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Soot modeling in turbulent diffusion flames: review and prospects

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Abstract

This work reviews the state of the art of the main soot modeling approaches used in turbulent diffusion flames. Accordingly, after a short introduction about the subject addressed here, the main soot formation mechanisms are described next. This description provides the basis for the discussions about the different soot modeling techniques employed nowadays for soot predictions. Since combustion and radiation models have a significant impact on soot predictions, as a consequence of the strong coupling between chemistry, turbulence and soot formation, a general overview about these models is also provided. For the sake of clarity, the main soot formation models reviewed in this work are classified as semiempirical soot precursor models and detailed ones. Both advantages and disadvantages of the referred soot modeling approaches are properly discussed. In the last part of this review, comparative results obtained using some of the main soot models currently available are presented along with a discussion about the prospects for soot modeling in turbulent flames. Finally, some conclusions and references are provided. Overall, based on the literature reviewed, it is concluded that there is yet a long path to be followed before understanding first and having then a soot model able to properly describe the formation of this critical pollutant for a variety of situations of industrial interest.

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Abbreviations

\({\dot{Q}}_{{{{\rm s}},i}}\) :

Production rate of soot mass fraction

\({\dot{q}}_{{{{\rm s}},i}}\) :

Soot volume fraction density

\(f_{{{\rm v}}}\) :

Soot volume fraction

\(C_{{{\rm a}}}\) :

Van der Waals enhancement factor

\(C_{i}\) :

Cunningham slip correction factor

\(C_{{{{\rm oxid}}}}\) :

Empirical rate scaling factor for oxidation

\(C_{\rm w,1}\) :

Empirical rate scaling factor for oxidation by OH

\(C_{\rm w,2}\) :

Empirical rate scaling factor for oxidation by O2

\(C_{\alpha }\) :

Empirical rate scaling factor for nucleation

\(C_{\beta }\) :

Empirical rate scaling factor for coagulation

\(C_{\gamma}\) :

Empirical rate scaling factor for surface growth

\(D_{{{\rm f}}}\) :

Fractal characteristic dimension

\(L_{k}\) :

Lagrange logarithmic interpolation function

\(M_{{{\rm C}}}\) :

Molar mass of carbon

\(M_{{{\rm p}}}\) :

Molar mass of an incipient soot particle

\(N_{{{\rm A}}}\) :

Avogadro number

\(N_{{{\rm p}}}\) :

Number of primary particles per aggregate

\(b_{{{{\rm nuc}}}}\) :

Normalized soot radical concentration

\(d_{{{\rm c}}}\) :

Diameter of the fractal aggregates

\(d_{{{\rm p}}}\) :

Particle diameter

\(d_{{{\rm prim}}}\) :

Primary particles diameter

\(k_{{{\rm B}}}\) :

Boltzmann constant

\(\bar{v}\) :

Gas velocity

\(v_{{{{\rm C}}2}}\) :

Carbon-equivalent volume of the carbon atoms number of two soot precursors and two acetylene molecules

\(v_{{{{\rm MAX}}}}\) :

Volume of the largest particle

\(v_{{{{\rm MIN}}}}\) :

Volume of the smallest particle

\(v_{{{\rm T}}}\) :

Thermophoretic velocity

\(w_{i}\) :

Weights

\(x_{i}\) :

Abscissas

\(\eta _{{{{\rm coll}}}}\) :

Collision efficiency

T w,1 :

Activation temperature for soot oxidation by OH

T w,2 :

Activation temperature for soot oxidation by O2

T α :

Activation temperature for soot nucleation

T β :

Activation temperature for soot coagulation

\(X\) :

Mole fraction

λ :

Gas mean free path

σ :

Prandtl number

\(B\) :

Nucleation rate

\(D\) :

Turbulent diffusion coefficient

\(G\) :

Rate of change of particle volume due to surface processes

\(Kn\) :

Knudsen number

\(M\) :

Soot mass concentration

\(N\) :

Soot number density

\(Nx\) :

Number of weights or abscissas

\(P\) :

Pressure

\(R\) :

Universal gas constant

\(T\) :

Temperature

\(Y\) :

Mass fraction

\(d\) :

Particle diameter

\(k\) :

Order of the moment

\(n\) :

Particle number density per unit of particle volume

\(t\) :

Time

\(v\) :

Particle volume

\(\beta\) :

Collision frequency factor

\(\mu\) :

Viscosity

\(\rho\) :

Gas phase density

coag:

Coagulation

cond:

Condensation

i :

Particles of size classes i

j :

Particles of size classes j

nuc:

Nucleation

ox:

Oxidation

s:

Soot

sg:

Surface growth

c:

Continuum regime

f:

Free molecular regime

t:

Transition regime

CQMOM:

Conditional quadrature method of moments

DOM:

Discrete ordinates method

DQMOM:

Direct quadrature method of moments

EQMOM:

Extended quadrature method of moments

FDF:

Filtered density function

FPVA:

Flamelet/progress variable approach

HACA:

Hydrogen-abstraction acetylene addition

HMOM:

Hybrid method of moments

LES:

Large eddy simulation

LHS:

Left-hand-side

MOM:

Method of moments

MOMIC:

Method of moments with interpolative closure

NDF:

Number density function

OAC:

Oligomers of aromatic compounds

OFR:

Ordinary flame radicals

OTA:

Optically thin approximation

PAH:

Polycyclic aromatic hydrocarbons

PBE:

Population balance equation

PCAB:

PAH with aliphatic branches

PCAH:

Peri-condensed aromatic hydrocarbons

PDF:

Probability density function

PGDE:

Particle general dynamic equation

PSDF:

Particle size distribution function

QMOM:

Quadrature method of moments

RANS:

Reynolds-averaged Navier–Stokes

RFPV:

Radiation flamelet progress variable

RHS:

Right-hand-side

RSR:

Resonantly stabilized radicals

RTE:

Radiative transfer equation

SHM:

Spherical harmonics method

SLFM:

Steady laminar flamelet model

TCI:

Turbulence-chemistry interactions

TRI:

Turbulence-radiation interactions

WSGG:

Weighted-sum-of-gray-gases

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Acknowledgements

This work has been supported by CONCYTEC-FONDECYT (Peru), Contract No. 415‐2019‐2019-FONDECYT, “Identification of soot precursors in turbulent combustion processes through numerical modeling to reduce the impact of soot on both health and environment.” During this work Luís Fernando Figueira da Silva was on leave from the Institut Pprime (CNRS—Centre National de la Recherche Scientifique, France). The authors also gratefully acknowledge the support provided by Brazil's Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, CNPq, under the Research Grants No. 306069/2015-6 and 403904/2016-1.

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Valencia, S., Ruiz, S., Manrique, J. et al. Soot modeling in turbulent diffusion flames: review and prospects. J Braz. Soc. Mech. Sci. Eng. 43, 219 (2021). https://doi.org/10.1007/s40430-021-02876-y

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