A method for synthesizing spatially distributed dynamic pressure distortion signals

Abstract

This invention relates to the field of turbomachinery technology and discloses a method for synthesizing spatially distributed dynamic pressure distortion signals. The method involves dividing the planar region where the pressure distortion occurs in the turbomachinery compression system into a grid, generating independent single-point random signals at each grid point, and using the distance information between each grid point to generate a coherence matrix to mix the single-point random signals after STFT transformation. The mixed signals are then subjected to inverse STFT transformation to form spatially distributed random signals. These spatially distributed random signals are then superimposed with the average pressure of the planar region where the pressure distortion occurs to form the pressure distortion signal. This method can synthesize dynamic pressure distortion signals with specified dynamic distortion indices and power spectral density characteristics. Furthermore, it can simultaneously provide distortion signals at multiple points in space that exhibit spatial correlation. These signals can be used as given inlet pressure boundary conditions in two-dimensional or three-dimensional stability analysis numerical simulations to achieve compressor stability analysis under dynamic pressure distortion conditions.

Description

Technical Field

[0001] This invention relates to the field of turbomachinery technology and discloses a method for synthesizing spatially distributed dynamic pressure distortion signals. Background Technology

[0002] Inlet pressure distortion negatively impacts the performance of compressors in aero-engines, typically causing performance degradation, a rightward shift of the stability boundary, and a reduction in stability margin. The loss of stability margin due to inlet pressure distortion is a crucial aspect of aero-engine stability assessment. Pressure distortion consists of steady-state and dynamic components. For fighter jets, unconventional maneuvering, missile loading and launch, and the use of S-shaped inlets all lead to highly unsteady pressure distortion. Therefore, the study of dynamic distortion is of great significance.

[0003] Currently, research on dynamic distortion in countries like the UK and the US primarily employs experimental methods, and numerical calculations generally use steady-state intake distortion for analysis. Russia uses a comprehensive distortion index to describe intake distortion, composed of steady-state and dynamic distortion indices, and has a complete engine calculation program; therefore, it is speculated that there may be one-dimensional or quasi-two-dimensional compressor stability analysis programs capable of calculating the effects of comprehensive distortion. Wang Zhiqiang et al. from Nanjing University of Aeronautics and Astronautics presented a numerical simulation method for random fluctuations in inlet total pressure, but this method does not consider the spatial distribution of the distortion signal and can only be used for zero-dimensional or one-dimensional numerical simulations. Summary of the Invention

[0004] The purpose of this invention is to provide a method for synthesizing spatially distributed dynamic pressure distortion signals. This method can synthesize dynamic pressure distortion signals with specified dynamic distortion index and power spectral density characteristics. Moreover, it can simultaneously provide distortion signals at multiple points in space and reflect spatial correlation. When performing two-dimensional or three-dimensional stability analysis numerical simulations, the resulting pressure distortion signals are used as given inlet pressure boundary conditions, thereby realizing compressor stability analysis under dynamic pressure distortion conditions.

[0005] To achieve the above-mentioned technical effects, the technical solution adopted by the present invention is as follows:

[0006] A method for synthesizing spatially distributed dynamic pressure distortion signals includes the following steps:

[0007] Step 1: Grid the planar region where the pressure distortion of the turbomachinery compression system occurs;

[0008] Step 2: Generate an independent single-point random signal at each grid point;

[0009] Step 3: Generate a coherence matrix using the distance information between each pair of grid points;

[0010] Step 4: Mix the single-point random signal after STFT transformation using the coherence matrix;

[0011] Step 5: Perform an inverse STFT transformation on the mixed signal to form a spatially distributed random signal;

[0012] Step 6: Superimpose the spatially distributed random signal with the average pressure of the plane region where the pressure distortion occurs to form a pressure distortion signal.

[0013] Furthermore, in step 1, the inlet boundary of the compression system is meshed within the computational grid of the numerical simulation for stability analysis.

[0014] Furthermore, the method for generating the single-point random signal in step 2 is as follows:

[0015] Given dynamic distortion index ε Time step t and coefficients with time units τ E The composition follows a normal distribution. N (0, ε A random sequence;

[0016] according to Recursive formula for synthesizing random sequences { y i}, { y i} That is, an independent single-point random signal for each corresponding grid point; where, .

[0017] Furthermore, the process of generating the coherence matrix in step 3 includes the following steps:

[0018] Given the frame length of the short-time Fourier transform K To obtain all angular frequencies ,in SR For sequence { y i The sampling rate of} It is the floor function;

[0019] For each circular frequency ω k Generate coherence matrix

[0020]

[0021] in, Any two grid points n and m The spatial correlation between them is determined by Given, Grid points n and m The distance between themc It's the speed of sound.

[0022] Furthermore, step 4, which involves mixing the single-point random signal after STFT transformation using the coherence matrix, includes the following steps:

[0023] For each Perform eigenvalue decomposition: And calculate the mixing matrix: ;

[0024] The points synthesized in step 2 p The sequence at { y i} is denoted as S p , and put it in the first i The value of each time step is denoted as S p ( i Performing STFT transformation on each sequence and using zero padding, we can obtain the th sequence. i Frame, number k frequency ω k STFT coefficient And the STFT coefficients at each point are combined into a vector.

[0025] ;

[0026] The mixture matrix is ​​obtained by mixing vectors using the mixture matrix. .

[0027] Furthermore, in step 5, for The p Each component Performing a short-time inverse Fourier transform yields... p Random signal after mixing at point .

[0028] Furthermore, in step 6, before superimposing the spatially distributed random signal with the average pressure of the planar region where the pressure distortion occurs, the standard deviation of all mixed random signals is pre-calculated. σ And multiply each of the mixed random signals by ε / σ The updated random signal is obtained, and the standard deviation of the new random signal is realized. σ Fitting a given dynamic distortion index ε .

[0029] Furthermore, based on the formation of pressure distortion signals, the point p At time step i The total pressure is given as

[0030] ,inp t,a This represents the average total pressure at the import boundary.

[0031] Compared with the prior art, the beneficial effects of the present invention are: the present invention can synthesize dynamic pressure distortion signals with specified dynamic distortion index and power spectral density characteristics, and can simultaneously provide distortion signals that can reflect spatial correlation at multiple points in space; when performing two-dimensional or three-dimensional stability analysis numerical simulation, the formed pressure distortion signal is used as a given inlet pressure boundary condition, thereby realizing compressor stability analysis under dynamic pressure distortion conditions. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the grid division of the planar region where the pressure distortion occurs in Example 2;

[0033] Figure 2 This is a curve comparing the probability density distribution of the synthesized signal at points a and c in Example 2 with the theoretical value;

[0034] Figure 3 This is a curve comparing the probability density distribution of the synthesized signal at points a and b in Example 2 with the theoretical value;

[0035] Figure 4 This is a curve comparing the probability density distribution of the synthesized signal at points b and c in Example 2 with the theoretical value;

[0036] Figure 5 This is a curve comparing the probability density distribution of the synthesized signal at points c and d in Example 2 with the theoretical value;

[0037] Figure 6 The total-static pressure rise characteristic curves under different intensities of dynamic total pressure distortion in Example 2 are shown.

[0038] Figure 7 This is a schematic diagram of the change in circumferential pressure distribution at the rotor outlet when there is steady-state distortion but no dynamic distortion in Example 2;

[0039] Figure 8 This is a schematic diagram of the rotor outlet circumferential pressure distribution under steady-state and dynamic distortion conditions in Example 2.

[0040] Figure 9 This is a flowchart of the method for synthesizing spatially distributed dynamic pressure distortion signals in Example 1 or 2. Detailed Implementation

[0041] The present invention will now be described in further detail with reference to the embodiments and accompanying drawings. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0042] Example 1

[0043] See Figure 9 A method for synthesizing spatially distributed dynamic pressure distortion signals, comprising the following steps:

[0044] Step 1: Grid the planar region where the pressure distortion of the turbomachinery compression system occurs;

[0045] Step 2: Generate an independent single-point random signal at each grid point;

[0046] Step 3: Generate a coherence matrix using the distance information between each pair of grid points;

[0047] Step 4: Mix the single-point random signal after STFT transformation using the coherence matrix;

[0048] Step 5: Perform an inverse STFT transformation on the mixed signal to form a spatially distributed random signal;

[0049] Step 6: Superimpose the spatially distributed random signal with the average pressure of the plane region where the pressure distortion occurs to form a pressure distortion signal.

[0050] In this embodiment, the planar region where the pressure distortion of the turbomachinery compression system is located is divided into grids. Then, an independent single-point random signal is generated at each grid point. A coherence matrix is ​​generated using the distance information between each grid point to mix the single-point random signals after STFT transformation. The mixed signal is then subjected to inverse STFT transformation to form a spatially distributed random signal. Finally, the obtained spatially distributed random signal is superimposed with the average pressure of the planar region where the pressure distortion is located to form the pressure distortion signal. This embodiment can synthesize dynamic pressure distortion signals with specified dynamic distortion index and power spectral density characteristics, and can simultaneously provide distortion signals that reflect spatial correlation at multiple points in space. During two-dimensional or three-dimensional stability analysis numerical simulations, the formed pressure distortion signal is used as a given inlet pressure boundary condition, thereby realizing compressor stability analysis under dynamic pressure distortion conditions.

[0051] Example 2

[0052] See Figure 1-5 and Figure 9 A method for synthesizing spatially distributed dynamic pressure distortion signals, comprising the following steps:

[0053] 1) In the computational grid for the numerical simulation of stability analysis, grid points on the inlet boundary are selected and numbered 1, 2, ..., M. In this embodiment, ... Figure 1Taking the grid shown as an example, dynamic distortion signals are generated for each point within it. The region in the figure is a 90° sector with an inner diameter of 0.54m and an outer diameter of 0.90m. There are 11 grid points radially and 10 grid points circumferentially, for a total of 110 grid points. The subsequent processing flow will be explained in detail using the signals from points a to d in the figure as examples.

[0054] 2) Given the dynamic distortion index, i.e., the standard deviation ε Given time step t Given coefficients with time units τ E The composition follows a normal distribution. N (0, ε A random sequence { x i}, synthesize random sequences according to the following recursive formula { y i}:

[0055]

[0056] in, The power spectral density of the random sequence generated by this method is: ,in f It is the frequency; the autocorrelation function is ,in t This refers to time. In this embodiment, the sampling rate is 8000Hz and the dynamic distortion index is 5%. Set to 50, generate dynamic distortion signals for each point { y i}

[0057] 3) Given the frame length of the Short Time Fourier Transform (STFT) K The STFT can analyze all the following angular frequencies:

[0058]

[0059] in It is the floor function. SR For sequence { y i The sampling rate of}. The frame length can be determined according to the required frequency resolution. K The value can generally be between 128 and 1024; the initial value in this embodiment is [value missing]. K =256.

[0060] 4) For each of the above circular frequencies ω k Generate coherence matrix

[0061]

[0062] in, Any two grid points n and m The spatial correlation between them is determined by Given, Grid points n and m The distance between them c It's the speed of sound.

[0063] 5) For each Perform eigenvalue decomposition:

[0064] And calculate the mixing matrix

[0065] 6) Combine the points synthesized in step 2 p The sequence at { y i} is denoted as S p , and put it in the first i The value of each time step is denoted as S p ( i By performing STFT transformation on each sequence and using zero padding, the th sequence can be obtained. i Frame (corresponding) S p The i (time step), the first k frequency ω k STFT coefficient:

[0066]

[0067] And the STFT coefficients at each point are combined into a vector:

[0068]

[0069] 7) Use a mixing matrix to mix the above vectors:

[0070]

[0071] 8) To The p Each component Performing an inverse short-time Fourier transform (inverse STFT) yields... p Signal after mixing at point .

[0072] 9) Statistics of all The total standard deviation, and each Multiply ε / σ To adjust the standard deviation so that the actual standard deviation is... σ Fitting the given standard deviation ε Adjusted The original power spectral density and variance are retained, and each and Follows a given correlation function .

[0073] 10) Let the average total pressure at the inlet boundary be... p t,a Then point p At time step i The total pressure is given as follows:

[0074]

[0075] This completes the setting of the entry boundary conditions.

[0076] Figure 2 Showing Figure 1 The figure shows the probability density distributions of the independent signals (raw) generated directly at points a and c via step 2), and the mixed signal (scaled) generated via steps 1)-10), as well as the theoretical values ​​of their probability density distributions. σ The value is the measured standard deviation, indicating that the signal synthesized by this method conforms to the given dynamic distortion index.

[0077] Figure 3-5 They were shown respectively Figure 1 The theoretical coherence between points ab, bc, and cd is compared with the measured coherence of the synthesized signal. It is evident that the synthesized dynamic distortion signal can reflect the spatial correlation of each point.

[0078] In this embodiment, the distortion signal on the inlet plane was synthesized through the above steps, and the synthesized signal was used as the inlet boundary condition to simulate the performance and stall dynamic process of a compressor under three conditions: no dynamic component, 0.5% dynamic component, and 1% dynamic component, with a 90° steady-state total pressure distortion (total pressure recovery coefficient ADP0 is 0.5%). Figure 6 The total-static pressure rise characteristics of the compressor under different conditions are shown. It can be seen that the performance gradually decreases as the dynamic component increases.

[0079] Figure 7 and 8The changes in rotor outlet circumferential pressure distribution over time are shown under conditions of steady-state distortion and / or 0.5% dynamic distortion. It can be seen that without dynamic distortion, a low-pressure region develops from the steady-state distortion region, gradually developing into rotating stall; with dynamic distortion, the appearance of the low-pressure region, the size and intensity of the stall cluster all exhibit characteristics of being subject to random disturbances.

[0080] The relevant data and curves of this embodiment show that the pressure distortion signal synthesis method of the present invention can be used to give the inlet boundary conditions in the numerical simulation of compressor stability, and can be used to simulate and examine the influence of inlet pressure distortion on compressor stability.

[0081] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for synthesizing spatially distributed dynamic pressure distortion signals, characterized in that, Includes the following steps: Step 1: Grid the planar region where the pressure distortion of the turbomachinery compression system occurs; Step 2: Generate an independent single-point random signal at each grid point; Step 3: Generate a coherence matrix using the distance information between each pair of grid points; Step 4: Mix the single-point random signal after STFT transformation using the coherence matrix; Step 5: Perform an inverse STFT transformation on the mixed signal to form a spatially distributed random signal; Step 6: Superimpose the spatially distributed random signal with the average pressure of the plane region where the pressure distortion occurs to form a pressure distortion signal.

2. The method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 1, characterized in that, In step 1, the inlet boundary of the compression system is meshed in the computational grid of the numerical simulation for stability analysis.

3. The method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 1, characterized in that, The method for generating the single-point random signal in step 2 is as follows: Given dynamic distortion index ε Time step t and coefficients with time units τ E The composition follows a normal distribution. N (0, ε A random sequence; according to Recursive formula for synthesizing random sequences { y i }, { y i } That is, an independent single-point random signal for each corresponding grid point; where, The synthesized data follow a normal distribution. N (0, ε The first random sequence of ) One data value, .

4. The method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 3, characterized in that, Step 3, generating the coherence matrix, includes the following steps: Given the frame length of the short-time Fourier transform K To obtain all angular frequencies ,in SR For sequence { y i The sampling rate of} It is the floor function; For each circular frequency ω k Generate coherence matrix in, It is any two grid points n and m The spatial correlation between them is determined by Given, Grid points n and m The distance between them c It's the speed of sound.

5. The method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 4, characterized in that, Step 4, which involves mixing the single-point random signal after STFT transformation using the coherence matrix, includes the following steps: For each Perform eigenvalue decomposition: And calculate the mixing matrix: ; The points synthesized in step 2 p The sequence at { y i } is denoted as S p , and put it in the first i The value of each time step is denoted as S p ( i Performing STFT transformation on each sequence and using zero padding, we can obtain the th sequence. i Frame, number k frequency ω k STFT coefficient And the STFT coefficients at each point are combined into a vector. ； The mixture matrix is ​​obtained by mixing vectors using the mixture matrix. .

6. The method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 5, characterized in that, In step 5, for The p Each component Performing a short-time inverse Fourier transform yields... p Random signal after mixing at point .

7. The method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 3, characterized in that, In step 6, before superimposing the spatially distributed random signal with the average pressure of the planar region where the pressure distortion occurs, the standard deviation of all mixed random signals is pre-calculated. σ And multiply each of the mixed random signals by ε / σ The updated random signal is obtained, and the standard deviation of the new random signal is realized. σ Fitting a given dynamic distortion index ε .

8. A method for synthesizing spatially distributed dynamic pressure distortion signals according to claim 6 or 7, characterized in that, Based on the formation of pressure distortion signals, point p At time step i The total pressure is given as ,in p t,a This represents the average total pressure at the import boundary.

Images