Pressure waveform identification method for upstream inlet wake flow and downstream outlet back potential flow

Abstract

The invention relates to the technical field of turbine engines, in particular to a pressure waveform recognition method for upstream inlet wake flow and downstream outlet back potential flow, and the method comprises the steps: S1, building a turbine blade flow channel CFD model; s2, simplifying and dispersing the excitation blade aerodynamic force system; s3, obtaining a kernel function of the aerodynamic reduced-order model by using a pulse method, a step method or a white noise method; s4, constructing a blade aerodynamic force reduced-order model excited by upstream wake flow or downstream back potential flow by using a kernel function; s5, a time domain deconvolution algorithm recognition method is used for conducting inversion on the blade aerodynamic force reduced-order model, and a Tikhonov regularization solution for upstream wake flow or downstream back potential flow waveform recognition is obtained; the measured aerodynamic force response of the blade is substituted into a regularization solution, and the waveform of upstream wake flow or downstream back potential flow is obtained through calculation; the invention provides an aerodynamic reduced-order model-based wake flow and back potential flow waveform indirect identification and measurement method.

Description

Technical Field

[0001] The invention relates to the technical field of turbine engines, in particular to a method for identifying pressure waveforms of an upstream inlet wake flow and a downstream outlet back-potential flow. Background Art

[0002] There are many counter-rotating blades in a turbine engine. When the turbine engine is working, the rotating upstream wake and downstream backflow cause the blades to be subjected to pressure fluctuations. This pressure fluctuation is a key factor affecting the fatigue life and performance of turbine engine blades. Therefore, it is very important to study the unsteady aerodynamic forces caused by the wake and backflow.

[0003] However, it is difficult to directly measure the pressure fluctuations of the wake and backflow during the operation of the turbine engine, which makes it very difficult to understand the working conditions of the turbine engine and thus grasp the performance and life of the turbine engine. If indirect measurement technology can be used to obtain the pressure fluctuations of the wake and backflow, it will be of great significance to monitor and diagnose the health of the turbine engine in real time.

[0004] Indirect measurement technology focuses on load identification. The research on load identification is based on the linear elastic dynamic model between structural response and load, and mainly determines the dynamic load on the structure through the structural response such as stress, strain, displacement and acceleration. At present, there is no research on using load identification method to identify flow characteristics in flow field. The reason is that NS equation is a nonlinear equation. For actual flow problems, its flow equation is very complex and difficult to solve. There is no way to directly convert it into a linear equation of load and response relationship, and it is even more impossible to invert the load and response relationship.

[0005] Therefore, it is necessary to invent a pressure waveform identification method for the upstream inlet wake and the downstream outlet back-potential flow to indirectly measure the pressure fluctuations of the wake and back-potential flow, which is of great significance to engine design and detection. Summary of the invention

[0006] The invention provides a pressure waveform identification method of an upstream inlet wake flow and a downstream outlet back-potential flow.

[0007] Previous studies have found that if the turbine engine blades and the surrounding flow field are regarded as a system, the fluctuations of the upstream inlet wake and the downstream outlet backflow will cause changes in the flow characteristics around the blades. The changes in time and space of this system can be described by the functional relationship between the observable variables of the flow field (such as pressure, velocity and blade aerodynamic force at each point).

[0008] The reduced order model (ROM) is a simplified mathematical model that can capture the linear and nonlinear dynamic relationship between the wake (backward potential flow) waveform and the blade response with a very low computational cost. To this end, the present invention proposes to use a reduced order model method to construct a model of the relationship between the wake or backward potential flow waveform and the blade aerodynamic response, predict the aerodynamic force of the blade under the excitation of the wake and backward potential flow, and establish a method for identifying the wake and backward potential flow waveforms through the blade aerodynamic force based on the model.

[0009] Therefore, the present invention proposes a pressure waveform identification method for an upstream inlet wake flow and a downstream outlet back-potential flow, the method comprising:

[0010] Step S1: Establishing a turbine blade flow channel CFD model;

[0011] Step S1.1: Establishing a turbine blade flow channel geometry model;

[0012] Step S1.2: Meshing the flow channel;

[0013] Step S1.3: Import the mesh model into the CFD solver and set the parameters and boundary conditions;

[0014] Step S1.4: Write a UDF program to use the upstream inlet wake flow or downstream outlet back-potential flow waveform as the inlet or outlet boundary condition of the turbine blade flow passage;

[0015] Step S1.5: Calculate the aerodynamic force of the turbine blade under the upstream inlet wake or downstream outlet back-potential flow waveform.

[0016] Step S2: Simplify the mathematical description of the turbine blade flow passage aerodynamic system under the excitation of the upstream inlet wake or the downstream outlet back potential flow, and establish a reduced-order model of the blade aerodynamic force under the excitation of the discrete upstream inlet wake or the downstream outlet back potential flow; the details are as follows:

[0017] Step S2.1: Take the waveform of the upstream inlet wake or the downstream outlet back-potential flow as input, represented by the total pressure fluctuation p(x0, y, z, t) of the flow channel; take the blade aerodynamic force as output, represented by the blade aerodynamic lift CL; construct the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back-potential flow, mathematically expressed as:

[0018] {CL(t)}=Ψ{p(x0, y, z, t)}; Formula (1);

[0019] Wherein, x=x0 is the axial position of the inlet or outlet, y is the circumferential position of the inlet or outlet, z is the spanwise height of the blade, p(x0, y, z, t) is the total pressure fluctuation at the inlet or outlet of the flow channel, and ψ is the system function.

[0020] Step S2.2: Simplify the mathematical expression of the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow;

[0021] At the spanwise height z, the total pressure at the flow channel inlet varies in time and space. If the pressure at each point of the flow channel inlet is regarded as an independent input, the system will have countless inputs. To simplify the problem, for the inlet wake or outlet backflow waveform at the spanwise height z, any point (x0, y l The total pressure at the known point (x0, y0, z) can be expressed as p(x0, y0, z, t) l , z, t) = p(x0, y0+(y l -y0),z,t)=p(x0,t-(y l -y0) / v, z), where v is the moving speed of the total pressure waveform along the inlet or outlet. Therefore, the input of the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow is simplified to the total pressure at point (x0, y0, z); let p(x0, y0, z, t) = p(z, t), the mathematical expression of the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow can be simplified to:

[0022] {CL(z,t)}=Ψ{p(z,t)}; Formula (2);

[0023] Step S2.3: discretizing the mathematical expression of the blade aerodynamic system excited by the simplified upstream inlet wake or downstream outlet back potential flow;

[0024] The Volterra series theory points out that any time-varying multi-input and multi-output system can be represented by an L-order discrete Volterra series. Therefore, the L-order discrete Volterra series is used to discretize the mathematical expression of the aerodynamic system of the blade excited by the simplified upstream inlet wake or downstream outlet back potential flow; the form is as follows:

[0025]

[0026] in, is the pressure fluctuation increment of the wake or backflow at the jth section in the span direction, is the aerodynamic lift of the spanwise i-th section, n = 0, 1, ..., N is the discrete time, ΔT is the time step, is the L-order discrete-time Volterra kernel, representing j1, j2, …j LThe influence of the pressure fluctuation input of the wake or back potential flow of equal cross section on the aerodynamic lift of the spanwise i-th section. For nonlinear systems, the second-order kernel is one order of magnitude smaller than the first-order kernel, and the first-order kernel is sufficient to predict the nonlinear response. Therefore, the first-order Volterra reduced-order model is used to obtain the reduced-order model of the blade aerodynamic force excited by the discretized upstream inlet wake or downstream outlet back potential flow.

[0027]

[0028] Step S3: Using the pulse method, step method or white noise method, apply a pulse waveform to each section at the inlet or outlet of the blade CFD model, calculate the corresponding blade aerodynamic response, identify the aerodynamic response relationship of the blade under the upstream inlet wake pulse waveform or the downstream outlet back potential flow pulse waveform of each section, and obtain the kernel function of the discretized blade aerodynamic reduced-order model excited by the upstream inlet wake or the downstream outlet back potential flow; once the kernel function of the reduced-order model is determined, the blade aerodynamic response caused by any upstream fluctuation can be predicted by formula (3) or formula (4).

[0029] Step S4: constructing a reduced-order model of the blade aerodynamic response relationship excited by the upstream wake or downstream back potential flow using the kernel function of the blade aerodynamic reduced-order model;

[0030] Step S4.1: Matrix the kernel function of the reduced-order model, i.e., formula (4);

[0031]

[0032] in,

[0033]

[0034] The reduced-order model after matrixization is:

[0035] CL=h0+HF; Formula (6);

[0036] Step S4.2: The reduced-order model of the blade aerodynamic response excited by the upstream wake or downstream backflow is obtained, namely:

[0037] Y=CL-h0=HF; Formula (7);

[0038] Among them, Y is the blade aerodynamic response increment, CL is the blade aerodynamic response, h0 is the blade aerodynamic reference response, H is the impulse response matrix, and f is the total pressure waveform input of the wake or back potential flow.

[0039] Step S5: using the Tikhonov regularization solution method identified by the time domain deconvolution algorithm, the reduced-order model of the blade aerodynamic response excited by the upstream wake or downstream back potential flow is inverted to obtain the Tikhonov regularization solution for upstream wake or downstream back potential flow waveform identification;

[0040] By analyzing formula (4), it can be found that the reduced-order model of the aerodynamic response relationship of the blade excited by the upstream wake or downstream back potential flow of the first-order Volterra series has a time domain deconvolution form, which has the same structure as the structural response in the load identification theory. Therefore, the present invention establishes a reduced-order model of the blade aerodynamic force excited by the waveform of the wake or back potential flow through the first-order Volterra series, and identifies the waveform of the upstream wake and / or downstream back potential by using the time domain deconvolution load identification method based on the reduced-order model.

[0041] The reduced-order model of the blade aerodynamic response to the upstream wake or downstream backflow excitation, that is, formula (7), is inversely transformed to obtain f = H- 1 Y, the wake or backflow waveform can be calculated through the aerodynamic response of the blade.

[0042] However, in actual measurement, the recognition accuracy of the instrument and signal noise will cause certain errors in the data. The solution of the above waveform is ill-posed. Therefore, it is necessary to use the Tikhonov regularization method to solve the wake or backflow waveform, add a suitable boundary constraint to the ill-posed inverse problem, make the problem well-posed, and improve the stability of the recognition result.

[0043] The total pressure waveform input of the wake or back-potential flow is solved by Tikhonov regularization method, and the calculation expression of the objective function is:

[0044]

[0045] Where: ||·|| is the 2-norm of the vector; the constant α>0 is the regularization parameter, which mainly controls the relative size between the residual norm ||HF-Y|| and the solution norm ||F||;

[0046] Solving formula (8), we can obtain the Tikhonov regularization solution for upstream wake flow or downstream backflow waveform identification, namely:

[0047] F=(H T H+α 2 I) -1 H T Y; formula (9);

[0048] Where: I is the unit matrix.

[0049] Step S6: using the Tikhonov regularization solution for upstream wake or downstream back-potential flow waveform identification, the pressure arbitrary waveform of the upstream wake or downstream back-potential flow can be identified according to the blade aerodynamic response;

[0050] For any other blade flow system under wake or back potential flow excitation, when the blade aerodynamic force Y response and impulse response matrix H are known, the total pressure waveform input f of the wake or back potential flow can be obtained by formula (9); that is, the pressure waveform of the upstream wake or downstream back potential flow.

[0051] The aerodynamic response of the present invention may be the lift, drag and torque of the blade, or may be a pressure measurement value or derived value at any point.

[0052] The present invention proposes a method for indirectly identifying and measuring wake flow and back potential flow pressure waveforms based on an aerodynamic reduction model. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a diagram showing the flow characteristic changes of the wake-excited blade in the first embodiment of the present invention.

[0054] Figure 2 This is a simplified diagram of the aerodynamic force input of the wake excitation blade in the first embodiment of the present invention.

[0055] Figure 3 It is the CFD model of the two-dimensional blade example in the first embodiment of the present invention.

[0056] Figure 4 It is the kernel function of the aerodynamic response of the blade under the inlet total pressure pulse disturbance in the first embodiment of the present invention.

[0057] Figure 5 It is the inlet total pressure fluctuation in the first embodiment of the present invention.

[0058] Figure 6 It is the aerodynamic response of the blade under the inlet total pressure fluctuation in the first embodiment of the present invention.

[0059] Figure 7 This is the identification result of the total pressure in the first embodiment of the present invention.

[0060] Figure 8 It is an upper enlarged view of the recognition result of the total pressure in the first embodiment of the present invention.

[0061] Fig. 9 It is an enlarged view of the lower part of the recognition result of the total pressure in the first embodiment of the present invention.

[0062] Fig.10 This is a diagram showing the flow characteristic changes of the wake-excited blade in the second embodiment of the present invention.

[0063] Fig.11This is a simplified diagram of the aerodynamic force input of the wake excitation blade in the second embodiment of the present invention.

[0064] Fig.12 It is the CFD model of the two-dimensional blade example in the second embodiment of the present invention.

[0065] Fig.13 It is the kernel function of the aerodynamic response of the blade under the inlet total pressure pulse disturbance in the second embodiment of the present invention.

[0066] Fig.14 It is the inlet total pressure fluctuation in the second embodiment of the present invention.

[0067] Fig.15 It is the aerodynamic response of the blade under the inlet total pressure fluctuation in the second embodiment of the present invention.

[0068] Fig.16 This is the identification result of the total pressure in the second embodiment of the present invention.

[0069] Fig.17 It is an upper enlarged view of the identification result of the total pressure in the second embodiment of the present invention.

[0070] Fig.18 It is an enlarged view of the lower part of the recognition result of the total pressure in the second embodiment of the present invention. DETAILED DESCRIPTION

[0071] Embodiment 1

[0072] The CFD model of a two-dimensional blade under the upstream inlet wake excitation is used as the research object to identify the pressure waveform of the upstream inlet wake. Figure 1 -Attached Fig. 9 The CFD model of the two-dimensional blade is shown in the attached Figure 3 shown.

[0073] Step S1: Establishing a turbine blade flow channel CFD model;

[0074] Step S1.1: Establishing a turbine blade flow channel geometry model;

[0075] Step S1.2: Meshing the flow channel;

[0076] Step S1.3: Import the grid model into the CFD solver, and use the blade aerodynamic lift CL as the output; set the inlet reference total pressure to 120500Pa, the reference outlet pressure to 101325Pa, ideal gas, Spallart-Allmaras viscosity model, and the blade wall as a solid wall; use the inlet total pressure fluctuation as input to characterize the wake waveform;

[0077] Step S1.4: Write a UDF program to use the upstream wake as the inlet boundary condition of the turbine blade flow channel;

[0078] Step S1.5: Solve the aerodynamic force of the turbine blade under the upstream wake waveform.

[0079] Step S2: Simplify the mathematical description of the turbine blade flow passage aerodynamic system under the upstream inlet wake excitation, and establish a discrete blade aerodynamic reduced-order model under the upstream inlet wake excitation; the details are as follows:

[0080] Step S2.1: Take the fluctuation of the upstream inlet wake as input and represent it with the total pressure fluctuation p(x0, y, z, t) of the flow channel; take the blade aerodynamic force as output and represent it with the blade aerodynamic lift CL; construct the blade aerodynamic system excited by the upstream inlet wake, which is mathematically expressed as:

[0081] {cL(t)}=Ψ{p(x0, y, z, t)}; Formula (1);

[0082] Where x = x0 is the inlet axial position, y is the inlet circumferential position, z is the blade span height, p(x0, y, z, t) is the total pressure fluctuation at the flow channel inlet, and ψ is the system function.

[0083] Step S2.2: Simplify the mathematical expression of the blade aerodynamic system excited by the upstream inlet wake;

[0084] The total pressure at the flow channel inlet varies in time and space. If the pressure at each point of the flow channel inlet is regarded as an independent input, the system will have countless inputs. To simplify the problem, for the inlet wake waveform, any point (x0, y l The total pressure at the known point (x0, y0, z) can be expressed as p(x0, y0, z, t) l , z, t) = p(x0, y0+(y l -y0),z,t)=p(x0,t-(y l -y0) / v, z), where v is the speed of the total pressure waveform moving along the inlet. The total pressure waveform moves along the inlet at a speed v, and the movement of the total pressure fluctuation is defined by the user subroutine; therefore, the input of the blade aerodynamic system excited by the upstream wake is simplified to the total pressure at the point (x0, y0, z); let p(x0, y0, z, t) = p(z, t), then the mathematical expression of the blade aerodynamic system excited by the upstream wake can be simplified to:

[0085] {CL(z, t)}=Ψ{p(z, t)}; Formula (2);

[0086] Step S2.3: discretize the mathematical expression of the simplified blade aerodynamic system excited by the upstream inlet wake;

[0087] The Volterra series theory points out that any time-varying multi-input and multi-output system can be represented by an L-order discrete Volterra series. Therefore, the L-order discrete Volterra series is used to discretize the mathematical expression of the simplified upstream inlet wake excitation blade aerodynamic system; the form is as follows:

[0088]

[0089] in, is the wake pressure fluctuation increment of the jth section in the spanwise direction, CL i [n]=CL i (t)| t＝nΔT =CL i (nΔT) is the aerodynamic lift of the i-th section in the span direction, n = 0, 1, ..., N is the discrete time, ΔT is the time step, is the L-order discrete-time Volterra kernel, representing j1, j2, …j L The influence of the wake pressure fluctuation input of uniform cross-section on the aerodynamic lift of the i-th cross-section in the spanwise direction.

[0090] For nonlinear systems, the second-order kernel is one order of magnitude smaller than the first-order kernel, and the first-order kernel is sufficient to predict the nonlinear response. Therefore, the first-order Volterra reduced-order model is used to obtain the reduced-order model of the blade aerodynamic force excited by the discretized upstream inlet wake.

[0091]

[0092] Step S3: Using the pulse method, step method or white noise method, a pulse waveform is applied to the inlet of the blade CFD model, and the aerodynamic response of the blade in the flow channel is calculated. The aerodynamic response of the blade under the pulse waveform is identified to obtain the kernel function of the reduced-order model. Once the kernel function of the reduced-order model is determined, the aerodynamic response of the blade caused by any upstream fluctuation can be predicted by formula (3).

[0093] Attached Figure 4 The kernel function of the effect of the inlet total pressure pulse disturbance on the blade lift is shown. Figure 4 It can be seen that the kernel function contains three stages: in the first stage, the pulse pressure just enters the flow field, and it takes a certain amount of time for the pulse pressure to advance to the vicinity of the blade, so it has no effect on the blade aerodynamic force; in the second stage, the pulse pressure moves at the flow field inlet. At this time, due to the increase or decrease in flow rate, the blade lift decreases accordingly, and the pulse pressure causes the flow field to oscillate, which in turn has a greater impact on the blade aerodynamic force; in the third stage, the pulse pressure moves out of the flow field inlet, the flow field damps free vibration, and the amplitude gradually decays to zero.

[0094] Step S4: constructing a reduced-order model of the blade aerodynamic response relationship to upstream wake excitation using the kernel function of the blade aerodynamic reduced-order model;

[0095] The kernel function of the reduced-order model, i.e., formula (4), is matrixed;

[0096]

[0097] in,

[0098]

[0099] The reduced-order model after matrixization is:

[0100] CL=h0+HF; Formula (6);

[0101] Then the reduced-order model of the blade aerodynamic response excited by the upstream wake is obtained, namely:

[0102] Y=CL-h0=HF; Formula (7);

[0103] Among them, Y is the blade aerodynamic response increment, CL is the blade aerodynamic response, h0 is the blade aerodynamic reference response, H is the impulse response matrix, and F is the total pressure waveform input of the wake.

[0104] The kernel function value (attached Figure 4 ) into formula (7), the reduced-order model of the blade aerodynamic response to upstream wake excitation is obtained. The reduced-order model and CFD are used to calculate the attached Figure 5 The calculation results of the blade aerodynamic lift under the inlet total pressure fluctuation are shown in the attached figure. Figure 6 As shown. Figure 6 It can be seen that the lift calculated by the reduced-order model is the same as that calculated by CFD, which indicates that the method of using the first-order Volterra series reduced-order model to characterize the aerodynamic force of the blade under wake excitation is feasible, and the kernel function identified by the step method is also accurate.

[0105] Step S5: using the Tikhonov regularization solution method identified by the time domain deconvolution algorithm, the reduced-order model of the blade aerodynamic response excited by the upstream wake is inverted to obtain the Tikhonov regularization solution for upstream wake waveform identification;

[0106] The reduced-order model of blade aerodynamic force excited by upstream wake, that is, formula (7), is inversely transformed to obtain F = H- 1 Y can calculate the upstream wake excitation through the blade aerodynamic force; however, in actual measurement, the recognition accuracy of the instrument and signal noise will cause certain errors in the data. The solution of the above wake waveform is ill-posed. Therefore, it is necessary to use the Tikhonov regularization method to solve the wake waveform and add a suitable boundary constraint to the ill-posed inverse problem to make the problem well-posed and improve the stability of the recognition result.

[0107] The total pressure waveform input of the wake is solved by Tikhonov regularization method, and the calculation expression of is obtained. Its objective function is:

[0108]

[0109] Where: ||·|| is the 2-norm of the vector; the constant α>0 is the regularization parameter, which mainly controls the relative size between the residual norm ||HF-Y|| and the solution norm ||F||;

[0110] Solving formula (8), we can obtain the Tikhonov regularization solution for upstream wake waveform identification, namely:

[0111] F=(H T H+α 2 I) -1 H T Y; formula (9);

[0112] Where: I is the unit matrix.

[0113] Step S6: using the Tikhonov regularization solution for upstream wake or downstream back-potential flow waveform identification, the pressure arbitrary waveform of the upstream wake or downstream back-potential flow can be identified according to the blade aerodynamic response;

[0114] According to load identification theory, for any other blade flow system under wake excitation, when the blade aerodynamic force Y response and impulse response matrix H and regularization parameter α are known, the total pressure waveform input F of the inlet wake can be obtained by formula (9); that is, the upstream wake waveform.

[0115] Attached Figure 7 The recognition results of the wake inlet total pressure waveform are given (marked as a=0.01, 0.001 and 0.0001 in the figure). It can be seen from the figure that the wake waveform recognition results are basically consistent with the wake waveform imposed on the inlet (marked as imposed in the figure), which shows that the method of the present invention can accurately recognize the wake waveform imposed on the inlet.

[0116] The solution accuracy of the Tikhonov regularization method is closely related to the selection of parameter a. In order to obtain a solution closer to the truth, the value of α should be as small as possible, while from the perspective of numerical stability, the value of α should be as large as possible. The present invention provides the recognition results of the inlet total pressure waveform when a=0.01, 0.001 and 0.0001. Overall, the recognition accuracy of the wake waveform is the highest when a=0.001.

[0117] Embodiment 2

[0118] The CFD model of a two-dimensional blade under the excitation of the downstream outlet back-potential flow is used as the research object to identify the pressure waveform of the downstream outlet back-potential flow. Fig.10 -Attached Fig.18 The CFD model of the two-dimensional blade is shown in the attached Fig.12 shown.

[0119] Step S1: Establishing a turbine blade flow channel CFD model;

[0120] Step S1.1: Establishing a turbine blade flow channel geometry model;

[0121] Step S1.2: Meshing the flow channel;

[0122] Step S1.3: Import the grid model into the CFD solver, and use the blade aerodynamic lift CL as the output; use the outlet static pressure fluctuation as the input to characterize the back potential flow waveform;

[0123] Step S1.4: Write a udf program to use the static pressure fluctuation of the downstream back-potential flow as the outlet boundary condition of the turbine blade flow channel;

[0124] Step S1.5: Calculate the aerodynamic force of the turbine blade under the downstream back-potential flow waveform.

[0125] Step S2: Simplify the mathematical description of the turbine blade flow passage aerodynamic system under the downstream outlet back potential flow excitation, and establish a reduced-order model of the blade aerodynamic force under the discrete downstream outlet back potential flow excitation; the details are as follows:

[0126] Step S2.1: Take the fluctuation of the downstream outlet back potential flow as input, represented by the total pressure fluctuation P(x0, y, z, t) of the flow channel; take the blade aerodynamic force as output, represented by the blade aerodynamic lift CL; construct the blade aerodynamic system excited by the downstream outlet back potential flow, mathematically expressed as:

[0127] {CL(t)}=Ψ{p(x0, y, z, t)}; Formula (1);

[0128] Where x = x0 is the outlet axial position, y is the outlet circumferential position, z is the blade span height, p(x0, y, z, t) is the total pressure fluctuation at the flow channel outlet, and ψ is the system function.

[0129] Step S2.2: Simplify the mathematical expression of the blade aerodynamic system excited by the downstream outlet back potential flow;

[0130] In order to simplify the problem, for the outlet backflow waveform, any point (x0, y l The total pressure at the known point (x0, y0, z) can be expressed as p(x0, y0, z, t) l , z, t) = p(x0, y0+(y l -y0),z,t)=p(x0,t-(y l-y0) / v, z), where v is the speed of the static pressure waveform moving along the outlet. The static pressure waveform moves along the outlet at a speed v, and the movement of the static pressure waveform is defined by the user subroutine; therefore, the input of the blade aerodynamic system excited by the downstream outlet back potential flow is simplified to the total pressure at the point (x0, y0, z); let p(x0, y0, z, t) = p(z, t), then the mathematical expression of the blade aerodynamic system excited by the downstream back potential flow can be simplified to:

[0131] {CL(z, t)}=Ψ{p(z, t)}; Formula (2);

[0132] Step S2.3: discretize the mathematical expression of the simplified blade aerodynamic system excited by the downstream outlet back potential flow;

[0133] The Volterra series theory points out that any time-varying multi-input and multi-output system can be represented by an L-order discrete Volterra series. Therefore, the L-order discrete Volterra series is used to discretize the mathematical expression of the simplified blade aerodynamic system excited by the downstream outlet back potential flow; the form is as follows:

[0134]

[0135] in, is the pressure fluctuation increment of the backflow at the jth section in the spanwise direction, CL i [n]=CL i (t)| t＝nΔT =CL i (nΔT) is the aerodynamic lift of the i-th section in the span direction, n = 0, 1, ..., N is the discrete time, ΔT is the time step, is the L-order discrete-time Volterra kernel, representing j1, j2, …j L The influence of back-potential flow pressure fluctuation input of uniform cross-section on the aerodynamic lift of the i-th cross-section in the span direction.

[0136] For nonlinear systems, the second-order kernel is one order of magnitude smaller than the first-order kernel, and the first-order kernel is sufficient to predict the nonlinear response. Therefore, the first-order Volterra reduced-order model is used to obtain the reduced-order model of the blade aerodynamic force excited by the discretized downstream outlet back potential flow.

[0137]

[0138] Step S3: Using the pulse method, step method or white noise method, a pulse waveform is applied to the outlet of the blade CFD model, and the aerodynamic response of the blade in the flow channel is calculated. The aerodynamic response of the blade under the pulse waveform is identified to obtain the kernel function of the reduced-order model. Once the kernel function of the reduced-order model is determined, the aerodynamic response of the blade caused by any downstream fluctuation can be predicted by formula (3).

[0139] Attached Fig.13 The kernel function of the effect of the outlet total pressure pulse disturbance on the blade lift is shown.

[0140] Step S4: constructing a reduced-order model of the blade aerodynamic response relationship excited by the downstream back potential flow using the kernel function of the blade aerodynamic reduced-order model;

[0141] The kernel function of the reduced-order model, i.e., formula (4), is matrixed;

[0142]

[0143] in,

[0144]

[0145] The reduced-order model after matrixization is:

[0146] CL=h0+HF; Formula (6);

[0147] Then the reduced-order model of the blade aerodynamic response excited by the downstream back-potential flow is obtained, namely:

[0148] Y=CL-h0=HF; Formula (7);

[0149] Among them, Y is the blade aerodynamic response increment, CL is the blade aerodynamic response, h0 is the blade aerodynamic reference response, H is the impulse response matrix, and F is the total pressure waveform input of the back potential flow.

[0150] The kernel function value (attached Fig.13 ) into formula (7), the reduced-order model of the blade aerodynamic response excited by the downstream backflow is obtained. The reduced-order model and CFD are used to calculate the attached Fig.14 The calculation results of the blade aerodynamic lift under the outlet total pressure fluctuation are shown in the attached figure. Fig.15 As shown. Fig.15 It can be seen that the lift calculated by the reduced-order model is the same as that calculated by CFD, which indicates that the method of using the first-order Volterra series reduced-order model to characterize the aerodynamic force of the blade under the excitation of the back potential flow is feasible, and the kernel function identified by the step method is also accurate.

[0151] Step S5: using the Tikhonov regularization solution method identified by the time domain deconvolution algorithm, the reduced-order model of the blade aerodynamic response excited by the downstream back potential flow is inverted to obtain the Tikhonov regularization solution for downstream back potential flow waveform identification;

[0152] The reduced-order model of blade aerodynamic force excited by the downstream backflow, that is, formula (7), is inversely transformed to obtain F = H- 1Y can calculate the downstream back potential flow excitation through the blade aerodynamic force; however, in actual measurement, the recognition accuracy of the instrument and signal noise will cause certain errors in the data, and there is an ill-posed problem in solving the downstream back potential flow waveform. Therefore, it is necessary to use the Tikhonov regularization method to solve the back potential flow waveform, add a suitable boundary constraint to the ill-posed inverse problem, make the problem well-posed, and improve the stability of the recognition result;

[0153] The total pressure waveform input of the back potential flow is solved by Tikhonov regularization method, and the calculation expression of the objective function is:

[0154]

[0155] Where: ||·|| is the 2-norm of the vector; the constant α>0 is the regularization parameter, which mainly controls the relative size between the residual norm ||HF-Y|| and the solution norm ||F||;

[0156] Solving formula (8), we can obtain the Tikhonov regularization solution for downstream back-potential flow waveform identification, namely:

[0157] f=(H T H+α 2 I) -1 H T Y; formula (9);

[0158] Where: I is the unit matrix.

[0159] Step S6: using the Tikhonov regularization solution for downstream back-potential flow waveform identification, the pressure arbitrary waveform of the downstream back-potential flow can be identified according to the blade aerodynamic response;

[0160] According to the load identification theory, for any blade flow system under other back potential flow excitation, when the blade aerodynamic force Y response and impulse response matrix H and regularization parameter α are known, the total pressure waveform input f of the outlet back potential flow can be obtained by formula (9); that is, the downstream back potential flow waveform.

[0161] Attached Fig.16 The recognition results of the total pressure waveform of the back-potential flow outlet are given (marked as a=0.01, 0.001 and 0.0001 in the figure). It can be seen from the figure that the recognition results of the back-potential flow waveform are basically consistent with the back-potential flow waveform applied to the outlet (marked as imposed in the figure), which shows that the method of the present invention can accurately recognize the back-potential flow waveform applied at the outlet.

[0162] The solution accuracy of the Tikhonov regularization method is closely related to the selection of parameter α. In order to obtain a solution closer to the truth, the value of α should be as small as possible, while from the perspective of numerical stability, the value of α should be as large as possible. The present invention provides the recognition results of the outlet total pressure waveform when α=0.01, 0.001 and 0.0001. Overall, the recognition accuracy of the back potential flow waveform is the highest when α is near 0.001.

[0163] In the present invention, blade aerodynamic force is used as an indicator to identify the wake or backflow waveform, and pressure, velocity, etc. at any point in the flow channel can also be used to identify the wake or backflow waveform. In the description of the present invention, the upstream wake total pressure waveform is used as an example for identification, and the method of the invention can be applied to the identification of velocity waveforms and other related quantities.

[0164] The present invention adopts the Tikhonov regularization method to identify the wake or back-flow waveform, and other load identification methods are also effective for the wake and back-flow waveform identification of the present invention.

[0165] In the description of the present invention, it is necessary to understand that the indicated orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0166] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet backflow, characterized in that: The method comprises the following steps: Step S1: Establishing a turbine blade flow channel CFD model; Step S2: Simplify the mathematical description of the turbine blade flow passage aerodynamic system under the excitation of the upstream inlet wake or the downstream outlet back potential flow, and establish a reduced-order model of the blade aerodynamic force under the excitation of the discrete upstream inlet wake or the downstream outlet back potential flow; Step S3: applying a pulse waveform to each section of the inlet or outlet of the blade CFD model by using a pulse method, a step method or a white noise method, calculating the corresponding blade aerodynamic response, identifying the aerodynamic response relationship of the blade under the upstream inlet wake pulse waveform or the downstream outlet back potential flow pulse waveform of each section, and obtaining the kernel function of the blade aerodynamic reduced-order model excited by the discretized upstream inlet wake or downstream outlet back potential flow; Step S4: constructing a reduced-order model of the blade aerodynamic response relationship excited by the upstream wake or downstream back potential flow using the kernel function of the blade aerodynamic reduced-order model; Step S5: using the Tikhonov regularization solution method identified by the time domain deconvolution algorithm, the reduced-order model of the blade aerodynamic response relationship excited by the upstream wake or downstream back potential flow is inverted to obtain the Tikhonov regularization solution for upstream wake or downstream back potential flow waveform identification; Step S6: Using the Tikhonov regularization solution for upstream wake or downstream back-potential flow waveform identification, the pressure arbitrary waveform of the upstream wake or downstream back-potential flow can be identified according to the blade aerodynamic response.

2. The method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet back-potential flow according to claim 1, characterized in that: The step S1: establishing a turbine blade flow channel CFD model, specifically as follows: Step S1.1: Establishing a turbine blade flow channel geometry model; Step S1.2: Meshing the flow channel; Step S1.3: Import the mesh model into the CFD solver and set the parameters and boundary conditions; Step S1.4: Write a UDF program to use the upstream inlet wake flow or downstream outlet back-potential flow waveform as the inlet or outlet boundary condition of the turbine blade flow passage; Step S1.5: Calculate the aerodynamic force of the turbine blade under the upstream inlet wake or downstream outlet back-potential flow waveform.

3. The method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet back-potential flow according to claim 2, characterized in that: The step S2 is to simplify the mathematical description of the turbine blade flow passage aerodynamic system under the excitation of the upstream inlet wake or the downstream outlet back potential flow, and establish a reduced-order model of the blade aerodynamic force under the excitation of the discrete upstream inlet wake or the downstream outlet back potential flow; specifically as follows: Step S2.1: Take the fluctuation of the upstream inlet wake or the downstream outlet back potential flow as input, represented by the total pressure fluctuation p(x0, y, z, t) of the flow channel; take the blade aerodynamic force as output, represented by the blade aerodynamic lift CL; construct the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow, mathematically expressed as: {CL(t)}=Ψ{p(x0, y, z, t)}; formula (1); Where x = x0 is the axial position of the inlet or outlet, y is the circumferential position of the inlet or outlet, z is the spanwise height of the blade, p(x0, y, z, t) is the total pressure fluctuation at the inlet or outlet of the flow channel, and ψ is the system function; Step S2.2: Simplify the mathematical expression of the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow; For the inlet wake or outlet backflow waveform at spanwise height z, any point (x0, y l The total pressure at the known point (x0, y0, z) can be expressed as p(x0, y0, z, t) l , z, t) = p(x0, y0+(y l -y0),z,t)=p(x0,t-(y l -y0) / v, z), where v is the moving speed of the total pressure waveform along the inlet or outlet. Therefore, the input of the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow is simplified to the total pressure at point (x0, y0, z); let p(x0, y0, z, t) = p(z, t), the mathematical expression of the blade aerodynamic system excited by the upstream inlet wake or the downstream outlet back potential flow can be simplified to: {CL(z,t)}=Ψ{p(z,t)}; Formula (2); Step S2.3: discretizing the mathematical expression of the blade aerodynamic system excited by the simplified upstream inlet wake or downstream outlet back potential flow; The mathematical expression of the blade aerodynamic system excited by the simplified upstream inlet wake or downstream outlet back potential flow is discretized using the L-order discrete Volterra series; the form is as follows: in, is the pressure fluctuation increment of the wake or backflow at the jth section in the span direction, CL i [n] = CL i (t)| t＝nΔT =CL i (nΔT) is the aerodynamic lift of the i-th section in the span direction, n = 0, 1, ..., N is the discrete time, ΔT is the time step, is the L-order discrete-time Volterra kernel, representing j1, j2, …j L The influence of the pressure fluctuation input of the wake or backflow of equal cross section on the aerodynamic lift of the i-th cross section in span direction; For nonlinear systems, the kernels above the second order are one order of magnitude smaller than the first order kernels, and the first order kernel is sufficient to predict the nonlinear response. Therefore, the first order Volterra reduced order model is used to obtain the reduced order model of the blade aerodynamic force excited by the discretized upstream inlet wake or downstream outlet back potential flow.

4. The method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet back-potential flow according to claim 3, characterized in that: The step S4: constructing a reduced-order model of the blade aerodynamic response relationship excited by the upstream wake or downstream back-potential flow using the kernel function of the blade aerodynamic reduced-order model; specifically as follows: Step S4.1: Matrix the kernel function of the reduced-order model, i.e., formula (4); in, The reduced-order model after matrixization is: CL=h0+HF;Formula (6); Step S4.2: The reduced-order model of the blade aerodynamic response excited by the upstream wake or downstream backflow is obtained, namely: Y=CL-h0=HF; formula (7); Among them, Y is the blade aerodynamic response increment, CL is the blade aerodynamic response, h0 is the blade aerodynamic reference response, H is the impulse response matrix, and F is the total pressure waveform input of the wake or back potential flow.

5. The method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet back-potential flow according to claim 4, characterized in that: Step S5: using the Tikhonov regularization solution method identified by the time domain deconvolution algorithm, inverting the reduced-order model of the blade aerodynamic response excited by the upstream wake or downstream backflow, and obtaining a Tikhonov regularization solution for upstream wake or downstream backflow waveform identification; The reduced-order model of the blade aerodynamic response relationship excited by the upstream wake or downstream back-potential flow is solved using the Tikhonov regularization method to obtain the calculation expression of the total pressure waveform input of the wake or back-potential flow, and its objective function is: Where: ||·|| is the 2-norm of the vector; the constant α>0 is the regularization parameter, which mainly controls the relative size between the residual norm ||HF-Y|| and the solution norm ||F||; Solving formula (8), we can obtain the Tikhonov regularization solution for upstream wake flow or downstream backflow waveform identification, namely: F = (H T H + α 2 I) -1 H T Y; Formula (9); Where: I is the unit matrix.

6. The method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet back-potential flow according to claim 5, characterized in that: The step S6: using the Tikhonov regularization solution for upstream wake or downstream back-potential flow waveform identification, the pressure arbitrary waveform of the upstream wake or downstream back-potential flow can be identified according to the blade aerodynamic response; For any other blade flow system under wake or back potential flow excitation, when the blade aerodynamic force Y response and impulse response matrix H are known, the total pressure waveform input f of the wake or back potential flow can be obtained by formula (9); that is, the pressure waveform of the upstream wake or downstream back potential flow.

7. The method for identifying pressure waveforms of upstream inlet wake flow and downstream outlet back-potential flow according to claim 1, characterized in that: The aerodynamic response may be the lift, drag and moment of the blade, or may be a pressure measurement or derived value at any point.

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