing three-dimensional constant numerical simulation on the target compressor, the flow field parameters on the meridian plane of the target compressor are obtained;

[0008] Determine the first eigenvalue parameter of the target compressor according to the flow field parameters and the Navier-Stokes equation, and determine the corresponding global mode according to the first eigenvalue parameter;

[0009] Determine adjoint equation and sensitivity analysis equation based on Lagrangian function and Navier-Stokes equation;

[0010] Solving the adjoint equation according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode;

[0011] The sensitivity of the target compressor is determined based on the sensitivity analysis equations of the adjoint modes and the global modes.

[0012] In addition, according to a compressor instability sensitivity analysis method according to one aspect of the present disclosure, determining a first eigenvalue parameter of a target compressor according to flow field parameters and the Navier-Stokes equation, and determining a corresponding global mode according to the first eigenvalue parameter includes:

[0013] The flow field parameters on the meridian plane of the target compressor are preprocessed according to the circumferential averaging method to obtain the intermediate parameters;

[0014] The eigenvalues ​​and corresponding global modes of the target compressor are obtained based on the intermediate parameters and the Navier-Stokes equations.

[0015] According to a compressor instability sensitivity analysis method according to one aspect of the present disclosure, the Navier-Stokes equation is:

[0016]

[0017] in, represents the symbol of partial derivative, ρ represents density, t represents time, represents the divergence operator, p represents pressure, e represents internal energy, F represents the blade force vector, u represents the velocity vector, W F Represents the work done by the blade force.

[0018] According to a compressor instability sensitivity analysis method according to one aspect of the present disclosure, solving the adjoint equation according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode includes:

[0019] The characteristic equation of the target compressor meridian plane is constructed according to the flow field parameters;

[0020] Solving the characteristic equation according to the disturbance parameter and the preset conditions to obtain the second characteristic value parameter of the target compressor;

[0021] An eigenvector parameter is determined based on the second eigenvalue parameter, and an adjoint mode is determined according to the eigenvector parameter.

[0022] According to a compressor instability sensitivity analysis method according to one aspect of the present disclosure, the disturbance parameter includes any one of a wall disturbance parameter, an inlet disturbance parameter and an outlet disturbance parameter.

[0023] According to a compressor instability sensitivity analysis method according to one aspect of the present disclosure, the characteristic equation is:

[0024]

[0025] Among them, i is the imaginary unit, A, B, C, E, G, F are all coefficient matrices, is the global mode, ω is the eigenvalue representing instability, r is the radial direction, and z is the axial direction.

[0026] According to a compressor instability sensitivity analysis method according to one aspect of the present disclosure, determining an adjoint equation and a sensitivity analysis equation according to the Lagrangian function and the Navier-Stokes equation includes:

[0027] Get the gradient parameters of different dimensions in the Lagrangian function;

[0028] The adjoint equation and the sensitivity analysis equation are determined when the gradient of each independent variable in the Lagrangian function is zero.

[0029] According to another aspect of the present disclosure, a compressor instability sensitivity analysis device is provided, which is applied to the compressor instability sensitivity analysis method provided in the first aspect, and the device includes: a first acquisition device, which acquires the flow field parameters on the meridian plane of the target compressor after performing a three-dimensional constant numerical simulation on the target compressor; a first determination device, which determines the first eigenvalue parameters of the target compressor according to the flow field parameters and the Navier-Stokes equations, and determines the corresponding global mode according to the first eigenvalue parameters; a second determination device, which determines the adjoint equation and the sensitivity analysis equation according to the Lagrangian function and the Navier-Stokes equations; a second acquisition device, which solves the adjoint equation according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode; and a third determination device, which determines the sensitivity of the target compressor to the sensitivity analysis equation based on the adjoint mode and the global mode.

[0030] According to another aspect of the present disclosure, an electronic device is provided, comprising at least one processor; and a memory for storing instructions executable by at least one processor; wherein the at least one processor is used to execute instructions to implement the steps of the above-mentioned compressor instability sensitivity analysis method.

[0031] According to another aspect of the present disclosure, a computer-readable storage medium is provided. When instructions in the computer-readable storage medium are executed by a processor of an electronic device, the electronic device is enabled to execute the steps of the above-mentioned compressor instability sensitivity analysis method.

[0032] At least one of the above-mentioned technical solutions adopted in the embodiments of the present disclosure can achieve the following beneficial effects: after performing a three-dimensional steady-state numerical simulation on the target compressor, the flow field parameters on the meridian plane of the target compressor are obtained, the first eigenvalue parameters of the target compressor are determined according to the flow field parameters and the Navier-Stokes equations, and the corresponding global mode is determined according to the first eigenvalue parameters, the adjoint equation and the sensitivity analysis equation are determined according to the Lagrangian function and the Navier-Stokes equations, the adjoint equation is solved according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode, and on this basis, the sensitivity of the target compressor is determined based on the global mode and the adjoint mode to the sensitivity analysis equation, and guidance can be provided for the design of the flow control method according to the sensitivity analysis results, thereby increasing the stable operating range of the target compressor and improving the design speed of the compressor, thereby solving the problem of slow iteration speed and non-universality caused by the design method relying on experience in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0034] Figure 1 A schematic diagram illustrating a process of applying a compressor instability sensitivity analysis method according to an embodiment of the present disclosure;

[0035] Figure 2 is a flow chart illustrating obtaining characteristic value parameters of a target compressor that characterize compressor instability according to an embodiment of the present disclosure;

[0036] Figure 3 is a flowchart further illustrating acquisition of a companion modality according to an embodiment of the present disclosure;

[0037] Figure 4 is a flowchart further illustrating determination of adjoint equations and sensitivity analysis equations according to an embodiment of the present disclosure;

[0038] Figure 5 is a schematic diagram further illustrating the prediction of the instability state of the TA36 test bench according to an embodiment of the present disclosure;

[0039] Figure 6 is a schematic diagram further illustrating a global mode of density disturbance according to an embodiment of the present disclosure;

[0040] Figure 7 is a schematic diagram further illustrating a global mode of radial velocity disturbance according to an embodiment of the present disclosure;

[0041] Figure 8 is a schematic diagram further illustrating a global mode of a circumferential velocity disturbance according to an embodiment of the present disclosure;

[0042] Fig. 9 is a schematic diagram further illustrating a global mode of an axial velocity disturbance according to an embodiment of the present disclosure;

[0043] Fig.10 is a schematic diagram further illustrating a global mode of pressure disturbance according to an embodiment of the present disclosure;

[0044] Fig.11 is a schematic diagram further illustrating a density disturbance adjoint mode according to an embodiment of the present disclosure;

[0045] Fig.12 is a schematic diagram further illustrating a radial velocity disturbance adjoint mode according to an embodiment of the present disclosure;

[0046] Fig.13 is a schematic diagram further illustrating a circumferential velocity disturbance accompanying mode according to an embodiment of the present disclosure;

[0047] Fig.14 is a schematic diagram further illustrating an axial velocity disturbance accompanying mode according to an embodiment of the present disclosure;

[0048] Fig.15 is a schematic diagram further illustrating a pressure disturbance accompanying mode according to an embodiment of the present disclosure;

[0049] Fig.16 is a schematic diagram further illustrating the sensitivity of radial velocity flow parameters according to an embodiment of the present disclosure;

[0050] Fig.17 is a schematic diagram further illustrating the sensitivity of circumferential velocity flow parameters according to an embodiment of the present disclosure;

[0051] Fig.18 is a schematic diagram further illustrating the sensitivity of axial velocity flow parameters according to an embodiment of the present disclosure;

[0052] Fig.19 is a schematic diagram further illustrating the sensitivity of pressure flow parameters according to an embodiment of the present disclosure;

[0053] Fig. 20 is a schematic diagram further illustrating the sensitivity of radial velocity external source terms according to an embodiment of the present disclosure;

[0054] Fig.21 is a schematic diagram further illustrating the sensitivity of the circumferential velocity external source term according to an embodiment of the present disclosure;

[0055] Fig. 22 is a schematic diagram further illustrating the sensitivity of the axial velocity external source term according to an embodiment of the present disclosure;

[0056] Fig.23 is a schematic diagram further illustrating the sensitivity of the pressure external source term according to an embodiment of the present disclosure;

[0057] Fig.24 Further illustrating a schematic structural diagram of a compressor instability sensitivity analysis device according to an embodiment of the present disclosure;

[0058] Fig.25 A schematic diagram of the structure of an electronic device according to an embodiment of the present disclosure is further illustrated;

[0059] Fig.26 The following is a schematic diagram of the computer system structure according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0060] Embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as being limited to the embodiments described herein, which are instead provided for a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are only for exemplary purposes and are not intended to limit the scope of protection of the present disclosure.

[0061] It should be understood that the various steps described in the method embodiments of the present disclosure may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present disclosure is not limited in this respect.

[0062] The term "including" and its variations used in this document are open inclusions, that is, "including but not limited to". The term "based on" means "based at least in part on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one other embodiment"; the term "some embodiments" means "at least some embodiments". Relevant definitions of other terms will be given in the description below. It should be noted that the concepts of "first", "second", etc. mentioned in this disclosure are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0063] It should be noted that the modifications of "one" and "plurality" mentioned in the present disclosure are illustrative rather than restrictive, and those skilled in the art should understand that unless otherwise clearly indicated in the context, it should be understood as "one or more".

[0064] The names of the messages or information exchanged between multiple devices in the embodiments of the present disclosure are only used for illustrative purposes and are not used to limit the scope of these messages or information.

[0065] Once the compressor of an aircraft engine stalls, the engine cannot generate enough thrust, which affects the safe flight of the aircraft. Engine designers are more concerned about what design methods can be used to give the engine a larger stall margin, so as to ensure that it can work safely while pursuing high-efficiency engines.

[0066] The current stabilization methods mainly include casing processing, blade shaping and blade tip jet, etc. The action positions and related parameters in the above stabilization methods often depend on the designer's design experience, and this design method is not universal. This empirical design method has no solid theoretical basis, which seriously slows down the design process of the compressor and is not conducive to the rapid iteration of the aero-engine design stage. At the same time, it will also result in a large consumption of human, material, financial and other resources.

[0067] In response to the above problems, an exemplary embodiment of the present disclosure provides a compressor instability sensitivity analysis method, device, electronic device and storage medium to solve the problem that the design method in the prior art relies on experience, resulting in slow iteration speed and lack of universal applicability.

[0068] A compressor instability sensitivity analysis method according to an embodiment of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0069] Figure 1 FIG. 1 is a schematic diagram of the process of applying the compressor instability sensitivity analysis method according to an embodiment of the present disclosure. Figure 1 As shown, the compressor instability sensitivity analysis method includes the following steps:

[0070] S101: After performing a three-dimensional steady-state numerical simulation on the target compressor, the flow field parameters on the meridian plane of the target compressor are obtained. It can be understood that the target compressor is subjected to a (Computational FluidDynamics) CFD steady-state numerical simulation, and a steady-state result of the compressor characteristics is obtained by using a self-programmed CFD program or a commercial CFD program, such as ANSYS.

[0071] S102: Determine the first eigenvalue parameter of the target compressor according to the flow field parameter and the Navier-Stokes equation, and determine the corresponding global mode according to the first eigenvalue parameter. It should be understood that the equation transforms the stability problem of the compressor into an eigenvalue problem, and by solving the eigenvalue, the instability of the compressor can be predicted.

[0072] S103: Determine the adjoint equation and sensitivity analysis equation based on the Lagrangian function and the Navier-Stokes equations.

[0073] S104: Solving the adjoint equation according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode.

[0074] S105: Determine the sensitivity of the target compressor based on the sensitivity analysis equation of the global mode and the adjoint mode.

[0075] After performing a three-dimensional steady-state numerical simulation on the target compressor, the flow field parameters on the meridian plane of the target compressor are obtained, the first eigenvalue parameters of the target compressor are determined according to the flow field parameters and the Navier-Stokes equations, and the corresponding global mode is determined according to the first eigenvalue parameters, the adjoint equation and the sensitivity analysis equation are determined according to the Lagrangian function and the Navier-Stokes equations, the adjoint equation is solved according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode, and on this basis, the sensitivity of the target compressor is determined based on the global mode and the adjoint mode to the sensitivity analysis equation, and the sensitivity analysis results can provide guidance for the design of the flow control method, thereby increasing the stable operating range of the target compressor and improving the design speed of the compressor, thereby solving the problem of slow iteration speed and non-universality caused by the design method relying on experience in the prior art.

[0076] Figure 2 FIG. 1 is a flowchart illustrating obtaining characteristic value parameters of a target compressor that characterize compressor instability according to an embodiment of the present disclosure. Figure 2 As shown, the first eigenvalue parameter of the target compressor is determined according to the flow field parameters and the Navier-Stokes equation, and the corresponding global mode is determined according to the first eigenvalue parameter, including:

[0077] S201: preprocessing the flow field parameters on the meridian plane of the target compressor according to the circumferential averaging method to obtain intermediate parameters;

[0078] S202: Obtain characteristic values ​​and corresponding global modes of the target compressor according to the intermediate parameters and the Navier-Stokes equations.

[0079] In practical applications, the flow control equation inside the target compressor is:

[0080]

[0081] In the above flow control equation, represents the symbol of partial derivative, ρ represents density, t represents time, represents the divergence operator, represents the velocity vector, p represents the pressure, represents the body force vector, D represents the total derivative, e represents the internal energy, T represents the temperature, and λ represents the thermal conductivity. Represents the heat generated. From the above flow control equation, it can be seen that the above flow control equation is formally an Euler equation, but due to the The viscous forces are strictly included in , so as long as the body force f is expressed accurately, the flow governing equations strictly follow the action of the Navier-Stokes equations.

[0082] Specifically, for the internal flow field of the compressor, the influence of heat conduction and heat radiation is usually ignored, the internal energy e is expressed by pressure and density, the blade force model is introduced, and the flow control equation is transformed from the original Navier-Stokes equation to the following equation, so that the flow control equation obtained is the Navier-Stokes equation. The Navier-Stokes equation is:

[0083]

[0084] in, represents the symbol of partial derivative, ρ represents density, t represents time, represents the divergence operator, p represents pressure, e represents internal energy, F represents the blade force vector, u represents the velocity vector, W F Represents the work done by the blade force.

[0085] According to the linear small perturbation theory, the flow field parameters can be regarded as the sum of the background flow field q and a small perturbation q′, which can be expressed by the following equation:

[0086]

[0087] Where ρ is density, u is velocity vector, p is pressure, and F is blade force. This assumption is introduced into the Navier-Stokes equations, and the circumferential average assumption is introduced, where θ is the coordinate in the circumferential direction. is the background flow field.

[0088]

[0089] The linearized Navier-Stokes equations can be obtained in operator form:

[0090]

[0091] Among them, A, B, C, E, G, F are coefficient matrices, r is radial, θ is circumferential, z is axial, φ′ is a small disturbance vector, and a harmonic assumption is made for the small disturbance and brought into the linearized Navier-Stokes equations.

[0092]

[0093] ω=ω real +iω imag

[0094] Among them, ω reflects the trend of small perturbations changing with time, which is the eigenvalue required by the Navier-Stokes equation, m is the circumferential wave number of the small perturbation, and e is the base of the natural exponential. q′ represents the small perturbation vector, Represents the magnitude of a vector. ω real represents the real part of the eigenvalue ω, ω imag represents the imaginary part of the eigenvalue ω.

[0095]

[0096]

[0097] Among them, P with_blade is the control equation of the blade control area, P without_blade is the governing equation for the bladeless region, Q is the basic flow in the meridian plane, and H F is the coefficient matrix representing the blade force, where J and ζ are both linear operators, as shown in the following equation:

[0098]

[0099] ζ=1+iτ(ω+mΩ)

[0100] Among them, i is the imaginary unit, τ is the time parameter, ω reflects the trend of small perturbations changing with time, m is the circumferential wave number of small perturbations, B, C, E, G are coefficient matrices, r is radial, J and ζ are both linear operators, Represents the symbol of partial derivative.

[0101] The boundary conditions for the Navier-Stokes equations are:

[0102]

[0103] Among them, n r is the radial component of the wall orthogonal vector, v r is the radial velocity, n z is the axial component of the wall orthogonal vector, v z is the radial velocity. represents the amplitude of the density perturbation, represents the amplitude of the radial velocity disturbance, represents the amplitude of the circumferential velocity disturbance, represents the amplitude of the axial velocity disturbance, Represents the amplitude of the pressure disturbance.

[0104] By introducing boundary conditions, the control equation of the blade control area constitutes the eigenvalue equation, where ω is the eigenvalue to be determined, The eigenvector corresponding to the eigenvalue is also called the global mode. The criterion for the Navier-Stokes equation to determine whether the compressor is unstable is to determine the eigenvalue in the linearized Navier-Stokes equation. ω The imaginary part ω imag The positive or negative number is positive. If the number is positive, small disturbances will decrease over time, and the compressor will maintain a stable working state. Conversely, if the number is negative, small disturbances will increase exponentially over time, resulting in compressor instability.

[0105] In addition, the blade force term F in the Navier-Stokes equations includes the work done by the blade force and its losses as well as the losses caused by viscosity. This term is deduced below. The effect of the blade on the airflow can be seen as consisting of two parts, one part deflects the airflow and the other part produces losses.

[0106] F=F turn t+F loss k

[0107] The direction of the turning force is t=(t r ,t θ ,t z ), loss force k = (k r ,k θ ,k z ) is in the following directions:

[0108]

[0109] Introducing the first law of thermodynamics and the axisymmetric momentum equation, we can get the loss force F loss and entropy increase. Where T is temperature, v l is the velocity vector along the streamline, s is the entropy increase, l is the streamline square,

[0110]

[0111]

[0112] Introduce the circumferential momentum equation, where F θ is the component of the blade force in the circumferential direction:

[0113]

[0114] Then the circumferential component of the turning force can be written as:

[0115] F turn,θ =F θ -F loss,θ

[0116] By introducing the local loss coefficient α and the turning coefficient β, the magnitude of the turning force and the loss force can be obtained, where Ω is the rotational speed.

[0117] F loss =α[v r 2 +(v θ -Ωr) 2 +v z 2 ]

[0118] F turn =βv l (v θ -Ωr)

[0119] Since there is a certain time lag between the effect of blade force on airflow and the change of airflow parameters, a first-order delay equation is introduced to describe this property. F′ is the disturbance of blade force, is the blade force in the basic flow.

[0120]

[0121] Through the above relationship, the blade force term F can be expressed in the form of local flow field velocity, and then introduced into the Navier-Stokes equation, making it a Euler equation in form, F = F (v r ,v θ ,v z ),W F =W F (v r ,v θ ,v z )

[0122] Figure 3 is a flowchart further illustrating the acquisition of the accompanying modality according to an embodiment of the present disclosure, such as Figure 3 As shown, solving the adjoint equation according to the flow field parameters and the first eigenvalue parameters to obtain the adjoint mode includes:

[0123] S301: Constructing a characteristic equation of a target compressor meridian plane according to flow field parameters.

[0124] S302 solves the characteristic equation according to the disturbance parameter and the preset condition to obtain the second characteristic value parameter of the target compressor.

[0125] S303: Determine eigenvector parameters based on the second eigenvalue parameters, and determine adjoint modes according to the eigenvector parameters.

[0126] In practical applications, the sensitivity equation is established as follows:

[0127] The characteristic equation of the target compressor meridian plane is:

[0128]

[0129] Among them, i is the imaginary unit, A, B, C, E, G, F are all coefficient matrices, is the global mode, and ω is the objective function. Let,

[0130]

[0131] The sensitivity equation obtained is:

[0132]

[0133] Figure 4 is a flowchart further illustrating determination of adjoint equations and sensitivity analysis equations according to an embodiment of the present disclosure, such as Figure 4 As shown in Figure 2, the adjoint equation and sensitivity analysis equation are determined based on the Lagrangian function and the Navier-Stokes equation:

[0134] S401: Obtaining gradient parameters of different dimensions in the Lagrangian function.

[0135] S402: Determine an adjoint equation and a sensitivity analysis equation when the gradient of each independent variable in the Lagrangian function is 0.

[0136] In practical applications, the disturbance parameters are input into the adjoint equation. It can be understood that the above disturbance parameters include any one of the wall disturbance parameters, the inlet disturbance parameters and the outlet disturbance parameters.

[0137] The wall perturbation parameters are actually non-penetrating, i.e. Specifically, according to the principle of integration by parts, the boundary condition of the adjoint equation can be obtained as follows:

[0138]

[0139] in, represents the symbol of partial derivative, ρ represents density, t represents time, represents the divergence operator, represents the velocity vector, p represents the pressure, represents the body force vector, It is a global mode.

[0140] The import disturbance parameter of the Navier-Stokes equation is actually the disturbance-free condition, that is, The specific corresponding import boundary condition of the adjoint equation is the following equation:

[0141]

[0142] in, represents the symbol of partial derivative, ρ represents density, t represents time, represents the divergence operator, represents the velocity vector, p represents the pressure, represents the body force vector, Represents the symbol of partial derivative.

[0143] The outlet perturbation parameter of the Navier-Stokes equation is the outlet condition, that is, The specific exit boundary condition of the adjoint equation is:

[0144]

[0145] Assuming that a small change δQ occurs in the flow field, where δ represents a small quantity, the characteristic value of the target compressor instability will also have a small change δω. Under the linear assumption, there is a certain relationship between the two. Here, it is assumed that δω can be written in the total differential form of δQ. The first term in the equation is That is, the sensitivity of the characteristic value ω to the flow field parameter Q, that is, the sensitivity of the compressor stall to the flow field parameter.

[0146]

[0147] However, since this relationship cannot be obtained directly, it is necessary to construct a Lagrangian function to solve the relationship. Assume that the form of the Lagrangian function is as follows, where L is the representative form of the Lagrangian function, is the global mode, is the adjoint mode, and P is the abbreviated form of the control equation.

[0148]

[0149] in, ω is the objective function, that is, the characteristic value of whether the target compressor is unstable.

[0150] The derivative of the Lagrangian function with respect to a vector is defined as follows, where a is an arbitrary vector and s is a minimum quantity.

[0151]

[0152] According to the principle of seeking extreme values ​​of Lagrangian function, the gradient of the variable is obtained to satisfy the gradient of 0 in all directions, so as to obtain the expression of sensitivity analysis, normalization condition and adjoint equation satisfied by the adjoint mode.

[0153]

[0154] Among them, equation (1) can be expanded and simplified to obtain the adjoint mode and global mode The normalization condition is shown in the following equation:

[0155]

[0156] Equation (2) can be expanded and simplified to obtain the adjoint mode The adjoint equation satisfied by this equation can be solved to obtain the adjoint mode The upper right subscript H represents the conjugate transpose of the corresponding coefficient matrix, for example, M H is the conjugate transpose of the matrix M.

[0157]

[0158] in, The superscript H represents the conjugate transpose of the matrix, * represents the conjugate complex number, i represents the imaginary unit, and α represents the characteristic time.

[0159] Since the method of integration by parts is used in the derivation of this equation, boundary terms will be generated, so it is necessary to impose certain boundary conditions to eliminate the boundary terms. The equation that the boundary conditions should satisfy is the following equation, where z1 and z2 are the starting and ending boundaries in the axial direction, and r1 and r2 are the starting and ending boundaries in the radial direction.

[0160]

[0161] The final boundary condition expression is given below, where ξ and η are the coordinates after the coordinate system is transformed.

[0162] Before solving equation (3), it should be noted that the Navier-Stokes equations use the background flow field as a known quantity to solve the global small perturbation mode of space. In equation (3), the variable is δQ, and the small perturbation global mode is is a known quantity, so the equation is first converted into an equation with the background flow field δQ as an unknown quantity.

[0163]

[0164] Among them, M C , N, O, S are all coefficient matrices, which are consistent with the global modes obtained by the meridian plane model. By expanding and simplifying equation (3), we can obtain the sensitivity equation of the characteristic value to the flow field parameters, that is, the sensitivity equation of the compressor stall to the flow field.

[0165]

[0166] The derivation process of the sensitivity analysis method of the external source term based on the adjoint method and the meridian plane model: First, it is assumed that the external source term only acts on the flow field itself, and the influence of the source term is an influence that does not change with time. At this time, the equation satisfied by the external source term can be regarded as the equation after removing the time term from the meridian plane model control equation:

[0167] BF(Q)=F external

[0168] Among them, BF is the operator form of the control equation, Q is the flow field change caused by the external source term, and F external is the imposed external source term, and the flow field parameter Q can be written as the expression of the external source term.

[0169] FB(F external )=Q

[0170] At this time, assuming that the external source term has a certain disturbance δF external , then the resulting flow field will also have a disturbance δQ external , thereby obtaining the relationship between the eigenvalue and the external source term.

[0171]

[0172] Among them, the first This is the sensitivity of the eigenvalue to the external source term, and the Lagrange multiplier method is also used to obtain the expression of this term. The Lagrange function is expressed as follows.

[0173]

[0174] Its limiting function is:

[0175]

[0176] Using the same derivation method as above, we can get the adjoint mode Q of the basic flow field: + The adjoint equation satisfied is:

[0177]

[0178] Among them, B, E, Γ are coefficient matrices, and the superscript H represents the conjugate transposed matrix. In order to show the sensitivity of the eigenvalue to the basic flow field parameters, the above derivative of the external source term F can be obtained as follows:

[0179]

[0180] Among them, Q + is the adjoint mode, ω is the eigenvalue, represents the divergence operator and F is the external source term.

[0181] In order to verify the stability of the above target compressor, the TA36 test bench is used as an example to verify. Figure 5 is a schematic diagram further illustrating the prediction of the instability state of the TA36 test bench according to an embodiment of the present disclosure, such as Figure 5 As shown, when the small disturbance growth rate is 0, the mass flow rate is 5.31kg / s. At this time, when the mass flow rate is greater than 5.31kg / s, it is unstable. Taking 5.4kg / s as an example, the global mode of spatial disturbance represented by the eigenvector is obtained. as follows: Figure 6 is a schematic diagram further illustrating a global mode of density disturbance according to an embodiment of the present disclosure, Figure 7 is a schematic diagram further illustrating a global mode of radial velocity disturbance according to an embodiment of the present disclosure, Figure 8 is a schematic diagram further illustrating a global mode of circumferential velocity disturbance according to an embodiment of the present disclosure, Fig. 9 is a schematic diagram further illustrating a global modal diagram of an axial velocity disturbance according to an embodiment of the present disclosure, Fig.10 It further illustrates a global modal diagram of pressure disturbance according to an embodiment of the present disclosure, inputs characteristic values ​​into a sensitivity equation, finds extreme points of the sensitivity equation according to the Lagrangian function, and determines the stability of the target compressor according to the extreme points.

[0182] Fig.11 is a schematic diagram further illustrating a density disturbance adjoint mode according to an embodiment of the present disclosure, Fig.12 is a schematic diagram further illustrating the radial velocity disturbance adjoint mode according to an embodiment of the present disclosure, Fig.13 is a schematic diagram further illustrating the accompanying modes of the circumferential velocity disturbance according to an embodiment of the present disclosure, Fig.14 is a schematic diagram further illustrating an axial velocity disturbance accompanying mode according to an embodiment of the present disclosure, Fig.15 is a schematic diagram of the pressure disturbance adjoint mode according to an embodiment of the present disclosure. Substituting the adjoint mode, basic flow field parameters and global mode into the sensitivity equation, the sensitivity analysis result of the flow field parameters is obtained. Fig.16 is a schematic diagram further illustrating the sensitivity of radial velocity flow parameters according to an embodiment of the present disclosure, Fig.17 is a schematic diagram further illustrating the sensitivity of circumferential velocity flow parameters according to an embodiment of the present disclosure, Fig.18 is a schematic diagram further illustrating the sensitivity of axial velocity flow parameters according to an embodiment of the present disclosure, Fig.19 FIG. 2 is a schematic diagram further illustrating the sensitivity of pressure flow parameters according to an embodiment of the present disclosure. Fig.16 - Fig.19 As shown, different eigenvalue directions have different flow parameter sensitivities.

[0183] Fig. 20 is a schematic diagram further illustrating the sensitivity of radial velocity external source terms according to an embodiment of the present disclosure, Fig.21 is a schematic diagram further illustrating the sensitivity of the circumferential velocity external source term according to an embodiment of the present disclosure, Fig. 22 is a schematic diagram further illustrating the sensitivity of the axial velocity external source term according to an embodiment of the present disclosure, Fig.23 is a schematic diagram further illustrating the sensitivity of the pressure external source term according to an embodiment of the present disclosure, Fig. 20 - Fig.23 is the sensitivity analysis result of TA36 external source term, given by Fig. 20 - Fig.23 It can be seen that the sensitivity of flow parameters to external source terms in different eigenvalue directions is different.

[0184] In the case of dividing each functional module according to each function, an exemplary embodiment of the present disclosure provides a compressor aerodynamic stability prediction device, which may be a server or a chip applied to a server. Fig.24 The following is a schematic diagram of the structure of the compressor instability sensitivity analysis device according to an embodiment of the present disclosure. Fig.24 As shown, the compressor instability sensitivity analysis device 2400 includes:

[0185] The first acquisition device 2401 acquires the flow field parameters on the meridian plane of the target compressor after performing a three-dimensional steady-state numerical simulation on the target compressor.

[0186] The first determining device 2402 determines the characteristic value parameters of the target compressor according to the flow field parameters and the Navier-Stokes equations.

[0187] The second determining means 2403 determines the adjoint equation and the sensitivity analysis equation according to the Lagrangian function and the Navier-Stokes equation.

[0188] The second obtaining means 2404 obtains the adjoint equation and the adjoint mode according to the flow field parameters and the eigenvalue parameters.

[0189] The third determining means 2405 determines the sensitivity of the target compressor based on the adjoint mode to the sensitivity analysis equation.

[0190] Fig.25 The following is a schematic diagram of the structure of an electronic device according to an embodiment of the present disclosure. Fig.25 As shown, the electronic device 2500 includes at least one processor 2501 and a memory 2502 coupled to the processor 2501. The processor 2501 can execute corresponding steps in the above method disclosed in the embodiment of the present disclosure.

[0191] The processor 2501 may also be referred to as a central processing unit (CPU), which may be an integrated circuit chip having signal processing capabilities. Each step in the method disclosed in the embodiment of the present disclosure may be completed by an integrated logic circuit of hardware in the processor 2501 or by instructions in the form of software. The processor 2501 may be a general-purpose processor, a digital signal processor (DSP), an ASIC, a field-programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component. A general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present disclosure may be directly embodied as being executed by a hardware decoding processor, or may be executed by a combination of hardware and software modules in a decoding processor. The software module may be located in a memory 2502, such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, or other mature storage media in the art. The processor 2501 reads the information in the memory 2502 and completes the steps of the method in combination with its hardware.

[0192] In addition, when various operations / processes according to the present disclosure are implemented by software and / or firmware, they can be transmitted from a storage medium or a network to a computer system having a dedicated hardware structure, for example, Fig.26 Further illustrating a schematic diagram of the computer system structure according to an embodiment of the present disclosure, as shown in Fig.26 As shown, the computer system 2600 is installed with the programs constituting the software. When the various programs are installed, the computer system can execute various functions, including the functions described above. Fig.26 The following is a schematic diagram of the structure of a computer system according to an embodiment of the present disclosure.

[0193] Computer system 2600 is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0194] like Fig.26As shown, the computer system 2600 includes a computing unit 2601, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 2602 or a computer program loaded from a storage unit 2608 into a random access memory (RAM) 2603. In RAM 2603, various programs and data required for the operation of the computer system 2600 can also be stored. The computing unit 2601, ROM 2602, and RAM 2603 are connected to each other via a bus 2604. An input / output (I / O) interface 2605 is also connected to the bus 2604.

[0195] A plurality of components in the computer system 2600 are connected to the I / O interface 2605, including: an input unit 2606, an output unit 2607, a storage unit 2608, and a communication unit 2609. The input unit 2606 may be any type of device capable of inputting information to the computer system 2600, and the input unit 2606 may receive input digital or character information, and generate key signal inputs related to user settings and / or function control of the electronic device. The output unit 2607 may be any type of device capable of presenting information, and may include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. The storage unit 2608 may include, but is not limited to, a disk, an optical disk. The communication unit 2609 allows the computer system 2600 to exchange information / data with other devices over a network such as the Internet, and may include, but is not limited to, a modem, a network card, an infrared communication device, a wireless communication transceiver, and / or a chipset, for example, a Bluetooth™ device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0196] The computing unit 2601 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 2601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 2601 performs the various methods and processes described above. For example, in some embodiments, the above methods disclosed in the embodiments of the present disclosure may be implemented as a computer software program, which is tangibly included in a machine-readable medium, such as a storage unit 2608. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 2500 via ROM 2602 and / or communication unit 2609. In some embodiments, the computing unit 2601 may be configured to perform the above methods disclosed in the embodiments of the present disclosure in any other appropriate manner (e.g., by means of firmware).

[0197] The embodiment of the present disclosure also provides a computer-readable storage medium, wherein when the instructions in the computer-readable storage medium are executed by a processor of an electronic device, the electronic device is enabled to execute the above method disclosed in the embodiment of the present disclosure.

[0198] The computer-readable storage medium in the embodiments of the present disclosure may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or apparatus. The computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the above. More specifically, the computer-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0199] The computer-readable medium may be included in the electronic device, or may exist independently without being incorporated into the electronic device.

[0200] The embodiments of the present disclosure also provide a computer program product, including a computer program, wherein the computer program implements the above method disclosed in the embodiments of the present disclosure when executed by a processor.

[0201] In embodiments of the present disclosure, computer program codes for performing the operations of the present disclosure may be written in one or more programming languages ​​or combinations thereof, including but not limited to object-oriented programming languages, such as Java, Smalltalk, C++, and conventional procedural programming languages, such as "C" language or similar programming languages. The program code may be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer.

[0202] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some implementations as replacements, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0203] The modules, components or units involved in the embodiments described in the present disclosure may be implemented by software or hardware, wherein the names of the modules, components or units do not, in some cases, limit the modules, components or units themselves.

[0204] The functions described above herein may be performed at least in part by one or more hardware logic components. For example, without limitation, exemplary hardware logic components that may be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chip (SOCs), complex programmable logic devices (CPLDs), and the like.

[0205] The above descriptions are only some embodiments of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of disclosure involved in the present disclosure is not limited to the technical solutions formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosed concept. For example, a technical solution formed by replacing the above features with the technical features with similar functions disclosed in the present disclosure (but not limited to).

[0206] Although some specific embodiments of the present disclosure have been described in detail by way of example, it should be understood by those skilled in the art that the above examples are for illustration only and are not intended to limit the scope of the present disclosure. It should be understood by those skilled in the art that the above embodiments may be modified without departing from the scope and spirit of the present disclosure. The scope of the present disclosure is defined by the appended claims.

Claims

1. A compressor instability sensitivity analysis method, characterized in that: include: After performing three-dimensional constant numerical simulation on the target compressor, the flow field parameters on the meridian plane of the target compressor are obtained; Determining a first eigenvalue parameter of the target compressor according to the flow field parameter and the Navier-Stokes equation, and determining a corresponding global mode according to the first eigenvalue parameter; Determine adjoint equation and sensitivity analysis equation based on Lagrangian function and Navier-Stokes equation; Solving the adjoint equation according to the flow field parameter and the first eigenvalue parameter to obtain an adjoint mode; The sensitivity of the target compressor is determined based on the adjoint mode and the global mode to the sensitivity analysis equation.

2. The compressor instability sensitivity analysis method according to claim 1, characterized in that: Determining a first eigenvalue parameter of the target compressor according to the flow field parameter and the Navier-Stokes equation, and determining a corresponding global mode according to the first eigenvalue parameter includes: Preprocessing the flow field parameters on the meridian plane of the target compressor according to the circumferential averaging method to obtain intermediate parameters; The characteristic value and the corresponding global mode of the target compressor are obtained according to the intermediate parameters and the Navier-Stokes equations.

3. The compressor instability sensitivity analysis method according to claim 2, characterized in that: The Navier-Stokes equations are: in, represents the symbol of partial derivative, ρ represents density, t represents time, represents the divergence operator, p represents pressure, e represents internal energy, F represents the blade force vector, u represents the velocity vector, W F Represents the work done by the blade force.

4. The compressor instability sensitivity analysis method according to claim 1, characterized in that: Solving the adjoint equation according to the flow field parameter and the first eigenvalue parameter to obtain the adjoint mode comprises: Constructing the characteristic equation of the target compressor meridian plane according to the flow field parameters; Solving the characteristic equation according to the disturbance parameter and the preset condition to obtain the second characteristic value parameter of the target compressor; An eigenvector parameter is determined based on the second eigenvalue parameter, and an adjoint mode is determined according to the eigenvector parameter.

5. The compressor instability sensitivity analysis method according to claim 4, characterized in that: The disturbance parameter includes any one of a wall disturbance parameter, an inlet disturbance parameter and an outlet disturbance parameter.

6. The compressor instability sensitivity analysis method according to claim 4, characterized in that: The characteristic equation is: Among them, i is the imaginary unit, A, B, C, E, G, F are all coefficient matrices, is the global mode, ω is the characteristic value to characterize the instability, r is the radial direction and z is the axial direction.

7. The compressor instability sensitivity analysis method according to claim 1, characterized in that: The adjoint equation and sensitivity analysis equation determined based on the Lagrangian function and the Navier-Stokes equation include: Obtaining gradient parameters of different dimensions in the Lagrangian function; The adjoint equation and the sensitivity analysis equation are determined when the gradient of each independent variable in the Lagrangian function is zero.

8. A compressor instability sensitivity analysis device, characterized in that: include: A first acquisition device, after performing a three-dimensional constant numerical simulation on the target compressor, acquires the flow field parameters on the meridian plane of the target compressor; A first determining device determines a first eigenvalue parameter of the target compressor according to the flow field parameter and the Navier-Stokes equation, and determines a corresponding global mode according to the first eigenvalue parameter; A second determining device determines an adjoint equation and a sensitivity analysis equation based on the Lagrangian function and the Navier-Stokes equation; A second acquisition device, which solves the adjoint equation according to the flow field parameter and the first eigenvalue parameter to obtain the adjoint mode; A third determining device determines the sensitivity of the target compressor based on the adjoint mode and the global mode to the sensitivity analysis equation.

9. An electronic device, characterized in that: include: at least one processor; a memory for storing the at least one processor-executable instruction; Wherein, the at least one processor is used to execute the instructions to implement the compressor instability sensitivity analysis method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: When the instructions in the computer-readable storage medium are executed by a processor of an electronic device, the electronic device is enabled to execute the compressor instability sensitivity analysis method as described in any one of claims 1 to 7.

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