Large eddy simulation of electrostatic effect on particle transport in particle-laden turbulent pipe flows
Graphical abstract
Introduction
Electrostatic charges are often generated in particle-laden turbulent pipe flows due to particle-wall collisions. Electrostatic charges accumulated on particles and the wall tend to reach a certain status as equilibrium state [1]. Under the electrostatic effect, particles tend to agglomerate, stick to the pipe wall and even block the pipe [[1], [2], [3]]. Such electrostatic hazard and related phenomenon have attracted many scientists to investigate the working mechanism of electrostatics generation and its effect on the behavior of charged particles.
A lot of work performed has reported the working mechanisms of electrostatics generation and its effect on particle transportation [1,[3], [4], [5]]. Most of them are based on experimental study including the factors effect on electrostatics generation [[6], [7], [8]] as well as electrostatic effect on particle behavior in particle-laden turbulent flows [9]. Based on experimental data, some mathematical models were developed to analyze the basic mechanism of electrostatics. Matsuyama and Yamamoto [10] set up a charging model called as “charge relaxation model” and used it to explain the relaxation problem of charge transfer. Matsusaka and Masuda [4,5] proposed a theory of impacting electrification and verified the correctness of this model by comparing with experimental results of glass bead repeatedly impacting on a plate. The effect of impact velocity, angle and initial charge on the charge accumulation on particles were investigated. Bunchatheeravate et al. [11] developed a method to predict electrostatics generation for particles transporting in straight tubes. In addition, particle electrification in particle-laden turbulent flows were investigated by numerical simulations. Watano et al. [12] analyzed electrostatic generation and particle dispersion using two-dimensional Discrete Element Method (DEM). Arif et al. [13] simulated particle charging and collecting in electrostatic precipitators and presented the space charge density distribution. Grosshans and Papalexandris [14,15] investigated several factors effect on particles charging using LES simulation in two-way coupling including the material properties of particle and pipe, particle mass flow and Reynolds number. Grosshans and Papalexandris [16] proposed a model for non-uniform contact charging of particles, which may be closer to the actual electrostatic charging progress for particles. Furthermore, the electrostatic effects on particle behavior have been investigated using simulation method. Large Eddy Simulation (LES) coupling with the Discrete Element Method (DEM) was conducted by Lim et al. [17] to investigate the distribution of particles in pipe flow under the influence of an additional electrostatic field. Yao et al. [18] analyzed the particle dispersion under the effect of electrostatics in turbulent pipe flows and concluded that electrostatics does obviously change particle dispersion near the pipe wall.
As analyzed above, it is clear that there are little research studying the effect of electrostatics on particle behavior in turbulent flows including the working mechanism of particle dispersion, distribution, resuspension, deposition under electrostatic effect. Particularly in the boundary layer, the working mechanism of turbulent coherent structure acting on particles in particle-laden flows has been one of core problems in the area of multiphase flows for long term rather than electrostatics acting on particles in the boundary layer. In this work, the electrostatic effect on particle behavior in particle-laden turbulent pipe flows was investigated by coupling LES with Lagrange particle tracking technology. Particularly, particles transporting in the boundary layer were analyzed by combining turbulent coherent structure with electrostatic effect. In addition, the electrostatic equilibrium in the whole system was considered. The statistics of particle field at the electrostatic saturation state was analyzed as well as compared with that in absence of electrostatics.
Section snippets
Mathematical model
In this work, gas phase was considered as continuous phase and predicted by Large Eddy Simulation (LES). Particles with small volume fraction was considered as dispersed phase using two-way coupling Lagrange approach. The interaction between particle and fluid worked through exchanging the momentum, which depended on the momentum equation including an extra term taking account of particle effect. The detail can be seen in the following sections.
A schematic diagram of the computational domain in
Verification of charging model
Two electrification models including collision electrification and triboelectrification were verified separately as shown in Fig. 4. Fig. 4 (a) shows that the results obtained by collision electrification model agree well with the experimental and simulation results from Matsusaka et al. [4], where electrostatic charges were generated by a rubber particle impacting on a mental plate at the height of 0.4 m. In this work, the initial charge was set as a dynamic contact potential difference to
Conclusions
In this work, particle dispersion in a turbulent pipe flow was simulated and considered under the combined effect of turbulence and electrostatics. Conclusions can be obtained as following.
It was found that the generation rate of electrostatic charge gradually decreases with increasing collisions, eventually reaches a saturated state. Particles in a turbulent boundary layer tended to carry much more electrostatic charges than those at pipe center. Electrostatics caused more difference of
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by National Natural Science Foundation of China (No. 51776225; 51876221) and High-end Foreign Expert Introduction Project (G20190001270; B18054). The authors would also like to express their gratitude to Profs W. P. Jones and M. Fairweather for providing the BOFFIN LES code and for many helpful discussions on its use.
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