basic concepts in multi phase and combustion modelling

8/2/2019 Basic Concepts in Multi Phase and Combustion Modelling

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Basic concepts in Multiphase and combustion Modelling

Multiphase Flow Modelling

Multiphase flow refers to a situation where more than one fluid is present and the fluids are

immiscible. A multiphase flow system consists of multiple phases occupying the same region of

space. Complex interactions arise due to the proximity of multiple phases. The fluids compete for

the same volume in space. The difference in fluid properties between the phases results in mass,

momentum and energy exchange between the phases. Models that describe these interactions are

complex and sophisticated

Multiphase flows can be broadly classified into

continuous-dispersed flows continuous-continuous flows.

Continuous-dispersed flows: are those where the primary phase is continuous, the secondary

phase is discontinuous and dispersed within theprimary phase. The dispersed phase occupies

disconnected regions of space and is present in the form of drops, bubbles or particles. Flow of

slurries, Ex:bubbles and particulate flows

Fig; Continuous-dispersed flows

Continuous-continuous flows : are those where all fluids are continuous. Flows involving a free

surface between fluids is an example of such a situation.

Fig: Continuous-continuous flows


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Computational models

Choosing a multiphase model

To select the most appropriate multiphase model, the physics of the system must be analysed and

understood. The model is selected based on following criteria Are the phases are continous(separated) or dispersed?

Will the particles follow the continuous phase? What is the Stokes number?

How large are the local volume fractions?

How many particles are there in the system?

What kind of coupling occurs? Is it one-, two- or four-way coupling?

Based on above criteria, The different kinds of model available for multiphase ow are

1. The EulerLagrange model : For dispersed multiphase systems

2. The EulerEuler model: general models for dispersed multiphase ow

3. The mixture or algebraic-slip model: General models for dispersed multiphase ow

4. The volume-of-uid (VOF) model : For separated ows

5. The porous-bed models: applicable to a system dominated by viscous and inertial forces

The EulerLagrange model:

This model is applicable to continuous-dispersed systems and is very often referred to as a discrete

particle model or particle transport model.

The primary phase is continuous, which may be a gas or a liquid. The secondary phase is discrete

and may be composed of particles, drops or bubbles.

In this technique the particles are tracked individually, and the gas phase is treated in a continuous

framework

The continuous phase flow field is computed by solving the Navier-Stokes equations. Flow

trajectories, heat and mass transfer from and to the discrete phase are computed by solving discrete

equations for the dispersed phase. The dispersed phase is represented by tracking a small number

of representative particle streams. For each particle stream ordinary differentialequations representing mass, momentum and energy transfer are solved to compute its state and

location. The two phases are coupled by including appropriate interaction terms in the continuous

phase equations.


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Fig: Lagrange point particle approach

In point-particle-approach simulations, the single-phase NavierStokes equations for the

continuous phase are solved in conjunction with tracking the individual particles. For successful

employment of the EulerLagrange model, the particles have to be much smaller than the uid-

phase grid cells(control volume). This restriction arises because the velocity eld, required to

calculate the source term needs to be the undisturbed velocity eld.

The single-phase NavierStokes equations for the continous phase is given by

Where Sc = is a source term describing mass transfer between the phases

Si,p = momentum exchange between the particles and the uid.

U= velocity eld

= volume fraction

The ow of the continuous uid equations can be solved with traditional RANS or LES models

with the additional terms describing the interaction between the continuous and dispersed phases.

The number of particles is limited because it involves solving an ODE for all particles.

However, it is possible to bundle particles that behave identically into packages containing

thousands of particles. This will give a correct source term for the continuous phase.The limitation

is that the bundle will be modelled assuming that the properties at the centre of gravity for the

bundle are valid for all particles and that the source term for the bundle is at the centre of gravity.


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EulerLagrange models are usually accurate at low volume fraction with one or two way

coupling. At higher volume fraction, when the particles collide the model requires additional

closures . The simulations become very demanding at high particle loading due to the high number

of collisions. It is not possible to calculate all potential collisions beween all particles, and most

CFD programs simulate collisions only for particles that are within the same computational

cell.More advanced algorithms may also include neighbouring cells. In all cases, the number of

particles must be low and the time step must be limited so that no particle moves by more than one

computational cell in one time step.

In addition it is not possible to model how the particles will collide. Even if the momentum is

conserved and the absolute value of the velocity is known, the direction is unknown. There are

stochastic models that calculate a probability distribution of velocities of a large number of

collisions after each time step. However, the use of EulerLagrange models with four-waycoupling is not yet a feasible approach in engineering.

Turbulence modeling

The continuous phase may be modelled using standard RANS or LES methods. In the k model a

source term for the additional turbulence energy arising from the movement of the particles may be

included.

EulerEuler modelsThe Euler-Euler model is applicable for continuous-dispersed as well as continuous-continuous

systems. For continuous-dispersed systems the velocity of each phase is computed using the

Navier-Stokes equations. The dispersed phase may be in the form of particles, drops or bubbles.

It is referred to as the two uid model. The two uid model is derived by ensemble averaging or

volume averaging. A very important quantity appearing in the equation because of the averaging is

the volume fraction k..

The forces acting on the dispersed phase are modeled using empirical correlations and included

as part of the interphase transfer terms. Drag, lift, gravity, buoyancy, virtual mass effects are some

of the forces that may be acting on the dispersed phase.

The volume fraction is dened on the basis of the distribution of phases and the size of the

computational volume. The local instantaneous equations describing both phases may then be

averaged in the volume, considering the bulk density of each of the phases .


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Turbulence modelling

Standard k and RSM models can be used with the EulerEuler multiphase model for dilute

systems and when the phases can be approximated with one set of momentum models for the

mixture

For the continuous phase in a dilute system k is modelled with the standard k equation with an

additional source term describing the additional turbulence energy arising from the relative

velocities of the continuous phase and the dispersed phases.

For the dispersed phases the timescales and length scales for the particles are used to evaluate

dispersion coefficients and the turbulent kinetic energy for each phase.

For dense systems, when a turbulence model is required for each phase, the commercial CFD

software usually includes only the k model. These models tend to be very unstable, and the

quality of the simulations is usually low. The simulations often need calibration and should becombined with validation experiments in similar systems.

The mixture model

The mixture model is similar to the EulerEuler model, but assumes one more simplication. This

simplication is that the coupling between the phases is very strong and the relative velocity

between the phases is in local equilibrium, i.e. they should accelerate together. In performing a

simulation with the mixture model, one set of equations is solved for the mixture, i.e. theunknowns are the ow properties of the mixture, not those of the individual phases. The ow

properties of the individual phases can be reconstructed with an algebraic model for the relative

velocity, which is often referred to as the algebraic-slip model.

Turbulence modelling

Standard RANS and LES models can be used for turbulence modelling using the average

properties for density and viscosity.

Volume-of-uid methods

Volume-of-uid (VOF) methods use the value of the volume fraction on a grid-cell basis to

describe the position of the interface. The advective part of the equation is solved by special


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advection schemes, such as Lagrangian schemes, geometrical schemes and compressive schemes.

These schemes can deal much better with cross-ow situations, and tend to be more mass-

conserving than their level-set counterparts.

Turbulence modellingk model ,Large-eddy simulation works better with VOF since the momentum transport across

the interface on the sub grid level is much less.

Case Study of Multi phase flow :

Fuel Drop Injection: Drop and bubble formation are studied to establish injection characteristics

and understand sparger behavior in a combustion chamber . An Euler Euler homogenous flow

model is applied to study drop formation from a nozzle. The inertial forces associated with such

flow fields are small and surface tension effects dominate. Shape, size and frequency of drop

formation are examined.

Liquid is injected through an injection tube, the injected fluid initially collects at the nozzle tip as

depicted in Figure

.


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As the fluid bubble grows in size the gravitational force becomes large and necking of fluid takes

place as depicted in Figure

At this stage, the fluid column is no longer able to hold the ejected fluid in place and it breaks from

the nozzle forming a drop as depicted in Figure

Combustion Modelling:

Combustion is defined as an exothermic reaction of a fuel and an oxidant. In gas turbine

applications, the fuel may be gaseous or liquid, but the oxidant is always air. The main products of

combustion are carbon dioxide and water vapor. Combustion is a very complex physical process

involving strong interactions between the aerodynamic field, thermal field, turbulence interactions,

mixing and chemical kinetics. Fuel is injected in the form of particles or droplets. In such cases

interaction between the gas phase and the particulate phase plays an important role. . Combustion


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systems involve high temperatures. At these temperatures heat transfer by radiation plays an

important role. An appropriate radiation model must be included when simulating combustion

systems. Computational models that account for thermal, prompt and fuel NOx have been

developed. Soot and NOx formation are modeled using semi-empirical mechanisms. These

mechanisms are not very reliable and accurate prediction of absolute quantities of pollutants is

difficult.

The different steps in modelling the oxidation of methane in air

First the look-up table is calculated The mole fraction of methane and temperature are

visualized, but a look-up table will be calculated for all compounds e.g. CO2,CO,H2O, H,

CH etc. Note that the variable ranges from 0 to1and ranges from 0 to 0.25, which is the

theoretical maximal variance of unmixed reactants.

Where stoichiometric mixture fraction and : viscocity

Fig: conguration

Fig: look-up table


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Secondly the ow, mean mixture fraction and variance are simulated. The temperature and

composition can then be found in the look-up tables to obtain the right properties of the uid.

Fig: Simulation of temperature, mean mixture fraction, variance and mole fraction of CH4.

It is also possible to use such methods for non-adiabatic reactions. The compositions and

temperatures in the look-up tables will then be functions of energy loss or gain also.During the

iterations the energy loss or gain is estimated, which allows convection and radiation from the

ame to be included in the simulations.

Common models used for Combustion modeling

By representing the combustion of fuel as a global one-step, infinitely fast, chemical reaction, the

simple chemical reacting system (SCRS) assumes the oxidant reacts with the fuel to form products

at stoichiometric proportions. The intermediate reactions are ignored since we are only concerned

with the global nature of the combustion process. With this model, the mass fractions of the


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reactants and products accompanied by the inert species can be expressed as fixed algebraic state

relationships in terms of a passive scalar called the mixture fractionf. As a consequence, it is only

necessary to solve one extra transport equation for f rather than individual transport equations for

each mass fraction. To account for the fluctuations of mass fractions due to turbulence, the average

scalars of these variables can be obtained by weighting the instantaneous value with a probability

density function for the mixture fraction f.Clipped Gaussian and beta functions are typical

probability density functions that have been applied to

provide the best results

The eddy break-up concepts introduced by Spalding (1971) and Magnussen and Hjertager (1976)

present an alternative approach to the SCRS where the rate of consumption of fuel is solved as a

function of local flow properties. Here, the mixing-controlled rate of reaction is expressed in terms

of the turbulence time scale. The model considers the slowest rate as the reaction rate of fueldepending on the minimum dissipation rates of fuel, oxygen, and products. Within this model, it is

also possible to accommodate kinetically controlled reaction terms expressed by the

Arrhenius kinetic rate expression to govern the reaction rate of fuel in addition to the mixing-

controlled rate of reaction. The implementation is straightforward and it has shown to yield

reasonably good predictions, but the quality of the predictions depends greatly on the turbulence

models used.

In addition to the development of the SCRS and eddy break-up models, another popular

combustion mode1 is the consideration of lamh'1ar flamelets. This approach is based on the

assumption that these flamelets are reaction-diffusionIayers in quasi-steady-state that are

continuously displaced and stretched within the turbulent medium. These layers are assumed

thinner than all the turbulent scales, so that their internal structures have the compositional

structure of laminar flames. Like the SCRS, a transport equation for the mixture fraction is solved.

However, the instantaneous species mass fractions are now deduced from the laminar state

relationships, which can be taken from experimental measurements. The species fluctuations can

also be accounted for through the probability density function described above to obtain the

average variables.

Many of the traditional combustion models developed above have been derived on the basis that

the flames are under near-equilibrium conditions. To predict highly nonequilibrium flame events

such as ignition, lift-off, or extinction, it would be possible to modify the state relationships to


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include the scalar dissipation rate dependence and distinguish between the burning and

extinguishing flamelets.

It is clear that combustion modeling is still very much an area of active research. With the

advancements in computer speed and parallel architectures, time-accurate LES of combusting

flames are becoming ever more feasible and prevalent.

basic concepts in multi phase and combustion modelling

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