CN104677495B - A kind of method being distributed based on spectral radiance measurement flame temperature and emissivity - Google Patents

Abstract

A kind of method being distributed based on spectral radiance measurement flame temperature and emissivity, the method obtains flame spectrum radiant intensity to be measured first with spectrogrph, duochrome method is used to solve temperature and emissivity as initial value according to the radiant intensity under two middle wavelength, Newton iteration method is used to solve emissivity with each level number of the polynomial relation of wavelength change and temperature to be asked, start from scratch and be stepped up the exponent number of polynomial relation, solve coefficient and the temperature of every single order, in addition to zeroth order uses duochrome method result as initial value, remaining all uses single order result as initial value；When solving result does not changes with solving exponent number increase, i.e. result, with exponent number change convergence, is considered as obtaining final result.The method that the present invention provides can obtain the temperature of flame to be measured according to flame spectrum intensity to be measured and be distributed with the emissivity of wavelength change, does not relies on hypothesis or priori conditions, reliable results.

Description

A kind of method being distributed based on spectral radiance measurement flame temperature and emissivity

Technical field

The present invention relates to flame temperature and emissivity distribution measurement method, particularly relate to measure based on spectral radiance Flame temperature and emissivity distribution technique field, belong to flame spectrometry technical field.

Background technology

Radiant heat transfer is one of three kinds of major ways of heat transmission, and measurement technology based on radiation is a kind of important survey Amount means, especially high to temperature as this kind of in the high temperature combustors such as station boiler, industrial furnace, dynamically, situation is complicated, do not allow to do When the object disturb, cannot closely observed measures, the superiority of radiometric technique is the most notable.Emittance is to send out Penetrating the function of rate and temperature, how to be calculated the two parameter by emittance is the problem that we want to solve.Many scholars couple This problem is studied, and gives many computational methods, such as duochrome method [Yan W., Zhou H., Jiang Z., Lou C.,Zhang X.,Energy&Fuels,27(2013)6754-6762.].But these methods are based on certain a priori assumption, Duochrome method assumes that under two wavelength of flame, emissivity is identical, and additive method is also required to assume that emissivity follows certain rule. Existing method limitation is bigger, it is impossible to obtain reliable, the result of no dependence, so development one can be strong based on radiation Degree effectively provides the measuring method of temperature and emissivity distribution and is of practical significance very much.

Summary of the invention

In order to overcome existing method measurement result to rely on certain deficiency assumed, the invention provides a kind of based on spectrum spoke Penetrating ionization meter flame temperature and the method for emissivity distribution, the method effectively can be given to be measured based on spectral radiance The temperature of flame and emissivity are with the distribution of wavelength.

The technical solution adopted in the present invention is as follows:

A kind of method being distributed based on spectral radiance measurement flame temperature and emissivity, it is characterised in that described method Comprise the steps:

1) spectrogrph is utilized to obtain flame spectrum radiant intensity to be measured, the response value in the range of the measurement of output spectrum instrument and phase Answer the spectral radiance of flame different wave length；

2) emissivity is expressed as the function of wavelength, spectral radiance is expressed as:

$I(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·I_b(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λ}T}}=(a_0+a_1\·\mathrm{\λ}+a_2\·{\mathrm{\λ}}^2+...a_n\·{\mathrm{\λ}}^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λ}T}}---\left(I\right)$

In formula, I is radiant intensity, and λ is wavelength, and T is temperature, and ε is emissivity, I_bFor blackbody radiation intensity, a₀、a₁…a_n Representing unknown multinomial coefficient, n is polynomial exponent number, for the integer more than or equal to 0, c₁And c₂For Planck's constant；

3) duochrome method is used to solve temperature T according to the radiant intensity under two middle wavelength_iAnd emissivity ε_iAs initial value；

4) n=0 is assumed, by ε_iAnd T_iAs initial value, solve a_{0, n=0}And T_N=0；

5) n=1 is assumed, by a_{0, n=0}, 0 and T_N=0As initial value, solve a_{0, n=1}、a_{1, n=1}And T_N=1；

6) incrementally increase the exponent number n of polynomial relation, and use upper single order solving result as initial value, solve every single order Coefficient and temperature, until solving result does not changes with solving exponent number increase, i.e. result is with exponent number change convergence；

7) according to the coefficient calculations emissivity distribution of convergence, the emissivity of calculating is distributed and the temperature of convergence is considered as flame Emissivity distribution and the measurement result of temperature.

In the technique scheme of the present invention, using step 1) in measuring instrument response value as solving multinomial coefficient and temperature The weight coefficient of degree, by step 2) in public formula I following formula represent:

${\mathrm{\α}}_j\·I_j(\mathrm{\λ},T)-{\mathrm{\α}}_j\·(a_0+a_1\·{\mathrm{\λ}}_j+a_2\·{\mathrm{\λ}}_j^2+...a_n\·{\mathrm{\λ}}_j^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/{\mathrm{\λ}}_{j}T}}=0---\left(II\right)$

In formula, α_jFor the instrumental response value under jth wavelength after normalization.

Step 2 of the present invention) in, solve the emissivity each level number a with wavelength change polynomial relation₀、a₁…a_n With in temperature T, Newton iteration method is used to solve, including following sub-step:

A. deviation and the partial derivative of input numerical value is drawn according to public formula I to be solved or public formula II；

B. according to deviation and partial derivative, method of least square is used to obtain the correction value of input numerical value；

C. utilize following equation that input numerical value is modified:

$\[a_0^{r+1},...,a_n^{r+1},T^{r+1}\]=\[a_0^r,...,a_n^r,T^r\]-\[{\mathrm{\Δa}}_0^r,...,{\mathrm{\Δa}}_n^r,{\mathrm{\ΔT}}^r\]---\left(III\right)$

In formula, r is iterations, and Δ is correction value；

D. according to the trend of input change in value, it is judged that whether iterative process restrains, and is, carries out step e, otherwise returns to Step a, using revised numerical value as input numerical value, repeats said process；

E. output iteration convergence value.

The method that the present invention provides can obtain the temperature of flame to be measured according to flame spectrum intensity to be measured and become with wavelength The emissivity distribution changed, does not relies on hypothesis or priori conditions, reliable results.

Accompanying drawing explanation

Fig. 1 is the overview flow chart of the inventive method.

Fig. 2 Newton iteration method solves Nonlinear System of Equations flow chart.

The instrumental response value of Fig. 3 calculated examples and corresponding spectral radiance.

Fig. 4 difference solves exponent number emissivity result of calculation.

The spectral intensity that Fig. 5 different rank is recalculated by solving result.

Fig. 6 difference solves exponent number temperature and equation residual sum of squares (RSS).

Detailed description of the invention

Fig. 1 is the overview flow chart of the inventive method, and the method obtains flame spectrum to be measured radiation first with spectrogrph Intensity, the response value in the range of the measurement of output spectrum instrument and the spectral radiance of corresponding flame different wave length；Utilize duochrome method Solving initial value, and progressively solve different rank result of calculation, final convergence result is output result, and specific implementation process is such as Under:

One, duochrome method solves iterative initial value

Newton iteration method has certain requirement to iterative initial value, so needing to calculate initial value, to avoid not according to duochrome method Initial value causes the iteration direction of mistake reliably.From Wien's law, the computing formula of radiant intensity is:

$I(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·I_b(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λ}T}}---\left(1\right)$

In formula, ε is emissivity, changes, c with wavelength X change₁、c₂Being Planck's constant (Planck) constant, T is to be measured Temperature.

For two wavelength X₁And λ₂Under radiant intensity, if the emissivity assumed under two wavelength is equal, then can basis The two radiant intensity obtains assuming equal emissivity and temperature；It is shown below:

$\begin{array}{c}{T}_i=c_2\left(\frac{1}{{\mathrm{\λ}}_2}-\frac{1}{{\mathrm{\λ}}_1}\right)/\ln \[\frac{I_1}{I_2}\·{\left(\frac{{\mathrm{\λ}}_1}{{\mathrm{\λ}}_2}\right)}^5\],\\ {\mathrm{\ϵ}}_i=I_1/\left(\frac{c_1}{{\mathrm{\π\λ}}_1^5{e}^{c_2/{\mathrm{\λ}}_{1}T}}\right).\end{array}---\left(2\right)$

The result of duochrome method can be used as the initial value that successive iterations solves.

Two, emittance solving equations

For one group of radiation intensity data shown in formula (1), if thinking, that most typically changes solves, and unknown number has same number Purpose emissivity and unique temperature T.Right such calculating is difficulty with, so, we will solve and radiant intensity number The problem of emissivity ε as much is changed into the variation relation solving emissivity ε with wavelength, can avoid number of parameters to be asked many Obstacle in known conditions number.

Assume that emissivity ε and wavelength have such corresponding relation:

ε (λ)=a₀+a₁·λ+a₂·λ²+...a_n·λⁿ (3)

In formula, a₁、a₂…a_nRepresent unknown multinomial coefficient, then formula (1) then can be expressed as:

$I(\mathrm{\λ},T)=(a_0+a_1\·\mathrm{\λ}+a_2\·{\mathrm{\λ}}^2+...a_n\·{\mathrm{\λ}}^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λ}T}}---\left(4\right)$

In such a situa-tion, problem is converted into and solves each level of emissivity according to spectroscopic data under different wave length by we Number a₁、a₂…a_nAnd temperature T.

Calculating process, as in figure 2 it is shown, obtain solving equation group according to spectroscopic data, chooses iterative initial value, substitutes into equation group, Draw equation deviation and partial derivative, and then obtain the correction value of parameter, after parameter is modified, if convergence, export knot Really, without convergence then as next step iteration initial value continue calculate until convergence:

A. formula (4) is expressed as:

$f_j(a_0^r,...,a_n^r,T^r)={\mathrm{\α}}_j\·I_j-{\mathrm{\α}}_j\·(a_0^r+...+a_i^r\·{\mathrm{\λ}}_j+...a_n^r\·{\mathrm{\λ}}_j^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/{\mathrm{\λ}}_{j}T}}---\left(5\right)$

In formula, r represents iterations, solves equation group (4), is converted into searching equation group (5) zero point, by iteration The result of initial value or previous step iteration substitutes into equation group (5) i.e. can draw the equation group numerical value of this step and the deviation of zero point.

B. solving partial derivative is then that specific implementation can by increasing little deviation acquisition on unknown point parameters To be expressed as:

$\begin{array}{c}\frac{\∂f_j}{\∂f_j}\≈\frac{f_j\left(a_0^r,\mathrm{...},a_i^r+{\mathrm{\δa}}_i,\mathrm{...},a_n^r,T^r\right)-f_j\left(a_0^r,\mathrm{...},a_i^r,\mathrm{...},a_n^r,T^r\right)}{{\mathrm{\δa}}_i},\\ \frac{\∂f_j}{\∂T}\≈\frac{f_j\left(a_0^r,\mathrm{...},a_i^r,\mathrm{...},a_n^r,T^r+\mathrm{\δ}T\right)-f_j\left(a_0^r,\mathrm{...},a_i^r,\mathrm{...},a_n^r,T^r\right)}{\mathrm{\δ}T}\end{array}---\left(6\right)$

In formula, δ represents small deviation.

C. solve parameter correction values according to the partial derivative of the deviation He this point that determine an equation, parameter correction values to be asked and This equation deviation and partial derivative have such relation:

$\left[\begin{array}{c}{f}_1^r\\ .\\ f_j^r\\ .\\ f_m^r\end{array}\right]=\left[\begin{array}{cccc}\frac{\∂{f_1}^r}{\∂a_0}& .& \frac{\∂{f_1}^r}{\∂a_n}& \frac{\∂{f_1}^r}{\∂T}\\ .& .& .& .\\ \frac{\∂{f_j}^r}{\∂a_0}& .& \frac{\∂{f_j}^r}{\∂a_n}& \frac{\∂{f_j}^r}{\∂T}\\ .& .& .& .\\ \frac{\∂{f_m}^r}{\∂a_0}& .& \frac{\∂{f_m}^r}{\∂a_n}& \frac{\∂{f_m}^r}{\∂T}\end{array}\right]\·\left[\begin{array}{c}{\mathrm{\Δa}}_0^r\\ .\\ {\mathrm{\Δa}}_n^r\\ {\mathrm{\ΔT}}^r\end{array}\right]---\left(7\right)$

In formula, Δ represents parameter correction values to be asked, and uses method of least square i.e. can obtain the parameter correction values of this point.

D. after obtaining parameter correction values, then can revise parameter to be asked, correcting mode as shown by the equation:

$\[a_0^{r+1},...,a_n^{r+1},T^{r+1}\]=\[a_0^r,...,a_n^r,T^r\]-\[{\mathrm{\Δa}}_0^r,...,{\mathrm{\Δa}}_n^r,{\mathrm{\ΔT}}^r\]---\left(8\right)$

By such mode, the value of continuous update equation, till or cyclically-varying the least until results change, draw Result be the result that Newton iteration method solves.

Three, embodiment

Use spectrometer measurement coaxial 194ml/min ethylene and 284L/min air Nonpremixed flames camber 10.5mm, Spectral radiant energy at radial position 2.3mm, with this emittance curve as calculated examples.Fig. 3 gives corresponding measuring instrument The response value of device, the energy curve in figure is then demarcated by this series of values and is obtained.The method using the present invention, i.e. can get not With the result that n is corresponding, as shown in table 1.Fig. 4 gives the emissivity distribution that each solving result is corresponding.Fig. 5 gives use and solves Result calculated spectral intensity curve and the curve comparison detected.What Fig. 6 was given is to calculate residual sum temperature with solving The result of variations of exponent number n.Calculate residual error and be defined as the quadratic sum of equation (5) deviation.

From table 1, Fig. 4 and Fig. 6, along with solving the increase of exponent number, solving result can converge on a certain value, be we Method wants the final result obtained.Fig. 5 then illustrates that each rank result of calculation can reduce experiment curv well.This is surveyed The measurement point that the amount curve of spectrum is corresponding, temperature is about 1625.71K, and emissivity is then that 2,3,4 rank almost overlapped in Fig. 4 are bent Line.

The different n result of calculation of table 1

Claims (3)

1. measure flame temperature and the method for emissivity distribution based on spectral radiance for one kind, it is characterised in that described method bag Include following steps:

1) utilize spectrogrph obtain flame spectrum radiant intensity to be measured, output spectrum instrument measure in the range of response value and accordingly fire The spectral radiance of flame different wave length；

2) emissivity is expressed as the function of wavelength, spectral radiance is expressed as:

$I(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·I_b(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λ}T}}=(a_0+a_1\·\mathrm{\λ}+a_2\·{\mathrm{\λ}}^2+...a_n\·{\mathrm{\λ}}^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λ}T}}---\left(I\right)$

In formula, I is radiant intensity, and λ is wavelength, and T is temperature, and ε is emissivity, I_bFor blackbody radiation intensity, a₀、a₁…a_nRepresent not The multinomial coefficient known；N is polynomial exponent number, for the integer more than or equal to 0；c₁And c₂For Planck's constant；

3) duochrome method is used to solve temperature T according to the radiant intensity under two middle wavelength_iAnd emissivity ε_iAs initial value；

4) n=0 is assumed, by ε_iAnd T_iAs initial value, wherein, a is solved_{0, n=0}And T_N=0；

5) n=1 is assumed, by a_{0, n=0}, 0 and T_N=0As initial value, solve a_{0, n=1}、a_{1, n=1}And T_N=1；

6) incrementally increase the exponent number n of polynomial relation, and use upper single order solving result as initial value, solve the coefficient of every single order And temperature, until solving result does not changes with solving exponent number increase, i.e. result is with exponent number change convergence；

7) according to the coefficient calculations emissivity distribution of convergence, the emissivity of calculating is distributed and the temperature of convergence is considered as flame emission Rate distribution and the measurement result of temperature.

The method being distributed based on spectral radiance measurement flame temperature and emissivity the most according to claim 1, it is special Levy and be: using step 1) in the response value of measuring instrument as the weight coefficient solving multinomial coefficient and temperature, by step 2) Middle public formula I following formula represents:

${\mathrm{\α}}_j\·I_j(\mathrm{\λ},T)-{\mathrm{\α}}_j\·(a_0+a_1\·{\mathrm{\λ}}_j+a_2\·{\mathrm{\λ}}_j^2+...a_n\·{\mathrm{\λ}}_j^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/{\mathrm{\λ}}_{j}T}}=0---\left(II\right)$

In formula, α_jFor the instrumental response value under jth wavelength after normalization.

The method being distributed based on spectral radiance measurement flame temperature and emissivity the most according to claim 1 and 2, its It is characterised by: in step 2) solve the emissivity each level number a with wavelength change polynomial relation₀、a₁…a_nWith in temperature T, adopt Solve by Newton iteration method, including following sub-step:

A. deviation and the partial derivative of input numerical value is drawn according to public formula I to be solved or public formula II；

B. according to deviation and partial derivative, method of least square is used to obtain the correction value of input numerical value；

C. utilize following equation that input numerical value is modified:

$\[a_0^{r+1},...,a_n^{r+1},T^{r+1}\]=\[a_0^r,...,a_n^r,T^r\]-\[{\mathrm{\Δa}}_0^r,...,{\mathrm{\Δa}}_n^r,{\mathrm{\ΔT}}^r\]---\left(III\right)$

In formula, r is iterations, and Δ is correction value；

D. according to the trend of input change in value, it is judged that whether iterative process restrains, and is, carries out step e, otherwise returns to step A, using revised numerical value as input numerical value, repeats said process；

E. output iteration convergence value.