Large Eddy Simulation of Pulverized Coal Jet Combustion and Flame Propagation

The characteristics of a pulverized coal jet flame ignited by a preheated gas flow are modeled with large eddy simulation (LES) method. An open-source computational fluid dynamics (CFD) code –OpenFOAM (open field operation and manipulation) is applied to predict the instantaneous temperature, pressure, vortices and species mass fraction of the whole combustion process. The sub-grid scale (SGS) turbulence and combustion models based on the one-equation eddy-viscosity model and the kinetic-diffusion limited rate surface reaction model are used in the modeling process. Jet combustions with different inlet velocities are simulated to get an optimal value under the condition that a good combustion kinetic filed can be established. In order to prove the advantages of LES on the predictions of turbulent combustion, Reynolds-averaged Navier-Stokes (RANS) simulation has been performed and compared with the results of LES. The results suggest that LES can predict the instantaneous values of turbulent combustion while RANS can only get average effects. The ability of LES to capture the high and low values of temperature and species concentrations is better, and it can capture the flame centre and predict the recirculation flows more accurately than RANS. Furthermore, the effect of coal particle diameters on the flame characteristics is also investigated by LES. It has been observed that the region of high temperature is wider, the flame center is closer to the nozzle exit, and the local temperature is higher for smaller particles. The results also show that the combustion is more intensive and complete for smaller particles, which are coincident with the combustion theory.


Introduction
Numerical simulation has been regarded as one of the most powerful tools for analyzing the characteristics of industrial systems recently. A great number of commercial computational fluid dynamics (CFD) software have been developed. However, in practical two-phase combustion devices such as pulverized coal combustion furnace and propulsive devices, the combustion process is a very complex phenomena in which dispersion of fuel particles, evaporation (devolatilization), inter-phase chemical reaction and so on take place interactively at the same time.
To get the details of the whole turbulent combustion process, the direct numerical simulation (DNS) method which solves the governing equations directly is developed. Although DNS can predict the flow physics and chemical reactions accurately, it needs to handle all the governing equations with different length scales, from the largest scale (characteristic length of the computational domain) to the smallest scale of turbulence (Kolmogorov scale) [1], almost without any model assumptions. The demand of computing consumption and computer memory is so high that it is restricted to solve turbulence even with low Reynolds numbers and simple geometries under the existing calculation condition [2,3] As the flow in combustion furnace is commonly high Reynolds number, markedly nonlinear and multiphase, DNS would not be widely used in researching of practical industry phenomenon for a long time in the future.
Since multi-phase reacting flow process is much more complex than singlephase process, the computational cost is also much higher. For such complex process, RANS (Reynolds-Averaged Navier-Stokes) simulation method is commonly utilized. In this approach, the mass, momentum and energy transport equations are averaged statistically. The Reynolds stress tensor and mean reaction rate terms which are included in the conservation equations are modeled by turbulence model and combustion model, respectively. Although the computer capacity and calculation time of this approach are reasonable [4][5][6][7], the reacting flow behavior cannot be analyzed in detail, because RANS can only get time averaged solutions and is unable to get the characteristics of small length or small time scales, which play important roles in reacting flows. In many cases, RANS is far from enough for prediction and design in engineering applications. The former is needed to determine the terms related to the SGS stress tensor [8,9] the latter is needed to solve the momentum and energy source terms [10,11] in reacting flows. However, although an increasing number of studies on LES for gas combustion have been reported recently [12][13][14][15], to the author's knowledge, little attention has been focused on LES for coal combustion [16][17][18][19].
The purpose of this paper is to apply LES employing an open-source CFD code -OpenFoam [20] (open field operation and manipulation) to pulverized coal turbulent horizontal jet combustion. The SGS turbulence model and char combustion model are based upon the one-equation eddy viscosity model and kinetic-diffusion limited rate surface reaction model, respectively. The devolatilization model and radiation model are based upon the constant rate devolatilization model and P-1 model, respectively. The gas phase combustion model is based upon a simplified turbulent combustion model proposed by K. Yamamoto [18] Jet combustions with different jet velocities are simulated to get an optimal value under the condition that the flame center is in the central regime. Different particle size distributions are simulated to predict their influence on flame characteristics. Furthermore, the simulated results of LES are compared with those of RANS using k-ε model. The results show that LES has higher accuracy.

Flow field description and computational conditions
In this study, LES is applied to predict the characteristics of a pulverized coal jet flame. Figure 1 shows the schematic drawing of the test furnace. The mixture of coal and air is injected through the nozzle (diameter: 10mm) horizontally and ignited by the preheated gas automatically. The combustion gas flows to the outlet. The velocity of primary jet is 10 m/s and the preheated gas temperature is 1000K. The test furnace is a cuboid furnace, whose dimension is 0.3m×0.1m×0.5m. The coal combusted is a kind of bituminous coal with 21.1% of volatile matter, 65.9% of fixed carbon, 10.4% of ash and 2.6% of moisture.
The computational domain and grids are also shown in figure 1. The computational domain is divided into about 11,090 hexahedra volumes and the minimum cell is located near the nozzle exit for both LES and RANS simulation. The coal particle distribution uses the Rosin Rammler type of pdf model, the min and max diameters of which are 5μm and 565μm, respectively. The CPU time required for this computation is about 90h on one CPU.

Governing equations of LES
The turbulent flow is composed by many vortices of different scales. The large scale vortices influence the average flow, and the small scale vortices influence dissipation.
The basic idea of LES is to decompose the turbulence into large scale and small scale motions, solve Navier-Stokes equations directly for the large scale motions, and solve the small scale motions and their interaction with large scales by establishing the SGS models.
The LES equations, which are derived from spatial filtering of Navier-Stokes equations with a filtering width, are given as [21],  (1) , is the SGS stress tensor, which is the momentum transport between the filtered small scales and the solved large scale motions, and modeled by the one-equation eddy-viscosity model [22,23].

SGS turbulent flow model
Recent years, some inherent limitations of the SGS models used in LES have been found. For example, it has been demonstrated that the coefficient in the algebraic eddyviscosity model of Smagorinsky [8] has to be fine tuned for different flows [24].
Moreover, the coefficient is strongly dependent on the Reynolds number [25,26]. To overcome the deficiencies of these models, the one-equation eddy-viscosity model (OEEVM) [22,23] has been developed.
The SGS models of the eddy-viscosity model are based upon the hypothesis that the deviatoric part of the SGS stress tensor ) (B dev is aligned with the filtered deviatoric part of the rate of strain tensor ) (D dev locally, while the normal stress is assumed to be isotropic and thus can be represented by the SGS kinetic energy k [26], Here, Where B is the SGS stress tensor, k is the SGS kinetic energy, I is the unit tensor, D is the strain rate tensor, sgs  is the SGS viscosity, is the trace of tensor D .
In the one-equation eddy-viscosity model, an exact balance equation for k can be derived from the exact balance equation for B . It could be assumed that the terms of diffusion and dissipation are reasonably well modeled by terms of the form Here,

The radiation model
A radiation heat transfer equation considering the radiation recuperation between particles and fluid is solved by the P-1 model [27]. The governing equation goes as follows: Where  is the absorption coefficient, s  is the scatter coefficient, G is the radiation input, C is the linear-anisotropic phase function.

Coal combustion models
In turbulent reacting flows, the chemical reactions occur only when the molecules of fuel and oxidizer mixing together. Since the mix of molecules is in small gas mass, the SGS models considering the combustion features are needed to be developed.
Generally, coal combustion process includes three steps, first the volatile fraction giving off, then the gas phase combustion, and finally the char combustion [28].
The three kinds of combustion models are introduced in the following passages.

Devolatilisation model
There are many sophisticated devolatilization models, such as the FLASHCHAIN model [29], the distributed activation energy model (DAEM) [30] and the chemical percolation devolatilization (CPD) model [31], which require large computational resources. Therefore, those sophisticated models are not applicable to LES. An accurate and computational inexpensively devolatilization model is required for turbulent reacting flow simulation in LES.
In this study, a constant rate devolatilization model is proposed, of which the vaporization temperature needs to be set as 600 K. The volatile residual coefficient res C is set to be 0.001.

Gas phase combustion model
There are many turbulent combustion models for gas phase. For turbulent coal combustion, the eddy-break-up (EBU) model and the eddy dissipation model are based on intuitive arguments. The flamelet [32] model is one of the most promising models for gas fuel combustion but hasn't been coupled with coal combustion model which takes both devolatilization and char oxidation into account. Therefore, a simplified turbulent combustion model [18] is adopted in this study, Where RK S is turbulent reaction rate, Where C is the model parameter set to be 1.0,  is the kinematic viscosity, and  is the dissipation rate.

Char combustion model
For char combustion model, the kinetic-diffusion limited rate surface reaction model for coal parcels is used for a single reaction of C(s) + Sb*O2 -> CO2 to determine the consumption of char, where Sb is the stoichiometrical coefficient of the reaction.
If SMALL f comb  , the surface combustion active combustible fraction is consumed.
Here, Change in char mass (kg):

Comparisons among different inlet velocities
Images of pressure, velocity vector and temperature distributions on the central plane Hereafter the simulations are performed with inlet velocity 5m/s.

Simulation results and comparisons between LES and RANS
In order to confirm the advantages of LES, the simulation results of LES are compared with those of RANS with the optimal velocity. The distributions are shown by instantaneous value for LES and time-averaged value for RANS, respectively. Figure 4 shows the comparison of temperature distributions predicted by RANS and LES. It is evident, as expected, that RANS gets a longer and narrower flame than the actual one, which is because RANS is not able to predict the turbulence structures that are generated downstream the burner. On the contrary, LES obtains a wider flame and a region of high temperature evidently. This means RANS can't capture the flame centre and can't describe the shape of flame after the nozzle exit but LES can predict these clearly.
Recirculation flow is very important for coal jet combustion. It can first lengthen the residence time of particles in the high temperature field near the nozzle exit, accelerate the evolution of volatile matter and the progress of char reaction, and then enhance the flame stability and combustion efficiency. Figure 5 shows the comparison of velocity vector distributions. It is found that a big backflow is formed above the nozzle for both LES and RANS. It is also found that a small backflow is formed below the nozzle for only LES, and the region of high velocity in recirculation zone is larger for LES than that for RANS. These probably stem from the fact that LES can predict the instantaneous turbulent accurately which influences the recirculation flows markedly while RANS can only get an average effect. Thus, LES has advantages in simulating coal combustion. Figure 6 shows the mass fraction distributions of main gas species (CO2, CH4 and O2) on the central plane. Figure 6

Effect of the coal particle distributions
The study of combustion characteristics with three different particle distributions are also carried out by LES. The average diameters are 10 m  , 48 m  and 90 m  represented by Ptc1, Ptc2 and Ptc3 in the following figures, respectively.
The instantaneous temperature distributions on the central plane for three particle sizes are shown in figure 8. It can be seen that, compared to Ptc2 and Ptc3, high temperature region expands for Ptc1. It is also found that the smaller the coal particle is, the closer the flame centre moves to the nozzle exit, and the higher local temperature can reach. These probably be attributed to the reason that smaller coal particle can promote the reaction activity and the ejection of volatile matter, and shorten the delay time of ignition, which lead to a stronger combustion intensity and more stable combustion. Figure 9 shows the velocity vectors on the central plane for three particle distributions. Compared to Ptc2 and Ptc3, the position at which the combustion gas begins to flow toward the outlet is closer to the nozzle, and the high velocity region is wider for Ptc1. These imply that the ignition place has moved forward because the mix of pulverized coal and gas is better for smaller coal particles. Figure 10 presents the comparisons of main species concentrations with different particle sizes. The concentrations of CO2 and CH4 are much higher and the concentration of O2 is much lower for Ptc1 than those anywhere for Ptc2 and Ptc3. The widths of high concentration region for CH4 and CO2, and low concentration region for O2 are likely to spread widely for Ptc1. These may be caused by the reason that the decrease of the particle diameter leads to a bigger coefficient of heat transfer. The number of the particle with the same mass is bigger, the gas-solid contact area is larger and the gas-solid mixing is enhanced. This indicates that the combustion is more intensive and complete for small particles. Furthermore, the ignition and complete combustion of volatile can lead to good flame stabilization, which is agree with the results of figures 8 and 9.

Conclusions
A three-dimensional large eddy simulation method is applied to study the characteristics of pulverized coal turbulent jet flame. The validity is investigated by comparing with RANS simulation. In addition, jet combustion with different inlet velocities are simulated to get a good combustion kinetic filed. Different particle diameters are used in the simulations to analyze their effects on the flame characteristics. The following conclusions can be drawn from this study: a. When the jet velocity is high, the coal jets directly to the opposite wall causing large collision loss, and the flame center is too close to the back wall. Therefore, we need to reduce the inlet velocity to make the coal particles slow down towards the opposite wall and to get the flame centre move forward to the furnace centre to get a better combustion condition. In this paper, it is found that 5m/s is an optimal jet velocity.
b. Compared with RANS, LES can predict the instantaneous values of turbulent combustion while RANS can only get average effects. The ability of LES to capture the high and low values of temperature and species concentrations is better. LES can capture the flame centre and predict the recirculation flows more accurately than RANS.
Shortly speaking, LES has advantages in simulating coal combustion.
c. From the comparisons of jet flame characteristics performed with different coal particle distributions, it is found that particle diameter plays an important part in reacting flow. The region of high temperature is wider, the flame centre is closer to the nozzle exit, and the local temperature is higher for smaller particles. These indicate that the combustion is more intensive and complete for small particles, which is corresponding to the combustion theory.