Numerical Simulation of a Small Scale Mild Combustor

Ricardo Manuel Batista de Oliveira

A thesis submitted in partial fulfillment of the requirements for the

Degree of Masters of Science in

Mechanical Engineering

Jury

Chair: Prof. Mário Manuel Gonçalves da Costa

Supervisor: Prof. Pedro Jorge Martins Coelho

Examiner: Prof. Viriato Sergio de Almeida Semião

October 2012

2

“You must be the change you want to see in the world”

Mahatma Gandhi

3

Acknowledgements

First, I would like to thanks to my supervisor Professor Pedro Coelho for all the unceasing support

and availability during this research work. All the meetings, emails or simple conversations contributed to

the development of the present work.

I also would like to thanks to Professor Mário Costa and Professor Daniel Vaz for the comments

and for the ideas expressed in all meetings. Without them the success of this work would certainly not be

possible.

I am grateful to Anton Veríssimo for all the support, the comments and for the help in the

development of this thesis.

I would like to thank André Duarte for all the support with the C-PDF method, for the time that I

“bored” him with doubts and for all the comments and ideas during this work.

Special thanks to Miguel Graça for all the support and help with ANSYS Fluent, for the valuable

comments about this work and for all these years of friendship. Without his knowledge my work would be

certainly more difficult.

I also need to thank Jorge Coelho for his excellent work with the figures and graphics included in

this dissertation.

Finally, I would like to thank my family and my friends for their love and their never ending support

through my whole life.

4

Abstract

This work reports numerical simulations of a small-scale cylindrical combustor operating in the

mild combustion regime. Preheated air is supplied by a central nozzle, while the fuel (methane) is injected

through 16 holes placed equidistantly in a concentric circumference. The calculations were carried out

using the commercial code Ansys-Fluent-v13. Turbulence was modelled using the realizable k-ε model.

A comparison between the experimental velocity field and the predictions from the numerical

simulations under isothermal conditions is done. Tests of grid and particles number independence were

also done.

Three different combustion models were employed, namely the finite rate/eddy dissipation, the

eddy dissipation concept and the joint composition probability density function transport model. A detailed

chemical mechanism, SK-17 was used. Subsequently, the pre-heated air temperature influence is studied

and compared with experimental measurements. The influence of the air nozzle diameter is also

investigated.

The computational results show that the turbulence model does not accurately predict the initial

decay of the air jet velocity for isothermal conditions. The combustion models with the detailed

mechanism are able to accurately predict the temperature and the O2 and CO2 molar fractions over most

of the combustor. Regarding the pre-heated combustion air temperature influence, there is a decrease in

the recirculation rate when that temperature is lower. When the air nozzle diameter decreases, the

reaction occurs closer to the burner.

5

Resumo

O presente trabalho descreve a simulação computacional de uma pequena câmara de

combustão laboratorial que funciona no regime de combustão sem chama visivel. A fornalha é

constituída por um tubo central onde é injectado ar pré-aquecido, enquanto o combustível (metano) é

injectado através de 16 orifícios colocados numa circunferência concêntrica. As simulações numéricas

foram realizadas recorrendo ao software comercial Ansys Fluent-v13. O modelo realizável foi

usado para modelar a turbulência.

Foram efectuadas comparações entre os dados experimentais e simulações numéricas para um

caso isotérmico. Foram realizados testes de independência de malha e do número de partículas.

O desempenho computacional de três modelos de combustão foi avaliado: finite rate/eddy

dissipation, eddy dissipation concept e joint composition probability density function transport model. Foi

analisado o desempenho de um mecanismo de cinética química detalhado, o SK-17. Foi igualmente

averiguada a influência da temperatura de pré-aquecimento do ar e do diâmetro do tubo de ar de

combustão.

Os resultados computacionais indicam que o modelo de turbulência não prevê correctamente o

decaimento da velocidade do jacto de ar. Os modelos de combustão juntamente com o mecanismo SK-

17 prevêem com relativa exactidão a temperatura e as fracções molarares de CO2 e O2 ao longo de

quase toda a câmara de combustão. Relativamente à influência da temperatura de pré-aquecimento do

ar de combustão, verificou-se uma diminuição da taxa de recirculação quando essa temperatura é mais

baixa. Observou-se ainda que quanto menor o diâmetro do tubo de ar, mais perto do queimador ocorrerá

combustão.

6

Keywords

Mild combustion

Numerical simulation

Joint composition transport PDF’s

Laboratorial furnace

Palavras-chave

Regime de combustão sem chama visível

Simulação numérica

Modelo do transporte da PDF de composição

Fornalha laboratorial

7

8

Contents

Figures List ............................................................................................................................................... 10

Tables List ................................................................................................................................................. 11

Nomenclature ........................................................................................................................................... 13

Acronyms .................................................................................................................................................. 17

1. Introduction ..................................................................................................................................... 18

1.1. Background ............................................................................................................................. 18

1.2. Mild combustion regime ...................................................................................................... 19

1.3. Literature review .................................................................................................................... 21

1.3.1. Introduction ..................................................................................................................... 21

1.3.2. Mild combustion regime .............................................................................................. 21

1.3.3. Composition Joint PDF model ................................................................................... 23

1.4. Innovative contribution ........................................................................................................ 25

1.5. Dissertation outline ............................................................................................................... 25

2. Computational Models ................................................................................................................. 26

2.1. Introduction ............................................................................................................................. 26

2.2. Conservation equations for reactive flows ..................................................................... 26

2.3. Conservation equations for turbulent flows ................................................................... 27

2.4. Turbulence models ............................................................................................................... 29

2.4.1. k-ε realizable model....................................................................................................... 29

2.5. Combustion models .............................................................................................................. 31

2.5.1. FR/ED model ................................................................................................................... 31

2.5.2. EDC model ....................................................................................................................... 32

2.5.3. Joint composition PDF model .................................................................................... 33

2.6. Radiation model ..................................................................................................................... 34

2.7. Numerical details ................................................................................................................... 37

3. Experimental setup and results ................................................................................................. 39

3.1. Introduction ............................................................................................................................. 39

3.2. Combustion chamber ........................................................................................................... 39

3.3. LDA (Laser Doppler Anemometry) system ..................................................................... 40

3.4. Experimental results ............................................................................................................. 40

4. Computational results discussion ............................................................................................ 41

4.1. Introduction ............................................................................................................................. 41

9

4.2. Isothermal solution ............................................................................................................... 41

4.3. Grid independence ................................................................................................................ 45

4.4. Number of particles independence ................................................................................... 46

4.5. Boundary conditions and geometry influence .............................................................. 49

4.6. Qualitative description of the flow in the combustion chamber ............................... 50

4.7. Combustion model influence ............................................................................................. 51

4.8. Chemical mechanism influence ......................................................................................... 55

4.9. Pre-heated combustion air temperature influence ....................................................... 56

4.10. Air nozzle diameter influence ......................................................................................... 60

5. Conclusions and future work ..................................................................................................... 65

5.1. Conclusions ............................................................................................................................ 65

5.2. Future work ............................................................................................................................. 66

References ................................................................................................................................................ 67

Appendix ................................................................................................................................................... 71

10

Figures List

Fig. 1.1 - U.S. energy-related carbon dioxide emissions by sector and fuel, 2005 and 2035 (million metric

tons) (Annual Energy Outlook 2012) ............................................................................................................... 18

Fig. 1.2 - Combustion regimes (Wünning & Wünning, 1997) ..................................................................... 19

Fig. 1.3 - Idealized process for a chamber in mild combustion regime (Wünning & Wünning, 1997) ....... 20

Fig. 2.1 – Radiative intensity reflected from a surface. .............................................................................. 35

Fig. 2.2 – Spatial and directional discretization in a two-dimensional domain. .......................................... 36

Fig. 3.1- Schematic of the combuster. ........................................................................................................ 39

Fig. 3.2 - Schematic representation of the combuster. ............................................................................... 39

Fig. 4.1 – Geometry A – Mesh 1 and 2 respectively. ................................................................................. 42

Fig. 4.2 – a) Axial velocity, b) Axial velocity profile at the combustion chamber inlet. ............................... 43

Fig. 4.3 - Radial profiles of the flow velocity. .............................................................................................. 44

Fig. 4.4 - Predicted and measured axial profiles of mean temperature, .................................................... 46

Fig. 4.5 - Predicted and measured axial profiles of mean temperature, .................................................... 47

Fig. 4.6 - Predicted and measured axial profiles of temperature, .............................................................. 49

Fig. 4.7 - Predicted velocity field. ................................................................................................................ 50

Fig. 4.8 - Predicted and measured axial profiles of mean temperature axial velocity, O2, CO2 and CO

mean molar fractions on a dry basis ........................................................................................................... 51

Fig. 4.9 - Predicted and measured radial profiles of mean temperature and velocity. ............................... 53

Fig. 4.10 - Predicted and measured radial profiles of O2, CO2 and CO mean molar fractions on a dry

basis............................................................................................................................................................ 54

Fig. 4.11 - Predicted and measured axial profiles of mean temperature axial velocity, O2, CO2 and CO

mean molar fractions on a dry basis. .......................................................................................................... 57

Fig. 4.12 - Predicted and measured radial profiles of mean temperature and velocity. ............................. 58

Fig. 4.13 - Predicted and measured radial profiles of O2, CO2 and CO mean molar fractions on a dry

basis............................................................................................................................................................ 59

Fig. 4.14 - Predicted and measured axial profiles of mean temperature axial velocity, O2, CO2 and CO

mean molar fractions on a dry basis ........................................................................................................... 61

Fig. 4.15 - Predicted and measured radial profiles of mean temperature and velocity. ............................. 62

Fig. 4.16 - Predicted and measured radial profiles of mean O2, CO2 and CO mean molar fractions on a

dry basis. .................................................................................................................................................... 63

Fig. 4.17 - Recirculation rate for different air nozzle diameters. ................................................................. 64

Fig. 1 - Predicted and measured radial profiles of mean temperature and velocity. .................................. 72

Fig. 2 - Predicted and measured radial profiles of mean O2 and CO2 mean molar fractions on a dry basis.

.................................................................................................................................................................... 72

Fig. 3 - Predicted and measured radial profiles of mean temperature and velocity. .................................. 72

Fig. 4 - Predicted and measured radial profiles of mean O2 and CO2 mean molar fractions on a dry basis.

.................................................................................................................................................................... 72

Fig. 5 - Predicted and measured radial profiles of temperature and velocity. ............................................ 72

Fig. 6 - Predicted and measured radial profiles of O2 and CO2 molar fractions on a dry basis. ................ 72

11

Tables List

Table 2.1 – Solution and discretization methods ........................................................................................ 37

Table 2.2 – Sum of residuals from Ansys fluent-v13 .................................................................................. 37

Table 2.3 – Monitoring points coordinates.................................................................................................. 38

Table 3.1 – Experimental conditions .......................................................................................................... 40

Table 4.1 – Mesh and geometry description .............................................................................................. 42

Table 4.2 – Isothermal conditions (test 1i).................................................................................................. 42

Table 4.3 – Test 1 input data ...................................................................................................................... 45

Table 4.4 – Iterations number influence ..................................................................................................... 48

Table 4.5 – Test 2 input data ...................................................................................................................... 54

Table 4.6 – Test 2, 3 and 4 input data ........................................................................................................ 55

12

13

Nomenclature

Roman Characters

Small Letters

- Radiative blackbody emitted energy fraction [-]

- Realizable model constant [-]

- Specific heat [J/(kg.K)]

- Gravity acceleration vector [m/s2]

- Specific fluid enthalpy [J/kg]

- Fick’s law mass diffusion flux [kg/(m2s)]

- Turbulent kinetic energy [m2/s

2]

- Species absorption coefficient [1/m]

- Largest turbulent eddy length scale [m]

- Rate of mass transfer to the fine structures [1/s]

- Surface normal unit vector [m]

- Pressure [Pa]

- Radiation heat flux vector [W/m3]

- Radiation heat flux energy source term [W/m

3]

- Position vector [m]

– Combustion chamber radial coordinate [m] or chemical reaction index [-]

- Path length [m]

- Direction vector [m]

- Time [s]

- Velocity vector [m/s]

- Velocity scale of the largest turbulent eddies [m/s]

- Fine structure velocity scale [m/s]

- Quadrature weight in direction [-]

- Spatial position vector [m] or combustion chamber axial coordinate [m]

- Mass fraction of species [-]

14

Capital Letters

- Turbulence model parameter [-]

- Turbulence model parameter [-]

- Control volume face areas normal to the , and directions [m2]

- EDC reactive fraction constant [-]

- Turbulence model variable [-]

- EDC time scale constant [-]

- Hydraulic diameter [m]

- Mass diffusivity coefficient of species [m

2/s]

- Incident radiation [W/m2]

- source term relative to buoyancy effects [kg/m.s3]

- Radiative intensity [W/m2.sr]

- Turbulence intensity [-]

- Molecular diffusion flux [kg/(m2s)]

- Recirculation rate [-]

- Fine structure length scale [m]

- Lewis number [-]

- Molecular weight [kg/kmol]

- Air mass flow rate [kg/s]

- Mass flow rate of recirculated flue gases [kg/s]

- Fuel mass flow rate [kg/s]

- Composition PDF

- Partial pressure of species [Pa]

- Ideal gas constant [J/mol.K]

- Rate of formation/destruction of species in reaction [kg/m3.s]

- Reynolds number based on the hydraulic diameter [-]

- Turbulence model parameter [1/s]

- Average velocity field strain rate [1/s]

- Radiation heat source term at node P [-]

- Turbulent Schmidt number [-]

15

- Radiation energy source in the joint composition probability density function equation [J/m3.s]

- Chemical reaction source in the joint composition probability density function equation [J/m3.s]

- Temperature [K]

- Turbulence model parameter [1/s]

- Control volume [m3]

- Turbulence model parameter [-]

Greek Characters

Small Letters

- Mass fraction of the total fluid occupied by the fine structures [-]

- Kronecker delta [-]

- Turbulent kinetic energy dissipation rate [m2/s

3] or emissivity [-]

- Surface emissivity [-]

- Permutation symbol [-]

- mean strain rate [-] or direction cosine [-]

- Medium absorption coefficient [1/m]

- Thermal conductivity [W/(m.K)] or excess air coefficient [-]

- direction cosine [-] or Mass fraction of the total fluid occupied by the fine structure regions [-]

- Fluid dynamic viscosity [kg/(m.s)] or direction cosine [-]

- Turbulent dynamic viscosity [kg/(m.s)]

- Fluid density [kg/m3]

- Surface reflectivity [-]

- Stefan-Boltzmann constant [W/(m2.K

4)]

- Energy Prandtl number [-]

- Turbulent kinetic energy Prandtl number [-]

- Turbulent kinetic energy dissipation rate Prandtl number [-]

- Fine structure residence time scale [s]

- Viscous stress tensor

- Transported scalar or turbulence model parameter [-]

– Composition space vector [-]

- Rotating frame of reference angular velocity [rad/s]

16

– Species source term [kg/m3.s]

Capital Letters

- Solid angle [sr]

- Rate of rotation tensor [rad/s]

Exponents

( ) - Reynolds time average

( ) - Favre mass-weighted average

( ) - Reynolds fluctuation

( ) - Favre fluctuation

( ) – Relative to the fine structure surroundings

( ) - Relative to the fine structures

Subscripts

- Relative to a blackbody

- direction or chemical specie

- direction

- direction or composition space

- Relative to the participative medium in radiation

- Relative to the node

- Enthalpy

17

Acronyms

CDC – Colourless Distributed Combustion

CFD - Computational Fluid Dynamics

C – PDF – Joint Composition Probability Density Function

CPU - Central Processing Unit

DOM – Discrete Ordinates Method

EBU - Eddy Break Up model

EDC - Eddy Dissipation Concept

EDM - Eddy Dissipation Model

EMST - Euclidean Minimum Spanning Tree

EPFM – Eulerian Particle Flamelet Model

FLOX – Flameless Oxidation

FR/EDM - Finite Rate/Eddy Dissipation Model

HiTAC – High Temperature Air Combustion

IEM - Interaction by Exchange with Mean

IP - Isotropization of Production

ISAT – In-Situ Adaptive Tabulation

JHC - Jet in Hot Coflow

LDA - Laser Doppler Anemometry

LES - Large Eddy Simulation

LRR - IP RSM – Launder-Reece-Rodi Isotropization of Production Reynolds Stress Model

MILD - Moderate and Intense Low Oxygen Dilution

NOx – Nitrogen Oxides

PDF – Probability Density Function

RAM - Random-Access Memory

TFL – Thermal Fuel Load

WSGG - Weighted Sum of Gray Gases

18

1. Introduction

1.1. Background

In the last few decades the combustion technologies experienced significant improvements. Much

of this high development is due to a higher awareness of the human beings about the adverse effects of

pollutant emissions from the combustion processes. Global warming, the limited availability of fossil fuels,

the need to improve combustion efficiency and recently the rising price of fuels around the world

associated with a global economic crisis are largely responsible for increasing investment in the search

and investigation of new combustion processes.

The emissions of CO2 represent approximately 60% of the anthropogenic greenhouse gases, so

the reduction of these pollutant emissions is one of the most important challenges of this century. In order

to achieve that, Kyoto Protocol was created in 1997 by United Nations Framework Convention on Climate

Change (UNFCCC or FCCC), aimed at fighting global warming and the expectation is a decrease in CO2

emissions, as can be seen in Fig. 1.1. The UNFCCC is an international environmental treaty with the goal

of achieving the stabilization of greenhouse gas concentrations in the atmosphere at a level that would

prevent dangerous anthropogenic interference with the climate system.

Nowadays one of the most challenging industrial processes is to develop new strategies to

minimize and to reduce the usage rate of fuel and the pollutants emissions, like soot, NOx, CO and

unburned HC. The development of these technologies is not a simple process due to the fact that the

phenomena that govern the formation of these pollutants act in divergent ways for each and for different

burning conditions.

Fig. 1.1 - U.S. energy-related carbon dioxide emissions by sector and fuel, 2005 and 2035 (million metric tons) (Annual Energy Outlook 2012)

19

In this context one of the most promising combustion technologies that emerged from these

research efforts is characterized by highly preheated reactants, typically exceeding the self-ignition

temperature of the mixture, and diluted systems. This combustion regime is generally referred to as

flameless combustion, flameless oxidation, moderate or intense low oxygen dilution (MILD)

combustion, colourless distributed combustion or high temperature air combustion.

Nowadays due to a need to reduce both costs and time, the numerical simulation emerges as

one of the main research tools, not only as a complement to experimental investigation but also due to

the ability to simulate more complex cases. It is in this context that this thesis falls, addressing the

numerical simulations of a small scale combustor operating in the mild combustion regime.

1.2. Mild combustion regime

In order to define mild combustion (Cavaliere and Joannon, 2004), Wünning and Wünning (1997)

proposed the diagram shown in Figure 1.2. In this diagram four zones are distinguished depending on

both the temperature of the combustion chamber and the rate of recirculation of combustion products.

This parameter is defined as the ratio of the recirculated gas flow, which mixes with the reactants (air and

fuel combustion) before the combustion process occurs, and the sum of the air and fuel mass flow rates.

The area A in Fig. 1.2 is characterized by low recirculation rates and corresponds to the

traditional combustion phenomena, area B is a transition region which is characterized by an unstable

and incomplete combustion and zone C represents the mild combustion regime. High temperatures

and high recirculation rates are required to achieve the mild combustion regime as is clearly illustrated in

fig 1.2.

Fig. 1.2 - Combustion regimes (Wünning & Wünning, 1997)

20

The mild combustion regime is presented schematically in figure 1.3 which shows two stages of

the process. In the first stage, region ‘I’, the combustion air is mixed with recirculated gases, from the

combustion. In the second step of the process, after a complete mixing between air and products

of combustion, fuel is added in region ‘II’ so combustion occurs. Due to the presence of inert species in

this part of the process, the temperature should not exceed 1850 K and therefore the thermal NO

formation mechanism is inhibited. Finally, in the third stage of the process, part of the energy has to be

withdrawn from the combustion products, keeping the temperature on a certain level to guarantee

reaction in stage ‘II’.

Fig. 1.3 - Idealized process for a chamber in mild combustion regime (Wünning & Wünning, 1997)

Compared with a conventional combustion process, the mild combustion develops slowly, due

to the limited amount of O2 available to react with the fuel. The Damköhler number, defined by equation

(1.1), is of the order of 1, due to the fact that the time scales associated with the flow and chemical

reactions are the same order of magnitude. This implies that the mild combustion regime should not be

simulated by models that assume infinitely fast chemical reaction.

( )

21

1.3. Literature review

1.3.1. Introduction

In order to integrate this research in the current scientific reality, the relevant studies to carry out

this work will be presented.

The literature review is organized into two sections; one referring to the mild combustion regime

(section 1.3.2) and the other one regarding the previous studies where the transport PDF model was

employed (section 1.3.3).

1.3.2. Mild combustion regime

In the last 20 years, several articles about the mild combustion regime have been published and

many universities and research departments of industry have experimentally and numerically investigated

this new technology, characterized by a high efficiency, low noise and low pollutants emission, particularly

NOx and CO.

Wünning and Wünning (1997) reviewed the mild combustion regime using experimental and

numerical techniques. The study reveals the ability of mild combustion regime to lower NOx emissions

through lowered adiabatic flame temperatures.

Plessing et al. (1998) presented experimental results for a rectangular laboratorial furnace (250

mm x 250 mm x 485 mm). In this research a regenerative burner was used and the exhaust was in the

same plane of the air and fuel inlets. The fuel used was methane in a stoichiometric condition and the

authors observed a soft and continuous rise of the temperature along the combustion chamber in the mild

combustion regime. They also concluded this type of combustion is similar to the combustion that occurs

in a perfect mixture reactor. Measurements in the exhaust show the capability of this combustion regime

in the control of NOx emissions, which for a thermal load of 10 kW and a preheated air temperature of 500

ºC, the NOx emissions were less than 10 ppm.

Afterwards, Coelho and Peters (2001) performed numerical studies in this laboratorial furnace

using an in-house code (PIPES) and the Fluent code. In order to perform the numerical simulations in

Fluent, the EPFM was used, in post-processing, instead of the combustion models available in Fluent.

The results were in fair agreement with the data, except in the vicinity of the burner, where the predicted

local mean residence time was under-estimated. The authors concluded that the fluent code can predict

well the magnitude of the NOx emissions. However, the PIPES code predicted the NOx emissions with an

order of magnitude above.

22

Tabacco et al. in 2002, performed numerical simulations in a furnace that has the exhaust on the

same side as the burner. The burner allows for mixing between pre-heated air and fuel just prior the

entrance in the furnace. Two combustion models were employed to perform the numerical simulations,

namely the conserved scalar/prescribed pdf method with chemical equilibrium assumption and the EDM

with a single step global reaction. The turbulence model used was the realizable k-ε model. The authors

did a theoretical and numerical analysis, where they observed the mild combustion regime for a process

temperature of 1150 ºC, and the Damköhler number is of the order of unity. None of these models could

successfully predict the main reaction zone, particularly the ignition zone.

Mancini et al. (2002) performed numerical simulations of a rectangular furnace working in the mild

combustion regime. The authors compared their predictions with the experimental results of temperature

and molar fraction of HC and NOx inside the furnace. Three turbulence models were employed, namely

the standard k-ε model, realizable k-ε model and Reynolds stress model. The change of the turbulence

model did not make a significant difference in the results. The combustion was simulated through the

EDC model considering a chemical mechanism with 13 chemical species; the EBU model considering a

chemical mechanism with 6 chemical species and two step global reactions; and the mixture fraction/pdf

model (ξ/PDF) with a chemical mechanism with 11 chemical species. Although the results at the furnace

exhaust are in fair agreement with the data, inside the furnace the predictions are not so satisfactory, i.e.

the models do not predict correctly the reaction zone. The authors concluded that these three models do

not show major differences when compared with each other and the NOx emissions were in good

agreement with experimental data.

Christo and Dally (2005) carried out numerical simulations of a non-enclosed flame. Three

turbulence models were employed, namely the standard k-ε model, realizable k-ε model and the

renormalized k-ε model. The combustion was simulated through the FR/EDM, which only allows a single

step global reaction; the EDC model considering two chemical mechanisms, one detailed and another

one simplified; and two models of conserved scalars, namely the flamelet model for diffusion flames and

the ξ/PDF model. The authors concluded that the standard k-ε model with the Cε1 constant modified to 1.6

leads to better results. Concerning the combustion models, the authors concluded that the EDC model

with a detailed chemical mechanism predicted in a reasonable way the experimental data and the models

based in conserved scalars was unsuitable to simulate this combustion regime.

Frassoldati et al. (2008) performed numerical simulations of a JHC in order to assess the

performance of the numerical models. In this research the combustion was simulated through the EDC

model considering a chemical mechanism with 48 chemical species and approximately 600 chemical

reactions in order to study NOx formation. Two turbulence models were employed, namely standard k-ε

model, an alternative of it, where the Cε1 value is modified to 1.6 and the Reynolds stress model. Once

again, the turbulence model with the Cε1 constant changed was the one that gives better agreement with

the experimental data. The computational simulations predicted well the flame structure, temperature and

the molar fractions of the main chemical species, and the NOx emissions was in a good agreement with

the data.

23

Galletti et al. (2007) performed numericallly and experimental studies of an industrial cylindrical

furnace working in the mild combustion regime. In this research the turbulence was simulated through the

standard k-ε model with the Cε1 constant of the dissipation transport equation set equal to 1.6 instead of

1.44 in order to overcome the deficiency of this model in predicting round jets properly. The FR/EDM

combustion model was employed and the authors concluded that the results are in good agreement with

the experimental data in the exhaust of the furnace. Since the furnace does not allow any access to the

interior for measurements, there was no possibility to assess the numerical predictions.

1.3.3. Composition Joint PDF model

Pope (1985) described the methods to numerical simulate turbulent reactive flows. In this work

the author set the fundaments for the velocity composition PDF model and for the composition joint PDF

model. The velocity composition PDF model statistically describes the flow through the three components

of velocity and the composition variables (species mass fractions and enthalpy). Due to this model

characterizing the fluid flow, a deterministic turbulence model is not necessary to model the viscous

interactions. However the model used in this work, composition joint PDF model only characterizes the

species mass fraction and the enthalpy and due to this a turbulence model was required.

Haworth (2009) presented the progress in probability density functions methods for turbulent

reactive flows. In this work the author deepened the knowledge about these methods. The author not only

described the governing equations and the PDF methods for turbulent reacting flows, the author also

describes the Lagrangian particle equations and the Eulerian field equation. In this work Haworth

described the RAS/PDF and LES/FDF formulation. Numerical algorithms and numerical descriptions of

boundary conditions formulation, sorting, chemistry acceleration, parallelization, particle number density

control, numerical convergence and accuracy, and other stuff regarding numerical applications of the

PDF methods have been described in Haworth’s work.

Wang and Chen (2004) carried out numerical simulations of the Sandia flame D. In this research

the turbulence was simulated through the multiple-time-scale (MTS) k-ε turbulence model. A detailed

chemical mechanism was employed, namely GRI-Mech 3.0, which contains 53 chemical species and 325

elementary reactions, with the joint scalar closure level PDF method to reduce the dimension of the joint

PDF and to facilitate the usage of node-based Monte-Carlo algorithm which makes the solution easier

and the Euclidean minimum spanning trees (EMST) mixing model was employed to model the small-

scale mixing term appearing in the PDF evolution equation. The authors concluded that the predictions

are in fairly good agreement with the measurements, however the NO emission was over-predicted.

Christo and Dally (2004) performed numerical simulations in the experimental installation

reported by Dally et al. (2002). In this work the authors used the joint composition PDF method, and the

standard k-ε model with the first constant of the dissipation transport equation Cε1 set equal to 1.6 instead

of 1.44. Molecular mixing of species and heat was modeled using the EMST model. In order to maintain a

low statistical error, 40 particles per cell were used in all the calculations, resulting of approximately 4

24

million particles been tracked at each iteration. The authors observed more accurate predictions for the

joint composition PDF method than the EDC model (Christo and Dally, 2005), particularly at 120 mm

(axial position). This conclusion however does not extend to the joint composition PDF method

performance at upstream locations of 30 mm and 60 mm, where both models have comparable accuracy.

Merci et al. (2005) presented numerical simulation results of a turbulent nonpremixed flame (Delft

flame III) with local extinction and reignition. In these simulations, the fuel is replaced by a mixture of pure

methane and nitrogen (85.3% CH4 and 14.7% N2 by volume). The fuel jet is surrounded by a primary air

annulus that supplies the air for combustion. The transported scalar PDF approach is applied to the

turbulence chemistry interaction. The turbulent flow field is obtained with a nonlinear two-equation

turbulence model, a detailed chemical mechanism was employed, which contains 16 chemical species

and 41 chemical reactions and 100 particles per cell are defined and the time averaging was set to the

latest 50 iterations to reduce statistical errors. The scope of this research was to study the performance of

three molecular mixing models, the IEM, the EMST and the modified Curl’s. The IEM model leads global

flame extinction in the numerical simulations. With the modified Curl’s model with the constant of the

molecular mixing set to 2, flame liftoff is observed; an alternative manner of obtaining an attached flame

with this molecular mixing model was to change the molecular mixing constant to the value of 3. Only the

EMST model leads to the qualitatively correct flame, attached to the burner head. The authors also

concluded that is not possible to find one value of the molecular mixing constant leading to good

predictions for both rms of mixture fraction and amount of local extinction. For EMST a low value of the

molecular mixing constant (value set equal to 1.5), leads to better agreement with experimental data of

mean temperature, at the cost of overprediction of rms of mixture fraction.

Merci et al. (2006) presented numerical studies for turbulent jet diffusion flames with various

levels of turbulence–chemistry interaction, stabilized behind a bluff body (Sydney Flames HM1–3). The

fuel is a mixture between methane (50% by volume) and hydrogen (50% by volume) and it is supplied by

a central jet with 3.6 mm of diameter. Interaction between turbulence and combustion is modeled with the

transported joint-scalar PDF approach. In this research the turbulence was simulated through the

modified LRR-IP RSM with the value of model constant Cε1 in the dissipation-rate transport equation was

increased to 1.6, in order to obtain better spreading-rate predictions for the round jet. A detailed chemical

mechanism was employed, which contains 16 chemical species and 31 chemical reactions, 100 particles

per cell was defined and the time averaging was set to the latest 100 iterations to reduce statistical errors.

The authors also modified the constants of the molecular mixing models, the constant of the Modified

Curl’s model was set to 2 and the value of 1.5 was defined for the EMST model. From the comparisons

between the experimental data and the numerical predictions the authors concluded there is no

significant difference between the two molecular mixing models. On the other hand with a detailed

observation the authors also concluded that the EMST model under predicts local extinction, while

Modified Curl’s model yields better agreement with experimental data. Nevertheless, Modified Curl’s

model overestimates incomplete combustion, while EMST model performed well.

25

1.4. Innovative contribution

An important contribution of this work is the use of a combustion model, joint composition PDF

transport model, under the mild combustion regime of an enclosed flame. This model has been widely

used to simulate free flames, but much fewer applications to combustion chambers have been reported.

In particular, its performance in the simulation of mild combustion regime in a laboratory combustor has

not been previously investigated, apart from the recent work of Graça et al. (2012).

1.5. Dissertation outline

This thesis is structured in five chapters, the present one being the introduction. Chapter two

describes the computational models that were used in the numerical simulations, including the turbulent,

combustion and radiation models. In chapter three the main characteristics of the experimental

installation, which is numerically investigated in the present work, are described. In chapter four the

results from numerical simulations are presented, and their ability to reproduce the experimental

measurements are discussed. In the last chapter, the main conclusions from the present work are

summarized and some possible new points for a future work in this area are suggested.

26

2. Computational Models

2.1. Introduction

This chapter describes the equations and models used to perform the numerical simulations.

Initially the equations that mathematically describe a reactive flow are presented. Subsequently, the

turbulence model used in all numerical simulations, the k-ε realizable model is described.

Following this, the combustion models used to perform numerical simulations are presented.

Three different combustion models were employed, namely the joint composition probability density

function transport model (C - PDF), the eddy dissipation concept (EDC) and the finite rate eddy

dissipation model (FR/EDM).

Finally the discrete ordinates method, which is the radiation model used to calculate the radiative

source term of the energy equation, is presented.

2.2. Conservation equations for reactive flows

This section gives the governing equations of the mathematical model employed for the modeling

of reactive flows, which is based on the principles of conservation of mass, momentum, and energy. This

section presents the equations of mass conservation, mass fractions of species, momentum, and energy

in terms of enthalpy.

The equation of mass conservation is written as follows:

( ) (2.1)

where represents the fluid density, t the time and is the velocity vector.

The equation of mass conservation of species i, assuming that the mass diffusion flux is given by

Fick's law, has the following form:

( )

( ) (2.2)

(2.3)

27

In this equation and represents the mass fraction and molecular diffusion coefficient of the

chemical species i, respectively, and is the rate of production/consumption of the chemical specie i

due to chemical reactions.

For a Newtonian fluid, the equation for the conservation of momentum has the following form:

[ [ ( ) ]

( ) ] (2.4)

where p represents the pressure, μ is the dynamic molecular viscosity, g is the gravity

acceleration vector and is the Kronecker symbol, which is if i j and if i j.

The energy conservation equation expressed in terms of specific enthalpy for a reactive system

with a constant pressure, neglecting the viscous dissipation, and assuming that for all chemical species

the thermal diffusivity is equal to mass diffusivity (Le = 1), has the following form:

( )

( ) [

]

(2.5)

where represents the specific enthalpy, λ the thermal conductivity, cp the specific heat capacity

at constant pressure and is the heat exchange by radiation.

2.3. Conservation equations for turbulent flows

The major challenge in mathematical modeling and computer simulation of turbulent flows is to

deal with the random nature of turbulence. Due to the turbulence, the distributions of velocity,

temperature and species concentrations show fluctuations that can be quite significant.

The equations presented in section 2.2 describe in detail the turbulent field of the respective

quantities. In the solution of flows of practical interest, in general, a statistical approach is employed,

known as the Reynolds averaging, which solves the equations for the time average field of the dependent

variables.

In a statistically stationary turbulent flow, a scalar ( ) is expressed as the sum of an average

time value ( ) and a fluctuation ( ).

( ) ( ) ( ) (2.6)

The time average value is defined as:

( )

∫ ( )

(2.7)

28

According to the definition of the equation (2.6), the average fluctuation value is null

( ) (2.8)

When compressibility effects are felt, for instance in terms of significant relative density

fluctuations, the use of Favre averaging is a desirable solution. In Favre decomposition, a scalar ( )

is defined as the sum of the weighted average density ( ) and a fluctuation ( ).

( ) ( ) ( ) (2.9)

The weighted average density value is defined as:

( )

∫ ( )

(2.10)

One simple method to define the Favre averaging is the following equation:

( ) ( )

(2.11)

As in Reynolds averaging, in Favre decomposition the average fluctuations value is null,

whereas, the time average (Reynolds averaging) is non-zero.

( ) (2.12)

( ) (2.13)

Therefore it is possible to write the conservation equations based in Favre averaging (Kuo, 1986,

Poinsot and Veynante, 2001).

The equation of mass conservation is written as follows:

( )

(2.14)

The equation of mass conservation of species i, assuming that the mass diffusion flux is given by

Fick's law, has the following form:

( )

( )

[

] (2.15)

The equation for the conservation of momentum is written as:

( )

( )

[ (

)

] (2.16)

29

The energy conservation equation expressed in terms of specific enthalpy, has the following form:

( )

( )

[

] (2.17)

When the equations are presented in this form, there are new terms that require modeling in

order to close the equations system. For this purpose, models of turbulence, combustion and radiation

must be used.

2.4. Turbulence models

2.4.1. k-ε realizable model

In the present work, the realizable k-ε model (Shih et al., 1995) was employed. The term

“realizable” means that the model satisfies certain mathematical constraints on the Reynolds stresses,

consistent with the physics of turbulent flows.

This model ensures that the normal stresses are always positive and the Schwarz inequality is

not violated for the shear stress (

(

) ( ) ), even when the deformation rate is very high. An

immediate benefit of the realizable k- ε model is that it predicts the spreading rate of both planar and

round jets more accurately than the standard k- ε model. It is also likely to provide superior performance

for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and

recirculation.

The modeled transport equations for k and ε in the realizable k- ε model are:

( )

( )

[(

)

] (2.18)

( )

( )

[(

)

]

√ (2.19)

(2.20)

[

] (2.21)

(2.22)

30

√ (2.23)

In these equations, Gk represents the generation of turbulence kinetic energy. C2ε and Cε are

constants and σk and σε are the turbulent Prandtl numbers for k and ε, respectively.

As in other k-ε models, the turbulent viscosity is computed from:

(2.24)

The difference between the realizable k-ε model and the standard model is that Cμ (coefficient of

dynamic viscosity) is no longer constant. It is computed from:

(2.25)

√ (2.26)

(2.27)

(2.38)

Where is the swapping tensor and is the mean rate-of-rotation tensor viewed in a rotating

reference frame with the angular velocity ( ) obtained from:

(

) (2.29)

The model constants A0 and As are given by:

(2.30)

√ (2.31)

Where is defined by:

(√ ) (2.32)

(2.33)

31

√ (2.34)

represents the rate of deformation of the average velocity field calculated by:

(

) (2.35)

The model constants have been established to ensure that the model performs well for certain

canonical flows. The model constants are:

; ;

2.5. Combustion models

The transport equations of mass, momentum and energy are not the only ones that need to be

solved in combustion problems. It is also necessary to solve the chemical species transport equations.

The combustion-turbulence interaction is an extremely complex phenomenon that continues to deserve

the attention of many researchers around the world.

The combustion models employed in this work enable the use of detailed chemical kinetics

mechanisms, where the reactions between the oxidizer and fuel are decomposed into elementary

reactions considering a series of intermediate chemical species.

2.5.1. FR/ED model

This model, FR/EDM (Magnussen and Hjertager, 1976), is simple and computationally

inexpensive and it can describe the turbulence/chemistry interaction. In the EDM model it is assumed that

the chemical reactions are extremely fast and the reaction rate of species is fully controlled by turbulent

mixing. One of the limitations of EDM is that it estimates a high combustion rate in the large dissipation

zones. Regarding this, the combination of this model with the finite rate model ensures a way to

overcome this situation. The reaction rate of the species is calculated by the FR/EDM considering the

minimum between the mixing rate and the kinetic rate, which is evaluated from an Arrhenius equation

based on the mean properties.

This combustion model does not allow the use of a detailed chemical reaction mechanism, as it

considers that the combustion reaction occurs in only one or two steps. In the present work a single

irreversible reaction was considered.

32

2.5.2. EDC model

The EDC model (Magnussen, 1981) is an extension of the eddy-dissipation model (EDM) to

include detailed chemical mechanisms in turbulent flows. In the present model, the flow is composed by 2

regions. The region that contains the small turbulent structures, called the fine scales, and its surrounding

region. This model assumes that reaction only occurs in the small turbulent structures, where all turbulent

kinetic energy is dissipated into heat.

The characteristic time scale of the mass transfer between the fine structure of turbulence and

the surrounding is modeled by the following expression

√(

) (2.36)

Where is a constant of the model, which is 0.4082, and represents the kinematic viscosity.

The mass fraction of the fine scales is modeled as:

(

)

⁄

(2.37)

Due to the fact that the fine scales exchange mass with the surroundings, Magnussen (1989),

developed the following expression to model the rate of mass transfer between the fine scales and its

surroundings:

(2.38)

The rate of mass transfer of each species to the region of the fine scales is defined by:

(

) (2.39)

Where

are the mass fraction of the specie i in the fine scales region and the

surrounding region, respectively.

The reaction rate of each species can be defined by the following equation:

( )

(2.40)

Where the mean mass fraction of species ( ) as defined as the following expression:

33

( )

(2.41)

Assuming the small turbulent structures are small reactors at constant pressure, the mass

fractions of chemical species in the fine structures are obtained from the integration between and

of the formation/destruction rate of each chemical specie, by the following equation:

( ( )) (2.42)

represents the formation/destruction rate of chemical species given by the following

expression:

∑ (2.43)

Before solving the species transport equation (2.15), equation (2.42) is solved for all control

volumes at each iteration of the calculation algorithm. In the solution of equation (2.42), the mean values

of temperature and mass fraction of species in each computational cell, are used to define the initial

conditions. The mass fraction of species in the fine structures is obtained from the integration of the

equation (2.42). With these values the source terms of the chemical species transport equation are

calculated by equation (2.40). The chemical species mass fraction, are obtained from the equation

(2.15).

The temperature is iteratively determined from the enthalpy according to the following equation:

∑ ( ) (2.44)

From the ideal gas law, the density is calculated according the following expression:

∑

(2.45)

2.5.3. Joint composition PDF model

The composition joint pdf (C-PDF) transport model is an alternative method for modeling

chemically reacting turbulent flows instead of the use of conventional combustion models. For reacting

flows, this offers the significant advantage of avoiding a closure for the chemical source term. However

this model requires a high computational effort and due to this the choice of this model is constrained to

the time required to perform the numerical simulations and to the performance of the computers that will

be used.

34

This model calculates the composition joint probability density function of the temperature and

mass fractions of chemical species. Their mean values are evaluated from the composition joint pdf,

which satisfies transport equation (2.46).

( )

( )

( )

[ ⟨ ⟩ ]

[ ⟨

| ⟩ ]

[ ⟨

⟩ ] (2.46)

Where the angle brackets denote an average value and the symbol <A|B> represents the

conditional probability of A, given that B occurs. The first two terms on the left side of this equation

represent the rate of change and advection of the pdf in the mean flow respectively, and the third one

describes the transport of the pdf in composition space by chemical reactions. On the other hand, the

three terms on the right-hand side require modeling. The first one accounts for the transport in physical

space due to turbulent convection, and is modelled using the gradient diffusion assumption as follows:

[ ⟨ ⟩ ]

(

) (2.47)

The second term on the right side of Eq. (2.46) represents the transport in scalar space due to

molecular mixing and the third term is relatively to the radiative absorption. The second term may be

modeled in Fluent by three different molecular mixing models, the IEM, the modified Curl’s and the

EMST. The IEM model assumes a linear relaxation of the scalar towards its mean value, which is a linear

deterministic process (Villermaux and Devillon, 1972). In the modified Curl’s (Curl, 1963) the particles mix

in pairs in a random way, which can be a source of error. This model uses stochastic ‘jump’ process to

imitate mixing. The last one, the EMST molecular mixing model (Masri et al., 1996) was used in the

present work because it is the model that allow better results. This mixing model takes into account the

physical position of the stochastic particles that are adjacent to each other, which makes this model the

most accurate mixing model available in the CFD code.

The joint composition pdf transport equation was solved using the Monte Carlo method. This is an

ideal method to solve high-dimensional equations since the computational cost increases linearly with the

number of dimensions. Notional particles with mass move randomly through the physical space

(computational domain), due to particle convection, and through the composition space, due to molecular

mixing and chemical reactions, in fractional time steps, allowing the position, the temperature and the

mass of the particles to be found after every time step. The disadvantage of this method is that statistical

errors are introduced, and these must be carefully managed.

2.6. Radiation model

According to Modest (1993), the radiative heat equation for a grey absorber/emitter medium can

be written as follows:

35

( ) ( ( ) ) (2.48)

Where ( ) represents the radiative intensity in the direction, is the black body radiative

intensity and is the medium absorption coefficient.

The boundary condition for a grey surface that emits and reflects diffusely is also given by Modest

(1993)

∫ ( )

(2.49)

Where is the local outward surface normal and is the cosine of the angle between

any incoming direction s' and the surface normal, as indicated in Fig. 2.1 and is the reflectivity of the

wall. Therefore, the outgoing intensity is not generally known explicitly, but is related to the incoming

intensity. An exception is the black surface, for which (with ),

(2.50)

In the discrete ordinates method the equation 2.48 is replaced by a set of N differential equations

that describe the radiative intensity field over N directions.

( ) (2.51)

The boundary condition defined by equation 2.49 is discretized as follows:

∑

(2.52)

The angular discretization of the equation 2.48 is done by the finite volume method that uses

exact integration to evaluate solid angle integrals, which is analogous to the evaluation of areas and

volumes in the finite volume approach. The method is fully conservative: exact satisfaction of all full- and

half-moments can be achieved for arbitrary geometries, and there is no loss of radiative energy.

Fig. 2.1 – Radiative intensity reflected from a surface.

36

For clarity, in this work the development will be limited to two-dimensional geometries; the

extension to the three is straightforward. For each volume element, such as the one surrounding point P

in Fig. 2.2, equation (2.53) is integrated over the volume element and over each of the solid angle

elements .

∫

∫

∫ ( )

∫

(2.53)

In the previous equation is the surface of the volume element consisting of 4 (two-dimensional)

or 6 (three-dimensional) faces and is the outward surface normal as indicated in the Fig. 2.2. In

equation (2.53) the unit direction vector can be moved inside the spatial -operator since directional

coordinates are independent from spatial coordinates. Conversion to a surface integral in the last step

follows from the divergence theorem.

It is assumed that the radiation is constant across each face of the element as well as over the

solid angle . Likewise, it is assumed for the volume integrals that values are constant throughout and

equal to the value at point P (Fig. 2.2). Using the notation of the Fig. 2.2:

∑ ( ) ( ) (2.53)

( )

∑

(2.54)

⁄ ∫ ∫ ( )

(2.55)

∫

(2.56)

Where subscripts l and P imply evaluation at the center of the volumes faces Al (as indicated by

an x in Fig. 2.2) and element center P, respectively; subscript m denotes a value associated with solid

angle .

Fig. 2.2 – Spatial and directional discretization in a two-dimensional domain.

37

What remains to be done is to relate the intensities at the face centers, to those at volume

centers, . Although there are many different ways to do this, some computationally more sophisticated

than others, the discretization scheme used was the second order upwind.

The medium properties were calculated by the weighted-sum-of-gray-gases model (WSGGM).

This model is a reasonable compromise between the oversimplified gray gas model and a complete

model which takes into account particular absorption bands. The basic hypothesis of the WSGGM is that

the total emissivity of our emitting/absorbing gas over the distance s can be presented as:

∑ ( )( ) (2.60)

Where is the emissivity weighting factor for the ith fictitious gray gas, the bracketed quantity is

the ith fictitious gray gas emissivity, is the absorption coefficient of the ith gray gas, pi is the partial

pressure of absorbing gas, and s is the path length. For the medium emissivity calculation only were

considered the CO2 and H2O as absorbing gases and for and Ansys fluent-v13 uses values

obtained from Smith et al. (1982) and Coppalle and Vervisch (1983).

The source term of the energy conservation equation related to heat exchange by radiation is

calculated by the following expression:

( ) (2.61)

Where, T is the temperature of the medium and is the Stefan-Boltzmann constant. The incident

radiation is calculated by:

∫

∑

(2.62)

2.7. Numerical details

A commercial CFD code, namely, ANSYS Fluent-v13 was used to calculate the reacting flow

inside the combustion chamber. The computational grid will be presented in chapter 4. As for the solution

methods, the pressure-based segregated algorithm simplec was selected for all simulation.. The ISAT (In-

Situ Adaptive Tabulation) algorithm of Pope (1997) was used in the solution process in order to reduce

the computational cost of chemistry calculations. The ISAT tolerance was set equal to 10-4

. As for the

remaining solution options and discretization schemes chosen for each solved equation, they are

described in table 2.1.

38

Pressure Second order

Momentum Second order upwind

Turbulent kinetic energy Second order upwind

Turbulent dissipation rate Second order upwind

Energy Second order upwind

Species Second order upwind

Discrete ordinates Second order upwind

Table 2.1 – Solution and discretization methods

Solution convergence was verified through two different criteria, the first being based on the sum

of the residuals throughout the computational domain for each equation, by ensuring that they fell below a

certain value. These values are listed table 2.2.

Equation Residuals C - PDF Residuals EDC Residuals FR/EDM

Continuity

X – velocity

Y – velocity

Z – velocity

Turbulent kinetic energy

Turbulent dissipation rate

Discrete ordinates

Energy -

Species -

Table 2.2 – Sum of residuals from Ansys fluent-v13

The second convergence criterion is based on the evolution of the values of temperature and O2

mass fraction in the reaction zone over the iterations, by ensuring that these quantities achieve a constant

state. For this purpose, three different monitoring points were chosen, located at the coordinates

presented in table 2.3.

Point [mm] [mm]

1 100 0

2 200 0

3 300 0

Table 2.3 – Monitoring points coordinates

39

3. Experimental setup and results

3.1. Introduction

In this chapter the main characteristics of the experimental setup, auxiliary equipment and also

the LDA (Laser Doppler Anemometry) system, which allows to measure the flow velocity inside the

combustion chamber without chemical reaction are briefly presented. The measurements were obtained

by Veríssimo (2011) in the framework of his Ph.D. thesis, and are used in this work for validation

purposes.

3.2. Combustion chamber

Figure 3.1 and figure 3.2 show a schematic representation of the combustor used in this study.

The combustion chamber is a quartz-glass cylinder with an inner diameter of 100 mm and a length of 340

mm. The burner is placed at the top end of the combustion chamber and the exhaust of the burned gases

is through the bottom end. The burner consists of a central orifice of 10 mm inner diameter, through which

the combustion air is supplied, surrounded by 16 small orifices of 2 mm inner diameter each, positioned

on a circle with a radius of 15 mm, for the fuel (methane) supply. The combustion air is preheated by an

electrical heating system that allows air inlet temperatures up to 700 ºC, which are monitored using a type

K thermocouple installed at the entrance of the burner.

Other different air nozzle diameters, namely 6, 7, 8, 9 mm were also used in order to study the

effect of the velocity of air injection. However there are only detailed measurements for the air nozzles

with 7 and 10 mm of diameter.

Fig. 3.1- Schematic of the combuster. Fig. 3.2 - Schematic representation of the combuster.

40

Local mean temperature measurements were obtained using 76 µm diameter fine wire

platinum/platinum: 13% rhodium (type R) thermocouples. The uncertainty due to radiation heat transfer

was estimated to be less than 5% by considering the heat transfer by convection and radiation between

the thermocouple bead and the surroundings.

The sampling of the gases for the measurement of local mean O2, CO2 and CO molar fractions

was achieved using a stainless steel water-cooled probe. The analytical instrumentation included a

magnetic pressure analyser for O2 measurements and a non-dispersive infrared gas analyser for CO2 and

CO measurements. The major sources of uncertainty in the concentration measurements inside the

combustor were associated with the quenching of chemical reactions and aerodynamic disturbances of

the flow (Veríssimo et al., 2012).

3.3. LDA (Laser Doppler Anemometry) system

The flow inside the combustion chamber, with no chemical reaction was characterized in terms of

average speeds by using a commercial LDA (Laser Doppler Anemometry) system. This measurement

system operates with an optical probe, which is simultaneously broadcaster of two pairs of laser beams

with different wavelengths and also receiving the scattered light, thereby allowing to measure

simultaneously two components of speed in dual-beam backward scattering operation, for more detailed

explanation see for example, Sousa and Pereira (2000).

3.4. Experimental results

In table 3.1 the experimental characteristics and the boundary conditions of the laboratorial

furnace are described.

Test Φar

(mm)

Excess

air (%)

Air temperature

(ºC)

TFL

(kW)

Vair

(m/s)

Vfuel

(m/s)

1i 10 - - - 48.1 -

1 10 30 700 10 157. 7 6.1

2 10 30 400 10 109.1 6.1

3 8 30 400 10 170.4 6.1

4 6 30 400 10 303.0 6.1

Table 3.1 – Experimental conditions

41

4. Computational results discussion

4.1. Introduction

This chapter presents and discusses the computational results that were obtained in this work.

Initially tests were performed under isothermal conditions in order to compare the predictions of the

velocity field with LDA measurements. Afterwards, numerical simulations were performed under the mild

combustion regime of the combustion chamber described in chapter 3. In a first stage numerical tests

were carried out to investigate grid independence and the influence of number of particles, used in the C

– PDF method on the results. The influence of the wall temperature of the combustion chamber and its

emissivity on the predictions was also investigated. The turbulence model used was the realizable k-ε

In a second stage, numerical simulations were performed in order to assess the combustion

models and the chemical mechanisms, the diameter of air inlet used, the inlet air temperature, and three

combustion models were employed, FR/EDM, EDC and the composition joint PDF. Computational results

were compared between themselves and with the available experimental data. The numerical simulations

were performed using the commercial software, Ansys Fluent-v13.

4.2. Isothermal solution

The first stage of the current work was the assessment of the numerical simulations under

isothermal conditions. Through a LDA system, measurements of the flow velocity along eight radial

profiles inside the combustor chamber without chemical reaction were reported. In order to evaluate the

predictions of the numerical simulations two different geometries were designed and for each one, two

different meshes were created. The computational domain of the two geometries corresponds to a

section of 1/16 (22.5º) of the combustion chamber, Fig 4.1. The fuel and air ducts are included in the

computational domain, in order to allow the flow to develop and to reduce the uncertainty in the definition

of the boundary conditions for the turbulent kinetic energy and dissipation rate at the entrance to the

combustor.

In geometry A the fuel and air ducts have 10 mm of length while for the geometry B this length

increased to 100 mm, in order to assess the influence of the ducts length on the predictions. For both

geometries two meshes were created, in order to assess the numerical error associated to the numerical

discretization. The grids are structured, except in the transition between zones of different refinement,

with rectangular control volumes over a large part of the computational domain, and non-uniform, being

42

more refined close to the inlets, in the vicinity of the burner region and mixing zones. Table 4.1 presents

the number of control volumes for both meshes and geometries.

Geometry Mesh Control volumes

A (Lducts = 10 mm) 1 137 000

2 249 000

B (Lducts = 100 mm) 1 140 000

2 264 000

Table 4.1 – Mesh and geometry description

In the inlet boundary, it is assumed that the radial velocities at the burner outlet are equal to zero

and axial velocities were taken as uniform and calculated from the mass flow rates of air and fuel,

respectively.

The value of the turbulent kinetic energy (k) was estimated assuming that the turbulence intensity

at the outlet of the nozzle is 5%. The turbulence dissipation rate was calculated by the following

expression ( )

⁄

⁄

(Versteeg e Malalasekera, 1995). The mixing length, l, was considered

equal to the hydraulic diameter of the air injector. In table 4.2 the main characteristics of this test and the

boundary conditions are presented.

x

r

Fig. 4.1 – Geometry A – Mesh 1 and 2 respectively.

43

Mass flow rate

Air nozzle diameter Air inlet velocity

ReDh air inlet Outlet pressure

Turbulent kinetic energy (air inlet)

⁄

Turbulent dissipation rate (air inlet)

⁄

Table 4.2 – Isothermal conditions (test 1i)

As can be seen in figure 4.2 b), the development of the axial flow velocity across the radius is

better when a longer length was employed for the numerical simulations. A longer length allows a fully

developed flow before it enters the combustion chamber. The length of 100 mm satisfies the following

condition for an internal flow inside a duct:

( ⁄ )

(4.1)

Regarding the different meshes, for the same geometry, the results of the numerical simulations

are coincident between themselves. However when a refinement for the grid of the geometry B was held,

a deviation for the second and third experimental points was observed in fig 4.2 a). This situation may be

due to the fact the turbulence model is not predicting accurately the decaying of the velocity of the jet.

Fig. 4.2 – a) Axial velocity, b) Axial velocity profile at the combustion chamber inlet.

Air nozzle radial distance (m)

Velo

city

(m

/s)

0

10

20

30

40

50

60

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

10

20

30

40

50

60

-0,006 -0,004 -0,002 0 0,002 0,004 0,006

U(r)

Velo

city

(m

/s)

Axial distance (m)

Air nozzle radial distance (m)

Velo

city (

m/s

)

0

10

20

30

40

50

60

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

10

20

30

40

50

60

-0,006 -0,004 -0,002 0 0,002 0,004 0,006

U(r)

Velo

city (

m/s

)

Axial distance (m)

a)

b)

44

Radial profiles of the flow velocity are displayed in Fig. 4.3. As can be seen in the figures above

the agreement between the numerical simulations and the experimental data is quite acceptable for the

radial profiles of the axial velocity under isothermal conditions.

Fig. 4.3 - Radial profiles of the flow velocity.

45

4.3. Grid independence

This section describes the study of the influence of the grid on the computational results for the

simulation under the mild combustion regime for the combustion chamber described in chapter three.

These tests were made using the geometry A and the meshes 1 and 2.

In table 4.3 the main characteristics of this test and the boundary conditions are presented. In

order to obtain ignition, 1400 K was set to the wall temperature of the combustion chamber. The

emissivity was set to 1.0. Experimental conditions of the test 1 mentioned in the previous chapter were

simulated. The turbulence was simulated through the realizable k-ε model and the combustion model was

the C - PDF.

Power

Excess air

Air inlet temperature

Mass flow rate of air

Air nozzle diameter

Air inlet velocity

ReDh air inlet

Turbulent kinetic energy (air inlet)

⁄

Turbulent dissipation rate (air inlet)

⁄

Fuel inlet temperature

Mass flow rate of fuel

Fuel nozzle diameter

Fuel inlet velocity

Turbulent kinetic energy (Fuel inlet)

⁄

Turbulent dissipation rate (Fuel inlet)

⁄

Outlet pressure

Wall temperature

Wall emissivity

Table 4.3 – Test 1 input data

46

Figure 4.4 represents the predicted axial profiles of mean temperature, mean molar fractions of

CO2 and O2 (dry basis) and the axial velocity. For the two different grids of geometry A, detailed in table

4.1 experimental data are also shown in the figure. As can be seen, the differences between the results

for the two grids are not significant (regarding the four profiles), however the molar fraction of CO2 and O2

near the exhaust of the combustion chamber presented some discrepancies. The reason behind this

situation is the lack of full convergence of the results for the refined grid when the C-PDF combustion

model was employed. This model is computational heavy and the grid is very fine, particularly in the

centerline and close to the inlet. Nevertheless the results are in a very good agreement between the two

different grids and they are consistent between them regarding the molar fractions.

The radial profiles are presented in appendix, Fig.1 and Fig 2, and, like in the axial profiles, there

are no significant differences between the two different grids, so the discretization error is quite low and

due to this the choice of the grid falls on the simple one, the grid 1.

4.4. Number of particles independence

The joint composition probability density function transport model uses a Monte Carlo method to

describe the transport processes of diffusion, convective and mixing. These transport processes were

determined using a number of particles in each computational cell. Thereby it is necessary to assess the

influence of the number of particles per cell in order to validate the numerical results, since the use of a

Monte Carlo method introduces statistical uncertainties into the numerical simulations.

0

1

2

3

4

5

6

7

8

9

10

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

600

800

1000

1200

1400

1600

1800

2000

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

Experimental

Mesh 1

Mesh 2

0

2

4

6

8

10

12

14

16

18

20

22

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

20

40

60

80

100

120

140

160

180

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

x (m) x (m)

Te

mp

era

ture

(ºC

)O

2(%

mo

le f

raction

, d

ry)

CO

2(%

mo

le f

raction

, d

ry)

a) b)

c)

Ve

locity (

m/s

)

d)

Fig. 4.4 - Predicted and measured axial profiles of mean temperature, velocity and O2 and CO2 mean molar fractions on a dry basis.

47

In order to reduce the statistical error, it would be ideal to have a large number of particles. In the

limit of an infinite number of particles the statistical error would be zero. However this situation is not

possible and then it becomes necessary to choose a reasonable number of particles to be introduced in

the computational domain. Bearing in mind that the number of particles is directly proportional to the

computational cost, in the present study 10 and 20 particles per cell were employed. In the entire

computational domain 1 370 000 and 2 740 000 of particles were used.

Figure 4.5 shows predicted and measured profiles of mean temperature, mean molar fractions of

O2, CO2 (dry basis) and axial velocity along the axis of the combustor. The axial profiles of mean

temperature display small oscillations, which are due to the relatively small number of stochastic particles

used in the simulations. These oscillations are attenuated when 20 stochastic particles per cell are used

and the oscillations will disappear with the increase of the number of particles, but then, the

computational time would increase as referred above. However as can be seen from the other axial

profiles, there are no significant differences between the use of 10 or 20 particles per computational cell.

According to this situation, 10 particles per computational cell were used in the others numerical

simulations tested, in order to decrease the computational effort.

Radial profiles of mean temperature, mean molar fractions of O2, CO2 (dry basis) and axial

velocity along the axis of the combustor can be assessed in appendix, Fig 3 and Fig 4.

0

1

2

3

4

5

6

7

8

9

10

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

600

800

1000

1200

1400

1600

1800

2000

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

Experimental

10 Particles

20 Particles

0

2

4

6

8

10

12

14

16

18

20

22

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

20

40

60

80

100

120

140

160

180

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

x (m) x (m)

Te

mp

era

ture

(ºC

)O

2(%

mo

le f

ractio

n, d

ry)

CO

2(%

mo

le f

raction

, d

ry)

a) b)

c)

Ve

locity (

m/s

)

d)

Fig. 4.5 - Predicted and measured axial profiles of mean temperature, velocity and O2 and CO2 mean molar fractions on a dry basis.

48

The software that was used to perform the numerical simulations allows to control how the

average values of temperature and mass fractions are calculated. It gives the user the option to choose

the number of iterations in which the average values of these quantities are calculated (initially set to 50).

In a control volume P, containing a given number of particles, each particle has its own

temperature and chemical composition. The mean value of a given quantity ( ) is obtained by the

arithmetic mean of that quantity for all the particles contained in this control volume in the last n iterations

earlier, namely:

{ ( )

( ( ))

( )

} (4.2)

In order to determine the influence of the number of iterations used in the evaluation of the mean

values given by the equation (4.2) the values of temperature and mass fraction of O2 were registered in

table 4.4 for n = 1, n = 50 and n = 100 iterations over a total of 1000 iterations after the convergence

process, at point where convergence was monitored. With these results the mean value for each variable

over 1000 iterations was calculated and the variations between this mean value and were recorded.

The results for this study were obtained for geometry A, mesh 1, and 10 particle per cell in a total of 1 370

000 particles in the entire computational domain. Table 4.4 shows the average values as well as the

maximum differences at each point for both variables.

Iterations number

Mo

nit

ore

d p

oin

t

(x,y

,z)

= (

0, 0.3

, 0)

Temperature

(ºC)

Average

value

Maximun

variation

O2 mass

fraction

Average

value

Maximun

variation

Table 4.4 – Iterations number influence

The mean values over 1000 iterations remain relatively constant for the three different averages

of corresponding to different values of n, while the maximum variations are reduced by increasing n.

When n = 1, the maximum variation is too high, however the maximum variation values are reduced in

approximately 85% when n was set equal to 50 iterations. The reduction of variations in the mean

temperature and mass fraction of O2 when n rises from 50 to 100 is quite low and the use of n = 100

iterations is not convenient since variations of the average value become too low when convergence is

approached. This may give the impression of convergence achieved when in reality it is not. As a

consequence of this, n = 50 was used in the all the calculations that follow.

49

4.5. Boundary conditions and geometry influence

The mesh 1 (for both geometries) was used to perform numerical simulations, in order to assess

the boundary conditions and geometry influence. Three simulations were carried out, where two individual

parameters of table 4.3 were modified. Numerical simulations were performed considering a wall

temperature equal to 1300 K and another one where the emissivity of walls was modified to 0.7. The third

one was the influence of the air and fuel ducts length in the mild combustion regime. The combustion was

simulated through the FR/EDM combustion model, which only allows a single step global reaction. The

choice of this combustion model was due to the lower computational time that it requires because the

purpose of this section is to evaluate the behavior of the numerical predictions to change of the boundary

conditions.

Fig 4.6 presents the axial profiles of temperature, molar fractions of the CO2 and O2 (dry basis)

and axial velocity that were obtained experimentally and from the numerical simulations for the three

different conditions. Radial profiles can be assessed in appendix, Fig. 5 and Fig. 6.

The predictions obtained with the emissivity of the walls equal to 0.7 are almost identical to the

predictions obtained with the boundary conditions indicated in table 4.3.

0

1

2

3

4

5

6

7

8

9

10

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

600

800

1000

1200

1400

1600

1800

2000

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

Experimental

FR/EDM

FR/EDM ε = 0,7

FR/EDM T_Parede = 1300 K

FR/EDM Geometry B

02468

10121416182022

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

20

40

60

80

100

120

140

160

180

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

x (m) x (m)

Te

mp

era

ture

(ºC

)O

2(%

mo

le f

raction

, d

ry)

a) b)

c)

Ve

locity (

m/s

)

d)

Fig. 4.6 - Predicted and measured axial profiles of temperature,

velocity and O2 and CO2 molar fractions on a dry basis.

50

However, when a temperature of 1300 K was imposed to the wall of the combustion chamber

instead of 1400 K initially tested, it was observed that the temperature imposed on the wall will influence

the final results. The axial profiles of temperature and axial velocity are the most affected by the change

in the boundary condition, while the mass fractions of O2 and CO2 are hardly affected.

When the length of the inlet ducts increases no significant differences were observed regarding

the axial profiles of temperature and molar fractions of the CO2 and O2 (dry basis), however some

differences are noted in the axial velocity profile. These differences are due to the development of the

flow as discussed in subchapter 4.1. Nevertheless, the mild combustion regime was not affected by the

ducts length, and for that reason the numerical simulations were carried out with the geometry A.

4.6. Qualitative description of the flow in the

combustion chamber

The predicted velocity field in a plane defined by the axis of the combustor and the axis of the fuel

duct is shown in Fig. 4.7. These results were obtained using the C-PDF along with the skeletal reaction

mechanism. The large momentum of the inlet air jet originates an internal recirculation zone that extends

up to about 80% of the length of the combustor. The recirculation rate, defined as the mass flow entrained

into the jet flow divided by the initial air and fuel jet, is obtained iteratively from the integration of the axial

velocity field in different radial sections of the combustion chamber and the highest recirculation rate

calculated is 1.9. The recirculated hot combustion products transport momentum and energy back to the

top of the combustor, where they mix with the incoming fuel. The mass flow rate of fuel is much lower

than the mass flow rate of recirculated combustion products, so that the fuel jet hardly penetrates through

the combustion products. The fuel entrains the flow of recirculated combustion products, and mixes with

them before ignition, which takes place in a diluted environment, as required in mild combustion.

Fig. 4.7 - Predicted velocity field.

51

4.7. Combustion model influence

In this section the three combustion models that were presented in chapter two were evaluated,

in the modeling of the mild combustion, namely the FR/EDM, EDC and the C – PDF transport model.

Once again the numerical simulations were performed under the conditions of test 1, presented in the

table 4.3. Combustion was simulated through the FR/EDM, which only allows a single step global

reaction; the EDC model considering two chemical mechanisms, the single step scheme (Westbrook and

Dryer, 1981) and the skeletal mechanism with 13 chemical species and 73 chemical reactions (Sankaran

et al., 2007); and the C - PDF model with the same chemical mechanisms that were employed with the

EDC combustion model. Fig 4.8, Fig 4.9 and Fig 4.10 present the axial and radial profiles of the mean

temperature, mean molar fractions of CO2, O2 and CO and the axial velocity that were obtained from the

experimental results and the numerical simulations with the three combustion models.

The temperatures of the combustion products in the recirculation zone are consistently

overpredicted by all models, as can be seen in Fig. 4.9. This may be due to the influence of the

prescribed temperature of the walls on the predictions. This influence is likely to be larger than in

conventional combustion processes. In fact, the temperature of the wall is quite high in the present mild

combustor, and therefore the radiation emitted by the wall is significant compared with the emission from

the medium, and may influence the temperature of the gases. The predictions of the molar fractions of O2

0

20

40

60

80

100

120

140

160

180

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

600

800

1000

1200

1400

1600

1800

2000

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

Exp_R0

PDF's 1 Step 10 P

PDF's SK 17

EDC 1-step

EDC sk17

FR/EDM

0

2

4

6

8

10

12

14

16

18

20

22

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

0

1

2

3

4

5

6

7

8

9

10

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

0

0,5

1

1,5

2

2,5

3

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35

x (m) x (m)

Te

mp

era

ture

(ºC

)

O2

(% m

ole

fra

ction

, d

ry)

CO

2(%

mo

le f

raction

, d

ry)

CO

(%

mole

fra

ction, dry

)a) b)

c)

e)

Ve

locity (

m/s

)

d)

x (m)

Fig. 4.8 - Predicted and measured axial profiles of mean temperature, axial velocity, O2, CO2 and CO mean molar fractions on a dry basis.

52

and CO2 in the recirculation zone, achieved by the three combustion models are very similar and they are

in a relatively good agreement with the experimental data. However, none of the combustion models

describes accurately the combustion process downstream of the combustion chamber, namely in the

region x = 50 mm to x = 150 mm, where x denotes the axial coordinate. In all cases, the increase of the

measured temperatures along the centerline is faster than the predicted one. Although the predictions of

the axial evolution of the major species are in fairly good agreement with the experimental data, the three

models underestimate the CO2 molar fraction downstream of the combustion chamber and near the

exhaust all the combustion models overestimate the CO2 molar fraction. The EDC yields a significant

overprediction of the peak of CO molar fraction, even though the location of this peak is in very good

agreement with the experimental data. The axial profile of CO obtained using the joint composition

probability density function transport model is much closer to the experimental one. Due to the lack of

experimental data of the axial velocity there is no possibility to assess the best combustion model,

however there are significant differences between the three different models, principally in the region x =

50 mm to x = 250 mm.

Radial profiles of mean temperature, mean molar fractions of O2, CO2 and CO and axial velocity

are displayed in Fig. 4.9 and Fig. 4.10. The mean temperature profiles at x = 11, 45 and 79 mm predicted

using the EDC and the FR/ED models exhibit a peak at r ~10 mm, overpredicting the measured values.

The maximum values of the measured temperature are closer to the centreline of the combustor than the

computed ones. The temperature profiles are consistent with an overprediction of CO2 and CO molar

fractions, and an underprediction of O2 molar fraction for both combustion models. The mean temperature

calculated using C - PDF model is closer to the measurements in that region, as well as the maximum

values of the CO molar fraction, however the differences in the CO2 and O2 molar fraction in comparison

with the EDC combustion model can be neglected. The CO spreads significantly over the radial direction,

while the predicted profiles are narrower and closer to the centreline. The EDC model consistently

overestimates the CO molar fraction, while the C - PDF model globally performs better as far as the

prediction of CO is concerned, but not acceptably.

53

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

Exp_310PDF's 1-stepPDF's SK 17EDC 1-stepEDC SK 17FR/EDM

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

Tem

pera

ture

(ºC

)

Radial distance (m) Radial distance (m)

Ve

locity (

m/s

)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 4.9 - Predicted and measured radial profiles of mean temperature and velocity.

54

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

0

0,5

1

1,5

2

2,5

3

0 0,01 0,02 0,03 0,04 0,05

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

310 mm

PDF's 1-step

PDF's SK 17

EDC 1-step

EDC SK 17

FR/EDM

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

O2

(% m

ole

fra

ctio

n, d

ry)

CO

2(%

mole

fra

ction, dry

)

CO

(%

mole

fra

ction, dry

)

Radial distance (m) Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 4.10 - Predicted and measured radial profiles of O2, CO2 and CO mean molar fractions on a dry basis.

55

4.8. Chemical mechanism influence

This section evaluates the influence of the chemical mechanism on the results of the numerical

simulations. Numerical simulations of test 1 were carried out using the EDC and the C-PDF with 2

chemical mechanisms, a single step scheme and a skeletal mechanism.

Fig. 4.8 represents the axial profiles of mean temperature, mean molar fractions of CO2, O2 and

CO (dry bases) and the axial velocity obtained from the measurements and by the numerical simulations

with two chemical mechanisms and two different combustion models. Generally the numerical simulations

predicted in a good way the trend of the experimental data for both chemical mechanisms and for both

combustion models. However, the predictions with the detailed chemical mechanism (skeletal

mechanism) are in better agreement with the experimental data than the predictions obtained when a

global simple scheme was employed. For the EDC combustion model, the chemical mechanism has a

large influence on the results, since the global reaction scheme overestimates the temperature and the

peak of the temperature occurs away from the burner when compared with the experimental

measurements and with the other chemical mechanism. For the C-PDF the single step scheme also

overestimates the temperature but its peak is in a relatively good agreement with the experimental data.

As can be seen in the axial profiles of the molar fractions of CO2 and O2, the EDC combustion

model with a detailed chemical kinetic mechanism allows a better approximation of numerical simulations

to the experimental data. In the case of the C – PDF, the variation of molar fraction of CO2 and O2 is not

significant, except from r = 200 mm where the simple step mechanism yields predictions closer to the

experimental results. The reason behind this circumstance is due to an extremely high computational

effort when the C – PDF model with a detailed chemical mechanism was employed. Although, the

residuals are stable over 70.000 iterations, the monitoring point 3 of O2 is not totally converged. As can

be seen in Fig. 4.8 the axial profiles of O2 and CO2 molar fractions are not fully converged from x = 200

mm to the exhaust. This simulation was performed using an i7 sandy bridge 3.4 GHz CPU with 8 GB of

RAM with six cores in parallel. The simulation was run over one month, and the expectation to obtain full

convergence exceeds two months. The same problem occurs in chapter 4.3, when the grid independence

is studied. The axial profiles of O2 and CO2 molar fractions are not completely converged from

to the exhaust, however in this particular case the problem is the number of control volumes

presented in mesh 2.

Although there are no experimental data for the axial velocity, some differences between the two

chemical mechanisms can be assessed. The C – PDF combustion model with a single step chemical

kinetic mechanism predicted a lower decay of the air jet velocity than the C – PDF combustion model with

the detailed chemical mechanism, while the EDC combustion model with the single step chemical kinetic

mechanism predicted a faster decay of the air jet velocity than the EDC combustion model with a detailed

chemical mechanism.

56

The Fig. 4.9 shows the radial profiles of mean temperature and axial velocity and Fig. 4.10

displays the molar fractions of CO2, O2 and CO obtained experimentally and by numerical simulations.

Some differences between the C-PDF combustion model with a single step chemical kinetic mechanism

and the detailed mechanism were observed. This difference is also seen for the EDC combustion model

with the two different chemical kinetics mechanisms. The C - PDF combustion model with the single step

mechanism overestimates the temperatures throughout the combustion chamber.

Regarding the chemical species, the largest discrepancy occurs at r = 250 mm and r = 310 mm

where the C - PDF combustion model with the detailed chemical kinetic mechanism predicted the mass

fractions of CO2 and O2 worse than the C – PDF with the single scheme chemical mechanism.

Nevertheless, the results are consistent between themselves. This worst prediction is likely to be due to

the lack of full convergence, as has been evidenced previously.

4.9. Pre-heated combustion air temperature

influence

In this section the influence of the temperature of the pre-heated combustion air was studied.

Comparisons between the tests 1, 2 and the experimental data were presented and discussed. The C –

PDF model was used along with a skeletal mechanism.

Power

Excess air

Air inlet temperature

Mass flow rate of air

Air nozzle diameter

Air inlet velocity

ReDh air inlet

Turbulent kinetic energy (air inlet)

⁄

Turbulent dissipation rate (air inlet)

⁄

Fuel inlet temperature

Mass flow rate of fuel

Fuel nozzle diameter

Fuel inlet velocity

Turbulent kinetic energy (Fuel inlet)

⁄

Turbulent dissipation rate (Fuel inlet)

⁄

Outlet pressure

57

Wall temperature

Wall emissivity

Table 4.5 – Test 2 input data.

Fig. 4.11, Fig. 4.12 and Fig. 4.13 presents the axial and radial profiles of the mean temperature,

the mean molar fractions of CO2, O2 and CO (dry bases) and the axial velocity, that were obtained from

the experimental results and the numerical simulations with different temperatures of pre-heated

combustion air.

The temperature of the combustion products in the recirculation zone are overpredicted for the

two tests, as can be seen in Fig. 4.12. The prescribed temperature of the walls has an influence on the

accuracy of the results, as can be seen in the axial profile of the temperature, Fig. 4.11 a). The

experimental temperature, along the combustion chamber, for test 2 is lower than for test 1 and the

predictions of the temperature at x = 200 mm to the exhaust, does not show major difference between the

two different numerical simulations. The recirculation rate is higher when the pre-heated combustion air

increases. In this case, for test 1 the recirculation rate is 1.9 (as previously mentioned) and for the test 2

the recirculation rate is equal to 1.5.

The prediction of the mean molar fractions of O2 and CO2 in the recirculation zone are very

similar for the two tests and they are in relatively good agreement with the experimental data, as can be

assessed in Fig. 4.13. However, the numerical predictions of test 2 are closer to the experimental data

downstream of the combustion chamber, namely in the region x = 50 mm to x = 150 mm than the

numerical predictions of the test 1. Nevertheless, near the exhaust the numerical predictions for both

cases overestimate the CO2 molar fraction. The peak location of the CO molar fraction for the test 2 is not

well predicted. The maximum value of CO molar fraction is underestimated.

0

2

4

6

8

10

12

14

16

18

20

22

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

1

2

3

4

5

6

7

8

9

10

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

500

1000

1500

2000

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

Exp. Temp air = 400 ºC

Temp air = 400 ºC

Exp. Temp air = 700 ºC

Temp air = 700 ºC0

20

40

60

80

100

120

140

160

180

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

x (m) x (m)

Te

mp

era

ture

(ºC

)

O2

(% m

ole

fra

ction

, d

ry)

CO

2(%

mo

le f

raction

, d

ry)

CO

(%

mo

le f

raction

, d

ry)

a) b)

c) e)

Ve

locity (

m/s

)

d)

x (m)

Fig. 4.11 - Predicted and measured axial profiles of mean temperature, axial velocity, O2, CO2 and CO mean molar fractions on a dry basis.

58

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

Exp. Temp air = 400 ºC

Temp air = 400 ºC

Exp. Temp air = 700 ºC

Temp air = 700 ºC

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Tem

pera

ture

(ºC

)

Radial distance (m)

Velo

city

(m

/s)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)Fig. 4.12 - Predicted and measured radial profiles of mean temperature and velocity.

59

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

Exp. Temp air = 400 ºC

Temp air = 400 ºC

Exp Temp air = 700 ºC

Temp air = 700 ºC

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

O2

(% m

ole

fra

ctio

n, dry

)

CO

2(%

mole

fra

ctio

n, dry

)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 0,01 0,02 0,03 0,04 0,05

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 0,01 0,02 0,03 0,04 0,05

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

0 0,01 0,02 0,03 0,04 0,05

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,01 0,02 0,03 0,04 0,05

CO

(%

mole

fra

ctio

n, dry

)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

Fig. 4.13 - Predicted and measured radial profiles of O2, CO2 and CO mean molar fractions on a dry basis.

60

Radial profiles of mean temperature, molar fractions of O2, CO2 and CO (dry bases) and axial

velocity are displayed in Fig. 4.12 and Fig 4.13. The influence of the prescribed wall temperature can

again been checked in all the temperature radial profiles. The experimental data of test 2 are lower than

the experimental data of the test 1 and the numerical predictions of the temperature from r = 15 mm to

the wall (r = 50 mm), do not show major differences between the two different numerical simulations. The

predictions of O2 and CO2 are in fairly good agreement with the experimental measurements for the two

tests and they are consistent between them. Although the numerical simulations of the two tests are

consistent between them for the predictions of the CO molar fraction, the results are not satisfactory

regarding the experimental data.

4.10. Air nozzle diameter influence

In this section the influence of the air nozzle diameter was studied. Comparisons between three

different air nozzle diameters, 6, 8, 10 mm and experimental data for the 10 mm case were presented

and discussed for the C-PDF combustion model.

Test

Power

Excess air

Air inlet temperature

Mass flow rate of air

Air nozzle diameter

Air inlet velocity

ReDh air inlet

Turbulent kinetic energy (air inlet)

⁄

⁄

⁄

Turbulent dissipation rate (air

inlet)

⁄

⁄

⁄

Fuel inlet temperature

Mass flow rate of fuel

Fuel nozzle diameter

Fuel inlet velocity

Turbulent kinetic energy (Fuel

inlet)

⁄

⁄

⁄

Turbulent dissipation rate (Fuel

inlet)

⁄

⁄

⁄

Outlet pressure

Wall temperature

Wall emissivity

Table 4.6 – Test 2, 3 and 4 input data.

61

Fig. 4.14 shows predicted and measured profiles of mean temperature, mean molar fractions of

O2, CO2 and CO (dry basis) and the axial velocity along the axis of the combustor for the three different

air nozzle diameters. When the air nozzle diameter decreases the reaction takes place closer to the air

and fuel injection zone as revealed by the axial mean temperature. From the same axial profile it is easy

to see that the peak of the temperature and the temperature along the axis increased with a higher

diameter of the air nozzle, and also the location of the peak tends away from the burner. The predictions

of the mean molar fractions of O2 and CO2 are consistent. For a lower air nozzle diameter the mean molar

fraction of CO2 slightly increased, while the mean molar fraction of O2 marginally decreased. The

numerical simulations of CO molar fraction shows a displacement of the peak towards the air and fuel

injection zone when the air nozzle diameter decreases. The molar fraction of CO is higher for an air

nozzle diameter of 8 mm.

From the axial velocity profile it is observed that a decrease of the air nozzle diameter leads to a

faster and pronounced decay of the air jet velocity.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

d = 10 mm

d = 8 mm

d = 6 mm

Experimental d = 10 mm

0

1

2

3

4

5

6

7

8

9

10

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

2

4

6

8

10

12

14

16

18

20

22

0 0,05 0,1 0,15 0,2 0,25 0,3 0,350

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

0

50

100

150

200

250

300

350

0 0,05 0,1 0,15 0,2 0,25 0,3 0,35

x (m) x (m)

Tem

pera

ture

(ºC

)

O2

(% m

ole

fra

ction, dry

)

CO

2(%

mole

fra

ction, dry

)

CO

(%

mole

fra

ction, dry

)

a) b)

c) e)

Velo

city (

m/s

)

d)

x (m)

Fig. 4.14 - Predicted and measured axial profiles of mean temperature, axial velocity, O2, CO2 and CO mean molar fractions on a dry basis.

62

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

Experimental d = 10 mm

d = 10 mm

d = 8 mm

d = 6 mm

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

-20

20

60

100

140

180

220

260

300

0 0,01 0,02 0,03 0,04 0,05

Ve

locity (

m/s

)

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,01 0,02 0,03 0,04 0,05 0,06

Tem

pera

ture

(ºC

)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 4.15 - Predicted and measured radial profiles of mean temperature and

velocity.

63

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05 0,06

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05 0,06

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

Experimental d = 10 mm

d = 10 mm

d = 8 mm

d = 6 mm

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,01 0,02 0,03 0,04 0,05

O2

(% m

ole

fra

ction, dry

)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

CO

2(%

mole

fra

ction, dry

)

CO

(%

mole

fra

ction, dry

)

Radial distance (m) Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

Fig. 4.16 - Predicted and measured radial profiles of mean O2, CO2 and CO mean molar fractions on a dry basis.

64

Radial profiles of mean temperature, mean molar fractions of O2, CO2 and CO and axial velocity

are displayed in Fig. 4.15 and Fig. 4.16. Although the predictions of the temperature of the combustion

products in the recirculation zone are equal for the three different air nozzles diameters, the expectation is

to see a lower temperature for the smaller air nozzle diameter. The prescribed temperature in the furnace

walls may be an influence for the accuracy of the computational results (as mentioned previously in

subchapter 4.5). The predictions of the molar fractions of O2, CO2 and CO (dry bases) in the recirculation

zone are very similar for the three tests; the main differences are registered near the centerline of the

combustion chamber, where for a smaller air nozzle diameter the reaction develops faster. The

recirculation rate increases when the air nozzle diameter decreases, as can be seen in figure 4.17.

As can be seen in the radial profiles of axial velocity, the recirculation zone (negative axial

velocity) increases when the air nozzle diameter decreases.

Fig. 4.17 - Recirculation rate for different air nozzle diameters.

65

5. Conclusions and future work

5.1. Conclusions

In this work, numerical simulations of a laboratory furnace operating on the mild combustion

regime were carried out. First tests under isothermal conditions were performed in order to assess the

velocity field. In a second stage of this work, numerical simulations under the mild combustion regime

were done. In all numerical simulations, the turbulence model used was the realizable k-ε model. Three

combustion models were evaluated, namely the C – PDF, the EDC and the FR/EDM. The performance

of two chemical kinetics mechanisms was also evaluated. A detailed chemical kinetics mechanism for

methane is used, namely SK-17 with 13 chemical species and 73 chemical reactions, as well as a global

single step reaction. Finally the influence of the pre-heated air temperature and the air nozzle diameter

was investigated.

In isothermal conditions, the length of the air and fuel ducts are important, in order to ensure a

fully developed flow at the entrance of the combustion chamber. However, under the mild combustion

regime, the length of the air and fuel ducts does not affect significantly the temperature or the molar

fraction of the species.

The k-ε realizable turbulence model does not accurately predict the initial decay of the air jet

velocity, for isothermal conditions.

The sensitivity of the results to changes in the boundary conditions was tested. The influence of

the walls emissivity on predictions is marginal. However, the influence of the imposed temperature of the

walls cannot be neglected.

The choice of the combustion model and the chemical kinetics mechanism have a significant

influence on the accuracy of the predictions of the temperature, molar fractions of CO2, O2 and CO and

axial velocity. The model that yields predictions in better agreement with the experimental data was the C

– PDF with the skeletal chemical kinetics mechanism. However, discrepancies have been observed

downstream of the burner, where the temperature tends to be overestimated (may be due to the imposed

wall temperatures) and the predicted profiles exhibit maximum values at a larger radial coordinate. The

predictions of CO are not satisfactory, particularly for the EDC model. The results computed using the

skeletal mechanism are closer to the experimental data than those calculated using a single-step global

reaction.

Regarding the influence of the pre-heated air temperature, no significant differences between the

experimental data and the predictions were found. Nevertheless, the recirculation rate increased when

the pre-heated air temperature was higher.

66

Finally, it was concluded that the reaction develops faster and the recirculation rate increases

with the decrease of the air nozzle diameter.

5.2. Future work

The following suggestions for future work are proposed:

It would be quite interesting to have access to experimental measurements of velocity under the

mild combustion regime and not only under the isothermal condition.

It will be important to improve the computational resources, in order to try new numerical

simulations with a large number of particles in each computational cell.

Due to the results obtained, it is suggested the use of an advanced turbulence model, such as

the Large Eddy Simulation model (LES).

On the other hand, to successfully simulate numerically the mild combustion regime would be

interesting to develop new chemical mechanisms, specifically for this type of combustion regime,

where a high degree of dilution of the reagents and moderate temperatures are involved.

67

References

Cavaliere A., and Joannon M. (2004). Mild Combustion. Progress in Energy and Combustion Science, 30,

pp. 329-366.

Christo F.C., Dally B. B. (2005). Modeling turbulent reacting jets issuing into a hot and diluted coflow.

Combust Flame, 142, pp. 117-129

Coelho P. J., Peters N. (2001). Numerical simulation of a mild combustion burner. Combust Flame, 24,

pp. 503-518.

Coppalle A., and Vervisch P. (1983). The Total Emissivities of High-Temperature Flames. Combustion

and Flame, 49, pp. 101–108.

Curl, R. L. (1963). Dispersed phase mixing: 1. Theory and effects in simple reactors. AIChE Journal 9, pp.

175–181.

Dally, B. B., Karpetis, A. N. and Barlow, R. S. (2002). Structure of turbulent non-premixed jet flames in a

diluted hot coflow. Proceedings of the Combustion Institue, 29, pp. 1147-1154.

Dally, B. B., Riesmeier, E. and Peters, N. (2004). Effect of fuel mixture on moderate and intense low

oxygen dilution combustion. Combustion and Flame, 137, pp. 418-431.

Flamme, M. (2001). Low NOx combustion technologies for high temperature applications. Energy

Conversion and Management, 42, pp. 1919-1935.

Flamme, M. (2004). New combustion systems for gas turbines (NGT). Applied Thermal Engineering, 24,

pp. 1551-1559.

FLUENT Theory Guide (2009). Version 13.0. Lebanon, NH: ANSYS Inc.

Frassoldati, A., Sharma, P., Cuoci, A., Faravelli, T. and Ranzi, E. (2010). Kinetic and fluid dynamics

modeling of methane/hydrogen jet flames in diluted coflow. Applied Thermal Engineering, 30, pp. 376-

383.

Galbiati, M. A., Cavigiolo, A., Effuggi, A., Gelosa, D. e Rota, R. (2004). Mild combustion for fuel-NOx

reduction. Combustion Science and technology, 176, pp. 1035-1054.

Galletti, C., Parente, A. and Tognotti, L. (2007). Numerical and experimental investigation of a mild

combustion burner. Combustion and Flame, 151, pp. 649-664.

68

Graça, M., Duarte, A., Coelho, P. J., & Costa, M. (2012). Numerical simulation of a reversed flow small

scale combustor. 11th Conference on Combustion and Energy Utilization. Coimbra.

Haworth, D. C. (2009). Progress in probability density function methods for turbulent reacting flows.

Progress in Energy and Combustion Science , 36, pp. 168-259.

Honnet, S. and Peters, N. (2007). Simulation of pollutant formation in mild combustion using the eulerian

particle flamelet model with detailed and reducd chemistry. Proceedings of the European Combustion

Meeting.

Kuo, K. K. (1986). Principles of combustion. John Wiley & Sons.

Magnussen, B. F. (1989). Modeling of pollutant formation in gas turbines combustors based on the eddy

dissipation concept. 18th International Congress on Combustion Engines, International Council on

Combustion Engines, Tianjin, China.

Magnussen, B. F. and Hjertager, B. H. (1976). On mathematical modeling of turbulent combustion with

special emphasis on soot formation and combustion. Proceedings of the Combution Institue, 16, pp. 719-

729.

Mancini, M., Schwoppe, P., Weber, R. and Stefano, O. (2007). On mathematical modelling of flameless

combustion. Combustion and Flame, 150, pp. 54-59.

Mancini, M., Weber, R. and Bollettini, U. (2002). Predicting NOx emissions of a burner operated in

flameless oxidation mode. Proceedings of the Combustion Institue, 29, pp. 1155-1163.

Merci, B., Roekaerts, D., & Naud, B. (2005). Study of the performance of three micro mixing models in

transported scalar PDF simulations of a piloted jet diffusion flame ("Delf Flame III"). Combustion and

Flame , 144, pp. 476-493.

Merci, B., Roekaerts, D., Naud, B., & Pope, S. B. (2006). Comparative study of micromixing models in

transported scalar PDF simulations of turbulent nonpremixed bluff body flames. Combustion and Flame ,

146, pp. 109-130.

Modest, M. F. (1993). Radiative Heat Transfer. McGraw-Hill, New York.

Özdemir, I. B. and Peters, N. (2001). Characteristics of the reaction zone in a combustor operating at mild

combustion. Experiments in Fluids, 30, pp. 683-695.

69

Parente, A., Galletti, C, and Tognotti, L. (2008). Effect of the combustion model and kinetic mechanism on

the MILD combustion in an industrial burner fed with hydrogen enriched fuels. International Journal of

Hydrogen Energy, 33, pp. 7553-7564.

P. J. Coelho and M. Costa (2007). Combustão, Amadora, Orion.

Peters, N. (2000). Turbulent combustion. Cambridge University Press.

Poinsot, T. and Veynante, D. (2001). Theorical and numerical combustion. Edwards,Inc.

Rebola, A. and Coelho, P. (2007) Numerical simulation of unconfined turbulent lifthed jet flames, 2th

ECCOMAS Thematic Computational Combustion 18-20 July, Delft, the Netherlands.

Plessing, T., Peters, N. e Wünning, J. (1998). Laseroptical investigation of highly preheated combustion

with strong exhaust gas recirculation. Proceedings of the Combustion Institue, 27, pp. 3197-3204.

Pope, S. B. (1985). PDF methods for turbulent reactive flowa. Progress in energy and combustion

science , 11, pp. 119-192.

Pope S. B. (1997). Computationally efficient implementation of combustion chemistry using in situ

adaptive tabulation, Combustion Theory and Modelling, 1, pp. 41-63,.

Sankaran R., Hawkes E. R., Chen J. H., Lu T. F. and Law C. K. (2007). Proc. Combust. Inst., 31, pp.

1291–8.

Shih, T. H., Liou, W. W., Shabbir, A., Yang, Z., e Zhu, J. (1995). A new k-ε eddy-viscosity model for high

Reynolds number turbulent flows – model development and validation. Computers Fluids, 24, pp 227-

238.

Smith, T. F., Shen, Z. F., and Friedman, J. N. (1982). Evaluation of Coefficients for the Weighted Sum of

Gray Gases Model. J. Heat Transfer, 104, pp. 602–608.

Sousa, J. M. M., Pereira, J. C. F., (2000). Rollup Region of a Turbulent Trailing Vortex Issued from a

Blade with Flow Separation, Experimental Thermal and Fluid Science, 20, pp. 150-161.

Tabacco D., Innarella C., Bruno C. (2002). Theoretical and numerical investigation on flameless

combustion. Combust Sci Tech, 174, pp. 1-35.

Veríssimo, A. (2011). Estudo Experimental de uma Câmara de Combustão Operando no Regime de

Combustão sem Chama Visível. Ph. D. Thesis

70

Veríssimo, A., Oliveira, R., Coelho, P. J., & Costa, M. (2012). Numerical simulation of a small-scale mild

combustor. EUROTHERM 2012. 6th European Thermal Sciences Conference. Poitiers - France.

Versteeg, H. K. and Malalasekera, W. (1995). An introduction to computational fluid dynamics The finite

volume method. Longman Scientific & Technical.

Villermaux, J. and J. C. Devillon (1972). Représentation de la coalescence et de la redispersion des

domaines de ségrégation dans un fluide par un modèle d’interaction phénoménologique. In Proceedings

of the 2nd International Symposium on Chemical Reaction Engineering, pp. 1–13. New York, Elsevier.

Wang, H., & Chen, Y. (2004). PDF modeling of turbulent non-premixed combustion with detailed

chemistry. Chemical Engineering Science , 59, pp. 3477-3490.

Westbrook C. K. and Dryer F. L. (1981). Combustion Science Tech, 27, pp. 31–43.

Wünning, J. A. and Wünning, J. G. (1997). Flameless oxidation to reduce thermal NO-formation.

Progress Energy Combustion Science, 23, pp. 81-94.

Wünning, J. A. e Wünning, J. G. (2001). Ten years of flameless oxidation technical application and

potentials. 4th HTAC High Temperature Air Combustion, November, Rome.

71

Appendix

72

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

Experimental

Mesh 1

Mesh 2

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Tem

pera

ture

(ºC

)

Radial distance (m) Radial distance (m)

Velo

city

(m

/s)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 1 - Predicted and measured radial profiles of mean temperature and velocity.

73

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

Esperimental

Mesh 1

Mesh 2

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

O2

(% m

ole

fra

ction, dry

)

CO

2(%

mole

fra

ction, dry

)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 2 - Predicted and measured radial profiles of mean O2 and CO2 mean molar fractions on a dry basis.

74

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

0

500

1000

1500

2000

0 0,01 0,02 0,03 0,04 0,05

Experimental

10 Particles

20 Particles

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

Velo

city (

m/s

)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Tem

pera

ture

(ºC

)

Radial distance (m) Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 3 - Predicted and measured radial profiles of mean temperature and

velocity.

75

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

Experimental

10 Particles

20 Particles

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

0

5

10

15

20

25

0 0,01 0,02 0,03 0,04 0,05

O2

(% m

ole

fra

ction, dry

)

CO

2(%

mole

fra

ction, dry

)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 45 - Predicted and measured radial profiles of mean O2 and CO2

mean molar fractions on a dry basis.

76

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

Exp_310

FR/EDM ε = 0,7

FR/EDM T_Parede = 1300 K

FR/EDM

FR/EDM Geometry B

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

600

800

1000

1200

1400

1600

1800

2000

0 0,01 0,02 0,03 0,04 0,05

-20

0

20

40

60

80

100

120

140

160

180

0 0,01 0,02 0,03 0,04 0,05

Velo

city (

m/s

)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Tem

pera

ture

(ºC

)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 181 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 5 - Predicted and measured radial profiles of temperature and velocity.

77

0

2

4

6

8

1012

14

16

18

20

22

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

14

16

18

20

22

0 0,01 0,02 0,03 0,04 0,05

0

2468

1012

1416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

Exp_310

FR/EDM ε = 0,7

FR/EDM T_Parede = 1300 K

FR/EDM

FR/EDM Geometry B

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

0

2

4

6

8

10

12

0 0,01 0,02 0,03 0,04 0,05

0123456789

101112

0 0,01 0,02 0,03 0,04 0,05

02468

10121416182022

0 0,01 0,02 0,03 0,04 0,05

O2

(% m

ole

fra

ction

, d

ry)

CO

2(%

mo

le f

raction

, d

ry)

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 250 mm

x = 310 mm

x = 11 mm

Radial distance (m)

x = 45 mm

x = 79 mm

x = 113 mm

x = 147 mm

x = 250 mm

x = 310 mm

x = 11 mm

Fig. 6 - Predicted and measured radial profiles of O2 and CO2 molar

fractions on a dry basis.