Radiant syngas cooler (RSC) is the key heat recovery equipment in coal gasification system. The syngas from gasifier carries large amount of slags in which the mass fraction of fly ash less than 100 μm is about 20%. Studying the optical properties of fly ash has high significance for the optimization of heat transfer calculation in RSC. A new experimental method was proposed to inversely calculate the radiative parameters of particles—“KBr transmittance-reflectance method”. By measuring the “directional-hemispherical” reflectance and transmittance of fly ash particles by FTIR under the wavelength range of 0.55 - 1.65 μm, using the four-flux model to solve the radiative transfer equation and combing with Mie theory, the absorption and scattering efficiency of 22.7 μm fly ash and optical constant (also known as complex refractive index, m = n + ik) of fly ash were inversely calculated. The results indicated that for fly ash with large size parameter, there was no obvious change of the absorption and scattering efficiency when the mass fraction of Fe 2O 3 was between 5.65% and 16.53%, which was well explained by Mie theory; The obtained optical constant was close to the results of KBr trans-mittance method.
The syngas produced by various gasifiers contains about 10% to 20% calorific value which exists in the form of sensible heat. Usually, this part of the energy is not effectively used. For example, the high-temperature syngas in coal-water slurry gasifier is directly cooled by chilling. The syngas temperature decreases from about 1400˚C to less than 300˚C, which causes huge energy loss. Radiant Syngas Cooler (RSC) is installed at the outlet of gasifier and plays a significant role in recovering this part of energy. The utilization of RSC can increase the power generation efficiency of Integrated Gasification Combined Cycle (IGCC) by 4 - 5 percents [
The syngas flowing into RSC carries a large amount of high-temperature slags, in which the mass fraction of particles less than 100 μm is about 20%. Because of its small size and large number density, this part of fly ash has a significant effect of light scattering on the radiation transfer in RSC [
The optical properties of fly ash are determined by chemical composition, size parameter x ( x = π D / λ ), surface condition and geometry [
In order to eliminate the errors from the extrapolation formula of the K-K relation and reduce the effects of forward scattering in KBr transmittance method, a “KBr transmittance-reflectance method” was proposed in this paper based on [
Lorenz-Mie theory is a classical algorithm used to solve the interaction between spherical particles and plane electromagnetic waves. It gives an exact solution to the scattering problem of spherical particles with any size. When a light with wavelength of λ is incident on an isotropic homogeneous spherical particle, the extinction, scattering and absorption efficiency of the particle can be expressed by the following formula [
Q e x t ( m , x ) = 2 x 2 ∑ n = 1 ∞ ( 2 n + 1 ) Re { a n + b n } (1)
Q s c a ( m , x ) = 2 x 2 ∑ n = 1 ∞ ( 2 n + 1 ) [ | a n | 2 + | b n | 2 ] (2)
Q a b s ( m , x ) = Q e x t ( m , x ) − Q s c a ( m , x ) (3)
where x is size parameter; r is particle radius; an and bn are called Mie scattering coefficients, which are calculated as follows:
a n = ψ ′ n ( m x ) ψ n ( x ) − m ψ n ( m x ) ψ ′ n ( x ) ψ ′ n ( m x ) ξ n ( x ) − m ψ n ( m x ) ξ ′ n ( x ) (4)
b n = m ψ ′ n ( m x ) ψ n ( x ) − ψ n ( m x ) ψ ′ n ( x ) m ψ ′ n ( m x ) ξ n ( x ) − ψ n ( m x ) ξ ′ n ( x ) (5)
where m = n + ik represents the optical constant; ξ n = ψ n − i η n ; ψ n and η n are the Bessel functions which follow the recurrence relation:
ψ n + 1 ( z ) = 2 n + 1 z ψ n ( z ) − ψ n − 1 ( z ) (6)
η n + 1 ( z ) = 2 n + 1 z η n ( z ) − η n − 1 ( z ) (7)
where,
ψ − 1 ( z ) = cos z , ψ 0 ( z ) = sin z (8)
η − 1 ( z ) = − sin z , η 0 ( z ) = cos z (9)
For dispersed particle system that satisfies the independent scattering condition, the scattering of particles has no effect on each other. The absorption and scattering coefficients of the particle system are the integral of the absorption and scattering efficiency by the particle size distribution, as follows:
μ λ = ∫ 0 ∞ Q μ π D 2 4 f ( D ) N d D (10)
where μ λ represents the absorption coefficient scattering κ λ , scattering coefficient σ λ , extinction coefficient σ λ ; Q μ represents the corresponding absorption, scattering and extinction efficiency; N denotes the number of particles per unit volume; f(D) is the normalized size distribution. For particles with same size, the relation is simplified as:
μ λ = π D 2 4 N Q μ (11)
Therefore, when the particle absorption, scattering coefficients and the size distribution are obtained from experiments, the absorption, scattering efficiency and optical constants of particles can be inversely calculated.
The four-flux model is an approximate solution of radiative transfer equation to determine the absorption and scattering coefficients of materials. In four-flux model, it is assumed that 1) there is no emission of the sample at room temperature; 2) only a collimated radiative flux is incident onto the front surface of the sample; 3) at any position z inside of the sample, there are four parts of energy: a collimated beam Ic(z) propagating to positive z, a collimated beam Jc(z) propagating to negative z, a diffuse beam Id(z) propagating to positive z, a diffuse beam Jd(z) propagating to negative z [
As shown in
According to energy balance, the differential equations and boundary conditions can be established, see [
R = ρ o u t + ( 1 − ρ i n ) [ C 2 + C 1 B + C 2 A + C 3 ( 1 − β ) + C 4 ( 1 + β ) ] (12)
T = ( 1 − ρ i n ) [ C 1 e − τ 1 + C 1 A e − τ 1 + C 2 B e τ 1 + C 3 ( 1 + β ) e − 2 β τ 2 + C 4 ( 1 − β ) e 2 β τ 2 ] (13)
The constants in the formulas are found to be:
C 1 = 1 − ρ o u t 1 − ρ i n 2 e − 2 τ 1 (14)
C 2 = ( 1 − ρ o u t ) ρ i n e − 2 τ 1 1 − ρ i n 2 e − 2 τ 1 (15)
C 3 = ( σ 1 μ 2 e 2 β τ 2 − σ 2 μ 1 e − τ 1 ) C 1 + ( σ 1 μ 1 e 2 β τ 2 − σ 2 μ 2 e τ 1 ) C 2 σ 1 2 e 2 β τ 2 − σ 2 2 e − 2 β τ 2 (16)
C 4 = ( σ 1 μ 1 e − τ 1 − σ 2 μ 2 e − 2 β τ 2 ) C 1 + ( σ 1 μ 2 e τ 1 − σ 2 μ 1 e − 2 β τ 2 ) C 2 σ 1 2 e 2 β τ 2 − σ 2 2 e − 2 β τ 2 (17)
where,
τ 1 = ( a + s ) L ; τ 2 = 0.5 ( M + N ) L ; μ 1 = ρ i n A − B ; μ 2 = ρ i n B − A ;
M = ε d [ a + ( 1 − ζ ) s ] ; N = ε d ( 1 − ζ ) s ; X = ε c ( 1 − ζ ) s ; Y = ε c ζ s ; T = a + s ;
σ 1 = ( 1 + β ) − ρ i n ( 1 − β ) ; σ 2 = ( 1 − β ) − ρ i n ( 1 + β )
A = Y ( M + T ) + N X M 2 − T 2 − N 2 ; B = X ( M − T ) + N Y M 2 − T 2 − N 2 ; β = M 2 − N 2 M + N .
where, a and s are the absorption and scattering coefficient respectively, and because KBr has no absorption in the infrared and partial visible spectrum, a and s are approximately treated as the absorption and scattering coefficient of the fly ash particles; L is the thickness of sample; ζ is the forward scattering ratio, which equals the energy scattered by a particle in the forward hemisphere over the total energy; ε is the average crossing parameter, which is defined by saying that, when the radiation light travels a length d z , the average path length is ε d z [
In order to make sure the accuracy of the four-flux model, the selection of ε d and ζ is particularly important. Since the size distribution of particles can be controlled in experiment, ε d and ζ are calculated under different size parameter x and k by Mie scattering theory, see
As shown in
The preparation of samples plays a crucial role in the experimental results. In the experiment, fully ground KBr was mixed with fly ash particles and then compressed into slab. The procedures of sample preparation are as follows: 1) Spectrum pure KBr pellets are ground into powder; 2) Fly ash and KBr are mixed with mass ratio 1:100; 3) The mixture was compressed using a tablet pressing machine under pressure 7 t/cm2; 4) Because KBr is deliquescent, infrared heating was used to ensure that the preparation of sample was in a dry environment.
Measurement of the hemispherical-directional reflectance and transmittance spectra of free-standing KBr sample was performed at room temperature, which means the emission of the sample can be neglected. The experiments examined the wavelength range of 0.55 - 1.65 μm using Fourier Transform Infrared Spectroscopy (FTIR). The experiment equipment illuminated hemispherical radiation onto sample slab. Then the effective radiation intensity of upper surface I e f f , 1 and lower surface I e f f , 2 were separately received by two FTIRs, see
R = I e f f , 1 / I λ , s o u r c e , T = I e f f , 2 / I λ , s o u r c e . According to the reversibility of light, the hemispherical-directional reflectance R and transmittance T were equal to directional-hemispherical reflectance and transmittance that are required in the four-flux model. Based on the experiment data, the absorption, scattering coefficients of the fly ash system can be calculated and then the absorption, scattering efficiency and optical constant of single particle can be further retrieved.
There is multiple value problem when calculating optical constant of particles with large size parameter, which means a group of testing data (R, T) will get multiple values of (n, k). Thus, the optical constant of fly ash was retrieved from particles D ¯ 43 = 3.21 μm . The reflectance and transmittance spectra are displayed in
As shown in
In the calculation of the heat transfer in RSC, the absorption, scattering coefficient and phase function of the fly ash particle system can be obtained according to the optical constant combining with suitable particle scattering model and particle size distribution, and the radiative transfer equation can be further solved.
In the experiment, the density of fly ash was ρ = 2225 kg/m 3 ; the thickness of
KBr sample was L = 1.1 mm ; particle size was D ¯ 43 = 22.7 μm . Five groups of controlled experiment were set up with the mass fraction of Fe2O3 ranging from 0.85% to 16.53%. The absorption and scattering efficiency calculated by genetic algorithm is shown in
It can be seen from
Since Fe2O3 has strong absorption characteristic when the incident wavelength is less than 4 μm [
As shown in
found that with the increase of the size parameter x, the scattering and absorption efficiency of the particles approach a constant respectively. And for materials with larger k value, the size parameter x is smaller when the absorption and scattering efficiency tends to be stable.
In the calculation of heat transfer in RSC, the absorption and scattering efficiency of large size parameter fly ash can be approximately determined as fixed values which are not affected by the variation of Fe2O3.
Fu, Z.F., Wang, Q. and Zhang, J.S. (2018) Experimental Study on the Radiative Properties of Fly Ash in the Radiant Syngas Cooler of Gasifier. Journal of Power and Energy Engineering, 6, 9-20. https://doi.org/10.4236/jpee.2018.69002