_{1}

^{*}

In coal-fired power generation industry, parameters such as particle size affect combustion efficiency. Especially in the application of two-phase flow clean energy, the parameters such as particle velocity, particle size distribution and concentration are very important, because the coal particle velocity, concentration or size range have an impact on the whole combustion process. This paper introduces an optical measurement setup based on the transmission fluctuation correlation spectrum measurement technique, which realizes the simultaneous measurement of particle velocity, particle size distribution and concentration. Compared with image method, ultrasonic spectrum method and other methods, the experimental device is simple and low-cost.

Based on the statistical characteristics of transmission fluctuation in flowing particle suspensions, transmission fluctuation spectrometry (TFS) as a new particle measurement method has been used to measure and analyze the particle parameters [

When the particle passes through the laser beam at a constant velocity, the transmitted light signal fluctuates with time due to the particle flow. The fluctuation is expressed by transmittance T ( t ) = I ( t ) / I 0 , where I ( t ) is the transmitted light intensity when the particle passes through the light radiation area at a certain time, I 0 is the incident light intensity, the transmission fluctuations are expressed in terms of the expectancy of the transmission square (ETS). By changing the averaging parameters, the ETS is obtained as a spectrum, which is related to the physical properties of the flowing particle suspension and the process of signal averaging.

Due to the low resolution of ETS for particle size distribution, so different TFS have been developed according to different signal average processing methods, such as transmittance fluctuation spectrum method of low-pass filter based on band-pass filter technology, transmittance fluctuation spatial average method, transmittance fluctuation time average method and their combination [

Particulate two-phase flow is widely used in many industrial processes, such as energy, environmental, processing, and power engineering. In order to improve process efficiency, reduce pollutant emission and improve product quality, it is necessary to measure and control the particle size distribution in particle two-phase flow. In the power generation industry, the particle size distribution of pulverized coal and biological objects is an important parameter related to combustion efficiency and greenhouse gas emission. Too large pulverized coal particles will lead to uneven flow distribution between burners and related combustion problems, while very fine particles will be taken away by wind during blowing, resulting in waste of raw materials. Keeping pulverized coal fed at a certain speed and concentration and ensuring particles with a certain particle size range in the combustion chamber will contribute to the improvement of combustion efficiency and heat transfer efficiency. Therefore, the particle size distribution and feed concentration should be kept within an acceptable range to ensure the optimal combustion process, maximize energy conversion and minimize pollutant emission [

The transmission fluctuation spectrum may also be obtained with correlation techniques [

In our work, we propose to use two pinholes to generate a pair of parallel beams, and then cross-correlation the two transmittance signals to obtain the particle flow velocity [

In Section 2.2, the theory of TFS-SC and TFS-AC are simply reviewed. Section 3 introduces the experimental setup in detail and the measurement results are given. It is found that the TFS-AC can give reasonable results for certainly concentrated particle suspensions. In Section 4 we further discuss the application prospect of on-line measurement of TFS-AC technology and Section 5 is the conclusion.

The test principle of transmission fluctuation correlation spectrometry (TFCS) method is shown in

Particle velocity can be obtained by cross-correlation calculation of two transmission fluctuation signals [

E T P L , τ = e { T 1 ( t ) T 2 ( t + τ ) } = lim t s → ∞ 1 t s ∫ 0 t s T 1 ( t ) T 2 ( t + τ ) d t (1)

with the change of correlation time τ , when the cross-correlation signal E T P L , τ reaches the maximum and the correlation time is recorded as τ max , which can be combined with the distance L between the two beams to obtain the particle velocity

v = L τ max (2)

In the technique of TFS-SC, the expectancy of the transmission product ETP is defined a

E T P = e { T 1 ⋅ T 2 } = lim t s → ∞ 1 t s ∫ 0 t s T 1 ( t ) ⋅ T 2 ( t ) d t (3)

where t s is the sampling time, T 1 ( t ) and T 1 ( t ) are the fluctuating transmission signals of the beams.

The theory of the TFS-SC is developed on the basis of a layer model [

E T P = e { T 1 ⋅ T 2 } ≈ ∏ i = 1 N M L e { T M L i , 1 ⋅ T M L i , 2 } = ( E T P M L ) N M L (4)

where N M L = 1.5 P ⋅ Δ Z x is the number of layers in the particle system, x is the

particle size, Δ Z is the thickness of the measurement zone. P is the structural parameter, and it has a value not less than 1.5, which is dependent on the flow field conditions.

With assumptions of geometrical ray propagation and completely absorbent spherical particles, an analytical expression of the ETP through the monolayer is expressed as

E T P M L = 1 − β ⋅ [ 2 − χ ( Γ , Λ ) ] + ο ( β 2 ) (5)

where ο ( β 2 ) is the higher-order term of layer density, describing the monolayer density effects, β is the fraction of the monolayer projected area covered by the particles, which is called the monolayer density. For spherical particles β = P C V and C V is the particle volume concentration. χ ( Γ , Λ ) is transition functions, which is expressed as

χ ( Γ , Λ ) = ∫ 0 ∞ F T ⋅ F S ⋅ F P ⋅ d u (6)

Here, Γ is the dimensionless beam separation defined as the ratio of the beam distance L to the particle diameter x

Γ = L x (7)

and Λ is the dimensionless beam diameter. Defined as the ratio of the beam diameter D to the particle diameter x

Λ = D x (8)

F T is the spatial correlation factor of two beam transmission fluctuation signals

F T = J 0 ( 2 u Γ ) (9)

F S is the Fourier transform of the beam profile, describing the properties of spatial averaging on the transmission signal over the cross section of the beam

F S = [ 2 J 1 ( Λ ⋅ u ) Λ ⋅ u ] 2 (10)

F P is the particle shape factor and for spherical particles

F P = 2 J 1 ( u Γ ) u (11)

The principle of TFS-AC is much similar to that of TFS-SC, but the operation is a little different. The transmission fluctuation signal T ( t ) of a single beam is recorded in a quite long period of sampling time t s The ETP is then calculated with a autocorrelation time τ

E T P = e { T ( t ) T ( t + τ ) } = lim t s → ∞ 1 t s ∫ 0 t s T ( t ) T ( t + τ ) d t (12)

By changing the autocorrelation time τ , the ETP is obtained as a spectrum.

When the particle are passing through the incident beam vertically at a constant velocity v, the product of particle velocity and autocorrelation time is equal to the beams separation.

L = v ⋅ τ (13)

So Equations (5)-(11) can be fully applied to the TFS-AC. The only difference is that the variable parameter Γ in Equation (7) is no longer the dimensionless beam separation, but the dimensionless correlation time and it is expressed as

Γ = v ⋅ τ x (14)

when the particle concentration is not too high, the higher-order term of the layer density ο ( β 2 ) has little effect on the ETP, so Equation (5) is re-expressed as

ln E T P M L ≈ ln ( 1 − β ⋅ [ 2 − χ ( Γ , Λ ) ] ) = − β ⋅ [ 2 − χ ( Γ , Λ ) ] (15)

and hence the logarithm of the ETP of a three-dimensional system of mono-dispersed particles can be obtained.

ln E T P = ln ( ∏ i = 1 N M L E T P M L ) = N M L ⋅ ln E T P M L = − 1.5 Δ Z x ⋅ C V ⋅ [ 2 − χ ( Γ , Λ ) ] (16)

Equation (16) shows that for parallel beam, the beam diameter remains unchanged in the beam propagation direction.

The discussions above are for a mono-dispersed spherical particle system. For a dilute poly-disperse suspension steric interactions between the particles which are independent of each other. The poly-disperse suspension can be modeled as a number of monodisperse suspensions. So the logarithm of ETP is the sum of the contributions from each fraction x ¯ j of particles

ln E T P ( τ i ) = − ∑ j = 1 n 1.5 Δ Z x ¯ j ⋅ C V ( x ¯ j ) Δ x j ⋅ [ 2 − χ ( Γ i j , Λ j ) ] (17)

Here, τ i ( i = 1 , 2 , ⋯ , m ) is the variable time difference for signal correlation, x ¯ j ( j = 1 , 2 , ⋯ , n ) is the mean particle diameter in the j^{th} fraction of particle size and C V ( x ¯ j ) is the corresponding volume concentration. Γ i j = v τ i / x j is the dimensionless correlation time.

Equation (17) shows that the logarithm of ETP is linear with respect to the particle concentration, and the effect from the different particle size fractions superimpose linearly to from the logarithm of ETP. Therefore, the particle size distribution and volume concentration information can be retrieved simultaneously by inverse calculation the logarithm of ETP with Chahine iterations inversion algorithm [

According to Equation (17), we can construct a linear vector equation M ⋅ X = Y

∑ j = 1 n M i , j 1.5 Δ Z x j C V ( x ¯ j ) Δ x j ︸ X j = − ln E T P ( τ i ) ︸ Y i (18)

where, { M i , j } is the theoretical interpolation matrix, corresponding to the test principle.

For a uniform beam with constant diameter, the theoretical matrix is calculated as follows

M i , j = 2 − χ ( Γ i j = v τ j x j , Λ j = d B x j ) χ ( Γ , Λ ) = ∫ 0 ∞ J 0 ( 2 u Γ ) ⋅ [ 2 J 1 ( u Λ ) u Λ ] 2 ⋅ 2 J 1 2 ( u ) u d u (19)

{ − ln E T P ( τ i ) } is the transmittance fluctuation correlation spectrum obtained by correlation calculation to experimental data. { X j } is particle size distribution with an appropriate inversion algorithm to solve Equation (18), the particle size distribution can be retrieved. In addition, the volume concentration C V of the poly-dispersed particle system can be obtained simultaneously

C V = ∑ j = 1 n C V ( x ¯ j ) ⋅ Δ x j (20)

The experimental setup is schematically shown in

The measurements are performed on spherical, transparent particles glass beads and on non-spherical and white opaque particles silica sand. The nominal particle sizes of glass beads are 500 μm, 700 μm and 1000 μm, respectively and their density is 2.45 g/cm^{3}, the nominal particle size of silicasand particles is 800 μm and its density is 2.65 g/cm^{3}. In order to ensure constant measurement conditions during experimental measurement, the circulating speed of

the circulating disperser is set to 600 rpm, the particle flow velocity is 1.13 m/s, which is measured by a laser velocimeter.

In

_{3} of spherical glass beads particle and non-spherical silica sand particle under different concentrations. It can be seen that most of the particle distribution curves obtained under different concentrations have good repeatability. There are obvious deviations in the test results of silica sand particles at different concentrations, this is because silica sand belongs to non-spherical particles, and its test results are related to the spatial orientation of particles when they pass through the measurement area.

Glass bead (500 μm) | Glass bead (700 μm) | Glass bead (1000 μm) | Silica sand (800 μm) | |
---|---|---|---|---|

1 | 1.1824 | 1.1589 | 1.1437 | 1.2411 |

2 | 1.1589 | 1.1513 | 1.1438 | 1.1667 |

3 | 1.1667 | 1.1363 | 1.1667 | 1.1589 |

4 | 1.1363 | 1.1218 | 1.1513 | 1.1744 |

5 | 1.1363 | 1.1290 | 1.1218 | 1.1290 |

6 | 1.1363 | 1.1076 | 1.1218 | 1.1147 |

7 | 1.1363 | 1.1218 | 1.1147 | 1.1147 |

8 | 1.1076 | 1.1218 | 1.1076 | 1.1076 |

9 | 1.1218 | 1.1076 | 1.1076 | 1.2903 |

10 | 1.0803 | 1.1076 | 1.1006 | 1.1076 |

Particulate two-phase flow widely exists in energy, industry, environment and other fields. Especially the determination of particle parameters in coal yard thermal power generation, due to the poor environmental conditions in the coal yard, the instruments used to measure the coal diameter are limited. In the process of coal feeding into the hall furnace, the accurate grasp of the effective size range of coal particles can improve the combustion efficiency, and the control of speed and concentration can ensure the sustainability of the combustion process.

Particle size distribution and concentration can be obtained simultaneously by taking the particle velocity as the known value and inverse calculating the transmittance spectrum with an appropriate inversion algorithm. That is to say, as long as the particle is in the flow state, we can use this technology for real-time and on-line measurement of particle size distribution, volume concentration and particle velocity. Therefore, in the next work, we will develop this technology so that it can be used to measure particle velocity, particle size and concentration in two-phase flow.

This paper introduces a simple transmittance fluctuation correlation spectrum measuring device for simultaneous measurement of particle size distribution, particle concentration and particle velocity. The particle velocity is obtained by using the transmittance cross-correlation spectrum of two parallel beams, and the particle size distribution and concentration are obtained by using the transmittance autocorrelation spectrum of a single beam.

In the actual test, the glass beads and silica sand particles dispersed in water are driven by the circulating dispersion device, their transmittance signals are measured and their transmittance correlation spectrum is obtained. The particle size distribution, concentration and velocity are obtained by inversion calculation. Most importantly, the particle size distribution and concentration measurements are agreed with what we know, and the consistency and repeatability of the multiple measurements are high from the experimental results, so the method is expected to be developed for multi-parameter measurements of particles in two-phase flow fields, especially in the energy and power fields, this technology will bring certain potential and application value to promote the development of clean energy.

The author declares no conflicts of interest.

Gong, P. (2022) Measurement of Particle Velocity, Particle Size Distribution and Concentration in Particulate Suspension by Transmission Fluctuation Correlation Spectrometry. International Journal of Clean Coal and Energy, 11, 13-23. https://doi.org/10.4236/ijcce.2022.112002