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%-------------------------------------------------------------------------------
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% This file is part of Code_Saturne, a general-purpose CFD tool.
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% Copyright (C) 1998-2011 EDF S.A.
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% This program is free software; you can redistribute it and/or modify it under
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% the terms of the GNU General Public License as published by the Free Software
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% Foundation; either version 2 of the License, or (at your option) any later
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% This program is distributed in the hope that it will be useful, but WITHOUT
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% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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% FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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% this program; if not, write to the Free Software Foundation, Inc., 51 Franklin
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% Street, Fifth Floor, Boston, MA 02110-1301, USA.
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%-------------------------------------------------------------------------------
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%===============================================
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\programme{ Introduction}
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{\huge sub-routines: co**, cp**, fu** ...}
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%===============================================
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%===============================================
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\section{Use \& call}
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From a CFD point of view combustion is a ({\small sometimes very})
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complicated way to determine $\rho$.\\ Models needs few extra scalar
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fields with regular transport equations, some of them with a
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reactive or interfacial source term.\\ Modelling of combustion is able
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to deal with gas phase combustion ({\small diffusion, premix, partial
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premix}), and with solid or liquid fuels.\\ Combustion of condensed
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fuels involves one-way interfacial flux due to phenomena in the
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condensed phase ({\small evaporation or pyrolisis}) and reciprocal
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ones ({\small heterogeneous combustion}). Many of the species injected
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in the gas phase are afterwards involved in gas phase combsution.\\
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That is the reason why many modules are similar for gas, coal and fuel
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combustion modelling. Obviously, the thermodynamical description of
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gas species is similar in every version as close as possible to the
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JANAF rules.\\ All models are developped in both adiabatic and
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unadiabatic ({\small permeatic: heat loss, eg. by radiation})
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version, beyond the standard, the rule to call models is:
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IPPMOD(index model) = -1 unused
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IPPMOD(index model) = 0 simplest adiabatic version
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IPPMOD(index model) = 1 simplest permeatic version
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IPPMOD(index model) = 2.p P� adiabatic version
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IPPMOD(index model) = 2.p+1 P� permeatic version
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Every permeatic version involves the transport of enthalpy ({\small one more variable}).
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%=================================
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\subsection{Gas combustion modelling}
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%=================================
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Gas combustion is limited by disponibility ({\small in the same fluid
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particle}) of both fuel and oxidant and by kinetic effects ({\small a
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lot of chemical reactions involved can be described using an Arrhenius
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law with high activation energy}). The mixing of mass ({\small atoms})
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incoming with fuel and oxydant is described by a mixture fraction
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({\small mass fraction of matter incoming with fuel}), this variable
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is not affected by combustion. A progress variable is used to describe
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the transformation of the mixture from fuel and oxydant to products
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({\small carbon dioxyde and so on}).Combustion of gas is,
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traditionnaly, splitted in premix and diffusion regimes.\\
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In premix combustion process a first stage of mixing have been
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realised ({\small without blast ...}) and the mixture is introduced in
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the boiler ({\small or combustor can}). In common industrial
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conditions the combustion is mainly limited by the mixing of fresh
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gases ({\small inert}) and burnt ones resulting in the inflammation of
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the first and their conversion to burnt ones; so an assumption of
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chemistry much faster than mixing induces an intermittent regime. The
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gas flow is constituted of totally fresh and totally burnt gases
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({\small the flamme containing the gases during their transformation
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is "extremely" thin}). With this previous assumptions,
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Spalding \cite{1} established the "Eddy Break Up" model, which allows
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a complete description with only one progress variable ({\small
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mixture fraction is homogeneous}).\\
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In diffusion flames the fuel and the oxydant are introduced by two
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({\small at least}) inlets, in common industrial conditions, their
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mixing is the main limitation and the mixture fraction is enough to
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qualify a fluid particle, but in turbulent flows a {\em P}robability
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{\em D}ensity {\em F}unction of the mixture fraction is needed to
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qualify the thermodynamical state of the bulk. So both the mean and
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the variance of the mixture fraction are needed ({\small two
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Real world's chemistry is not so fast and, unfortunately, the mixing
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can not be so homogeneous as wished. Then industrial combustion occurs
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in partial premix regime. Partial premix occurs if mixing is not
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finished ({\small at molecular level}) when the mixture is introduced,
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or if air or fuel, are staggered, or if a diffusion flame is blown
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off. For these situations, and specifically for lean premix gas
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turbines Libby \& Williams \cite{2} developped a model allowing a
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description of both mixing and chemical limitations. A collaboration
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between the LCD Poitiers \cite{3} and EDF R\&D allows a simpler
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version of their algorithm. Not only the mean and the variance of both
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mixture fraction and progress variable are needed but also their
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covariance ({\small five variables}).
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%=================================
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\subsection{Coal combustion modelling}
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%=================================
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Coal combustion is the main way to produce electricity in the world.
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Coal is a natural product with a very complex composition. During the
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industrial process of milling the raw coal is broken in tiny particles
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of different sizes. After its introduction in the boiler, coal
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particles undergoes drying, devolatilisation ({\small heating of coal
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turn it in a mixture of char and gases}), heterogenous combustion
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({\small of char in carbon monoxide}) leaving ash particles.\\ Each of
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these phenomena are taken into account for some class of particles: a
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class is caracterised by a coal ({\small it is useful to burn mixture
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of coals with differents ranks or mixture of coal with biomasse ...})
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and an initial diameter. For each class, \CS computes the number and
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the mass of particles by unit mass of mixture.\\ The main assumption
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is to solve only one velocity ({\small and pressure}) field: it means
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the discrepancy of velocity between coal particles and gases is
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assumed negligible.\\ Due to the radiation and heterogeneous
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combustion, temperature can be different for gas and different size
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particles: so the specific enthalpy of each particle class is
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solved.\\ The description of coal pyrolysis proposed by Kobayashi \&
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Ubhayakar \cite{4} is used, leading to two source terms for light and
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heavy volatile matters ({\small the moderate temperature reaction
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produces gases with low molecular mass, the high temperature reaction
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produces heavier gases and less char}) represented by two passive
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scalars: mixture fractions. The description of the heterogeneous
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reaction ({\small which produce carbon monoxide}) produces a source
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term for the carbon: a mixture fraction who can't be greater than the
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results of stoechiometric oxidation of char by air ({\small carbon
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can't be free in gas phase, it is always linked in an oxide}).\\ The
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retained model for the gas phase combustion is the assumption of
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diffusion flammelets surrounding each particle, so the previous
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gaseous fuels are mixed in a local mean fuel and the mixing with air
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is represented by a pdf between air and the mean local fuel
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constructed with the variance of a passive scalar linked with air
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({\small interfacial mass flux produce a source term for this
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%===============================================
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From a CFD point of view, combustion is a (sometimes very) complicated way to
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determine $\rho$, the density.\\
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Depending on the presence of a match or not, two solutions exist, known as
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ignited and extinguished. From a numerical point of view, it means that these
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two solutions have two attraction basin; the more representative the model, the
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more difficult the stabilisation of the combustion ( may be difficult to
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However, combustion models needs few extra fields of scalar with regular
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transport equations, some of them with a reactive or interfacial source term. \\
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This 2011 version of \CS focuses on stationnary industrial combustion processes
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propagating fires are out of the present range (but in the short coming release). \\
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In \CS~ modelling of combustion is able to deal with gas phase combustion
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(diffusion, premix, partial premix), and with solid or liquid finely dispersed
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fuels (fixed and fluidised beds are out of range).\\
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Combustion of condensed fuels involves one-way interfacial flux due to phenomena
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in the condensed phase (evaporation or pyrolisis) and reciprocal ones
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(heterogeneous combustion and gasification). Many of the species injected in the
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gas phase are afterwards involved in
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gas phase combustion.\\
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That is the reason why many modules are similar for gas, coal and fuel oil
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combustion modelling. Obviously, the thermodynamical description of gas
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species is similar in every version as close as possible to the JANAF rules.\\
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All models are developped in both adiabatic and unadiabatic (permeatic : heat
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loss, e.g. by radiation) version, beyond the standard (\fort{-1, 0, 1}), the
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rule to call models in \fort{usppmo} is:
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\fort{ippmod(index ; model)} &=& -1 ~~\quad \text{unused} \nonumber \\
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\fort{ippmod(index ; model)} &=& ~~ 0 ~~~\quad \text{simplest adiabatic version} \nonumber \\
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\fort{ippmod(index ; model)} &=& ~~ 1 ~~~\quad \text{simplest permeatic version} \label{Eqs_00A}\\
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\text{and possibly:}\qquad\qquad\qquad\qquad\qquad\qquad\qquad \nonumber & &\\
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\fort{ippmod(index ; model)} &=& 2.p \qquad \text{p} ~\text{adiabatic version} \nonumber \\
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\fort{ippmod(index ; model)} &=& 2.p+1 ~ \text{p} ~\text{permeatic version} \nonumber
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Every permeatic version involves the transport of enthalpy (one more variable).
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%===============================================
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\section{Gas combustion modelling}
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%===============================================
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Gas combustion is limited by disponibility (in the same fluid particle) of both
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fuel and oxidizer and by kinetic effects (a lot of chemical reactions involved
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can be described using an Arrhenius law with high activation energy). The mixing
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of mass (atoms) incoming with fuel and oxydizer is described by a mixture
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fraction (mass fraction of matter incoming with fuel), this
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variable is not affected by combustion.\\
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A progress variable is used to describe the transformation of the mixture from
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fuel and oxydant to products (carbon dioxyde and so on).
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Combustion of gas is, traditionnaly, splitted in premix and diffusion regimes.\\
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In premixed combustion process a first stage of mixing has been realised
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(without blast ...) and the mixture is introduced in the boiler (or combustor
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can). In common industrial conditions the combustion is mainly limited by the
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mixing of fresh gases (frozen) and burnt gases (exhausted) resulting in the
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inflammation of the first and their conversion to burnt ones ; so an assumption
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of chemistry much faster than mixing (characteristic time for chemistry much
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smaller than characteristic time for turbulent mixing) induces an intermittent
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regime. The gas flow is constituted of totally fresh and totally burnt gases
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(the flamme containing the gases during their transformation is extremely
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thin). With this previous assumptions, Spalding \cite{1} established the "Eddy
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Break Up" model, which allows a complete description of the combustion process
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with only one progress variable (mixture fraction is both constant
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- in time - and homogeneous - in space).\\
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In diffusion flames the fuel and the oxydant are introduced by, at least, two
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inlets. In ordinary industrial conditions, their mixing is the main limitation
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and the mixture fraction is enough to qualify a fluid particle, but in turbulent
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flows a {\em P}robability {\em D}ensity {\em F}unction of the mixture fraction
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is needed to qualify the thermodynamical state of the bulk. So, at least, both
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the mean and the variance of the mixture fraction are needed (two variables) to
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fit parameters of the pdf (the shape of whose is presumed).\\
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Real world's chemistry is not so fast and, unfortunately, the mixing can not be
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as homogeneous as wished. The main part of industrial combustion occurs in
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partial premix regime. Partial premix occurs if mixing is not finished ( at
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molecular level) when the mixture is introduced, or if air or fuel, are
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staggered, or if a diffusion flame is blown off. For these situations, and
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specifically for lean premix gas turbines \cite{2} developped a model allowing a
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description of both mixing and chemical limitations. A collaboration between the
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LCD Poitiers \cite{3} and EDF R\&D has produced a simpler version of their
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algorithm. Not only the mean and the variance of both mixture fraction and
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progress variable are needed but also their covariance (five variables).
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%=================================
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\subsection{Heavy Fuel Oil combustion modelling}
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%=================================
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Heavy fuel oil combustion have been hugely used to produced electrical
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energy. Environmental regulation turning it more difficult and less
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acceptable, a focus is needed on pollutant emission mainly sulphur
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oxide and particles ({\small condensation of sulphuric acid can
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aggregate soot}).\\ The description of fuel evaporation is done with
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respect to its heaviness: after a minimum temperature is reached, the
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gain of enthalpy is splitted between heating and evaporation. This way
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the evaporation takes place on a range of temperature ({\small which
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can be large}). The "total" evaporation is common for light ({\small
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domestic}) oil but impossible for heavy ones: at high temperature,
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during the last evaporation, a crakink reaction appears: so a
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particle similar to char leaves. The heterogeneous oxydation of this
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char particle is very similar to coal char ones.\\ Fuel injection is
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described ({\small 2006 version}) with only one class of particles
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({\small i.e. initial diameter}), the number, mass and specific
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enthalpy of particles are calculated eveywhere. So three variables are
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used to describe the condensed phase. In the same way as for coal,
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only one velocity field is computed.\\ The model for gas combustion is
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very similar to coal one but a special attention is paid to sulphur
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({\small assumed to leave the particle as H2S during evaporation and
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to be converted to SO2 during gas combustion}).
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%==================================
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%==================================
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%===============================================
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\section{Two-phase combustion modelling}
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%===============================================
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Coal combustion is the main way to produce electricity in the world. Heavy fuel
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oil combustion have been hugely used to produce electrical energy.
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Biomass is a promising fuel to be used alone or in blend.\\
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Advanced combustion process may include exhaust gases recycling, pure oxygen or
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steam injection, so the 2011 release of \CS ~takes in account
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three oxidizers (tracked by three mixture fractions).\\
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Coal is a natural product with a very complex composition. During the industrial
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process of milling, the raw coal is broken in tiny particles of different
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sizes. After its introduction in the boiler, coal particles undergoes drying,
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devolatilisation (heating of coal turn it in a mixture of char and gases),
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heterogenous combustion (of char by oxygen in carbon monoxide), gasification (of
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dioxide or by water steam in carbon monoxide), leaving ash particles.\\
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The description of fuel evaporation is done with respect to its heaviness :
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after a minimum temperature is reached, the gain of enthalpy is splitted between
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heating and evaporation. This way the evaporation takes place on a range of
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temperature (which can be large). The total evaporation is common for light
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(domestic) oil but impossible for heavy ones : at high temperature, during the
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last evaporation, a craking reaction appears : so a particle similar to the char
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is leaved. The heterogeneous oxydation of this char particle is very similar to
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Each of these phenomena are taken into account for some classes of particles : a
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solid class is caracterised by a coal (it is useful to burn mixture of coals
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with differents ranks or mixture of coal with biomass ...) and an initial
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diameter, for heavy fuel oil, liquid classes refer to initial diameter (neither
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possibility of blending after injection nor cofiring with oil and coal). \CS~
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computes the number, the mass and the enthalpy for each class of particles by
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unit of mass of mixture; allowing the determination of local diameter and
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temperature (for each class;
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e.g. the finest will be be heated the fastest).\\
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The main assumption is to solve only one velocity (and pressure) field : it
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means that the discrepancy of velocity between coal particles and
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gases is assumed to be negligible.\\
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Due to the radiation, evaporation and heterogeneous combustion, temperature can
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be different for gas and different size particles : so the specific enthalpy of
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each particle class is solved.\\
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The description of coal pyrolysis proposed by \cite{4} is used, leading to two
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source terms for light and heavy volatile matters (the moderate temperature
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reaction produces gases with low molecular mass, the high temperature reaction
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produces heavier gases and less char) represented by two passive scalars :
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mixture fractions. The description of the heterogeneous reaction (which produce
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carbon monoxide) produces a source term for the carbon : the corresponding
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mixture fraction is bounded far below one (the carbon can't be free, it is
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always in carbon monoxide form, mixed with nitrogen or other).\\
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The retained model for the gas phase combustion is the assumption of diffusion
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flammelets surrounding particle (for a single paticvle or a cloud), this
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diffusion flame establish itself between a mixing of the previous gaseous fuels
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issued from fast phenomenon (pyrolysis or fuel evaporation) mixed in a local
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mean fuel and the mixing of oxidizers, water vapor (issued from drying) and
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carbon monoxide issued from slow phenomenon (heterogeneous oxydation and
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gasification of char). The PDF diffusion approcah is used to describe the
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conversion of hydrocarbon to carbon monoxide (hydrocarbon conversion is assumed
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fast vs. mixing); the further conversion of carbon monoxide to carbon dioxyde
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was (in previous release, still existing for fast first evaluation of carbon
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dioxide usefull to initialize the kinetic model) ruled by mixing or is (now
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recommended for better prediction of carbon monoxide at outlet and corrosion
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risks) kineticaly ruled with respect to the mean mass fraction and temperature
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(reach of equilibrium assumed slow vs. mixing). Special attention is paid to
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pollutant formation (conversion of $H_{2}S$ to $SO_{2}$ involved in soot
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agglomeration, NOx formation).
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%================================================
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\section{Bibliography}
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%==================================
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%==================================
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%================================================
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\begin{thebibliography}{4}
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\bibitem{1}%Spalding_1971a
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{\sc Spalding, D.B., {\em et al.}},\\
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{\em Mixing and chemical reaction in steady confined turbulent turbulent flames},\\
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13th Int.Symp. on Combustion , pp. 649-657, (1971).
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\bibitem{2}%Libby_2000a
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{\sc Libby, P.A. and Williams, F.A.},\\
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{\em A presumed PDF analysis of lean partially premixed turbulent combustion},\\
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Combust. Sci. Technol., 161, pp. 351-390, (2000)
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\bibitem{3}%Ribert_2004a
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{\sc Ribert, G.; Champion, M. and Plion, P.},\\
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{\em Modeling turbulent reactive flows with variable equivalence ratio: application to the calculation of a reactive shear layer},\\
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Combust. Sci. Technol., 176, pp. 907-923, (2004)
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\bibitem{4}%Kobayashi_1976
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{\sc Kobayashi, H. {\em et al.}},\\
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16th Int.Symp. on Combustion , pp. 425-441, (1976).
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\end{thebibliography}
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\section{Discr\'etisation}
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On se reportera aux sections relatives aux sous-programmes
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\fort{cfmsvl} (masse volumique), \fort{cfqdmv}
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(quantit\'e de mouvement) et \fort{cfener} (\'energie).
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La documentation du sous-programme
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\fort{cfxtcl} fournit des \'el\'ements relatifs aux
added
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doc/theory/combbase.tex
