A method for identifying acoustic modes in a solid rocket engine test process

Abstract

The present application relates to a kind of solid engine test process combustion chamber acoustic mode identification method, comprising: based on finite element analysis, engine acoustic mode is simulated and estimated, according to the frequency and vibration mode of engine acoustic cavity in calculation result, reasonable arrangement test engine pressure measuring point;Engine test process uses pressure measuring point to carry out pressure response test in combustion chamber, according to the identification dynamic pressure signal of pressure test result;The dynamic pressure of each measuring point is carried out FFT conversion to obtain the frequency of acoustic cavity in combustion chamber, carries out STFT conversion to obtain the time domain variation of acoustic cavity in combustion chamber frequency, according to the phase and amplitude of each measuring point each stage frequency, fitting combustion chamber axial vibration mode;According to frequency time domain variation and axial vibration mode, check simulation analysis precision.This method realizes the identification of combustion chamber acoustic cavity acoustic mode in the process of engine ground test, provides test verification for the precision improvement of acoustic mode simulation calculation, thereby providing theoretical support for engine unstable combustion indication.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of unstable combustion of solid rocket engine, and relates to a sound mode identification method in a solid rocket engine test process. BACKGROUND

[0002] The combustion instability of solid rocket engine is one of the thorny problems encountered in the development process of the engine. In the working process of the solid rocket engine, the internal combustion chamber is subjected to weak disturbance, which produces sound waves with certain vibration mode and frequency. When the pressure oscillation frequency generated by the disturbance is close to the natural frequency of the sound field in the combustion chamber, the acoustic unstable combustion phenomenon may occur, which makes the combustion gas in the combustion chamber produce a large amplitude of pressure oscillation. In severe cases, the strong pressure oscillation may lead to engine disintegration and the serious consequences of test failure. In the development process of solid rocket engine, the tactical and strategic missile engines and the launch vehicle boosters in many research fields are plagued by unstable combustion. It is particularly important to analyze the inherent sound field characteristics in the combustion chamber for studying combustion instability.

[0003] For solid rocket engine, the combustion chamber can be simplified as an acoustic cavity by appropriate assumptions when calculating and analyzing the acoustic modes of the acoustic cavity, and the sound wave propagates in it. When the shape of the acoustic cavity is regular and simple, the internal acoustic characteristics can be processed by classical acoustics, and the acoustic theory has given the analytical expression of the acoustic vibration mode of the uniform and equal cross-section cylindrical acoustic cavity f 纵=nc / 2L, but this only applies to solid propellant charges without airfoil slots and where there are no abrupt changes in the cross-section of the combustion chamber. The combustion chamber of a solid rocket motor is typically a slender, near-cylindrical acoustic cavity, and its first few longitudinal acoustic modes are the most important in describing the acoustic vibrations within the cavity. When the boundary shape of the combustion chamber is complex, solving the acoustic wave equation analytically becomes difficult. Furthermore, because the temperature distribution within the combustion chamber is non-uniform and time-varying during combustion flow, and this non-uniformity is not considered in the acoustic frequency calculation formula, the acoustic mode frequencies calculated using analytical formulas are essentially constant values ​​throughout the combustion process. Moreover, in actual engines, the sound pressure within the combustion chamber is often not just a single acoustic mode distribution, but a weighted superposition of all acoustic modes at their corresponding frequencies, sometimes even exhibiting mixed mode distributions. Therefore, analytical methods are far from meeting the needs of engine engineers, necessitating numerical calculations. The finite element method (FEM) is an effective computational analysis tool, with the advantages of adapting well to the mesh generation and calculation of complex and varied geometries within the propellant cavity, and reliable calculation accuracy. The lack of experimental verification for finite element method (FEM) simulations of combustion chamber acoustic modes under high-temperature test conditions leads to low calculation accuracy. Currently, numerous experiments and simulations have been conducted both domestically and internationally, using sound sources placed inside the combustion chamber at ambient temperature and pressure to create acoustic cavities. In these ambient temperature and pressure tests, the speed of sound in air is clearly defined as 340 m / s, resulting in high simulation accuracy. However, engine test conditions are characterized by high temperature and pressure, and the presence of numerous condensed particles in the combustion gas introduces errors in sound velocity calculations, leading to significant errors in finite element simulations. Therefore, a method is urgently needed to obtain acoustic mode testing and identification methods during solid rocket engine test processes, providing accuracy verification for simulation analysis. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a method for acoustic mode identification during solid rocket engine testing. This method can obtain the axial frequency and mode shape of the combustion chamber acoustic cavity at different times during engine testing and can be used to verify the accuracy of engine acoustic cavity frequency simulation analysis during testing.

[0005] The solution of this invention is: a method for acoustic mode identification during solid rocket engine testing, comprising the following steps:

[0006] Based on finite element analysis, the acoustic modes of the combustion chamber of the test engine were initially simulated and estimated. According to the estimated vibration mode distribution, a reasonable number and position of pressure measuring points were arranged along the axial direction of the combustion chamber of the test engine to ensure that the position and number of measuring points could fully cover the low-order axial acoustic vibration modes of the engine cavity.

[0007] When the engine is working, it generates instantaneous high pressure in the combustion chamber through pulse excitation, which excites the pressure oscillation in the combustion chamber. The pressure time domain signal during the engine operation is obtained by using pressure measuring points, and the neighbor averaging method is used for filtering to filter out the DC component and distinguish the dynamic pressure signal.

[0008] Fast Fourier Transform was performed on the dynamic pressure signals at each measuring point to obtain the frequencies, phases, and amplitudes of each order. Then, time-domain analysis was performed on the dynamic pressure signals at each measuring point: short-time Fourier Transform was performed based on the Hanning window function to obtain the time-varying forms of each order frequency.

[0009] The axial vibration mode of the engine combustion chamber is obtained by fitting the phase and amplitude of all measuring points at each frequency.

[0010] A discrete time-point combustion chamber combustion surface configuration is constructed, and acoustic modal finite element analysis is performed on the combustion chamber combustion surface configuration to obtain the frequencies and mode shapes of the engine combustion chamber acoustic cavity. Based on the time-varying form of the frequencies and the axial mode shapes of the engine combustion chamber, the frequencies and mode shapes of the acoustic cavity are checked to ensure that the acoustic modal finite element analysis model meets the set calculation accuracy requirements.

[0011] Furthermore, before performing preliminary simulation and estimation of the acoustic modes of the test engine combustion chamber based on finite element analysis, the following steps are also performed: calculating the engine combustion chamber thermodynamic parameters, including specific heat ratio, mixed molecular weight, and combustion chamber temperature, based on the test engine propellant formulation and internal ballistic performance, for use in the finite element analysis.

[0012] Furthermore, the pressure measurement point uses a sensor with a pressure test error of no more than 0.5% and a sampling frequency of no less than 10kHz.

[0013] Furthermore, the neighbor averaging method is used for filtering to remove the DC component and distinguish the dynamic pressure signal. Specifically, this includes calculating the neighbor average value using the movemean function in MATLAB data processing software as follows: smoothed_data = movemean(data,k), where smoothed_data represents the filtered pressure data, data represents the test pressure data during engine operation, and k is the size of the filtering window. The selection principle for the size of the filtering window is to smooth the data while retaining the details of the data, especially during the secondary excitation process of engine operation, where the time is only in milliseconds and the data during the secondary excitation needs to be retained.

[0014] The dynamic pressure data is obtained by subtracting the filtered pressure data (smoothed_data) from the test pressure data (data).

[0015] Furthermore, the step of obtaining the time-varying form of each frequency order based on the short-time Fourier transform using the Hanning window function specifically includes:

[0016] The engine operating time is segmented according to the following rules: a fast Fourier transform is performed on the pressure curve during engine testing to obtain the frequency domain result. The frequencies of the pressure oscillation segments overlap. The oscillation segments are identified according to the pressure curve. The oscillation segments are then divided into multiple segments based on the oscillation start, middle and end. After segmentation, a fast Fourier transform is performed on the segmented dynamic pressure signal again. If the frequencies still overlap, the time period is further subdivided.

[0017] After segmentation, the dynamic pressure signal at each measuring point is subjected to STFT short-time Fourier transform. The window function is selected as the Hanning window to reduce spectral leakage, and the frequency value of the characteristic time period after segmentation is obtained.

[0018] The mathematical expression for the Hanning window is as follows:

[0019]

[0020] in, This is the index of the window function. The length of the window function. This is the value of the window function at index n.

[0021] Furthermore, the fitting process for obtaining the axial vibration mode of the engine combustion chamber specifically includes: based on the single-degree-of-freedom vibration principle, performing FFT transformation on the dynamic pressure signals of each measuring point for the same time period to obtain the oscillation amplitude and phase at each frequency; for each frequency, connecting the oscillation amplitude and phase corresponding to each measuring point within the selected time period and normalizing the oscillation amplitude to obtain the axial vibration mode of each order.

[0022] Furthermore, the verification of the frequencies and mode shapes of the acoustic cavity to ensure that the acoustic modal finite element analysis model meets the set calculation accuracy requirements specifically includes:

[0023] (1) Based on the combustion surface shift law, determine the characteristic time points in the engine working process, construct the combustion surface configuration of the engine combustion chamber at discrete time points, and conduct combustion chamber acoustic cavity analysis at characteristic time points based on the acoustic modal finite element analysis model.

[0024] (2) Based on the propellant formulation and the internal ballistic performance of the engine, thermodynamic calculations were performed using NASA CEA software to obtain the content of condensed particles, molar mass, gas phase gas molar mass, specific heat ratio and gas temperature in the combustion products, and to calculate the sound velocity c required for the combustion chamber acoustic cavity analysis at characteristic moments.

[0025] (3) The calculated sound velocity c is used as the input of the acoustic modal finite element analysis model. The combustion chamber acoustic cavity is re-analyzed at characteristic moments for the combustion surface configuration of the engine combustion chamber. The frequencies and mode shapes of the acoustic cavity are obtained. Based on the time-varying form of the frequencies and the axial mode shape of the engine combustion chamber, steps (2) to (3) are repeated until the frequencies and mode shapes of the acoustic cavity meet the set calculation accuracy requirements.

[0026] Furthermore, the method for calculating the speed of sound c is as follows:

[0027]

[0028] in k For specific heat ratio, R Let be the gas constant of the fuel gas. , R g The molar gas constant, M g The molar mass of the mixed gas containing condensed phase particles. T This refers to the gas temperature.

[0029] Furthermore, the set calculation accuracy requirements include:

[0030] Compared with the frequency values ​​of the segmented characteristic time periods, the acoustic cavity frequency calculation error is ≤3%; the mode shape is consistent with the axial mode shape of the engine combustion chamber.

[0031] The beneficial effects of this invention compared to the prior art are:

[0032] This invention performs multi-point testing of the axial pressure distribution in the combustion chamber during test engine operation, identifies the dynamic pressure signal, and processes the data. The dynamic pressure is then analyzed to obtain the time and frequency domain information of the acoustic modes in the combustion chamber. This allows for the accurate acquisition of the frequencies and mode shapes of the acoustic cavity in the combustion chamber, providing experimental verification for improving the accuracy of acoustic mode simulation calculations and thus providing theoretical support for predicting unstable combustion in engines. Attached Figure Description

[0033] Figure 1 This is a flowchart of an acoustic mode identification method for a solid rocket engine during test firing according to the present invention.

[0034] Figure 2 This is a schematic diagram of the arrangement of pressure measuring points on the test engine in an embodiment of the present invention;

[0035] Among them, 1-test engine, 2-pressure sensor;

[0036] Figure 3 This is a pressure distribution curve during the test run of an embodiment of the present invention;

[0037] Figure 4This is a schematic diagram of data filtering based on the neighborhood averaging method in an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of the frequency and amplitude obtained by FFT transformation in an embodiment of the present invention;

[0039] Figure 6 The curves showing the frequency variations over time obtained by STFT conversion in this embodiment of the invention are shown.

[0040] Figure 7 This is a schematic diagram of the axial vibration mode of the combustion chamber obtained by fitting an embodiment of the present invention;

[0041] The left figure shows the first-order vibration mode, and the right figure shows the second-order vibration mode.

[0042] Figure 8 The results of the axial first-order acoustic cavity frequency simulation calculation are shown in the embodiments of the present invention.

[0043] Figure 9 The results of the axial second-order acoustic cavity frequency simulation calculation are shown in the embodiments of the present invention.

[0044] Figure 10 The left side shows a comparison of the simulation and experimental vibration modes of this invention (first-order vibration mode).

[0045] Figure 10 The right side shows a comparison of the simulation and experimental vibration modes of this invention (second-order vibration mode). Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] like Figure 1 As shown, the present invention proposes a method for acoustic mode identification during solid rocket engine testing, comprising the following steps:

[0048] Step 1: Based on finite element analysis, perform preliminary simulation and prediction of the acoustic modes of the combustion chamber of the test engine. According to the predicted vibration mode distribution, arrange a reasonable number and position of pressure measuring points along the axial direction of the combustion chamber of the test engine to ensure that the position and number of measuring points can fully cover the low-order axial acoustic vibration modes of the engine cavity.

[0049] Step 2: When the engine is working, it generates instantaneous high pressure in the combustion chamber through pulse excitation, which excites the pressure oscillation in the combustion chamber. The pressure time domain signal during the engine operation is obtained by using pressure measuring points. The neighborhood averaging method is used for filtering to filter out the DC component and distinguish the dynamic pressure signal.

[0050] Step 3: Perform fast Fourier transform on the dynamic pressure signal at each measuring point to obtain the frequency, phase and amplitude of each order. Then, perform time-domain analysis on the dynamic pressure signal at each measuring point: perform short-time Fourier transform based on the Hanning window function to obtain the frequency variation over time.

[0051] Step 4: Fit the phase and amplitude of all measuring points at each frequency to obtain the axial vibration mode of the engine combustion chamber;

[0052] Step 5: Construct the combustion surface configuration of the engine combustion chamber at discrete time points, perform acoustic modal finite element analysis on the combustion surface configuration of the engine combustion chamber, obtain the frequencies and mode shapes of the acoustic cavity of the engine combustion chamber, and use the time variation of the frequencies obtained in Step 3 and the axial mode shapes of the engine combustion chamber obtained in Step 4 as the benchmark to check the frequencies and mode shapes of the acoustic cavity, so that the acoustic modal finite element analysis model meets the set calculation accuracy requirements.

[0053] Example 1

[0054] The acoustic mode identification method during engine testing in this embodiment includes the following steps:

[0055] Step 1: Calculate the engine combustion chamber thermodynamic parameters, including specific heat ratio, mixed molecular weight, and combustion chamber temperature, based on the propellant formulation and internal ballistic performance of the test engine. Using finite element analysis, perform preliminary simulation and prediction of the acoustic modes of the test engine combustion chamber acoustic cavity based on these thermodynamic parameters. Arrange a reasonable number and location of pressure measuring points along the axial direction of the test engine combustion chamber according to the predicted vibration mode distribution, ensuring that the location and number of measuring points fully cover the low-order axial acoustic vibration modes of the engine acoustic cavity. The low-order axial acoustic vibration modes generally do not exceed the third order. Figure 2 As shown.

[0056] In this embodiment, a high-precision fast-response pressure sensor is used for the pressure measurement point. The sensor pressure test error is no greater than 0.5%, and the sampling frequency is no less than 10kHz.

[0057] Step 2: When the engine is running, it generates instantaneous high pressure in the combustion chamber through pulse excitation, which induces pressure oscillation in the combustion chamber. The test curve is as follows: Figure 3 As shown; the pressure time-domain signal during engine operation is obtained using pressure measuring points. Post-processing of the pressure time-domain signal from each measuring point is performed using Matlab data processing software: the neighborhood averaging method is used for filtering to remove the DC component and distinguish the dynamic pressure signal, such as... Figure 4 As shown.

[0058] In step 2, the neighbor averaging method is used for filtering to remove the DC component and distinguish the dynamic pressure signal. Specifically, in MATLAB data processing software, the neighbor average value is calculated using the movemean function as follows: smoothed_data = movemean(data,k), where smoothed_data represents the filtered pressure data, data represents the test pressure data during engine operation, and k is the size of the filtering window. Choosing an appropriate filtering window size can smooth the data while preserving its details, especially during the secondary excitation process of engine operation, where the time is only in milliseconds, it is necessary to retain the data during the secondary excitation. The preferred window size is 200. Subtracting the filtered data smoothed_data from the test pressure data data data yields the dynamic pressure data, i.e., the distinguished dynamic pressure signal; see [link to relevant documentation]. Figure 4 .

[0059] Step 3: Perform Fast Fourier Transform (FFT) on the dynamic pressure signal at each measuring point to obtain the frequency, phase, and amplitude of each order, such as... Figure 5 As shown; secondly, time-domain analysis is performed: based on the Hanning window function, a short-time Fourier transform (STFT) is conducted to obtain the time-varying form of each frequency order, as shown in the figure. Figure 6 As shown.

[0060] In step 3, a short-time Fourier transform is performed based on the Hanning window function to obtain the frequency-time variation curves of each order, specifically as follows:

[0061] During engine operation, the frequency changes over time. After FFT transformation alone, adjacent frequency peaks tend to overlap, making them difficult to distinguish. To address this issue, the following processing method is proposed:

[0062] The engine operating time is segmented according to the following rules: a fast Fourier transform is performed on the pressure curve during engine testing to obtain the frequency domain result. The frequencies of the pressure oscillation segments overlap. The oscillation segments are identified according to the pressure curve. The oscillation segments are then divided into multiple segments based on the oscillation start, middle and end. After segmentation, a fast Fourier transform is performed on the segmented dynamic pressure signal again. If the frequencies still overlap, the time period is further subdivided.

[0063] After segmentation, the dynamic pressure signal at each measuring point is subjected to STFT (Short Time Fourier Transform). A Hanning window is selected as the window function to reduce spectral leakage, yielding the frequency values ​​of the characteristic time periods after segmentation. The mathematical expression for the Hanning window is:

[0064]

[0065] in, This is the index of the window function. The length of the window function. Let N be the value of the window function at index n. Since there is a lot of engine test data, a preferred solution is to set N to 1024.

[0066] Step 4: Based on the phase and amplitude of all measuring points at each frequency, the axial vibration mode of the engine combustion chamber is obtained through fitting, as shown in Table 1 and... Figure 7 As shown.

[0067] Table 1. Frequency values ​​obtained at different times during the experiment.

[0068]

[0069] The fitting process yielded the axial vibration mode of the engine combustion chamber, specifically as follows:

[0070] Based on the principle of single-degree-of-freedom vibration, the dynamic pressure signals of each measuring point are subjected to FFT transformation for the same time period to obtain the oscillation amplitude and phase at each frequency. For each frequency, within the selected time period, the oscillation amplitude and phase corresponding to each measuring point are connected and the oscillation amplitude is normalized to obtain the axial vibration mode of each order.

[0071] Step 5: Construct the combustion surface configuration of the engine combustion chamber at discrete time points, perform acoustic modal finite element analysis on the combustion surface configuration of the engine combustion chamber, obtain the frequencies and mode shapes of the acoustic cavity of the engine combustion chamber, and use the time variation of the frequencies obtained in Step 3 and the axial mode shapes of the engine combustion chamber obtained in Step 4 as the benchmark to check the frequencies and mode shapes of the acoustic cavity, so that the acoustic modal finite element analysis model meets the set calculation accuracy requirements.

[0072] Step 5 is as follows:

[0073] (501) Based on the idea of ​​“state solidification”, the characteristic time points in the engine working process are determined according to the law of combustion surface movement, and the combustion surface configuration of the engine combustion chamber at discrete time points is constructed. Based on the acoustic modal finite element analysis model, the combustion chamber acoustic cavity analysis of the combustion surface configuration of the engine combustion chamber at characteristic time is carried out.

[0074] (502) Based on the propellant formulation and the internal ballistic performance of the engine, thermodynamic calculations were performed using NASA CEA software to obtain the content of condensed particles, molar mass, gas phase gas molar mass, specific heat ratio and gas temperature in the combustion products, which were used to calculate the key input parameter, the speed of sound c.

[0075] The calculation of the sound velocity c must take into account the molecular weight of the gas mixture, which includes condensed particles. ,in, k For specific heat ratio, RLet be the gas constant of the fuel gas. , R g The molar gas constant, M g The molar mass of the mixed gas containing condensed phase particles. T This refers to the gas temperature.

[0076] (503) The calculated sound velocity c is used as the input of the acoustic modal finite element analysis model. The combustion chamber acoustic cavity is reanalyzed at characteristic moments to obtain the acoustic cavity frequencies and mode shapes. Based on the time variation of the frequencies obtained in step 3 and the axial mode shapes of the engine combustion chamber obtained in step 4, steps (502) to (503) are repeated until the acoustic cavity frequencies and mode shapes meet the set calculation accuracy requirements.

[0077] In this embodiment, the calculation accuracy requirements are as follows: compared with the "frequency value of the characteristic time period after segmentation" obtained in step 3, the calculation error of the acoustic cavity frequency is ≤3%; the mode shape is consistent with the axial mode shape of the engine combustion chamber obtained in step 4.

[0078] Figure 8 and Figure 9 The figures show the accuracy verification results of the axial first-order acoustic cavity frequency simulation calculation and the accuracy verification results of the axial second-order acoustic cavity frequency simulation calculation, respectively, according to embodiments of the present invention. Figure 8 The display shows that at 2 seconds, the first-order axial acoustic cavity frequency of the combustion chamber is 469Hz. Figure 9 The simulation results show that the second-order axial acoustic cavity frequency of the combustion chamber at 2 seconds is 923Hz, which meets the set calculation accuracy requirements. The comparison results of the simulation and experimental mode shapes are as follows: Figure 10 Left, Figure 10 As shown on the right.

[0079] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0080] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for acoustic mode identification during solid rocket engine testing, characterized in that, Includes the following steps: Based on finite element analysis, the acoustic modes of the combustion chamber of the test engine were initially simulated and estimated. According to the estimated vibration mode distribution, a reasonable number and position of pressure measuring points were arranged along the axial direction of the combustion chamber of the test engine to ensure that the position and number of measuring points could fully cover the low-order axial acoustic vibration modes of the engine cavity. When the engine is working, it generates instantaneous high pressure in the combustion chamber through pulse excitation, which excites the pressure oscillation in the combustion chamber. The pressure time domain signal during the engine operation is obtained by using pressure measuring points, and the neighbor averaging method is used for filtering to filter out the DC component and distinguish the dynamic pressure signal. Fast Fourier Transform was performed on the dynamic pressure signals at each measuring point to obtain the frequencies, phases, and amplitudes of each order. Then, time-domain analysis was performed on the dynamic pressure signals at each measuring point: short-time Fourier Transform was performed based on the Hanning window function to obtain the time-varying forms of each order frequency. The axial vibration mode of the engine combustion chamber is obtained by fitting the phase and amplitude of all measuring points at each frequency. A discrete time-point combustion surface configuration of the engine combustion chamber is constructed, and acoustic modal finite element analysis is performed on the combustion surface configuration of the engine combustion chamber to obtain the frequencies and mode shapes of the acoustic cavity of the engine combustion chamber. Based on the time-varying form of the frequencies and the axial mode shapes of the engine combustion chamber, the frequencies and mode shapes of the acoustic cavity are checked to ensure that the acoustic modal finite element analysis model meets the set calculation accuracy requirements. Before performing preliminary simulation and prediction of the acoustic modes of the combustion chamber of the test engine based on finite element analysis, the following steps are also performed: calculate the thermal parameters of the engine combustion chamber, including specific heat ratio, mixed molecular weight, and combustion chamber temperature, based on the propellant formulation and internal ballistic performance of the test engine, for use in the finite element analysis; The method of obtaining the time-varying form of each frequency order based on the short-time Fourier transform using the Hanning window function specifically includes: The engine operating time is segmented according to the following rules: a fast Fourier transform is performed on the pressure curve during engine testing to obtain the frequency domain result. The frequencies of the pressure oscillation segments overlap. The oscillation segments are identified according to the pressure curve. The oscillation segments are then divided into multiple segments based on the oscillation start, middle and end. After segmentation, a fast Fourier transform is performed on the segmented dynamic pressure signal again. If the frequencies still overlap, the time period is further subdivided. After segmentation, the dynamic pressure signal at each measuring point is subjected to STFT short-time Fourier transform. The window function is selected as the Hanning window to reduce spectral leakage, and the frequency value of the characteristic time period after segmentation is obtained. The mathematical expression for the Hanning window is as follows: in, This is the index of the window function. The length of the window function. The value of the window function at index n; The fitting process for obtaining the axial vibration mode of the engine combustion chamber specifically includes: based on the single-degree-of-freedom vibration principle, performing FFT transformation on the dynamic pressure signals of each measuring point for the same time period to obtain the oscillation amplitude and phase at each frequency; for each frequency, connecting the oscillation amplitude and phase corresponding to each measuring point within the selected time period and normalizing the oscillation amplitude to obtain the axial vibration mode of each order.

2. The method for acoustic mode identification during solid rocket engine testing according to claim 1, characterized in that, The pressure measurement point uses a sensor with a pressure test error of no more than 0.5% and a sampling frequency of no less than 10kHz.

3. The method for acoustic mode identification during solid rocket engine testing according to claim 1, characterized in that, The neighbor averaging method is used for filtering to remove the DC component and distinguish the dynamic pressure signal. Specifically, the neighbor average value is calculated using the movemean function in MATLAB data processing software as follows: smoothed_data = movemean(data,k), where smoothed_data represents the filtered pressure data, data represents the test pressure data during engine operation, and k is the size of the filtering window. The principle for selecting the size of the filtering window is to smooth the data while retaining the details of the data, especially during the secondary excitation process of engine operation, where the time is only in milliseconds and the data during the secondary excitation needs to be retained. The dynamic pressure data is obtained by subtracting the filtered pressure data (smoothed_data) from the test pressure data (data).

4. The method for acoustic mode identification during solid rocket engine testing according to claim 1, characterized in that, The verification of the acoustic cavity's frequencies and mode shapes ensures that the acoustic modal finite element analysis model meets the set calculation accuracy requirements, specifically including: (1) Based on the combustion surface shift law, determine the characteristic time points in the engine working process, construct the combustion surface configuration of the engine combustion chamber at discrete time points, and conduct combustion chamber acoustic cavity analysis at characteristic time points based on the acoustic modal finite element analysis model. (2) Based on the propellant formulation and the internal ballistic performance of the engine, thermodynamic calculations were performed using NASA CEA software to obtain the content of condensed particles, molar mass, gas phase gas molar mass, specific heat ratio and gas temperature in the combustion products, and to calculate the sound velocity c required for the combustion chamber acoustic cavity analysis at characteristic moments. (3) The calculated sound velocity c is used as the input of the acoustic modal finite element analysis model. The combustion chamber acoustic cavity is re-analyzed at characteristic moments for the combustion surface configuration of the engine combustion chamber. The frequencies and mode shapes of the acoustic cavity are obtained. Based on the time-varying form of the frequencies and the axial mode shape of the engine combustion chamber, steps (2) to (3) are repeated until the frequencies and mode shapes of the acoustic cavity meet the set calculation accuracy requirements.

5. The method for acoustic mode identification during solid rocket engine testing according to claim 4, characterized in that, The speed of sound c is calculated as follows: in k For specific heat ratio, R Let be the gas constant of the fuel gas. , R g The molar gas constant, M g The molar mass of the mixed gas containing condensed phase particles. T This refers to the gas temperature.

6. The method for acoustic mode identification during solid rocket engine testing according to claim 4, characterized in that, The set calculation accuracy requirements include: Compared with the frequency values ​​of the segmented characteristic time periods, the acoustic cavity frequency calculation error is ≤3%; the mode shape is consistent with the axial mode shape of the engine combustion chamber.

Images