Brief Summery

8/12/2019 Brief Summery

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the flame surface and tear it into dispersed small pieces. The surface of each piece

has a thin layer of closed laminar combustion zone.

2. Control-volume model

high turbulence intensity, the combustion reactions are not concentrated in the thin

combustion zone, but penetrated into the deeper zone. The thickness of the flame zone is

about several ten times of the laminar flame surface.This model is usedto estimate the

spreading rate of turbulent flame.

2.1.3 the concept of self-turbulence flow

It is used In order to explain the difference between the experimental value and the

calculated value of spreading rate of turbulent flame S T. the flame itself has fluctuations,

giving turbulent flow that affects the combustion process and increases the value of S T. It has

not yet been investigated thoroughly.

2.1.4 laminar premixed flame

Fresh gases and products are separated by a thin reaction zone. A strong temperature gradiant

is observed (T fresh gases/ T burnt gases = 5 to 7). Because of ability of premixed flame to

propagate towards the fresh gases, fresh gases are preheated and then start to burn.

It is applicable for one-step irreversible simple chemical reactions. Used for a fuel rich,

without heat losses and compressibility effects. Therefor, mass and energy balance equations

reduce to a single balance equation for the progress variable and by introducing the

displacement speed of the iso-c surface. Molecular diffusion normal to iso-c surface and

reaction rate may be modeled with the laminar flame speed.

2.1.5 finite rate chemistry model

finite rate chemical reaction model involves tens of components which undergo several

hundreds of intermediate basic reactions. the combustion process also includes heat transfer,

radiation, convection and diffusion of the chemical components, and also anisotropy due to

buoyancy.

Since the chemical reaction rate is very fast, the time-scale is much smaller than that of the

fluid transport. . The finite rate combustion model has a stiffness problem on the time scale.

Since the chemical reaction rate is generally very fast, the time interval must be very short in

using the explicit difference method. A much longer spatial increment can be used for the

flow process. The explicit method cannot be adopted generally. The implicit approach has to

be used. But this would make the diffusion of fuel difficult, and in turn greatly delay the

combustion process.


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2.2 Diffusion (non-premixed) combustion

The rate of mixing that controls the combustion rate.

2.2.1 Laminar diffusion flames

Chemical reactions take place in proper ratio of fuel and oxygen on the surface of the flame.

The flows of fuel and oxygen are one-dimensional flows with uniform and same velocity.

Mole and pressure are not changed throughout the whole process. The diffusion of fuel and

oxygen in inert gases is regarded as the diffusion of two components, their diffusion

coefficients are equal.

The product density and diffusion coefficient of mixed gases is not related to temperature and

is constant in radial direction. steady-state diffusion combustion process is considered.

Reaction is faster than mixing process.

2.2.2 Fundamental Aspects of Laminar Diffusion Flames with Fast Chemistry (One-

Step Reaction)

Reaction time is much shorter than the mixing time.

If the reaction is reversible, there will be both fuel and oxidizer at stoichiometric numbers

close to the mixture fraction. Under the assumption of fast reaction, both the forward and

backward reactions are faster than the mixing process, so that the mixed chemical

components can attain dynamic equilibrium.

Favre Probability Density Function (PDF) is often used to integrate the spatial distribution of

mixture fraction f. This spatial distribution also includes the effect of turbulent fluctuations.

2.2.3 Simple chemical reacting system (SCRS) and mixture fraction

Fuel and oxidizer will undergo a series of reactions to give combustion products. For

example, the combustion of the simplest hydrocarbon methane CH 4involves more than 40

basic dynamic reactions.

The production and dissipation rate of the component in component transport equation andradiation loss or increase, pressure work and chemical energy in enthalpy equation should be

considered and energy consumption due to viscosity can be neglected. Temperature can be

calculated by calorific value.

A simple chemically reacting system (SCRS) is adopted where the reaction rates are very fast

compared with the mixing rates.Char oxidizes to CO at the particle surface; CO oxidizes to

CO2in the bulk gas.

2.3 premixed turbulent combustion

2.3.1 eddy break-up (EBU) model and time-averaged reaction rate of turbulent flow


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EBU model is the earliest model used in turbulent premixed combustion, then for non-

premixed flames .It is based directly on a physical assumption on the turbulent reaction rate.

As the reaction rate in laminar flow depends on the horizontal mixing, whereas the reaction

rate in turbulent flow depends on the mixing of the turbulent eddies.

The reaction rate is dependent to temperature and is calculated with Arrhenius equation for

both laminar and turbulent state When the reaction consists of two components, fuel F and

oxidizer O, and the reaction is assumed as a second-order reaction.

The relationship between concentration and temperature pulsations, and the temperature

pulsations itself have enhanced and increased the time-averaged reaction rate.

Not only folding occurred, the surface was also broken into pieces of different sizes to

expand the flame surface. Therefore, more combustible mixed gases were burnt per unit time.

Although EBU model has already been widely applied, its chemical reaction dynamic processis still not very satisfactory. For example, some problems concerning the CO species cannot

be represented by fast chemistry.

2.3.2 Eddy dissipation model

the concept of EBU was extended to eddy dissipation model (EDM).

The eddy dissipation model is best applied to turbulent flows when the chemical reaction rate

is fast relative to the transport processes in the flow. There is no kinetic control of the

reaction process. Thus, ignition and processes where chemical kinetics may limit reaction rate

may be poorly predicted.

In the EBU model proposed by Spalding, the reaction rate (as equation (3-4)) is only related

to the turbulent dissipation rate of the premixed gas. Whereas in the EDM model, the

reaction rate is related to the minimum value of turbulent dissipation rate of the

premixed gas, oxidizer and combustion products with higher temperature.

2.3.3. Expansion of the EBU model

It is assumed in the expanded EBU model that, in premixed reaction flow where both

Arrhenius reaction dynamic mechanism and turbulent mixing mechanism have an effect.

Because of lack of understanding of the reaction mechanism, when reaction time is larger

than turbulent mixing time, average reaction rate is directly related to average Arrhenius rate,

and when the turbulent mixing time is larger than reaction time, average reaction rate is

directly related to turbulent rate.

2.3.4. simplified PDF model of fast reaction flow

The reaction rate is much faster than turbulent mixing. The reaction flow is controlled by thecomparatively slower diffusion process.


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The basic assumption in diffusion combustion is that fuel and oxygen would not exist at the

same time or in the same space. Considering equations in oxygen side which contains oxygen

and combustion products with no fuel and equations in region near to the fuel which there is

no oxygen,, and the assumption that fuel and oxygen composition on the flame surface are

equal to zero model would be drived.

2.3.5 Flame surface model

The model is only applicable for two-feed system( fuel and oxidizer). Average temperature

and composition of fuel and oxidizer can be calculated via instantaneous equations for each

species and time-averaged equation for f. results show on the flame surface

isolines. However, the results obtained are still too simplified and not very

satisfactory. The reason is that an infinitely thin flame surface with zero concentration of fuel

and oxygen does not exist in real turbulent diffusion flames. But on the flame surface with a

finite thickness, the time-averaged values of fuel and oxygen concentration coexist in the

same space.

2.3.6 Model of Partial Instantaneous Non-Mixing

The model describes the internal state of turbulent eddies. Rather than all above model

equations and time-averaged equation for f, In addition, mean square equation of the

mixture fraction pulsations has to be solved.

There is a special problem about finding time averaged composition of species.

results indicated that the equation sets combined with the simplified PDF agreed

better with the experimental data, when compared with the flame surface model.

The cut-off Gauss distribution PDF model is slightly better than step functions pulsations

PDF model, and the differences are very little.

The diffusion flame mechanism of this model is similar to the dynamic equilibrium model.

However, there are limitations in applying this kind of partial dynamic equilibrium model.

The reaction might be too fast in practice to get a partial dynamic equilibrium.

2.3.7 Simplified PDF Assumptions of Finite Reaction Rate

For more general situations, instantaneous laminar reaction is assumed within the turbulent

eddies. Reaction rate is finitely fast and not under partial dynamic equilibrium state.

Time averaged equations for species, mixture fraction, mean square mixture fraction and

reaction rate are considered. Assuming both mixture fraction and mean square mixture

fraction are the function of spatial location.


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Solving steps are:

1. Solve for the continuity equation, momentum equation and the equations for the

turbulent time-averaged flow to get the preliminary spatial distribution of and g;

2. Calculate from the values of and g, and the given values of and

3. Put w sinto the conservation equation (3-37) of species s to solve for Y s;

4. Solve the conservation equation of enthalpy h;

5. Calculate T from h and Y s;

6. Solve again by including the effect of the estimated T on density variation, on the

momentum equation and the equations;

7. Repeat the above steps until convergence.

2.3.8. Simplified PDF Model of Premixed Reaction Flow (Reaction Flow

Controlled by Both Diffusion and Chemical Reaction)

the reaction flow is controlled by both diffusion and chemical reaction.

The simplified PDF model was developed for studying premixed reaction flow. Assuming

that the reaction is a one-step second-order reaction.

1. By assuming that inside each turbulent eddy is an instantaneous adiabatic laminarflamelet and PDF function of density, instantaneous temperature and compositions equal to a

function of reaction level leads to the calculation of time-averaged reaction rate.

2. Relationship between the time-averaged reaction level and other time-averagedquantities From the energy equation and conservation equation of either instantaneous

component Y For Y o, the equation of the instantaneous reaction level can be obtained.

3. In solving the equations, apart from solving the continuity equation, momentumequation, and the k and equations, equations have to be solved jointly. To solve for these

five equations, the method of trial and error has to be used.

Statistical fluid dynamics and probability concept are applied to derive turbulent combustion.

The calculations involved are too complicated, for engineering application.

2.3.9. Brief Introduction of Laminar Flamelet Model

Laminar flamelet combustion model is different from SCRS in the way that it does not

require a linear relationship between the mixture fraction, mass fraction and temperature.

More complicated experimental correlation relationships between these variables are


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considered. From the laminar flamelet relation, the species mass fraction can be derived.

The mixture fraction of the transport equation can be solved.

the concentration, temperature, soot concentration, viscosity, enthalpy and pressure of all

species are all functions of the mixture fraction in the flamelet. A simple variation diagram

of combustion products, oxygen and fuel concentration can be derived as functions of the

mixture fraction.

In the laminar flamelet model, it is assumed that chemical reactions only take place within

the basic element in the laminar flame, that is, exists near the fire source

If turbulent flame is believed to be composed of many tiny parts, then the concept of

laminar flamelet can be applied to turbulent flames such as fires. Each tiny part is composed

of undisturbed laminar diffusion flames.

The chemical reaction time is shorter than other turbulent and transport processes.

As an example of using this model, starting from the oxygen side, the mixture fraction is

zero. While moving towards the center of the flamelet with increasing temperature, a certain

quantity of combustion products including the components is taken from the fuel to

determine the concentration of carbon and hydrogen atoms, or other related molecules such

as O, CO 2and free radicals H and HO 2at that point.

2.4 Partially premixed combustion2.4.1. Thickened Flame Models

Thickened flame models for LES solve transport equations for chemical species, and use

Arrhenius rate expressions to describe species reactions.resolving realistic flame structures

is not affordable in LES, thickened flame models artificially broaden flame structures to

ensure convergence of the species equations.

The artificial flame broadening is accomplished by multiplying the diffusive terms in the

scalar transport equations by a thickening factor, F, that may be as large as ten or twenty.

This model has two perspectives:

1. One perspective, for example, would be that the approach is regime independent. Thisperspective would stem from the idea that no information about flame asymptotics is required

in the implementation. It would suggest that the approach is very general, and it has indeed

been applied in a variety of simulations where partially premixed combustion would be

expected.

2. A second perspective, however, would be that this approach changes the nature ofturbulence and chemistry interactions by reducing the time scale for transport and increasing

the time scale for chemistry.

This second perspective, then, emphasizes the idea that small-scale transport and chemistry

processes are critically important, and that altering the associated time scales leads tosignificant errors in predictions.


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2.4.2. Linear Eddy Models (LEM)

Linear Eddy Models (LEMs) attempt to explicitly solve for a reduced representation of

subfilter turbulence/chemistry interaction.Arrhenius rates are used to describe the subfilter chemical source terms, and once the 1-D

solutions have been solved.

Just as with thickened flame models, one of the particular advantages of LEM models is that

they do not require a priori assumptions about the burning regime. Unlike thickened flame

models, however, the 1-D subfilter meshes are capable of resolving and accounting for how

transport and chemistry balance on the smallest scales. The LEM model therefore has the

advantage of representing the multi-scale nature of combustion processes.

In spite of its ability to capture the coupling between diffusion and reaction on the small

scales, quantities such as the stirring frequency in the model are empirically determined.

because chemistry is locally and explicitly solved for, LEM models for combustion can be

relatively costly.

While this empiricism has resulted in good agreement with experimental predictions in

realistic combustor settings, its performance has not yet been fully characterized.

2.4.3. Conditional Moment Closure Models

Conditional Moment Closure (CMC) approaches attempt to describe chemistry by solving for

values of chemical species that have been conditioned on a particularly relevant scalar.

An approach that is closely related to CMC is Conditional Source term Estimation (CSE). In

this approach, independent variables are not added to the problems dimensionality or to the

computational mesh. This approach requires solving transport equations for several

reactive quantities, so that there are an adequate

number of mean or filtered scalar values to accomplish the inversion at a given mesh

point.

If CSE were to be employed for partially premixed modeling, the nature of the inversioncould grow considerably more complex due to the conditioning on progress variable as well

as mixture fraction. Furthermore, separate premixed and non-premixed solutions might need

to be used to deal with the ill conditioning along the separate directions.

Another consideration of importance in a CSE method for partially premixed combustion

LES is the issue of flame structure resolution. Reactive scalar equations need to be

transported in these methods, but numerical errors are likely to contaminate these solutions if

they are solved using traditional transport schemes.


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2.4.4. Transported FDF Models

Transported FDF models for LES (and PDF models for RANS) attempt to describe

chemical reactions by explicitly solving for subfilter distribution functions. FDF approaches

use a transport equation for the filtered density function (FDF) as a starting point.

If a very accurate mixing model were in place, transported FDF approaches would be able to

fully characterize partially premixed combustion, regardless of whether or not the typical

mixture fraction and progress variable coordinates are aligned in any way. Indeed, the

approach would then be fully closed and would not be subject to any a priori assumptions

about the regime.

Although the transported FDF approach is therefore very promising and powerful, the

difficulties associated with describing mixing temper its current applicability.

It may be possible to argue that the advantages of fully closed chemical source terms anddetailed chemistry outweigh the inaccuracies of the mixing model in partially premixed

flows. Conversely, errors in the description of mixing in a flow may overwhelm any

advantages gained by the access to many chemistry realizations.

2.4.5. Flamelet Models

These models attempt to describe the subfilter evolution of chemistry by mapping

combinations of 1-D pre-computed asymptotic flame solutions into a 3-D flow field.

Three advantages of the flamelet model have led to its relatively widespread consideration

and study. These advantages include the methods minimal computational cost, the methods

ability to consider arbitrarily detailed chemistry in

the flamelet space, and the methods multi-scale nature that is based on the correct prediction

of the balance that exists between chemistry and transport on the smallest scales.

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