A DNS study on the stabilization mechanism of a turbulent lifted

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Direct Numerical Simulation Study on the Stabilization Mechanism of a Turbulent Lifted Pulverized Coal Jet Flame in a Heated Coflow Kun Luo, Yun Bai, Tai Jin, Kunzan Qiu, and Jianren Fan* State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, 310027, China ABSTRACT: The stabilization mechanism of a turbulent lifted pulverized coal jet flame in a heated coflow is investigated by means of three-dimensional direct numerical simulation. The coal particles are tracked in the Lagrangian frame with experience of moisture evaporation, volatile releasing, and carbon combustion. The devolatilization process is modeled with a competing two-step model, and the carbon reaction is described by a single-film model. It is found that the mean velocities for the gas-phase and particles can develop into self-similar profiles, while the fluctuation velocities have not achieved the self-similar status. The turbulence can be enhanced by ignition and combustion processes. By investigating the correlations among the temperatures, heat release rate, and devolatilization rate, it is found that autoignition of the volatile is the key mechanism responsible for coal flame stabilization under the present condition. The heating effects from the stripe flames in the shear layers, heated coflow, and flame base upstream can also contribute a larger convection term in the temperature equation near the jet center and create a favorable environment for the formation of a stable flame base there. The local gaseous convection along with the flame propagation and particles’ movements can cause the downward migration of the flame stabilization point. The migration of the flame base along with the formation of a new flame base upstream due to the autoignition forms a cycle and the coal flame can burn stably. structures, namely, interspersed flame, stripe flame, and stabile continuous flame, by analyzing a three-dimensional pointsource DNS of a turbulent coal jet flame performed by Luo et al.25 It is found that these three flame zones have a similar gaseous reaction. The stripe flame is the foundation of the stable flame base due to a significant heat release contribution to the whole jet flame. Hara et al.26 performed a DNS to investigate the experimental coal jet flame1 employing the proposed two-step global reaction scheme for the volatile matter. The DNS reveals that there appears premix and diffusion flame layers with different reaction patterns inside and outside in the pulverized coal jet flame. In the inner layer, the reaction of the volatile matter and O2 in coal-carrier air occurs, whereas the reactions of volatile matter and CO and O2 in surrounding air occur in the outer layer. After a successful forced ignition, to stabilize the flame becomes an important issue because a stable flame is always necessary for an efficient combustion system. Some experimental studies27−29 have emphasized that the stabilization of pulverized coal flames relies on the near burner region (NBR) aerodynamics. The stable flames can be established by creating the regions of low flow velocity and the environment conductive to volatile matter evolution by swirling the entire secondary air or using bluff-body techniques in industrial boilers. Besides, in the studies of rotary kilns,29−31 it is found that particle clustering in pulverized coal flames can have a significant influence on flame stability improvement. A new burner consisting of a central precessing air jet is applied to stabilize pulverized coal flames. For the oxy-coal combustion,

1. INTRODUCTION The coal-fired furnace is still one of the main energy production ways nowadays in the world. For developing the nextgeneration clean coal combustion technology, there is a need to improve the fundamental understandings of coal combustion, such as the flame stabilization mechanism and the pollutants’ generation and migration patterns and so on. Because of the complex interactions among the two-phase flow and multiple processes in pulverized coal combustion, it is still difficult to obtain detailed information about flow field and particles’ behaviors through experiments, although some new measuring technologies have been utilized in some laboratoryscale flames, such as the pulverized coal combustion in round or swirling jet burners and one-dimensional (1-D) strained methane/air flame, and single coal particle combustion in droptube furnaces or entrained-flow reactors.1−7 With the development of computer science, the numerical simulation of pulverized coal combustion is becoming a promising tool to investigate coal combustion. Researchers have applied Reynolds averaged Navier−Stokes (RANS) and large eddy simulation (LES) to study the pulverized coal flames, from the laboratory scale to the semi-industrial scale.8−21 As a more accurate numerical method, direct numerical simulation (DNS), which does not apply a turbulence model or a turbulent combustion model, can provide more detailed information and access to study the phenomenon of pulverized coal combustion. In order to analyze the effects of turbulent velocity fluctuation, particle equivalence ratio, and particle diameter on the early stages of pulverized coal combustion, Brosh et al.22,23 carried out several DNS cases of localized forced ignition of coal particle-laden mixtures in a cubic box domain. It is found that these parameters can greatly affect the extent of burning and combustion sustaining. To investigate the coal flame structures, Bai et al.24 identified three typical flame © XXXX American Chemical Society

Received: May 9, 2017 Revised: June 30, 2017 Published: July 3, 2017 A

DOI: 10.1021/acs.energyfuels.7b01342 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels the flame characterization is different and some research studies on stabilization of oxy-coal combustion are reviewed by Chen et al.32 Though these studies have investigated the influence factors on pulverized coal flame stabilization, the detailed coal flame stabilization mechanism still remains vague and confined to the engineering level. For developing the next-generation clean coal combustion technology, there is a need to further understand the stabilization mechanism of coal combustion flame. Many experimental and numerical studies33−40 have been conducted to investigate the stabilization mechanism of lifted gaseous flame, and some stabilization mechanism theories have been proposed, such as the premixed flame theory, nonpremixed flame theory, edgy-flame concept and large eddy theory and so on.41−43 In addition, many studies have recently shown that autoignition plays an important role in the lifted flame stabilization both in gaseous flames35−38,44,45 and spray flames.46−48 By investigating the evolutions of intermediate species using DNS, Yoo et al.35,37 found that autoignition in a fuel-lean mixture at the flame base was the key mechanism responsible for flame stabilization both in hydrogen and ethylene jet flames, and proposed that the flame stabilization is determined by a balance between the local flow velocity and autoignition events. Navarro-Martinez et al.36 studied the Cambridge flames and Berkeley flames using large eddy simulation-conditional moment closure (LES-CMC) approach. By analyzing the convective-diffusive-reactive (CDR) budgets, i.e., each term in the species transport equation, the autoignition is identified as the flame stabilization mechanism. With laser diagnostics, Juddoo et al.45 studied the evolution of extinction and reignition events in nonpremixed compressed natural gas flames by analyzing the high-speed images of OHPLIF (planar laser-induced fluorescence) qualitatively. Three types of flame structures, namely “break”, “closure”, and “growing kernels”, are identified and could play a significant role in the dynamics of extinction/reignition. For spray combustion, O’Loughlin et al.46 used high-speed LIF-OH imaging and joint imaging of LIF-OH-CH2O to study the flame structure of dilute sprays. The “break” and “closure” events are also observed in spray flames. All these various flame structures are closely associated with the autoignition, indicating its important role in flame stabilization. For coal combustion, the flame stabilization mechanism could be more complicated and different from gaseous or spray flames because of the complicated interactions between gasphase and particles involved. However, there has been little study on this point so far. In the present work, the threedimensional DNS of a pulverized coal jet flame in a heated coflow performed by Luo et al.25 is further investigated. The global flame characteristics and the dynamic evolution of the flame base are analyzed. The flame stabilization mechanism is then investigated in detail.

∂ ∂ (ρg ug, i) + (ρ ug, iug, j) ∂t ∂xj g =−

∂ ∂ (ρg Yk) + (ρ (ug, j + Vk , j)Yk) = ω̇ k + Sk̇ ∂t ∂xj g cv

∂t

+

∂ (ρ ug, j) = Sṁ ∂xj g

∂ρg Tg

= −cv

∂t

∂ρg ug, jTg

− ρg + σij

∂xj N

∂Tg

∑ (YkVk , jcp, k) +

∂xj

k=1

∂ug, j ∂xi

∂ + ω̇T − RTg (ρg ∂xj

(2)

(3)

N

∑ YkVk , j/Wk) k=1

∂ ⎛⎜ ∂Tg ⎞⎟ λg ∂xj ⎜⎝ ∂xj ⎟⎠

N

+ ρg

∑ Ykfk ,i Vk ,j + Q + Ω̇ + SṪ k=1

(4)

p = ρg

R Tg W

(5)

In these equations, the subscript g represents gas phase and the subscript p represents coal particles. Equation 4 is the temperature transport equation, where Q and Ω̇ are the convective and radiative heat transfer between the particles and gas phase, respectively, and calculated as Q = πd pNuλs(Tg − Tp)

A exp(A) − 1

Ω̇ = εσπdp(Tg4 − Tp4)

(6) (7)

where A is the transfer number, ε is the blackness of particles, ̇ , SV,i ̇ , Sk̇ and ṠT are and σ is the Stefan−Boltzmann constant. Sm source terms of mass, momentum, species and temperature originated from the particles. For the coal particle combustion, the shrinking core model with a constant coal density and point-source assumption that the volume effect is not considered are used. The particles are tracked in the Lagrangian frame only considering the Stokes force and gravity. The governing equations for particles are written as

dx p dt du p dt

= up =

dm p dt

2. NUMERICAL METHOD 2.1. Governing Equations. In the present study, the fully compressible form of governing equations for the mass, momentum, species, and temperature are directly solved. Considering the effects of coal particles, these equations and the ideal gas state equation read: ∂ρg

∂τij ∂p + ρg gi − β(ug, i − u p, i) + SV̇ , i + ∂xj ∂xi

c ppmp

(8)

(u g − u p) τp

+g (9)

= ṁ w + ṁ v + ṁc dTp dt

= πd pNuλs(Tg − Tp)

(10)

A exp(A) − 1

+ εσπdp(Tg4 − Tp4) − ṁ w Lw − ṁ vQ v + ṁcΔHc

(11)

Equation 10 is the mass equation which shows that the total mass change of the particles includes the moisture evaporation rate ṁ w, volatile releasing rate ṁ v and carbon combustion rate ṁ c. The devolatilization process is modeled with the competing two-step devolatilization model49 considering the different

(1) B


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Figure 1. Calculated flame thickness of (a) laminar premixed flame and (b) laminar nonpremixed flame using the current two-step chemical mechanism.

respectively. An explicit tenth-order filter method is applied to suppress numerical errors. The improved Navier−Stokes characteristic boundary conditions (NSCBC) are used to prescribe the boundary conditions. For more details about the governing equations, the coal combustion models and the numerical methods, please refer to previous relevant studies.24,25,52 2.2. Computational Configuration. The DNS is configured according to the experimental gaseous jet flame carried by Cabra et al.53 with the same mean jet velocity of Uj = 107 m/s and the same nozzle diameter of D = 4.57 mm. In the present DNS, the coal jet flame consists of two streams, namely, the center jet and the heated coflow. The cold center jet is issuing through a nozzle with a mixture of pulverized coal particles and air (YO2 = 0.233, YN2 = 0.767, T = 320 K) at a mean velocity Uj. The inflow Reynolds number based on the nozzle is Re = 28284. The heated coflow jet is designed as the production of a premixed hydrogen-air flame with an equivalence ratio of ϕ = 0.478 (YO2 = 0.12, YH2O = 0.1237, YN2 = 0.7563, T = 1600 K) to mimic the background temperature of coal-fired furnaces. The velocity is set as 0.5 m/s. The inflow axial velocity profile is given using the 1/7 law and a random velocity fluctuation is superimposed on the mean flow.52 The maximum central inflow velocity is about U0 = 1.25Uj. The computational domain is set as 35.6D in the streamwise direction and 20D in the other two directions after studying the domain effect. In the Cabra flame,53 the estimated mean Kolmogorov scale is between 50 μm and 500 μm. To resolve the flame reaction zone, the flame thickness for laminar premixed flame and nonpremixed flame are calculated using the current two-step chemical mechanism. For laminar premixed flame, the flame thickness δP is defined according to the temperature profile and computed as54

devolatilization rates under high and low temperatures, and the devolatilization rate ṁ v is calculated as ṁ v = ṁ v1 + ṁ v2 ⎛ E ⎞ ⎛ E ⎞ = −α1mdaf B1 exp⎜⎜ − 1 ⎟⎟ − α2mdaf B2 exp⎜⎜ − 2 ⎟⎟ ⎝ RTp ⎠ ⎝ RTp ⎠ (12)

where mdaf is the mass of the daf (dry and ash free) coal. A single-film model is utilized to describe the reaction on the surface of the coal particles:50 C + O2 → CO2, 2C + O2 → 2CO, and C + CO2 → 2CO. The corresponding char reaction rate ṁ c is expressed as ⎡ ⎛ E ⎞ 1 1 ṁc = −πd p2ρg × ⎢ YO2,sBA exp⎜⎜ − A ⎟⎟ + YO2,sBB ⎢⎣ γA γB ⎝ RTp ⎠ ⎛ E ⎞ ⎛ E ⎞⎤ 1 exp⎜⎜ − B ⎟⎟ + YCO2 ,sBC exp⎜⎜ − C ⎟⎟⎥ γC ⎝ RTp ⎠ ⎝ RTp ⎠⎥⎦

(13)

YO2,s and YCO2,s are the oxygen and carbon dioxide concentrations at the particle surface, and can be calculated by solving the species diffusion equation near the surface as YO2,s = −

ṁ O2 ṁ p

YCO2,s = −

⎛ ṁ O2 ⎞ ⎟ exp( −A) + ⎜⎜YO2, g + ṁ p ⎟⎠ ⎝

ṁ CO2 ṁ p

⎛ ṁ CO2 ⎞ ⎟ exp( −A) + ⎜⎜YCO2,g + ṁ p ⎟⎠ ⎝

(14)

(15)

As YO2,s and YCO2,s are coupled with the mass change rates ṁ O2, ṁ CO2, and ṁ p, the iterative procedure is applied to determine the char reaction rate.50 The volatile matter is assumed as CH4, and burnt with a reduced two-step chemical mechanism,51 as detailed species and chemistry prevent such DNS. Readers are referred to refs 24 and 25 for more detailed information about the related coefficients in the models above. To solve the gas-phase governing equations, an eighth-order central spatial differencing scheme and a fourth-order Runge− Kutta scheme are used for spatial and temporal discretization,

⎛ ∂T ⎞ ⎟ δ P = (Tmax − Tmin)/max⎜ ⎝ ∂x ⎠

(16)

The calculated premixed flame thickness at different equivalence ratios are shown in Figure 1a. The minimum value is about 300 μm. For lamina nonpremixed flame, the opposed flame is used to determine the flame thickness. By studying different stoichiometric scalar dissipation rate χst, it is C


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Figure 2. Particle distributions and vortex isosurface superimposed with gas-phase temperature.

Figure 3. Instantaneous contours of (a) gas-phase temperature and (b) heat release rate at a typical central plane superimposed by the distributions of devolatilizing coal particles (white points) and carbon-combusting particles (black points) at the time of 9.750 ms.

The coal studied here contains 1.5% moisture, 23.4% volatile matter, 39.1% fixed carbon and 36.0% ash. The coal particles are issued into the domain with a mass rate of 0.2112 × 10−3 kg/s. The particle diameter is set as 10 μm to make sure it is small enough compared with the gird size so that the pointsource assumption is reasonable. The initial temperature and velocity of the coal particles are set to be the same as those of the local fluid. The time step is taken as Δt = 6.5 × 10−2 μs, and a flow-through time is 1.52 ms. About 7 flow-through periods are marched to obtain the stationary statistics with about 2.2 million CPU hours. When achieving the stationary statistics, there are about 0.6 million coal particles in the computational domain at each time step.

found that the extinction value of stoichiometric scalar dissipation rate is about χst,q = 20 s−1. The flame thickness δD is determined either based on the full width at half-maximum of the temperature profile (δD1)55 or using the mixture fraction profile analogous to eq 16, δD2 shown in Figure 1b. It is obvious that the minimum flame thickness is about 700 μm. Considering the turbulence influence on the flame thickness, 1 a uniform g rid size o f Δx = 45 D = 101.6 μm and 1

Δy = Δz = 60 D = 76.2 μm are adopted in the central zones (|r/D| ≤ 4) where the combustion mainly takes place, to resolve both turbulent and chemical reaction scales. Outside of the central reaction zone, another uniform grid size of Δy = Δz = 392 μm is applied to reduce the computational cost. The total gird number is 1664 × 656 × 640, about 700 millions. D


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3. RESULTS AND DISCUSSION 3.1. General Flame Features. Figure 2 depicts the particle distributions and vortex isosurface with gas-phase temperature

gradually appear in the shear-layer region attached to these devolatilizing particles. As the jet advances, more coal particles devolatilize and disperse more widely in the radial direction. Some particles pass through the shear layers and burn the char in the coflow region after devolatilization, while some other devolatilizing coal particles burn the volatile in the inner sides of the shear layers. The discontinuous flames begin to grow into stripe flames with the increase of the downstream distance. At the location of x/D = 27, these stripe flames merge across the central axis and form a stable flame base of the coal flame, with a large number of devolatilizing coal particles concentrated there as shown in Figure 3b. For the carbon-combusting particles, they are distributed in the outer sides of the shear layers in the upstream region, which are usually observed as luminous spots or streaks in experiments.1,6 While in the downstream region, the carbon-combusting particles are found not only in the hot coflow regions but also in the central reaction zones. In general, the whole flame is lifted and stabilized with the assistance of the hot coflow. The reaction zones with high heat release rate all come out around the devolatilizing particles as shown in Figure 3b, which indicates the importance of volatile devolatilization and combustion to the formation of a stable coal jet flame. To investigate the flow characteristics, an overall description of the jet flow should be provided. Figure 4 presents the downstream evolution of time-averaged gas-phase axial velocity at the centerline U̅ g,c and the jet half-width δ1/2, which is defined as the half of the radial distance at which the mean gaseous axial velocity U̅ g reaches to 50% of the corresponding axial velocity at the centerline. It is readily observed that the δ1/2 grows faster than the decrease rate of U̅ g,c. After x/D = 10, the jet half-width increases significantly, indicating the expansion of the jet flow due to the presence of the flame. Figure 5 presents the downstream evolution of mean and root-mean-square (rms) axial velocities and temperatures for both gas-phase and particles at the centerline. It is found that the particle velocity is slightly larger than gas-phase velocity since the Stokes number of most particles at the centerline is around 2.8,24 showing a certain inertia for moving particles.

Figure 4. Downstream evolution of the time-averaged gas-phase axial velocity at the centerline Ug,c and the jet half-width δ1/2.

superimposed. It is clear that the current coal jet flame has been fully developed and has complicated vortex structures. The flame are much more curved and three-dimensional. Figure 3 presents the instantaneous contours of the gasphase temperature and heat release rate at the typical central plane of the jet flame at the time of 9.750 ms. The distributions of the devolatilizing coal particles (white points) and carboncombusting particles (black points) are also superimposed. Here the particles with the devolatilization rate exceeding 1.0 × 10−10 kg/s denote the devolatilizing coal particles and the particles whose carbon reaction rate exceeds 1.0 × 10−12 kg/s are marked as the carbon-combusting particles, considering the maximum devolatilization rate and carbon reaction rate are about 3.27 × 10−9 kg/s and 1.76 × 10−11 kg/s respectively in the present study. It is found that the coal particles are largely influenced by the jet vortex structures to concentrate in certain regions with high strain and low vorticity. In the upstream region, some coal particles begin to devolatilize due to the preheating of the coflow, and some isolated reaction zones

Figure 5. Downstream evolution of (a) mean axial velocities; (b) rms axial velocities; (c) mean temperatures; and (d) rms temperatures for gasphase and particles at the centerline. E


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Figure 6. Axial distributions of gas-phase Reynolds stresses at the centerline: (a) normal stresses and (b) shear stresses.

Figure 7. Radial profiles of (a) the time-averaged gas-phase axial velocity U̅ g; (b) the gas-phase velocity fluctuation u′g; (c) the time-averaged particle axial velocity U̅ p; and (d) the particle velocity fluctuation u′p at different axial locations.

combustion initiates at x/D = 10, the Reynolds stresses begin to increase obviously. Then the Reynolds stresses have a relatively moderate increase until a significant rise happens after x/D = 27, where the stable flame base forms as shown in Figure 3. The distributions of time-averaged and fluctuating axial velocities for gas-phase and particles at six typical axial locations are presented in Figure 7. The radial direction is normalized by the jet half-width δ1/2. It is readily observed that the mean velocities for both gas-phase and coal particles develop into self-

The gas-phase temperature is always larger than particle temperature, which means that the increase of particle temperature at the centerline is mainly due to the heat transfer from the reacting high-temperature gas. Figure 6 shows the Reynolds stresses of gas-phase at the centerline. The Reynolds stresses are nondimensionalized by the square of the centerline velocity. This figure shows evidence that the turbulence can be enhanced signally by combustion. In upstream, the turbulence is weaker, and both the gas-phase and particles have smaller velocity fluctuations as shown in Figure 5b. When the F


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Figure 8. Downstream evolution of statistically radial displacement for the coal particles with different (a) devolatilization rates and (b) carbon reaction rates.

Figure 9. Pdfs of movement angles for (a) devolatilizing particles; (b) volatile matter; and (c) reaction zones.

G


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Figure 10. Radial profiles of time-averaged (a) gas-phase temperature T̅ g; (b) heat release rate ω̇ T; (c) particle temperature T̅ p; and (d) particle devolatilization progress variable ψ̅ at different axial locations.

similar profiles as the jet advances, while the velocity fluctuation profiles have not attained self-similar status because of the effect of combustion. The velocity fluctuations are highest in the middle of the shear layer (r = ± δ1/2) due to the shear between the central jet and coflow. Note that the fluctuations at the centerline remain relatively smaller compared to the fluctuations in the shear layers upstream, whereafter gradually increase downstream. After x/D = 27 where the stable flame is formed, the velocity fluctuations tend to stabilize. In coal flames, the particle distribution is of great importance to investigate the flame features and the related stabilization mechanism. To study the dispersion of coal particles, the statistical mean radial displacement along the streamwise direction is calculated as

from the centerline. Figure 8 presents the downstream evolution of statistically displacement for the coal particles with different devolatilization rates and carbon reaction rates. It is found that the devolatilization and carbon combustion all initiate outside of the shear layer and gradually appear inside the shear layer as the jet advances. For the particles with the devolatilization rate exceeding 2.0 × 10−9 kg/s, the displacement variance is relatively smaller, and these particles have a smaller dispersion in radial direction. For the rest devolatilizing particles, the displacement variances are close, indicating that these devolatilizing particles exhibit similar dispersion levels. Particles with more rapid devolatilization rate tend to disperse further away from the centerline. For the carbon-combusting particles, they are all distributed outside the shear layer as observed in Figure 3b. To investigate the detailed movements for particles and gasphase, the pdfs of movement angles for devolatilizing particles, volatile matter, and reaction zones are presented in Figure 9. Here the movement angle is defined as the angle between the projection of the local velocity (for particle or gas-phase) on the transverse section and radial direction. For an arbitrary point P (xp, yp, zp) with a local velocity of (up, vp, wp), the movement angle θ is calculated as

n(x)

Ym(x) =

∑i = 1 |Yi(x)| n(x)

(17)

and its variance is expressed as n(x)

Yv(x) =

∑i = 1 [Yi(x) − Ym(x)]2 n(x)

(18)

where n(x) is the total number of the coal particles distributed in a given axial locations x, Yi(x) is the particle displacement H


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Figure 11. Temporal evolutions of statistical average values, ⟨Tg⟩area, ⟨Tp⟩area, ⟨ω̇ T⟩area, and ⟨ṁ V⟩area for (a) Zone A; (b) Zone B; and (c) Zone C as shown in Figure 3b.

⎛ (y − y , z 0 − z p)·(vp , wp) ⎞ 0 p ⎟ × 180° θ = arccos⎜⎜ ⎟ | ( y − y , z − z ) || ( v , w ) | π 0 p p p ⎠ ⎝ 0 p

Figure 10. Here the devolatilization progress variable ψ describes the devolatilization degree for coal particles: ⎛ m ⎞ ψ = ⎜⎜1 − daf ⎟⎟ × 100% mdaf,0 ⎠ ⎝

(19)

in which y0 and z0 are the coordinates of the corresponding centerline at the location of xp. According to this definition, when θ > 90°, the local gas or particle is moving outward, while moving inward when θ < 90°. From Figure 9a, it is found that the devolatilizing particles tend to move outward, away from the centerline, and the particle cloud expands as the jet advances. The corresponding volatile matter and reaction zone exhibit some differences. In upstream, most of the volatile matter is moving toward the centerline to ignite the inner combustible matter with autoignition taking place and the flames are shown as stripes. After x/D = 20, the volatile matter and reaction zone begin to expand rapidly along with the devolatilizing particles moving outward to form extensive reaction zones. In addition to the flow characteristics, global characteristics of the flame represented by the time-averaged gas-phase temperature T̅ g, heat release rate ω̇ T, particle temperature T̅ p, and particle devolatilization progress variable ψ̅ are presented in

(20)

When ψ = 100%, the daf coal is all consumed and only char and nonreactive matters remain. Note that the local peak of ω̇ T occurs at r = ± 1.5δ1/2, outside the shear layer, indicating the initiation of autoignition. The corresponding devolatilization progress variable ψ at r = ± 1.5δ1/2 is about 20%. Subsequently the peak of ω̇ T shifts toward the centerline. After x/D = 27, the mean heat release rate in the centerline becomes large and tends to have a top-hat distribution. Moreover the mean particle temperature reaches 1000 K above with a significant enhancement in devolatilization process. According to Figure 10b, three typical zones, identified as interspersed flame, stripe flame, and stable continuous flame in the previous study,24 as marked in Figure 3b, whose peaks of the mean heat release rate occur at the locations of x/D = 10, x/D = 20, and x/D = 27 respectively, are selected to reveal the I


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Figure 12. Temporal evolution of reaction zones between the times of 9.555 ms and 10.140 ms. White points denote the devolatilizing coal particles.

characteristic of the flame. The temporal evolution of statistical average temperatures, heat release rate, and volatile matter release rate in each zone are displayed in Figure 11. Here these statistical average values are defined as area =

area =

area =

∭ Tg dx dy dz ∭ dx dy dz 1 N

zone A, namely in the upstream region, their relevance is a little weaker. Therefore, we can speculate that the change of the temperatures is not only due to the violent chemical reaction but also due to the influence from the surrounding environment, such as the entrainment of hot coflow, especially in the upstream regions. In zone C, it is observed that the high heat release rate occurs more frequently with a larger mean value, indicating that the stable flame base forms herein. In the following sections, the evolutions of coal jet flames are investigated. By defining the flame stabilization points, studying the statistics of the flame stabilization points and studying the terms in the temperature equation, the stabilization mechanism for the present coal jet flame can be concluded. 3.2. Statistics of Flame Stabilization Points. In previous studies,35,37,38,45−47 some intermediate species, such as OH, HO2, and CH2O, are used as the markers of the high temperature reaction region. In the present study, due to the lack of intermediate species in the two-step chemical reaction, the heat release rate is directly used to identify the reaction zones. Figure 12 displays the representative temporal evolution of the reaction zones in the typical central plane. These figures can provide a visual illustration of the flame base movement qualitatively. It is obvious that there are many devolatilizing coal particles (white points) in chemical reaction zones, especially in the

(21)

N

∑ Tp,i i=1

∭ ω̇ T dx dy dz ∭ dx dy dz

(22)

(23)

N

area =

∑i = 1 ṁ v , i

∭ dx dy dz

(24)

From this figure, it is obvious that the heat release rate shows the consistent trend with the devolatilization rate in all zones implying that the devolatilization process is crucial to the combustion of the gas-phase. Besides the evolutions for area and area are similar, and they have a close correlation with the heat release rate. It is noteworthy that in J


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Figure 13. Temporal evolution of (a) stabilization point position; (b) flow velocity ug, particle slip velocity up − ug and displacement speed Sd; (c) mixture fraction ξ; and (d) scalar dissipation rate χ.

flame base. At the time of 9.555 ms, the flame base is observed at the location of x/D = 31 and migrating downstream. Meanwhile some stripe flames begin to join together at x/D = 25 due to the consecutive autoignition events of the volatile matter with the assistance of the entrained heated coflow and stripe flames, and grow up into a new flame base at the time of 9.685 ms subsequently. As more volatiles come out, the flame base expands and moves downstream during the interval of 9.750 ms and 10.075 ms. According to a previous study,24 the nonpremixed flame dominates in the flame base, where the premixed flame only contributes about 10% to the total heat release rate. Finally, a new flame base forms at x/D = 27 at the time of 10.140 ms. This process is one cycle of the flame base movement, similar to the observation in the conventional gaseous jet flames.35,37 It should be noted that not all the stripe flames can form the stable flame base, because some can break down into interspersed flames and be diluted with extinction taking place. To further study the flame stabilization mechanism, a legible definition of the stabilization point should be given. In the studies35,37,42 of conventional gaseous flame, the most upstream point of a particular isosurface of temperature or an intermediate species mass fraction, usually at the leading edge on the left or right branch of the lifted flame, is regarded as the stabilization point. Because of the presence of multiple localized ignition phenomena in three spatial directions with time, Yoo et al.35,37 used the local stabilization point in a given plane, instead of the whole domain, as the stabilization point. However, in the present study, the flame at the leading edge is discontinuous, and not all the flames can eventually develop into a stable flame base as illustrated in Figure 12. Thus, the stabilization point is tracked in the flame base, and the local flame stabilization point

is defined as the most upstream point of the temperature isosurface of 1700 K at the centerline in the present study. The temporal evolutions of the stabilization point position along with the local flow velocity (ug), particle slip velocity (up − ug), flame displacement speed (Sd), mixture fraction (ξ) and scalar dissipation (χ) are presented in Figure 13. All these values are calculated at the stabilization point locally. The displacement speed Sd is defined as Sd =

ω̇ T ρc p|∇Tg|

(25)

The local displacement speed direction is defined according to the local mixture fraction gradient, i.e., the flame front moves toward the fuel-rich side since the nonpremixed flame dominates in the flame base. In this case, the fuel-rich area is always in the downstream of the stabilization point, so a positive Sd represents that the flame is moving downstream. Here the mixture fraction ξ is defined based on the element mass fraction:24 ξ = {2(YC − YC,2)/WC + 0.5(YH − YH,2) /WH − (YO − YO,2)/WO} /{2(YC,1 − YC,2)/WC + 0.5(YH,1 − YH,2) /WH − (YO,1 − YO,2)/WO}

(26)

in which W is the element molecular weight and Y is the element mass fraction. The subscript 1 and 2 denote the coal particle and the center jet flow, respectively. According to the definition, the stoichiometric mixture fraction is ξst = 0.10535. K


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Energy & Fuels

Figure 14. Instantaneous radial distributions of (a) gas-phase temperature Tg; (b) particle temperature Tp; (c) devolatilization rate ṁ v; and (d) carbon reaction rate ṁ c at different axial locations at the time of 9.750 ms.

flame where the flame base’s movement is usually caused by the passage of the large-scale flow structures.35,37,42 Besides the positive Sd also implies that the flame propagation in the flame base is also another cause of the downstream migration of the flame base. Additionally the local particle velocity up is a little larger than the local flow velocity ug, indicating that the flame base’s downward movement is also influenced by the particles’ movements. 3.3. Stabilization Mechanism. To examine the characteristics near the flame stabilization point, the instantaneous radial distributions of gas-phase temperature Tg, particle temperature Tp, devolatilization rate ṁ v, and carbon reaction rate ṁ c at different axial locations at the time of 9.750 ms are presented in Figure 14. These values are statistically averaged in the azimuthal direction. It is found that before the stabilization point of x/D = 27, the devolatilization happens mainly on the periphery of the jet, from the outside of the shear layer to the middle of the shear layer. While in the downstream region of the stabilization point, the gas temperature is above 1100 K and the particle temperature reaches above 1000 K near the jet center, which can lead to a rapid devolatilization nearby. Interestingly, the carbon reaction rate ṁ c has a similar distribution except at the more downstream location of x/D

The scalar dissipation rate χ based on the mixture fraction is calculated as χ = D |∇ξ|2

(27)

where D is the diffusion coefficient. Figure 13a shows that the stabilization point moves downstream gradually with a nearly uniform velocity, and a sudden jump upward can take place due to a new flame base formed in the upstream regions as shown in Figure 12. At the time of 9.66 ms, a sudden jump occurs, and the corresponding ξ is fuel lean, close to ξst, and the corresponding χ is relatively low. By checking other sudden jump locations, the same findings can be observed. Therefore, the local conditions with lower χ and close to ξst are favorable to the formation of the flame base. Besides the displacement speed Sd is usually positive, having the same direction as that of the jet flow, which strongly suggests that the present coal jet flame cannot be stabilized by the flame propagation except the autoignition. It is also found that the downward movement between two jumps is usually associated with a stable local flow velocity ug and a positive Sd . Thus, the downstream movement of the stabilization point is primarily attributed to the large local gaseous convective velocity, which is similar in the gaseous jet L


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Energy & Fuels

Figure 15. (a−d) Instantaneous distributions of the relevant terms in the temperature equation along with the gas-phase temperature in the radial direction at different axial locations at the time of 9.750 ms.

the flame base and the surrounding heated coflow, has a particular influence on the flame base, especially near the jet center. At the location of x/D = 24, the convection term has a large negative value near the jet center. With this negative convection term, the high-temperature area formed upstream (x/D = 20) vanishes and the extinction may take place as indicated in Figure 3. At the location of x/D = 27, the convection term becomes positive and even larger than the reaction term. This leads to a significant increase of the gasphase temperature near the jet center, which is good for coal devolatilization. However, massive devolatilization can result in a large negative source term since the devolatilization process is endothermic. This negative source term imposes an additional effect on the flame base. Moreover, the alternatively positive and negative values of the convection term appearing near the jet center may cause local ignition, extinction and reignition, which is related to the oscillation of the flame luminosity. The above discussions suggest that the autoignition of the volatile is the key mechanism responsible for the present coal jet flame stabilization. Similar to the stabilization mechanism of the turbulent lifted jet gaseous flame,35,37,42 we postulate a stabilization mechanism for the present coal jet flame in a hot coflow shown schematically in Figure 16. As demonstrated in Figure 9, the gas-phase has mainly two kinds of movement

= 35. It indicates that the formation of coal flame base is mainly due to the rapid devolatilization near the jet center rather than the carbon reaction. Therefore, a favorable devolatilization environment is the key to the coal flame stabilization. To identify the dominant formation mechanism of the present coal jet flame base, relevant terms in the gas-phase temperature eq (eq 4), i.e., the convection term (Conv = −c v

∂ρg ug, jTg ∂xj

), chemical reaction term (Chem = ω̇ T),

d i ff u s i o n t e r m ( Diff =

∂ ⎛ ∂Tg ⎞ ⎜λ ⎟) , ∂xj ⎝ g ∂xj ⎠

viscosity term

∂ug, j (Visc = σi , j ∂x ) and source term (Sour = Q + Ω̇ + SṪ ) are i

calculated and analyzed. Figure 15 presents the distributions of these terms and the gas-phase temperature in the radial direction at different axial locations. It is obvious that the diffusion term and the viscosity term are relatively small and their effects on the flame base formation are not as important as the rest terms. The chemical reaction term is always dominant and responsible for the significant temperature increase implying that the autoignition events dominate the flame base. It is notable that the convection term, regarded as the preheating effects advected from the stripe flames in shear layers, the high-temperature reaction zones in M


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Energy & Fuels

Figure 16. Schematic of the coal flame movement: (a) autoignition occurs in fuel-lean mixtures (near stoichimetric condition) with low scalar dissipation rate to form the flame base; (b) the stabilization point is advected downstream by high local gaseous convective veloctiy; (c) the stabilization point migrates downstream also due to the flame propagation and particle movement in the flame base; and (d) a new flame base occurs in upstream region and stabilization point jumps upstream. The gray dot represents the stabilization point, and the dashed line denotes the shear layer.

centerline occurring in fuel-lean mixtures, near stoichiometric conditions, with low dissipation rate, a stable flame base dominated by nonpremixed flame is formed and expands outward (Figure 16a). The corresponding stabilization point migrates downstream primarily by the local gaseous convection (Figure 16b). Besides the flame propagation and the local particle velocity in the flame base can also influence the stabilization point’s movement (Figure 16c). When a new flame base forms in the upstream region with massive devolatilizing particles concentrating near the centerline, the stabilization

directions, i.e., moving inward and expanding outward in upstream and downstream regions, respectively. In the upstream regions, the coal particles located in the shear layer begin to devolatilize due to the preheating of the entrained heated coflow. The volatile matter moves inward with autoignition to form stripe flames. In downstream, a favorable devolatilization environment is created in the centerline because of the significant convective heat transfer from the neighboring stripe flames, heated coflow, and flame base upstream. With massive autoignition of volatile near the N


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point jumps upstream (Figure 16d). A comparison of Figures 12 and 16 readily shows one cycle of the flame base movement and the importance of autoignition for the stabilization of the present coal jet flame.

4. CONCLUSIONS In the present study, a compressible point-source DNS of a turbulent lifted pulverized coal jet flame in a heated coflow is analyzed to investigate the stabilization mechanism. By studying the flow and flame profiles, it is found that self-similar profiles can be attained for mean velocities of gas-phase and particles but not achieved for fluctuation velocities. The turbulence can be enhanced by ignition and combustion processes. By investigating the correlations among the temperatures, heat release rate, and devolatilization rate, it is found that the autoignition of the volatile is the key mechanism responsible for coal jet flame stabilization under the present condition. The heated coflow can be entrained upstream to initiate the coal devolatilization. The volatile moves inward with autoignition to form the stripe flames in the shear layers. As the jet advances, the preheating effects from the neighboring stripe flames, heated coflow, and flame base upstream can contribute a larger convection term in the temperature equation and create a favorable devolatilization environment followed by the massive autoignition of volatiles occurring in fuel-lean mixtures with a low dissipation rate near the centerline. It is also found that the cycle of the flame stabilization point movement, with the downstream migration primarily caused by the local gaseous convection and the formation of a new flame base upstream due to the autoignition, makes the coal flame burn in a stabilized way.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 86-0571-87951764. ORCID

Kun Luo: 0000-0003-3644-9400 Jianren Fan: 0000-0002-6332-6441 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Nature Science Foundation of China (No. 51390493). The authors are grateful for the inspired and useful suggestion from Prof. Heinz Pitsch at RWTH Aachen University about the grid resolution check.

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REFERENCES

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A DNS study on the stabilization mechanism of a turbulent lifted

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