CN109061221B - Airflow three-dimensional velocity distribution measuring method based on laser absorption spectrum tomography technology - Google Patents

Airflow three-dimensional velocity distribution measuring method based on laser absorption spectrum tomography technology Download PDF

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CN109061221B
CN109061221B CN201811024114.4A CN201811024114A CN109061221B CN 109061221 B CN109061221 B CN 109061221B CN 201811024114 A CN201811024114 A CN 201811024114A CN 109061221 B CN109061221 B CN 109061221B
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absorption spectrum
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airflow
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徐立军
曲前伟
曹章
常刘勇
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Beihang University
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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
    • 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 invention provides an airflow three-dimensional velocity distribution measuring method based on a laser absorption spectrum tomography technology, which comprises the following steps of: 1. acquiring laser absorption spectrum projection data of a plurality of different angles; 2. discretizing the detected region and calculating a sensitivity matrix of tomography; 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; 4. and solving the nonlinear equation system to obtain three-dimensional velocity distribution. The method provided by the invention can measure and reconstruct the three-dimensional velocity distribution of the airflow in a non-contact manner, and has the advantages of strong applicability, high reliability and very wide application prospect.

Description

Airflow three-dimensional velocity distribution measuring method based on laser absorption spectrum tomography technology
Technical Field
The invention relates to a method for measuring the three-dimensional velocity distribution of airflow based on a laser absorption spectrum tomography technology, mainly comprising the steps of measuring and reconstructing the distribution of the airflow velocity in a three-dimensional space 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) technique, researchers also realize the measurement and reconstruction of distribution 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 reconstructing gas flow three-dimensional velocity distribution by using the laser absorption spectrum.
Fundamental to which laser absorption spectroscopy reliesThe physical principle is the Beer-L ambert law which states that incident light intensity is I at a frequency vin(v) When the laser light 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:
Figure BDA0001787764170000011
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,
Figure BDA0001787764170000012
the equation (1) formally expresses the integral relationship of the gas state parameter to the path, and the absorbance tau (v) is mathematically considered as a projection on the path L.
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 spectrum
Figure BDA0001787764170000013
The 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 three-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 three-dimensional velocity distribution of an airflow based on a laser absorption spectrum tomography technology, which realizes the measurement and reconstruction of the three-dimensional velocity distribution of the airflow by obtaining laser absorption spectrum absorption rate measurement values 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 three-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 line of a known gas molecule in a gas flow, utilizing a laser beam which corresponds to the absorption line of the gas molecule and has a frequency v, respectively penetrating through three-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 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 mark M, and recording the projection data generated by the mth laser beam as taum(v)；
Step 2, discretizing the detected region and calculating a sensitivity matrix of tomography: according to the resolution requirement of tomography, the three-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), (2)
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； (3)
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 spatial stereo rectangular coordinate system O-xyz on a plane where the three-dimensional measured area is located, wherein a direction vector of the mth laser beam can be expressed as:
Figure BDA0001787764170000021
assuming that the x, y and z directional velocity components of the airflow in the nth grid corresponding to the rectangular coordinate system are respectively
Figure BDA0001787764170000024
And
Figure BDA0001787764170000025
the gas flow doppler shifts the laser absorption spectrum produced by the mth laser beam in the nth grid by:
Figure BDA0001787764170000022
wherein v isCIs 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:
Figure BDA0001787764170000023
wherein σn、γnIs two unknown parameters of said linear function
Figure BDA0001787764170000031
The mathematical form of (a) is:
Figure BDA0001787764170000032
assuming that there are J measurement points of different frequencies in the actual measurement and the measurement points of different frequencies are distinguished by reference number J, the line function of the absorption line generated by the m laser beam passing through the n grid is taken at the J frequency measurement point vjThe linear function values above are:
Figure BDA0001787764170000033
according to the basic principle of laser absorption spectroscopy, the absorption line is measured at the jth frequency measurement point v by the mth laser beamjThe projection values of (d) are:
Figure BDA0001787764170000034
to be provided with
Figure BDA0001787764170000035
Δvn、σn、γnFor unknowns, using the quantitative relationship described in equation (9), a nonlinear system of equations of the form:
Figure BDA0001787764170000036
and 4, solving the nonlinear equation set to obtain three-dimensional velocity distribution, wherein the nonlinear equation set (10) comprises J × M nonlinear equations, and can be solved by using a numerical method, and the nonlinear equation set (10) is solved as an equivalent nonlinear optimization problem as follows:
Figure BDA0001787764170000037
wherein,
Figure BDA0001787764170000038
is the m-th laser obtained during an iteration of solving the non-linear optimization problem (11)The line-type function generated by the beam passing through said nth grid is measured at the jth frequency measurement point vjCalculation of linear function values, if global optimization algorithms are used, for calculating
Figure BDA0001787764170000039
Will gradually converge to a solution of said system of non-linear equations (10) comprising three components of said velocity profile
Figure BDA00017877641700000310
And synthesizing the velocity components into vectors to obtain the three-dimensional velocity distribution of the airflow.
And reconstructing the three-dimensional air flow velocity distribution shown by the flow line in the figure 3 by using the air flow three-dimensional velocity distribution measuring method to obtain a reconstruction result shown by the flow line in the figure 4. In fig. 3 and 4, the change in the gradation indicates the magnitude of the velocity, and the unit is [ m/sec ]. Comparing the two images shows that the three-dimensional airflow velocity distribution obtained by the method for measuring the two-dimensional airflow velocity distribution is consistent with the given distribution regardless of the size or the direction, which shows that the method for measuring the three-dimensional airflow velocity distribution is effective.
Drawings
The arrows in FIG. 1 represent the directional vectors covering the 12 laser projection angles of the measured area of the cube;
the arrows in FIG. 2 represent (1,0,0)TParallel laser beams arranged in the direction, wherein the total number of the parallel laser beams is 10 × 10-100;
FIG. 3 gives a three-dimensional velocity distribution in a cube in streamline form, with the gray scale representing the magnitude of the velocity;
fig. 4 is a three-dimensional air flow velocity distribution reconstructed using the air flow three-dimensional velocity distribution measuring method.
Detailed Description
In the present embodiment, the distribution of state parameters in a cubic region is given, and the entire region is divided into 5 × 10 × 10 grids, and calculation is performed by a parallel beam laser absorption spectrum tomography method, to give a reconstruction result of velocity distribution.
The following further describes embodiments of the present invention with reference to the drawings.
Step 1, selecting the center frequency of 7495.5cm-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.
And 2, giving the temperature, the pressure, the water vapor concentration, the air flow speed, the non-Doppler frequency shift, a linear function and the like in a cubic area, uniformly dividing the cubic area into 5 × 10 × 10 grids, wherein the state parameters are uniform in each grid.
The cube was probed with parallel laser beams at 12 projection angles, the direction vectors of which are shown in fig. 1, and the coordinates of which are shown in table 1.
TABLE 1.12 Direction vectors of laser projection angles
Figure BDA0001787764170000041
Each angle has 10 × 10-100 parallel laser beams, so the total number of laser beams used in the measurement process is 1200, and the arrows in fig. 2 show (1,0,0)TThe arrangement of the parallel laser beams in the direction. The optical path of the mth laser beam passing through the nth grid is lmnAccording 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), (12)
and sequentially arranging the sensitivity matrix components according to the labels m and n to obtain the sensitivity matrix of the tomography:
A＝[Amn]1200×500(13)
step 3, the direction vector of the mth laser beam can be expressed as:
Figure BDA0001787764170000051
as shown in fig. 3, the x-direction and y-direction velocity components of the airflow in the nth grid corresponding to the rectangular spatial coordinate system are respectively
Figure BDA00017877641700000510
And
Figure BDA00017877641700000511
the gas flow doppler shifts the laser absorption spectrum produced by the mth laser beam in the nth grid by:
Figure BDA0001787764170000052
wherein v isCIs the center frequency of the gas molecule absorption line, c is the speed of light; the non-Doppler-induced frequency shift in the given nth grid is Δ νnThe line function of the absorption line resulting from the passage of the mth laser beam through the nth grid is:
Figure BDA0001787764170000053
wherein σn、γnIs a parameter of said given linear function, said linear function
Figure BDA0001787764170000054
The mathematical form of (a) is:
Figure BDA0001787764170000055
at 7495.5cm-1Nearby 0.4cm-1Within the range of (A) and (B),selecting 40 different frequency measurement points, the line function of the absorption line generated by the mth laser beam passing through the nth grid is used to measure the point v at the jth frequencyjThe linear function values above are:
Figure BDA0001787764170000056
according to the basic principle of laser absorption spectroscopy, the absorption line is measured at the jth frequency measurement point v by the mth laser beamjThe projection values of (d) are:
Figure BDA0001787764170000057
step 4, in the process of simulation calculation, the method comprises
Figure BDA0001787764170000058
Δvn、σn、γnFor unknowns, according to the derivation process in step 3, a nonlinear system of equations of the form:
Figure BDA0001787764170000059
step 4, 48000 nonlinear equations in the nonlinear equation set (20) can be solved by using a numerical method, and the nonlinear equation set (20) is solved by converting into an equivalent nonlinear optimization problem as follows:
Figure BDA0001787764170000061
wherein,
Figure BDA0001787764170000062
is a linear function at the jth frequency measurement point v, resulting from the passage of the mth laser beam through the nth grid during an iteration of solving the nonlinear optimization problem (21)jCalculation of linear function values, if global maximum is usedOptimization algorithm for calculating
Figure BDA0001787764170000063
Will gradually converge to a solution of said system of non-linear equations (20) comprising three-dimensional components of said velocity profile
Figure BDA0001787764170000064
Figure BDA0001787764170000065
Vector synthesis is performed on the three-dimensional components of the velocity distribution, so that the velocity distribution of the airflow in the three-dimensional cube can be obtained, as shown in fig. 4.

Claims (1)

1. A method for measuring the three-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 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 three-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 three-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 is 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 XnCalculating the three kinds of state parameters by combining the optical pathThe m laser beam passes through the sensitivity matrix component A corresponding to the n gridmnThe 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 spatial rectangular coordinate system O-xyz on a plane where the three-dimensional measured area is located, wherein the direction vector of the mth laser beam is expressed as:
Figure FDA0002403266120000011
assuming that the x, y and z directional velocity components of the airflow in the nth grid corresponding to the rectangular coordinate system are respectively
Figure FDA0002403266120000012
And
Figure FDA0002403266120000013
the gas flow doppler shifts the laser absorption spectrum produced by the mth laser beam in the nth grid by:
Figure FDA0002403266120000014
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:
Figure FDA0002403266120000015
wherein σn、γnIs two unknown parameters of said linear function
Figure FDA0002403266120000016
The mathematical form of (a) is:
Figure FDA0002403266120000017
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:
Figure FDA0002403266120000021
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:
Figure FDA0002403266120000022
to be provided with
Figure FDA0002403266120000023
Δνn、σn、γnFor unknowns, using the quantitative relationship of equation (8), a nonlinear system of equations of the form:
Figure FDA0002403266120000024
and 4, solving the nonlinear equation set to obtain three-dimensional velocity distribution, wherein the nonlinear equation set (9) comprises J × M nonlinear equations, the numerical method is used for solving, and the nonlinear equation set (9) is changed into the following equivalent nonlinear optimization problem solution:
Figure FDA0002403266120000025
wherein,
Figure FDA0002403266120000026
is a linear function at a j-th frequency measurement point v of the m-th laser beam through the n-th grid obtained during an iteration of solving the nonlinear optimization problem (10)jCalculation of linear function values, if global optimization algorithms are used, for calculating
Figure FDA0002403266120000027
Will gradually converge to a solution of said system of non-linear equations (9) comprising three components of said velocity profile
Figure FDA0002403266120000028
And synthesizing the velocity components into vectors to obtain the three-dimensional velocity distribution of the airflow.
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