CN109061220A - A kind of air-flow two-dimension speed distribution measurement method based on laser absorption spectrum chromatography imaging technique - Google Patents
A kind of air-flow two-dimension speed distribution measurement method based on laser absorption spectrum chromatography imaging technique Download PDFInfo
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- 238000000034 method Methods 0.000 claims abstract description 21
- 239000011159 matrix material Substances 0.000 claims abstract description 12
- 230000035945 sensitivity Effects 0.000 claims abstract description 12
- 238000005259 measurement Methods 0.000 claims description 24
- 238000003325 tomography Methods 0.000 claims description 21
- 238000010521 absorption reaction Methods 0.000 claims description 20
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- 238000012804 iterative process Methods 0.000 claims description 3
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- 238000002591 computed tomography Methods 0.000 abstract 1
- 238000002835 absorbance Methods 0.000 description 4
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
- G01P5/26—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft by measuring the direct influence of the streaming fluid on the properties of a detecting optical wave
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P5/00—Measuring speed of fluids, e.g. of air stream; Measuring speed of bodies relative to fluids, e.g. of ship, of aircraft
- G01P5/001—Full-field flow measurement, e.g. determining flow velocity and direction in a whole region at the same time, flow visualisation
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Abstract
The present invention provides a kind of air-flow two-dimension speed distribution measurement method based on laser absorption spectrum chromatography imaging technique, and be divided into following steps: 1. obtain the laser absorption spectrum data for projection of multiple and different angles；2. by the tested region discretization and the sensitivity matrix of computed tomography；3. establishing equation group according to the laser absorption spectrum data for projection of laser absorption spectrum Doppler frequency shift principle and the different angle；4. solving the Nonlinear System of Equations obtains VELOCITY DISTRIBUTION.Method proposed by the present invention can be measured and be rebuild the two-dimension speed distribution of air-flow by non-contacting mode, and strong applicability, high reliablity have very extensive application prospect.
Description
Technical Field
The invention relates to an airflow two-dimensional velocity distribution measuring method based on a laser absorption spectrum tomography technology, mainly comprising a method for measuring and reconstructing the distribution of airflow velocity on a two-dimensional plane by using the laser absorption spectrum tomography technology, and relates to the fields of the laser absorption spectrum velocity measurement technology, the tomography technology and the like.
Background
The laser absorption spectrum measurement technology is an important technology for measuring gas environment state parameters, and is widely applied to various fields of industrial process detection, combustion detection, atmospheric environment monitoring and the like. Researchers have conducted studies on gas temperature, component concentration, gas flow velocity, etc. on a single path using laser absorption spectroscopy. In combination with a tomography (also called tomography) technology, researchers also realize the measurement and reconstruction of two-dimensional distribution of parameters such as gas temperature, component concentration and the like, however, reports on the measurement and reconstruction of gas flow velocity distribution by using a laser absorption spectrum are not available, and the invention provides a feasible method for the measurement and reconstruction of the gas flow two-dimensional velocity distribution by using the laser absorption spectrum.
The basic physical principle on which laser absorption spectroscopy relies is the Beer-Lambert law, which states that the incident light at a frequency v has a light intensity Iin(v) when the laser passes through a gas environment with a length of L, specific gas molecules can absorb the light intensity, so that the emergent light intensity is attenuated, and the absorption rate tau (v) is as follows:
where l is the position of the laser interaction with the substance, T is the temperature, S (T) is the linear intensity function, P is the pressure, X is the concentration of the component corresponding to the gas molecule that produces the absorption,is a linear function of the absorption spectrum. (1) The equation formally expresses the integral of the gas state parameter over the path, and the absorbance τ (v) is mathematically considered as a projection onto the path L. The relation is the same as the mathematical form of the tomography technology, so the laser absorption spectrum technology and the tomography technology can be combined to realize the measurement and reconstruction of the gas state parameter distribution on the two-dimensional plane. According to the method described in the article "Development of an afan-beam TDLAS-based tomogrAN _ SNhic sensor for rapid imaging of temporal and concentration" (Optics express.2015.23(17):22494-22511.), the distribution of the absorption spectrum local integrated absorbances can be accurately reconstructed when different absorbancy measurements are obtained from multiple viewing angles, in the form:
A(l)＝P(l)X(l)S(T(l)), (2)
this enables further reconstruction of the velocity profile.
According to the principle of single-view laser absorption spectrum velocity measurement, when laser passes through the measured airflow, the airflow velocity can make the linear function of the absorption spectrumThe central wavelength of (2) produces a doppler shift effect, which causes a change in the linear function, which is further transferred to the absorbance by the relationship of equation (1), causing a change in the absorbance. Equation (1) also shows that the change of the absorption rate caused by the airflow speed is also related to the path integral, so that the two-dimensional distribution of the airflow speed can be measured and reconstructed by combining the tomography technology.
Based on the background, the invention provides a method for measuring the two-dimensional velocity distribution of an airflow based on a laser absorption spectrum tomography technology, which realizes the measurement and reconstruction of the two-dimensional velocity distribution of the airflow by obtaining the measured values of the absorption rate of the laser absorption spectrum at a plurality of angles and combining the tomography technology.
Disclosure of Invention
Aiming at a non-uniform flowing gas environment, the invention provides a gas flow two-dimensional velocity distribution measuring method based on a laser absorption spectrum tomography technology, and the adopted scheme is as follows:
step 1, acquiring laser absorption spectrum projection data of a plurality of different angles: selecting an absorption spectral line of a known gas molecule in gas flow, utilizing a laser beam which corresponds to the absorption spectral line of the gas molecule and has a frequency of v to respectively pass through two-dimensional measured areas through which the gas flow flows from different angles, enabling the gas molecule and the laser beam to interact to generate laser absorption spectrum projection data corresponding to the absorption spectral line of the gas molecule, assuming that the laser beams at different angles have M in total, distinguishing the laser beams at different angles by a label M, and recording the projection data generated by the mth laser beam as taum(ν)；
Step 2, discretizing the detected region and calculating a sensitivity matrix of tomography: according to the resolution requirement of tomography, the two-dimensional measured area is discretely divided into N different grids, the different grids are distinguished by the labels N, and the optical path length l of the mth laser beam passing through the nth grid can be calculated according to the geometrical relationship between the laser beams with different angles and the gridsmnAccording to the temperature T of said air flow in said gridnPressure PnComponent concentration XnThe state parameters are equal and the optical path is combined, so that the sensitivity matrix component A corresponding to the mth laser beam passing through the nth grid can be calculatedmnThe calculation formula is as follows:
Amn＝lmn×Pn×Xn×S(Tn), (3)
wherein, S (T) is a line intensity function corresponding to the gas molecule absorption spectrum line, and the sensitivity matrix components are sequentially arranged according to the labels m and n to obtain the sensitivity matrix of the tomography:
A＝[Amn]M×N； (4)
step 3, establishing an equation set according to the Doppler frequency shift principle of the laser absorption spectrum and the projection data of the laser absorption spectrum at different angles: establishing a planar rectangular coordinate system xOy on a plane where the two-dimensional measured area is located, wherein the included angle between the mth laser beam and the positive direction of the x axis of the planar rectangular coordinate system is thetamThen, the direction vector of the mth laser beam can be expressed as:
nm＝(cosθm,cosθm,0), (5)
assuming that the x-direction and y-direction velocity components of the airflow in the nth grid corresponding to the rectangular coordinate system of the plane are respectivelyAndthe gas flow doppler shifts the laser absorption spectrum produced by the mth laser beam in the nth grid by:
wherein, vCIs the center frequency of the gas molecule absorption line, c is the speed of light; suppose that the frequency shift in the nth grid due to other factors is Δ νnThe line function of the absorption line resulting from the passage of the mth laser beam through the nth grid is:
wherein σn、γnIs two unknown parameters of said linear functionThe mathematical form of (a) is:
assuming that there are J measurement points of different frequencies in the actual measurement and the measurement points of different frequencies are distinguished by the reference number J, the linear function of the absorption line produced by the mth laser beam passing through the nth grid is measured at the jth frequency at the measurement point vjThe linear function values above are:
according to the basic principle of laser absorption spectrum technology, the absorption spectrum line is measured at the jth frequency measurement point v by the mth laser beamjThe projection values of (d) are:
to be provided withΔνn、σn、γnFor unknowns, using the quantitative relationship described by equation (10), a nonlinear system of equations of the form:
step 4, solving the nonlinear equation system to obtain the velocity distribution: the nonlinear equation set (11) has J × M nonlinear equations, which can be solved by a numerical method, and the nonlinear equation set (11) is solved by an equivalent nonlinear optimization problem as follows:
wherein,is that the obtained linear function generated by the mth laser beam passing through the nth grid in the iterative process of solving the nonlinear optimization problem (12) is used for measuring the j frequency measurement point vjCalculation of linear function values, if global optimization algorithms are used, for calculatingWill gradually converge to a solution of said system of non-linear equations (11), including the two-dimensional components of said velocity profile, and vector-synthesizing the two-dimensional components of said velocity profile to obtain the velocity profile of said gas flow in said two-dimensional plane.
The two-dimensional velocity distribution of the air flow shown in fig. 4 is reconstructed by using the method for measuring the two-dimensional velocity distribution of the air flow. In fig. 4, the change in gradation indicates the magnitude of the velocity in [ m/sec ], and the white arrow indicates the direction of the velocity. The image shown in fig. 5 is a reconstructed two-dimensional velocity distribution image of the air flow, the gray scale change still indicates the magnitude of the velocity in meters/second, and the white arrow still indicates the direction of the velocity. Comparing the two images shows that the two-dimensional velocity distribution of the air flow obtained by the measuring method of the two-dimensional velocity distribution of the air flow is consistent with the given distribution no matter the size or the direction of the two-dimensional velocity distribution of the air flow, which shows that the measuring method of the two-dimensional velocity distribution of the air flow is effective.
Drawings
FIG. 1 is a schematic view of parallel laser beams covering a square measured area, comprising 15 projection angles, each angle having 15 parallel laser beams;
in FIG. 2, the square area is divided into 10 × 10 grids, and the angle between the m-th beam and the positive direction of the x-axis is θmThe optical path length through the nth mesh is lmn；
FIG. 3 is a schematic diagram of the geometrical relationship between the in-plane component of the airflow velocity in the nth grid and the mth beam;
FIG. 4 is a given two-dimensional velocity profile image;
fig. 5 is a two-dimensional velocity distribution of an air flow reconstructed using the method for measuring a two-dimensional velocity distribution of an air flow.
Detailed Description
In this embodiment, the distribution of state parameters in a square region is given, the whole region is divided into 10 × 10 grids, numerical simulation is performed by using a parallel beam laser absorption spectral tomography method, and the reconstruction result of the velocity distribution is given.
The following further describes embodiments of the present invention with reference to the drawings.
Step 1, selecting center frequency of 7444cm-1Nearby H2And (4) researching the molecular spectral line, obtaining characteristic parameters of the spectral line according to a HITRAN database, and calculating a line intensity function S (T) of the spectral line.
Step 2, the square area is uniformly divided into 10 x 10 grids given the temperature, pressure, water vapor concentration, air flow velocity, non-doppler shift, line type function, etc. in the square area, and the state parameters are uniform in each grid. The square area is covered with a parallel laser beam as shown in fig. 1. There are a total of 15 projection angles in figure 1,there are 15 parallel laser beams per angle, so the total number of laser beams used for the entire measurement process is 225. As shown in fig. 2, the optical path of the mth laser beam through the nth grid is lmn. According to the temperature T of the air flow in the gridnPressure PnComponent concentration XnThe state parameters are equal and the optical path is combined, so that the sensitivity matrix component A corresponding to the mth laser beam passing through the nth grid can be calculatedmnThe calculation formula is as follows:
Amn＝lmn×Pn×Xn×S(Tn), (13)
and sequentially arranging the sensitivity matrix components according to the labels m and n to obtain the sensitivity matrix of the tomography:
A＝[Amn]255×100(14)
and 3, as shown in fig. 2, establishing a planar rectangular coordinate system xOy on the plane where the square region is located, and taking a straight line where two adjacent sides of the square are located as two coordinate axes of the coordinate system. The included angle between the mth laser beam and the positive direction of the x axis of the plane rectangular coordinate system is thetamThen, the direction vector of the mth laser beam can be expressed as:
nm＝(cosθm,cosθm,0), (15)
as shown in fig. 3, the x-direction and y-direction velocity components of the airflow in the nth grid corresponding to the rectangular coordinate system areAndthe gas flow doppler shifts the laser absorption spectrum produced by the mth laser beam in the nth grid by:
wherein, vCIs the center frequency of the gas molecule absorption line, c is the speed of light; the non-Doppler-effect induced frequency shift in the given nth grid is DeltavnThe line function of the absorption line resulting from the passage of the mth laser beam through the nth grid is:
wherein σn、γnIs a parameter of said given linear function, said linear functionThe mathematical form of (a) is:
at 7444cm-1Nearby 2cm-1In the range of 400 measurement points of different frequencies, the absorption line is then generated as a linear function of the m laser beam passing through the n grid at the j frequency measurement point vjThe linear function values above are:
according to the basic principle of laser absorption spectrum technology, the absorption spectrum line is measured at the jth frequency measurement point v by the mth laser beamjThe projection values of (d) are:
from the velocity profile given in fig. 4 and equation (20), it can be seen that all absorbance measurements are obtained.
Step 4, in the process of simulation calculation, the method comprisesΔνn、σn、γnFor unknowns, according to the derivation process in step 3, a nonlinear system of equations of the form:
step 4, 90000 nonlinear equations in the nonlinear equation set (21) can be solved by using a numerical method, and the nonlinear equation set (21) is solved by converting into an equivalent nonlinear optimization problem as follows:
wherein,is a linear function generated by the m laser beam passing through the n grid in the iterative process of solving the nonlinear optimization problem (22) at the j frequency measuring point vjCalculation of linear function values, if global optimization algorithms are used, for calculatingWill gradually converge to a solution of said system of non-linear equations (21), comprising the two-dimensional component of said velocity profileVector synthesis is carried out on the two-dimensional components of the velocity distribution, so that the velocity distribution of the airflow on the two-dimensional plane can be obtained,as shown in fig. 5.
Claims (1)
1. A method for measuring two-dimensional velocity distribution of airflow based on a laser absorption spectrum tomography technology comprises the following steps:
step 1, acquiring laser absorption spectrum projection data of a plurality of different angles: selecting an absorption spectral line of a known gas molecule in the gas flow, utilizing a laser beam which corresponds to the absorption spectral line of the gas molecule and has a frequency of v to respectively pass through two-dimensional measured areas through which the gas flow flows from different angles, wherein the interaction of the gas molecule and the laser beam generates laser absorption spectrum projection data corresponding to the absorption spectral line of the gas molecule, and falseSetting the total number of the laser beams with different angles to be M, distinguishing the laser beams with different angles by using a mark M, and recording projection data generated by the mth laser beam as taum(ν)；
Step 2, discretizing the detected region and calculating a sensitivity matrix of tomography: according to the resolution requirement of tomography, the two-dimensional measured area is discretely divided into N different grids, the different grids are distinguished by the labels N, and the optical path length l of the mth laser beam passing through the nth grid can be calculated according to the geometrical relationship between the laser beams with different angles and the gridsmnAccording to the temperature T of said air flow in said gridnPressure PnComponent concentration XnThe state parameters are equal and the optical path is combined, so that the sensitivity matrix component A corresponding to the mth laser beam passing through the nth grid can be calculatedmnThe calculation formula is as follows:
Amn＝lmn×Pn×Xn×S(Tn), (1)
wherein, S (T) is a line intensity function corresponding to the gas molecule absorption spectrum line, and the sensitivity matrix components are sequentially arranged according to the labels m and n to obtain the sensitivity matrix of the tomography:
A＝[Amn]M×N； (2)
step 3, establishing an equation set according to the Doppler frequency shift principle of the laser absorption spectrum and the projection data of the laser absorption spectrum at different angles: establishing a planar rectangular coordinate system xOy on a plane where the two-dimensional measured area is located, wherein the included angle between the mth laser beam and the positive direction of the x axis of the planar rectangular coordinate system is thetamThen, the direction vector of the mth laser beam can be expressed as:
nm＝(cosθm,cosθm,0), (3)
assuming that the x-direction and y-direction velocity components of the airflow in the nth grid corresponding to the rectangular coordinate system of the plane are respectivelyAndthe gas flow doppler shifts the laser absorption spectrum produced by the mth laser beam in the nth grid by:
wherein, vCIs the center frequency of the gas molecule absorption line, c is the speed of light; suppose that the frequency shift in the nth grid due to other factors is Δ νnThe line function of the absorption line resulting from the passage of the mth laser beam through the nth grid is:
wherein σn、γnIs two unknown parameters of said linear functionThe mathematical form of (a) is:
assuming that there are J measurement points of different frequencies in the actual measurement and the measurement points of different frequencies are distinguished by the reference number J, the linear function of the absorption line produced by the mth laser beam passing through the nth grid is measured at the jth frequency at the measurement point vjThe linear function values above are:
according to the basic principle of laser absorption spectrum technology, the absorption spectrum line is measured at the jth frequency measurement point v by the mth laser beamjThe projection values of (d) are:
to be provided withΔνn、σn、γnFor unknowns, using the quantitative relationship described in equation (8), a nonlinear system of equations of the form:
step 4, solving the nonlinear equation system to obtain the velocity distribution: the nonlinear equation set (9) has J × M nonlinear equations, which can be solved by a numerical method, and the nonlinear equation set (9) is solved by an equivalent nonlinear optimization problem as follows:
wherein,is that the obtained linear function generated by the mth laser beam passing through the nth grid in the iterative process of solving the nonlinear optimization problem (10) is used for measuring the jth frequency vjCalculation of linear function values, if global optimization algorithms are used, for calculatingWill gradually converge to a solution of said system of non-linear equations (9), including the two-dimensional components of said velocity profile, and vector-synthesizing the two-dimensional components of said velocity profile to obtain the velocity profile of said gas flow in said two-dimensional plane.
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