CN104677495A - Method for measuring flame temperature and emissivity distribution based on spectral radiance intensity - Google Patents

Abstract

The invention discloses a method for measuring flame temperature and emissivity distribution based on spectral radiance intensity. The method comprises the following steps: firstly, acquiring the spectral radiance intensity of flame to be measured by using a spectrometer; solving and taking temperature and emissivity as initial values by using a double-color method according to radiance intensity of two middle wavelengths; solving different order coefficients and temperature to be solved in polynomial relationship that the emissivity changes along with the wavelengths by using a Newton iteration method, increasing the orders of the polynomial relationship from zero step by step, solving the coefficients and the temperature of each order, except that the zero order takes the double-color method result as an initial value, taking the result of a previous order as the initial value for other steps; requiring final result when the solving result does not change along with increase of solving orders, that is, the result is converged along with the change of the orders. By adopting the method disclosed by the invention, the temperature of the flame to be measured and the emissivity distribution of the flame along with change of the wavelength can be obtained according to the spectral intensity of the flame to be measured, the measurement does not depend on assumption or priori conditions, and the result is reliable.

Description

A kind of method measuring flame temperature and emissivity distribution based on spectral radiance

Technical field

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

Background technology

Radiant heat transfer is one of three kinds of major ways of heat transmission, measuring technique based on radiation is a kind of important measurement means, especially to such as this kind of temperature of the high temperature combustors such as station boiler, industrial furnace is high, dynamic, situation is complicated, do not allow the object disturbing, cannot closely observe to measure time radiometric technique superiority just more remarkable.Emittance is the function of emissivity and temperature, and how to calculate these two parameters by emittance is problems that we want to solve.Many scholars are studied this problem, and give many computing method, such as duochrome method [Yan W., Zhou H., Jiang Z., Lou C., Zhang X., Energy & Fuels, 27 (2013) 6754-6762.].But these methods are all based on certain a priori assumption, under duochrome method hypothesis flame two wavelength, emissivity is identical, and additive method also all needs hypothesis emissivity to follow certain rule.Existing method limitation is comparatively large, cannot obtain reliably, the result of no dependence, is of practical significance very much so develop a kind of measuring method that can effectively provide temperature and emissivity distribution based on radiation intensity.

Summary of the invention

The deficiency of certain hypothesis is relied in order to overcome existing method measurement result, the invention provides a kind of method measuring flame temperature and emissivity distribution based on spectral radiance, the method can provide the distribution with wavelength of the temperature of flame to be measured and emissivity effectively based on spectral radiance.

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

Measure a method for flame temperature and emissivity distribution based on spectral radiance, it is characterized in that described method comprises the steps:

1) spectrometer is utilized to obtain flame spectrum radiation intensity to be measured, the spectral radiance of the response in output spectrum instrument measurement range and corresponding flame different wave length;

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

$I(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·I_b(\mathrm{\λ},T)=\mathrm{\ϵ}\left(\mathrm{\λ}\right)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λT}}}=(a_0+a_1\·\mathrm{\λ}{+a}_2\·{\mathrm{\λ}}^2+...a_n\·{\mathrm{\λ}}^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/\mathrm{\λT}}}---\left(I\right)$

In formula, I is radiation intensity, and λ is wavelength, and T is temperature, and ε is emissivity, I _bfor blackbody radiation intensity, a ₀, a ₁a _nrepresent unknown multinomial coefficient, n is polynomial exponent number, for being more than or equal to the integer of 0, c ₁and c ₂for Planck's constant;

3) duochrome method is adopted to solve temperature T according to the radiation intensity under two middle wavelength _iand emissivity ε _ias initial value;

4) n=0 is supposed, by ε _iand T _ias initial value, solve a _{0, n=0}and T _n=0;

5) n=1 is supposed, 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) progressively increase the exponent number n of polynomial relation, and adopt upper single order solving result as initial value, solve coefficient and the temperature of every single order, until solving result does not change with solving exponent number increase, namely result is with exponent number change convergence;

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

In technique scheme of the present invention, using step 1) in surveying instrument response as the weight coefficient solving multinomial coefficient and temperature, by step 2) in formula (I) represent with following formula:

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

In formula, α _jfor the instrumental response value under the wavelength of jth after normalization.

Step 2 of the present invention) in, solve each rank coefficient a of emissivity with wavelength variations polynomial relation ₀, a ₁a _nwith in temperature T, adopt Newton iteration method to solve, comprise following sub-step:

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

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

C. following formula is utilized to revise input numerical value:

$[a_0^{r+1},...,a_n^{r+1},T^{r+1}]=[a_0^r,...,a_1^r,T^r]-[{\mathrm{\Δa}}_0^r,...,{\mathrm{\Δa}}_n^r,{\mathrm{\ΔT}}^r]---\left(\mathrm{III}\right)$

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

D. according to the trend of input numerical value change, judge whether iterative process restrains, and is, carry out step e, otherwise get back to step a, using revised numerical value as input numerical value, repeat said process;

E. iteration convergence value is exported.

Method provided by the invention can obtain the temperature of flame to be measured according to flame spectrum intensity to be measured and distribute with the emissivity of wavelength variations, does not rely 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 process flow diagram.

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).

Embodiment

Fig. 1 is the overview flow chart of the inventive method, and first the method utilizes spectrometer to obtain flame spectrum radiation intensity to be measured, the spectral radiance of the response in output spectrum instrument measurement range and corresponding flame different wave length; Utilize duochrome method to solve initial value, and progressively solve different rank result of calculation, final convergence result is Output rusults, and specific implementation process is as follows:

One, duochrome method solves iterative initial value

Newton iteration method has certain requirement to iterative initial value, so need to calculate initial value, with the iteration direction avoiding insecure initial value to lead to errors according to duochrome method.From Wien's law, the computing formula of radiation 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 change ₁, c ₂be Planck's constant (Planck) constant, T is for treating testing temperature.

For two wavelength X ₁and λ ₂under radiation intensity, if the emissivity under hypothesis two wavelength is equal, then can obtain hypothesis equal emissivity and temperature according to these two radiation intensity; Be shown below:

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

Namely 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), carry out the most general solving if want, unknown number has same number of emissivity and unique temperature T.So such calculating is difficult to realize, so we change the problem solved with the emissivity ε of radiation intensity number as much into solve emissivity ε and wavelength variation relation, can avoid the obstacle of number of parameters to be asked more than known conditions number.

Suppose that emissivity ε and wavelength have such corresponding relation:

ε(λ)＝a ₀+a ₁·λ+a ₂·λ ²+...a _n·λ ⁿ(3)

In formula, a ₁, a ₂a _nrepresent unknown multinomial coefficient, so 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 emissivity each rank coefficient a according to spectroscopic data under different wave length by we ₁, a ₂a _nand temperature T.

Computation process as shown in Figure 2, solving equation group is obtained according to spectroscopic data, choose iterative initial value, substitute into system of equations, draw equation deviation and partial derivative, and then obtain the modified value of parameter, after parameter is revised, if restrained, Output rusults, if do not have convergence, the initial value as next step iteration continues to 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, to solving of system of equations (4), convert to and find system of equations (5) zero point, the result of iterative initial value or previous step iteration is substituted into system of equations numerical value and the deviation at zero point that system of equations (5) namely can draw this step.

B. solving partial derivative is then obtain by increasing little deviation on unknown point parameters, and specific implementation can be expressed as:

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

In formula, δ represents small deviation.

C. solve parameter correction values according to the partial derivative of the deviation He this point of determining point equation, parameter correction values to be asked has such relation with this point equation deviation and partial derivative:

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

In formula, Δ represents parameter correction values to be asked, and adopts least square method namely 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:

$[a_0^{r+1},...,a_n^{r+1},T^{r+1}]=[a_0^r,...,a_1^r,T^r]-[{\mathrm{\Δa}}_0^r,...,{\mathrm{\Δa}}_n^r,{\mathrm{\ΔT}}^r]---\left(8\right)$

By such mode, the value of continuous update equation, until results change till very little or cyclical variation, the result drawn is the result that Newton iteration method solves.

Three, embodiment

Adopt the spectral radiant energy at height 10.5mm, radial position 2.3mm place in the coaxial 194ml/min ethene of spectrometer measurement and 284L/min air Nonpremixed flames, with this emittance curve for calculated examples.Fig. 3 gives the response of corresponding surveying instrument, and the energy trace in figure is then demarcated by this series of values and obtained.Adopt method of the present invention, the result that different n is corresponding can be obtained, as shown in table 1.Fig. 4 corresponding to each solving result gives at emissivity distribution.Fig. 5 gives and uses the spectral intensity curve that solving result calculates and the curve comparison detected.What Fig. 6 provided is calculate residual sum temperature with the result of variations solving exponent number n.Calculate the quadratic sum that residual error is defined as equation (5) deviation.

From table 1, Fig. 4 and Fig. 6, along with the increase solving exponent number, solving result can converge on a certain value, is the net result that this method is wanted to obtain.Fig. 5 then describes each rank result of calculation can reduce experiment curv well.For the measurement point that this measure spectrum curve is corresponding, temperature is about 1625.71K, and emissivity is then 2,3, the 4 rank curves almost overlapped in Fig. 4.

The different n result of calculation of table 1

Claims (3)

1. measure a method for flame temperature and emissivity distribution based on spectral radiance, it is characterized in that described method comprises the steps:

1) spectrometer is utilized to obtain flame spectrum radiation intensity to be measured, the spectral radiance of the response in output spectrum instrument measurement range and corresponding flame different wave length;

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

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

In formula, I is radiation intensity, and λ is wavelength, and T is temperature, and ε is emissivity, I _bfor blackbody radiation intensity, a ₀, a ₁a _nrepresent unknown multinomial coefficient; N is polynomial exponent number, for being more than or equal to the integer of 0; c ₁and c ₂for Planck's constant;

3) duochrome method is adopted to solve temperature T according to the radiation intensity under two middle wavelength _iand emissivity ε _ias initial value;

4) n=0 is supposed, by ε _iand T _ias initial value, wherein, a is solved _{0, n=0}and T _n=0;

5) n=1 is supposed, 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) progressively increase the exponent number n of polynomial relation, and adopt upper single order solving result as initial value, solve coefficient and the temperature of every single order, until solving result does not change with solving exponent number increase, namely result is with exponent number change convergence;

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

2. the method measuring flame temperature and emissivity distribution based on spectral radiance according to claim 1, it is characterized in that: using step 1) in the response of surveying instrument as the weight coefficient solving multinomial coefficient and temperature, by step 2) in formula (I) represent with following formula:

${\mathrm{\α}}_j\·I_j(\mathrm{\λ},T)-{\mathrm{\α}}_j\·(a_0+a_1\·{\mathrm{\λ}}_j+a_2\·{\mathrm{\λ}}_j^2+...a_n\·{\mathrm{\λ}}_j^n)\·\frac{c_1}{{\mathrm{\π\λ}}^5{e}^{c_2/{\mathrm{\λ}}_{j}T}}=0---\left(\mathrm{II}\right)$ In formula, α _jfor the instrumental response value under the wavelength of jth after normalization.

3. the method measuring flame temperature and emissivity distribution based on spectral radiance according to claim 1 and 2, is characterized in that: in step 2) solve each rank coefficient a of emissivity with wavelength variations polynomial relation ₀, a ₁a _nwith in temperature T, adopt Newton iteration method to solve, comprise following sub-step:

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

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

C. following formula is utilized to revise input numerical value:

$[a_0^{r+1},...,a_n^{r+1},T^{r+1}]=[a_0^r,...,a_1^r,T^r]-[{\mathrm{\Δa}}_0^r,...,{\mathrm{\Δa}}_n^r,{\mathrm{\ΔT}}^r]---\left(\mathrm{III}\right)$

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

D. according to the trend of input numerical value change, judge whether iterative process restrains, and is, carry out step e, otherwise get back to step a, using revised numerical value as input numerical value, repeat said process;

E. iteration convergence value is exported.