A device and method for measuring the heat release rate of combustion based on ultrafast spectroscopy

Abstract

The application discloses a kind of based on ultrafast spectrum's combustion heat release rate measuring device and method, belong to combustion optical diagnostic technical field, including femtosecond light frequency comb, collimator, first beam splitter, first transmission grating, first lens, flame sample, displacement platform, second lens, second transmission grating, first mirror, second beam splitter, spatial light coupler, dispersive optical fiber, photoelectric detector, oscilloscope, computer, and second mirror is also set between first beam splitter to second beam splitter, reference sample cell.The application provides a kind of high time resolution test means for high-frequency combustion oscillation.

Description

Technical Field

[0001] This invention belongs to the field of combustion optical diagnostic technology, specifically relating to a device and method for measuring combustion heat release rate based on ultrafast spectroscopy. Background Technology

[0002] Combustion instability is a critical bottleneck problem that urgently needs to be solved in the development of liquid and solid rocket engines. It can lead to abrupt fluctuations in combustion chamber pressure and heat release, causing damage and ablation of engine components. Combustion instability involves research in multiple fields, including atomization, evaporation, mixing processes, chemical kinetics, and the acoustic characteristics of nozzles and combustion chambers, and is also affected by the supply system. For high-frequency combustion instability, it is generally considered to be the result of the coupled feedback of flow oscillations, heat release rate fluctuations, and combustion chamber pressure oscillations within the combustion chamber. Therefore, the heat release rate is a key parameter in this feedback loop during combustion instability analysis. Simultaneously, as a response term in the flame transfer function, the heat release rate plays an important role in solving the acoustic modes of the combustion chamber. To accurately describe the flame transfer function, it is necessary to measure the heat release rate fluctuations of various flames with high spatiotemporal resolution.

[0003] Currently, existing methods such as chemiluminescence, planar laser-induced fluorescence, and laser interferometry have achieved heat release rate measurement to some extent, providing effective means for obtaining the flame transfer function. However, in complex application environments, heat release rate measurement methods based on chemiluminescence and planar laser-induced fluorescence face two major challenges: first, the limitations of the measurement principle mean that these methods are mainly applicable to the measurement of premixed flames, and difficult to apply to the more common diffusion combustion modes; second, the spatiotemporal resolution of existing methods is still limited, making it difficult to meet the requirements for high temporal resolution measurement of turbulent combustion pulsed heat release rate. Laser interferometry, based on the relationship between combustion heat release rate and density, can achieve heat release rate measurement not limited to combustion modes.

[0004] For example, CN112326731A proposes a method for measuring combustion heat release rate. Based on laser interferometry, it uses a photomultiplier tube to detect changes in light intensity to calculate the density fluctuations of combustion gases, and then inverts the heat release rate fluctuations of the flame. Although this measurement method has a high time resolution, its time resolution is still limited by the sampling rate of the photomultiplier tube and is limited to single-point measurement. Another example is CN114061783A, which provides a high-frequency heat release rate fluctuation field measurement device and method based on Mach-Zehnder interferometry. It uses laser interferometry supplemented by a high-speed camera to measure density and then realizes two-dimensional measurement of heat release rate. However, the measurement rate of this method is also limited by the frame rate of the high-speed camera, making it difficult to achieve heat release rate measurement with higher time resolution. Therefore, it is urgent to develop a new heat release rate measurement method to advance the analysis and modeling of combustion instability in real combustion chambers and provide technical support for the development of high-thrust liquid rocket engines. Summary of the Invention

[0005] In view of this, the present invention provides a combustion heat release rate measurement device and method based on ultrafast spectroscopy, which has a faster measurement speed and can achieve high time resolution measurement of premixed and non-premixed combustion heat release rates.

[0006] The combustion heat release rate measurement device based on ultrafast spectroscopy provided by this invention adopts the following technical solution: It includes a femtosecond optical frequency comb, collimator, first beam splitter, first transmission grating, first lens, flame sample, displacement platform, second lens, second transmission grating, first reflector, second beam splitter, spatial optical coupler, dispersive fiber, photodetector, oscilloscope, and computer. A second reflector and a reference sample cell are also provided between the first and second beam splitters. During operation, a collimator positioned at the output end of the femtosecond optical frequency comb ensures that the incident light is horizontally incident on a first beam splitter with a splitting ratio of 50:50. The transmitted light from the first beam splitter serves as the measurement pulse, which, after dispersion by the first transmission grating, achieves spatial expansion of the broadband light source spectrum. The dispersed measurement pulse, after being collimated by the first lens, passes through a flame sample placed on a displacement platform, is converged by the second lens, and then incident on a second grating mirrored with the first grating, striking the first mirror at a 45° angle. The reflected measurement pulse is then perpendicularly incident on the second beam splitter with a splitting ratio of 50:50, and after reflection by the second beam splitter, it is incident on the space... Optical coupler; the reflected light from the first beam splitter is incident on the second mirror at a 45° angle. After reflection, the reference pulse passes through the reference sample cell and is incident perpendicularly on the second beam splitter, where it overlaps with the measurement pulse and interferes. After being transmitted through the second beam splitter, the light is incident on the spatial optical coupler. The output end of the spatial optical coupler is equipped with a dispersive fiber. The spatial optical coupler transmits the interference pulse to the dispersive fiber, which transmits the time-stretched interference signal to the photodetector. The photodetector converts the optical signal into an electrical signal, which is acquired by the oscilloscope. The oscilloscope outputs the signal to the computer, which calculates the combustion heat release rate based on the received interference signal. Furthermore: The femtosecond optical frequency comb is used to generate frequency-locked femtosecond pulsed lasers; The collimator is used to collimate the femtosecond pulse laser from the optical fiber into space; The first beam splitter is used to separate the probe pulse and the reference pulse; The first transmission grating is used to detect the spatial dispersion of the pulse; The first lens is used for collimation of spatial dispersion detection pulses to achieve a one-to-one mapping with spatial positions; The displacement platform is used to change the lateral position of the flame sample; The second lens is used to detect the convergence of pulses; The second transmission grating is used for combining spatial dispersion detection pulses; The first reflector is used to reflect the measurement pulse; The second mirror is used to reflect the reference pulse; The second beam splitter is used to combine the detection pulse and the reference pulse; The spatial optical coupler is used to couple the combined pulses into the dispersive fiber. The dispersive fiber is used to perform time-domain stretching of the combined pulses. The photodetector is used for photoelectric conversion of the broadened optical pulse; The oscilloscope is used to record the time-varying interference fringes of the two interference arms.

[0007] Furthermore, the flame sample is confined using a quartz tube to prevent the heat flow from interacting with the surrounding ambient air. Furthermore, the reference sample cell uses the same quartz tube as the one used to confine the flame sample.

[0008] Furthermore, the first beam splitter is a beam splitting prism or a semi-transparent, semi-reflective mirror; The second beam splitter is a beam splitter prism or a semi-transparent, semi-reflective mirror.

[0009] The present invention provides a method for measuring the heat release rate of combustion based on ultrafast spectroscopy, which employs the above-mentioned device for measuring the heat release rate of combustion based on ultrafast spectroscopy and includes the following steps: Step 1: Adjust the attitude of the flame sample, beam splitter, and reflector to ensure that the measurement optical path is collimated with the reference optical path; Step 2: Output time-varying interference fringes at different times using the oscilloscope (17). ,in For time; Step 3: Based on the time-frequency mapping relationship Convert the time-varying interference fringes into an interference spectrum. ,in For frequency, The center frequency of the femtosecond pulse. and These are the sum and length of the dispersive fiber, respectively; Step 4: Based on grating line density grating diffraction angle Diameter of the collimated beam incident on the grating The center wavelength of the femtosecond optical frequency comb and spectral bandwidth Determine spectral resolution and the number of distinguishable points This allows for the determination of the number of measurable spatial points;

[0010] Step 5: Analyze the interference spectrum corresponding to a specific spatial location. The time-domain spectrum is obtained by inverse Fourier transform to the time domain. :

[0011] in, For time variables, To measure the time delay difference between the optical path and the reference optical path, These are parameters related to the light source, and their values ​​are twice those obtained by the Fourier transform of the light source's power spectral density function. Let be the impact function; Step Six: Use a bandpass filter with a finite width to separate the peaks, input the frequency domain through Fourier transform, and calculate the phase using the arctangent function. :

[0012] in, The imaginary unit, Indicates the imaginary part. Indicates the real part; Step 7: Unpack the package to obtain Non-package value Then, the time delay along the optical path can be obtained by differentiation. Value:

[0013] Step 8: Based on the relationship between the refractive index of the combustion region and the time delay along the optical path, and the Gladstone-Dale law, correlate the time delay with the measured density change information of the combustion region, that is:

[0014] In the formula, It is the speed of light in a vacuum. It is the length of the flame area. The refractive index of the flame region, The refractive index of the air region. and These are the densities of the combustion zone and the surrounding atmosphere, respectively. It is approximated as unchanged. It is the Glaston-Dale constant; Step 9: Using the approximate relationship between heat release rate and density, obtain the heat release pulsation in the test flame area. :

[0015] in, The average speed of sound This is the specific heat capacity ratio.

[0016] Beneficial effects: 1. This invention can provide a high time-resolution testing method for high-frequency combustion oscillations, expand and deepen the understanding of combustion instability mechanisms, enrich experimental detection methods for unstable combustion in engines, and provide research support for the development of aero-engines and high-thrust liquid rocket engines.

[0017] 2. This invention constructs a Mach-Zehnder laser interferometer using a femtosecond optical frequency comb. Based on spectral coding technology, the broadband femtosecond optical frequency comb is spatially broadened into a line light source, achieving a one-to-one correspondence between spectral frequencies and space, enabling simultaneous measurement at multiple spatial locations. Based on time-domain stretching technology, ultrashort femtosecond pulses are dispersed into broadband pulses in the time domain, realizing frequency-time conversion. Spectral information is acquired using a photodetector, enabling continuous measurement with the repetition frequency of the femtosecond optical frequency comb as the refresh rate, greatly improving the time resolution of combustion heat release rate measurement.

[0018] 3. This invention utilizes optical frequency comb dispersive interference combined with Fourier transform algorithm to achieve high-precision demodulation of combustion heat release rate.

[0019] 4. This invention uses a quartz tube to confine the flame sample, isolate environmental interference, stabilize diffusion combustion, ensure the accuracy of the density signal of the non-premixed flame, and improve measurement precision.

[0020] 5. The quartz tube in the reference cell of this invention is the same as the quartz tube in the flame sample, which eliminates systematic errors in the optical path and improves measurement accuracy. Attached Figure Description

[0021] Figure 1 A schematic diagram illustrating the composition principle of a combustion heat release rate measurement device based on ultrafast spectroscopy provided by the present invention; Figure 2 A schematic diagram of a combustion heat release rate measurement process based on ultrafast spectroscopy provided by the present invention; Wherein: 1-Femtosecond optical frequency comb; 2-Collimator; 3-First beam splitter; 4-First transmission grating; 5-First lens; 6-Flame sample; 7-Displacement platform; 8-Second lens; 9-Second transmission grating; 10-First reflecting mirror; 11-Second reflecting mirror; 12-Reference sample cell; 13-Second beam splitter; 14-Spatial optical coupler; 15-Dispersive fiber; 16-Photodetector; 17-Oscilloscope; 18-Computer. Detailed Implementation

[0022] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] Example 1: Reference Figure 1A combustion heat release rate measurement device based on ultrafast spectroscopy includes a femtosecond optical frequency comb 1, a collimator 2, a first beam splitter 3 (which can be a beam splitter prism or a semi-transparent mirror), a first transmission grating 4, a first lens 5, a flame sample 6, a displacement platform 7, a second lens 8, a second transmission grating 9, a first reflector 10, a second reflector 11, a reference sample cell 12, a second beam splitter 13 (which can be a beam splitter prism or a semi-transparent mirror), a spatial optical coupler 14, a dispersive fiber 15, a photodetector 16, an oscilloscope 17, and a computer 18, wherein: Collimator 2 is located at the output end of femtosecond optical frequency comb 1 to ensure that the incident light is horizontally incident on the first beam splitter 3 with a splitting ratio of 50:50. The transmitted light from the first beam splitter 3 serves as a measurement pulse, which, after being dispersed by the first transmission grating 4, achieves spatial expansion of the broadband light source spectrum. The dispersed measurement pulse is collimated by the first lens 5, passes through the flame sample 6 set on the displacement platform 7, is converged by the second lens 8, and then incident on the second grating 9, which is mirrored with the first grating 4. The pulse is then incident on the first reflecting mirror 10 at a 45° angle. The reflected measurement pulse is then perpendicularly incident on the second beam splitter 13 with a splitting ratio of 50:50, and after being reflected by the second beam splitter 13, it is incident on the first beam splitter 10. The light reflected from the first beam splitter 3 is incident at a 45° angle onto the second mirror 11. After reflection, the reference pulse passes through the reference sample cell 12 and is incident perpendicularly onto the second beam splitter 13, where it overlaps with the measurement pulse and interferes. After being transmitted through the second beam splitter 13, the light is incident onto the spatial optical coupler 14. A dispersive fiber 15 is provided at the output end of the spatial optical coupler 14. The dispersive fiber 15 transmits the time-stretched interference signal to the photodetector 16. The photodetector 16 converts the optical signal into an electrical signal, which is acquired by the oscilloscope 17. The oscilloscope 17 outputs a signal to the computer 18 for subsequent data processing to calculate the combustion heat release rate.

[0024] Specifically, the femtosecond optical frequency comb 1 is used to generate frequency-locked femtosecond pulsed lasers; the collimator 2 is used to collimate the femtosecond pulsed lasers from the optical fiber into space; the first beam splitter 3 (beam splitter prism or semi-transparent mirror) is used to separate the probe pulse and the reference pulse; the first transmission grating 4 is used to detect the spatial dispersion of the pulse; the first lens 5 is used to collimate the spatial dispersion probe pulse, achieving a one-to-one mapping with the spatial position; the flame sample 6 is confined by a quartz tube to avoid the interaction of heat flow with the surrounding air (one end of the quartz tube is open, the other end is closed, and the quartz tube covers the flame); the displacement platform 7 is used to change the lateral position of the flame sample; the second lens 8 is used to converge the probe pulse; and the second transmission grating 9 is used to combine the spatial dispersion probe pulse. The first reflecting mirror 10 is used to reflect the measurement pulse; the second reflecting mirror 11 is used to reflect the reference pulse; the reference sample cell contains a quartz tube without flame, and the quartz tube 12 in the reference sample is the same as the quartz tube in the flame sample 6; the second beam splitter 13 (beam splitter prism or semi-transparent semi-reflective mirror) is used to combine the probe pulse and the reference pulse; the spatial optical coupler 14 is used to couple the combined pulse into the dispersive fiber; the dispersive fiber 15 is used to perform time-domain broadening of the combined pulse; the photodetector 16 is used for photoelectric conversion of the broadened optical pulse; the oscilloscope 17 is used to record the time-varying interference fringes of the two interferometer arms; and the computer 18 is used to calculate the combustion heat release rate information based on the received interference signal.

[0025] The two interferometer arms described above include a measuring arm and a reference arm. The measuring arm is the optical path containing the flame sample 6: femtosecond optical frequency comb 1 → collimator 2 → first beam splitter 3 (transmission) → first transmission grating 4 → first lens 5 → flame sample 6 → second lens 8 → second transmission grating 9 → first reflector 10 → second beam splitter 13 (reflection). The reference arm is the optical path containing the reference sample cell 12: first beam splitter 3 (reflection) → second reflector 11 → reference sample cell 12 → second beam splitter 13 (transmission). The two beams propagate along different paths and then recombine, producing interference fringes due to the optical path difference. The time-varying interference fringes recorded by the oscilloscope 17 are the result of the superposition of the light waves from the two interferometer arms, and their phase difference carries information about the density change in the combustion region. The dual interferometer arm design significantly improves measurement accuracy by compensating for system errors (such as vibration and temperature drift) through the reference arm.

[0026] In this embodiment, the probe pulse is diffracted by the transmission grating. Different frequencies have different diffraction angles, and the same spectral component is focused on a point in space by a lens to form a one-dimensional linear array spot, thereby realizing the spatial separation of the spectrum and making the spectral frequency correspond one-to-one with the spatial position. Combined with a one-dimensional displacement platform, two-dimensional scanning test is realized.

[0027] The quartz tube encloses the flame under test. Its core function is to physically isolate the combustion zone from the outside air, preventing uncontrolled convection or diffusion of flame heat flow with external gases, and ensuring that the combustion process is in a stable and controllable state. In diffusion combustion (non-premixed flame) measurements, this design can accurately capture density pulsations within the combustion zone, avoiding measurement distortion caused by environmental interference. The reference sample cell 12 uses the exact same quartz tube structure as the flame sample 6, ensuring that the optical paths (such as tube wall refraction and transmission loss) in the two interferometer arms are completely consistent except for the flame region. The quartz tube of the reference sample cell 12 contains normal air (non-combustion gas), and its optical path delay is used as a reference value. It is compared with the flame path delay of the measurement arm to accurately extract the pure optical phase change caused by the flame.

[0028] After the pulses are bundled, they are coupled into a dispersive fiber. Because light travels at different speeds in the medium, light of different frequencies arrives at the detector at different times, thus broadening the ultrashort femtosecond pulses in the time domain into wide pulses on the order of hundreds of nanoseconds.

[0029] Example 2: Reference Figure 1 and Figure 2 Based on the above embodiment one, a method for measuring combustion heat release rate based on ultrafast spectroscopy is provided, including: Step 1: Adjust the attitude of the flame under test, beam splitter, and reflector to ensure that the measurement optical path is collimated with the reference optical path; Step 2: Output time-varying interference fringes at different times using the oscilloscope (17). ,in For time; Step 3: Based on the time-frequency mapping relationship Convert the time-varying interference fringes into an interference spectrum. ,in For frequency, The center frequency of the femtosecond pulse. and These are the sum and length of the dispersive fiber, respectively; Step 4: Based on grating line density grating diffraction angle Diameter of the collimated beam incident on the grating The center wavelength of the femtosecond optical frequency comb and spectral bandwidth Determine spectral resolution and the number of distinguishable points This allows for the determination of the number of measurable spatial points;

[0030] Step 5: Analyze the interference spectrum corresponding to a specific spatial location. The time-domain spectrum is obtained by inverse Fourier transform to the time domain. :

[0031] in, For time variables, To measure the time delay difference between the optical path and the reference optical path, These are parameters related to the light source, and their values ​​are twice those obtained by the Fourier transform of the light source's power spectral density function. Let be the impact function; Step Six: Use a bandpass filter with a finite width to separate the peaks, input the frequency domain through Fourier transform, and calculate the phase using the arctangent function. :

[0032] in, The imaginary unit, Indicates the imaginary part. Indicates the real part; Step 7: Unpack the package to obtain Non-package value Then, the time delay along the optical path can be obtained by differentiation. Value:

[0033] Step 8: Based on the relationship between the refractive index of the combustion region and the time delay along the optical path, and the Gladstone-Dale law, correlate the time delay with the measured density change information of the combustion region, that is:

[0034] In the formula, It is the speed of light in a vacuum. It is the length of the flame area. The refractive index of the flame region, The refractive index of the air region. and These are the densities of the combustion zone and the surrounding atmosphere, respectively. It is approximated as unchanged. It is the Glaston-Dale constant; Step 9: Using the approximate relationship between heat release rate and density, obtain the heat release pulsation in the test flame area. :

[0035] in, The average speed of sound This is the specific heat capacity ratio.

[0036] The above formula can be used to determine the changes in heat release pulsation in the test flame area by measuring the direction of light propagation.

[0037] This invention constructs a Mach-Zehnder laser interferometer system using a femtosecond optical frequency comb, and utilizes optical frequency comb dispersive interference combined with spectral coding, time-domain stretching, and Fourier transform algorithms to achieve high-precision demodulation of combustion heat release rate.

[0038] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., 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 device for measuring the heat release rate of combustion based on ultrafast spectroscopy, characterized in that, The system includes a femtosecond optical frequency comb (1), a collimator (2), a first beam splitter (3), a first transmission grating (4), a first lens (5), a flame sample (6), a displacement platform (7), a second lens (8), a second transmission grating (9), a first reflector (10), a second beam splitter (13), a spatial optical coupler (14), a dispersive fiber (15), a photodetector (16), an oscilloscope (17), and a computer (18). A second reflector (11) and a reference sample cell (12) are also provided between the first beam splitter (3) and the second beam splitter (13). The femtosecond optical frequency comb (1) is used to generate frequency-locked femtosecond pulse laser; The collimator (2) is used to collimate the femtosecond pulse laser from the optical fiber into space; The first beam splitter (3) is used to separate the probe pulse and the reference pulse; The first transmission grating (4) is used to detect the spatial dispersion of the pulse; The first lens (5) is used for collimation of spatial dispersion detection pulses to achieve a one-to-one mapping with spatial positions; The displacement platform (7) is used to change the lateral position of the flame sample; The second lens (8) is used to detect the convergence of pulses; The second transmission grating (9) is used for combining spatial dispersion detection pulses; The first reflector (10) is used to reflect the measurement pulse; The second reflector (11) is used to reflect the reference pulse; The second beam splitter (13) is used to combine the probe pulse and the reference pulse; The spatial optical coupler (14) is used to couple the combined pulse into the dispersive fiber; The dispersive fiber (15) is used to stretch the pulses after they are bundled in the time domain. The photodetector (16) is used for photoelectric conversion of the broadened light pulse; The oscilloscope (17) is used to record the time-varying interference fringes of the two interference arms; During operation, the collimator (2) set at the output end of the femtosecond optical frequency comb (1) causes the incident light to be horizontally incident on the first beam splitter (3) with a splitting ratio of 50:50; the transmitted light from the first beam splitter (3) serves as the measurement pulse, and the spatial expansion of the broadband light source spectrum is achieved by the dispersion effect of the first transmission grating (4); the dispersed measurement pulse is collimated by the first lens (5) and passes through the flame sample (6) set on the displacement platform (7), and is converged by the second lens (8) and incident on the second transmission grating (9) set mirror to the first transmission grating (4) and incident on the first reflector (10) at a 45° angle; the reflected measurement pulse is incident perpendicularly on the second beam splitter (13) with a splitting ratio of 50:50, and is incident on the spatial optical coupler (14) after being reflected by the second beam splitter (13); the first The reflected light from the beam splitter (3) is incident on the second mirror (11) at a 45° angle. After reflection, the reference pulse passes through the reference sample cell (12) and is incident perpendicularly on the second beam splitter (13). It overlaps with the measurement pulse and interferes. After being transmitted through the second beam splitter (13), it is incident on the spatial optical coupler (14). The output end of the spatial optical coupler (14) is provided with a dispersive fiber (15). The spatial optical coupler (14) transmits the interference pulse to the dispersive fiber (15). The dispersive fiber (15) transmits the time-stretched interference signal to the photodetector (16). The photodetector (16) converts the optical signal into an electrical signal, which is collected by the oscilloscope (17). The oscilloscope (17) outputs the signal to the computer (18). The computer (18) calculates the combustion heat release rate based on the received interference signal.

2. The combustion heat release rate measuring device based on ultrafast spectroscopy according to claim 1, characterized in that, The flame sample (6) is confined by a quartz tube to prevent the heat flow from interacting with the surrounding air.

3. The combustion heat release rate measuring device based on ultrafast spectroscopy according to claim 1, characterized in that, The reference sample cell (12) uses the same quartz tube as the one used to confine the flame sample (6).

4. A combustion heat release rate measuring device based on ultrafast spectroscopy according to claim 1 or 2, characterized in that, The first beam splitter (3) is a beam splitter prism or a semi-transparent and semi-reflective mirror; The second beam splitter (13) is a beam splitter prism or a semi-transparent and semi-reflective mirror.

5. A method for measuring combustion heat release rate based on ultrafast spectroscopy, characterized in that, The combustion heat release rate measuring device based on ultrafast spectroscopy according to any one of claims 1 to 3 includes: Step 1: Adjust the attitude of the flame sample, beam splitter, and reflector to ensure that the measurement optical path is collimated with the reference optical path; Step 2: Output time-varying interference fringes at different times using the oscilloscope (17). ,in For time; Step 3: Based on the time-frequency mapping relationship Convert time-varying interference fringes into an interference spectrum ,in For frequency, The center frequency of the femtosecond pulse. and These are the sum and length of the dispersive fiber, respectively; Step 4: Based on grating line density grating diffraction angle Diameter of the collimated beam incident on the grating The center wavelength of the femtosecond optical frequency comb and spectral bandwidth Determine spectral resolution and the number of distinguishable points This allows for the determination of the number of measurable spatial points; Step 5: Analyze the interference spectrum corresponding to a specific spatial location. The time-domain spectrum is obtained by inverse Fourier transform to the time domain. : in, For time variables, To measure the time delay difference between the optical path and the reference optical path, These are parameters related to the light source, and their values ​​are twice those obtained by the inverse Fourier transform of the light source's power spectral density function. Let be the impact function; Step Six: Use a bandpass filter with a finite width to separate the peaks, input the frequency domain through Fourier transform, and calculate the phase using the arctangent function. : in, The imaginary unit, Indicates the imaginary part. Indicates the real part; Step 7: Unpack the package to obtain Non-wrapped phase value Then, the time delay along the optical path can be obtained by differentiation. Value: Step 8: Based on the relationship between the refractive index of the combustion region and the time delay along the optical path, and the Gladstone-Dale law, correlate the time delay with the measured density change information of the combustion region, that is: In the formula, It is the speed of light in a vacuum. It is the length of the flame area. The refractive index of the flame region, The refractive index of the air region. and These are the densities of the combustion zone and the surrounding atmosphere, respectively. Approximately unchanged, It is the Glaston-Dale constant; Step 9: Using the approximate relationship between heat release rate and density, obtain the heat release pulsation in the test flame area. : in, The average speed of sound This is the specific heat capacity ratio.

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