Kaidi Wan

Zhihua Wang
email: wangzh@zju.edu.cn

Jun Xia
email: jun.xia@brunel.ac.uk

Luc Vervisch

Pascale Domingo

Yu Lv

Yingzu Liu

Yong He

Kefa Cen

Numerical study of HCl and SO2 impact on sodium emissions in pulverized-coal flames

Keywords: Pulverized-coal combustion, Emission, Sodium chemistry, Alkali metal, HCl, SO2

Sodium emissions during pulverized-coal combustion (PCC) are known to result in severe ash-related operating issues of coal furnaces, e.g., fouling, slagging and corrosion. To relieve these issues and advance the clean utilization technologies of coal, a better understanding of the fundamental mechanisms driving the formation and transformation of the sodium species is required.

In the present study, sodium emissions have been simulated in both one-dimensional (1D) premixed/diffusion flames of the coal volatile and an early-stage two-dimensional (2D) pulverized-coal flame. The properties of Loy Yang brown coal are used. The DRM22 skeletal mechanism is employed for volatile-gas combustion, and the reaction of sodium species is modeled by a detailed mechanism encompassing the elements Na, C, H, O, S and Cl. The compositions of the volatile fuels are obtained from the chemical percolation devolatilization (CPD) model, including CH4, C2H2, CO, H2, CO2 and H2O. The initial species of Na, Cl and S in the volatile gas is set to be NaOH, HCl and SO2, respectively. The transformation characteristics of 12 sodium species are investigated in both the 1D volatile flames and the 2D pulverized-coal flame. The response of the sodium chemistry to volatile-gas combustion is analyzed under fuel-lean, stoichiometric and fuel-rich conditions. Na, NaOH and NaCl are found to be the major sodium species during the combustion. Parametric studies with HCl, SO2 or both species removed from the volatile are then performed to investigate their effects on the sodium transformation characteristics in both the 1D and 2D flames. The results show that HCl has a much stronger ability to react with sodium species than SO2.

Introduction

Coal has been widely utilized to support the worldwide electric power consumption due to the overall flexibility of coal combustion systems [START_REF]Key world energy statistics[END_REF]. In the near future, coal will continually play a major role in the energy structure of the world, considering its broad availability [START_REF] Liu | Inhibition of sodium release from Zhundong coal via the addition of mineral additives: A combination of online multi-point LIBS and offline experimental measurements[END_REF]. In practical utilization of coal, alkali metals such as sodium (Na) presented in coals lead to severe ash-related operating issues, e.g., fouling, slagging and corrosion [START_REF] Wu | Ash deposition and slagging behavior of Chinese Xinjiang high-alkali coal in 3 MWth pilot-scale combustion test[END_REF]. This issue is also found in the combustion of biomass, which is a promising renewable energy source [START_REF] Ca | Correlations of chemical properties of high-alkali solid fuels: A comparative study between Zhundong coal and biomass[END_REF]. Potassium (K), an important element for plants, is usually rich in biomass. The alkali metal, i.e., Na and K, released from the combustion of coal and biomass can condense on heat transfer surfaces and form an initial sticky layer, which captures fly ash and leads to rapid ash deposition [START_REF] Niu | Ash-related issues during biomass combustion: Alkali-induced slagging, silicate melt-induced slagging (ash fusion), agglomeration, corrosion, ash utilization, and related countermeasures[END_REF][START_REF] Jurado | Effect of co-firing coal and biomass blends on the gaseous environments and ash deposition during pilot-scale oxy-combustion trials[END_REF]. Besides, alkali metal can also react with sulfur and chlorine species to form complex compounds, which causes fouling and corrosion of the furnaces [START_REF] Liu | In Situ Measurements of the Release Characteristics and Catalytic Effects of Different Chemical Forms of Sodium during Combustion of Zhundong Coal[END_REF]. These alkali metal emissions significantly limit the utilization of potassium-rich biomass such as straw and sodium-rich coals such as North Dakota coal in the US, Loy Yang coal in Australia and Zhundong coal in China [START_REF] Guo | Correlating the sodium release with coal compositions during combustion of sodium-rich coals[END_REF]. Thus, to develop appropriate control technologies of reducing or capturing these harmful alkali metal emissions, it is essential to better understand the fundamental mechanisms driving the formation and transformation of alkali species and their interactions with the complex multi-phase turbulent reacting flows during the combustion of pulverized coal and biomass.

In the past decades, experimental research on sodium release and reacting dynamics evolves from offline measuring techniques to online measurements using advanced laser diagnostics. Offline sampling measurements can obtain the final amount and composition of sodium species by analyzing the fly ash and ash deposits in the post-combustion stage [START_REF] Quann | Mineral matter and trace-element vaporization in a laboratory-pulverized coal combustion system[END_REF]; while online techniques, e.g., planar laser-induced fluorescence (PLIF) [START_REF] Van Eyk | Simultaneous measurements of the release of atomic sodium, particle diameter and particle temperature for a single burning coal particle[END_REF][START_REF] Liu | Measurement and kinetics of elemental and atomic potassium release from a burning biomass pellet[END_REF] and laser-induced breakdown spectroscopy (LIBS) [START_REF] Liu | Measurement and kinetics of elemental and atomic potassium release from a burning biomass pellet[END_REF][START_REF] He | In-situ measurement of sodium and potassium release during oxy-fuel combustion of lignite using laser-induced breakdown spectroscopy: effects of O2 and CO2 concentration[END_REF][START_REF] Liu | Characteristics of alkali species release from a burning coal/biomass blend[END_REF], can directly capture the time-resolved sodium release process during the combustion. In our recent study, the dynamic release of atomic and elemental sodium during the combustion of a Zhundong coal pellet has been quantitatively measured by using PLIF [START_REF] Wang | Measurement of atomic sodium release during pyrolysis and combustion of sodium-enriched Zhundong coal pellet[END_REF] and multi-point LIBS methods [START_REF] Liu | Multi-point LIBS measurement and kinetics modeling of sodium release from a burning Zhundong coal particle[END_REF], respectively.

On the numerical side, van Eyk et al. [START_REF] Van Eyk | Mechanism and kinetics of sodium release from brown coal char particles during combustion[END_REF] firstly proposed a one-step Arrhenius sodium release model during the combustion of a single char pellet. A two-step kinetics model has been developed in our recent study [START_REF] Wang | Measurement of atomic sodium release during pyrolysis and combustion of sodium-enriched Zhundong coal pellet[END_REF][START_REF] Liu | Multi-point LIBS measurement and kinetics modeling of sodium release from a burning Zhundong coal particle[END_REF] to quantify the sodium release during all stages of coal combustion, based on simultaneous online measurements of the sodium release, pellet diameter and surface temperature of a burning coal pellet. Since the burnout time and coal pellet diameter in these studies are on the same order of magnitude as in a typical circulating fluidized bed (CFB) boiler, these sodium release models are appropriate for CFB combustion [START_REF] Liu | Multi-point LIBS measurement and kinetics modeling of sodium release from a burning Zhundong coal particle[END_REF]. Sodium release models for pulverized-coal combustion (PCC) must still be developed.

Considering the homogeneous chemical reactions of alkali species, the final forms of alkali species in post-combustion gases can be modeled via thermodynamic equilibrium calculation, e.g. [START_REF] Liu | Multi-point LIBS measurement and kinetics modeling of sodium release from a burning Zhundong coal particle[END_REF][START_REF] Van Eyk | The release of water-bound and organic sodium from Loy Yang coal during the combustion of single particles in a flat flame[END_REF][START_REF] Fatehi | Modeling of alkali metal release during biomass pyrolysis[END_REF]. It has been found that the main alkali species are atomic Na/K, NaOH/KOH and NaCl/KCl in equilibrium [START_REF] Fatehi | Modeling of alkali metal release during biomass pyrolysis[END_REF]. Alkali chlorides can lead to severe ash deposition and corrosion issues, and a feasible method to mitigate these issues is to convert the alkali chlorides to sulfates, whose melting temperatures are higher and which are therefore less problematic [START_REF] Ekvall | K-Cl-S chemistry in air and oxy-combustion atmospheres[END_REF]. Hence, the homogeneous chemical reaction, especially the sulfation of alkali has received more and more attentions recently, e.g. [START_REF] Glarborg | Mechanism and modeling of the formation of gaseous alkali sulfates[END_REF][START_REF] Hindiyarti | An exploratory study of alkali sulfate aerosol formation during biomass combustion[END_REF][START_REF] Garba | Prediction of Potassium Chloride Sulfation and Its Effect on Deposition in Biomass-Fired Boilers[END_REF]. Glarborg and Marshall [START_REF] Glarborg | Mechanism and modeling of the formation of gaseous alkali sulfates[END_REF] proposed a detailed chemical reaction mechanism for homogeneous alkali reactions, which was validated against experimental results on sulfation of gaseous alkali chlorides. Takuwa and Naruse [START_REF] Takuwa | Emission control of sodium compounds and their formation mechanisms during coal combustion[END_REF] investigated the transformation characteristics of gaseous sodium compounds in a hydrogen-air combustion system via zero-dimensional (0D) isothermal simulations. However, the homogeneous reaction dynamics of alkali species in a pulverized-coal flame has not been reported yet.

As the sharp increase of computing capacity continues, computational fluid dynamics (CFD) methods for the carrier-gas flow of PCC have evolved from Reynolds-averaged Navier-Stokes (RANS) simulation (e.g. [START_REF] Bermúdez | Numerical simulation of group combustion of pulverized coal[END_REF][START_REF] Hashimoto | A numerical simulation of pulverized coal combustion employing a tabulated-devolatilization-process model (TDP model)[END_REF][START_REF] Vascellari | Influence of turbulence-chemical interaction on CFD pulverized coal MILD combustion modeling[END_REF]) towards high-fidelity approaches, i.e., large-eddy simulation (LES, e.g. [START_REF] Yamamoto | Large eddy simulation of a pulverized coal jet flame ignited by a preheated gas flow[END_REF][START_REF] Franchetti | Large eddy simulation of a pulverised coal jet flame[END_REF][START_REF] Rabaçal | Large Eddy Simulation of coal combustion in a large-scale laboratory furnace[END_REF][START_REF] Wan | Online-CPD-coupled large-eddy simulation of pulverized-coal pyrolysis in a hot turbulent nitrogen jet[END_REF][START_REF] Wen | LES of pulverized coal combustion with a multi-regime flamelet model[END_REF][START_REF] Rieth | Flamelet LES modeling of coal combustion with detailed devolatilization by directly coupled CPD[END_REF][START_REF] Wan | Large-eddy Simulation of Pilot-assisted Pulverized-coal Combustion in a Weakly Turbulent Jet[END_REF][START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF]) and direct numerical simulation (DNS, e.g., [START_REF] Hara | Direct numerical simulation of a pulverized coal jet flame employing a global volatile matter reaction scheme based on detailed reaction mechanism[END_REF][START_REF] Muto | Numerical simulation of ignition in pulverized coal combustion with detailed chemical reaction mechanism[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF]). The high-fidelity approaches of LES and DNS have demonstrated advantages over RANS in predicting local distributions of gas temperature and species concentrations. Particularly in DNS, the turbulence-chemistry interaction is directly resolved instead of being modeled, the simulation results can therefore provide more physical insights into complex PCC dynamics and also serve as important data references for the development of subgrid scale modeling.

In summary, the transformation dynamics of sodium species in a pulverized-coal flame have not been fully revealed by previous studies. Within this context, the objective of the present study is twofold. First, the responses of sodium species to one-dimensional (1D) premixed/diffusion flames of coal volatile are investigated. Second, the transformation characteristics of sodium species in a two-dimensional (2D) early-stage pulverized-coal flame are simulated and analyzed, excluding char combustion. In our previous studies [START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF], the reaction dynamics of sodium species in PCC were investigated using a subset sodium mechanism without considering the effects of S and Cl. Here, the full detailed sodium mechanism proposed by Glarborg and Marshall [START_REF] Glarborg | Mechanism and modeling of the formation of gaseous alkali sulfates[END_REF] including the elements Na, C, H, O, S and Cl is employed to model the sodium reactions, and the effects of HCl and SO2 on the sodium transformation characteristics are then investigated. It should be noted that the detailed sodium mechanism has been carefully validated by Glarborg and Marshall [START_REF] Glarborg | Mechanism and modeling of the formation of gaseous alkali sulfates[END_REF] against the experimental results of the gas-phase sulfation of alkali chloride at combustion conditions [START_REF] Iisa | Sulfation of Potassium Chloride at Combustion Conditions[END_REF].

It was found in [START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF] that the multidimensional two-phase pulverized-coal flame showed a partially premixing combustion mode, with first the premixed combustion mode dominating when pulverized-coal particles are heated and ignited in the shear layer region where the high-temperature co-flow mixes with the low-temperature air flow carrying pulverized-coal particles. After ignition stabilizes, volatile fuels are rapidly released from pulverized-coal particles, leading to a dominantly diffusion burning mode. In view of this fact, in order to better understand how minor sulfur and chlorine species affect sodium emissions in pulverized-coal flames, it will be instructive to first investigate prototype one-dimensional premixed and diffusion gaseous flames of the coal volatile using detailed chemistry, leaving behind the complexity of interactions between dispersing pulverized-coal particles and the gas phase, turbulent flow effects, etc. This inspection will provide a first guiding light on S/Cl-affected sodium emissions in both the prototype premixed and diffusion volatile flames. By comparing the one-dimensional prototype gaseous volatile flames and a more realistic multidimensional two-phase pulverized-coal flame, a comprehensive understanding of sodium emissions impacted by minor sulfur and chlorine species can be obtained.

One-dimensional premixed/diffusion flames of coal volatile

The reaction dynamics of sodium species in 1D premixed/diffusion flames of coal volatile is studied. The volatile is released from the Loy Yang brown coal [START_REF] Van Eyk | The release of water-bound and organic sodium from Loy Yang coal during the combustion of single particles in a flat flame[END_REF], for which the coal analysis data are shown in Table 1. The volatile combustion is modeled by the previously validated DRM22 skeletal mechanism proposed by Kazakov and Frenklach [START_REF] Kazakov | Reduced reaction sets based on GRI-Mech 1.2[END_REF], involving 22 chemical species and 104 elementary reactions. The compositions of the volatile fuels are obtained from the chemical percolation devolatilization (CPD) model [START_REF] Grant | Chemical-Model of Coal Devolatilization Using Percolation Lattice Statistics[END_REF] and the Tar species is replaced by C2H2 [START_REF] Rieth | Flamelet LES modeling of coal combustion with detailed devolatilization by directly coupled CPD[END_REF], as shown in Table 2. The compositions predicted by the CPD model have been slightly adjusted to fulfill the elemental mass conservation.

According to [START_REF] Takuwa | Emission control of sodium compounds and their formation mechanisms during coal combustion[END_REF], the initial species of Na in the volatile is set to be NaOH, while those of Cl and S are set to be HCl and SO2, respectively. The percentage of sodium that is releasable during the coal pyrolysis stage is set to 19.1%, according to the experimental data [START_REF] Van Eyk | The release of water-bound and organic sodium from Loy Yang coal during the combustion of single particles in a flat flame[END_REF]. However, the release of sulfur and chlorine has not been measured. Considering sulfur and chlorine can be fully released during the pyrolysis and char burning stages of coal combustion, their releasable proportions during the pyrolysis stage are both set to 55.1%, which is the percentage of volatile yields predicted by the CPD model. The mass fractions of NaOH, HCl and SO2 in the volatile gas can then be calculated (see Table 2). The detailed reaction mechanism of alkali metal species developed by Glarborg and Marshall [START_REF] Glarborg | Mechanism and modeling of the formation of gaseous alkali sulfates[END_REF] includes elementary reactions over the elements Na, K, C, H, O, S and Cl. In the present study, since the concentration of potassium in the coal is an order of magnitude lower than that of sodium (see Table 1), the element K is not considered, which results in a detailed reaction mechanism of sodium involving 36 species and 153 elementary reactions. For the premixed condition, a 1D freely propagating premixed flame of the volatile is simulated using CANTERA [START_REF] Goodwin | Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes[END_REF]. Three equivalence ratios (ϕ = 0.5, 1.0 and 2.0) of the volatile-air mixture are considered and the inlet mixture temperature is 300 K. The equivalence ratio is computed based on the molar fractions of atomic carbon, hydrogen and oxygen [START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF], which is therefore conserved during homogeneous combustion but not conserved during mixing. For the diffusion condition, a 1D counterflow diffusion flame of the volatile is simulated using CANTERA [START_REF] Goodwin | Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes[END_REF]. The mass flow rates of the volatile fuel and air inlets are 0.024 (kg/m 2 s) and 0.072 (kg/m 2 s), respectively, while the temperatures of both inlets are 300 K. To investigate the effects of HCl and SO2 on sodium transformation characteristics, four different configurations with HCl and/or SO2 removed are set up.

The removed HCl/SO2 is replaced by N2. In total 16 cases are simulated with the three equivalence ratios in the premixed condition and different configurations of HCl and SO2 in both the premixed and diffusion conditions. The grid is limited to 250 points and the 1D domain length for premixed and diffusion flame is 1.0 m and 3.0 cm, respectively.

Pulverized-coal flame configuration and numerics

A two-dimensional temporally evolving pulverized-coal jet flame is studied (Fig. 1). The physical dimensions of the computational domain are 51.2 mm and 51.2 mm in the streamwise (x)

and spanwise (y) directions, respectively. A uniform mesh of h = 100 µm is employed, which has been shown to be able to resolve the flame structure [START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF]. High-speed air (bulk velocity: 10 m/s, 300 K) laden with pulverized-coal particles is initially set up for |y| < 2.5 mm. The initial number of particles is 171 and their locations follow a random uniform distribution. The initial density of particles is 1400 kg/m 3 with a mono-disperse distribution of diameter of 25µm. Properties of Loy Yang brown coal [START_REF] Van Eyk | The release of water-bound and organic sodium from Loy Yang coal during the combustion of single particles in a flat flame[END_REF] are employed (Table 1). A low-speed hot burnt product of the hydrocarbon volatile at an equivalence ratio of 0.45 (3 m/s, 1559 K) is introduced as the coflow surrounding the air. The coflow stream promotes the ignition of coal particles, as the mixing of the solid-fuel/air mixture with burnt products would do in a real pulverized-coal furnace. Periodic boundary conditions are introduced in all directions. To facilitate the jet flow development, turbulent fluctuations of 0.2 m/s (2% of the primary air velocity) are initially set within the shear layers between the primary air and the coflow. The parameters of the present case are chosen according to [START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF]. Pulverized-coal particles are treated as point sources and two-way coupling between the gas phase and particles are considered. Figure 1. Schematic diagram of computational configuration.

Coal pyrolysis, including Na/Cl/S release, volatile-gas combustion and Na/Cl/S reactions are simulated. Heterogeneous reaction of char is not considered, because its contribution is weak in a small-scale pulverized-coal flame, as already demonstrated in [START_REF] Rieth | Flamelet LES modeling of coal combustion with detailed devolatilization by directly coupled CPD[END_REF][START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Knappstein | Devolatilization and volatiles reaction of individual coal particles in the context of FGM tabulated chemistry[END_REF].

Gas phase modeling

The governing equations for the gas and coal-particle phases are solved in the Eulerian and Lagrangian frameworks, respectively, using a low-Mach-number in-house code [START_REF] Wan | Online-CPD-coupled large-eddy simulation of pulverized-coal pyrolysis in a hot turbulent nitrogen jet[END_REF][START_REF] Wan | Large-eddy Simulation of Pilot-assisted Pulverized-coal Combustion in a Weakly Turbulent Jet[END_REF][START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF]. The conservation equations for mass, momentum, species and temperature are solved for the gas phase:

(

(2)

(3) (4)
where Dt(Φ) = ∂t(Φ) + ∂j(Φuj), ∂j ≡ ∂xj, ρ is gas density (kg/m 3 ), ui is gas velocity (m/s), Yn is the mass fraction of the nth chemical species, T is gas temperature (K). The pressure is denoted by p, and τij = µ(∂jui + ∂iuj -2/3 ∂kukδij) is the viscous stress tensor. Dn is the molecular mass diffusivity coefficient (m 2 /s), λ and CP,g are the thermal conductivity (W/m K) and specific heat capacity (J/kg K)

, D t mp S r = ! ( ) , , D t i i j i j m o mpi u p S r t = - ¶ + ¶ + ! ( ) ( ) , , , D t n j n j n Yn Y pn Y D Y S r r w = ¶ ¶ + + ! ! ( ) , , , 2 , , D t j j j P g j T Tp T R P g P g T T C T S S C C l l r w ae ö = ¶ ¶ + ¶ ¶ + + + ç ÷ è ø ! ! !
of the gas mixture, respectively. , , and are the two-way coupling terms due to the effects of particles on the gas phase. is the chemical reaction source term due to homogeneous reaction. In the temperature equation, the radiative heat transfer ( ), heat exchange between the gas phase and coal particles ( ), and heat effects of homogeneous reaction ( ) are considered. In the present study, the Lewis number (Le = 1.0) and Prandtl number (Pr = 0.7) are assumed to be constant.

Particle phase modeling

The momentum equation of a Lagrangian coal particle can be written as:

(

where up,j is the velocity of the particle (m/s). The dynamic response time (s) of a particle is , where ρp is the particle density (kg/m 3 ), and dp is the particle diameter (m). f is the drag coefficient, accounting for the high particle Reynolds number effects and the blowing effects of volatiles at the particle surface [START_REF] Miller | Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream[END_REF].

The particle temperature equation is: [START_REF] Jurado | Effect of co-firing coal and biomass blends on the gaseous environments and ash deposition during pilot-scale oxy-combustion trials[END_REF] where Tp is the temperature of the particle (K), mp mass of the particle (kg), CP,p specific heat capacity of the particle (J/kg K). The heat transfer due to convection, radiation, and pyrolysis

(devolatilization) is , , and
, respectively. Nu is the Nusselt number and calculated by the Ranz-Marshall correlations [START_REF] Ranz | Evaporation from drops[END_REF]. The radiation temperature (K) is estimated by TR = (G/4σ) 1/4 , where G is the incident radiation (W/m 2 ) determined by the Discrete Ordinates Method (DOM) [START_REF] Chandrasekhar | Radiative transfer[END_REF]. σ is the Stefan-Boltzmann constant (5.67 × 10 -8 W/m 2 K 4 ). εp is the particle emissivity and set to 0.9 [START_REF] Wan | Experimental and modeling study of pyrolysis of coal, biomass and blended coal-biomass particles[END_REF].

The weighted-sum-of-the-gray-gases model (WSGGM) [START_REF] Smith | Evaluation of Coefficients for the Weighted Sum of Gray Gases Model[END_REF] is employed to determine the gas

, m p S ! , , mom p i S ! , , Y p n S ! , T p S ! , Y n w ! , T R S ! , T p S ! T w ! ( ) , , d t p j j p j p u f u u t = - 2 18 p p p d t r µ = ( ) ( ) , d t p conv rad dev p P p T Q Q Q m C = + + ( ) , Nu 3Pr conv P g p p p Q C m T T t = - ( ) 2 4 4 rad p p R p Q d T T e p s = - d d dev dev vol Q h m t = -D
absorption coefficient. Finally, the mass loss rate of each coal particle (dmp/dt), due to the pyrolysis, is directly predicted by the CPD model, as in [START_REF] Wan | Online-CPD-coupled large-eddy simulation of pulverized-coal pyrolysis in a hot turbulent nitrogen jet[END_REF][START_REF] Wan | Large-eddy Simulation of Pilot-assisted Pulverized-coal Combustion in a Weakly Turbulent Jet[END_REF][START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF].

Gas phase chemistry

The gas phase chemistry employed here is the same as that in Section 2. The homogeneous combustion of the hydrocarbon volatile and the sodium species reaction are modeled by the DRM22 skeletal mechanism [START_REF] Kazakov | Reduced reaction sets based on GRI-Mech 1.2[END_REF] and the detailed alkali reaction mechanism [START_REF] Glarborg | Mechanism and modeling of the formation of gaseous alkali sulfates[END_REF], respectively. The compositions of the volatile gas including the non-hydrocarbon compounds of Na, S and Cl can be found in Table 2.

The release rate of sodium of pulverized-coal is assumed to be proportional to the volatile release rate [START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF], because the sodium vapor generated inside the porous structure of a coal particle will be transported outward by the volatile yielded during the pyrolysis stage and the sodium release was found proportional to the burnout of a coal particle during the early combustion stage [START_REF] Liu | Multi-point LIBS measurement and kinetics modeling of sodium release from a burning Zhundong coal particle[END_REF]. Similarly, the release rates of sulfur and chlorine are also assumed to be proportional to the volatile release rate.

Numerical schemes

The numeric of our in-house code is based on an approach previously employed for both DNS and LES [START_REF] Pierce | Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion[END_REF][START_REF] Desjardins | High order conservative finite difference scheme for variable density low Mach number turbulent flows[END_REF]. A second-order Crank-Nicolson scheme is used for the time advancement. A second-order central difference scheme is applied to all terms in the momentum equation and the scalar diffusion terms in the species and temperature equations. To secure the scalar boundedness, a Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme is employed for the scalar advection terms in the species and temperature equations. An Alternating Direction Implicit (ADI) method has been used, and therefore semi-implicit tridiagonal/pentadiagonal equations are solved separately for each direction. A second-order Runge-Kutta (RK2) scheme is used to explicitly advance the particle equations.

Results and discussion

Transformation characteristics of sodium species in 1D premixed flame

To investigate the transformation characteristics of sodium species under different burning conditions, the reactions of sodium species in 1D freely propagating volatile flames have been simulated for three equivalence ratios (ϕ = 0.5, 1.0 and 2.0), which are selected to illustrate fuel-lean, stoichiometric and fuel-rich conditions. As shown in Fig. 2, the concentration of NaOH rapidly decreases after the volatile mixture is injected through the inlet, which is due to the following two reaction paths. First, Na2O2H2 is produced by 2NaOH → Na2O2H2. Second, NaOH reacts with HCl in the volatile gas by NaOH + HCl → NaCl + H2O, and NaCl subsequently forms Na2Cl2 via 2NaCl → Na2Cl2. It can be found that Na2O2H2 and Na2Cl2 are the two major sodium species in the initial unburned region with T = 300 K. In the combustion region where the gas temperature rapidly increases, Na2O2H2 and Na2Cl2 are decomposed to NaOH and NaCl, respectively, and then transformed to other sodium species, i.e., Na, NaSO2, NaHSO4 and Na2SO4. In the post-flame, high-temperature flue-gas region, the sodium species are then gradually evolving towards the equilibrium. All the sulfurous sodium species are consumed, and the atomic sodium Na is the most significant sodium product (> 10 ppm) under stoichiometric and fuel-rich conditions while NaCl is the main sodium product (> 10 ppm) under fuel-lean condition. H radical generated from the hydrocarbon combustion helps to produce Na via the following two reaction paths: NaOH + H → Na + H2O and NaCl + H → Na + HCl. NaOH is another major sodium product which shows a concentration of 1-10 ppm under different conditions. The other four minor sodium species, i.e., NaO, NaO2, NaSO3 and NaSO3Cl, have a maximum concentration less than 0.5 ppm during the whole reaction process for all the three equivalence ratios (not shown here).

Transformation characteristics of sodium species in 1D diffusion flame

To investigate the transformation characteristics of sodium species in diffusion flame, four cases have been set up, which are Case E (the baseline case), Case F (HCl is removed from the volatile and replaced by N2), Case G (SO2 is removed from the volatile and replaced by N2) and Case H (both HCl and SO2 are removed from the volatile and replaced by N2).

Characteristics of the 2D pulverized-coal flame

The transformation characteristics of the sodium species in the 2D pulverized-coal flame are now examined. Figure 5 shows the instantaneous distributions of the (a) gas temperature and particle burnout, (b) OH mass fraction, (c) Na mass fraction, (d) NaCl mass fraction, and (e) flame index and particle temperature of the pulverized-coal flame. In the early stage, the coal particles in the jet shear layers are heated by the high-temperature coflow. Volatiles including sodium, sulfur and chlorine compounds are then released from the particles due to the pyrolysis. Isolated flame structures [START_REF] Yamamoto | Large eddy simulation of a pulverized coal jet flame ignited by a preheated gas flow[END_REF][START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF] are observed at t = 10 and 15 ms. Some particles are ignited at first in the shear layers, but the heat release is not strong enough to ignite adjacent coal particles. At t = 20 ms, more and more particles are ignited and YOH propagates around them, indicating a strong heat release and rapid spreading of the flame. Atomic sodium Na reaches a high concentration in the high-temperature flame region, while NaCl accumulates around the ignited particles. With most of the coal particles in the computational domain burn out at t = 30 ms, the burning tends to be weaker, but a wider combustion regime can be found as the mixing continues. The mass fractions of OH radical and atomic Na are decreasing, but NaCl achieves a high concentration.

The flame index, F.I., [START_REF] Hara | Direct numerical simulation of a pulverized coal jet flame employing a global volatile matter reaction scheme based on detailed reaction mechanism[END_REF][START_REF] Domingo | DNS analysis of partially premixed combustion in spray and gaseous turbulent flame-bases stabilized in hot air[END_REF] Figure 7 shows the instantaneous distributions of the mass fractions of all the twelve sodium species in the DNS at t = 20 ms, along with the distributions of the equivalence ratio ϕ and the mass fractions of HCl and SO2. High values of ϕ are induced by the volatile stream released from coal particles. The isoline of ϕ = 1 superimposed in Fig. 7 represents the stoichiometric conditions for reactions between the volatile and the oxidizer. It can be found that both HCl and SO2 are mainly located in the fuel-rich (inside the isoline) region, as they are released simultaneously with the volatile stream. For the sodium species, atomic Na is also found to have a high concentration in the fuel-rich region, which is in accordance with our previous study [START_REF] Wan | Modelling alkali metal emissions in large-eddy simulation of a preheated pulverised-coal turbulent jet flame using tabulated chemistry[END_REF][START_REF] Wan | Alkali metal emissions in an early-stage pulverized-coal flame: DNS analysis of reacting layers and chemistry tabulation[END_REF]. Both NaOH and NaCl feature a high concentration in the fuel-rich region, a moderate concentration in the fuel-lean region (outside the isoline), while a low concentration in the stoichiometric region. Since NaOH is the released sodium species along with the volatile, the reaction NaOH + HCl → NaCl + H2O explains the high concentration of NaCl in the fuel-rich region. NaHSO4 and Na2SO4 are the two main sulfated sodium species, but their concentrations are much lower than that of NaCl. It can be observed that the two sulfated sodium species mainly form in the fuel-lean region, similar to Na2Cl2 and Na2O2H2, which are favored sodium species in the pre-combustion mixture. The other five minor sodium species, i.e., NaO, NaO2, NaSO2, NaSO3 and NaSO3Cl, are also found to be produced under the fuel-lean condition, except that NaSO2 is also largely generated in the fuel-rich region where abundant sodium and sulfur exist. Figure 7. Instantaneous distributions of the equivalence ratio (ϕ), the mass fractions of HCl, SO2 and all the twelve sodium species at t = 20 ms. The isoline of ϕ = 1 is superimposed. Figure 8. Scatter plots of instantaneous mass fractions of Na, NaCl, NaOH, NaHSO4, Na2SO4 and Na2Cl2 against Z at t = 20 ms. Blue solid line and red dash line are the sodium profiles obtained from 1D counterflow diffusion flames, corresponding to the lowest (23 s -1 ) and highest strain rates (11318 s -1 ).

Sodium species dynamics

Figure 8 shows the scatter plots of instantaneous mass fractions of six sodium species against the mixture fraction, Z, at t = 20 ms. For the three-stream mixing, 2D pulverized-coal flame, the mixture fractions of the volatile released from pulverized-coal particles (the fuel stream), the air jet which carries pulverized-coal particles (the oxidizer stream) and the high-temperature coflow are Z = 1, Z = 0 and Z = 0.068, respectively. Na, NaCl and NaOH are found to be the three major sodium species in the reaction products. YNa stays almost zero in the range of Z < 0.05, and then increase rapidly with Z. The distributions of YNaCl and YNaOH are subtler. Their mass fractions reach the first peak around Z = 0.05, then decrease to a much lower value under the stoichiometric condition of Zst = 0.138, then increase again for higher Z and reach a much higher value under the fuel-rich condition than the first peak. Finally, YNaHSO4, YNa2SO4 and YNa2Cl2 feature a single-peak distribution within the fuel-lean regime of Z < 0.138, similar to the mass fractions of other sodium species, i.e., YNa2O2H2, YNaO, YNaO2, YNaSO3, YNaSO3Cl (not shown here). The distribution of YNaSO2 is similar to YNaCl, which has higher values both in the fuel-lean and fuel-rich regimes (not shown here).

The blue solid line and the red dash line in Fig. 8 are the sodium profiles obtained from 1D counterflow diffusion flames, corresponding to the lowest and highest strain rates, respectively. The high-strain rate (red dash line) slow down the consumption of NaOH and the production of NaHSO4 and Na2SO4 in the fuel-lean regime. The generation of NaCl is also limited under the high-strain rate, but the generation of atomic Na is found to be promoted. Compared with the sodium profiles from 1D counterflow diffusion flames, the DNS scatters basically follow a similar trend, but many data points fall outside the region between the two profiles corresponding to the lowest and highest strain rates. These points are likely to be representative of unsteadiness and/or partial premixing of the reactants, since the volatile, after being ejected from the particles, and the ambient air are rapidly mixed in a partially premixed mode, as in [START_REF] Reveillon | Analysis of weakly turbulent dilute-spray flames and spray combustion regimes[END_REF]. In addition, the radiation heat loss also contributes to the mismatch between DNS scatters and profiles from 1D diffusion flames.

Statistics of the 2D pulverized-coal flame

Figures 9 and 10 show the time evolutions of the averaged mass fractions of OH, HCl, SO2, Zvol and six sodium species, and the averaged gas temperature of the 2D pulverized-coal flame, all of which are calculated as the mean over the 2D computational domain. Zvol is the volatile mixture fraction, which is obtained from the following equation: [START_REF] Liu | In Situ Measurements of the Release Characteristics and Catalytic Effects of Different Chemical Forms of Sodium during Combustion of Zhundong Coal[END_REF] where DZ is the diffusivity coefficient of volatile (m 2 /s) and is set equal to the thermal diffusivity coefficient.

is the source term of the mass of the volatile released from coal particles. Figure 9. Time evolutions of the mean mass fractions of OH, HCl, SO2 and Zvol averaged over the 2D computational domain. Figure 10. Time evolutions of the averaged mass fractions of Na, NaOH, NaCl, NaHSO4, Na2SO4 and Na2Cl2, and the averaged gas temperature. At t = 5 and 10 ms, small peaks can be observed for YOH, YHCl and YSO2, and also for the mass fractions of sodium species in log-scale (not shown here). This is because the volatile around some coal particles is ignited and the flame heats the particles rapidly, which therefore leads to a high flux of volatile release. After t = 15 ms, both Zvol and T increase rapidly, which indicates the pulverized-coal jet is actively burning. The mass fractions of YOH, YHCl, YSO2, YNa and YNaCl also start to significantly increase after t = 15 ms. After t = 30 ms, both Zvol and T remain almost constant, indicating that the volatile release and homogeneous combustion have both ended. However, although the averaged gas temperature remains after t = 30 ms, the variance of the gas temperature in the domain decreases due to the turbulent mixing of the hot products and the surroundings. It explains the variation of the species mass fractions after t = 30 ms, e.g. the decreasing YHCl, which should be attributed to the reaction NaOH + HCl → NaCl + H2O. At the end of the simulation (t = 50 ms), NaCl is found to be the major sodium product while the other sodium species are minor.

Effects of HCl and SO2 on sodium emissions in the 2D pulverized-coal flame

To investigate the effects of HCl and SO2 on sodium transformation characteristics, three additional DNS cases were set up, which are Case K (HCl is removed from the volatile), Case L (SO2 is removed from the volatile) and Case M (both HCl and SO2 are removed from the volatile).

All the removed species are replaced by N2. The original baseline DNS case is referred to as Case J.

Figure 11 shows the comparison between the cases on the time evolution of the representative sodium species Na, NaOH, NaCl and Na2SO4. It can be found that without HCl and SO2, NaOH is the main sodium product at the end of the simulation (Case M). When only HCl is included in the volatile, NaOH is largely consumed by HCl and NaCl forms as the main sodium product (Case L). If SO2 is presented while HCl is not, NaOH is then partly transformed to Na2SO4, and both NaOH and Na2SO4 become the major sodium products (Case K). Interestingly, when both HCl and SO2 are presented (Case J), the reaction characteristics of the sodium species are very similar to Case L with HCl but no SO2. It implies that SO2 has only a minor contribution to the reactions with sodium species when HCl also exists in the released volatile. Hence, HCl has a much stronger ability to react with sodium species than SO2. In view of the reaction paths, HCl reacts with sodium species in a straightforward way, e.g., HCl + NaOH → NaCl + H2O and HCl + Na → NaCl + H. However, the reactions between SO2 and sodium species are more complex. The SO2 is first oxidized to SO3, to then reacts with sodium species, e.g., NaOH, to form NaHSO4, and finally produce Na2SO4 via shuffle reactions, e.g., NaHSO4 + NaOH → Na2SO4 + H2O.

Comparison of sodium emission characteristics in 1D and 2D flames

The 1D premixed flame simulation results (Fig. 2) show that Na has the highest concentration in the sodium products at ϕ = 1.0 and 2.0, which is consistent with the 1D diffusion flame simulation results (Fig. 4). However, under the fuel-lean condition of ϕ = 0.5, the 1D premixed flame results

show the major sodium product is NaCl while in the 1D diffusion flame results it is Na. The discrepancy should be attributed to the fact that the 1D premixed flame is freely propagating while the 1D diffusion flame is strained. From the statistics of the 2D simulation under the baseline condition, NaCl is found to be the major sodium product. The dilution effect of the coflow in the 2D pulverized-coal flame leads to an overall low equivalence ratio of 0.26 (corresponding to a mixture fraction Z = 0.043). From the 1D flame results, it can be found that indeed NaCl is the major sodium product under this fuel-lean condition.

Conclusions

The transformation characteristics of sodium species in pulverized-coal combustion are numerically investigated via 1D freely propagating premixed and 1D counterflow diffusion flames of coal volatile, and a 2D pulverized-coal flame. Detailed chemistry has been employed for both the combustion of volatile hydrocarbon fuels and the reactions of sodium species. From the 1D premixed flame simulations, it is found that the most significant sodium product is Na under stoichiometric (ϕ = 1.0) and fuel-rich conditions (ϕ = 2.0) while it is NaCl under fuel-lean condition (ϕ = 0.5). NaOH is another major sodium product. HCl is found to have a significant influence on the profile of NaOH in the initial unburned region. It also affects the distribution of Na2SO4. However, the effects of SO2 on the sodium profiles are minor. From the 1D diffusion flame simulations, HCl is found to decrease the concentrations of Na and NaOH in the fuel-rich region with ϕ > 2.0.

The transformation characteristics of the sodium species in a 2D pulverized-coal flame are then examined. From the instantaneous distribution characteristics, atomic Na is found to have a high concentration in the fuel-rich region. Both YNaOH and YNaCl feature a complex distribution over the mixture fraction space, as they reach higher concentrations under both fuel-rich and fuel-lean conditions and decrease to a much lower concentration under the stoichiometric condition. NaHSO4 and Na2SO4 are the two main sulfated sodium species which form mainly in the fuel-lean region, but their concentrations are much lower than that of NaCl. From the statistics of the 2D simulation, NaCl is found to be the major sodium product, which is consistent with the 1D simulations. Finally, the parametric study shows that HCl has a much stronger ability to react with sodium species than SO2.

Color figures can be used for the online PDF version and the gray style for hardcopy

reproduction.

Figure 2 .

 2 Figure 2. Sodium species distribution versus distance along the 1D premixed volatile flame at equivalence ratio ϕ = 0.5 (a), ϕ = 1.0 (b) and ϕ = 2.0 (c). The heat release zone is zoomed in and shown on the left side while the overall flame is shown on the right side.

Figure 4

 4 shows the comparison among the cases on the representative sodium species Na, NaOH, NaCl and Na2SO4. Here, only the results of the mixture fraction Z < 0.5 are shown, because a higher mixture fraction is rarely observed in the following 2D DNS study (see Fig.8 below). The mixture fraction is defined as Z = 1.0 -YN2/0.767. For the two-stream mixing, 1D diffusion flame, Z = 1 and Z = 0 indicate the coal-volatile and oxidizer streams, respectively. The positions of ϕ = 0.5, 1.0 and 2.0 in the mixture fraction coordinate are also indicated. It can be found that in all the four cases the mole fraction of Na increases rapidly with Z in the fuel-lean region. In the fuel-rich region with ϕ > 2.0, the profiles of Na show a decreasing trend in the cases with HCl (Cases E/G), which is not observed in the cases without HCl (Cases F/H). Both NaCl and NaOH have higher concentrations in fuel-lean and fuel-rich regions while relatively low concentrations under the stoichiometric condition. HCl is also found to decrease the concentrations of NaOH and Na in the fuel-rich region with ϕ > 2.0. For Na2SO4, it can reach a higher concentration when HCl is not presented but its mole fraction is still below 1 ppm in the whole range of Z. Since the concentrations of sulfurous sodium species are quite low, the effects of SO2 on the profiles of Na, NaCl and NaOH are minor, as shown in the comparison between the cases with SO2 involved (Cases E/F) and the cases without SO2 (Cases G/H).

Figure 4 .

 4 Figure 4. Comparison of sodium species distribution in the mixture fraction space of the 1D diffusion volatile flame among Case E (the baseline case), Case F (HCl removed), Case G (SO2 removed) and Case H (both HCl and SO2 removed).

10 W/m 3 .

 103 Figure 5. Time evolutions of instantaneous distributions of the (a) gas temperature and particle burnout, (b) OH mass fraction, (c) Na mass fraction, (d) NaCl mass fraction and (e) flame index and particle temperature.

Figure 11 .

 11 Figure 11. Comparison of time evolutions of the averaged mass fractions of sodium species among Case J (the baseline case), Case K (HCl removed), Case L (SO2 removed) and Case M (both HCl and SO2 removed).

Figure 1 .

 1 Figure 1. Schematic diagram of computational configuration.

Figure 2 .

 2 Figure 2. Sodium species distribution versus distance along the 1D premixed volatile flame at equivalence ratio ϕ = 0.5 (a), ϕ = 1.0 (b) and ϕ = 2.0 (c). The heat release zone is zoomed in and shown on the left side while the overall flame is shown on the right side.

Figure 3 .

 3 Figure 3. Comparison of sodium species distribution versus distance along the 1D premixed volatile flame between Case A (the baseline case), Case B (HCl removed), Case C (SO2 removed) and Case D (both HCl and SO2 removed) at equivalence ratio ϕ = 0.5 (a), ϕ = 1.0 (b) and ϕ = 2.0 (c).

Figure 4 .

 4 Figure 4. Comparison of sodium species distribution in the mixture fraction space of the 1D diffusion volatile flame among Case E (the baseline case), Case F (HCl removed), Case G (SO2 removed) and Case H (both HCl and SO2 removed).

Figure 5 .

 5 Figure 5. Time evolutions of instantaneous distributions of the (a) gas temperature and particle burnout, (b) OH mass fraction, (c) Na mass fraction, (d) NaCl mass fraction and (e) flame index and particle temperature.

Figure 6 .

 6 Figure 6. Time evolutions of instantaneous distribution of the flame index and particle temperature from t = 14.0 ms to t = 15.0 ms.

Figure 7 .

 7 Figure 7. Instantaneous distributions of the equivalence ratio (ϕ), the mass fractions of HCl, SO2 and all the twelve sodium species at t = 20 ms. The isoline of ϕ = 1 is superimposed.

Figure 8 .

 8 Figure 8. Scatter plots of instantaneous mass fractions of Na, NaCl, NaOH, NaHSO4, Na2SO4 and Na2Cl2 against Z at t = 20 ms. Blue solid line and red dash line are the sodium profiles obtained from 1D counterflow diffusion flames, corresponding to the lowest (23 s -1 ) and highest strain rates (11318 s -1 ).

Figure 9 .

 9 Figure 9. Time evolutions of the mean mass fractions of OH, HCl, SO2 and Zvol averaged over the 2D computational domain.

Figure 10 .

 10 Figure 10. Time evolutions of the averaged mass fractions of Na, NaOH, NaCl, NaHSO4, Na2SO4 and Na2Cl2, and the averaged gas temperature.

Figure 11 .

 11 Figure 11. Comparison of time evolutions of the averaged mass fractions of sodium species among Case J (the baseline case), Case K (HCl removed), Case L (SO2 removed) and Case M (both HCl and SO2 removed).

Table 1 .

 1 Analysis of Loy Yang brown coal[START_REF] Van Eyk | The release of water-bound and organic sodium from Loy Yang coal during the combustion of single particles in a flat flame[END_REF].

	Dry basis, wt%
	C	67.8
	H	5.20
	N	0.57
	S	0.24
	Cl	0.06
	Ash	0.80

Table 2 .

 2 Modeled volatile-gas compositions of Loy Yang brown coal.

	Hydrocarbon volatile compositions predicted by the CPD model (mass fractions)
	CH4	C2H2	CO	H2	CO2	H2O
	0.03707	0.30698	0.20664	0.02976	0.15394	0.25979
	Non-hydrocarbon volatile compositions (mass fractions)
	NaOH	HCl	SO2
	4.0E-4	6.2E-4	48.0E-4

Acknowledgements

This work was jointly supported by the National Natural Science Foundation of China (51706200), the China Postdoctoral Science Foundation (2018M632460), the Fundamental Research Funds for the Central Universities (2018FZA4012), the Engineering and Physical Sciences Research Council (EPSRC) and the Royal Society of the UK. Y.L. is funded by the Open Topic Exploration Program of the ZJU CEU laboratory. Special thanks are due to Prof. Peter Glarborg of DTU, who provided us the detailed mechanism of alkali metal species. Computing resources were provided by the National Supercomputer Center in Tianjin, China (http://www.nscc-tj.cn).


Kaidi Wan

Zhihua Wan
email: wangzh@zju.edu.cn

Jun Xia
email: jun.xia@brunel.ac.uk

Luc Vervisch

Pascale Domingo

Yu Lv

Yingzu Liu

Yong He

Kefa Cen

Zhihua Wang

Numerical study of HCl and SO2 impact on potassium emissions in pulverized-biomass combustion

Keywords: Pulverized-biomass combustion, Emission, Potassium chemistry, Alkali metal, HCl, SO2

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

As a renewable fuel source, biomass resources have been utilized to supply 10-15% of the worldwide energy consumption [1], especially with an increasing application in the production of thermal power. However, advanced biomass utilization is significantly limited by severe ash formation and deposition problems resulting from alkali metal issues [2]. Potassium (K) is usually rich in biomass, since it is an important element for plants. The potassium vapor released during the combustion of biomass is easy to condense on heat transfer surfaces and form an initial sticky layer, which then captures fly ash and therefore results in rapid ash deposition [3,4]. In addition, potassium also reacts with chlorine and sulfur species to form complex compound, which leads to serious fouling and corrosion issues [5,6]. Thus, understanding the fundamental formation and transformation mechanisms of potassium in biomass combustion is essential for the development of potassium control technologies and a better utilization of this renewable fuel [7][8][9].

Experimental research on the release and reacting dynamics of potassium evolves from offline sampling techniques to online measurement methods using laser diagnostics [2,[10][11][12].

Non-intrusive, time-resolved laser techniques, e.g., tunable diode laser absorption spectroscopy (TDLAS) [13], collinear photo-fragmentation atomic absorption spectroscopy (CPFAAS) [14] and laser induced fragmentation fluorescence (ELIF) [15], can directly capture the dynamic release process of potassium during biomass combustion. In our recent study [16], the release of atomic and elemental potassium from a burning biomass pellet has been quantitatively measured via planar laser-induced fluorescence (PLIF) and multi-point laser-induced breakdown spectroscopy (LIBS) methods.

On the modeling side, Zhang et al. [17] proposed an one-step Arrhenius potassium release model during the combustion of a pinewood pellet. In our recent work [16], a two-step model was developed to describe the potassium release during both the pyrolysis and char burnout stages of two biomass samples, based on simultaneous measurements of the pellet-surface temperature, pellet diameter and potassium release of a burning biomass pellet. Since the pellet diameter and burnout time of biomass in these studies are on the same order of magnitude as in a typical circulating fluidized bed (CFB) boiler, these potassium release models are suitable for CFB combustion [18].

Potassium release models for pulverized-biomass combustion are still required to be developed.

Considering the post-release homogeneous reactions of alkali species, it has been found that the main alkali species are atomic K/Na, KOH/NaOH and KCl/NaCl in chemical equilibrium of post-combustion gases [19], which can be well predicted by thermodynamic equilibrium calculation, e.g., [18][19][20]. A detailed chemical reaction mechanism for alkali species has been proposed by Glarborg and Marshall [21], and validated with experimental data on sulfation of potassium chlorides.

However, the numerical investigation on reaction dynamics of alkali species in turbulent reacting flows is still quite limited. Most of the relevant research employs Reynolds-averaged Navier-Stokes (RANS) simulation (e.g. [22,23]) with simplified alkali reaction mechanisms to study the response of potassium in biomass combustion.

With the rapid increase of computing capacity in recent years, computational fluid dynamics (CFD) approaches for multi-phase flows are evolving towards high-fidelity methods, i.e., direct numerical simulation (DNS,e.g.,(24)(25)(26)) and large-eddy simulation (LES,). The two high-fidelity methods have shown advantages over RANS on the prediction of local gas temperature and species distributions. Our previous work [26,34] on pulverized-coal combustion demonstrated that DNS and LES can provide detailed physical insights into complex multi-phase reacting flow dynamics and the homogeneous evolution of alkali species.

In sum, the reaction dynamics of potassium species in pulverized-biomass combustion have not been fully revealed by previous studies. In the present work, the responses of potassium species to one-dimensional (1D) premixed/diffusion flames of biomass volatile are firstly investigated. Then, the transformation dynamics of potassium species in a two-dimensional (2D) early-stage pulverized-biomass flame are numerically studied, excluding char combustion. Information about the major potassium product under various conditions and the comparison between the impacts of HCl and SO2 on potassium conversion are revealed, which could potentially benefit the biomass combustion community. The full detailed potassium mechanism including the elements K, C, H, O, S and Cl proposed by Glarborg and Marshall [21] is utilized to model the potassium reactions during the simulation. It should be noted that Glarborg and Marshall [21] have carefully validated their detailed potassium mechanism against the experimental results of the homogeneous sulfation of potassium chloride at combustion conditions. The readers might notice that there exists a newer version of potassium mechanism by Hindiyarti et al. [35], which includes additional sulfation pathways of potassium to mainly improve the prediction of the mechanism at lower temperatures [36]. However, since the present study focus on the potassium transformation under combustion conditions, thus at rather high temperature levels, the original version of the mechanism [21] is used to save the computational cost.

One-dimensional premixed/diffusion flames of biomass volatile

The reaction dynamics of potassium species in 1D premixed/diffusion flames of biomass volatile are studied. The volatile is released from corn straw [16], for which the chemical analysis data is shown in Table 1. The combustion of biomass volatile is modeled by the previously validated DRM22 skeletal mechanism involving 22 chemical species and 104 elementary reactions, which is proposed by Kazakov and Frenklach [37]. The bio-chemical percolation devolatilization (bio-CPD) model [38][39][40] is used to preliminary obtain the compositions of the volatile fuels and in which the Tar species is replaced by C2H2 [32]. Then the obtained compositions are adjusted to fulfill the elemental mass conservation and the lower heating value of the corn straw, as in [30,33,34]. The final volatile compositions used in the present study is shown in Table 2 To study the potassium reactions under the premixed condition, a 1D freely propagating premixed flame of the biomass volatile is simulated using CANTERA [42]. The inlet volatile-air mixture temperature is 300 K and three equivalence ratios, i.e., ϕ = 0.5, 1.0 and 2.0, of the mixture are considered. To investigate the diffusion condition, a 1D counterflow diffusion volatile flame is simulated also using CANTERA [42]. The mass flow rates of the biomass volatile and air inlets are 0.024 (kg/m 2 s) and 0.072 (kg/m 2 s), respectively, while their temperatures both are 300 K. Four configurations with HCl and/or SO2 replaced by N2 are set up to study the effects of HCl and SO2 on potassium reaction characteristics. In total 16 cases are simulated. The grid is limited to 250 points while the length of the 1D computational domain for premixed and diffusion condition is 1.0 m and 3.0 cm, respectively.

Pulverized-biomass flame configuration and numerics

A two-dimensional temporally evolving pulverized-biomass jet flame is studied (Fig. 1). The computational domain has physical dimensions of 51.2 mm in both the streamwise (x) and spanwise (y) directions. A uniform mesh of h = 100 μm is used, which has been demonstrated to be able to resolve the flame structure [26]. Initially, high-speed primary air (10 m/s, 300 K) laden with pulverized-biomass particles is set up for |y| < 2.5 mm, and the 902 biomass particles follow a random uniform distribution. The initial density of a particle is set to 550 kg/m 3 [43] and its diameter is 25 μm, following a mono-disperse diameter distribution. The particle diameter used here might be finer than common diameters of pulverized-biomass employed in other studies, e.g., 60-200 μm [12, 44]. However, the particle diameter cannot be larger in order to fulfill the grid resolution required by DNS and the point-particle assumption. On the other hand, this fine diameter of 25 μm can be achieved with torrefied biomass [44]. Same as the 1D simulations, properties of corn straw [16] are employed (Table 1). Surrounding the primary air, a hot coflow (3 m/s, 1519 K) is introduced with a composition and temperature of the burnout gas of the biomass volatile at an equivalence ratio of 0.45. Periodic boundary conditions are employed in all directions. Turbulent fluctuations of 0.05 m/s are initially put within the shear layers between the primary air and the coflow, for the purpose of facilitating the jet development. The parameters of the present configuration are chosen according to our previous study on pulverized-coal flames [26]. Two-way coupling between the gas and particle phases are considered and biomass particles are treated as point sources.

Biomass pyrolysis, including K/Cl/S release, volatile-gas combustion and K/Cl/S reactions are simulated. Heterogeneous reaction of solid char is not considered, since its contribution has been demonstrated to be weak in small-scale pulverized-coal flames [32,34,45]. The char content of biomass is much lower than that of coal (see Table 1). Hence, the contribution of char combustion in the present pulverized-biomass flame should be even weaker and therefore can be safely ignored.

Gas phase modeling

The governing equations for the gas and biomass-particle phases are solved in the Eulerian and Lagrangian frameworks, respectively, using a low-Mach-number in-house code [26,30,33,34]. The conservation equations for mass, momentum, species and temperature solved for the gas phase are:

, D t mp S ρ = & (1) ( ) , , D t i i j i j m o mpi u p S ρ τ = -∂ + ∂ + & (2) ( ) ( ) , , , D t n j n j n Yn Y pn Y D Y S ρ ρ ω = ∂ ∂ + + & & (3) ( ) , , , 2 , , D t j j j P g j T Tp T R P g P g T T C T S S C C λ λ ρ ω   = ∂ ∂ + ∂ ∂ + + +     & & & (4)
where Dt(Φ) = ∂t(Φ) + ∂j(Φuj), ∂j ≡ ∂xj, ρ is gas density (kg/m 3 ), ui is gas velocity (m/s), Yn is the mass fraction of the nth chemical species, T is gas temperature (K). The pressure is denoted by p, and τij = μ(∂jui + ∂iuj -2/3 ∂kukδij) is the viscous stress tensor. Dn is the molecular mass diffusivity coefficient (m 2 /s), CP,g and λ are the specific heat capacity (J/kg K) and thermal conductivity (W/m K) of the gas mixture, respectively.

Particle phase modeling

The momentum equation of a Lagrangian biomass particle is:

( ) , , d t p j j p j p u f u u τ = - (5)
where up,j is the particle velocity (m/s). The dynamic response time (s) of a particle is 2 18

p p p d τ ρ µ =
, where ρp is the density of the particle (kg/m 3 ), and dp is its diameter (m). f is the drag coefficient, which considers both the high particle Reynolds number effects and the blowing effects of volatiles at the particle surface [46].

The particle temperature equation can be written as:

( ) ( ) , d t p conv rad dev p P p T Q Q Q m C = + + ( 6
)
where Tp is the temperature of the particle (K), mp its mass (kg), CP,p its specific heat capacity (J/kg K). The heat transfer terms by convection, radiation, and pyrolysis (devolatilization) are ( ) The kinetic parameters of the SFOM pyrolysis model, i.e., Av (2.5 × 10 9 s -1 ), Ev (11 × 10 4 J/mol) and

, Nu 3 Pr conv P g p p p Q C m T T τ = - , ( ) 2 4 4 rad p p R p Q d T T ε π σ = - ,
Qv (1.10), have been calibrated by the bio-CPD model [38], as in [30,33,34].

Gas phase chemistry

Same as in Section 2, the oxidization of hydrocarbon biomass volatile and the reactions of potassium species are modeled by the DRM22 skeletal mechanism [37] and the detailed alkali reaction mechanism [21], respectively. The compositions of the volatile gas can be found in Table 2, including the non-hydrocarbon compounds of potassium, sulfur and chloride.

The release rate of potassium from biomass particles is assumed to be proportional to the volatile release rate [26,34], since the potassium vapor generated inside the porous structure of a biomass particle will be transported outward by the volatile yielded during the pyrolysis stage.

Besides, in our previous study the alkali release from a coal particle was found proportional to its burnout during the early combustion stage [18]. Similarly, the release rates of sulfur and chlorine are also assumed to be proportional to the volatile release rate here.

Numerical schemes

The numeric of our in-house code is based on an approach previously validated for both DNS and LES [51,52]. A second-order Crank-Nicolson scheme is employed for the time advancement. A second-order central difference scheme is applied to all terms in the momentum equation and the scalar diffusion terms in the species and temperature equations. In order to secure the scalar boundedness, a Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme is used for the scalar advection terms in the species and temperature equations. An Alternating Direction Implicit (ADI) approach has been adopted, and semi-implicit tridiagonal/pentadiagonal equations are solved separately for each direction. A second-order Runge-Kutta (RK2) scheme is employed to explicitly advance the particle equations.

Results and discussion

Transformation characteristics of potassium species in 1D premixed flame

The reactions of potassium species in 1D premixed volatile flames have been investigated for three equivalence ratios (ϕ = 0.5, 1.0 and 2.0), representing fuel-lean, stoichiometric and fuel-rich conditions. From Fig. 2, it can be found that the concentration of KOH rapidly decreases in the initial unburned region with T = 300 K, which should be attributed to the following two reaction paths:

2KOH → K2O2H2 (R1); KOH + HCl → KCl + H2O (R2), 2KCl → K2Cl2 (R3).
First, KOH is consumed to generate K2O2H2 via Reaction R1. In addition, KOH also reacts with HCl in the volatile as Reaction R2, and K2Cl2 is subsequently formed through Reaction R3. K2O2H2 and K2Cl2 are the two major potassium species in the initial unburned region. It should be noted that at low temperature, the potassium is in condensed form, possibly as aerosol. Hence, the results in the initial unburned region of the canonical laminar flame are questionable. However, this issue will get relieved in the following investigation of 2D pulverized-biomass flame (Section 4.3) because the potassium is released along with volatile and therefore at much higher temperature. When the combustion happens and therefore the temperature increases around Distance of 0.15 cm, K2O2H2

and K2Cl2 are then decomposed to KOH and KCl, respectively, and further transform to other potassium species, e.g., K, KO2, KSO2, KHSO4 and K2SO4. In the post-flame region, the potassium species then gradually evolve towards equilibrium. It can be observed that KOH is the most significant potassium product (~10 3 ppm) for all the three equivalence ratios, while KCl has the second highest concentration (~10 2 ppm). The sulfurous potassium species K2SO4 is found to be the third major potassium product (34 ppm) under the fuel-lean condition; while under the stoichiometric and fuel-rich conditions, the third major potassium product changes to atomic potassium K (> 60 ppm). Another minor potassium species, KSO3Cl, has a maximum concentration less than 0.01 ppm during the whole reaction process for all the three equivalence ratios and therefore is not shown in the figure. it can be found in Fig. 2 that the potassium reactions almost reach equilibrium at this position. KOH is found to be the main potassium product for the four cases. When HCl and/or SO2 is presented, a minor part of potassium is transformed to KCl and/or K2SO4. However, the mole fraction of the produced KCl and/or K2SO4 is much lower than that of KOH. Hence, the profiles of KOH are close to each other for the four cases in the combustion and post-flame regions.

Transformation characteristics of potassium species in 1D diffusion flame

To further investigate the response of potassium species in diffusion flame, other four cases

Characteristics of the 2D pulverized-biomass flame

The transformation of potassium species in the 2D pulverized-biomass flame is then sequentially examined. Figure 5 shows the evolution of some important quantities of the flame: (a)

gas temperature and particle burnout, (b) OH mass fraction, (c) K mass fraction, (d) KOH mass fraction, and (e) flame index and particle temperature. In the early stage of t = 10-15 s, biomass particles in the jet shear layers are heated by the high-temperature coflow. Volatiles including potassium, chlorine and sulfur compounds are then released from these particles via the pyrolysis process. Isolated flame structures [27,34] can be observed at t = 15 ms, which are formed due to individual particles ignited in the shear layers. At t = 20 ms, more and more particles get ignited and YOH propagates, representing a strong heat release of the rapid spreading flame. Atomic potassium K has a high concentration in the high-temperature burning zone, while KOH accumulates around the ignited particles. Finally, at t = 30 ms, the flame tends to be weak as most of the biomass particles in the computational domain burn out. However, a wider flame regime can be observed since the turbulent mixing continues. The concentrations of OH radical and atomic K drop, but that of KOH remains a significant level. W/m 3 and therefore are actively reacting regions. The maximum heat release rate in the 2D domain is 3.03×10 10 W/m 3 . It can be found that at the beginning stage of t < 15 ms, the first ignition of biomass particles is controlled by premixed combustion. Then after the biomass jet reaches actively reacting state, the volatile released from particles accumulates before burning and therefore leads to a dominant diffusion combustion mode [26].

Figure 6 shows the instantaneous distributions of all the twelve potassium species considered in the DNS at t = 20 ms. The isoline of ϕ = 1 is superimposed, which represents the stoichiometric condition of combustion between the biomass volatile and the oxidizer. It can be found that atomic K has a high concentration in the regime close to the isoline, where the volatile fuel is actively burning and the temperature is high. Both KOH and KCl feature a high concentration in the fuel-rich region (inside the isoline), and a moderate concentration in the fuel-lean region (outside the isoline). KOH is the released potassium species along with the volatile, while the high concentration of KCl in the fuel-rich region can be explained by the Reaction R2. KHSO4 and K2SO4 are the two major sulfated potassium species, which mainly form in the fuel-lean region, but their concentrations are much lower than the potassium chloride KCl. The two favored potassium species in the pre-combustion mixture K2Cl2 and K2O2H2 are observed only in the fuel-lean region, since they will decompose under high temperature. The other five minor potassium species, i.e., KO, KO2, KSO2, KSO3 and KSO3Cl, are produced under the fuel-lean condition, while KSO2 achieves a high concentration in the fuel-rich region where abundant potassium and sulfur exist.

Potassium species dynamics

Figure 7 shows the instantaneous scatter plots of six representative potassium species against the mixture fraction at t = 20 ms. For the three-stream mixing in the 2D pulverized-biomass flame, the mixture fractions of the volatile released from biomass particles (the fuel stream), the air jet carrying these particles (the oxidizer stream) and the high-temperature coflow are Z = 1, Z = 0 and Z = 0.093, respectively. K, KCl and KOH are the three major potassium species in the reaction products. The distributions of YKCl and YKOH are almost linear with Z, while that of YK is subtler. YK stays almost zero for the lower range of Z < 0.05, to then increases rapidly until Z = 0.22, and then holds a moderate increasing rate for the fuel-rich regime of Z > 0.22. Finally, YKHSO4, YK2SO4 and YK2O2H2 feature a single-peak distribution within the fuel-lean regime of Z < Zst = 0.189.

The potassium profiles obtained from 1D diffusion flames are also shown in Fig. 7 with the blue solid line and the red dash line corresponding to the lowest and highest strain rates, respectively. It can be found that the high-strain rate (red dash line) helps to enhance the transformation of KOH to K, KHSO4 and K2SO4, while the production of KCl is insensitive to the strain rate. This is because the KCl-formation reactions are almost instantaneous (of the order of a few micro seconds), and therefore can hardly be affected by the relatively much slowly varying strain rate. It can also be observed in Fig. 2 that the reaction zone of KCl is much thinner than the other potassium products.

Compared with the line plots from 1D diffusion flames, the DNS scatters generally follow a similar trend, but lots of data points fall outside the region between the red dash and blue solid lines. These points are likely to represent the unsteadiness and/or partial premixing of the reactants, because the volatile ejected from the particles is rapidly mixed with the ambient air in a partially premixed mode, as in [55]. Besides, the radiation heat loss also contributes to the discrepancy between line plots from ) and highest strain rates (8556 s -1 ).

Figures 8 and9 show the time evolutions of the mean mass fractions of OH, HCl, SO2, Zvol and six representative potassium species, and the mean gas temperature of the biomass flame. All of these quantities are averaged over the entire 2D computational domain. Zvol is the volatile mixture fraction, which can be obtained from:

( ) ( ) , , D t v o l j Z j v o l Y pv o l Z D Z S ρ ρ = ∂ ∂ + & (7)
where DZ is the diffusivity coefficient of volatile gas (m 2 /s) and its value is set equal to the thermal diffusivity.

, ,

Y p vol S &
is the source term of the volatile mass released from biomass particles. It can be observed that the first ignition of the biomass jet happens at t = 5 ms. The mass fractions of potassium species and the gas temperature start to increase and small peaks can be found for YOH and YHCl. This is because the volatile fuel gets ignited around some particles, which in turn heats up the particles rapidly and therefore bring a high flux of volatile release. After t = 15 ms, the biomass jet is actively burning which reflects in both T and Zvol increase rapidly, same as the mass fractions of YOH, YHCl, YSO2, YKOH and YKCl. After t = 30 ms, both T and Zvol remain almost constant, indicating the end of the combustion of the biomass jet. However, although the average of gas temperature in the domain becomes stable, its variance is further decreasing due to turbulent mixing of the hot burnout gases and the surroundings. This explains the variation of the species mass fractions after t = 30 ms, e.g. the decreasing of YHCl due to Reaction R2. At the end of the simulation (t = 50 ms), KOH is found to be the major potassium product. Comparing the DNS predictions at the end of the simulation to a reference equilibrium calculation by CANTERA [42] of a zero-dimensional (0D) homogeneous reactor under the temperature of 1538 K, which is the final averaged temperature of the 2D DNS domain, the relative errors are of 2.07% for KOH, 2.93% for KCl and 21.85% for K2SO4. The larger error for K2SO4 should be attributed to the slower sulfation reactions, as shown in Fig. 2a, and therefore it would take a much longer time for K2SO4 to reach equilibrium. Furthermore the 2D DNS domain does not reach a homogeneous state at t = 50 ms, which also contributes to the discrepancy between the DNS predictions and equilibrium results. Figure 9. Time evolutions of the mean mass fractions of K, KOH, KCl, KHSO4, K2SO4 and K2Cl2, and the mean gas temperature.

The major pathways of potassium transformation in the pulverized-biomass flame is summarized in Fig. 10. It can be found that HCl reacts with potassium species in a straightforward way, i.e., HCl + KOH → KCl + H2O and HCl + K → KCl + H. In contrast, the formation of sulfated potassium species is more complex. The SO2 is first oxidized to SO3, to then reacts with KOH to form KHSO4, and finally produce K2SO4 through a shuffle reaction, KHSO4 + KOH → K2SO4 + H2O. where M denotes the molar mass. The obtained conversion rate of KCl in Case L is αKCL = 95.1%, while that of K2SO4 in Case K is αK2SO4 = 14.7%. The conversion rate of KCl is much higher than that of K2SO4, indicating HCl has a much stronger ability to react with potassium species than SO2.

Comparison of potassium emission characteristics in 1D and 2D flames

The 1D premixed flame simulations (Fig. 2) show that KOH is the most significant potassium product under various equivalence ratios in fuel-lean, stoichiometric and fuel-rich conditions. This is consistent with the 1D diffusion flame simulation results (Fig. 4). However, some discrepancies can be observed between the premixed and diffusion flame predictions. For instance, the premixed flame results show that the second major potassium product is KCl under all the conditions, which is not the case in the diffusion flame under stoichiometric condition, where atomic K has a higher concentration than KCl. The reason of the discrepancy should be that the 1D diffusion flame is strained while the 1D premixed flame is freely propagating. In fact, Fig. 7 indeed shows that a higher strain rate could promote the production of K, while KCl is insensitive to the variation of strain rate.

Finally, the statistics of the 2D biomass flame also demonstrates that KOH is the major potassium product. The overall equivalence ratio of the 2D flame is 0.55 (corresponding to a mixture fraction Z = 0.094), and therefore its potassium emission statistics are close to that of the 1D flames under the fuel-lean condition.

Conclusions

The emission characteristics of potassium species in biomass combustion are numerically investigated via 1D premixed/diffusion flames of biomass volatile, and a 2D pulverized-biomass flame. Complex chemistry has been used for both the volatile hydrocarbon combustion and the potassium species reactions. From the 1D premixed flame simulations, it is found that KOH is the most significant potassium product for all the three equivalence ratios, while KCl has the second highest concentration. The 1D diffusion flame simulations also support that KOH is the major potassium products while the productions of sulfurous and chloric potassium species are secondary.

The emission characteristics of the potassium species in a 2D pulverized-biomass flame are then examined. The instantaneous distribution characteristics show that KOH, KCl and K are the three major potassium species in the reaction zone. The distributions of YKCl and YKOH are almost linear

Figure 1 .

 1 Figure 1. Schematic diagram of computational configuration. Periodic boundary conditions in all directions

  the two-way coupling terms considering the effects of particles on the gas. , Y n ω & is the source term due to homogeneous chemical reactions. In the temperature equation, the radiative heat transfer ( , T R S & ), heat exchange between the gas phase and biomass particles ( , T p S & ), and thermal effects of homogeneous reactions ( T ω & ) are taken into consideration. In the present study, the Lewis number (Le = 1.0) and Prandtl number (Pr = 0.7) are assumed to be constant.

  is the Nusselt number and computed by the Ranz-Marshall correlations[47]. The radiation temperature (K) is calculated by TR = (G/4σ) 1/4 , where G is the incident radiation (W/m 2 ) obtained via the Discrete Ordinates Method (DOM)[48]. σ is the Stefan-Boltzmann constant (5.67 × 10 -8 W/m 2 K 4 ). εp is the particle emissivity and here is set to 0.9[39]. The weighted-sum-of-the-gray-gases model (WSGGM)[49] is employed to estimate the gas absorption coefficient. Finally, the mass loss rate of each biomass particle (dmp/dt), due to the pyrolysis, is predicted by the single first-order reaction model (SFOM) proposed byBadzioch and Hawskley [50].

Figure 2 .

 2 Figure 2. Potassium species distribution versus distance along the 1D premixed volatile flame at equivalence ratio ϕ = 0.5 (a), ϕ = 1.0 (b) and ϕ = 2.0 (c). The heat release zone is zoomed in and shown on the left side while the overall flame is shown on the right side.

Figure 3 .

 3 Figure 3. Comparison of potassium species distribution versus distance along the 1D premixed volatile flame between Case A (the baseline case), Case B (HCl replaced by N2), Case C (SO2 replaced by N2) and Case D (both HCl and SO2 replaced by N2) at equivalence ratio ϕ = 0.5 (a), ϕ = 1.0 (b) and ϕ = 2.0 (c).

  have been set up: Case E (the baseline case), Case F (HCl in the volatile is replaced by N2), Case G (SO2 in the volatile is replaced by N2) and Case H (both HCl and SO2 in the volatile are replaced by N2). Comparison among these cases on the representative potassium species K, KOH, KCl and K2SO4 is shown in Fig.4. It may be noted that only the region of the mixture fraction Z < 0.6 are shown, because a higher mixture fraction is hardly observed in the following 2D DNS study (see Fig.

7

  below). The mixture fraction could be calculated as Z = 1.0 -YN2/0.767. For the present two-stream mixing case of 1D diffusion flame, Z = 0 and Z = 1 indicate the oxidizer and biomass-volatile streams, respectively. The positions of ϕ = 0.5, 1.0 and 2.0 in the mixture fraction space are also illustrated in Fig.4. It can be found that in the fuel-lean region the mole fraction of K increases rapidly with Z for all the cases. In the very rich region of Z > 0.5, the profile of K drops in the cases (E/F) with SO2, which is not observed in the cases (G/H) without SO2. Both KOH and KCl show a monotonically increasing trend along with Z, although the increasing rate get suppressed at the stoichiometric condition. For Na2SO4, it reaches a concentration of ~20 ppm at the fuel-lean region around Z = 0.05, but becomes minor (< 0.1 ppm) for all the other conditions. Similar as in the previous premixed flames, the profiles of KOH in the four cases here are also close to each other, because the productions of sulfurous and chloric potassium species are limited.

Figure 4 .

 4 Figure 4. Comparison of potassium species distribution in the mixture fraction space of the 1D diffusion volatile flame among Case E (the baseline case), Case F (HCl replaced by N2), Case G (SO2 replaced by N2) and Case H (both HCl and SO2 replaced by N2).

Figure 5 .

 5 Figure 5. Time evolutions of instantaneous distributions of the (a) gas temperature and particle burnout, (b) OH mass fraction, (c) K mass fraction, (d) KOH mass fraction and (e) flame index and particle temperature.

Figure 6 .

 6 Figure 6. Instantaneous distributions of all the twelve potassium species at t = 20 ms. The isoline of ϕ = 1 is superimposed.

Figure 7 .

 7 Figure 7. Scatter plots of instantaneous mass fractions of K, KCl, KOH, KHSO4, K2SO4 and K2O2H2against Z at t = 20 ms. Blue solid line and red dash line are the potassium profiles obtained from 1D counterflow diffusion flames, corresponding to the lowest (21 s -1 ) and highest strain rates (8556 s -1 ).

Figure 8 .

 8 Figure 8. Time evolutions of the mean mass fractions of OH, HCl, SO2 and Zvol averaged over the 2D computational domain.

Figure 10 .

 10 Figure 10. Major pathways of potassium transformation during pulverized-biomass combustion.

Figure 11 .

 11 Figure 11. Comparison of time evolutions of the mean mass fractions of potassium species among Case J (the baseline case), Case K (HCl replaced by N2), Case L (SO2 replaced by N2) and Case M (both HCl and SO2 replaced by N2).

Table 1 .

 1 . Chemical analyses of corn straw.

	Proximate analysis (wt%)		Ultimate analysis (wt%)
	Mad	Aad	Vad	FCad	Cdaf	Hdaf	Ndaf	Sdaf	Odaf
	11.6	7.9	64.2	16.3	43.9	4.5	1.8	0.4	49.3
	Ash analysis (wt%)						Clad	Kad
	SiO2	Al2O3	Fe2O3	CaO	MgO	K2O	Na2O	(mg/g)	(mg/g)
	47.52	5.64	1.04	4.51	12.6	7.87	1.97	1.34	13.1

Table 2 .

 2 Modeled volatile-gas compositions of corn straw.

	Hydrocarbon volatile compositions (mass fractions)
	CH4	C 2H2	C O	H 2	C O 2	H 2O
	0.0322	0.1805	0.2536	0.0215	0.1853	0.3024
	Non-hydrocarbon volatile compositions (mass fractions)
	KOH	HCl	SO2
	0.0147	0.0018	0.0080
	Similar as previous studies on sodium emissions in coal combustion [41], KOH is set as the
	initial species of K, while HCl and SO2 are set as the initial species of Cl and S, respectively.
	According to our previous experimental data [16], the percentage of potassium which is releasable
	during the biomass pyrolysis stage is set to 58.1%. Since the release of chlorine and sulfur has not
	been measured, their releasable proportions during the pyrolysis are both set to 87.3%, the volatile
	yields ratio predicted by the bio-CPD model [38], based on the consideration chlorine and sulfur can
	be fully released during the pyrolysis and char stages of biomass combustion. Mass fractions of
	KOH, HCl and SO2 in the volatile can then be obtained, as shown in Table 2. The detailed alkali
	mechanism developed by Glarborg and Marshall [21] includes elementary reactions over Na, K, C,
	H, O, S and Cl. Here, the element Na is not considered, which leads to a detailed mechanism of
	potassium involving 35 species and 153 elementary reactions.

Table 2

 2

	K2SO4 as:
		KCl α =	Z	vol	,final	⋅	min	( Y final,KCl 0,KOH Y	KCl KOH M M	,	0,HCl Y	M	HCl	)	×	100%	(8)
	α	2 K SO	4	=	Z	vol	,final	⋅	( min 0.5 final,K SO 2 o,KOH 4 Y Y	2 K SO KOH M M	4 ,	0,SO Y	2	M	SO	2	)	×	100%	(9)

) and the final mass fractions (Yfinal) of KCl/K2SO4 in the burnout gases, we can calculate the conversion rate (α) of KCl and