I. S. ANUFRIEV ET AL. 307

burnout process, – the high-temperature combustion of

coals of wide quality range in the regime of liquid slag

removal in the vortex chamber. Obviously the vortex

transfer appears to be the aerodynamic basis of entire

combustion process in the studied vortex furnace. With

this the appropriate aerodynamic structure can enhance

the combustion efficiency, stability of temperature and

heat flux distributions, and reduce toxic emissions.

Therefore the purpose of the presented work is to inves-

tigate the features of two-phase turbulent reacting flow

inside the furnace with aim to estimate and justify the

new design and operating parameters for prospective

boiler units with vortex furnace.

2. Mathematical Model of Aerodynamics

and Coal Combustion Processes

Flow in the vortex furnace is subsonic, turbulent and

essentially three-dimensional due to the constructional

features of the furnace. The mathematical formulation of

the steady-state 3-D turbulent two-phase reacting flow is

based on Euler-Lagrange approach. The Favre-averaged

governing equations of momentum, enthalpy and the

species concentration transport for carrier gas phase are

closed with “realizable” modification of k- turbulence

model [3]. This model, compared to the “standard” k-

model [4], provides more accurate predictions for swirl

flows (which is essential for the vortex furnace) and de-

monstrates good numerical robustness.

For description of the heat-mass transfer and combus-

tion processes, the carrier gas phase is represented by

mixture of the following sp ecies: {O2, CHnOm, CO, CO2,

H2O, N2}. Here CHnOm denotes the generalized formula

for hydrocarbons released during the volatiles’ pyro lysis.

Coefficients m and n in CHnOm formula were calculated

from elementary composition of the coal which is pre-

sumed to consist of the volatiles, ash, wet and free car-

bon. Berezovskij brown coal (rank “2B”) of siberian

Kansk-Achinsk field has been taken in simulations, with

the following data of its proximal analysis: W = 33 %, A0

= 4.7%, Cf0 = 44.2%, OV0 = 14.4%, HV0 = 3.1%, NV0 =

0.4%, S0 = 0.2%. Its volatiles content related to dry

ash-free fraction is Vdaf = 48%, and burnout heat release

Q = 15.66 MJ/kg. Then the coefficients in CHnOm were

estimated as: n = 3.037, m = 0.889, and volatiles’ molar

weight = 29.3 g/mol. The rate of the hydrocarbon

gas-phase burning reaction in the turbulent flow has been

determined according to eddy-dissipation model [5]. The

radiation energy transport equation is based on the

known P-1 approximation of the spherical harmonics

method, with this the gas-phase absorption coefficients

are calculated according to the weighted sum of gray

gases model [6], while the dispersed phase absorption

and scattering coefficients are determined on the basis of

the optically large particles approximatio n [7].

Within Lagrangian particle-tracking framework, ODEs

of mass, momentum and heat transfer for representative

clusters of polydispersed coal particles are solved along

each trajectory calculated via random walk model to ac-

count for turbulent dispersion of particles. The rate of

heterogeneous coke combustion reaction has been mod-

eled by diffusion-kinetic relations [7]. To account for

polydispersity, the clusters of fresh coal particles were

split into ~100 fractions according to Rosin-Rammler

size distribution law, with this the co al milling dispersity

(specified as mass fraction of remainder on 90 m sieve)

was taken as R90 = 0.15 and polydispersity degree =

1.2.

To predict the nitric oxides emission in the vortex fur-

nace, at the stage of post-processing of main solution

data, the transport equations for the concentrations of

{NO, HCN, NH3} species have been solved. With this

the following NOx formation mechanisms are taken into

account: a) extended “thermal” N2 oxidation mechanism

of Ya.B.Zeldovich; b) “prompt” NO formation in reac-

tion of N2 with hydrocarbon radicals following C. P. Fe-

nimore mechanism; c) “fuel” NO formation mechanism.

Also the factors of NO reduction are accounted: – via

“reburn-mechanism” in reaction with CHi radicals; – via

heterogeneous consumption of NO on the surface of coke

particles.

3. Boundary Conditions and Numerical

Algorithm

Because the studied vortex furnace has a symmetry plane

SXY (in the section zsymm=3 m) between two nozzles (see

Figure 1), the mirror symmetry of the flow is assumed in

relation to this plane, thus to save computational re-

sources only half of the furnace volume was considered

in simulations. The bounding dimensions of computa-

tional domain were taken as: xmax=D0= 6 m, ymax= 36 m,

zmax= zsymm= 3 m. The upper nozzle angle of inclination to

horizon (XZ plane) was =24°. The unstructured com-

putational grid built for finite-volume discrimination of

equations consists of 351784 hexahedral cells. The

“sticking” boundary conditions are set for velocity com-

ponents at walls, and “enhanced wall treatment” method

[8] is applied for near-wall turbulence modeling. A uni-

form profile of mean flowrate velocity is prescribed at

inlet sections of rectangular nozzles, with this the inten-

sity of inlet turbulen t pulsations is assumed equal to 5%.

The known Marsha bound ary conditions [7] f or the ra-

diation energy transport equation have been set at walls,

with emissivity of the furnace walls taken as w = 0.8 and

the temperature of superheated water-vapor inside the

heat-exchange tubes presumed at 390℃. Also to set

boundary conditions for radioactive and convective heat

transfer at the heat-exchange surfaces, the integral heat

transfer coefficient w through the walls (from ash- de-

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