A theoretical study on the attenuation characteristic of sound wave in boiler furnace
Xu Weilong1, Jiang Genshan2,*, An Liansuo1
1Department of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China
2Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
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Abstract
The characteristics of sound propagation in furnace is of great significance for acoustic technology applied in power plant for equipment state monitoring and control. In this paper, acoustic attenuation mechanism in the furnace has been analyzed in the range of sonic frequencies. Sound absorption in the fluid due to viscosity and thermal conductivity, sound absorption by the particles due to thermal conductivity, sound generated by the self-active of moving particles, scattering attenuation and viscous friction have been found to be the main factors in boiler furnace. A formula of sound attenuation coefficient has been established, some curves has been depicted to describe the relationship between the coefficient with the sound frequency, particle volume fraction, particle size and the flue gas temperature.
Keywords
sound propagation; acoustic attenuation coefficient; boiler furnace
1. Introduction
Acoustic technology applied in power plant equipment state monitoring and control has received wide attention and widely researched, mainly includes the monitoring on furnace temperature field and dynamic field, power station tube leak detection and location, sonic soot cleaning, acoustic combustion, etc[1-4]. For the lack of basic acoustic theory research applied in furnace issues such as the sound propagation characteristics are still unclear in the furnace, impeding the further development of the application of acoustic technology. Inside the power plant boiler furnace, the environment is complicated with high temperature and negative pressure state, along with pulverized coal particles suspended randomly. As acoustic wave propagation law in the furnace is directly affecting the application prospect of acoustic technology, it is of great significance to study the propagation characteristics in the boiler furnace contained with granular medium.
The general problem of acoustic attenuation in particle medium dates back to the theoretical study by Stokes[5] in 1851. Based on Rayleigh’s long-wave scattering theory, Swell[6] investigated the acoustic attenuation in viscosity fluid with immobilized spherical hard particles, and fixed Rayleigh’s results. In 1945, Lamb[7] investigated the acoustic attenuation in viscosity fluid with free movement spherical hard particles. In 1948, Urick[8] modified the theoretical formula of Lamb on the basis of . In 1972, combined with the equations of mass conservation, momentum conservation, and energy conservation, Allegra and Hawley[9] worked out the sound absorption coefficient which took particle scattering, viscosity and thermal conductivity into account, established the most comprehensive theory. In 1988, J. Sheng and A. E. Hay[10] established model expression of spherical particles scattering attenuation coefficient based on Johnson’s theory, which is the common expression to calculating scattering attenuation coefficient. In 1995, Qian Zuwen[11,12] took the sedimentary in marine shallow and bubbles in liquid for examples, investigated the acoustic propagation characteristics in thick particle medium by using multi-body and multiple scattering theory, and proposed the method to get related parameters in the medium through the measurement data and the propagation theory of acoustic wave in the medium. Based on the mathematical model of Allegra & Hawley, Su Mingxu[13,14] investigated the acoustic attenuation characteristics and phase velocity in two kinds(titanium dioxide –water and iron powder-water) of ultrafine particle suspension, analyzed the influence characteristics of frequency, particle size and particle volume fraction on attenuation and phase velocity, and they have been engaged in research on measuring particle medium parameters with acoustic inversion method. In 2008, Peng Linhui[15] and others investigated the acoustic attenuation in particle suspension which is in China offshore waters under sonar acoustic frequency , that is at the basis of the mechanism of sound absorption. In 2013, Valverde[16] investigated the acoustic streaming in gas-fluidized beds of small particles, in which acoustic attenuation characteristics were detailly discussed.
In this paper, considering the particle medium in power plant, acoustic attenuation characteristics in furnace have been analyzed under sonic frequencies. The different attenuation mechanisms are discussed, so are the impact of frequency, concentration, temperature and particle diameters. The formula of attenuation coefficient in power plant boiler furnace has also been given.
2. Basic theory
2.1. Attenuation due to the fluid
In the range of sonic frequencies, the relaxation effect of medium can be ignored. According to the classical sound absorption formula, acoustic absorption is calculated as follows(the so-called second viscosity can be also ignored):
(1)
where is the oscillating angular frequency, is the medium density, is the sound velocity, is the dynamic viscosity, is the heat transfer coefficient, is the constant pressure heat capacity, is the constant volume heat capacity. It can be seen that the sound attenuation coefficient of medium is associated with the physic properties of the medium. As shown in Table 1 is the thermal physical properties of the flue gas.
Table 1.Thermal physical properties of flue gas under furnace pressure
TTemperature
(℃) /
Density
() /
Constant pressure
heat capacity
() /
Heat transfer coefficient ) /
dynamic viscosity
() /
Kinematic viscosity
()
600 / 0.405 / 1.214 / 7.42 / 37.9 / 93.61
800 / 0.330 / 1.264 / 9.15 / 43.4 / 131.8
1000 / 0.275 / 1.306 / 10.90 / 48.4 / 174.3
1200 / 0.240 / 1.340 / 12.62 / 53.0 / 221.0
As shown in Figure1, the sound absorption coefficient increases accompany with the increasing of the frequency in the same temperature. The higher the temperature of the medium is, the bigger the coefficient will be in the same frequency. It can be also found that the change of sound absorption coefficient of the medium with temperature impacts little.
Figure 1.The distribution of sound attenuation coefficient changed with frequency in different gas temperature
2.2. Attenuation due to the particles
Acoustic attenuation in particle medium depends on several factors such as dissipation of sound energy on the solid surface, sound wave scattering. Each one of these contributions will be addressed in detail in this section. Except for circulating fluidized bed boiler, the particle volume fraction in the boiler furnace is less than 0.1 (the interaction between particles can be ignored). In this paper, only the general boiler will be discussed.
Firstly, approximate a solid particle of characteristic size to a sphere of radius . A sphere oscillating in a viscous fluid with a velocity would generate in turn a sound wave of the intensity,given by , where would be the sound intensity of the effective acoustic field observed from a frame of reference solidary to the sphere. The value of is completely negligible in the range of sonic frequencies and for propagation in the flue gas.
By considering dissipation due to heat conduction produced by local temperature gradients when the sound wave impinges on the body, the total effective cross-section for the absorption of sound by a sphere of radius R can be calculated as
(3)
Hereis the fluid thermometric conductivity(), is the Stokes boundary layer thickness(). By multiplying by the number of particles per unit volume n, the absorption of sound by particles can be calculated as
(4)
Here , is the concentration of particles medium in flue gas.
According to equation (4), acoustic attenuation coefficient due to heat conduction produced by local temperature gradients when the sound wave impinges on the body is connecting with the concentration of the particle medium, diameters of the particles, frequency and physical properties of the flue gas.
The particle will cause the acoustic scattering in particle medium, and in viscous fluid, viscous wave will be generated except for scattering wave. Acoustic attenuation coefficient due to the acoustic scattering and viscous attenuation can be written as
(5)
According to the law of Rayleigh scattering , the scattering attenuation in particle medium can be calculated as
(6)
Based on the range of the diameters of the particles and the sonic frequency, equation (5) can be simplified as
(7)
where the first item on the right side of the equality is the viscous attenuation , meanwhile the second item is the scattering attenuation. According to the equation (7), in can be inferred that attenuation caused by viscous damping is far more bigger than it caused by scattering attenuation in the range of sonic frequency in boiler furnace.
From what has been discussed above, the total attenuation coefficient in boiler furnace can be calculated as
(8)
3. Results and Discussion
Figure 2. Penetration depth of a sound wave in the boiler furnace as a function of particle size and frequency. (a) Taking into account all the attenuation mechanisms considered in the text and for different values of the wave frequency as indicated.(b) As a function of particle volume fraction and at different frequencies as indicated. (c) As a function of particle size and at different frequencies as indicated. (d) As a function of particle size and at different temperatures as indicated. .unless otherwise stated, The gas is supposed to be flue gas at T=1200 ℃ when the pressure is 101225 Pa and the particle volume fraction is and the particle size is .
In order to assess the relevance of sound attenuation in boiler furnace, the penetration depth as the distance in which the sound intensity level SIL is reduced by 10 dB (). Figure 2(a) shows a plot of d10 as function of particle size for a boiler furnace () in flue gas at T=1200 ℃. It may be observed that for particles of size smaller than 200, d10<1 m, while for particles smaller than 100, d10 would decrease blow just 1m. on the other hand, penetration depths close to five meter are predicted for particles of size larger than 400at low frequencies. Figure 2(b) shows the effect of particle volume fraction on the sound intensity attenuation. Sound is markedly attenuated asis increased.
Concerning the effect of sound frequency, it can be seen in Figure 2(a) and Figure 2(b) that d10 is increased is increased asis decreased. The augmentation is more marked as the particle size is increased. Thus, a recommendation to avoid excessive attenuation and to use sound for enhancing process in boiler furnace would be to select low frequencies. As regards the effect of temperature, and due to the dependence of gas properties on it, an increase of temperature would lead generally to a decrease of d10 as may be observed in Figure 2(c) and Figure 2(d).
Finally, sound intensity attenuation due to divergence of the wave should be assessed for industrial scale boiler wherein the sound wave should propagate over large distances and cannot be longer considered as a plane wave. At large distances r from the wave source the total energy of the wave front is spread out over a spherical surface area , therefore, the intensity of an expanding spherical wave decreases proportionally to , which would lead to the so-called spherical spreading loss. Spreading losses can be overcome in practical implementations by placing an array of sound generators capable of reproducing a plane-wave acoustic field.
4. Conclusions
This manuscript has been devoted to a detailed analysis on the attenuation characteristics of sound wave in the power plant boiler furnace. The source of acoustic attenuation in the range of sonic frequencies stems from sound absorption due to viscosity and thermal conductivity of the fluid itself, dissipation of sound energy on the solid surface, and sound wave scattering. But it mainly stems from energy losses due to viscous friction and thermal conduction on the surface of the particles. Acoustic attenuation coefficient is connecting with the temperature of the flue gas, the particle volume fraction, frequency, and particle size. An increase of particle volume fraction or frequency or particle size would all lead to the increase of acoustic attenuation.
Acknowledgements
Support is acknowledged from the National Natural Science Foundation of China (11474091 and 1127111) , the Natural Science Foundation of Hebei Province of China (A2015502077) and the Fundamental Research Funds for the Central Universities(2015XS105)
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